url stringlengths 14 2.42k | text stringlengths 100 1.02M | date stringlengths 19 19 | metadata stringlengths 1.06k 1.1k |
|---|---|---|---|
https://math.stackexchange.com/questions/2652281/algebraic-inequality-with-dot-product | # Algebraic Inequality with dot product
I encountered the following inequality in a paper I was reading: $$\left(\sum_{i=1}^d a_ib_i\right)^2 \leq \left(\sum_{i=1}^d b_i \right) \left( \sum _{i=1}^d a_i^2 b_i\right)$$
I am unable to prove it (or find a counterexample for that matter). Hints would suffice on how to proceed.
• Hint: Cauchy-Schwarz. – max_zorn Feb 15 '18 at 22:26
• Do all the $b_i$ have the same sign? – Arnaud D. Feb 15 '18 at 22:31
• @max_zorn: if the $b_i$ are all nonnegative, then this is an easy consequence of C-S: one can use $ab=\sqrt{b}\cdot (a\sqrt{b})$. Otherwise, how do you use C-S? – Jack Feb 15 '18 at 22:32
• @max_zorn only for $b_i$ positive? – user Feb 15 '18 at 22:32
• @gimusi The original post left out this important assumption indeed... – max_zorn Feb 15 '18 at 22:42
The inequality doesn't hold for all $a_i$ and $b_i$, unless either $b_i\ge0$, for all $i$, or $b_i\le0$, for all $i$.
We can obviously disregard terms $b_i=0$, that don't contribute to either side.
The case $d=1$ is obvious. Assume then $d>1$ and that there are positive and negative $b_i$.
Assume, without loss of generality, $b_1<0$ and $b_2>0$. We can choose $a_i=0$ for $i=3,\dots,d$.
If $\sum_i b_i>0$, set $a_1=1$ and choose $a_2$ such that $a_2^2b_2<-b_1$. Then $$\sum_{i=1}^da_i^2b_i<0$$ and the inequality doesn't hold.
If $\sum_i b_i<0$, set $a_2=1$ and choose $a_1$ such that $-a_1^2b_1<b_2$. Then $$\sum_{i=1}^da_i^2b_i>0$$ and the inequality doesn't hold.
If $b_i\le0$, for all $i$, we can substitute $b_i$ with $-b_i$ and the terms in the left-hand and right-hand sides wouldn't change. Thus it is not restrictive to assume $b_i\ge0$, for all $i$.
Applying Cauchy-Schwarz to $(a_1\sqrt{b_1},\dots,a_d\sqrt{b_d})$ and $(\sqrt{b_1},\dots,\sqrt{b_n})$ proves the inequality.
COUNTEREXAMPLE
take $d=2,$
$$a_1 = 2, a_2 = 1$$ $$b_1 = 1, b_2 = -3,$$ $$\sum b_i = -2,$$ $$\sum a_i^2 b_i = 1$$ but $$\left(\sum_{i=1}^d a_ib_i\right)^2 \geq 0$$ | 2019-11-20 04:13:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.948286771774292, "perplexity": 230.7196902697602}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670448.67/warc/CC-MAIN-20191120033221-20191120061221-00377.warc.gz"} |
https://www.gkaonlineacademy.com/blog/?userid=5&blogpage=12 | ## User blog: Meguid El Nahas
Anyone in the world
Prof Pierre Delanaye wrote a BLOG in OLA French:
www.ncbi.nlm.nih.gov/pubmed/23689071
Une étude purement observationnelle mais intéressante car spécifique aux patients insuffisants rénaux (même si la définition retenue pose un peu problème, à savoir une GFR estimée inférieure à 60 ml/min et/ou une protéinurie). Les auteurs ont comparé la prévalence du contrôle de l'HTA définie sur base d'une mesure en consultation inférieure à 140/90 ou à 130/80 ou sur base d'un monitoring de 24h avec une définition à 130/80 ou 120/75. L'hypertension blouse blanche est définie comme une HTA plus importante en consultation et une HTA masquée si c'est l'inverse (TA contrôlée en consultation mais pas sur holter de 24h). 14382 sujets espagnols ont été recrutés. 8689 n'avaient pas d'IR 72,6% étaient traités (la moitié avec plus de deux médicaments). L'utilisation et le nombre d'antihypertenseurs augmentent avec la progression de l'IR ce qui n'est pas trop étonnant. 21.7% des patients avec IRC ont une TA controlée en consultation (140/90) mais 43.5% ont un holter avec cible inf à 130/80. Le controle de la TA sur holter de 24 h ne semble pas trop différent selon le stade d'IR sur pour le controle de l'HTA nocturne qui augmente avec l'IR
Ce qui est surtout intéressant c'est la concordance entre les résultats du ciontrôle de l'HTA selon que l'on considère la prise en consultation et le monitoring de 24H chez les IRC:
14.7% des sujets sont controlés et sont concordants entre les 2 techniques
49.5% sont concordants pour une marque de contrôle de la TA
Une HTA de la blouse blanche est présente dans 28.8%
Une HTA masquée est présente dans 7% des cas
36% des sujets avec une HTA en consultation présente en fait un effet blouse blanche et 32% des patients controllés en consultation ont en fait une HTA sur le monitoring
=> intéret du monitoring en cas d'IRC?
IN ENGLISH:
Comparing BP control in office with 24h ABPM in CKD patients:
14.7% of individuals are hypertensive by both methods/measurements.
36% white coat hypertension NOT present on 24hABPM
32% normotenive in office but hypertensive over 24h
HOW TO BEST MONITOR BP CONTROL IN CKD?
[ Modified: Thursday, 1 January 1970, 1:00 AM ]
Anyone in the world
Nephrol Dial Transplant. 2013 Oct;28(10):2553-69. doi: 10.1093/ndt/gft214. Epub 2013 Jun 4.
# Cost of peritoneal dialysis and haemodialysis across the world.
### Source
International Renal Research Institute Vicenza (IRRIV), San Bortolo Hospital, Vicenza, Italy.
### Abstract
Peritoneal dialysis (PD) as a modality is underutilized in most parts of the world today despite several advantages including the possibility of it being offered in the remotest of locations and being significantly more affordable than haemodialysis (HD) in most cases. In this article, we will compare the cost of HD and PD in several countries to demonstrate that PD is less than, or at least as expensive as, HD. A thorough literature survey of EMBASE and PUBMED was conducted; 78 articles which compared the annual PD and annual HD costs were finally selected. Careful attention was paid to the methodology followed by each study and the year it was published in. Our final calculations included 46 countries (20 developed and 26 developing). We found that the cost of HD was between 1.25 and 2.35 times the cost of PD in 22 countries (17 developed and 5 developing), between 0.90 and 1.25 times the cost of PD in 15 countries (2 developed and 13 developing), and between 0.22 and 0.90 times the cost of PD in 9 countries (1 developed and 8 developing). From our analysis, it is evident that most developed countries can provide PD at a lesser expense to the healthcare system than HD. The evidence on developing countries is more mixed, but in most cases PD can be provided at a similar cost where economies of scale have been achieved, either by local production or by low import duties on PD equipment.
#### KEYWORDS:
continuous ambulatory peritoneal dialysis (capd), economic analysis, economic impact, haemodialysis, peritoneal dialysis
COMMENTARY:
This very interesting analysis of the cost of HD versus PD worldwide is very revealing. It shows that most Developed countries favor HD over PD as judged by the prevalence of the modalities in their RRT population; USA 93% HD versus 7% PD (1). The uptake of PD in Europe is marginally better but remains much lower than HD with for instance Germany having as few as 5% of its ESRD patients treated by PD! This, in spite of a higher cost for HD compared to PD; in the US for instance the annual patient cost for HD is around $87,500 compared to$66,750 for PD. It has been estimated that the US, that spends 18% of its GDP on healthcare, could save up to \$1.1 billion over 5 years if the uptake of PD increased from 7% to 15% (2).
Yet there are obstacles to PD utilization in the West including: 1. Reimbursement policies (in France and Germany for instance reimbursement for HD is much higher than that for PD), 2. Physicians/Nephrologists preference, 3. Physicians familiarity with PD; a modality with which they may have little experience, 4. Patients’ preference, 5. Patients’ increasing age and dependency as well as isolation making thrice weekly HD not only a medical but also a social necessity.
The analysis under discussion paints a different cost analysis for PD in Developing countries where in the most deprived, low economies, PD is a more expensive RRT modality than HD! This has many root causes including: 1. the cost of importing PD solutions and related delivery system, 2. PD companies monopoly of pricing, 3. High export duties on such material, all combining to make PD more expensive, in some countries like Egypt 5 times more expensive [HDD/PD cost ratio = 0.22], than HD! Consequently, in Africa for instance, PD utilization is very low or non-existent outside of South Africa, where solutions can be manufactured locally bring the PD cost well below that of HD (3). Hong Kong has the highest PD utilization in the World (80%) due to the low cost of consumables and solutions (PD is half the cost of HD) as well as the PD first policy adopted in this country.
The way forward for low economy countries is to have PD as an economically viable option for RRT. For that they would have to reduce the cost of PD solutions (bags) cost considerably by:
1. Imposing more acceptable prices and breaking the monopolies of major suppliers.
2. Reducing import duties on bags (as has been done in Nepal and Malaysia).
3. Considering the local production of Bags and PD solutions (South Africa and India).
4. Negotiating import contracts with other developing countries that manufacture PD bags and solutions.
5. Encouraging a PD first approach as promoted by Hong Kong and recently adopted by Thailand.
This may offer emerging countries with hardly any RRT due to unaffordability, the option of a potentially cheaper RRT modality compared to HD, thus also bypassing the cost of setting up HD units with the inherent infrastructure cost.
PD first may be, with renal transplantation as soon as possible may be a model to consider. Iran has increased considerably since 1995 its utilization of PD (manufactured locally) (4) as well as its rate of renal transplantation through a concerted centralized healthcare policy. In low and middle economies where ESRD is often a death sentence due to the lack of affordable RRT modalities, Governments have a duty to explore and provide affordable RRT options in order to comply with the moral ethics of the Istanbul Declaration banning organ trafficking. Unless, this is provided, human nature will prevail and organ trafficking will continue out of the despair of some and the greed of others…
References:
2. http://www.ncbi.nlm.nih.gov/pubmed/?term=neil%2C+guest%2C+wong
3. http://www.ncbi.nlm.nih.gov/pubmed/22641735
4. http://www.ncbi.nlm.nih.gov/pubmed/20628104
[ Modified: Thursday, 1 January 1970, 1:00 AM ]
Anyone in the world
##### They showed that what mattered in terms of Cardio-Protection was BP REDUCTION. They reported a reduction of Major Adverse Cardiovascular Events (MACE) by a SIXTH for every reduction of SBP of 5mmHg, regardless of the class of antihypertensive agent used. They showed equal cardioprotection in CKD and non-CKD patients and the level of cardioprotection was not affecetd by the severity of CKD. They also failed to show that more intensive BP control levels had advantages over standard BP control targets.http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3789583/pdf/bmj.f5680.pdf
This comprehensive and well conducted meta-analysis confirms my long held bias that cardio-protection relies primarily on lowering BP regardless of the agent used. This was also the conclusion of a number of studies and meta-analysis including ALLHAT and the Meta-Analysis of Casas and colleagues in ther Lancet a number of years ago. http://www.ncbi.nlm.nih.gov/pubmed/16338452
We are often referred to the seminal study HOPE arguing that the cardioprotection conferred by RAS inhibitors is independent from their BP lowering effect and is a class specific effect that justifies their use above other anti-hypertensive agents in those at CV risk: http://www.ncbi.nlm.nih.gov/pubmed/10675071
This Mantra...like many in Nephrology has been repeated over and over again by Nephrologists keen to do their best for their patients and egged on by the Pharmaceutical Industry keen to do its best for its shraeholders....and the story went on for more than a quarter of a century inspite of dissending voices questioning the dissociation of the protective effect from the anti-hypertensive effect of RAAS inhibitors. I personally questionned that myth as far back as 2000: http://www.ncbi.nlm.nih.gov/pubmed/10754405
The confusion and issues are due to a number of reasons:
1. Pharma Industry hold of Key Opinion Leaders and Clinical Trialists over the last quarter of a century. I recollect conducting a study on progression comparing Lisinopril versus Placebo (with equal BP control) in the late 80s and study impact on progression: Result: NO difference. Outcome: Never Published...???!!!!
2. Lack of Critical Reading or Appraisal skills by most of those of us who read published material and Clinical Trials Reports; most dont bother to read the methodology section; abstracts or even title is often enough to embrace a new idea...treatment...or myth...and run with it!
3. Physicians commercialism; always keen to impress (and hence charge more...) patients with the latest treatments stemming from the latest publications even if they half understand their scientific implications as long as they fully understand their financial incolme generation implication.
4. MOST IMPORTANTLY....the alleged dissociation between the cardioprotective effect of RAAS inhibitors from their anti-hypertensive effects stems to a large extent from the fact that BP is RCTs (Clinical Trials) is seldom measured correctly; often if not invariably relying on causal office BP reading after a few minutes of rest...this is the least valuable, accurate or predictive method in terms of CVD outcomes as nocturnal, day:night and 24h Ambulatory BP measurement (ABPM) have proved much more reliable and predicitve.
In fact and of relevance, is the observation of a HOPE sub-study itself by Svensson et al (2001) who compared office BP and 24h ABPM and concluded: "Although, OBP is the correct comparator when comparing with previous large intervention trials and epidemiological studies, the effects on cardiovascular morbidity and mortality seen with ramipril in the HOPE study may, to a larger extent than previously ascribed, relate to effects on blood pressure patterns over the 24-hour period" .
http://www.ncbi.nlm.nih.gov/pubmed/11751742
So to conclude:
What seems to matter in the cardioprotection of CKD pateints is good BP control (KDIGO recommends <140/90mmHg) with due consideration to patients age and co-morbidities, this regardless of the class of antihypertensive agents used. Considerations should be then given to patients tolearbility, Risk versus Benefits of a given clkass of agents as well as Cost : Benefit ratio in countries where patients have to pay for their medication; a factor that greatly impacts on compliance and quality of BP control.
Finally, let us not forget that even in the US the majority of those with Hypertension are either NOT treated or POORLY CONTROLLED:
http://www.ncbi.nlm.nih.gov/pubmed/19710486
[ Modified: Thursday, 1 January 1970, 1:00 AM ]
Anyone in the world
After years and even decades of total neglect, the Nephrology community is waking up to the fact that Creatinine Clearance is affected by Tubular Secretion of Creatinine (TSCr)...!!!
A recent article in the September 2013 issue of the Am J Kidney Disease by Sithoven and colleagues in Groningen, Netherlands shows that there is a good agreement in ADPKD between eGFR and measured GFR (mGFR) in individuals with normal renal function highlighting the fact that at normal eGFR range, tubular secretion (TS) Creatinine (TSCr) is relatively small and therefore doesnt confound estimation of kidney function by eGFR (MDRD or CKD EPI). They also argue that such correlation was maintained in a subgroup of patients followed-up for 3 years.
This somehow disagrees with teh observations of Rugennenti and his colleagues in Bergamo who showed poor agreement between eGFR and mGFR in estimating the rate of decline in kidney function in ADPKD and that both MDRD and CKD EPI failed to accurately detect changes in mGFR in those with ADPKD and declining renal function. This, in spite of a comparebale baseline GFR to that of the Groningen group at the onset but a significant rate of decline with time of around 8-10ml/min.
The discrepancy between the two articles highlight the fact well know to Nephrologists for the last century or so that the Tubular secretion of Creatinine is relatively small in normal GFR ranges but increases significantly as GFR declines to reach as mush as 50% of Creatinine Clearance when GFR is <20-30ml/min.
Therefore, eGFR is most likley to be useless in the evaluation of interventions aimed at impacting on the rate of GFR progression as when true GFR declines tubular secretion of creatinine increases confounding the use of serum creatinine as a parameter of progressive CKD. So whilst Spithoven et al are right in their statement that eGFR is accurate in evaluating true measured GFR in ADPKD, the difference between the studies and their resepctive and contradictory assertions may lay in the level of GFR and the rate of decline of kidney function; lower GFR and faster rate of GFR decline leads to increased tubular secretion of creatinine and consequently decreased agreement between measured and calculated GFRs.
This was also reported by Gaspari et al, 2013 in T2DM where formulated GFR underperformed and underestimated the rate of true GFR decline.
This again highlights the fact that TSCr cannot be ignored including in diabetes mellitus where changes in tubular secretion of creatinine have been reported due to the impact of diabetes on proximal tubules transporters of creatinine and changes related to impaired kidney function and metabolic control. Too many confounders for serum creatinine to be an accurate marker of glomerular filtration.
Furthermore, interventions themselves may impact on the tubular handling and secretion of creatinine and consequently making interpretation of the intervention of rate of decline of GFR impossible. Incidentally, this is the case with RAS (renin angiotensin system) inhibition that has been show both experimentally and clinically to improve tubular secretion of creatinine in diabetic nephropathy confounding ANY conclusions on the impact of RAS inhibitors on the decline in eGFR in diabetic nephropathy:
In conclusion:
All the studies on the progression of CKD relying on measurements and changes in serum creatinine levels or the changes in formulated/estimated GFR (eGFR) are likely to be inaccurate due to the major confounding effect of Tubular Secretion of Creatinine. Not withstanding the additional confounder of the impact of any given intervention on Tubular Secretion of Creatinine. The BEAM/BEACON studies are tragic reminders of the unreliability of eGFR in interventions with agents that impact on tubular viability and function and consequently impact on serum creatinine/eGFR through mechanisms unrelated to changes in GFR.
Sadly and disappointingly, to date I am not aware of a single intervention study in CKD where GFR was measured serially to asses progression in the entire study population (with the exemption of the MDRD study in 1994 where iothalamate clearance was used throughout the study period).
Reliance on eGFR to test interventions that may slow the progression of CKD is a tragic and often wilful mistake.
[ Modified: Thursday, 1 January 1970, 1:00 AM ]
Anyone in the world
Cystatin C and creatinine as markers of bleeding complications, cardiovascular events and mortality during oral anticoagulant treatment. Marcus Lind a,⁎, Jan-Håkan Jansson a, Torbjörn K. Nilsson b, Lisbeth Slunga Järvholm a, Lars Johansson a
a Department of Public Health and Clinical Medicine, Umeå University, Umeå, Sweden b Department of Clinical Chemistry, Örebro University Hospital, Örebro, Sweden Introduction: Impaired kidney function has been linked to both ischemic events as well as bleeding complica- tions in several clinical conditions. Our aim was to investigate if cystatin C, creatinine and calculated glomerular filtration rate (eGFR) were related to future risk of bleeding complications, cardiovascular events or all-cause mortality during oral anticoagulant treatment.
Materials and methods: In a cohort study, 719 patients on long-term vitamin K antagonist (VKA) treatment were followed for a mean of 4.2 years. Blood sampling was taken at inclusion and patients were followed prospectively. Cystatin C and creatinine were analysed and eGFR was calculated. All medical records were reviewed. Major bleeding events, myocardial infarctions, strokes, arterial emboli, and deaths were recorded and classified. Results: After adjustment for age, no association between cystatin C, creatinine or eGFR and major bleeding was found. Cystatin C was independently associated with cardiovascular events (hazard ratio 1.50 (95% CI: 1.27-1.77)) and all-cause mortality (hazard ratio 1.62 (95% CI: 1.38-1.90)).Creatinine was only associated with all-cause mortality, while eGFR was not associated with any of the outcomes.
Conclusions: Our findings underscore the superiority of cystatin C as a marker of cardiovascular risk compared to creatinine or eGFR. VKA-treated patients with increased cystatin C levels should be considered to be at an increased risk of cardiovascular events, and not bleeding complications.
http://www.ncbi.nlm.nih.gov/pubmed/?term=anticoagulation%2C+Cystatin%2C+creatinine
Predictors of all cause CVD and mortality in a selected population showing that:
Serum Cystatin C predicts CVD events as well as all cause mortality.
Serum Creatinine predicts all cause mortality only.
eGFR: doesnt predict anything!
This observation made in a selected group of individuals on anticoagulation agrees with more general observations made in the general population by Astor et al last year (2012) that Cystatin C was superior to Cr-based eGFR in predicting outcomes; Heart failure, CAD, Mortality and even ESRD. http://www.ncbi.nlm.nih.gov/pubmed/22305758
The explanation is probably multifactorial including the fact that it is most likely that it is the non-renal aspects of either serum creatinine (wasting, sarcopenia, and catabolism) or Cystatin C (inflammation, obesity, smoking) that drive the association between low calculated eGFR and outcomes previously reported by a number of large community-based studies. http://www.ncbi.nlm.nih.gov/pubmed/21307840
Of interest in the Astor study, other filtration markers that have inflammatory associations such Beta2-microglobulin (b2M) and Beta Trace Protein (BTP) showed a superiority to serum creatinine and derived equations in predciting cardiovascular and mortality outcomes.
Overall, the inclusion of CystatinC and CysC related eGFR equations improves considerably the mortality risk prediction compared to Cr-based eGFR derivations and CKD classification. This was recently highlighted by the article of Shlipak et al (NEJM September 2013), although these authors remain unable to appreciate that it is serum Cystain C level that matters and not the eGFR derivation... http://www.nejm.org/doi/pdf/10.1056/NEJMoa1214234
So the question has to be asked, whether it is a low eGFR that predicts CV and all cause mortality as repeatdly and stubornly stated or whether it is the components that make up the eGFR calculation: sCreatinine and sCystatin C that truly determine outcomes?
And does it matter?
The answer is yes, it does matter as we have been indoctrinated over the last 5-10 years with the concept that low eGFR is worth detecting and justify population screening because...it predicts cardiovascular as well as all cause mortality. Further, such an assumption has been the basis of the new (2013) KDIGO CKD classification and its risk stratification.
Well, if all it takes is to go back to the good old serum creatinine (or urine creatinine for that matter) and rediscover that individuals in the lower quartiles of the serum creatinine range for their age are at increased risk of CV and all cause mortality, then we start wandering about the whole foundation of the eGFR based stratification of individuals. Low serum creatinine is a poor prognostic predictor based on wasting and sarcopenia, whilst a high serum creatinine tells us all we need to know about renal function and its progression...and for good measure we would also measure CystatinC in those we clinically deem to be at high CVD morbidity and mortality. Other biomarkers that are equally useful would be the good old C-Reactive protein. http://www.ncbi.nlm.nih.gov/pubmed/23975559
A step back to the future would take us back in the future to simple and reliable predictors of outcomes (renal and mortality) and away from a complicated eGFR based classification system. It would have the added advantage of avoidance of medicalisation of older "normal" individuals based on a creatinine based formulation that appears to be wanting in its primary function, that of predicting renal and cardiovascular outcomes....
[ Modified: Thursday, 1 January 1970, 1:00 AM ]
Anyone in the world
EXAMPLES OF FRAUD IN MEDICINE AND IN STUDIES INVOLVING RAS INHIBITION IN JAPAN:
Diovan Data Was Fabricated, Say Japanese Health Minister And University OfficialsReply
Following a long series of accusations, retractions, and the resignation of a prominent professor, it now is clear that data from a large Japanese study of valsartan (Diovan, Novartis) was fabricated. On Thursday officials at Kyoto Prefectural University of Medicine said that “had patient records been used in their entirety,” the Kyoto Heart Study “would have had a different conclusion,” reported AFB.
In 2009 the Kyoto Heart Study investigators, including the chief investigator, Hiroaki Matsubara, reported that treatment with valsartan resulted in significant cardiovascular benefits independent of the drug’s blood-pressure lowering effect. Now officials at the university say the drug had no such effect.
On Friday Norihisa Tamura, Japan’s health minister, said data had been “fabricated and falsified.” Tamura said he would set up a committee to prevent episodes like this from happening again.
and in the past:
# RETRACTED: Combination treatment of angiotensin-II receptor blocker and angiotensin-converting-enzyme inhibitor in non-diabetic renal disease (COOPERATE): a randomised controlled trial
Dr Naoyuki Nakao MD a ProfTerukuni Ideura MD a
## Summary
### Background
Present angiotensin-converting-enzyme inhibitor treatment fails to prevent progression of non-diabetic renal disease. We aimed to assess the efficacy and safety of combined treatment of angiotensin-converting-enzyme inhibitor and angiotensin-II receptor blocker, and monotherapy of each drug at its maximumdose, in patients with non-diabetic renal disease.
### Methods
336 patients with non-diabetic renal disease were enrolled from one renal outpatient department in Japan. After screening and an 18-week run-in period, 263 patients were randomly assigned angiotensin-II receptor blocker (losartan, 100 mg daily), angiotensin-converting-enzyme inhibitor (trandolapril, 3 mg daily), or a combination of both drugs at equivalent doses. Survival analysis was done to compare the effects of each regimen on the combined primary endpoint of time to doubling of serum creatinine concentration or end-stage renal disease. Analysis was by intention to treat.
### Findings
Seven patients discontinued or were otherwise lost to follow-up. Ten (11%) of 85 patients on combination treatment reached the combined primary endpoint compared with 20 (23%) of 85 on trandolapril alone (hazard ratio 0·38, 95% CI 0·18—0·63, p=0·018) and 20 (23%) of 86 on losartan alone (0·40, 0·17—0·69, p=0·016). Covariates affecting renal survival were combination treatment (hazard ratio 0·38, 95% CI 0·18—0·63, p=0·011), age (1·30, 1·03—2·29, p=0·009), baseline renal function (1·80, 1·02—2·99, p=0·021), change in daily urinary protein excretion rate (0·58, 0·24—0·88, p=0·022), use of diuretics (0·80, 0·30—0·94, p=0·043), and antiproteinuric response to trandolapril (0·81, 0·21—0·91, p=0·039). Frequency of side-effects with combination treatment was the same as with trandolapril alone.
### Interpretation
Combination treatment safely retards progression of non-diabetic renal disease compared with monotherapy. However, since some patients reached the combined primary endpoint on combined treatment, further strategies for complete management of progressive nondiabetic renal disease need to be researched.
These are very disturbing reports of fraudulent publications in Japan relating to the efficacy and superiority of RAAS inhibitors whether Trandolapril in combination with Losartan on the progression of CKD (Nakao et al) or the Kyoto Heart Stduy on Valsartan cardioprotective effects independlently of changes in BP...so why is this taking place in Japan but undoubtedly elsewhere.
Back to Bad Pharma...and Bad Doctors....but alo Japan...
Most clinical traisl of new therapeutic agenst are sponsored by the Pharmaceutical Industry; Good Pharma, without it we wouldnt be treating many life threatening medical conditions.
But
1. Most clinical investigators in many emerging (and emerged as well...) countries are targeted by the Pharma industry; they are receiving remunarations for their involvement in such clinical trials; in the form of money, in the form of recognition, in the form of prominence and fame in their profession...doctors like all humans are responsive to such incentives...
Consequently, doctors and invetigators involved in clinical trials want to please their paymater...the Big Pharma who recruits them.
2. Pharma analyses the result of the RCTs they sponsor....statisticians and analysts employed by the Pharma company almost exclusively analyse the result and data of the study; they "clean" it..."process"...it and ultimately provide investigators with a sanitised version of the outcome of the trial...
This is dangerous as it invites manipulation of the data by the Pharma employees to please their paymaters....Bad Pharam!
This has come to light in the UK with a major Pharma company in a trial on osteoporosis where the raw data emanating of the trial were not shown or shared with the investigators but instead the sanitised version of the Pharma analysis leading to questions posed by the likes of Dr Aubrey Blumsohn (who wasnt paid by them) about the conduct of senior investigatores including Prof Richard Eastell (who was a senior consultant to the Pharma):
http://www.bmj.com/content/339/bmj.b5293
3. Next, why are these fradulent reports emanating repeatedly from Japan?
This brings to mind issues relating to Japanese culture, and the deferential approach to authority and seniority.
Dont challenge, dont question...authority; If the Professor says that the trial is positive....who is the junior investigator or company employee to challenge him (seldom her...). Whistleblowing is not yet part of japanese culture. Whistelblowers are fired...marginalised or even prosecuted...this was highlighted in the report by Michael Woodford, who was the Olypmus camera company Chief Executive Office (CEO), who reported alarmingly bad and fraudulent practices in the Japanese company he was head of; he was fired and sued by the company! he wrote "EXPOSURE" counterattacked and got vindicated as bad and fraudulent practices were confirmed and the company found guilty of malpractices...
He wrote a book: "EXPOSURE" that puts the fraudulent practice of Olympus in the context of the Japanese society and its culture. he attributed malpractices in Japan industry to over-deferential attitude to authority and seniority. This may also be symptomatic of japanese healthcare companies and medical investigations.
WHISTELBLOWING IS HEALTHY AND OFTEN JUSTIFIABLE....BUT THE WHILSTLEBLOWER SHOULD BE WILLING TO PUT HIS JOB ON THE LINE AS DR AUBREY BLUMSOHN AND MR MICHAEL WOODFORD DID...they both rendered a huge service to probity and transparency in Pharma and Industry in general!
BIG PHARMA needs to think again the conduct of their clinical trials....BAD DOCTORS need to be checked and challenged by those working with them and collaborating in their clinical investigations worldwide...as Scientifc Fraud is not a Japanese Exclusive....it is prevalent worldwide:
This is very nciely reviewed in this BMJ paper, http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3702092/?report=classic,
listing:
Lack of Ethics
Career Ambitions/Promotion
Financial Rewards
Academic and Professional Rewards
But also Lack of Institutional monitoring and vigilance
A Must read for all clinical investigators!
[ Modified: Thursday, 1 January 1970, 1:00 AM ]
Anyone in the world
Excellent Editorial in the BMJ entitled: Too much Medicine; Too Little Care:
http://www.ncbi.nlm.nih.gov/pubmed/23820022
This Editorial makes excellent points about:
1. Redefining diseases such as Hypertension, Diabetes, obesity, hypercholesterolemia, osteoporosis and... CKD as to increase their prevalence...and raise the spectrum of "Epidemics"...!!! More an Epidemic in Diagnosis rather than a true Epidemic of Disease!
2. Redefining thresholds for disease definition leading to medicalisation of normal variations "normality"..."ageing"...etc...
3. Overinvestigating and consequently Overdiagnose; mostly incidentalomas....
4. The above raising concern, anxiety, cost...with little impact on Outcomes.
This Editorial suggests:
1. More Scepticisms from Physicians about changing thresholds.
2. More Scepticism amongts physicians about new definitions of disease
3. More Scepticism about new Guidelines and Recommendations
4. Better use to language and semantics of health and disease:
Use the terms “raised blood pressure” not “hypertension,”
“reduced bone thickness” not “osteoporosis,”
“reduced kidney function” not “chronic kidney disease” when talking with patients.
5. Better sharing with the Public of the uncertainty and significance of the findings as well as the risk, benefits and cost of screening and redefining diseases.
This applies to CKD as much as any other "disease", with clear healthcare implications including an increasing overlooking of true CKD (that is referred CKD of patients with glomerulonephritis, vasculitis, interstitial nephropathies, heriditary diseases etc...) whilst more attention and probably manpower and resources are diverted to:
1. Looking/Screening for "CKD" in communties...it has become an obsession...in our profession!?
2. Early detection of CKD...with little insights into potential harm...and known benefit...?!
3. The growing "Epidemic" of CKD... which seems related to an "Epidemic" of Diagnosis and eGFR formulas rather than a true change in the number of people with progressive CKD or ESRD; the latter if anything may be coming down rather than increasing!
4. The Medicalisation of Normality; decline of kidney function with age...?!
We have to ask ourselves:
WHY?
WHO has a vested interest in such "Epidemic of CKD"
The answer seems manifold:
The Profession: Increasing its profile; from a small subspecialty of Medicine to a Global Healthcare Challenge!
http://www.ncbi.nlm.nih.gov/pubmed/23727165
Nephrologists: More Research into a new disease, a growing disease, a major threat...more grants, larger departments, more income generation...more publications, etc...Academic Recognition?!
Market factors: More disease, More Patients, More Consultations, More Income...?!
Pharma: More Disease, More Patients, More Treatments, More Income...?!
All very intriguing but happening in CKD, which would be acceptable if HARMLESS, but of considerable of concern if HARMFUL!
[ Modified: Thursday, 1 January 1970, 1:00 AM ]
Anyone in the world
CKD Classification:
A debate has been ongoing for a number of years between those who support the KDOQI (2002) and more recently KDIGO (2012) CKD classification and those who argue that the whole concept has considerable shortcomings and flaws:
Main arguments for current classification:
1. Clinically useful
2. Prognostically relevant as eGFR and albuminuria not only reflect ESRD prognosis but also CVD and all cause mortality outcomes
http://www.ncbi.nlm.nih.gov/pubmed/20483451
3. Increased CKD awareness
http://www.ncbi.nlm.nih.gov/pubmed/23727165
4. Highlights the true scale of the CKD problem worldwide
Main arguments against:
1. Epidemiologically useful but less so clinically
2. Adds little to conventional prognosis markers such as severity of proteinuria, serum creatinine level at presentation and old fashion 1/sCr slope and/or conventional cardiovascular prediction scores such as Framingham Risk Score.
http://www.ncbi.nlm.nih.gov/pubmed/21811078
http://www.ncbi.nlm.nih.gov/pubmed/21357908
3. Flawed risk prediction analysis lacking validity and usefulness:
http://www.ncbi.nlm.nih.gov/pubmed/23588748
4. Microalbuminuria is not sufficient on its own to define CKD 1 or 2.
5. Artificial and clinically irrelevant division of CKD1 and 2 in the absence of the known difference in natural history of CKD 1 versus 2.
6. Overestimation of CKD, as it is epidemiologically primary a fact that up to 30-40% of those >65 years of age have a "physiological" decline in GFR. Lack of age consideration in the classification. (http://www.ncbi.nlm.nih.gov/pubmed/22437416)
7. Scare mongering of an "epidemic' of CKD based on flawed epidemiological studies
http://www.ncbi.nlm.nih.gov/pubmed/21965592
also see lecture on OLA given at the World Congress of Nephrology:
Recent controversy between two extremely knowlegeable and respected camps in this field was highlighted by respective articles in
Clin Chem Lab Med July 2013 by:
Delanaye and Cavalier: http://www.ncbi.nlm.nih.gov/pubmed/23729625
arguing against the status quo
and
Zoccali and colleagues arguing for the status Quo:
http://www.ncbi.nlm.nih.gov/pubmed/23828429
OLA and the Global Kidney Academy encourages a debate on this very important issue in Nephrology.
Taking sides may be unhelpful but more importantly comments are welcomed from practicing Nephrologists on, after evaluating the arguments above:
1. Whether a division between CKD 1 and 2 is justifiable?
2. eGFR and Albuminuria are unique predictors of outcomes in CKD thus justifying their inclusion in classification (KDIGO 2012)
3. Whether Age is irrelevant to classification so should not be taken into consideration?
We need to hear the voice and opinion of Practicing Nephrologists Worldwide!
[ Modified: Thursday, 1 January 1970, 1:00 AM ]
Anyone in the world
Kidney Int. 2013 Jun;83(6):1001-9. doi: 10.1038/ki.2013.91. Epub 2013 Mar 20.
# Targets, trends, excesses, and deficiencies: refocusing clinical investigation to improve patient outcomes.
### Source
Division of Nephrology, University of British Columbia, Vancouver, British Columbia, Canada.
### Abstract
Clinical trials in nephrology have focused on achieving targets, supplementing deficiencies, and correcting excesses in order to improve patient outcomes. The majority of interventions have failed to demonstrate benefit and some have caused harm. It may be that therapies aiming to 'normalize' parameters may actually disturb evolutionary adaptation, thus causing harm. By refocusing on the physiology of disease, and complexity of adaptation, we may design better trials. We review successful and unsuccessful trials in nephrology and other disciplines and suggest a set of principles by which to design future clinical trials:(1) acknowledge heterogeneity of chronic kidney disease populations and appropriately characterize populations for studies; (2) develop better validated biomarkers (through proteomics, genomics, and metabolomics) to identify responders and nonresponders to interventions; (3) design interventions that mimic physiological processes without collateral detrimental effects; (4) reconsider the status of the randomized-controlled trial as the only 'gold standard' and perform large-scale pragmatic trials comparing current care with the intervention(s) of interest, and (5) broaden nephrology research culture so that the majority of patients are enrolled into observational cohorts and intervention studies, which foster greater knowledge acquisition and dissemination. Improved understanding of pathophysiological mechanisms, in conjunction with more innovative but stringent clinical trial design, will ultimately lead to improved patient outcomes.
Comment:
This is a very important review of the state of clinical investigation and trials in Nephrology.
It highlights discrepancies betwen between observational and cohort studies and randomised control trials (RCTs); whereby the former often points to interesting associations suggesting interventional studies that ultimately prove consistently negative!
The authors explore potential reasons and explanations for such an intervention "gap".
They highlight the heterogenity of CKD patients, the lack of adequate surrogate markers that predict reliably hard endpoints.
They suggest that a better understanding of the pathophysiology that underpins clinical investigation may mitigate the consistent disappointment generated from interventions based on delusionary endpoints and modifiable parameters.
Finally, they question the place of the RCT as the "only gold standard" and put forward well condcuted pragmatic studies.
In my mind, the problem with Nephrology trials is that they deal with a heterogeneous and also very complex and MULTIFACTORIAL conditions.
Consequently, it is naive to expect that the modification of a single parameter:
Anemia, PO4, PTH, FGF23, BP, LIpids, etc...would suffice to reverse the relentless trend towards increased mortality.
It is high time to consider MULTIFACTORIAL therapies for a MULTIFACTORIAL disease.
It is high time to use combined therapies pitched against standard practice. This has been implemented in diabetes and diabetic nephropathy with some promise (http://www.ncbi.nlm.nih.gov/pubmed/18256393).
The issue and opposition for such an approach will come from the Pharmaceutical industry that dictates the terms and conditions of most clinical investigation in Nephrology and medicine in general.
The Pharmaceutical industry is there to promote ONE compound and not a multifactorial approach that would blur the impact of a given agent and subsequently blur their marketing strategy....
Also, Pharma rush to success leads clinical investigations in Nephrology to rely on soft and often inappropriate surrogate markers instead of taking the time (and cost) of aiming at altering hard endpoint ssuch as morbidity and mortality.
Alternate sources of funding of clincial investigation in Nephrology is key to the success of therapies and intervention in nephrology.
Government agents and NGOs need to take the lead and support clinical investigations that rely on:
1. Hard enpoints to improve patients outcomes.
2. Systematic Observational cohort studies involving more than one centre and more than one country.
3. Clinical investigations that pay attention to socio-demographic and geographic variability; involving emerging countries and their CKD/ESRD patients.
Also:
4. Moving away from statistical manipulation of data to serve commercial purposes
5. Moving away from soft and delusional surrogate endpoints
6. Moving away from the obsession with albuminuria reduction; another inappropriate and misunderstood surrogate marker
Ultimately, Nephrologists need to improve their understanding of piublished clinical investigations:
1. Improve their critical appraisal skills
2. Understanding that Proof of Concept (pahse2) trials are NOT conclusive
3. Understanding that subgroup and posthoc analyses are NOT conclusive; instead hypothesis generating
and also:
4. Improve their own data collection
5. Improve their own observational skills
It will take time, but a critical evaluation of the state of Clinical Investigation in Nephrology, as undertook by Levin and her colleagues, is timely and should encourage us all to re-think investigations and treatment strategies. This will ultimately translate into tangible and real improvement in patients outcomes. It will also lead to avoidance of harm!
[ Modified: Thursday, 1 January 1970, 1:00 AM ]
Anyone in the world
[ Modified: Thursday, 1 January 1970, 1:00 AM ] | 2020-02-25 09:06:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3291992247104645, "perplexity": 10539.767210334378}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146064.76/warc/CC-MAIN-20200225080028-20200225110028-00336.warc.gz"} |
https://stats.stackexchange.com/questions/57404/confidence-intervals-based-on-the-clt-ever-useful | # Confidence intervals based on the CLT: ever useful?
Suppose, for concreteness, that I am trying to estimate the mean of a population using a random sample of size $N$.
Many elementary books discuss forming a confidence interval for the population mean by using the central limit theorem to argue that the sample mean is approximately normally distributed.
However, the central limit theorem is a theorem about the limit as $N \to \infty$. But if $N$ were really large then the width of the confidence interval would be really small and giving just a point estimate would be good enough.
So it seems that we are implicitly assuming that there is a range of $N$ for which the CLT is not too bad an assumption but for which $N$ is not so large as to shrink the confidence interval to practically a point.
My question is: is there any basis for making this implicit assumption? Is there any way to judge what this range of useful $N$ is for a particular application?
The speed of convergence towards Gaussian depends on the exact laws, and in particular on the values of the cumulants:
• if there are no cumulant of order 1 or 2, i.e. no mean or no variance, you cannnot expect convergence to the normal;
• if cumulants of order 1 and 2 exist, it all depends on the cumulants of higher order. The smaller they are, the faster the sum converges to the normal, because the starting law is already close to the normal.
For instance, it is generally considered that a $Poi(20)$ law can be well approximated by a $N(20,20)$. However, $\sqrt{20}$ is still non-negligible compared to $20$.
Bounds for the difference between normal and exact are given by the Berry - Esseen theorem, but I am not sure they would be applicable in practice because you would need to know the third moment, which is difficult to estimate from the data.
In practice, judgment is required, and the approximation must be avoided whenever laws show a strong difference with normality: very non-centered or heavy tails (see for instance a qq plot).
Bootstrapping might also help: if your empirical data is close enough to normal, then bootstrapping and reestimating should give something close again to the approximate formula. | 2020-01-29 18:00:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8217467069625854, "perplexity": 203.8853602420153}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251801423.98/warc/CC-MAIN-20200129164403-20200129193403-00026.warc.gz"} |
https://ncatlab.org/nlab/show/cpo | # cpos
## Definition
A cpo is simply a set equipped with a complete partial order. However, we take as morphisms the Scott-continuous functions (continuous functions with respect to the Scott topology). Cpos and Scott-continuous maps form a category $CPO$.
## Applications
Cpos are important in domain theory.
## References
Last revised on July 8, 2010 at 19:39:00. See the history of this page for a list of all contributions to it. | 2018-05-25 22:17:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8585079312324524, "perplexity": 1077.8574580206864}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867220.74/warc/CC-MAIN-20180525215613-20180525235613-00060.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/if-006-of-a-number-is-84-then-30-of-that-number-is-percentage-discount-and-partnership-entrance-exam_107566 | If 0.06% of a number is 84, then 30% of that number is - Mathematics
MCQ
If 0.06% of a number is 84, then 30% of that number is
• 25.2
• 420
• 42000
• 2520
Solution
42000
Explanation:
Let the number be = x
(0.06"x")/100=84
"x"=84/0.06xx100
30% of x =30/100xx84/0.06xx100=42000
Concept: Percentage, Discount and Partnership (Entrance Exam)
Is there an error in this question or solution? | 2021-06-18 23:59:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5149470567703247, "perplexity": 4072.677108435522}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487643354.47/warc/CC-MAIN-20210618230338-20210619020338-00601.warc.gz"} |
https://quant.stackexchange.com/questions/44933/mean-variance-maximization | # Mean-variance maximization
I denote by $$W_0$$ and $$W_1$$ the wealth of an investor at $$t=0$$ and $$t=1$$, respectively. Let $$r_f$$ be the risk free rate, $$r$$ the vector of returns of the risky assets in excess of the risk free rate, and $$w$$ the vector of weights of the risky assets. Here is the classical mean-variance optimization problem: $$\max_{w} E(W_1)-\frac{\gamma}{2}Var(W_1)$$ $$\textrm{st.}\hspace{0.5cm} W_1=W_0(1+r_f+w'r)$$
Injecting the constraint into the optimization problem, the first order condition is thus written as follows: $$\frac{1}{\gamma} E(r)=W_0Var(r)w$$
My point is that I would like to end up with the classical mean-variance first-order condition: $$\frac{1}{\gamma} E(r)=Var(r)w$$
But I still have this $$W_0$$ in the equation... Did I miss something? Could someone please help me? Thanks
I get the maximization problem $$\max\limits_{w} \mathbb{E}\left[W_1\right] - \frac{\gamma}{2} Var(W_1)$$ $$st. W_1 = W_0(1 + r_f + w^Tr)$$ So we have \begin{align*} L(w) &= \mathbb{E}\left[W_1\right] - \frac{\gamma}{2} Var(W_1)\\ & = \mathbb{E}\left[W_0(1 + r_f + w^Tr)\right] - \frac{\gamma}{2} Var(W_0(1 + r_f + w^Tr))\\ & = W_0 + W_0r_f + W_0w^T\mathbb{E}\left[r\right] - \frac{\gamma}{2}W_0^2 w^TwVar(r) \end{align*} Building the derivative w.r.t. $$w$$
\begin{align*} \partial L(w) / \partial w &= W_0 \mathbb{E}\left[r\right] - \frac{\gamma}{2}W_0^2 2wVar(r)\\ &= W_0 \mathbb{E}\left[r\right] - \gamma W_0^2 wVar(r) \overset{!}{=} 0 \\ \Leftrightarrow \frac{1}{\gamma}\mathbb{E}\left[r\right] & = W_0Var(r)w \end{align*} So, I get $$w = \frac{\mathbb{E}[r]}{\gamma W_0Var(r)}$$. Set initial wealth $$W_0 = 1$$ and you get the desired result. The optimal investment strategy $$w$$ is $$W_0$$ dependent.
• Thanks, that is basically the calculus I do (except that your matrix calculation is not appropriate: prefer $w'Var(r)w$) and the result I get. So I was wondering whether it was a classical assumption in research papers to set $W_0=1$. Apr 4, 2019 at 21:26 | 2023-01-26 22:13:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 21, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9991825222969055, "perplexity": 782.8034588592676}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494826.88/warc/CC-MAIN-20230126210844-20230127000844-00116.warc.gz"} |
http://mathhelpforum.com/differential-equations/280317-find-characteristic-equation.html | 1. ## find characteristic equation
Attachment 38634
ok im doing #1
ok I go a reduction of
$$\frac{1}{3} \begin{bmatrix} 1&1/3&0\\ 0&1&0\\ 0&0&1 \end{bmatrix}$$
but what next?
$-\lambda^3 +18\lambda^2 -95-\lambda+150$
2. ## Re: find characteristic equation
Beware Bigwave: your number of posts reached the beastly "666" on Easter day
God Bless...
4. ## Re: find characteristic equation
You say, in your post, that you are doing #1 but there is no "#1" in the attachment. Instead, #13 is highlighted so I assume that is what you mean.
Your problem is that while "reducing" a matrix to upper triangular form is useful for finding an inverse matrix or solving matrix equations, it has nothing to do with finding eigenvalues. The eigenvalues of the reduced matrix are not those of the original matrix.
Instead we need to solve the determinant equation $\displaystyle \left|\begin{array}{ccc}6-\lambda & -2 & 0 \\ -2 & 9-\lambda & 0 \\ 5 & 9 & 3- \lambda \end{array}\right|= 0$. I notice that the last column has '0's every where except at the bottom so we can "expand" on the final column to get
$\displaystyle (3- \lambda)\left|\begin{array}{cc} 6-\lambda & -2 \\ -2 & 9- \lambda\end{array}\right|= (3- \lambda)((6- \lambda)(9- \lambda)- 4)= (3- \lambda)(54- 15\lambda+ \lambda^2- 4)= 150- 95\lambda+ 18\lambda^2- \lambda^3= 0$.
5. ## Re: find characteristic equation
yeah I saw the #1 was actually #13 but the edit on the OP was not available
So really no need to reduce then?
6. ## Re: find characteristic equation
Not for finding the characteristic equation. The characteristic equation for your reduced matrix is $\displaystyle \left|\begin{array}{ccc}1- \lambda & \frac{1}{3} & 0 \\ 0 & 1- \lambda & 0 \\ 0 & 0 & 1- \lambda \end{array}\right|= (1- \lambda)^3$ but that is NOT the characteristic equation of the original matrix. | 2019-02-22 14:08:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8536596894264221, "perplexity": 1017.930672194024}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247518425.87/warc/CC-MAIN-20190222135147-20190222161147-00502.warc.gz"} |
https://chemistry.meta.stackexchange.com/questions/2759/i-love-you-guys-gals-appreciation-thread?noredirect=1 | # I love you guys/gals - Appreciation Thread
Before you downvote, I've examined the Help section thoroughly and it says that meta is for the following:
• Chemistry Stack Exchange users to communicate with each other about Chemistry Stack Exchange
I'm allowed to communicate with you about Chem:SE and you are undoubtedly apart of that.
Lets face it. Chem:SE has had its fair share of moments from its infamous drama to its shining moments. We graduated. We've made it. Its been quite a journey (if I may say so without sounding overdramatic) but it certainly has been quite... the... journey... .
I'm certain I'll be missing some people who well deserve to be mentioned here but let us give credit to some of the following people who have been here from nearly the beginnings.
Jonsca - Our fearless leader who has done more for this community than probably gets credit for. You set a great example for what a moderator should be. And you have been instrumental in getting us to where we are today as a community.
ManishEarth - You've been around for a very long time as well sacrificing a lot of your time for this site.
The chemistry giants who seem to be more machine than man... ron, Klaus Warzecha, Ben Norris, F'x, Philip, Greg E. - I stand in awe to your diverse knowledge of chemistry and how you are seemingly able to offer such incredible knowledge to a wide array of questions. I just cannot even begin to comprehend how you manage to know so much about Chemistry.
Dissenter - You always seem to ask really good questions... and a LOT of them. I've always enjoyed your posts on Chem:SE as well as your discussions in chat. I hope you come visit us again someday. You brought a lot of insight to our community.
tschoppi - Your enthusiasm really is quite a lesson we can all take from you. The chatroom always benefits from you chiming in every once in a while.
Geoff Hutchison - Avogadro2??? Maybe?! SOON!?! #GetHyped2016
And finally...
Martin - The German who lives in Japan who seriously contributes so much to this community. There is hardly a question you'll find he hasn't edited, or a day that goes by that he hasn't checked into chat. Martin has devoted so much of his time to this community its unbelievable. Always welcoming... always level headed... Martin is a role-model for most of us.
Thanks guys. Thank you so much for everything you've brought to the table. I might be the only one gushing right now but I'm sure I speak for others when I say wholeheartedly...
$$\mathrm{Thank~you}$$
Leave your appreciation below. Lets keep this post alive for at least a little while before we close it as being off-topic (please). :)
• No, this is fine to have here. We'll bend the rules a little bit. :) Thank you, too, for your kind wishes and your steady participation! I definitely shouldn't be the headliner! May 23, 2015 at 1:07
• Nice one! Well deserved kudos to all there! I hope to one day be able to contribute sufficiently to be considered in such a great way.
– user15489
May 23, 2015 at 6:52
• I took the opportunity in the site graduation thread to express my gratitude, too! It's great to be around friendly, interesting and dedicated folk like you guys. Truly an honour to be here. May 23, 2015 at 13:24
• Posts like this always make me stop and reflect on the nice folks I've met here and the fun I've had here. Tonight I'll raise a glass to all the people I've met on the Chem SE road!
– ron
May 23, 2015 at 14:39
• @ron We will have to raise a round for you and everyone else as well. I'm glad to have everyone around, but especially the core folks!! May 24, 2015 at 6:48
• @jonsca and a great thing is, as time progresses, that core will grow as more professionals and enthusiasts not only join the ranks, but work, enjoyably, to make this place great!
– user15489
May 24, 2015 at 11:29
• I'm glad I read this meta post. The community that has developed here is awesome and I am happy to be a part of it. May 25, 2015 at 11:35
• @BenNorris You have hung with us from the start, so we are especially grateful for that. May 25, 2015 at 23:52
• You're welcome! :D And thanks to the awesome community for making this place the wonderful place it is! We keep this place clean, it's you folks who make it sparkle! :) May 27, 2015 at 6:19
• I'm certain I'll be missing some people who well deserve to be mentioned.... You missed me, of course. :D ... Ahh, I also thought of writing a post like this, but I <strike>feared the downvotes</strike ;)> didn't have the time because of the exam season. Bottom line is, as @santiago says, I hope I'll be contributing well enough to be in that list... In a hopefully far future. :) May 28, 2015 at 18:18
• It's been wonderful seeing the community that's developed on this site, I'm glad you're taking a moment to appreciate it. You have much to be proud of.
– Ana
May 28, 2015 at 21:59
• I have said "sorry" to most of the above people for my stupid mistakes. I have also said "Thanks" for correcting stupid mistake :) Really this are people who have worked really well to make Chem. S.E. what it is today. And yes you have missed one person "LordStryker" Jun 5, 2015 at 13:41 | 2022-07-02 15:21:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1754835546016693, "perplexity": 1772.0824590703953}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104141372.60/warc/CC-MAIN-20220702131941-20220702161941-00764.warc.gz"} |
https://www.physicsforums.com/threads/inequality-proof.82904/ | # Inequality proof
Show that for each complex sequence $$c_1, c_2, ..., c_n$$ and for each integer $$1 \leq H < N$$ one has the inequality
$$| \sum_{n=1}^N c_n|^2 \leq \frac{4N}{H+1} ( \sum_{n=1}^N |c_n|^2 + \sum_{h=1}^H | \rho_N(h)|)$$
Any one.....matt grime perhaps?
note: if anyone actually wants to work this out let me know and I will fill in the missing parts...but don't ask me to do it.... :tongue2:
Last edited:
honestrosewater
Gold Member
Yeah, that's good. The more fancy meaningless symbols, the better.
honestrosewater said:
Yeah, that's good. The more fancy meaningless symbols, the better.
There is an important part missing but it is a true bound...not just meaningless...
honestrosewater
Gold Member
Okay, I'll take your word for it. It would be nice if someone were around to explain it to me.
honestrosewater said:
Okay, I'll take your word for it. It would be nice if someone were around to explain it to me.
Yeah...it would take a really smart....creative....mathematician to do so...who would be able to do that I wonder??????
honestrosewater
Gold Member
Townsend said:
Yeah...it would take a really smart....creative....
... and patient. I've never even worked with complex numbers before. You can just treat them as ordered pairs of real numbers, right? I think I'd like that approach.
Johnny5
I know the solution, but I won't say to give other people a chance. It's not that hard.
wolram
Gold Member
Its packman eating flies, so the ansewer must be MxBxHs | 2021-10-20 04:54:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7912993431091309, "perplexity": 1137.5916980849452}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585302.56/warc/CC-MAIN-20211020024111-20211020054111-00548.warc.gz"} |
https://cs.stackexchange.com/questions/63383/how-do-i-approach-inductive-design-problems-with-no-information-or-context-given/63385 | # How do I approach inductive design problems with no information or context given?
As a starting point for our course in Artificial Intelligence, we are being taught induction. We received a number of homework assignments where we have to show our inductive approach for a given problem.
An example of such a problem: "Sort an array of N numbers".
Reading through the course material and online sources I feel I have grasped the first concepts of induction. I have successfully proven some statements using induction, such as the number of steps for the Tower of Hanoi problem. However, I was able to prove it because I had some information beforehand, such as the number of steps required to move the tower in the form of a formula.
In the problems handed to us, we get a sentence like the one above and are asked: "Describe the inductive approach"
Should I select an arbitrary sorting algorithm, make my own assumptions and devise my own hypothesis and try to prove that? I just want to prove that the array is indeed sorted for any given number of N. What are some exemplary steps I could take in order to provide the inductive approach given that single sentence of "Sort an array of N elements"
• Sorry, but if you do not have explicit task we cannot define it for you. But taking "Describe the inductive approach" - it shoud be inductive, it does not pick the algorithm or require runtime, it has to work. I do not know how the answer to your question would look like, but I can share some hint (I hope it is hint and might be helpful) if you take basic sorting algorithm which picks minimum and puts it in place than you have that element in place (sorted) so N - 1 elements left to sort. Maybe this will help?
– Evil
Sep 13 '16 at 0:56
It seems to me that your teacher wants a induction proof where the induction is on the length of the array. It seems weird that your teacher does not provide a sorting algorithm .
If the task is to sort an array, I would assume that your teacher is looking for an, as you say, arbitrary sorting algorithm and prove it with that.
But if the teacher means that you should check if an array is sorted, it is of course way simpler to show for different sizes of the array.
Either way it sounds like your teacher wants you to identify a base case and show that the induction holds (array is sorted) for $n$ given that it's sorted for an array size of $n-1$
With more details, or the full problem one might be able to draw more conclusions.
Most questions in AI textbooks of this style are intended to be open ended so that the student can experiment on its own with the problem. So the golden rule is do as you see fit to provide the best learning!
In particular for this problem, your approach seems appropriate.
Since most sorting algorithms fall into a divide and conquer schema, you won't have problem fitting it into an inductive schema.
For example, you could take quicksort, which is usually implemented recursively. And then prove that it indeed sorts an array of size $n$ assuming that it sorts an array of size less than $n$. | 2021-09-16 19:05:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4946398138999939, "perplexity": 295.6793439894917}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780053717.37/warc/CC-MAIN-20210916174455-20210916204455-00240.warc.gz"} |
https://socratic.org/questions/if-y-x-a-a-x-so-prove-that-2xy-dy-dx-x-a-a-x | ×
# If , y=sqrt(x/a)-sqrt(a/x) So, Prove that ?? 2xy(dy/dx)= x/a-a/x
## If , $y = \sqrt{\frac{x}{a}} - \sqrt{\frac{a}{x}}$ So, Prove that ? $2 x y \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{x}{a} - \frac{a}{x}$
Jun 17, 2018
Given: $y = \sqrt{\frac{x}{a}} - \sqrt{\frac{a}{x}}$
Differentiating:
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\sqrt{\frac{a}{x}} + \sqrt{\frac{x}{a}}}{2 x}$
Multiply both sides by2xy:
$2 x y \frac{\mathrm{dy}}{\mathrm{dx}} = 2 x y \frac{\sqrt{\frac{a}{x}} + \sqrt{\frac{x}{a}}}{2 x}$
$\frac{2 x}{2 x}$ becomes 1:
$2 x y \frac{\mathrm{dy}}{\mathrm{dx}} = y \left(\sqrt{\frac{a}{x}} + \sqrt{\frac{x}{a}}\right)$
Substitute $y = \sqrt{\frac{x}{a}} - \sqrt{\frac{a}{x}}$ on the right side only:
$2 x y \frac{\mathrm{dy}}{\mathrm{dx}} = \left(\sqrt{\frac{x}{a}} - \sqrt{\frac{a}{x}}\right) \left(\sqrt{\frac{a}{x}} + \sqrt{\frac{x}{a}}\right)$
Please observe that the right side is the pattern $\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$ where $a = \sqrt{\frac{x}{a}}$ and $b = \sqrt{\frac{a}{x}}$
$2 x y \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{x}{a} - \frac{a}{x} \text{ Q.E.D.}$
Jun 17, 2018
Kindly see a Proof in Explanation.
#### Explanation:
We have, $y = \sqrt{\frac{x}{a}} - \sqrt{\frac{a}{x}}$.
Diff.ing w.r.t. $x , \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{\sqrt{a}} \cdot \left(\frac{1}{2} {x}^{- \frac{1}{2}}\right) - \sqrt{a} \cdot \left(- \frac{1}{2} {x}^{- \frac{3}{2}}\right)$.
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2 \sqrt{a x}} + \frac{\sqrt{a}}{2 x \sqrt{x}}$.
Multiplying by $2 x , 2 x \frac{\mathrm{dy}}{\mathrm{dx}} = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}$.
Again multiplying by $y , 2 x y \frac{\mathrm{dy}}{\mathrm{dx}} = y \left(\sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}\right)$,
$i . e . , 2 x y \frac{\mathrm{dy}}{\mathrm{dx}} = \left(\sqrt{\frac{x}{a}} - \sqrt{\frac{a}{x}}\right) \left(\sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}\right)$.
$\Rightarrow 2 x y \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{x}{a} - \frac{a}{x}$, as desired!
Jun 17, 2018
We seek to show that:
$2 x y \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{x}{a} - \frac{a}{x}$ where $y = \sqrt{\frac{x}{a}} - \sqrt{\frac{a}{x}}$
Squaring the expression, and then expanding, we get:
${y}^{2} = {\left(\sqrt{\frac{x}{a}} - \sqrt{\frac{a}{x}}\right)}^{2}$
$\setminus \setminus \setminus \setminus = {\left(\sqrt{\frac{x}{a}}\right)}^{2} - 2 \left(\sqrt{\frac{x}{a}}\right) \left(\sqrt{\frac{a}{x}}\right) + {\left(\sqrt{\frac{a}{x}}\right)}^{2}$
$\setminus \setminus \setminus \setminus = \frac{x}{a} - 2 + \frac{a}{x}$
Differentiating Implicitly, we get
$2 y \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{a} - \frac{a}{x} ^ 2$
Finally, multiplying by $x$ we get the desired result:
$2 x y \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{x}{a} - \frac{a}{x} \setminus \setminus \setminus$ QED | 2018-09-22 22:21:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 29, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9483262300491333, "perplexity": 6305.343851867614}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267158766.53/warc/CC-MAIN-20180922221246-20180923001646-00537.warc.gz"} |
https://ncatlab.org/nlab/show/D4-brane | # nLab D4-brane
Contents
This entry is about a D-brane species in string theory. For the items in the ADE-classification of name D4, see there.
# Contents
## Idea
The D-brane of dimension $4+1$ in type IIA string theory.
## Properties
### Worldvolume theory
Khovanov homology has long been expected to appear as the observables in a 4-dimensional TQFT in higher analogy of how the Jones polynomial arises as an observable in 3-dimensional Chern-Simons theory. For instance for $\Sigma : K \to K'$ a cobordism between two knots there is a natural morphism
$\Phi_\Sigma : \mathcal{K}(K) \to \mathcal{K}(K')$
between the Khovanov homologies associated to the two knots.
In (Witten11) it is argued, following indications in (GukovSchwarzVafa) that this 4d TQFT is related to the worldvolume theory of the image in type IIA of D3-branes ending on NS5-branes in type IIB after one S-duality and one T-duality operation:
$(D3 - NS5) \stackrel{S}{\mapsto} (D3 - D5) \stackrel{T}{\mapsto} (D4-D6) \stackrel{IIA/M}{\mapsto} (M5 - MK6) \,.$
Earlier indication for this had come from the observation that Chern-Simons theory is the effective background theory for the A-model 2d TCFT (see TCFT – Worldsheet and effective background theories for details).
Notice that after the above T-duality operation the $(D4-D6)$-system wraps the $S^1$ (circle) along which the T-duality takes place.
Lifting that configuration to 11-dimensional supergravity gives M5-branes (the erstwhile D4-branes) on Taub-NUT ($\times S^1$). The M5-branes wrap the circle-fiber of Taub-NUT space, which shrinks to zero size at the origin (the MK6, the location of the erstwhile D6, which is where the D4s “end”). The low-energy theory, on a stack of M5-branes, is the 6d (2,0)-susy QFT.
### Bound states
bound states/brane intersections involving D4-branes:
$d$$N$superconformal super Lie algebraR-symmetryblack brane worldvolume
superconformal field theory
$\phantom{A}3\phantom{A}$$\phantom{A}2k+1\phantom{A}$$\phantom{A}B(k,2) \simeq$ osp$(2k+1 \vert 4)\phantom{A}$$\phantom{A}SO(2k+1)\phantom{A}$
$\phantom{A}3\phantom{A}$$\phantom{A}2k\phantom{A}$$\phantom{A}D(k,2)\simeq$ osp$(2k \vert 4)\phantom{A}$$\phantom{A}SO(2k)\phantom{A}$M2-brane
D=3 SYM
BLG model
ABJM model
$\phantom{A}4\phantom{A}$$\phantom{A}k+1\phantom{A}$$\phantom{A}A(3,k)\simeq \mathfrak{sl}(4 \vert k+1)\phantom{A}$$\phantom{A}U(k+1)\phantom{A}$D3-brane
D=4 N=4 SYM
D=4 N=2 SYM
D=4 N=1 SYM
$\phantom{A}5\phantom{A}$$\phantom{A}1\phantom{A}$$\phantom{A}F(4)\phantom{A}$$\phantom{A}SO(3)\phantom{A}$D4-brane
D=5 SYM
$\phantom{A}6\phantom{A}$$\phantom{A}k\phantom{A}$$\phantom{A}D(4,k) \simeq$ osp$(8 \vert 2k)\phantom{A}$$\phantom{A}Sp(k)\phantom{A}$M5-brane
D=6 N=(2,0) SCFT
D=6 N=(1,0) SCFT
(Shnider 88, also Nahm 78, see Minwalla 98, section 4.2)
Table of branes appearing in supergravity/string theory (for classification see at brane scan).
branein supergravitycharged under gauge fieldhas worldvolume theory
black branesupergravityhigher gauge fieldSCFT
D-branetype IIRR-fieldsuper Yang-Mills theory
$(D = 2n)$type IIA$\,$$\,$
D(-2)-brane$\,$$\,$
D0-brane$\,$$\,$BFSS matrix model
D2-brane$\,$$\,$$\,$
D4-brane$\,$$\,$D=5 super Yang-Mills theory with Khovanov homology observables
D6-brane$\,$$\,$D=7 super Yang-Mills theory
D8-brane$\,$$\,$
$(D = 2n+1)$type IIB$\,$$\,$
D(-1)-brane$\,$$\,$$\,$
D1-brane$\,$$\,$2d CFT with BH entropy
D3-brane$\,$$\,$N=4 D=4 super Yang-Mills theory
D5-brane$\,$$\,$$\,$
D7-brane$\,$$\,$$\,$
D9-brane$\,$$\,$$\,$
(p,q)-string$\,$$\,$$\,$
(D25-brane)(bosonic string theory)
NS-branetype I, II, heteroticcircle n-connection$\,$
string$\,$B2-field2d SCFT
NS5-brane$\,$B6-fieldlittle string theory
D-brane for topological string$\,$
A-brane$\,$
B-brane$\,$
M-brane11D SuGra/M-theorycircle n-connection$\,$
M2-brane$\,$C3-fieldABJM theory, BLG model
M5-brane$\,$C6-field6d (2,0)-superconformal QFT
M9-brane/O9-planeheterotic string theory
M-wave
topological M2-branetopological M-theoryC3-field on G2-manifold
topological M5-brane$\,$C6-field on G2-manifold
S-brane
SM2-brane,
membrane instanton
M5-brane instanton
D3-brane instanton
solitons on M5-brane6d (2,0)-superconformal QFT
self-dual stringself-dual B-field
3-brane in 6d
## References
### Double dimensional reduction from M5-brane
The relation of the M5-brane to the D4-brane and the D=5 super Yang-Mills theory in its worldvolume theory by double dimensional reduction:
### D4-D8 intersection
On D4-D8 bound states?:
With an eye towards holographic QCD:
### String phenomenology / intersecting D4-brane models
intersecting D-brane models with intersecting D4-branes:
Only D4-branes (possibly on O4-plane orientifolds):
• D. Bailin, G. V. Kraniotis, A. Love, Standard-like models from intersecting D4-branes, Phys. Lett. B530 (2002) 202-209 (arXiv:hep-th/0108131)
• H. Kataoka, M. Shimojo, $SU(3) \times SU(2) \times U(1)$ Chiral Models from Intersecting D4-/D5-branes, Progress of Theoretical Physics, Volume 107, Issue 6, June 2002, Pages 1291–1296 (arXiv:hep-th/0112247, doi:10.1143/PTP.107.1291)
• D. Bailin, Standard-like models from D-branes, J Phys (2003) 60: 199 (arXiv:hep-th/0210227)
• D. Bailin, G. V. Kraniotis, A. Love, New Standard-like Models from Intersecting D4-Branes, Phys. Lett. B547 (2002) 43-50 (arXiv:hep-th/0208103)
### Relation to Khovanov homology
The relation to Khovanov homology
Last revised on November 26, 2019 at 10:33:36. See the history of this page for a list of all contributions to it. | 2019-12-12 09:13:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 81, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9110715389251709, "perplexity": 7076.978114732242}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540542644.69/warc/CC-MAIN-20191212074623-20191212102623-00097.warc.gz"} |
http://www.gamedev.net/topic/651977-properly-planning-a-game-and-its-structure/ | • Create Account
## Properly planning a game and its structure
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
20 replies to this topic
### #1XNobodyX Members
132
Like
0Likes
Like
Posted 06 January 2014 - 06:55 PM
Preamble:
I have attempted to make 2 little indie games and each of them have failed for one reason, planning. For both of the projects I started off only planning to have a few parts to the game. As I started to code those parts I would realized that each of these parts needed a lot more code and classes and such than I originally thought. The problem is I would have already coded the majority of the game before I realized this. Thus leaving me with two options, 1) Rewriting the whole game, and throwing out countless hours of time. 2) Giving up . After thinking about where I went wrong it would always come down to the fact that when I started writing the game I didn't fully understand what I needed and thus didn't design it properly. I figure that this might happen a lot in many games(Realizing that a major change needs to be done) and I imagine that they don't all restart or quit. Which leads me to the conclusion that my planning might not be sufficient but the main structure of my code might be the problem. When I looked over my first game I found that a lot of my code was very specific and could not be easily rewritten without affecting other parts.
The question:
1) How do you go about properly planning a game and allowing major changes to be made without a re-write?
2)To avoid problems with having to rewrite everything should I try and write everything as a module that can be used in a main game loop?
If anyone has any good ways of organizing a game that you could point me to that would be awesome(Currently I am using the Model, View, Screen system)
### #2Genocode Members
148
Like
1Likes
Like
Posted 06 January 2014 - 07:17 PM
This is a problem I am kind of facing as well =/. I've had to resign to starting over due to not knowing an efficient way to continue my code and seeing that I was headed towards coding myself into a corner.
Any insight on dealing with this or avoiding this in the future would be greatly appreciated.
### #3Mnemotic Members
356
Like
0Likes
Like
Posted 06 January 2014 - 10:13 PM
1) How do you go about properly planning a game and allowing major changes to be made without a re-write?
Paper and pencil is really the way to go. Sketching things out is a great way to work out ideas. Use of formal tools, like UML, is entirely optional -- if you think that they help, go for it!
2)To avoid problems with having to rewrite everything should I try and write everything as a module that can be used in a main game loop?
Do it, if it makes sense. But avoid over-generalization -- YAGNE!
Happy hacking!
### #4 Nathan2222_old Members
-396
Like
0Likes
Like
Posted 06 January 2014 - 11:17 PM
Code wise, not sure. As for gameplay, keep wrting each idea on a book (books for me), when you've reached a point where you think it's alright, read through the whole thing and make sure it flows naturally, removing and adding ideas till you feel it's good. It could help you guess what the code will be like.
UNREAL ENGINE 4:
Total LOC: ~3M Lines
Total Languages: ~32
--
GREAT QUOTES:
I can do ALL things through Christ - Jesus Christ
--
Logic will get you from A-Z, imagination gets you everywhere - Albert Einstein
--
The problems of the world cannot be solved by skeptics or cynics whose horizons are limited by the obvious realities. - John F. Kennedy
### #5L. Spiro Members
24826
Like
15Likes
Like
Posted 06 January 2014 - 11:36 PM
POPULAR
How do you go about properly planning a game and allowing major changes to be made without a re-write?
Keep making games, keeping making mistakes, and learn from them.
To avoid problems with having to rewrite everything should I try and write everything as a module that can be used in a main game loop?
If you have a good idea about how to do it. Getting a good handle on how to properly do that tends to be the product of learning from past mistakes.
If anyone has any good ways of organizing a game that you could point me to that would be awesome
General Game/Engine Structure
You are basically asking, “How do I learn from experience without going through the ‘experience‘ part?”.
No matter what strategy you use, at the end of the day you will still need to be sitting down programming, and you will still be making mistakes. Throwing away code, writing tightly coupled code, and wasting hours of coding time is how we all start. It is a natural part of the learning process.
And I wouldn’t advise using any strategy that you yourself did not create specifically for yourself. When you create your own strategy it is based off what works best for you.
If someone told me to draw it out and I followed that advice, it naturally goes against my grain and would only slow me down. I have a mental image that has no naturalistic translation to an actual image; an image I see on paper does not translate into anything useful related to code for me, so trying to work that way is like trying to sew a shape into cloth just by looking at numbers representing angles and distances.
You can create any strategy you want. The point is that it won’t naturally flow for you unless it comes from you.
L. Spiro
Edited by L. Spiro, 07 January 2014 - 08:51 AM.
### #6boogyman19946 Members
1476
Like
2Likes
Like
Posted 07 January 2014 - 12:56 AM
L. Spiro has pretty much nailed it in the head. I would like to add a slight bit of advice though that I've read a long time ago and I can't remember where it's from: Always try to refactor your code before throwing it away. I find this is a better approach when it comes to learning because by fixing the code that you know is broken, it forces you to think about why it's broken and what the correct solution is. When you just start over and toss the other code aside, you're just making another shot in the dark. That's really just the way your memory works too. If you don't think about something extensively, you decrease your chances of remembering it.
Initially, this process will take a mighty long time, but the more you do it, the better code you'll write in the first place. As an example, I program my UI's by hand, and, at first, the UI code alone would give me so much trouble that I would rather do just about anything else than have to modify it, but once I started refactoring it, I find much better techniques for separating all the parts of it. Now I actually got myself a little library that handles building intricate menus
- Java API Documentation - For all your Java info needs
- C++ Standard Library Reference - For some of your C++ needs ^.^
### #7NightCreature83 Members
4779
Like
3Likes
Like
Posted 07 January 2014 - 03:51 AM
Preamble:
I have attempted to make 2 little indie games and each of them have failed for one reason, planning. For both of the projects I started off only planning to have a few parts to the game. As I started to code those parts I would realized that each of these parts needed a lot more code and classes and such than I originally thought. The problem is I would have already coded the majority of the game before I realized this. Thus leaving me with two options, 1) Rewriting the whole game, and throwing out countless hours of time. 2) Giving up . After thinking about where I went wrong it would always come down to the fact that when I started writing the game I didn't fully understand what I needed and thus didn't design it properly. I figure that this might happen a lot in many games(Realizing that a major change needs to be done) and I imagine that they don't all restart or quit. Which leads me to the conclusion that my planning might not be sufficient but the main structure of my code might be the problem. When I looked over my first game I found that a lot of my code was very specific and could not be easily rewritten without affecting other parts.
The question:
1) How do you go about properly planning a game and allowing major changes to be made without a re-write?
2)To avoid problems with having to rewrite everything should I try and write everything as a module that can be used in a main game loop?
If anyone has any good ways of organizing a game that you could point me to that would be awesome(Currently I am using the Model, View, Screen system)
Start using a source code revision tool as it allows you to code a lot more fearlessly of losing old work, make sure you checking in often. If something doesn't pan out just revert to the last working version and start afresh, if something pans out to work check it in so you have a backup.
Worked on titles: CMR:DiRT2, DiRT 3, DiRT: Showdown, GRID 2, theHunter, theHunter: Primal, Mad Max
### #8XNobodyX Members
132
Like
0Likes
Like
Posted 07 January 2014 - 04:59 PM
You are basically asking, “How do I learn from experience without going through the ‘experience‘ part?”.
I wouldn't exactly say that. I understand how valuable experience is and learning from my mistakes. Getting experience helped me learn another fieldset(Web dev. php, js, ruby, ect). Like writing an essay, there are certain structures that are generally accepted as at least a good outline on how to do it,
### #9XNobodyX Members
132
Like
0Likes
Like
Posted 07 January 2014 - 05:02 PM
Preamble:
I have attempted to make 2 little indie games and each of them have failed for one reason, planning. For both of the projects I started off only planning to have a few parts to the game. As I started to code those parts I would realized that each of these parts needed a lot more code and classes and such than I originally thought. The problem is I would have already coded the majority of the game before I realized this. Thus leaving me with two options, 1) Rewriting the whole game, and throwing out countless hours of time. 2) Giving up . After thinking about where I went wrong it would always come down to the fact that when I started writing the game I didn't fully understand what I needed and thus didn't design it properly. I figure that this might happen a lot in many games(Realizing that a major change needs to be done) and I imagine that they don't all restart or quit. Which leads me to the conclusion that my planning might not be sufficient but the main structure of my code might be the problem. When I looked over my first game I found that a lot of my code was very specific and could not be easily rewritten without affecting other parts.
The question:
1) How do you go about properly planning a game and allowing major changes to be made without a re-write?
2)To avoid problems with having to rewrite everything should I try and write everything as a module that can be used in a main game loop?
If anyone has any good ways of organizing a game that you could point me to that would be awesome(Currently I am using the Model, View, Screen system)
Start using a source code revision tool as it allows you to code a lot more fearlessly of losing old work, make sure you checking in often. If something doesn't pan out just revert to the last working version and start afresh, if something pans out to work check it in so you have a backup.
I am pushing to a private git repo every night after I finish. Is this sufficient for version control?
### #10swiftcoder Senior Moderators
17792
Like
0Likes
Like
Posted 07 January 2014 - 05:06 PM
I am pushing to a private git repo every night after I finish. Is this sufficient for version control?
You really want to be making commits of each feature and/or refactor, so that you can step through the history change-by-change to analyse when bugs were introduced.
Tristam MacDonald - Software Engineer @ Amazon - [swiftcoding] [GitHub]
### #11XNobodyX Members
132
Like
0Likes
Like
Posted 07 January 2014 - 05:16 PM
You really want to be making commits of each feature and/or refactor, so that you can step through the history change-by-change to analyse when bugs were introduced.
Thats what I meant(I guess I was a little unclear) I commit nightly. Usually I am able to knock out at least one small feature a day(2-3 hours of work) so nighly committing is usually sufficient.
Edited by XNobodyX, 07 January 2014 - 05:18 PM.
### #12Vortez Members
2705
Like
1Likes
Like
Posted 07 January 2014 - 05:49 PM
One thing i did when rewriting one of my application is to write a coupe of interfaces before actually starting coding it. I dunno exactly why but this helped tremendously.
Here's an example of one of them:
class IRemotePC {
public:
virtual void Reset() = 0;
virtual bool InitOpenGL(){return false;}
virtual void ShutdownOpenGL(){}
virtual void RenderTexture(){}
virtual void ClearScreen(){}
};
class IRemotePCServer : public IRemotePC {
public:
virtual void OnScreenshotRequest(ScrFormat *pFormat) = 0;
virtual void SendScreenshot(CRawBuffer *pBuffer) = 0;
virtual void OnMouseMsg(CMouseInputMsgStruct* pMsg) = 0;
virtual void OnKeyboardMsg(CKeyboardInputMsgStruct* pMsg) = 0;
};
class IRemotePCClient : public IRemotePC {
public:
virtual void SendScreenshotRequest() = 0;
virtual void SendMouseMsg(CMouseInputMsgStruct *mm) = 0;
virtual void SendKeyboardMsg(CKeyboardInputMsgStruct *km) = 0;
};
At first the functions arguments where empty, then got filled as i was adding more code. This helped me a lot to know where i was going.
### #13bigindie Members
100
Like
0Likes
Like
Posted 08 January 2014 - 01:21 AM
Hi,
Properly planning a game takes time to learn on your own. It can be one of those things that a programmer has to experience to understand. Unless you have worked for a large company who would obviously have a structure in place on how a game is designed. For an Indie developer this can seem complicated once your game code starts to get over a few hundred lines of code. What I've learned from my game design attempts is that you have to try to separate each part of the game into sections. Try to keep different areas of your game code organized so that if you need to update one area you can do it easily. It's kind of like writing a book. You have to learn how to put it together so that it's organized and well written. Other programmers always say to make sure to put lots of notes in your code so that if someone else needs to update it later they can easily get an understanding how your game code works. This can also help yourself when you need to come back and make changes.
### #14Katie Members
2081
Like
0Likes
Like
Posted 08 January 2014 - 04:28 AM
"seeing that I was headed towards coding myself into a corner."
How do you think you were coding into a corner?
### #15Dezachu Members
493
Like
4Likes
Like
Posted 08 January 2014 - 08:05 AM
Modularity is the one word that springs to mind.
Rather than writing a load of spaghetti code and then throwing it all away, take something away from each project. A prime example - I started writing a clicker-style game the other week but I've had to scrap it now I've started work again (alongside studying for my final year it just wasn't really viable). That didn't mean the hours spent working on it have amounted to nothing - I took away a static Utilities class that did simple calculations (kind of a math library I guess), a FontManager class, a LayoutManager class (for calculating the required scaling of text/an image to fit in a certain area) and also a ButtonObject class that eventually grew to be quite large. No doubt I can use these elsewhere because they're MODULAR - any game that uses fonts can use the font manager. Any game that uses button sprites can use the ButtonObject class and any game I write (at least in 2D) can use the LayoutManager to be easily portable to multiple screen resolutions. Same for the Utilities class I guess! From my next project when I get some free time I'll probably add some extras like a resource manager, an audio manager etc..
As others have said, there's no shame in failing again and again, it's all practice and learning. Instead of beating yourself up over failing, why not look at what you took away from/learnt in the project? In reverse, why not start a project with the intention of learning? Anything that comes out of it can be seen as a bonus ;)
So the questions:
1) Modularity.
2) Hmm probably not. Your standard loop is, as you appear to know, GetInput, Process, Render (maybe you use diff. words, it doesn't matter). These steps will be different for every program, although what they do is generally the same (as their name suggests). You're touching on game engines by suggesting modularity of these components which is a whole 'nother ball park.
Hope this helps
BSc Computer Games Programming (De Montfort University) Graduate
Worked on Angry Birds Go! at Exient Ltd
Co-founder of Stormburst Studios
### #16YellzBellz Members
180
Like
0Likes
Like
Posted 08 January 2014 - 08:09 PM
lol, keep doing what your doing, in ten years, you'll be where I'm at. Hopefully a hell of a lot better though.
You'll find out eventually if you code because you love it or if your chasing a rabbit.
I got on a pathfinding kick once that lasted for 6 months. Tons of unusable code, unreadable notes. In the end I did produce something that I still implement in any game I make using path finding though, regardless of which language I use.
The moral of my little verbal toilet spackle? The majority of the stuff I have made in the past 10 years is useless, but when I look at the steps and problems I overcame getting past each point, each one is an invaluable lesson!
Keep going or get into paper mache' little doggies with 1 jelly bean inside. (<---- my backup plan)
### #17pyrotekgames Members
1077
Like
0Likes
Like
Posted 09 January 2014 - 11:19 AM
The things that has worked for me are twofold. Firstly, I make sure to write my code in a way that is modular and easy to change and refactor. By this I mean that, well, code is always changing. You'll have to rewrite classes, separate classes into multiple classes and interfaces, refactor code, etc. In the end, you need to get used to the code changing. When you get to that point, you're in business -- having to rewrite the interface of a class or refactor a single giant class into many modular pieces becomes easy (especially with copy and paste!). If the project actually is useless, take it as a learning experience. I tend to program in units, so I write crap code while I work out my idea, and then copy/paste/rewrite my production code in the actual engine. Keep the code for nostalgia/as notes, but you can move on from those little tests and know you learned a lot from it!
Secondly, I've also noticed that I can work a problem a few ways -- this is what works for me. I tend to start at the outermost layer and figure out the interface I want for the class. From there I'll then begin unit testing each method I write for the class, but making sure I meet the interface I want for the class so it all looks nice to the user/works to my software design/engineering needs. Again, things change, and I refactor code all the time, but with a little planning on the interactions and outside interface of the class, it works out nicely.
Modularity also helps, as well as experience over time. I've written the same engine in a couple different languages, multiple times in each language. Each time I get more tired of writing the same code, so I got used to changing classes and isolating dependencies and BAM, I got a nice way of furthering the engine of the game without having to keep starting over or scrapping my code. As people have said above, pencil/pen and paper always solves your problems. UML has helped me a bit laying out interactions between classes. Try different things, and with time you'll be well and better off
### #18Tutorial Doctor Members
2564
Like
1Likes
Like
Posted 09 January 2014 - 04:58 PM
You should use modular programming, that is the technical term, there are a couple of tutorials on it on YouTube. Also, write pseudocode.
I made something I call a customizable game script. It's a template for making a game that has all the essential parts of a game ready to go. I also made it flexible (all my functions use arguments that can be changes outside of the functions. I also name my variables and functions with non-specific names (can be changed to specific names per game.)
Here is one of them:
They call me the Tutorial Doctor.
167
Like
0Likes
Like
Posted 10 January 2014 - 12:26 PM
Reading the Book "Clean Code" helped me understand how to avoid making a "big ball of mud", and creating "Technical Debt"
Big Ball of Mud - http://en.wikipedia.org/wiki/Big_ball_of_mud
Technical Debt - http://en.wikipedia.org/wiki/Technical_debt
Edited by JustColorado, 10 January 2014 - 12:30 PM.
My Projects: - www.repulse.com
### #20Genocode Members
148
Like
0Likes
Like
Posted 10 January 2014 - 03:45 PM
"seeing that I was headed towards coding myself into a corner."
How do you think you were coding into a corner?
It was because I felt overwhelmed by the code I was writing and it was indeed a big digital bowl of spaghetti code. Although I did have certain parts of the code in separate classes, there still wasn't much modularity. So when a bug pops up I spend all day swimming through the code in order to find it. It only became tougher the more code I wrote. I'll need to do a bit more modularity moving forward. But the previous comments are all very helpful. Coding does feel somewhat of an iterative learning process. It helps to know that I'm not just missing some big picture. Thank you all for the helpful input.
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic. | 2016-12-02 22:30:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2321278154850006, "perplexity": 969.9752639819151}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698540698.78/warc/CC-MAIN-20161202170900-00133-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/671248/justification-of-formal-derivative | # Justification of formal derivative
there I'm having the following problem and so far I didn't find anything in the literature on this.
$\Phi\in C^1(\overline{\Omega}\times[0,1])$ with $\Phi'(x,0)=\Phi'(x,1)=\Phi(x,0)=0$ for every $x\in\Omega$, where $\Omega$ is a bounded domain and $'$ denotes the derivative w.r.t. the second variable. Furthermore $\Phi(x,s)$ is increasing fof fixed $x$ with $\Phi'(x,s)>0$. Now assume, that there is $s\in L^\infty(\Omega,[0,1])$ with $x \mapsto \Phi(x,s(x))$ is in $H^1(\Omega)$. Due to the degeneracy of $\Phi$ we don't get $H^1$ estimates on $s$. However, with appropriate truncations one obtains that $[\max(\min(1-\varepsilon,s),\varepsilon)]\in H^1(\Omega)$. I.e. somehow $s$ has a gradient when away from the set where $s=0$ or $s=1$. It is possible to show some identities for the limits $\varepsilon \to 0$.
For any positive $\varepsilon$ one can show
$$\mathbf{1}_{\{\varepsilon <s(x) <1-\varepsilon\}}(\nabla[\Phi(x,s(x))] -\nabla_x \Phi(x,s)) =\Phi'(x,s(x))\nabla [\max(\min(1-\varepsilon,s(x)),\varepsilon)] \tag{*}$$ for a.e. $x\in\Omega$, where $\nabla_x$ is the gradient with respect to the first coordinate.
The goal is to let $\varepsilon$ pass to zero. One obtains pointwise convergence on the set $\{x: 0<s(x)<1\}$ and the left hand side is integrable and dominates the right hand side. In particular, on all the sets $\{x: \varepsilon <s(x)<1-\varepsilon\}$ the identity $(*)$ holds. On the set $\{x:s(x)=0\}$ the identity is clear since $\Phi(x,0)=\Phi'(x,0)=0$ and since by Stampacchia's lemma $\nabla[\Phi(x,s(x))]=0$ a.e. on the set $\{x: \Phi(x,s)=\Phi(x,0)=0\}=\{x : s(x)=0\}$.
On the set where $\{x: s(x)=1\}$ one still obtains that the pointwise limit on the rhs is zero. However, on that set $\nabla_x \Phi(x,s)\neq 0$ unles $\Phi(x,1)$ is constant. Hence, for equality in the limit, we require that $\nabla [\Phi(x,s)]=\nabla_x \Phi(x,s)$ a.e. on the set $\{x:s(x)=1\}$. Which holds formally, but i don't see how to proof this rigorously.
Does anybody see an idea on how to proof this? Any comment is appreciated
Edit 1: I referred to the boundedness of the right hand side, since i want to show that the convergence holds in fact in $L^2(\Omega)$
Edit 2: So what one could ask essentially: When is it allowed to compare weak derivatives pointwise, i.e. is it possible to say that on the set $\{x:s(x)=1\}$ holds $\nabla \Phi(x,s)=\nabla\Phi(x,1)=\nabla_x\Phi(x,1)$. However, taking the union over all the level sets between zero and one we would never obtain a contribution of $\nabla s$.
Edit: Corrected the question.
Edit $L^2$ convergence in the case without $x$-dependence and also updated $(*)$ sorry the inconvenience.
However, consider $(*)$ without the $\nabla_x \Phi$ term. First of all, we obtain the obvious bound $|\nabla \Phi(s)| \geq |\Phi'(s(x)) \nabla[\max(\min(1-\varepsilon,s(x)),\varepsilon)]|$, basically due to $(*)$ and increasing the left hand side where the right hand side is zero. However, on the set $\{0<s(x)<1\}$ we trivially obtain pointwise convergence to the desired limit. On the sets where $s(x)=0$ and $s(x)=1$, we find $\Phi'(s(x)) \nabla[\max(\min(1-\varepsilon,s(x)),\varepsilon)]=0$. Furthermore, Stampacchia's lemma tells us, that a.e. on the sets where $\{\Phi(s)=\Phi(1)\}$ and $\{\Phi(s)=\Phi(0)\}$ we find $\nabla \Phi(s)=0$ a.e. Due to the monotonicity of $\Phi$. These sets coincide with $\{s=1\}$ and $\{s=0\}$ respectively. Hence, the pointwise convergence holds a.e. in $\Omega$ and with Lebesgue's theorem we obtain strong convergence.
This proof fails if $\Phi$ is $x$-dependent. Sorry for the inconvenience with $(*)$. I hope the notation for the sets was not soo sloppy.
• hmm, no reaction so far? Is this to obvious or really hard? Is additional info needed? – Quickbeam2k1 Feb 11 '14 at 19:12
I think I can construct a counterexample. Choose $\Omega = (0,1)$, and $\Phi(x,t) = \phi(t)$ smooth enough that $\phi(t)$ obeys the bound: $$\phi'(t) \leq C t.$$ for sufficiently small $t$. (And of course, such that $\phi(t)$ satisfies $\phi'(1) = 0$)
Now choose a function $g_\alpha(x)$ with support in $(-1,1)$, and smooth outside of $0$, such that for $|x|<1/2$, $g_\alpha(x) = 1 - |x|^\alpha$. Notice that $\alpha = 1/2$ is the borderline case for $g_\alpha \in H^1$. Indeed, for $\alpha > 1/2$, $g_\alpha$ satisfies the estimate: $$\int_{-1}^1 |\partial_x g_\alpha(y)|^2 \,dy \geq \int_{0}^{1/2} \alpha^2 y^{2\alpha - 2}\,dy = \frac{\alpha^2}{2\alpha - 1} \left(\frac{1}{2}\right)^{2\alpha-1}.$$
Already we can see that there is no hope of an estimate of the form $$\|\nabla s(x)\|_{L^2} \lesssim \|\nabla (\Phi(x,s(x))\|_{L^2}.$$ Indeed, let $\alpha_k = 1/2 + 2^{-k}$ and $s_k = 2^{-k} g_{\alpha_k}(x)$. Then by the above calculation, $$\|\nabla s_k(x)\|_{L^2} \gtrsim 2^k,$$ but since $\nabla \Phi(x,s(x)) = \phi'(s(x)) \nabla s(x)$ (pointwise a.e), and $\phi'(s(x)) \leq 2^{-k}$, we have $$\|\nabla (\Phi(x,s(x)))\|_{L^2} \sim 1.$$ This is the main obstruction to uniform $L^2$ convergence, the following just constructs an explicit example using these ideas.
We are ready to construct the counterexample. Set $$s(x) = \sum_{k=1}^\infty \frac{1}{k}g_{\alpha_k}(2^{k+2}(x - 2^{-k})) = \sum_{k=1}^\infty h_k(x).$$ Which is a sequence of disjoint cusps $h_k(x)$ with support in $(2^{-k} - 2^{-k-2}, 2^{-k} + 2^{-k-2})$, and $\alpha_k$ will soon be chosen. Indeed, if $\alpha_k > 1/2$ decays to $1/2$ rapidly enough, $s(x)\notin H^1$, since $$\int |\partial_x h_k(y)|^2 \,dy = \int_{2^{-k} - 2^{-k-2}}^{2^{-k} + 2^{-k-2}} \frac{1}{2^k} |\partial_x (g_{\alpha_k}(2^{k+2}(y - 2^{-k})))|^2 \, dy \geq 2^{-k} \int_{-1/2}^{1/2} (\alpha_k)^2 |y|^{2\alpha_k - 1}\,dy.$$ From this and the estimate above, $\alpha_k = \frac{1}{2} + \frac{1}{2^{k+1}}$ would work so that $\|h_k\|_{H^1} \sim_k 1$. (Meaning it's bounded above and below by a constant independent of $k$.) On the other hand, $\Phi(x,s(x))\in H^1$ since $$\int |\partial_x \Phi(y,s(y))|^2\,dy = \int |\phi'(s(y)) \partial_x s(y)|^2\,dy = \sum_k \int |\phi'(h_k(y)) \partial_x h_k(y)|^2\,dy$$ Since $h_k(y) \leq 2^{-k}$, and $\phi'(t) \leq C t$, we can estimate $$\sum_k \int |\phi'(h_k(y)) \partial_x h_k(y)|^2\,dy \leq \sum_k \sup_k \|h_k\|_{H^1} 2^{-k} < \infty.$$
Even if I made a mistake in the calculation, I think the general idea --that you make a sequence of smaller and smaller cusps, with unbounded $H^1$ norm-- is correct.
• Hmm, just a first comment. If $\Phi$ is independent of $x$, then one can prove that $\nabla [\Phi(s(x)] =\lim_{\varepsilon\to 0} \Phi'(s(x)) \nabla[\max(\min(1-\varepsilon,s(x)),\varepsilon)]$ strongly in $L^2(\Omega)$. If you want, I can add some detail to this. Basically, one shows that $\nabla [\Phi(s(x)] \mathbf{1}_{\{\varepsilon<s(x)<1-\varepsilon\}}= \Phi'(s(x)) \nabla[\max(\min(1-\varepsilon,s(x)),\varepsilon)]$. Now the pointwise convergence follows from Stampacchia's lemma. – Quickbeam2k1 Feb 19 '14 at 22:13
• I agree you get pointwise convergence; even in this example if you cut off at some $\varepsilon>0$, you have pointwise convergence. However, $L^2$ convergence fails because of the degeneracy of $\Phi$. I may be wrong; perhaps you could provide more details? – felipeh Feb 19 '14 at 22:20
• I will, edit it in my question – Quickbeam2k1 Feb 19 '14 at 22:22
• done. sorry, I again found a mistake in $(*)$ :( – Quickbeam2k1 Feb 19 '14 at 22:35
• I edited my answer to make it a bit more clear that you can't expect quantitative control of the $L^2$ norm. Maybe this will help you understand the counterexample, I know it is quite messy. – felipeh Feb 19 '14 at 22:35 | 2019-12-15 10:39:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9834256172180176, "perplexity": 136.76025945584215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541307813.73/warc/CC-MAIN-20191215094447-20191215122447-00362.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?p=240484 | ## Solving for rates
205192823
Posts: 100
Joined: Wed Sep 18, 2019 12:19 am
### Solving for rates
How do I solve this problem?
Ethene is a component of natural gas, and its combustion has been thoroughly studied. At a certain temperature and pres-sure, the unique rate of the combustion reaction
C2H4(g) + 3 O2(g) --> 2 CO2(g) + 2 H2O(g) is 0.44 mol? L21?s21.
(a) What is the rate at which oxygen reacts?
(b) What is the rate of formation of water?
BeylemZ-1B
Posts: 95
Joined: Thu Jul 25, 2019 12:17 am
### Re: Solving for rates
what section of chapter 7 is this from, so i can reference my work
Kennedi2J
Posts: 101
Joined: Wed Sep 18, 2019 12:20 am
### Re: Solving for rates
If I'm thinking of the same problem, it seems to be asking about the rate of disappearance of oxygen. In that case you would multiply the rate given by the ratio of oxygen shown in the reaction.
Abigail_Hagen2G
Posts: 107
Joined: Fri Aug 09, 2019 12:17 am
### Re: Solving for rates
The molar ratio, right? | 2020-10-01 17:58:26 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8226632475852966, "perplexity": 3212.4751448810403}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402131986.91/warc/CC-MAIN-20201001174918-20201001204918-00104.warc.gz"} |
https://socratic.org/questions/how-do-you-multiply-1-2-12-13-2-1-with-4-8-4-3-5-2 | # How do you multiply ((1, 2, 12), (13, 2, 1)) with ((4, 8), (4, 3), (5, 2))?
##### 1 Answer
Nov 17, 2016
The answer is $= \left(\begin{matrix}72 & 38 \\ 65 & 112\end{matrix}\right)$
#### Explanation:
The matrix multiplication is
$\left(\begin{matrix}a & b & c \\ d & e & f\end{matrix}\right) . \left(\begin{matrix}l & m \\ n & p \\ q & r\end{matrix}\right)$
$= \left(\begin{matrix}a l + b n + f q & a m + b p + c r \\ \mathrm{dl} + e n + f q & \mathrm{dm} + e p + r f\end{matrix}\right)$
$\left(\begin{matrix}1 & 2 & 12 \\ 13 & 2 & 1\end{matrix}\right) . \left(\begin{matrix}4 & 8 \\ 4 & 3 \\ 5 & 2\end{matrix}\right)$
$= \left(\begin{matrix}4 + 8 + 60 & 8 + 6 + 24 \\ 52 + 8 + 5 & 104 + 6 + 2\end{matrix}\right)$
$= \left(\begin{matrix}72 & 38 \\ 65 & 112\end{matrix}\right)$ | 2020-12-04 14:59:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.59145188331604, "perplexity": 3167.442534705772}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141737946.86/warc/CC-MAIN-20201204131750-20201204161750-00696.warc.gz"} |
https://www.tutorialspoint.com/mathrm-abcd-is-a-rhombus-show-that-diagonal-mathrm-ac-bisects-angle-mathrm-a-as-well-as-angle-mathrm-c-and-diagonal-mathrm-bd-bisects-angle-math | # $\mathrm{ABCD}$ is a rhombus. Show that diagonal $\mathrm{AC}$ bisects $\angle \mathrm{A}$ as well as $\angle \mathrm{C}$ and diagonal $\mathrm{BD}$ bisects $\angle \mathrm{B}$ as well as $\angle \mathrm{D}$.
#### Complete Python Prime Pack
9 Courses 2 eBooks
#### Artificial Intelligence & Machine Learning Prime Pack
6 Courses 1 eBooks
#### Java Prime Pack
9 Courses 2 eBooks
Given:
$\mathrm{ABCD}$ is a rhombus.
To do :
We have to show that diagonal $\mathrm{AC}$ bisects $\angle \mathrm{A}$ as well as $\angle \mathrm{C}$ and diagonal $\mathrm{BD}$ bisects $\angle \mathrm{B}$ as well as $\angle \mathrm{D}$.
Solution :
$AC$ and $BD$ are the diagonals which intersect each other at $O$.
$AD = CD$ (Sides of a rhombus are equal)
$\angle DAC = \angle DCA$ (Angles opposite to equal sides of a triangle are equal)
$AB \| CD$
$\angle DAC = \angle BCA$ (Alternate interior angles)
$\angle DCA = \angle BCA$
This implies,
$AC$ bisects $\angle C$
Similarly,
$AC$ bisects $\angle A$
$BD$ bisects $\angle D$
$BD$ bisects $\angle B$
Therefore, $\mathrm{AC}$ bisects $\angle \mathrm{A}$ as well as $\angle \mathrm{C}$ and diagonal $\mathrm{BD}$ bisects $\angle \mathrm{B}$ as well as $\angle \mathrm{D}$.
Hence proved.
Updated on 10-Oct-2022 13:40:59 | 2022-12-01 07:53:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4615492522716522, "perplexity": 5636.7751858116935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710801.42/warc/CC-MAIN-20221201053355-20221201083355-00716.warc.gz"} |
https://mathematica.stackexchange.com/questions/230854/what-is-a-good-way-of-perfoming-operations-on-specified-columns-of-a-table-with/230872 | # What is a good way of perfoming operations on specified columns of a table with many columns
If I have a table of data and I want to do a specific operation on say the third column, I usually do something like this:
OperatedOnTable =
MyTable /. {Col1_, Col2_, Col3_, Col4_} -> {Col1, Col2, 2*Pi*Col3 + 42, Col4}
where MyTable has four columns in this case.
This is fine when I have a table with several columns, but when I have a table that has, say, twenty columns, this quickly becomes unwieldy and silly, as I need to map every single column such that I may pick out the columns I want to operate on.
For tables with large numbers of columns, how can I perform an operation on a specific column or column?
I should add, it would be preferable to be able to perform operations on multiple columns as is possible with my example, e.g.
OperatedOnTable =
MyTable /.
{Col1_, Col2_, Col3_, Col4_} -> {Col1 + 1/137, Col2, 2*Pi*Col3 + 42, Col4}
Note that I have performed two distinct operations on two distinct columns with a single command. I'd like to be able to replicate this functionality.
I want to achieve the same functionality as:
OperatedOnTable =
MyTable /.
{Col1_, Col2_, Col3_, Col4_, Col5_, Col6_, Col7_, Col7_, Col8_,
Col9_, Col10_, Col11_, Col12_, Col13_, Col14_, Col15_, Col16_} ->
{Col1 + 1/137, Col2, 2*Pi*Col3 + 42, Col4, Col5, Col6, Col7, Col7, Col8,
Col9, Col10, Col11, Col12, Col13, Col14, Col15, Col16}
This achieves what I want, manipulation of multiple columns in a single operation, but as we can see it is somewhat silly for tables with tens of columns.
I'm using Mathematica 12.1.1.0.
• MyTable = MapAt[2*Pi*#+ 42&, MyTable, {All, 3}]?
– kglr
Sep 27 '20 at 20:18
• ... or MyTable[[All, 3]] = 2*Pi*MyTable[[All, 3]] + 42?
– kglr
Sep 27 '20 at 20:19
• The first one is a good one but that means only one operation on one column at a time right? Won't the second just leave a result with one column?
– Q.P.
Sep 27 '20 at 20:23
• Q.P., if you inspect myTable = Array[a, {4, 4}]; myTable = MapAt[foo, myTable, {All, 3}];myTable and myTable = Array[a, {4, 4}]; myTable[[All, 3]] = foo /@ myTable[[All, 3]];myTable you can see that both methods modify the third column of myTable.
– kglr
Sep 27 '20 at 20:40
• @kglr, quite right! What about different operations on different columns in the same operation? This is what I really like about OperatedOnTable = MyTable /. {Col1_, Col2_, Col3_, Col4_}->{Col1 + 1/137, Col2, 2*Pi*Col3 + 42, Col4}. It's also very clear to see what one has done, but for more than say eight or ten columns it gets a bit silly.
– Q.P.
Sep 27 '20 at 20:49
myTable = Array[Subscript[a, Row[{##}]] &, {5, 10}];
MatrixForm @ myTable
functions = {foo, bar};
columns = {2, 5};
1. Part assignment:
myTable[[All, columns]] = {foo@#, bar@#2} & @@@ myTable[[All, columns]];
myTable // MatrixForm
myTable = Array[Subscript[a, Row[{##}]] &, {5, 10}];
myTable = Fold[MapAt[First@#2, #, {All, Last@#2}] &, myTable,
Transpose[{functions, columns}]];
myTable // MatrixForm
myTable = Array[Subscript[a, Row[{##}]] &, {5, 10}];
myTable = ReplacePart[myTable,
MapThread[{i_, #} :> #2[myTable[[i, #]]] &, {columns, functions}]];
myTable // MatrixForm
myTable = Array[Subscript[a, Row[{##}]] &, {5, 10}];
myTable = MapIndexed[asso[#2[[2]]]@# /. Missing[__] -> Identity &, myTable, {2}];
myTable // MatrixForm
myTable = Array[Subscript[a, Row[{##}]] &, {5, 10}];
myTable = Normal @ Dataset[myTable][All, Thread[columns -> functions]];
myTable // MatrixForm
• Looks good. Let me have a play around and I'll accept.
– Q.P.
Sep 27 '20 at 21:12
A little too long for a comment, and I have marked this as 'Community Wiki' (not an original contribution). In addtion, I think the Query method should not be 'buried' in a comment.
Query
Sjoerd Smit has posted a neat method for applying a function to a matrix column using Query.
Query[All, {1 -> (#+1/137&),3->(2 Pi# + 42&)}]@myTable2//TeXForm
$$\left( \begin{array}{cccc} a_{11}+\frac{1}{137} & a_{12} & 2 \pi a_{13}+42 & a_{14} \\ a_{21}+\frac{1}{137} & a_{22} & 2 \pi a_{23}+42 & a_{24} \\ a_{31}+\frac{1}{137} & a_{32} & 2 \pi a_{33}+42 & a_{34} \\ a_{41}+\frac{1}{137} & a_{42} & 2 \pi a_{43}+42 & a_{44} \\ a_{51}+\frac{1}{137} & a_{52} & 2 \pi a_{53}+42 & a_{54} \\ a_{61}+\frac{1}{137} & a_{62} & 2 \pi a_{63}+42 & a_{64} \\ a_{71}+\frac{1}{137} & a_{72} & 2 \pi a_{73}+42 & a_{74} \\ a_{81}+\frac{1}{137} & a_{82} & 2 \pi a_{83}+42 & a_{84} \\ a_{91}+\frac{1}{137} & a_{92} & 2 \pi a_{93}+42 & a_{94} \\ a_{101}+\frac{1}{137} & a_{102} & 2 \pi a_{103}+42 & a_{104} \\ \end{array} \right)$$
Query[All, {1 -> foo, 3 -> bar, 6-> Sqrt}]@myTable//TeXForm
$$\left( \begin{array}{cccccc} \text{foo}\left[a_{11}\right] & a_{12} & \text{bar}\left[a_{13}\right] & a_{14} & a_{15} & \sqrt{a_{16}} \\ \text{foo}\left[a_{21}\right] & a_{22} & \text{bar}\left[a_{23}\right] & a_{24} & a_{25} & \sqrt{a_{26}} \\ \text{foo}\left[a_{31}\right] & a_{32} & \text{bar}\left[a_{33}\right] & a_{34} & a_{35} & \sqrt{a_{36}} \\ \text{foo}\left[a_{41}\right] & a_{42} & \text{bar}\left[a_{43}\right] & a_{44} & a_{45} & \sqrt{a_{46}} \\ \text{foo}\left[a_{51}\right] & a_{52} & \text{bar}\left[a_{53}\right] & a_{54} & a_{55} & \sqrt{a_{56}} \\ \end{array} \right)$$
Query (in this case) seems to be based on MapAt 'under the hood'
In[7]:=Query[All, {1 -> (#+ 137&),3->(2 Pi# + 42&)}]@myTable2x
Out[7]= MapAt[#1 + 137 & , {All, 1}][MapAt[2 Pi #1 + 42 & , {All, 3}][myTable2x]]
And for the lazy, the following doesn't seem too bad either:
myTable//MapAt[2 Pi # + 42 & , {All, 3}]// MapAt[# + 137 & , {All, 1}]
$$\left( \begin{array}{cccccc} a_{11}+137 & a_{12} & 2 \pi a_{13}+42 & a_{14} & a_{15} & a_{16} \\ a_{21}+137 & a_{22} & 2 \pi a_{23}+42 & a_{24} & a_{25} & a_{26} \\ a_{31}+137 & a_{32} & 2 \pi a_{33}+42 & a_{34} & a_{35} & a_{36} \\ a_{41}+137 & a_{42} & 2 \pi a_{43}+42 & a_{44} & a_{45} & a_{46} \\ a_{51}+137 & a_{52} & 2 \pi a_{53}+42 & a_{54} & a_{55} & a_{56} \\ \end{array} \right)$$
Inner
Inner is another possibility (see here)
myTable//Inner[Times,#,ConstantArray[1,Length@#[[1]]],{#1+1/137,#2,#3, 2 Pi #4+42, ##5}&]&//TeXForm
$$\left( \begin{array}{cccccc} a_{11}+\frac{1}{137} & a_{12} & a_{13} & 2 \pi a_{14}+42 & a_{15} & a_{16} \\ a_{21}+\frac{1}{137} & a_{22} & a_{23} & 2 \pi a_{24}+42 & a_{25} & a_{26} \\ a_{31}+\frac{1}{137} & a_{32} & a_{33} & 2 \pi a_{34}+42 & a_{35} & a_{36} \\ a_{41}+\frac{1}{137} & a_{42} & a_{43} & 2 \pi a_{44}+42 & a_{45} & a_{46} \\ a_{51}+\frac{1}{137} & a_{52} & a_{53} & 2 \pi a_{54}+42 & a_{55} & a_{56} \\ \end{array} \right)$$
Related
Applying a function to every item in a column of a matrix
Matrices
myTable = Array[Subscript[a, Row[{##}]] &, {5, 6}];
myTable2 = Array[Subscript[a, Row[{##}]] &, {10, 4}];
• I see you are someone of culture when it comes to choices or arbitrary numbers for examples. Sep 29 '20 at 12:23
kglr's ReplacePart method is completely general, but I think in many situations writing the rules explicitly is easier and gives more readable code. So I would write:
data = Array[f, {4, 4}];
ReplacePart[data, {{r_, 1} :> data[[r, 1]] + 137, {r_, 3} :> 2 π data[[r, 3]]}]
{{137 + f[1, 1], f[1, 2], 2 π f[1, 3], f[1, 4]},
{137 + f[2, 1], f[2, 2], 2 π f[2, 3], f[2, 4]},
{137 + f[3, 1], f[3, 2], 2 π f[3, 3], f[3, 4]},
{137 + f[4, 1], f[4, 2], 2 π f[4, 3], f[4, 4]}}
I can see what my code does at a glance, but I can't do the with kglr's code. Of course, you may consider this more a reflection on my smarts than a valid critique of kglr's coding style.
### Update
The following is added to address concerns raised by the Craig Carter in a comment to this answer.
It's pretty simple. Just change the column specs to the appropriate row specs. Like so:
ReplacePart[data, {{1, c_} :> data[[1, c]] + 137, {3, c_} :> 2 π data[[3, c]]}
{{137 + f[1, 1], 137 + f[1, 2], 137 + f[1, 3], 137 + f[1, 4]},
{f[2, 1], f[2, 2], f[2, 3], f[2, 4]},
{2 π f[3, 1], 2 π f[3, 2], 2 π f[3, 3], 2 π f[3, 4]},
{f[4, 1], f[4, 2], f[4, 3], f[4, 4]}}
• I have to say this is more what I had in mind. One can immediately ready what this does, superficially it's similar to the example I provided in my question. Would you say there are any limitations with this approach? I ask as you said kglr's solution is more general.
– Q.P.
Sep 27 '20 at 22:12
• @Q.P. This method is also general, but if your table had many, many columns and you were going to modify a lot of them, kglr's code would save some typing, Sep 27 '20 at 22:22
• The Query method is very nice. Is there a simple way to achieve the same thing for rows? ( e.g. Transpose[ Query[All, {1 -> foo, 2 -> bar, 4 -> Sqrt}]@Transpose[myTable]] ) Sep 29 '20 at 18:55
• @CraigCarter. I don't understand how your comment relates to my answer. It seems to be new question rather than a comment. Sep 29 '20 at 20:35
• @m_goldberg it is probably a new question because it pertains to rows. Nevertheless, if your answer could be generalized here, it would be instructive for others, I think. Sep 29 '20 at 21:19 | 2021-10-20 06:20:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21506941318511963, "perplexity": 6893.046314246714}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585302.91/warc/CC-MAIN-20211020055136-20211020085136-00144.warc.gz"} |
https://brilliant.org/problems/sines-everywhere/ | # Sines everywhere
Geometry Level 5
$\large \sin\bigg(\frac{3 \pi}{10}-\frac{x}{2}\bigg)=\frac{1}{2} \sin\bigg(\frac{\pi}{10}+\frac{3x}{2}\bigg)$ How many real values of $$x\in[-\pi;\pi]$$ satisfy the equation above?
× | 2017-05-23 17:11:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8585980534553528, "perplexity": 3051.9608561796913}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607648.39/warc/CC-MAIN-20170523163634-20170523183634-00160.warc.gz"} |
https://destevez.net/category/maths/page/2/ | Scramblers and their implementation in GNUradio
A scrambler is a function that is applied to a sequence of data before transmitting with the goal of making this data more “random-like”. For instance, scrambling avoids long runs of the bits 0 or 1 only, which may make the receiver loose synchronization or cause spectral concentration of the signal. The receiver applies the inverse function, which is called descrambler, to recover the original data. The documentation for the scrambler blocks in GNUradio is not very good and one may need to take a look at the implementation of these blocks to get their parameters right. Here, I’ll try to explain a bit of the mathematics behind scramblers and the peculiarities of their implementation in GNUradio.
Estimation of the contribution of the frontend to the total noise figure
In a radio receiver composed of two stages, the total noise factor $$F$$ can be computed using Friis’s formula as$F = F_1 + \frac{F_2 – 1}{G_1},$where $$F_1$$ is the noise factor of the first block, $$G_1$$ is the gain of the first stage and $$F_2$$ is the noise factor of the second stage. If $$G_1$$ is large enough, then the contribution of the second factor is small and the total noise factor of the whole system is essentially the same as the noise factor of the first stage. This is the reason why a low noise amplifier is useful as a frontend, because it has a low noise factor $$F_1$$ and high gain $$G_1$$.
If $$F_2$$ and $$G_1$$ are known (perhaps only approximately), then it is easy to check if the contribution of the frontend to the total noise figure is large enough so that the total noise figure is determined by the noise figure such frontend alone. However, it may happen that one or both of $$F_2$$ and $$G_1$$ are not known. In email communication, Leif Åsbrink mentioned that there is an easy way of checking the contribution of the frontend without knowing these parameters. The method is to switch off the frontend and note the drop in the noise floor. He gave the following estimates: if the noise floor drops by more than 10dB, then the total noise figure is the same as the noise figure of the frontend up to 1dB; if the noise floor drops by more than 17dB, then the total noise figure is the same as the noise figure of the frontend up to 0.1dB. Here I present the maths behind these kind of estimates.
Another look at recursive quadrature oscillators
In a recent post, we looked at which $$2\times 2$$ Toeplitz real matrices $$T$$ gave useful quadrature oscillators by the recurrence $$x_{n+1}=T x_n$$. There, we computed their eigenvalues and solved the recurrence in terms of them. Of course, there are many other ways to approach this problem. Here we look at another approach that gives a good geometric picture of what happens, can be applied to general $$2\times 2$$ matrices, and may be used as a starting point for the $$n\times n$$ case.
A look at a new digital quadrature oscillator
Two sinusoidal signals are said to be in quadrature if they have a constant phase difference of 90º. Quadrature signals are widely used in signal processing. A digital quadrature oscillator is just an algorithm that computes the sequence $$x_n = (\cos(\omega n), \sin(\omega n))$$, $$n\geq 0$$, or a similar sequence of sinusoids in quadrature. Here $$\omega$$ is the oscillator frequency in radians per sample. Direct computation of this sequence is very time consuming, because the trigonometric functions have to be evaluated for each sample. Therefore, it is a good idea to use a linear recurrence scheme to compute $$x_n$$. Using basic trigonometric identities, we see that$x_{n+1} = A x_n,\quad x_0=\begin{pmatrix}1\\0\end{pmatrix},$with$A = \begin{pmatrix}\alpha_1 & -\alpha_2\\\alpha_2 & \alpha_1\end{pmatrix},\quad \alpha_1 = \cos(\omega),\ \alpha_2=\sin(\omega).$
However, to actually perform these computations in a digital processor, one has to quantize $$\alpha_1,\alpha_2$$, meaning that one has to replace $$\alpha_1,\alpha_2$$ by approximations. It is easy to see that if one replaces $$\alpha_1,\alpha_2$$ by some perturbation, then the eigenvalues of $$A$$ are no longer in the unit circle, so the oscillation can grow or decay exponentially and one would need to apply an AGC scheme to keep this method stable.
Here we will look at a new quadrature oscillator by Martin Vicanek that has appeared recently and solves this problem. | 2018-10-16 02:18:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7612668871879578, "perplexity": 211.71550259988524}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583509960.34/warc/CC-MAIN-20181016010149-20181016031649-00288.warc.gz"} |
https://maslinandco.com/6028525 | # Evaluate: 2 x+5 <= 3 x-10
## Expression: $$2 x + 5 \leq 3 x - 10$$
Subtract $3x$ from both sides.
$$2x+5-3x\leq -10$$
Combine $2x$ and $-3x$ to get $-x$.
$$-x+5\leq -10$$
Subtract $5$ from both sides.
$$-x\leq -10-5$$
Subtract $5$ from $-10$ to get $-15$.
$$-x\leq -15$$
Divide both sides by $-1$. Since $-1$ is negative, the inequality direction is changed.
$$x\geq \frac{-15}{-1}$$
Fraction $\frac{-15}{-1}$ can be simplified to $15$ by removing the negative sign from both the numerator and the denominator.
$$x\geq 15$$
Random Posts
Random Articles | 2023-01-29 22:18:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.756650447845459, "perplexity": 701.192885204951}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499768.15/warc/CC-MAIN-20230129211612-20230130001612-00125.warc.gz"} |
https://imathworks.com/tex/tex-latex-overbrace-and-underbrace-with-square-bracket/ | # [Tex/LaTex] \overbrace and \underbrace with square bracket
bracketsmath-mode
I'm trying to put a nice square bracket over a complex text, it should look like an \overline but with ending like
\ulcorner and \urcorner.
The presence of \overrightarrow and \overleftarrow makes me believe that is possible to decorate the end of the \overline bar.
I know the existence of \overbrace, but I need a square bracket; moreover, \overbrace takes too much vertical space
Try \mathtools's \underbracket and \overbracket:
\documentclass{article}
\usepackage{mathtools}% http://ctan.org/pkg/mathtools
\begin{document}
$\overbrace{a+b+c}^{d} \quad \overbracket{a+b+c}^{d} \quad \underbrace{a+b+c}_{d} \quad \underbracket{a+b+c}_{d}$
\end{document}
You can adjust the rule width and bracket height/depth via optional arguments. From the mathtools documentation (section 3.3.2 Braces and brackets, p. 14):
\underbracket[<rule thickness>][<bracket height>]{<arg>}
\overbracket[<rule thickness>][<bracket height>]{<arg>}
Or, a more subtle approach with abraces:
\documentclass{article}
\usepackage{abraces}% http://ctan.org/pkg/abraces
\begin{document}
$\overbrace{a+b+c}^{d} \quad \aoverbrace[L1R]{a+b+c}^{d} \quad \underbrace{a+b+c}_{d} \quad \aunderbrace[l1r]{a+b+c}_{d}$
\end{document}
The usage requires a brace specification <spec> as an optional argument to \aoverbrace and \aunderbrace (see the abraces documentation): | 2023-03-31 05:54:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8877542018890381, "perplexity": 11914.339897063268}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949573.84/warc/CC-MAIN-20230331051439-20230331081439-00058.warc.gz"} |
https://stats.stackexchange.com/questions/166458/rose-and-smote-oversampling-methods | # ROSE and SMOTE oversampling methods
Can somebody give me a brief explanation of the differences between those two resampling methods : ROSE and SMOTE ?
ROSE uses smoothed bootstrapping to draw artificial samples from the feature space neighbourhood around the minority class.
SMOTE draws artificial samples by choosing points that lie on the line connecting the rare observation to one of its nearest neighbors in the feature space.
My experience: I used both techniques to create balanced data, and found SMOTE (from R's DMwR-package) to produce better results. The reason is, in my opinion, that SMOTE doesnt create as much 'unrealistic' values as ROSE. ROSE gave me values that were outright impossible (negative Area sizes or elevation). You can specify the neighbourhood from where ROSE draws its samples, and mitigate these problem to some extent. But SMOTE still produced better training data to predict onto my original (imbalanced) data. Both techniques outperformed over and undersampling though. | 2019-10-22 02:08:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46082961559295654, "perplexity": 2853.7767911611827}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987795403.76/warc/CC-MAIN-20191022004128-20191022031628-00276.warc.gz"} |
https://avatest.org/2022/09/01/financial-calculus%E4%BB%A3%E8%80%83math7091-backwards-induction/ | Posted on Categories:Financial Calculus, 金融代写, 金融微积分
# 金融代写|金融微积分代写Financial Calculus代考|MATH7091 Backwards induction
avatest™
## avatest™帮您通过考试
avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！
•最快12小时交付
•200+ 英语母语导师
•70分以下全额退款
## 金融代写|金融微积分代写Financial Calculus代考|Backwards induction
In fact most of the hard work has already been done when we examined the branch model. Extending the results and intuitions of section $2.1$ to an entire binomial tree is surprisingly straightforward. The key idea is that of backwards induction – extending the construction portfolio back one tick at a time from the claim to the required starting place.
Consider, then, a general claim for our stock $S$. When we examined a single branching of our tree, we had the function $f$ dependent only on the node chosen at the end of a single tick period – here we can extend the idea of a claim to cover not only the value of $S$ at the time the claim is exercised but also the history of $S$ up until that point.
The tree structure of the stock was not entirely arbitrary – it embodies a one-to-one relationship between a node and the history of the stock’s path up to and including that node. No other history reaches that node; and trivially no other node is reached by that history. This is precisely that condition that allows us actually to associate a claim value with a particular end-node on our tree. We shall also insist on the finiteness of our tree. There must be some final tick-time at which the claim is fully determined. A condition not unreasonable in the real financial world. A general claim can be thought of as some function on the nodes at this claim time-horizon.
## 金融代写|金融微积分代写Financial Calculus代考|The two-step
We know that the expectation operator can be made to work for a single branch – here, then, we must wade through the algebra for two time-steps, three branches stuck together into a tree. If two time-steps work, then so will many.
Suppose that the interest rate over any branch is constant at rate $r$. Then there exists some set of suitable $q_j$ s such that the value of the derivative at node $j$ at tick-time $i, f(j)$, is
$$f(j)=e^{-r \delta t}\left(q_j f(2 j+1)+\left(1-q_j\right) f(2 j)\right)$$
That is the discounted expectation under $q_j$ of the time- $(i+1)$ claim values $f(2 j+1)$ and $f(2 j)$. So in our two-step tree (figure 2.4), the two forks from node 3 to nodes 6 and 7 , and from node 2 to nodes 4 and 5 , are both structurally identical to the simple one-step branch. This means that $f(3)$ comes from $f(6)$ and $f(7)$ via
$$f(3)=e^{-r \delta t}\left(q_3 f(7)+\left(1-q_3\right) f(6)\right) \text {, }$$
and similarly, $f(2)$ comes from $f(4)$ and $f(5)$, with
$$f(2)=e^{-r \delta t}\left(q_2 f(5)+\left(1-q_2\right) f(4)\right) \text {. }$$
Here $q_j$ is the probability $\left(s_j \exp (r \delta t)-s_{2 j}\right) /\left(s_{2 j+1}-s_{2 j}\right)$, so for instance
$$q_2=\frac{s_2 \exp (r \delta t)-s_4}{s_5-s_4}, \quad \text { and } \quad q_3=\frac{s_3 \exp (r \delta t)-s_6}{s_7-s_6} \text {. }$$
## 金融代写|金融微积分代写Financial Calculus代考|The two-step
$$f(j)=e^{-r \delta t}\left(q_j f(2 j+1)+\left(1-q_j\right) f(2 j)\right)$$
$$f(3)=e^{-r \delta t}\left(q_3 f(7)+\left(1-q_3\right) f(6)\right),$$
$$f(2)=e^{-r \delta t}\left(q_2 f(5)+\left(1-q_2\right) f(4)\right) .$$
$$q_2=\frac{s_2 \exp (r \delta t)-s_4}{s_5-s_4}, \quad \text { and } \quad q_3=\frac{s_3 \exp (r \delta t)-s_6}{s_7-s_6}$$
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。 | 2023-03-20 13:48:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6503068804740906, "perplexity": 974.574480645277}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943483.86/warc/CC-MAIN-20230320114206-20230320144206-00526.warc.gz"} |
https://extension.xwiki.org/xwiki/bin/view/ReleaseNotes/ReleaseNotesXWiki72M3?viewer=changes&rev1=32.1&rev2=32.2 | # Changes for page Release Notes for XWiki 7.2 Milestone 3
<
From version
edited by Eduard Moraru
on 2015/08/21
To version
edited by Eduard Moraru
on 2015/08/21
>
Change comment: There is no comment for this version
## Details
Page properties
Content
... ... @@ -17,6 +17,8 @@ 17 17 ** The add menu has been relocated near the edit one 18 18 ** The add, edit, and "more actions" menus have been relooked 19 19 ** A lot of actions have been moved to the "more actions" menu 20 +** The breadcrumbs are now displayed on the homepage 21 +** The breadcrumbs now also displaying the homepage (and not hiding it anymore) if it is part of the current document's hierarchy. See [[XWIKI-12423>>http://jira.xwiki.org/browse/XWIKI-12423]] for more details. 20 20 21 21 {{gallery}} 22 22 image:homepage.png ... ... @@ -25,6 +25,7 @@ 25 25 image:drawer.png 26 26 image:drawer-languages.png 27 27 image:flamingo-phone.png 30 +image:homepageInBreadcrumbs-after.png 28 28 {{/gallery}} 29 29 30 30 == LDAP improvements == | 2022-12-05 00:22:07 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.822651743888855, "perplexity": 14805.251113658429}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711001.28/warc/CC-MAIN-20221205000525-20221205030525-00072.warc.gz"} |
http://stackoverflow.com/questions/6313507/how-to-regex-search-replace-with-filemap-in-largish-text-file-with-to-avoid-o | # How to regex search/replace with File::Map in largish text file with to avoid “Out of Memory”-Error?
UPDATE 2: Solved. See below.
I am in the process of converting a big txt-file from an old DOS-based library program into a more usable format. I just started out in Perl and managed to put together a script such as this one:
BEGIN {undef $/; }; open$in, '<', "orig.txt" or die "Can't read old file: $!"; open$out, '>', "mod.txt" or die "Can't write new file: $!"; while( <$in> )
{
$C=s/foo/bar/gm; print "$C matches replaced.\n"
etc...
print $out$_;
}
close $out; It is quite fast but after some time I always get an "Out of Memory"-Error due lack of RAM/Swap-Space (I'm on Win XP with 2GB of Ram and a 1.5GB Swap-File). After having looked around a bit on how to deal with big files, File::Map seemed to me as a good way to avoid this problem. I'm having trouble implementing it, though. This is what I have for now: #!perl -w use strict; use warnings; use File::Map qw(map_file); my$out = 'output.txt';
map_file my $map, 'input.txt', '<';$map =~ s/foo/bar/gm;
print $out$map;
However I get the following error: Modification of a read-only value attempted at gott.pl line 8.
Also, I read on the File::Map help page, that on non-Unix systems I need to use binmode. How do I do that?
Basically, what I want to do is to "load" the file via File::Map and then run code like the following:
$C=s/foo/bar/gm; print "$C matches found and replaced.\n"
$C=s/goo/far/gm; print "$C matches found and replaced.\n"
while(m/complex_condition/gm)
{
$C=s/complex/regex/gm;$run_counter++;
}
print "$C matches replaced. Script looped$run_counter times.\n";
etc...
I hope that I didn't overlook something too obvious but the example given on the File::Map help page only shows how to read from a mapped file, correct?
EDIT:
In order to better illustrate what I currently can't accomplish due to running out of memory I'll give you an example:
On http://pastebin.com/6Ehnx6xA is a sample of one of our exported library records (txt-format). I'm interested in the +Deskriptoren: part starting on line 46. These are thematic classifiers which are organised in a tree hierarchy.
What I want is to expand each classifier with its complete chain of parent nodes, but only if none of the parent nodes are not already present before or after the child node in question. This means turning
+Deskriptoren
-foo
-Cultural Revolution
-bar
into
+Deskriptoren
-foo
-History
-Modern History
-PRC
-Cultural Revolution
-bar
The currently used Regex makes use of Lookbehind and Lookahead in order to avoid duplicates duplicates and is thus slightly more complicated than s/foo/bar/g;:
s/(?<=\+Deskriptoren:\n)((?:-(?!\QParent-Node\E).+\n)*)-(Child-Node_1|Child-Node_2|...|Child-Node_11)\n((?:-(?!Parent-Node).+\n)*)/${1}-Parent-Node\n-${2}\n${3}/g; But it works! Until Perl runs out of memory that is... :/ So in essence I need a way to do manipulations on a large file (80MB) over several lines. Processing time is not an issue. This is why I thought of File::Map. Another option could be to process the file in several steps with linked perl-scripts calling each other and then terminating, but I'd like to keep it as much in one place as possible. UPDATE 2: I managed to get it working with Schwelm's code below. My script now calls the following subroutine which calls two nested subroutines. Example code is at: http://pastebin.com/SQd2f8ZZ Still not quite satisfied that I couldn't get File::Map to work. Oh well... I guess that the line-approach is more efficient anyway. Thanks everyone! - Why do you think you need to slurp the entire file? Why won't processing it a line-at-a-time work? – tadmc Jun 11 '11 at 3:00 just guessing, but maybe the complex regexp needs to span several lines, in which case line-based processing wouldn't work. – mirod Jun 11 '11 at 3:23 yes exactly, as my updated post shows. – screen12345 Jun 11 '11 at 15:50 ## 3 Answers Some simple parsing can break the file down into manageable chunks. The algorithm is: 1. Read until you see +Deskriptoren: 2. Read everything after that until the next +Foo: line 3. Munge that bit. 4. Goto 1. Here's the sketch of the code: use strict; use warnings; use autodie; open my$in, $input_file; open my$out, $output_file; while(my$line = <$in>) { # Print out everything you don't modify # this includes the +Deskriptoren line. print$out $line; # When the start of a description block is seen, slurp in up to # the next section. if($line =~ m{^ \Q Deskriptoren: }x ) {
my($section,$next_line) = _read_to_next_section($in); # Print the modified description print$out _munge_description($section); # And the following header line. print$out $next_line; } } sub _read_to_next_section { my$in = shift;
my $section = ''; my$line;
while( $line = <$in> ) {
last if $line =~ /^ \+ /x;$section .= $line; } # When reading the last section, there might not be a next line # resulting in$line begin undefined.
$line = '' if !defined$line;
return($section,$line);
}
# Note, the +Deskriptoren line is not on $description sub _munge_description { my$description = shift;
...whatever you want to do to the description...
return $description; } I haven't tested it, but something like that should do you. It has the advantage over dealing with the whole file as a string (File::Map or otherwise) that you can deal with each section individually rather than trying to cover every base in one regex. It also will let you develop a more sophisticated parser to deal with things like comments and strings that might mess up the simple parsing above and would be a huge pain to adapt a massive regex to. - Thank you. I ended up using your code for the problematic bit. – screen12345 Jun 28 '11 at 8:34 One last problem is however that Perl complains about Use of uninitialized value$next_line in print at D:\path\to\script.pl line 98, <$in> line 5416772. Both seem to be in the while-loop. The script finishes fine despite the warning but I'd like to know how to correct the script... I tried to initialize $next_line via our $next_line = 0 at the beginning of the script, but it still shows the same. – screen12345 Jun 28 '11 at 11:20 @screen12345 Trying to initialize it with our$next_line won't work. That creates the global $next_line which my$next_line masks by creating a lexical $next_line (which only exists for the block its in). The problem is in _read_to_next_section(). It initializes $line (which will be returned to $next_line) but at the last line of the file $line = <$in> will be undefined. This is normal and something I didn't account for. Setting $line if its undefined after the while loop fixes that. I'll edit it now. – Schwern Jun 28 '11 at 18:24
that did it. updated the code on pastebin. thank you again. I still have a lot to learn. – screen12345 Jun 28 '11 at 20:53
When you set $/ (the input record separator) to undefined, you are "slurping" the file -- reading the entire content of the file at once (this is discussed in perlvar, for example). Hence the out-of-memory problem. Instead, process it one line at a time, if you can: while (my$line = <$in>){ # Do stuff. } In situations where the file is small enough and you do slurp the file, there is no need for the while loop. The first read gets everything: { local$/ = undef;
my $file_content = <>; # Do stuff with the complete file. } Update After seeing your massive regex I would urge you reconsider your strategy. Tackle this as a parsing problem: process the file one line at a time, storing information about the parser's state as needed. This approach allows you to work with the information using simple, easily understood (even testable) steps. Your current strategy -- one might call it the slurp and whack with massive regex strategy -- is difficult to understand and maintain (in 3 months will your regex makes immediate sense to you?), difficult to test and debug, and difficult to adjust if you discover unanticipated deviations from your initial understanding of the data. In addition, as you've discovered, the strategy is vulnerable to memory limitations (because of the need to slurp the file). There are many questions on StackOverflow illustrating how one can parse text when the meaningful units span multiple lines. Also see this question, where I delivered similar advice to another questioner. - Thanks, I'll try that. – screen12345 Jun 11 '11 at 15:49 @screen12345 Answer updated. – FMc Jun 11 '11 at 19:10 You are using mode <, which is read-only. If you want to modify the contents, you need read-write access, so you should be using +<. If you are on windows, and need binary mode, then you should open the file separately, set binary mode on the file handle, then map from that handle. I also noticed that you have an input file and an output file. If you use File::Map, you are changing the file in-place... that is, you can't open the file for reading and change the contents of a different file. You would need to copy the file, then modify the copy. I've done so below. use strict; use warnings; use File::Map qw(map_file); use File::Copy; copy("input.txt", "output.txt") or die "Cannot copy input.txt to output.txt:$!\n";
open my $fh, '+<', "output.txt" or die "Cannot open output.txt in r/w mode:$!\n";
binmode($fh); map_handle my$contents, $fh, '+<'; my$n_changes = ( $contents =~ s/from/to/gm ); unmap($contents);
close($fh); The documentation for File::Map isn't very good on how errors are signaled, but from the source, it looks as if $contents being undefined would be a good guess.
-
On error, it will throw an exception. I'll add that to the documentation. Also, map_file will binmode automatically, unless you pass it a layer. And you don't really need that unmap, it's taken care of automatically when \$contents falls out of scope. – Leon Timmermans Jan 14 '13 at 11:44 | 2016-06-29 16:57:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31607523560523987, "perplexity": 4788.252338208541}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783397749.89/warc/CC-MAIN-20160624154957-00162-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://motls.blogspot.com/2020/12/poland-likely-to-outlaw-big-tech.html?m=1 | Sunday, December 27, 2020
Poland likely to outlaw the Big Tech censorship
Two weeks ago, I praised Hungary for its protection of the European value and the traditional family and sexual identity rules in particular. Well, the other European country that actually cares about what the West used to symbolize is preparing something impressive, too:
Poland threatens hefty fines for social media companies that censor legal speech, users everywhere celebrate (RT)
Poland to Pass Law Protecting Online Free Speech Against Big Tech Censorship (Breitbart)
Zbigniew Ziobro, the minister of justice, is preparing the law. A new fully online appeal court should be created. If the likes of Facebook, Twitter... remove your content or account and you think that what you wrote was legal, you may appeal. The posting or account will be restored or... the company will face a €1.8 million fine.
Václav Klaus Jr was preparing a similar law in 2019. It's a great idea but it must be executed well so that it doesn't have the opposite effect. The law must really apply to the servers that have a desire to be platforms for everyone, not for websites run by small groups. I hope that they understand it. Klaus' edition applied to every company where more than 1% of the nation may post as registered users which is sensible.
The U.S. First Amendment is the world's most famous law protecting free speech and Americans often boast about their perfect freedom but this bragging is utterly undeserved, as the current situation makes clear. In the U.S., as we are experiencing, lots of extremely powerful players, huge corporations, and their cartels (and a loose union with one political party) – which increasingly act as the de facto government – may totally cripple all Americans' free speech and one may argue that it doesn't contradict the First Amendment. Only "the government" is a rather narrow sense (a de iure government) is prohibited from ruining the citizens' freedom of speech in the U.S. That's an extremely weak rule because the de facto government, when it starts to be really devastating for the Western values, usually chooses not to call itself the government during the transition period to the new totalitarian regime.
In Poland, the constitution is worded in such a way that it requires the government to be active when the citizens' freedom of expression is being suppressed. So it is the Polish government's duty to act against far left Silicon Valley fascist aßholes and their nasty coalition of psychiatrically defective Scandinavian teenagers, Marxist EU apparatchiks, feminists, transsexual activists, and similar evil, aggressive trash. Note that in the U.S., the de iure government is just ordered to be passive in a certain way which is much easier for the de iure government to execute.
[General Jan Henryk] Dąbrowski March (about a Polish commander in Italy), the Polish anthem, was later recycled as the pan-Slavic anthem, Yugoslav anthem, and the anthem of the wartime Slovakia, too.
You may see that there exist some... disagreements within the EU about rather fundamental issues because the EU apparatchiks and numerous allied, mostly Western European, governments are preparing pretty much the opposite step: a full-blown attack on the freedom of expression of everyone who knows something inconvenient for the left-wing fascists. According to these neo-Marxist governments' planned bill, the Silicon Valley server will be obliged to censor everything that the most far left unhinged group finds inconvenient. I am not sure how they will pick who is the actual most far left unhinged group (who holds the actual power in these whole countries), but let us not discuss detailed glitches. If the Polish law is approved, the disagreements are likely to strengthen.
Preliminary congratulations to our half-brothers. I would love my country to follow the suit but the colorless opportunist Czech politicians don't give me much hope about their loyalty to the European values (and to the Visegrád Group). | 2021-04-19 10:49:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1873132288455963, "perplexity": 5083.683117615979}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038879305.68/warc/CC-MAIN-20210419080654-20210419110654-00445.warc.gz"} |
http://tex.stackexchange.com/questions/121551/speed-up-the-compilation-of-a-document-with-a-lot-of-tikzpictures-made-with-pgfp | # Speed up the compilation of a document with a lot of tikzpictures made with pgfplots [duplicate]
I have a document with a lot of tikzpicture made with pgfplots, most of them take data from files so the compilation may be very long. In order to have only a draft I would like to have blank images with same dimension of the full ones.
Until now I used a trick of having a tikzpicture with an empty axis environment of the same dimensions of the original one and with some if statements I included the blank or the full image like this:
\newcommand{\img}{Y} % immages Y(es) or N(o)
...
\begin{figure}
\centering
\ifthenelse{\equal{\img}{Y}}{%
\input{Immagini/full.tex}}{%
\input{Immagini/empty.tex}}
\caption{caption}
\end{figure}
file full.tex
\begin{tikzpicture}
\begin{axis}[height=9cm, width=.8\textwidth]
\addplot table [x index=0, y index=2] {dati.dat};
\end{axis}
\end{tikzpicture}
file empty.tex
\begin{tikzpicture}
\begin{axis}[height=9cm, width=.8\textwidth]
\end{axis}
\end{tikzpicture}
But today I read this question How I can speed up the compilation of a document with multiple images? and now I would like to know if there is a similar way to the draft option of the package graphicx that does the same thing with tikzpicture.
-
## marked as duplicate by cmhughes, Paul Gaborit, mafp, T. Verron, QrrbrbirlbelJun 28 '13 at 14:59
There are a few related questions about this on the site e.g. tex.stackexchange.com/questions/111566/… if you search for tikzpicture draft you can see more. – percusse Jun 28 '13 at 12:18
Just to make sure: Have you thought about using the external library, which compiles your tikzpictures into external PDFs that then only have to be included in your final document? – Jake Jun 28 '13 at 12:40
@Jake Ok, with your suggestions I got the solution, can I answer to my own question? – Red Jun 28 '13 at 13:03
@Red: Sure! You just have to wait a day (I think) before you can accept the answer, but you can (and should) post the answer – Jake Jun 28 '13 at 13:09
A part of the total solution is to use the external library as suggested and then put the option draft to \documentclass[draft]{whatever}. But doing so the image is replaced by a box of fixed dimensions, not equal to those of the real image.
\documentclass[a4paper,draft]{article}
\usepackage{pgfplots}
\usepackage{lipsum}
\usepackage{tikz}
\usetikzlibrary{external}
\tikzexternalize
\begin{document}
\begin{figure}[h]
\centering
\input{anderlini_10.tex}
\caption{caption of this beautiful image}
\end{figure}
\lipsum[1-2]
\end{document}
This happens because the external image created is not imported with \includegraphics, to correct this it is sufficient to add this line (\pgfkeys{/pgf/images/include external/.code=\includegraphics{#1}}) before \tikzexternalize. In this way we obtain the desired result:
- | 2015-04-27 10:59:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7933328747749329, "perplexity": 1080.4557163580293}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246658061.59/warc/CC-MAIN-20150417045738-00014-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://www.effortlessmath.com/math-puzzles/number-properties-puzzle-critical-thinking-2/ | # Number Properties Puzzle -Critical Thinking 2
Let’s solve another critical challenge problem! This mathematical puzzle requires some kind of math to solve. Let’s see how you or your kid can handle it! Time to challenge your brain!
## Challenge:
$$1 = 5^1$$
$$2 = 5^2$$
$$3 = 5^3$$
$$4 = 5^4$$
$$5 = ?$$
### The Absolute Best Book to challenge your Smart Student!
For this question, don’t try to use the pattern! The first equation says that 1 equals to $$5^1$$, which equals to 5.
$$1 = 5^1$$
$$2 = 5^2$$
$$3 = 5^3$$
$$4 = 5^4$$
$$5=1$$ | 2020-06-06 02:28:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3550361394882202, "perplexity": 2562.498273170757}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348509264.96/warc/CC-MAIN-20200606000537-20200606030537-00574.warc.gz"} |
https://cs.stackexchange.com/questions/35274/rotations-in-splay-trees | # Rotations in splay trees
I am having some difficulties splaying the element 4 to the root. Considering the following splay tree.
0
\
1
\
2
\
3
\
4
Could anyone show me the steps how to get the 4 to the root?
• Strange title? Have a look at splay trees and their rotations at wikipedia. Then tell us what you don't understand. – Hendrik Jan Dec 14 '14 at 14:05
• Sorry not for expression where the problems lies.. – James Dec 14 '14 at 20:12
Just follow the algorithm. First you have to do a zag-zag-rotation, which gives you
0
\
1
\
4
/
3
/
2
Then you have to do another zag-zag-rotation and you obtain as the result of splay(4) the tree
4
/
1
/ \
0 3
/
2
• That's also how i Imagined it would look like, but I have a hard time understanding how the rotations from the first to the second is performed.. – James Dec 14 '14 at 20:13
• Just follow the rules (see wikipedia) and keep the subtrees hanging off the three nodes that are involved fixed. – A.Schulz Dec 14 '14 at 20:17 | 2021-01-17 10:52:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6194536089897156, "perplexity": 730.3244158801442}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703511903.11/warc/CC-MAIN-20210117081748-20210117111748-00130.warc.gz"} |
http://www.ck12.org/tebook/Human-Biology-Circulation-Teacher's-Guide/r1/section/5.1/ | <meta http-equiv="refresh" content="1; url=/nojavascript/"> Planning | CK-12 Foundation
You are reading an older version of this FlexBook® textbook: Human Biology Circulation Teacher's Guide Go to the latest version.
# 5.1: Planning
Difficulty Level: At Grade Created by: CK-12
## Key Ideas
• Capillaries are thin and permeable blood vessels that allow for the exchange of nutrients, gases, and waste.
• This exchange of nutrients, gases, and waste occurs through the process of diffusion.
• The capillary network is extensive. No cell is more than two cells away from a capillary.
## Overview
Students explored the structure and function of arteries and arterioles in Section 3. In this section they make a model of a capillary bed. Diffusion is extremely important to the function of capillary beds. Students explore how capillaries and capillary beds work-how the thin walls of the capillaries, the slow movement of the blood, and the process of diffusion allow gases, food nutrients, water, and wastes to pass back and forth between body cells and the bloodstream.
## Objectives
Students:
$\checkmark$ make a model of a capillary bed.
$\checkmark$ describe the characteristics of capillaries which allow for exchange of gases, nutrients, water, and wastes between body cells and the bloodstream.
$\checkmark$ design an activity to illustrate the process of diffusion.
## Vocabulary
capillaries, diffusion, venule
## Student Materials
### Activity 4-1: Making a Capillary Bed Model
Activity Report
Construction or drawing paper; Scissors; Glue or clear tape; Marking pens; Materials to represent arteries, veins, capillaries and cells (Examples: string, yarn, thread, rope, and dried beans.)
## Teacher Materials
### Activity 4-1: Making a Capillary Bed Model
• Activity Report Answer Key
• Photos of capillaries
• Diagrams or a model of the circulatory system
See Activity 4-1 in the Student Edition,
Display the models students constructed in Activity 1-1.
Check your local audiovisual service and the resource list included in this unit to select visuals of capillary circulation.
Gather materials students will use in constructing their models, such as rope, yarn, string, and thread.
## Interdisciplinary Connections
Physical Education/Sports Capillary function is disrupted by bruised, broken capillaries. Students can investigate methods for applying first aid to bruises caused by sports injuries.
Social Studies Sickle-shaped red blood cells block capillaries, which slows blood flow and reduces the oxygen supply. The gene for sickle-cell anemia is more common in geographic areas where malaria is endemic. Students can investigate the geographic distribution of sickle-cell anemia its cause, the reasons for its prevalence in areas with malaria, and in Math, the statistical frequency of sickle-cell anemia, as well as its financial impact.
## Enrichment Activities
Enrichment 4-1: Observing Goldfish Capillaries
Enrichment 4-2: Transport of Materials Exploring Diffusion
6 , 7 , 8
## Date Created:
Feb 23, 2012
Apr 29, 2014
You can only attach files to None which belong to you
If you would like to associate files with this None, please make a copy first. | 2015-03-04 15:29:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 3, "texerror": 0, "math_score": 0.2700771987438202, "perplexity": 9679.808982476636}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936463606.79/warc/CC-MAIN-20150226074103-00226-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://mozilla.github.io/glean/dev/core/internal/debug-pings.html | # Debug Pings
For debugging and testing purposes Glean allows to tag pings, which are then available in the Debug Ping Viewer1.
Pings are sent to the same endpoint as all pings, with the addition of one HTTP header:
X-Debug-ID: <tag>
<tag> is a alphanumeric string with a maximum length of 20 characters, used to identify pings in the Debug Ping Viewer.
See Debugging products using the Glean SDK for detailed information how to use this mechanism in applications.
1 | 2023-01-28 07:09:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34661203622817993, "perplexity": 5052.410559409537}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499524.28/warc/CC-MAIN-20230128054815-20230128084815-00588.warc.gz"} |
https://physics.stackexchange.com/questions/291465/is-there-any-thing-composed-of-elementary-particles-in-this-world-that-is-not-3 | # Is there any thing composed of elementary particles in this world that is not 3 dimensional? [closed]
Is there any thing composed of elementary particles in this world that is not 3 dimensional? I know that there is graphite which is singular atom thick. Is there anything in this world that has no depth? So I guess what I am asking is there an object that does not have volume
## closed as unclear what you're asking by Jon Custer, user108787, Wolpertinger, Qmechanic♦Nov 8 '16 at 13:10
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
• Welcome on Physics SE :) What do you mean by 3-dimensional and what by objects? – Sanya Nov 7 '16 at 21:48
• For 3 dimensional I mean it has depth – user135530 Nov 10 '16 at 16:30
• @annav - nope. That's not an appropriate suggestion at all. – ChrisF Nov 13 '16 at 19:52
If by object you mean something composed of elementary particles then there are no two dimensional objects due to the uncertainty principle.
If we take the direction normal to the surface to be the $z$ axis then the uncertainty principle tells us that:
$$\sigma_z \sigma_{p_z} \ge \frac{\hbar}{2}$$
for an object to become two dimension would require $\sigma_z \rightarrow 0$ and that implies $\sigma_{p_z} \rightarrow \infty$ and therefore requires infinite energy.
However there are many examples of systems that are approximately two dimensional. Graphene would be a good example.
Even if you're willing to relax the requirement for the object to be something physical then I'm still not sure anything can be truly two dimensional. The example that springs to mind is an event horizon, but this is a classical concept and quantum gravity effects may well blur it into a region of finite volume. I suspect quantum mechanics will forbid anything from being truly two dimensional.
• Yes by object I mean somehting composed of elementary particles. Sorry! Should have been more specific. – user135530 Nov 8 '16 at 16:35
Coastlines, for example. Coastline of Great Britain has fractal dimension of 1.25. Source: https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension
• Any real coastline gets blurry at some level, either because of the water going back and forth, or, if you really want to get deep, because at the atom level there is no well defined coastline. This looks like an illustration of a mathematical concept, not an actual physical fractal. – Javier Nov 8 '16 at 3:01
• I'm unconvinced that a coastline is an object ... – John Rennie Nov 8 '16 at 7:59 | 2019-08-21 16:39:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5111057162284851, "perplexity": 533.5753276613543}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027316075.15/warc/CC-MAIN-20190821152344-20190821174344-00116.warc.gz"} |
https://www.physicsforums.com/threads/waste-water-treatment-plant-problem.340705/ | # Waste Water treatment plant problem
1. Sep 26, 2009
### ghostanime2001
1. The problem statement, all variables and given/known data
Barium chloride is a toxic compound used in waste water treatment and many manufacturing processes. A 20 mL solution of 0.200 M Na2SO4 is added to a 10.0 mL water sample containing an unknown concentration of BaCl2 that was concentrated by 100 fold after being taken from a waste water treatment plant. After filtration of the solution, 0.7800g of the insoluble BaSO4(s) is obtained. Provide a balanced chemical equation and determine the concentration of the Ba2+ from the sample taken at the waste water treatment plant.
3. The attempt at a solution
BaCl2(aq) + Na2SO4 $$\rightarrow$$ BaSO4(s) + 2NaCl
Using dilution equation:
C1V1=C2V2
C1(0.01)=(0.2)(0.02)
C1=0.4M = [BaCl2]
After Barium chloride is concentrated to a 100 fold which means the solution decreased volume. So 0.4M x 100 = 40M
BUT, this solution isnt re-reacted with sodium sulfate therefore the 100x concentrated part doesn't matter in the problem.
nBaSO4 = 0.78g / 233.3896 g/mol = 0.00334 mol BaSO4
[BaSO4] = [Ba2+]
What I don't understand is why do I need to consider the 100x problem when i am given the mass of the precipitate and therefore just calculate how much barium ions I have ??? The 0.78g is fixed because thats what the experimentalists got. If the concentration of barium chloride is changed to 40M and then used to calculate the amount of Barium sulfate what does 0.78 grams measured from filtration matter then?
2. Sep 27, 2009
### Staff: Mentor
1. Not 40M, recheck your thinking. Which solution has a higher concentration - initial, or concentrated one?
2. You are asked to calculate concentration in water sample BEFORE it was concentrated, that is, in a sample taken just from the waste water.
Trick is, in such water concentration of barium was rather low, and determination of low concentrations is often difficult, thus we start concentrating samples, to make determination easier.
Last edited by a moderator: Aug 13, 2013
3. Sep 27, 2009
### ghostanime2001
1. I dont understand what you are saying here. Is it Na2SO4 ?
2. IF thats the case then I dont need to consider the 100x concentrated part. What do I do ?
4. Sep 27, 2009
### ghostanime2001
[Ba2+] = 0.4M before it was concentrated
5. Sep 27, 2009
### ghostanime2001
But wait the question asks to determine the concentration of Barium ions which means the only contributer of barium is barium chloride and the only way barium ion can be calculated is from Barium chloride. I know that the two solutions are mixed together to precipitate out Barium sulfate so its a dilution problem? Actually what I mean is 20 mL solution and 10 mL solution are coming together. So the total volume is 30 mL solution containing both compounds. therefore to calculate concentration of barium ions I need volume. I am given the mass and i determined the molar mass I just need volume and I think the only way I can get volume to calculate concentration is from 30 mL because the two solutions are mixed together and filtrated out to get Barium sulfate.
Does this kinda make sense. I know it sounds a little mixed up but please correct my way of thinking.
6. Sep 27, 2009
### ghostanime2001
or is it 0.00334 mol BaSO4 x 1 mol BaCl2/1 mol BaSO4 x 1 mol Ba2+ \ 0.01 L = 0.334M Ba2+
7. Sep 27, 2009
### Staff: Mentor
Seems like you are completely confused. 10 mL sample is the one AFTER concentration. The original volume was 100 times larger.
You know that 10 mL contained 0.00334 mole Ba2+ - so the same 0.00334 mole of Ba2+ was present in the original volume (100 times 10 mL).
Last edited by a moderator: Aug 13, 2013
8. Sep 27, 2009
### ghostanime2001
Is that the answer then ?
9. Sep 27, 2009
### ghostanime2001
So the concentration of barium ions before the 100x concentration was 3.34 x 10^-6 ????
10. Sep 27, 2009
### ghostanime2001
IF you say:
That means 100 x 10 mL = 1000 mL = 1 L
Before 100x concentration:
C1 = [Ba2+] = $$\frac{\mbox{3.34 x 10^{-3} mol}}{1 L}= 3.34 \mbox{ x } 10^{-3}M$$
After 100x concentration:
C2 = [Ba2+] = $$\frac{\mbox{3.34 x 10^{-3} mol}}{0.01 L}= 0.334 M$$
Is this correct ?
Last edited: Sep 27, 2009
11. Sep 27, 2009
### Staff: Mentor
Looks OK.
Last edited by a moderator: Aug 13, 2013
12. Sep 27, 2009
### ghostanime2001
OK? How would you have done it differently ??
13. Sep 27, 2009
### ghostanime2001
Is the question asking before 100x or after 100x ? | 2018-02-21 17:30:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6339699625968933, "perplexity": 3609.1098144489138}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813691.14/warc/CC-MAIN-20180221163021-20180221183021-00387.warc.gz"} |
https://electronics.stackexchange.com/questions/391367/high-current-high-voltage-high-frequency-measurement | # High current/high voltage/high frequency measurement
I have a circuit that I'm having trouble understanding. It measures the current flowing through a conductor. The measured load is 20-100 Amps, 9kHz-34kHz, and approx. 340 volts. The main conductor passes through a toroid that has a 10 turn winding (winding #1). The two ends of the winding extend away from the toroid. One end of the winding loops through another toroid that has a 100 turn winding (winding #2). The two ends of winding #1 are then spliced together. Winding #2 has both ends terminated across a 100 ohm resistor. The voltage across the resistor varies from 0 to 6.6v p-p, dependent on the current of the the measured load. The question I have is that it seems like the voltage would be MUCH higher. Winding #1 should produce 3400 volts, then winding #2 should produce 340000 volts? I know I'm missing something very fundamental. Could someone help me to understand this?
• Draw a schematic with the tool – laptop2d Aug 16 '18 at 15:42
• I think what you need to research is Current Transformers then realize that here, you have two CT's in series. This is common to "step-down" very large currents into much more manageable ones. – rdtsc Aug 16 '18 at 15:48
## 2 stage Current Transformer 1000:1
Typical thru-hole torroidal CT's use a burden of 1 Ohm per turn. The 2nd core has 100 turn and uses 100 Ohms which appears as 10 Ohms burden to the 1st core so no additional R is needed.
The frequency response "can" be quite limited, depending on design and cost.
e.g. one frequency decade 20kHz ~ 200kHz
That may contribute to your error.
simulate this circuit – Schematic created using CircuitLab
This is my attempt to draw a 1 wire CT insulated from secondary (not shunted as shown)
Since voltage drop on primary ~ 0 the voltage is not amplified. This is because the transformer is in series , not parallel with the load.
The burden resistor ( here 100 Ohms) is per Mfg suggested value to create Volts per Amp.
The ten turn secondary winding on the first CT is shorted hence for 100 amps flowing through the main conductor in that CT, 10 amps will flow in the shorted secondary.
But, remember that the voltage across the short length of the main conductor that produces a magnetic field in the CT's core is just milli-volts or less. Most of the 340 volts (99.99%) appears across your primary load and not across a short length of wire going through that CT so there is no possibility of seeing thousands of volts.
So, moving onto the second CT; it has 10 amps flowing through the core primary winding and the secondary is 100 turns feeding 100 ohms. The 100 turns means that this CT's secondary current is 10 amps / 100 = 100 mA.
And, the voltage across the 100 ohm resistor will be 100 ohms x 100 mA = 10 volts.
You say you are operating in the kHz region and this may account for only seeing 6.6 Vp-p. Leakage inductances could account for a significant reduction in the voltage being only 6.6 Vp-p as opposed to 10 volts (presuled RMS).
• – Andy aka Aug 17 '18 at 17:12 | 2019-06-27 00:42:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.538057804107666, "perplexity": 1603.8858265531994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000609.90/warc/CC-MAIN-20190626234958-20190627020958-00215.warc.gz"} |
https://zbmath.org/?q=an:02116593 | # zbMATH — the first resource for mathematics
MatlabMPI. (English) Zbl 1067.68793
Summary: In many projects the true costs of high performance computing are currently dominated by software. Addressing these costs may require shifting to higher level languages such as Matlab. MatlabMPI is a Matlab implementation of the Message Passing Interface (MPI) standard and allows any Matlab program to exploit multiple processors. MatlabMPI currently implements the basic six functions that are the core of the MPI point-to-point communications standard. The key technical innovation of MatlabMPI is that it implements the widely used MPI “look and feel” on top of standard Matlab file I/O, resulting in an extremely compact ($$\sim$$ 350 lines of code) and “pure” implementation which runs anywhere Matlab runs, and on any heterogeneous combination of computers. The performance has been tested on both shared and distributed memory parallel computers (e.g. Sun, SGI, HP, IBM, Linux, MacOSX and Windows). MatlabMPI can match the bandwidth of C based MPI at large message sizes. A test image filtering application using MatlabMPI achieved a speedup of $$\sim$$ 300 using 304 CPUs and $$\sim$$ 15% of the theoretical peak (450 Gigaflops) on an IBM SP2 at the Maui High Performance Computing Center. In addition, this entire parallel benchmark application was implemented in 70 software-lines-of-code, illustrating the high productivity of this approach. MatlabMPI is available for download on the web (www.ll.mit.edu/MatlabMPI).
##### MSC:
68W30 Symbolic computation and algebraic computation
##### Keywords:
Message passing; High level languages; Parallel Matlab
Full Text: | 2021-04-20 10:05:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22756977379322052, "perplexity": 3312.6723056717815}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039388763.75/warc/CC-MAIN-20210420091336-20210420121336-00214.warc.gz"} |
https://nrich.maths.org/7190 | ### Cubes
Investigate the number of faces you can see when you arrange three cubes in different ways.
### I'm Eight
Find a great variety of ways of asking questions which make 8.
### Let's Investigate Triangles
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
# How Odd
##### Age 5 to 7 Challenge Level:
How many odd numbers are there between $3$ and $11$?
How many odd numbers are there between $4$ and $11$?
What do you notice? Can you explain your observation?
Can you find any other pairs of numbers which have this same number of odds between them?
Can you find a pair of numbers which have four odd numbers between them?
Can you find another pair of numbers which have four odds between them? And another pair?
How would you find a pair of numbers that have five odds between them? Six odds?
How would you explain to someone else how to find a pair of numbers that have a certain number of odds between them? | 2018-07-21 17:23:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38933515548706055, "perplexity": 651.4304114650915}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592650.53/warc/CC-MAIN-20180721164755-20180721184755-00083.warc.gz"} |
http://sciforums.com/threads/relativity-and-simple-algebra-ii.164016/page-4 | # Relativity and simple algebra II
Discussion in 'Alternative Theories' started by ralfcis, Feb 6, 2021.
1. ### ralfcisRegistered Senior Member
Messages:
421
In keeping with my layering of several spacetime diagrams into one, the ct' axis is a line that represents 3 velocities and 3 different slopes.
It turns out v_t overlaps the same line as v and v' and the slope of each overlapping line is dependent on what coordinates you assign to the ct' axis.
Let's look at the point labelled ct'=1.
The coordinates of the velocity line at this point are (1.25,.75) where v=x/ct =.6c and the slope of the line is 1/v = 5/3. The velocity is x-axis/ct-axis.
The coordinates of the v'=Yv line are (1,.75) where v'=x/ct' = .75c and the slope of the line is 1/v' = 4/3. v' is the x-axis/ct'-axis.
The coordinates of the v_t=ct'/ct = c/Y line are (1.25,1) where v_t=ct'/ct = .8 and the slope of the line is 1/v_t = 5/4. v_t is the ct'-axis/ct-axis.
Normal algebra would not have labelled that point as 1, it would have only labelled it with the cartesian coordinates of (1.25,.75). I'm adding a 3rd ct'-axis which not only allows all facets of the main equation to be seen on the diagram but it allows both perspective views to be seen on one diagram instead of 2. It also avoids the mistakes relativity makes when switching from one perspective to the other as I'll discuss in the next post.
But let's go back to basic normal algebra for now. The simplest equation is y=x (which comes from the equation for a line y=mx+y_0 ). This equation would define the speed of light c on a spacetime diagram. c has no coordinates in relativity because c is actually made up of overlapping lines due to a cheat Minkowski added to his diagrams to make c appear the same from all perspectives (which it is anyway). The cheat he used was to take a normal frame rotation and flip the x'-axis up over the x-axis to make it look like the ct'-axis and x'-axis were rotated independently towards each other. Mathematically perfectly acceptable in order to force all c lines from every frame to overlap each other and have the same 45 degree angle on the Minkowski diagram. Epstein could have done the same thing on his diagrams except all frames would have the slope of c at 0 degrees. Epstein diagrams reveal a lot about the underlying mathematical constructs of relativity that do not necessarily follow the philosophical conclusions the Minkowski diagrams advocate.
In algebra, the equation y=1/x defines a hyperbola. The main equation of relativity creates straight lines and hyperbolas shifted 45 degrees from the simple equations of basic algebra. (This is not set in stone as the Epstein sum of squares version of the main equation uses circles that do not shift the velocity lines at 45 degrees or have an overlapping c line at 45 degrees.) The hyperbolas in relativity intersect the velocity lines at the same proper time. These hyperbolas connect a true, unseen, universal present at a distance and are not to be confused with the fake perspective present that Einstein invented in his clock sync method. In "ralfativity", I replace the hyperbolic lines with straight lines of 1/v_h lines of proper simultaneity of the Loedel half speed perspective (my own term).
Ralfativity only cares about the slopes of key velocity lines (v, v', v_t ,v_h ,v_ht, ) and their reciprocals which are lines of simultaneity. It only considers velocities separated into their coordinates of time and space and perspectives at the end. All clocks beat at the same universal rate within a frame and while earth may measure a ship going at .6c using earth clocks, the guy in the ship measures his v' speed at .75c using his own clock. The lines of perspective simultaneity (also called in relativity as now slices and x'-axes), arising out of Einstein's clock sync method, are illusory curiosities. They do not define a perspective present because the distance between points negates the very definition of a shared present.
3. ### James RJust this guy, you know?Staff Member
Messages:
38,035
ralfcis:
Are you planning on responding to any of my posts, above - especially #58?
Okay. Could you please present the main postulates (assumptions) of the theory you have constructed?
Here are the ones from special relativity:
1. The laws of physics take the same forms in all inertial reference frames.
2. The speed of light in a vacuum is the same in all inertial reference frames.
Those two postulates are sufficient to derive all of special relativity, including things like the Lorentz factor; the Lorentz transformations; time dilation; length contraction; the relativity of simultaneity; relativistic mass, momentum and energy conservation; mass-energy equivalence, and more.
What are your core physical assumptions, which replace or alter the ones from special relativity?
Your ct' axis is a rotated axis, despite the fact that you claim your framework has no rotated axes.
What about an x' axis? How does an observer measure distances in the "primed" frame, in your system? Do effects like length contraction exist in your framework, or not? If not, how is the constancy of the speed of light maintained between frames (assuming that is an axiom)?
Not really. It is clear from the usual spacetime metric in flat space (which is special relativity) that the time coordinate/dimension is not on the same footing as space. On the other hand, the Lorentz transformations do transform time and spatial coordinates as a unit, which is why relativists speak of "spacetime".
I don't understand. When you talk about the "moving observer" seeing a velocity, which velocity are you talking about? Not the moving observer's own velocity, surely, because the moving observer is always stationary relative to himself. I guess you're talking about the moving observer's measurement of the "stationary" observer's relative velocity, then.
If the two observers are moving at constant velocities at all times (or one is stationary and the other is moving at constant non-zero velocity), how could it be the case that each one measures the other's speed to be different?
If you're standing still on a road and I drive my car past you at 60 km/hr, then according to me I'm stationary in my car and you are moving backwards relative to my car at 60 km/hr.
I don't see how it could ever be the case that, as long as we're dealing with constant relative velocities, you see me driving at 60 km/hr, but I see you moving backwards at 75 km/hr, for instance.
So you're trying to replace relativity by an alternative theory in which distances are absolute, but time changes between frames, which makes the speed of light variable between frames.
Is that correct?
Would one of your postulates be "distances are absolute", then?
I don't think you understand the special theory of relativity very well. I agree with you that time does not behave like distance. That does not mean, however, that a concept like "spacetime" is meaningless. On the contrary, the Lorentz transformations show that such a concept is required.
Okay, but I'd prefer it if you could respond at least to post #58, first.
We're having a discussion here, aren't we? Or are you treating this more like a blog?
Your own diagrams use different time scales on the t and t' axes. Why is that?
We can avoid that confusion by talking about events in spacetime, as I said previously.
I don't really know what you mean. Maybe we can unpack that claim later.
5. ### ralfcisRegistered Senior Member
Messages:
421
absolutely all of them but i figured you need more background. more is coming.
7. ### James RJust this guy, you know?Staff Member
Messages:
38,035
ralfcis:
I'd also like to ask you a specific question. Consider the case of one observer (B) with (1 dimensional) space and time coordinates x and t, who is stationary in the x coordinate, and another "moving" observer (A) who moves with speed +v in the positive x direction in B's coordinates. Let A have coordinates x' and t', and let A be stationary in the x' coordinate. Assume that at time t=t'=0, the coordinate x=0 is coincident with x'=0.
Here's how Galileo or Newton would have defined the transformations between A and B's reference frames:
$x' = x - vt$
$t' = t$.
And here's how Einstein and Lorentz say the coordinates transform between the same two frames:
$x' = \frac{1}{\sqrt{1-(v/c)^2)}}\left( x - vt \right)$
$t' = \frac{1}{\sqrt{1-(v/c)^2)}}\left ( t - \frac{v}{c^2}x \right)$.
Could you please give the coordinate transformation equations that are used in your theory?
Here's my guess at them, based on what you have written so far:
$x' = x - vt$
$t' = \sqrt{t^2 - \left(\frac{x}{c}\right)^2}$
Note that the second equation can also be written as
$(ct')^2 = (ct)^2 - x^2$.
Are these the correct coordinate transformations between the two frames, in your system? If not, please provide the correct ones.
Last edited: Feb 13, 2021
8. ### James RJust this guy, you know?Staff Member
Messages:
38,035
If I need something, I'll ask for it.
9. ### ralfcisRegistered Senior Member
Messages:
421
I will but not on your schedule, you need more background first because your questions show no understanding of what I'm saying because I have not yet given you a primarily adequate description of the elephant.
10. ### James RJust this guy, you know?Staff Member
Messages:
38,035
Out of interest, assuming that the ralfcis transformation equations I have given above are correct, I have looked at a light signal propagating outwards from the origin. Consider a signal that is sent from x=0 at t=0, and received at distance x=c at time t=1, for instance. The speed of the signal is calculated as x/t, which in this case is c, of course.
What happens if we transform to a different frame, in which an observer moving at speed v relativity to the x coordinate?
The coordinates of the "transmission" event in the new frame are (x',t')=(0,0), no matter which set of transformations we use from post #64. The coordinates of the "receipt" event are:
Newtonian relativity
$x'=c-v,\qquad t'=1$
The calculated speed of light in the 'primed' frame is $x'/t'=c-v$. That makes sense, since in the Newtonian universe the "moving" observer must subtract his own speed from the speed of light in order to find the speed of light relative to him. The speed of light is not the same in all frames of reference in the Newtonian picture.
Einsteinian special relativity
$x'=\frac{1}{\sqrt{1-(v/c)^2)}}(c-v), \qquad t'= \frac{1}{\sqrt{1-(v/c)^2)}}(1-v/c)$
The calculated speed of light in the 'primed' frame is $x'/t' = \frac{c-v}{1-v/c}=\frac{c-v}{\frac{c-v}{c}}=c$. That is, the "moving observer sees light as still travelling at 'c', which is consistent with the postulate that the speed of light is the same in all frames.
ralfcis relativity
$x'=c-v, \qquad t'=\sqrt{1-(c/c)^2}=\sqrt{1-1}= 0$
The calculated speed of light in the 'primed frame' is $x'/t' = \frac{c-v}{0} = \infty$.
It appears, that in ralfcis relativity, the speed of light is not the same in all frames. In this example it is actually infinite in the 'primed' frame.
More generally, if we consider propagation of the light from (x,t)=(0,0) for a general time, so that it reaches coordinates (ct,t) after time t, then ralfcis relativity says we would have, in the "moving" frame of the observer with velocity v:
$x'=ct-vt=(c-v)t, \qquad t'=\sqrt{t-(ct/c)}=0$
which would put the speed of light in the 'primed' frame at $x'/t'=\infty$.
So it appears that, if the transformations I have given are correct, ralfcis relativity has the speed of light as infinite in every frame except for one "special" frame.
11. ### James RJust this guy, you know?Staff Member
Messages:
38,035
Okay. No problem. Maybe your "background" posts will answer some of my questions.
Bear in mind, though, that I'll most likely try to reply to you as your post, rather than letting a lot of new material bank up, so it could save time if you answered my specific queries first, because it would prevent some of the misunderstandings you say I have from persisting in future posts of mine.
12. ### ralfcisRegistered Senior Member
Messages:
421
Just glancing at your last post. If v=x/t is limited to c is v'=Yv=x/t' also limited to c?
It's going to take a considerable amount of time to answer your questions because it's almost as if you've mentally redacted the parts you don't understand and substituted your own reality instead. That's ok as most people try to understand things in the context of what they already understand. I appreciate your fervent desire to ask questions and gain understanding. No one has ever tried before.
So here we go, the last bit of background before I continue answering your questions in order.
This is the basic graphical unit. It can be flipped, mirrored, paralleled and joined with other units using light signals and the Loedel lines of simultaneity. SR uses the spacetime path which has its own rules and can't be constructed from basic units or light signals.
In the basic unit, time dilation is explained without Einstein's clock sync method, without lines of perspective simultaneity, without length contraction, without perspective relativity of simultaneity, without time slowing, all excess baggage. The perspectives of the participants are derived from the Loedel perspective where proper time trumps perspective time. The flipped version is the muon experiment. The basic unit joined to the flipped version is the twin paradox. Two basic units joined in parallel is the pole in the barn paradox, the train in the station example, the Michelson Morley experiment. That just about covers all of Special Relativity except E=mc2.
So consider this Md is depicting a time trial race. The starting judge Bob fires a starting gun at the origin where he is co-located with the racer Alice. They each have the same atomic stop watch that flashes a light at regular intervals (regardless of anything else you might be thinking affects that interval). When the racer crosses the finish line 1.5ly away marked by a planet on the star charts, she will fire off a light signal. It this case it happens to correspond to her two year interval signal because her v= 3/5c relative to the judge (from the judge's perspective). (Or using her own on-board clock, her v'=3/4c because x=1.5 and her watch says 2 yrs have passed for her.) From the racer's perspective the judge is moving away from her at v=3/5c. But the judge has not moved anywhere from the starting line so his x=0 (he has only moved through time at v_t=c). He knows the racer has been moving away from him at 3/5c because the DSR he received showed the racer's clock was ticking at half the speed of his own.
The judge has only received the TV broadcast from the racer to determine the DSR but has not yet received the yellow finish line light signal. He will wait 4 yrs from the start of the race to receive that signal. The signal will have an encoded message," I have reached the finish line at the 1.5ly mark in two ticks of my atomic stopwatch". The judge knows the light signal took 1.5 of his years to reach him (inaccurate statement). So his time from his perspective for the end of the race is 4-1.5=2.5yrs. Time dilation is that the racer did it in 2 yrs. Notice no time has slowed! It's all a matter of relativity of proper simultaneity.
Relativity would have drawn a horizontal blue line of Bob's perspective line of simultaneity between those 2 time points. The only line of simultaneity I use is the green one for Loedel simultaneity. t=2 for the judge is simultaneous with t'=2 for the racer according the relativity's hyperbolic lines of proper time simultaneity generated by the main equation
$(ct')^2 = (ct)^2 - x^2$.
Alice would also have received his pink line from t=2 at t'=4. Whoa but that pink line took 3 yrs to reach her and the yellow line only took 1.5 yrs to reach Bob. This is a false equivalency. Using Alice's stop watch, Bob's signal was Loedel simultaneous with her proper time of t'=2 sent at a distance of 1.5 ly away from her. At t'=4, the pink light travelled a total of 3 ly in two of her years according to her watch so the c' of this light was 3/2 = 1.5c.
Ok, so what? How do I get from c'=1.5c the same result of 4-1.5=2.5yrs from Alice's perspective of Bob's t=2? First of all there is no c' in relativity. But using Yv, the light signal using Alice's watch must be faster than her Yv (the velocity according to her watch). If she was going at .8c, her Yv=4/3c, that does not mean she would suddenly be able to beat light, which should be c from all perspectives. v is not the same as v' and neither are c and c'. Nothing can exceed c and that rule is actually preserved by having factors for c when you apply the Y factor to v.
Secondly, Alice can be set as the stationary frame which would mean all the numbers that applied to Bob's perspective would now apply to Alice's. So why is Alice's c' so much higher than Bob's when there should be symmetry between the perspectives? The problem began in Bob's perspective with the assumption that the yellow light took 1.5 of Bob's years to return when in fact it took 2 of his proper years to return just like it took the pink signal 2 of Alice's proper years. The good thing about proper yrs is that they're not subject to Bob's or Alice's perspectives. The Loedel perspective allows a glimpse into proper time which is independent of perspective. Difficult to understand this fine point that a perspective allows a glimpse into proper time which is independent of perspective.
So if you want to depict both perspectives equally on one Md, Bob's equation should really be $(ct')^2 = (ct)^2 - (x/Y_0)^2$ where $Y_0$ =1 and Alices equation should really be $(ct')^2 = (ct)^2 - (x/Y_1)^2$ where $Y_1$ =5/4. c' represents the number of proper years light has travelled although I have not yet proved that mathematically, only empirically so far by doing examples. So for Alice, the light travel is also 1.5 yrs and 4-1.5= Alice 2.5 yrs when Bob sent the signal at t=2 which is the correct reciprocal of Bob's time dilation when his t=2.5, Alice's t'=2.
So plugging these values into the new equation for Alice $(ct')^2 = (ct)^2 - (x/Y_1)^2$:
$2^2 = 2.5^2 - (1.875/1.25)^2$ correct!
You can depict both perspectives on one Md if you alter the main equation in the way I showed.
Last edited: Feb 13, 2021
13. ### ralfcisRegistered Senior Member
Messages:
421
Let's flip the basic graphic unit to see how it would apply to the muon experiment
I'll show the next example (sometime in the future after I answered all of James' questions) using real muon numbers, the above Md is to demonstrate the concept of time dilation from relativity of proper simultaneity.
The first consideration is that since no velocity change has occurred during the journey in from space, the proper times must be the same at the muon's crash landing. (Of course if this flipped graphic unit was joined to the basic one to show how the twin paradox works, the proper times at re-unification would not be the same.) So we count down the numbers from the apex to set the start of the muon's journey at t'=0, 3ly away from Earth. We draw the green line of the Loedel simultaneity to join both zeroes on the ct and ct' axes. The hyperbolic purple line from the main equation is also drawn in to join the zeroes. I've also added the blue lines of the stationary perspective simultaneity to make it easier to follow how relativity of simultaneity causes time dilation in this race to Earth. Again it has to do with the perspective of when the race starts as opposed to any notion of time slowing.
So the bottom blue line says the race began at t=-1 while it actually began at proper time simultaneity of t=t'=0 as seen by the Loedel perspective (of proper time). The length of the velocity line above 0 is the same length as the stationary perspective (both have t=t'=4 years). From Bob's perspective the total time in from the start at t=-1 is 5 of his years. So the time dilation is 5 for Bob, 4 for Alice and the proper relativity of simultaneity is 5-4=1.
In relativity there is no proper relativity of simultaneity only a perspective one. This is shown by Alice's perspective line of simultaneity intersecting at t=.8. So RoS in relativity is -1+.8 = 1.8. The formula for RoS is vx/c^2 so plugging in the values you get .6*3=1.8.
Anyhow Bob's view of the simultaneous start is one year more than the proper time start which is where time dilation really comes from, relativity of simultaneity and not of time slowing. The same can be applied to relativity's notion of length contraction. It's not due to any physical phenomenon of length actually shrinking in the direction of motion and then magically springing back when the motion stops. It's due to relativity of simultaneity. No where in my math of the muon example is time dilation or length contraction mentioned.
14. ### James RJust this guy, you know?Staff Member
Messages:
38,035
ralfcis:
I am replying to your post #69 here. I won't look at your muon experiment one until we reach agreement on this one. If we cannot agree on this one, then I am afraid we will part company on the matter of relativity.
Before I get into the details, I want to tell you the main problem that I'm seeing in your analysis. It is that, while you take into account the different rate at which A's clock ticks relative to B's (i.e. time dilation), you do not take into account that A's measurements of distance are also different from B's. The reason you end up concluding that light signals travel faster than c in A's frame is because you're using the wrong distance units in A's frame. Specifically, instead of using A's rulers, you want A to use B's rulers. You can't do that and get consistent results.
First, I don't know where you get v'=Yv from. That is an incorrect expression for transforming velocities between reference frames. In your example in post #59, things are very simple: B says that A's velocity is (3/5)c, and A says that B's velocity is -(3/5)c.
You also need to be careful to distinguish the velocity of some object or person inside a reference frame from the velocity of the frame itself. This is what the special relativistic velocity addition formula does - it allows us to transform velocities of objects between two reference frames. I should also note that, according to special relativity (hereafter referred to as SR), the speed of anything that travels at velocity c in one frame must be c in every other frame.
To me, it looks like, most of the time, your "Loedel lines" are equivalent to SR's lines of simultaneity, although in several posts above you have made errors when drawing those lines. The ones in post #59 look okay, though.
I should point out that the "Loedel lines" on your graph look like* SR lines of simultaneity for Alice (A). Bob's (B's) lines of simultaneity are horizontal lines on that graph. SR lines of simultaneity, in general, connect points with the same time coordinate in a given frame.
---
* P.S. Further down, you will see that I discovered that your "Loedel lines" are not the same as SR lines of simultaneity, after all. I'm not sure what they are, now.
---
You have not yet responded to tell me whether you agree with my definition of "proper time" or to note that yours is different, so for the moment I will ignore parts of your posts that use that term, until you explain how you define it.
From B's perspective, A has to travel 1.5 ly at a speed of (3/5) light years per year, which will take 2.5 years.
From A's perspective, she travels nowhere (she is stationary in her own frame). Instead, the "finish line" travels towards her at a speed of (3/5)c. The initial distance to the "finish line" is 1.2 ly, according to her own rulers, so it will take 2 years according to her clocks.
Notice that I have used SR length contraction to calculate the "contracted" distance for the trip in A's frame of reference. A must use rulers in her reference frame to measure distances; she can't use B's rulers, because B measures distances differently than she does. This is a consequence of the need to measure the two endpoints of any length interval simultaneously, or else the "length" measurement makes no sense. Since A and B do not agree on which sets of events are simultaneous, similarly they do not agree on the measured lengths of objects - or other distance interval measurements.
Your graph, though, doesn't show A's length measurements. You have shown the time axis in A's frame, in effect - it is the same as her worldline, which you have drawn. Distances in her frame must be measured along lines of simultaneity.
I don't know what your v' is. In A's frame of reference, her speed is zero, because her frame of reference moves with her (obviously). In A's frame, Bob (B) moves with a speed of -0.6c. In B's frame, A moves with a speed of +0.6c and B's speed is zero. Neither of them sees the other, or themselves as travelling at 0.75c.
You can see above how A could calculate B's speed in her frame. She sees B moving away from her, to a final distance (when the finish line, which is also moving in her frame, reaches her) of 1.2 ly. She measures, on her clock, that this takes 2 years, so she can calculate B's speed as (1.2 ly)/(2 years) = 0.6 ly/year = 0.6 c.
Correct. Remember, x is B's coordinate. A must use coordinate x', in her own frame. B does not move in his own x coordinate, but he certainly moves in A's x' coordinate - from, say, x'=0 to x'=-1.2 ly.
I agree. B sees A's regular "tick" signals coming at half the rate, because A is moving away from him and there is a Doppler shift.
Similarly, in her frame, A see's B's signals coming at her at half the rate, because B is moving away from her (at the same speed).
Almost, but not quite right. The encoded message from A will be "I have reached the finish line at the 1.2 ly mark (according to my own stationary rulers) in two ticks of my atomic stopwatch."
I don't know why you say it is inaccurate. Your graph shows that, correctly. We can read off the times from the graph axis. The axes are B's reference frame.
Yes.
If B's watch tells him the race took 2.5 years and A's tells her that the race took 2 years, then it seems bizarre of you to claim that time was running at the same rate for both A and B. If it was, why would their watches end up showing different times? We're assuming these are well-calibrated atomic clocks, aren't we? What went wrong with them?
Correct. B's lines of simultaneity are horizontal on your graph. A's are similar to, but apparently not the same as your "Loedel" lines, on that graph (see below).
No!
SR doesn't have "hyperbolic lines of proper time simultaneity". SR's lines of simultaneity are similar to (but not the same as) your "Loedel lines" - certainly straight lines on your graph in this example.
I think you're possibly confusing SR curves that has a constant value for the quantity $(ct)^2 - x^2$, which obviously has both space and time components, not just time. That quantity is essentially similar to what, in SR, is called the "spacetime interval". Note carefully: spacetime interval, which is not the same as time interval.
origin likes this.
15. ### James RJust this guy, you know?Staff Member
Messages:
38,035
(continued...)
Correct.
Why should there be equivalency? The yellow line shows a light signal sent to B (who is stationary) from a fixed point in space that is 1.5 ly from him. Since the speed of light is c, the signal must take 1.5 years to reach him.
On the other hand, the pink line shows a light signal sent to A, who is continuously moving away from the light source at a speed of 0.6c. The light must "catch up" to A as she moves away from it, and that takes extra time. By the time it gets to her, she is 3 light years away from the source, as measured by B. We can see that clearly on your graph. At the time that B sent that signal, A was 1.2 ly away from him, according to your graph, but she didn't stay at that distance; she moved further away from him.
Again, you're ignoring the fact that A's frame doesn't use B's rulers.
Let's do this using the Lorentz transformations, for clarity. There are two events of interest:
Event 1. B sends the pink signal. This occurs at (x,t)=(0,2 years).
Event 2. A receives the pink signal. This occurs at (x,t)=(3 ly, 5 years).
Note: coordinates here are given in B's frame of reference and can be clearly read from the graph.
Now, from SR, we have $\gamma = 1.25$, due to the speed at which B's frame moves according to A.
Consider event 1. Using the Lorentz transformations, we find:
$x' = \gamma (x-vt) = (1.25)(0-(0.6)(2)) = -1.5$ ly
$t' = \gamma (t-vx/c^2) = (1.25)(2 - 0) = 2.5$ years.
Your graph wrongly indicates that the pink signal was sent at 2 years on A's clocks. In fact, it was sent at 2.5 years, according to A's clocks. That means the green line on your graph is not a line of simultaneity for A. Your "Loedel lines", whatever they are, aren't lines of simultaneity at all, but something else.
I would appreciate it if you explained what your "Loedel lines" are. Previously I assumed they were lines of simultaneity.
The Lorentz transformation makes it clear that when the pink signal is sent (i.e at the time, on A's clocks, when the signal is sent), A is 1.5 ly away from B, as measured using A's rulers. But that corresponds to when A was at a distance of 1.875 ly, as measured by B's rulers.
Thinking about it, maybe the mistake you've made is to draw the line where B measures the distance as 1.5 ly, rather than drawing it where A measures the distance as 1.5 ly. In other words, it might all come back to your error in assuming that A and B share the same rulers.
And for event 2:
$x' = (1.25)(3 - (0.6)(5))=0$
$t' = (1.25)(5 - (0.6)(3)) = 4$ years.
This makes perfect sense. Notice that the receipt of the pink signal happens at x'=0 in A's frame. A is always at x'=0 in her own frame, of course, so if she is receiving the signal, it must occur at x'=0.
The receipt time, according to A's clock, is 4 years, and you apparently agree with that.
---
That brings us to the speed that A calculates for the pink light signal.
According to A, that light signal had to travel 1.5 ly to reach her, and it took 4-2.5 = 1.5 years, so its speed was 1 light year per year in her frame, as expected from SR.
I am still not clear on whether you are trying to replace SR by your own theory, with your own theory having a variable speed of light. Is that what you're trying to do?
Here, you say that the speed of light should be c from all perspectives. But above, you just calculated a c'=1.5c. So which is correct?
Notice that my SR calculation shows a speed of c in both frames of reference: A's and B's. It appears to be only your theory that calculates different speeds for the light in different frames.
I don't understand how you justify applying a Y factor to any v. What are you doing when you do that?
No! Alice's clocks run at different rates from Bob's clocks; you agree with this, apparently. Alice's rulers also are not the same lengths as Bob's rulers; you appear to be consistently ignoring this.
Because you made some mistakes. Because you're trying to use a theory of relativity of your own making - one that is not consistent with SR or with real-world experiments.
Define "proper year".
You're clearly using the term "proper time" in a completely non-standard way. Please define it.
Difficult to understand until you post your definition of "proper time".
Last edited: Feb 14, 2021
origin likes this.
16. ### ralfcisRegistered Senior Member
Messages:
421
Take a look at this video course from Brian Greene:
It talks about much of what I mentioned about special relativity that I don't think you've seen before. It's where I learned relativity before I discovered my own math to predict the same things with a completely different philosophy.
Also take a look at this highly rated post I made on the Physics Stack Exchange:
https://physics.stackexchange.com/q...ing-twin-also-come-back-permanently-length-co
17. ### James RJust this guy, you know?Staff Member
Messages:
38,035
Why add more things for me to look at?
Can't you deal with the questions I have asked you, first?
I'm happy to discuss Brian Greene's video after you have responded to my previous posts, especially posts #58, #71 and #72.
You said you wanted some feedback on your work from somebody who understands Minkowski diagrams. But now that I've given you a lot of feedback, you seem uninterested. Why is that?
Later. After we've discussed the posts above that you haven't responded to.
Last edited: Feb 15, 2021
18. ### Michael 345New year. PRESENT is 72 years oldlValued Senior Member
Messages:
12,964
Looks to me the above is a hook to a
outing
19. ### ralfcisRegistered Senior Member
Messages:
421
Look I'm working on the answers starting with #27. In the meantime I wanted you to see where I got some of my ideas specifically on the definition of length contraction. There is no measuring device for length in relativity besides a clock that is subject to "time dilation" (via relativity of simultaneity). So if your clock is affected so are your measurements of length contraction. The two are the same thing. There is no separate ship odometer or ruler or crunching of matter in relativity but there are methods separate from using a clock, such as the parallax method and super nova candle method, to measure proper distance. Even though time can be permanently altered in the twin paradox, there is no permanent form of length contraction that survives re-unification of the participants. Here's a quick video from Greene:
20. ### originHeading towards oblivionValued Senior Member
Messages:
11,713
Of course there is. For the twin "paradox" the traveling twin will say that less time has passed and the distance traveled was less than that of the earth bound twin. The time difference and the distance difference are both 'permanent'.
21. ### ralfcisRegistered Senior Member
Messages:
421
Constant velocity only results in reciprocal time dilation, not permanent age difference. If Alice leaves at 3/5c and passes by Proxima Centauri 3ly away, she has not aged 1 yr less than Bob just because time dilation says t=5 yrs for Bob and t'=4 yrs for Alice. From Alice's time dilation perspective, Bob has only aged 3.2yrs when her t'=4. She has no odometer reading that says she's only travelled 2.4ly but she does have an on-board clock that says she has travelled 4 yrs. It's relativity that concludes the distance she travelled must have contracted to maintain a constant c from all perspectives. Or she can trust her clock and her star charts and Yv= x/t' = 3/4c while v from Bob's perspective is 3/5 c and Alice can verify that her relative velocity to Bob is also 3/5c because her measurable DSR = .5. Relative velocity v is not the same thing as Yv, only v as a relative velocity is subject to being limited by c but Yv is not technically a relative velocity the same way v is.
So if Alice stops at Proxima Centauri, I say she can say she has permanently aged 1 yr less than Bob by comparing light messages between them but relativity can't say that because their atomic clocks are not co=located and still subject to other perspectives. So Alice has to turn back to Bob and if she does it at 3/5c, their atomic clocks will show she has aged 2 yrs less than Bob.
Not correct. The reason Alice aged 2 yrs less is because the earth twin didn't travel any distance at all so it's because she travelled all of the distance and because of the main formula:
$ct'^2 =ct^2 - x^2$
notice the minus sign, distance subtracts from time in a spacetime path. So according to the formula, ct'=8 for Alice, ct=10 for Bob and x=6 (roundtrip of 3ly). 3ly not 2.4 ly! There is no record of any length contraction. It's exactly the same length as the star charts. There is also no physical odometer that recorded any length contraction. There is no physical evidence that the space between earth and proxima centauri was contracted by the ship which somehow had the power to draw an entire star system closer to earth. All we have is the philosophy that if c is the same from all perspectives, a conclusion that agrees with the MMX, then length contraction is the only possible explanation. I have another explanation that also does not violate the results of the MMX.
22. ### James RJust this guy, you know?Staff Member
Messages:
38,035
You can go through all my posts in order if you like, but I'm trying to save you some time by pointing you towards posts #58, #71 and #72. Up to you.
Wrong. In principle, somebody could use a wooden ruler - or, say, a whole bunch of wooden rulers connected end-to-end if a much longer ruler was needed.
I already explained what a reference frame is to you, in some detail, along with how observers in that frame can take measurements of events in spacetime. I guess you'll get to replying to that post later (?)
I don't have much interest in quibbling with you. A measurement of length of obviously not the same thing as a measurement of time. However, I agree with you that time dilation and length contraction are both effects that derive from the same cause - namely the nature of spacetime itself, or from the postulates of special relativity, if you prefer.
I can't comment until you define "proper distance". I have asked you many times to do that, now, but you still haven't done it. The only thing I know so far is that whatever you think "proper distance" is, it isn't the way that it is usually defined by those (like me) who understand special relativity.
I agree with you that the elapsed time on different clocks can be permanently altered as a result of relative motion. I also agree with you that whenever two observers come to rest relative to one another, they will agree on all length measurements, so that in that sense length contraction is no "permanent". Nothing important turns on that.
I'm not going to watch any videos until you have responded, at least, to post #58 and/or #71/72.
Greene agrees with me, by the way, about special relativity.
23. ### James RJust this guy, you know?Staff Member
Messages:
38,035
Agreed.
For Alice, subjectively, the trip only took 4 years, so she only aged biologically 4 years. Bob, on the other hand, says the trip took 5 years, but to him Alice's clocks (including her biological age) appeared to be ticking slowly as she travelled, so that she only aged 4 years biologically while Bob aged 5 years biologically. From Alice's point of view, Bob travels away from her to a distance of 2.4 ly at a speed of 3/5c while she remains at rest in her frame, so the trip takes 4 years. But in Alice's frame, Bob's clocks tick slow, so Bob only apparently ages 3.2 years during Alice's 4 year trip.
Correct. We are in agreement.
She could measure the distance in any number of different ways, in principle. If Bob can measure the distance as 3 ly, then Alice could use exactly the same procedure (whatever it is) to measure the distance as 2.4 ly.
Yes.
Yes.
You're wasting time posting "new" examples of the same thing. You should instead spend your time addressing the comments I put to you regarding your scenario in posts #71 and #72.
I don't know what your Yv is supposed to represent, and it is clear that you are mixing frames inappropriately whenever you write something like x/t', rather than x'/t'.
It appears to be the case, though you will not confirm, that you think different observers all agree on length measurements. They do not. Not if SR is correct. You seem scared to say whether you are claiming that SR is incorrect or not. It would be good for you to clarify your position. Are you proposing an alternative theory to SR? Are you pointing our what you believe to be errors in SR? Or what?
What is Yv? Why is it useful?
Why do we need to worry about Yv? What is it, physically?
If Alice stops, then she has accelerated. In that case, the symmetry between Alice and Bob's frames is broken, because Alice accelerates while Bob does not. That acceleration can certainly result in a "permanent" discrepancy between their clock readings, and thus their ages.
You say that "relativity can't say that", but it can and it does. There's a myth that SR can't handle accelerations. It can, but the maths is more complicated since we have to approximate a non-inertial frame of reference by a whole bunch of approximately-inertial frames, then add up cumulative effects of all the frame changes. In practice, it requires integration. However, fortunately we can avoid all of that mess by looking at a spacetime diagram like the one I analysed in posts #71 and #72, above.
The way you're using that formula doesn't really make much sense, seeing as it is, essentially, a formula about the SR spacetime interval. I think that, probably, you don't understand where it comes from or what it actually means. Also, clearly, you don't understand that you're using a special case of the formula, in which x'=0. Obviously, in this specific example, Alice remains at x'=0 at all times, but Alice travels in Bob's x coordinates. So, if you're going to calculate some kind of spacetime interval for Alice's trip, of course you're going to have Alice's trip distance being non-zero in Bob's x coordinates, while it is zero in Alice's x' coordinates.
But none of that is very important, because you're using that formula incorrectly anyway. While the answer you pull out of it makes some kind of sense, that's more by accident than by design.
I could walk you through what that formula is really doing, but showing you actual spacetime intervals in the two frames, but I won't do that until you've responded to previous posts of mine, especially #58 or #71/72.
Rulers typically don't keep records. A stopwatch, on the other hand, records elapsed time.
Bob's star charts are drawn up based on measurements of distance made in Bob's reference frame. Alice could just as well draw up her own star charts while she is moving relative to the stars, but her distances would all be contracted in the direction of her motion, compared to Bob's distances in that direction.
It's probably better if you think about it this way: when Alice changes her state of motion with respect to the star system, she doesn't alter anything about the star system itself. She doesn't "draw it closer to Earth". Instead, she changes her own perception of space and time. She "rotates" her perception in a strange way - one that is described precisely by the Lorentz transformations of SR.
You apparently agree that when Alice moves, her perception and records of time change, compared to Bob's. But you're not claiming that Alice magically altered Bob's clocks. So why are you claiming that Alice magically alters Bob's distances? We're talking about the same thing, just with distance instead of time. Alice alters herself when she moves. She doesn't change the world around her. She doesn't change spacetime.
No you don't. Different observers measure different speeds of light if we use your "explanation", which is contrary to actual experiments, including the Michelson-Morley experiment. | 2023-03-28 02:57:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6367522478103638, "perplexity": 895.5906449734881}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948756.99/warc/CC-MAIN-20230328011555-20230328041555-00491.warc.gz"} |
https://socratic.org/questions/how-is-wave-refraction-measured#545781 | # How is wave refraction measured?
This allows you to calculate the refractive index $n$ of the material, which is defined as $n = \frac{\sin i}{\sin r}$, and generally has a value $1.003 < n < 2.43$.
From this you can find the speed of light in the material as $n = \frac{c \left(v a c u u m\right)}{c \left(m a t e r i a l\right)}$ | 2022-01-24 23:01:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 4, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9563850164413452, "perplexity": 112.72909131894197}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304686.15/warc/CC-MAIN-20220124220008-20220125010008-00144.warc.gz"} |
http://ieeexplore.ieee.org/xpl/tocresult.jsp?reload=true&isnumber=5009397&punumber=12 | # IEEE Transactions on Computers
## Filter Results
Displaying Results 1 - 22 of 22
• ### [Front cover]
Publication Year: 1985, Page(s): c1
| PDF (548 KB)
• ### IEEE Computer Society
Publication Year: 1985, Page(s): nil1
| PDF (182 KB)
• ### [Breaker page]
Publication Year: 1985, Page(s): nil1
| PDF (182 KB)
• ### The Exclusive-Writer Approach to Updating Replicated Files in Distributed Processing Systems
Publication Year: 1985, Page(s):489 - 500
Cited by: Papers (9) | Patents (10)
| | PDF (3179 KB)
Consistency control protocols can be classified as either pessimistic or optimistic. Pessimistic protocols check for conflicting file accesses before a transaction references shared files; this prevents transaction restarts but adds intercomputer synchronization delays to execution response times TE. Optimistic protocols avoid intercomputer synchronization delays for TE, but ... View full abstract»
• ### The Structure of Periodic Storage Schemes for Parallel Memories
Publication Year: 1985, Page(s):501 - 505
Cited by: Papers (29) | Patents (2)
| | PDF (1995 KB)
The use of parallel memories in SIMD machines requires special data mappings, known as skewing schemes,'' for storing matrices for the purposes of efficient vector computations. Some schemes have explicitly been implemented in current super-computers. Periodic skewing schemes are of particular interest because they have a regular structure and can be represented by simple formulas. In this paper... View full abstract»
• ### A Versatile Mechanism to Move Data in an Array Processor
Publication Year: 1985, Page(s):506 - 522
Cited by: Papers (7) | Patents (2)
| | PDF (3239 KB)
Selection of elements and alignment of operands are fundamental operations on data, just as are arithmetic operations. Whereas sophisticated algorithms have been devised for the latter, vector processors usually lack a flexible and efficient routing unit. This is especially true of SIMD computers, to which the present study is devoted. Examples of required manipulations are: transfer, shift, diffu... View full abstract»
• ### Symmetric Minimal Covering Problem and Minimal PLA's with Symmetric Variables
Publication Year: 1985, Page(s):523 - 541
Cited by: Papers (7)
| | PDF (3900 KB)
This paper first discusses the symmetric property of the minimal covering problem in terms of group theory and then the use of this property in the branch-and-bound method for solving the problem. Computational results on solving sample problems are shown to demonstrate the improvement of computational efficiency of the branch-and-bound method by the utilization of the symmetric property. The samp... View full abstract»
• ### On Permuting Properties of Regular Rectangular SW-Banyans
Publication Year: 1985, Page(s):542 - 546
Cited by: Papers (10)
| | PDF (963 KB)
This correspondence analyzes the permuting properties of a reconfigurable multicomputer architecture based on a regular rectangular SW-banyan interconnection network with arbitrary fan-out and an arbitrary number of stages. An analytical expression for the total number of distinct permutations performable by a rectangular SW-banyan (in one pass) is derived. It is shown how the combinatorial power ... View full abstract»
• ### Complete Binary Spanning Trees of the Eight Nearest Neighbor Array
Publication Year: 1985, Page(s):547 - 549
Cited by: Papers (3)
| | PDF (641 KB)
Complete binary spanning trees of an n x n array of processors with an eight nearest neighbor interconnection pattern exist for a limited value of n. These spanning trees provide a fast route to accumulate information from all processors of the array, and allow certain problems to be solved as efficiently on an eight-neighbor array as on a tree-structured array. The condition under which complete ... View full abstract»
• ### Combinatorial Approach to Multiple Contact Faults Coverage in Programmable Logic Arrays
Publication Year: 1985, Page(s):549 - 553
Cited by: Papers (9)
| | PDF (924 KB)
The increasing number of applications of programmable logic arrays (PLA's) has evoked the development of test generation methods for these circuits. There are known methods for complete single contact fault detection test set generation. These test sets fail to detect all multiple faults in a PLA due to the phenomenon of masking. In this correspondence, we present a method to quantitively predict ... View full abstract»
• ### Detecting I/O and Internal Feedback Bridging Faults
Publication Year: 1985, Page(s):553 - 557
Cited by: Papers (16)
| | PDF (1024 KB)
The testing of bridging faults (short circuits) has become increasingly important with the increasing density in VLSI (very large scale integration) chips. Yet very little work has been done in this area. In this correspondence, based on a two-state sequential machine model, we present the conditions for a circuit with feedback bridgings to oscillate and to exhibit stable sequential behavior. It i... View full abstract»
• ### SEC-BED-DED Codes for Error Control in Byte-Organized Memory Systems
Publication Year: 1985, Page(s):557 - 562
Cited by: Papers (17) | Patents (5)
| | PDF (1236 KB)
SEC-ED-DED codes are single error correcting and double error detecting while simultaneously providing byte error detection. SEC-BED-DED codes are constructed for byte lengths of 5 and larger. For many byte lengths and code lengths, these codes require fewer check bits or have implementation advantages when compared to other SEC-BED-DED codes. View full abstract»
• ### Counting Sequences with Large Local Distance
Publication Year: 1985, Page(s): 562
| | PDF (225 KB)
The 2n n-bit vectors can be ordered so that any vector in the sequence has some minimum Hamming distance from any vector near it in the sequence. View full abstract»
• ### A Maximally Parallel Balancing Algorithm for Obtaining Complete Balanced Binary Trees
Publication Year: 1985, Page(s):563 - 565
Cited by: Papers (9)
| | PDF (589 KB)
We present a new iterative balancing algorithm for binary trees of size N = 2n -1 by exploiting the similarity of pointer restructuring at each level. We also extract parallelism from this algorithm to yield a constant time complexity balancing algorithm for an N-processor configuration. This achieves the theoretical limit of speedup possible. View full abstract»
• ### Insertion Networks
Publication Year: 1985, Page(s):565 - 570
| | PDF (802 KB)
The problem of inserting an item in a list is frequently encountered in various application fields such as sorting, compiling, etc. It is shown that the insertion of an item in a list of N members may be realized at a cost proportional to N and within a delay proportional to log N. View full abstract»
• ### Some Aspects of the Dynamic Behavior of Hierarchical Memories
Publication Year: 1985, Page(s):570 - 573
Cited by: Papers (1)
| | PDF (828 KB)
In a computer system with a cache memory, the cache is effectively empty following a job switch, leading to a low hit rate and consequently lowered performance until the cache becomes reasonably full. The analysis shows that a job must run for several milliseconds before the average performance approaches that expected from a steady-state analysis. Care may therefore be needed in designing memory ... View full abstract»
• ### A Radix-4 FFT Using Complex RNS Arithmetic
Publication Year: 1985, Page(s):573 - 576
Cited by: Papers (32)
| | PDF (562 KB)
Recent advancements in residue arithmetic have given rise to a complex number system variant which better than halves RNS multiplication complexity. This advantage is applied to the problem of implementing a high-speed radix-4 RNS FFT. It is shown that a significant improvement in both complexity and speed can be achieved. View full abstract»
• ### Polynomial Division on Systolic Arrays
Publication Year: 1985, Page(s):577 - 578
Cited by: Papers (8)
| | PDF (361 KB)
In this correspondence we show how long division of polynomials can be performed in a pipelined fashion on a linear systolic array in linear time. View full abstract»
• ### A Hypergraph Model for Fault-Tolerant VLSI Processor Arrays
Publication Year: 1985, Page(s):578 - 584
Cited by: Papers (14)
| | PDF (1325 KB)
We study here a formal version of a strategy for constructing fault-tolerant VLSI processor arrays in an environment of wafer-scale integration. The strategy achieves tolerance to faults by running buses past the implemented PE's and interconnecting the fault-free ones into an array of the desired structure by having PE's tap into the bank of buses. Earlier studies [12] have shown this strategy to... View full abstract»
• ### Correction to "Computational Geometry - A Survey"
Publication Year: 1985, Page(s): 584
Cited by: Papers (5)
| | PDF (155 KB)
First Page of the Article
View full abstract»
• ### IEEE Computer Society Publications
Publication Year: 1985, Page(s): nil2
| PDF (178 KB)
• ### [Front cover]
Publication Year: 1985, Page(s): c2
| PDF (200 KB)
## Aims & Scope
The IEEE Transactions on Computers is a monthly publication with a wide distribution to researchers, developers, technical managers, and educators in the computer field.
Full Aims & Scope
## Meet Our Editors
Editor-in-Chief
Paolo Montuschi
Politecnico di Torino
Dipartimento di Automatica e Informatica
Corso Duca degli Abruzzi 24
10129 Torino - Italy
e-mail: pmo@computer.org | 2017-12-12 20:12:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1805090457201004, "perplexity": 6782.550401677244}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948517917.20/warc/CC-MAIN-20171212192750-20171212212750-00135.warc.gz"} |
https://notasrigorosas.pt/agen-milo-qsnjg/3cca51-difference-between-symmetric-and-asymmetric-fission | The Difference Between Symmetric and Asymmetric Key Cryptography Main Facts Symmetric key cryptography (also called Secret key cryptography) features one key that two people can use to encrypt and decrypt data send between themselves. Difference Between Asymmetrical And Symmetrical Light Distribution Dec. 3rd, 2017 For lighting designing, there are usually two options of light beams to choose when it comes to choose the right luminaire for a specific lighting project, symmetrical beam or asymmetrical beam. The Types and Complexities of the Encryption Algorithms. Symmetric encryption is an old technique, while asymmetric encryption is the newer one. L80 >60,000 hours at 25C ambient temperature. Symmetric encryption heavily relies on the fact that the keys must be kept secret. Explain the difference between symmetric and asymmetric encryption and describe at least one advantage and one disadvantage of each type of encryption. However, they behave quite differently. The figure at the right shows two sequences of shapes, "Red" and "Red ∪ Green". Widely used symmetric encryption algorithms include AES-128, AES-192, and AES-256. Let's examine the primary differences between symmetric and asymmetric balls: 1. The main difference between symmetric and asymmetric encryption is that the symmetric encryption uses the same key for both encryption and decryption while the asymmetric encryption uses two different keys for encryption and decryption.. I was watching this short video and apparently every time users set an HTTPS connection, a handshake between client & server happens. As we know the mass and energy distributions of thermal neutron induce fission of {235}^U is asymmetric and be symmetric for fast neutron induced fission of {235}^U. Through 4 bonds: Carbon that binds at least 2 of the same group is called “Symmetric Carbon”. October 1, 2018. Symmetric Key Encryption: Encryption is a process to change the form of any message in order to protect it from reading by anyone. In mathematics, a relation is a set of ordered pairs, (x, y), such that x is from a set X, and y is from a set Y, where x is related to yby some property or rule. September 22, 2018. Optics Advanced asymmetric optical system optimized for LED source and arrayed for specific lumen output and distribution. When rhodium (atomic number 45) is produced with some probability (cross section), silver (atomic number 47) is the counter fragment. While communicating on an unsecured medium like the internet, you have to be careful about the confidentiality of the information you are sharing with other. On the other hand, asymmetric encryption uses the public key for the encryption, and a … It means that the sender and the receiver share the same key. Recent studies of the mass and energy distributions from fission of nuclei lighter than Ra at low and moderate energies are reviewed in order to inquire into problems related to the boundaries of the fission asymmetry, distinct fission modes, complexity of the fission fragment mass and energy distributions. Once the secure channel is created using the asymmetric encryption, the symmetric key is transferred and a new encrypted channel setup that is much faster. Results The number of crypts in fission in the 89 sections was 3586; of those, 2930 (81.7%) were asymmetric and the remaining 656 (18.3%), symmetric. Difference Between Symmetric and Asymmetric Key Encryption Last Updated: 28-06-2020. When the Hausdorff distance between them becomes smaller, the area of the symmetric difference between them becomes larger, and vice versa. Also, for isotopes at the upper limit of the sizes that have been studied (near the shores of the "island of stability"), I believe fission is often predicted to be symmetric. Common asymmetric encryption techniques include RSA, DSA, and PKCS. 3. The main difference between symmetric and asymmetric multiprocessing is that, in symmetric multiprocessing, the CPUs are identical and they share the main memory while, in asymmetric multiprocessing, the CPUs are not identical and they follow slave-master relationship.. A processor or the CPU is an important component in the computer. In Summary: In the Debate of Symmetric vs Asymmetric Encryption, Both Are Important. The probability of mass-asymmetric fission decreases significantly with increasing excitation energy, from $\ensuremath{\approx}70$ to $\ensuremath{\approx}40%$ over a 10-MeV range. Distributing the key in a secure way is one of the primary challenges of symmetric encryption, which is known as the “ key distribution problem. Asymmetric encryption is an encryption model that requires two keys, for example, Key A and Key B. Antisymmetric means that the only way for both $aRb$ and $bRa$ to hold is if $a = b$. Symmetric encryption uses a private key to encrypt and decrypt an encrypted email. We’ve just about gone over all the main concepts around symmetric vs asymmetric encryption. Asymmetric multiprocessing is the use of two or more processors handled by one master processor. Asymmetric encryption uses the public key of the recipient to encrypt the message. By now, queries around “what is the difference between symmetric and asymmetric encryption” and “symmetric key vs asymmetric key” should have been cleared up. The Hausdorff distance and the (area of the) symmetric difference are both pseudo-metrics on the set of measurable geometric shapes. This is very important reason why ONLY OVERHEAD two post lifts should be used to lift heavier vehicles in an a "TRUE" asymmetric configuration (30/70). Keeping the private keys. Here's something interesting! Difference between Asymmetric and Symmetric Multiprocessing. This type of encryption is relatively new as compared to symmetric encryption, and is also referred to as public-key cryptography. . Symmetric Encryption. Asymmetric encryption is the more secure one, while symmetric encryption is faster. The are two techniques use to preserve the confidentiality of your message, Symmetric and Asymmetric Encryption. For the fissioning Fm and No nuclei, the transitions from a two-peaked to a single-peaked mass distributions are predicted. In the case of low-energy fission of pre-actinides, the mass/charge distribution shows a single central maximum, while the same distributions resulting from the fission of U–Cf nuclei exhibit two maxima. It works in such a way that the information that Key-A can encrypt while Key-B can decrypt. Asymmetric encryption. Binary fission mainly occurs in paramecium, archaea, amoeba, and bacteria; conversely, budding occurs in plants, parasites, fungi, yeast, hydra, and metazoans like … They interchange the public keys. September 29, 2018. Binary fission mainly occurs in paramecium, archaea, amoeba, and bacteria; conversely, budding occurs in plants, parasites, fungi, yeast, hydra, and metazoans like … Load more Key differences. 3. Symmetric encryption is a simple technique compared to asymmetric encryption because only one key is used to undertake both encryption and decryption. Asymmetric encryption, on the other hand, requires the use of two separate keys i.e., a … The roots of encryption date back to the times of the great Julius Caesar. Before getting to the difference between Symmetric and Asymmetric encryption, let’s clear a few concepts first. Then if the recipient wants to decrypt the message the recipient will have to use his/her private key to decrypt. The U.S. Department of Energy's Office of Scientific and Technical Information Symmetric encryption uses a single key that needs to be shared among the people who need to receive the message while asymmetrical encryption uses a pair of public key and a private key to encrypt and decrypt messages, Then if the recipient wants to decrypt the message the recipient will have to use his/her private key to decrypt. It becomes more vital when exchanging confidential data. The first variance that makes the two different is that symmetric encryption uses one key to both encrypt and decrypt the information (Kahate, 2013). Symmetric encryption uses a private key to encrypt and decrypt an encrypted email. Usually, these keys can be used interchangeably such that if you use Key A to encrypt data, you can use Key B to decrypt this information, and if you use Key B to encrypt information, you can decrypt the same information using Key A. Difference Between Symmetric and Asymmetric Encryption. Exactly, the total mass of the asymmetric fission products are higher than the total mass of the symmetric products. Copyright © 2020 Elsevier B.V. or its licensors or contributors. The difference between symmetric and asymmetric coroutines is described particularly well by Ana Lúcia de Moura and Roberto Ierusalimschy in their paper "Revisiting Coroutines":A well-known classification of coroutines concerns the control-transfer operations that are provided and distinguishes the concepts of symmetric and asymmetric coroutines. They’re both very effective in different ways and, depending on the task at hand, either or both may be deployed alone or together. However, in symmetric encryption, the message is encrypted and decrypted using the same key. https://doi.org/10.1016/j.nuclphysa.2017.10.001. First, let’s recall that carbon can share 4 electrons, thus has 4 bonds that can bind a maximum of 4 different groups through 4 single bonds. In asymmetric encryption, the message is encrypted using the public key, and the private key is used to decrypt the message. Nuclear Physics AS02 (1989) 243c-260c North Holland, Amsterdam 243 c SYMMETRIC AND ASYMMETRIC FISSION OF NUCLEI LIGHTER THAN RADIUM Michael G. Itkis, Vladimir N. Okolovich, Georgi N. Smirenkin Nuclear Physics Institute, SU-480082, Alma-Ata, USSR Recent studies of the mass and energy distributions from fission of nuclei lighter than Ra at low and moderate energies are … Symmetrical Core (undrilled) - A ball where the RG (radius of gyration) values of the Y (high RG) and Z (intermediate RG) axes of the ball do not differ by more than 5% of the total differential of the ball. Such fault occur between line to ground and two lines. Binary fission is generally considered as symmetric division; on the contrary, budding is usually considered as an asymmetric division. Symmetric keys are frequently 128 bits, 192 bits, and 256 bits, whereas asymmetric keys are recommended to be 2048 bits or greater. What is the difference between symmetric and asymmetric encryption? Symmetric keys are also typically shorter in length than their asymmetric counterparts. In symmetric encryption, the sender and receiver use a separate instance of the same key to encrypt and decrypt messages. Get more help from Chegg. Asymmetric information. Symmetric encryption is an old technique while asymmetric encryption is relatively new. Let's examine the primary differences between symmetric and asymmetric balls: 1. Copyright © 2020 Elsevier B.V. or its licensors or contributors. Thus, the nuclear fission observed by Nishina and Kimura is highly symmetric. By continuing you agree to the use of cookies. On each side, the public-private key pair is generated using an algorithm called RSA. Comparisons between the three Bi isotopes hint at an increase in the mass-symmetric fission yield with increasing neutron number, which could be due to a decrease in the difference between the symmetric and asymmetric fission barriers. http://www.gregsmithequipment.com/Shop/2-Post-Lifts - What is the difference between symmetric and asymmetric? This is howeve… We use cookies to help provide and enhance our service and tailor content and ads. Thus, the nuclear fission observed by Nishina and Kimura is highly symmetric. Difference Between Symmetric and Asymmetric Key Encryption Last Updated: 28-06-2020. By continuing you agree to the use of cookies. As seen in Figure 6.2, thermal fission of 235U leads overwhelmingly to asymmetric fission.9 The fission yield is dominated by cases where one fragment has a mass number A between about 89 and 101, and the other has a mass number between about 133 and 144. Out of 927 vertically-cut crypts (in well-oriented sections), 912 (98.4%) were asymmetric, and the remaining 14 (1.6%), symmetric, and out 2660, cross-cut (transected) crypts in fission, 2018 (75.9%) were asymmetric and the remaining 642 … For example, ${}^{180}\text{Hg}$ is found to undergo symmetric fission, and that finding is reproduced in the potential energy surface calculated by Ichikawa. The fundamental difference that distinguishes symmetric and asymmetric encryption is that symmetric encryption allows encryption and decryption o… Shunt faults are Single Line to Ground fault (L-G) Fault, Line to Line fault (L-L Fault),Line to Line To Ground fault(L-L-G) fault as shown in figure below. The daughter product of natural fission has a heavy fraction plateau range that lies between about 131 and 145 nucleons with a center of 138 nucleons. With decreasing Z and A of the fissile nucleus, the fission- OSTI.GOV Conference: From symmetric cold fission fragment mass distributions to extremely asymmetric alpha decay One of the big differences between symmetric vs asymmetric encryption is the types of encryption algorithms used in each process. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. Transitions between symmetric and asymmetric modes in the region of heavy actinides. http://www.gregsmithequipment.com/Shop/2-Post-Lifts - What is the difference between symmetric and asymmetric? Difference Between Monoalphabetic Cipher and Polyalphabetic Cipher. Explanation: Asymmetric algorithms can use very long key lengths in order to avoid being hacked. As discussed in the comparison between overhead and base plate lifts; the overhead two post lift offers more stability than the base plate two post lift because of the overhead beam between the columns. We use cookies to help provide and enhance our service and tailor content and ads. If we let F be the set of all f… Using the improved scission-point model, the mass and charge distributions of fragments resulting from the fission of californium, fermium, and nobelium isotopes are calculated and compared with the available experimental data. Findings These bonding differences between layers result from varying number of protons sites that are filled on each layer. Asymmetric encryption, also called as public key cryptography, is a relatively new method which uses two keys, a private key and a public key, to encrypt and decrypt data. When rhodium (atomic number 45) is produced with some probability (cross section), silver (atomic number 47) is the counter fragment. Difference Between Symmetric and Asymmetric Encryption. Antisymmetric means that the only way for both $aRb$ and $bRa$ to hold is if $a = b$. Encryption & Cryptographic Keys. In the same way, ruthenium (atomic number 44) and cadmium (atomic number 48) are the pairing fragments. Symmetric encryption uses a single key that needs to be shared among the people who need to receive the message while asymmetric encryption uses a pair of public key and a private key to encrypt … The main difference between symmetric and asymmetric encryption is that the symmetric encryption uses the same key for both encryption and decryption while the asymmetric encryption uses two different keys for encryption and decryption.. But that means the binding energy released in the fission is higher for the symmetric products, since difference in mass of the parent nuclei and its products is larger. Difference between Symmetric and Asymmetric Encryption. Caesar used this technique to send his confidential messages. Most of our customers ask that question. © 2017 Elsevier B.V. All rights reserved. What is the difference between symmetric and asymmetric encryption? Asymmetric encryption algorithms, on the other hand, include algorithms … spectrum near Z=46, i.e. The primary difference between these two types of encryption is that, with Symmetric encryption, the message to be protected can be encrypted and decrypted using the same key. Think $\le$. Landlords who know more about their properties than tenants; Mortgages: A borrower knows more about their ability to repay a loan than the lender, insufficient checks might be made Asymmetric being slower is a major disadvantage, so many crypto create a one time symmetric encryption key and then use asymmetric encryption to create a secure channel. The transition between asymmetric and symmetric fission modes with the variation of neutron number is shown to be related to the change of the potential energy surface at scission point. The basic idea behind a symmetric and asymmetric key is to have the ability to encrypt and decrypt a secret message using a secret key. 1. Difference Between Symmetric and Asymmetric Encryption. Asymmetric Multiprocessing. It is important to ensure that information shared over the internet is secure. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. Symmetric and asymmetric fission of nuclei lighter than radium. It handles arithmetic and logical operations and … All CPUs are interconnected but are not self-scheduling. This key is meant to keep the message exchange (or store) secure and only readable by trusted parties.. Symmetric Key Encryption: The key difference between symmetric and asymmetric top molecules is that symmetric top molecules have one proper rotation axis and two moments of inertia that are equal to each other whereas asymmetric top molecules have all the principal components of the moment of inertia different from each other.. Asymmetric encryption uses the public key of the recipient to encrypt the message. Symmetric Key Encryption: Encryption is a process to change the form of any message in order to protect it from reading by anyone. Copyright © 1989 Published by Elsevier B.V. https://doi.org/10.1016/0375-9474(89)90665-9. Most of our customers ask that question. Symmetric algorithms are typically hundreds to thousands of times slower than asymmetric algorithms. Computers Computer Network Computer Engineering. Think $\le$. Suppose that Riverview Elementary is having a father son picnic, where the fathers and sons sign a guest book when they arrive. It is important to ensure that information shared over the internet is secure. The key difference between symmetric and asymmetric karyotype is that symmetric karyotype shows a smaller difference between the smallest and largest chromosomes in the set while asymmetric karyotype shows a larger difference between the smallest and largest chromosomes in the set.. A karyotype is a diagram which shows the correct number and structure of the complete set of … asymmetric distribution in 3000K, 3500K or 4000K color temperature options. midway between Z=36 and 56, which are common f.p.s However, even spontaneous fissions are asymmetric which would indicated that internal resonances are asymmetric. Asymmetric encryption is relatively complex in nature, because separate cryptographic keys are used to carry out both operations. Results The number of crypts in fission in the 89 sections was 3586; of those, 2930 (81.7%) were asymmetric and the remaining 656 (18.3%), symmetric. Symmetric keys are identical, whereas asymmetric public and private keys are mathematically related yet still unique. One such feature is the physical origin of the transition between the symmetric and asymmetric fission modes , , , , , , , , , , , , . As seen in Figure 6.2, thermal fission of 235U leads overwhelmingly to asymmetric fission.9 The fission yield is dominated by cases where one fragment has a mass number A between about 89 and 101, and the other has a mass number between about 133 and 144. Symmetric encryption uses a single key that needs to be shared among the people who need to receive the message while asymmetrical encryption uses a pair of public key and a private key to encrypt and decrypt messages when communicating. In the same way, ruthenium (atomic number 44) and cadmium (atomic number 48) are the pairing fragments. A 665, 221 (2000)] in which fission-fragment charge distributions were obtained for 70 nuclides, asymmetric distributions were seen above nucleon number A ≈ 226 and symmetric ones below. It can be reflexive, but it can't be symmetric for two distinct elements. Difference Between Kernel and Operating System. This type of fault mainly have two types (a) shunt fault (b) series fault. Hopefully, you now have an understanding of the difference between symmetric encryption vs asymmetric encryption. The Difference Between Symmetric and Asymmetric Key Cryptography Main Facts Symmetric key cryptography (also called Secret key cryptography) features one key that two people can use to encrypt and decrypt data send between themselves. Symmetrical Core (undrilled) - A ball where the RG (radius of gyration) values of the Y (high RG) and Z (intermediate RG) axes of the ball do not differ by more than 5% of the total differential of the ball. Finish Symmetric encryption algorithms are either block ciphers or stream ciphers, and include algorithms like DES, TDEA/3DES, AES, etc. Comparisons between the three Bi isotopes hint at an increase in the mass-symmetric fission yield with increasing neutron number, which could be due to a decrease in the difference between the symmetric and asymmetric fission barriers. Components are designed to be serviceable and replaceable. Asymmetric information is when there is an imbalance in information between buyer and seller which can distort choices Examples. the asymmetric components, which were obtained as the difference between the total and the extrapolated symmetric yield Y~(M)= Y(M)-Y~(M) [4]; and the dependencies of the average kinetic energy and of the variance of that on the fragment mass. Binary fission is generally considered as symmetric division; on the contrary, budding is usually considered as an asymmetric division. This results in the use of significantly increased resources and time compared to symmetric algorithms. The term symmetric and asymmetric top molecules come under the classification of … The key difference between symmetric and asymmetric top molecules is that symmetric top molecules have one proper rotation axis and two moments of inertia that are equal to each other whereas asymmetric top molecules have all the principal … Unlike symmetric encryption, it uses a pair of keys to encrypt and decrypt data; one key is used to encrypt the data and the other key is used to decrypt the data. Example of Series fault is open conductor circuit. I was thinking mainly of fast neutrons, which result in more symmetric fissions as is evidenced by the proportion of the f.p. The fundamental difference that distinguishes symmetric and asymmetric encryption is that symmetric encryption allows encryption and decryption of the message with the same key. This list of fathers and sons and how they are related on the guest list is actually mathematical! 2. It becomes more vital when exchanging confidential data. It can be reflexive, but it can't be symmetric for two distinct elements. Now that we have a basic understanding of both the encryption types, let’s glance through the key differences between them. Just about gone over all the main concepts around symmetric vs asymmetric encryption a! Asymmetric key encryption: encryption is relatively new as compared to symmetric algorithms are hundreds... Must be kept secret HTTPS connection, a handshake between client & server happens son picnic where! Rsa, DSA, and PKCS the area of the same key to encrypt the message on. Both the encryption types, let ’ s glance through the key differences between them becomes smaller, the of! To ensure that information shared over the internet is secure Key-B can decrypt you agree the. 4 bonds: Carbon that binds at least 2 of the difference between symmetric and asymmetric balls:.! Encryption techniques include RSA, DSA, and the ( area of same... Explanation: asymmetric algorithms when there is an imbalance in information between buyer and seller can. The public key, and AES-256 symmetric division ; on the guest is... Describe at least 2 of the recipient to encrypt and decrypt an encrypted.... Than their asymmetric counterparts let ’ s clear a few concepts first which can distort choices Examples are. Processors handled by one master processor arrayed for specific lumen output and.! Separate cryptographic keys are used to carry out both operations number 44 ) and cadmium ( number. A guest book when they arrive is actually mathematical distinct elements other hand, requires the use two! Two-Peaked to a single-peaked mass distributions to extremely asymmetric alpha decay difference between symmetric and asymmetric encryption is relatively in! Red difference between symmetric and asymmetric fission Green '' symmetric Carbon ” it from reading by anyone while symmetric is. Was thinking mainly of fast neutrons, which result in more symmetric fissions as is evidenced by proportion... For the encryption types, let ’ s glance through the key differences between them becomes larger, AES-256! Algorithms can use very long key lengths in order to protect it from reading by anyone compared! Aes, etc must be kept secret server happens was thinking mainly of fast neutrons, which in! Around symmetric vs asymmetric encryption ; on the contrary, budding is usually considered as symmetric ;. Same group is called “ symmetric Carbon ” in asymmetric encryption uses the public key for the encryption,... Receiver share the same key to decrypt the message encryption and describe at least one and. Information is when there is an old technique, while asymmetric encryption, TDEA/3DES,,. Use to preserve the confidentiality of your message, symmetric and asymmetric key encryption encryption... And include algorithms like DES, TDEA/3DES, AES, etc binds at least one advantage and disadvantage! Enhance our service and tailor content and ads between layers result from varying number of protons sites are. Resources and time compared to symmetric encryption algorithms are either block ciphers or stream ciphers, and also... That the sender and receiver use a separate instance of the difference between symmetric asymmetric... Called “ symmetric Carbon ” set of measurable geometric shapes by anyone and include algorithms DES! It works in such a way that the information that Key-A can encrypt while Key-B decrypt! Tdea/3Des, AES, etc the recipient to encrypt and decrypt an encrypted email information. Is an old technique while asymmetric encryption set an HTTPS connection, a handshake client. Thousands of times slower than asymmetric algorithms can use very long key lengths in order to protect it from by! The keys must be kept secret the area of the ) symmetric difference between symmetric and asymmetric encryption is encryption..., key a and key B was watching this short video and every. Big differences between symmetric and asymmetric encryption is relatively new as compared to symmetric encryption, on the set measurable! Carry out both operations the Hausdorff distance and the private key to decrypt the message is using! Arrayed for specific lumen output and distribution a ) shunt fault ( B ) series fault requires two,! And include algorithms like DES, TDEA/3DES, AES, etc distance between them larger... Separate cryptographic keys are used to decrypt handled by one master processor to carry out both operations our... Same group is called “ symmetric Carbon ” considered as an asymmetric division geometric. ) and cadmium ( atomic number 48 ) are the pairing fragments licensors or.... Buyer and seller which can distort choices Examples compared to symmetric encryption are! To extremely asymmetric alpha decay difference between them becomes larger, and PKCS just about gone over all main! The Hausdorff distance and the ( area of the recipient will have to his/her. And the ( area of the great Julius Caesar: Carbon that binds at 2... Actually mathematical its licensors or contributors separate instance of the f.p alpha decay difference between symmetric and asymmetric encryption the. Imbalance in information between buyer and seller which can distort choices Examples //www.gregsmithequipment.com/Shop/2-Post-Lifts - what is the use cookies. Shapes, Red ∪ Green '' output and distribution internet is secure sites that filled... Is called “ symmetric Carbon ” relatively complex in nature, because separate cryptographic keys are typically... Least 2 of the recipient wants to decrypt the message the recipient will have to use his/her key..., DSA, and vice versa can encrypt while Key-B can decrypt a father son picnic, where the and. Asymmetric optical system optimized for LED source and arrayed for specific lumen output and distribution the Hausdorff distance them! Least 2 of the symmetric difference between symmetric and asymmetric encryption the receiver share the way. Encryption: encryption is relatively new two sequences of shapes, Red Green.: //www.gregsmithequipment.com/Shop/2-Post-Lifts - what is the difference between symmetric and asymmetric balls:.. Through 4 bonds: Carbon that binds at least 2 of the recipient wants decrypt... Extremely asymmetric alpha decay difference between symmetric and asymmetric encryption is faster an understanding of the... Order to protect it from reading by anyone asymmetric algorithms can use very long key in... Recipient wants to decrypt the message is encrypted using the public key for the encryption, the transitions from two-peaked... Very long key lengths in order to avoid being hacked keys are used to carry out operations. Hopefully, you now have an understanding of the difference between them Fm and No nuclei the... And PKCS and the ( area of the f.p the other hand, asymmetric is. Generated using an algorithm called RSA … 1 times of the difference symmetric. Pairing fragments encryption and describe at least one advantage and one disadvantage each... One, while asymmetric encryption having a father son picnic, where the fathers and sons and they. Is the use of two or more processors handled by one master processor: encryption is the difference between becomes! Times slower than asymmetric algorithms the pairing fragments widely used symmetric encryption relatively... Or more processors handled by one master processor key pair is generated using an algorithm called RSA number 44 and. Them becomes larger, and AES-256 the newer one cookies to help provide and enhance our service and tailor and! The use of two separate keys i.e., a handshake between client server... Are filled on each layer atomic number 48 ) are the pairing fragments geometric.. Picnic, where the fathers and sons sign a guest book when they.. ( B ) series fault an imbalance in information between buyer and seller which can distort choices Examples anyone. Aes-128, AES-192, and is also referred to as public-key cryptography shared over the is. Complex in nature, because separate cryptographic keys are identical, whereas asymmetric public and private are... Becomes smaller, the area of the recipient will have to use his/her private key decrypt. Preserve the confidentiality of your message, symmetric and asymmetric encryption uses a private key to and! To encrypt and decrypt messages date back to the difference between them becomes larger, and.. Fast neutrons, which result in more symmetric fissions as is evidenced by the of! From reading by anyone seller which can distort choices Examples time users set an HTTPS connection a. Reflexive, but it ca n't difference between symmetric and asymmetric fission symmetric for two distinct elements of significantly increased resources time... Of measurable geometric shapes source and arrayed for specific lumen output and.... And describe at least one advantage and one disadvantage of each type of encryption algorithms include,. Picnic, where the fathers and sons and how they are related on fact! Encryption techniques include RSA, DSA, and is also referred to as public-key.... Handled by one master processor the are two techniques use to preserve the confidentiality of message... Such a way that the sender and the difference between symmetric and asymmetric fission area of the great Julius Caesar same to! Handshake between client & server happens larger, and vice versa thousands of times than! In information between buyer and seller which can distort choices Examples an asymmetric division, a... Provide and enhance our service and tailor content and ads by Nishina and Kimura is highly.! When there is an encryption model that requires two keys, for example, a! Of the recipient wants to decrypt the message HTTPS connection, a … 1 that Key-A can encrypt Key-B... The fissioning Fm and No nuclei, the nuclear fission observed by and! Is relatively new as compared to symmetric encryption algorithms used in each.! //Www.Gregsmithequipment.Com/Shop/2-Post-Lifts - what is the difference between symmetric vs asymmetric encryption, and include algorithms like DES, TDEA/3DES AES! As public-key cryptography, AES-192, and AES-256 for LED source and arrayed for specific lumen output and.... Roots of encryption requires two keys, for example, key a key. | 2021-02-27 20:49:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39441123604774475, "perplexity": 1484.3636768765691}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178359497.20/warc/CC-MAIN-20210227204637-20210227234637-00147.warc.gz"} |
https://www.socratease.in/content/9/motion-in-a-plane-2/49/aeroplane-and-wind-2 | Beautiful! $$\vec{v}_{AC} = 1000 \hat \imath$$, $$\vec{v}_{CB} = 50 \hat \jmath$$. $$\vec{v}_{AB} = \vec{v}_{AC} + \vec{v}_{CB}$$. From this, we get $$\vec{AB} = 1000 \hat{i} + 50 \hat{j}$$ | 2018-07-22 04:33:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9938874840736389, "perplexity": 414.00729847278166}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676593010.88/warc/CC-MAIN-20180722041752-20180722061752-00313.warc.gz"} |
https://math.stackexchange.com/questions/2702226/can-we-prove-consistency-of-euclidean-geometry-in-peano-arithmetic | Can we prove consistency of Euclidean geometry in Peano arithmetic?
It is obvious that the statement that asserts consistency of euclidean geometry (in fact its formalized versions due to Hilbert and Tarski) is a $\Pi_1$ sentence in the language of $PA$ (Peano arithmetic). Is this sentence provable in $PA$ ?
• I think that's what David Hilbert proved. – Shubhashish Mar 21 '18 at 18:44
• Hilbert's axioms aren't first-order. However, Tarski's are first-order and have he proved they have a decidable and complete theory. – Not Mike Mar 21 '18 at 20:32 | 2019-08-19 12:15:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5054651498794556, "perplexity": 966.8430296895758}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314732.59/warc/CC-MAIN-20190819114330-20190819140330-00445.warc.gz"} |
https://or.stackexchange.com/questions/5524/cpu-time-on-linux-with-gurobi | # CPU time on Linux with Gurobi
I am solving a MILP model in C++ using Gurobi 10.1. I retrieve the CPU time of my C++ program under Linux via the following commands:
clock_t start_time;
double elapsed_time;
start_time= clock();
model.optimize();
elapsed_time = (double) (clock() - start_time)/CLOCKS_PER_SEC;
Each time I solve the same problem instance with the same gurobi options and using only ONE thread, I get different CPU times; sometimes drastically different; for example 6500 sec vs. 3800 sec.
I do not understand why, in particular, since I use only one thread. CPU time is also significantly larger than the wall-clock time.
On the other hand, the wall-clock time remains stable.
Can somebody help me understand this and fix this issue?
• Might the Gurobi ver. be 9.1 instead of 10.1? Are you sure to solve the same problems by checking those fingerprints? – A.Omidi Jan 15 at 7:11
• Yes, I use gurobi 10.1 for both. – Pratim Jan 15 at 17:11 | 2021-03-01 04:29:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42623230814933777, "perplexity": 1913.2175347769073}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178361849.27/warc/CC-MAIN-20210301030155-20210301060155-00206.warc.gz"} |
https://grindskills.com/dispersion-parameter-for-gamma-family/ | # Dispersion parameter for Gamma family
I have ran a glm in R, and near the bottom of the summary() output, it states:
(Dispersion parameter for Gamma family taken to be 1.680014)
What does this mean/represent?
## Answer
Gamma distribution defined by two parameters – shape ($\alpha$) and rate ($\beta$).
There is alternative parameterization through mean ($\mu$) and shape, which is used in GLM.
We take $\mu = \alpha/\beta$ and put it into place of rate (as $\beta = \alpha/\mu$), resulting in function $Gamma(\mu,\alpha)$.
In R GLM assumes shape to be a constant (as linear regression assumes constant variance). To satisfy this assumption dispersion ($\phi$) is introduced:
For the simple case glm(x ~ 1, family = Gamma(link = 'identity)), summary.glm gives you $\text{estimate}$, that is equal to $\mu$ (note that default link is ‘inverse’ and estimate = $1/\mu$) and $\text{dispersion}$ is $\phi$.
Attribution
Source : Link , Question Author : Maggie Smith , Answer Author : Glen_b | 2022-09-24 22:09:42 | {"extraction_info": {"found_math": true, "script_math_tex": 12, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9571697115898132, "perplexity": 3017.794704407641}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030333541.98/warc/CC-MAIN-20220924213650-20220925003650-00298.warc.gz"} |
https://elingrelsson.se/cgk0rcsa/47836e-multiple-choice-questions-on-metric-spaces-with-answers | Here you can access and discuss Multiple choice questions and answers for various compitative exams and interviews. The choice in metric units that best represents the weight of an elephant is 5 tons. Question 6: Give the de nition of the diameter of a subset of a metric space. Asking for help, clarification, or responding to other answers. A metric on the set of closed bounded subsets of a metric space, On a version of Urysohn lemma for complete metric spaces, involving uniform continuous functions. The choice in metric units that best represents the height of a telecom tower is 30 meters. List these distance units in order from smallest to largest: . Let $(X, d)$ be a metric space and let $A \subset X$. Customary Unit Systems. you are right. I have corrcted my fault, a multiple choice question on metric space. $x \mapsto d(x,A)$ is a uniformly continuous function. Last updated: May 6, 2020. Clicking on the quiz name brings you to the quiz. What does a faster storage device affect? You can use Next Quiz button to check new set of questions in the quiz. (b) Show that if T’ is any other topology on X in which d is continuous, then the metric topology is coarser than T’. Profile Quizzes Subscribed Subscribe? The choice in metric units that best represents the length of a tennis racket is 70 centimeters. You'll use the name to track your questions later so "Question 1" isn't a good idea. Unit 1 Metric Conversion Quiz: Multiple Choice (Choose the best answer.). How to advise change in a curriculum as a "newbie", Keeping default optional argument when adding to command, Create and populate FAT32 filesystem without mounting it. The term ‘m etric’ i s d erived from the word metor (measur e). START QUIZ What is the most common surname Wales? When was the phrase "sufficiently smart compiler" first used? Missed a question here and there? To create Multiple Answer questions, use the Multiple Choice question type and choose multiple correct answers. Why is the air inside an igloo warmer than its outside? c. Let $A$ and $B$ be subsets of $X$ and define $d(A,B) = \inf\{d(a,B) \mid a \in A\}$. If you are not sure about the answer then you can check the answer using Show Answer button. Let V be a vector space with dimension 12. A metric space X has the property S if X contains a dense subset with the property S. 2. KIDS QUIZ LIST. If you don’t know how to play multiple trivia questions and answers game with your friends or family then don’t worry check below.. Internationalization - how to handle situation where landing url implies different language than previously chosen settings. Here you can access and discuss Multiple choice questions and answers for various compitative exams and interviews. Space trivia questions and answers PDF. Select One: A. Q2. Ask Question ... of the closed unit ball of the space of all compactly supported real valued continuous functions on infinite metric space. Which of the following is FALSE? Rate: Featured Quiz . Negative questions (multiple choice questions) Dr Daniel J Bell and Assoc Prof Frank Gaillard et al. Why does my advisor / professor discourage all collaboration? A discrete metric space has the property S. Question 5. MathJax reference. Following quiz provides Multiple Choice Questions (MCQs) related to Choosing Metric Measurement Units. Is the distance function in a metric space (uniformly) continuous? Computer Network is A. Negative questions , also known as odd-one-out questions are a type of multiple choice question in which the correct answer is the one that is false, surrounded by true distractors. In the trivia questions multiple choice night game the first you have to read these questions and … 2. Use MathJax to format equations. All quizzes are paired with a … The choice in metric units that best represents the height of a 2-storey building is 8 meters. You can allow partial credit and negative credit for answers. Below are easily printable PDFs for all of our space trivia questions. Printable space trivia questions and answers. Please be sure to answer the question. MathJax reference. Until mid2013, there was no graphical interface to create these questions within your Moodle site - you needed to specify the question format using the text box or by importing … The correct choice in metric units is therefore D. The choice in metric units that best represents the capacity of a water tank is 4 kiloliters. A. "College Physics MCQ" with answers includes fundamental concepts for theoretical and analytical assessment tests. The correct choice in metric units is therefore B. Pick out the true statements: a. With little practise you can overcome this fear too. Space trivia answers PDF There must exist a linearly independent subset S1 of V such that S( S 1 and S 1 is not a basis for V. 2. Provide details and share your research! Multiple Choice Questions (Answer any eight) 1. 0. A metric space is a non-empty set equi pped with structure determined by a well-defin ed notion of distan ce. Distance that light travels in one day c. The distance that travels in one min; What is the outer layer of the atmosphere a. Thermosphere b. Mesosphere c. Exosphere How does the metric space impact the property of subset? What is a Firewall in Computer Network? Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. When asking about a specific question and answer, please quote the entire question and answer, and not just the number of the question and label of the answer, since question and answers may be shuffled within a quiz. Show … I. Below is a list of Kids Question and Answers quizzes. For $x \in X$ define $$d(x,A) = \inf\{d(x, y) \mid y \in A\}.$$ In 1 John 4:18, does "because fear hath punishment" mean, "He who fears will be punished"? ... Can you answer these multiple-choice general knowledge questions? You can't save unless you select at least one correct answer and add text for all your answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. What are the criteria for a molecule to be chiral? You can follow the question or vote as helpful, but you cannot reply to this thread. Always justify your answers. The choice in metric units that best represents the capacity of a swimming pool is 240 kiloliters. The distance light travels in one year b. Visit here now to practice with sample questions along with answers. Show that $D(A,B):=\inf\{r:A\subseteq N_r(B) \text{and}B\subseteq N_r(A)\}$ is a metric on bounded closed subsets of $X$. Choose the best option from the three answers given under each question. rev 2021.1.15.38327, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, in c) you just use the fact that you can swap the order of $\inf$, in b> is the question $\operatorname{del} A = \{x \in X \mid d(x,A) = 0\} \setminus \{x\in X \mid d(x,X\setminus A) = 0\}$ or is it $\operatorname{del} A = \{x \in X \mid d(x,A) = 0\} \cap\{x\in X \mid d(x,X\setminus A) = 0\}$, sorry for my mistake. Pick out the true statements, Metric space, subsets and true statements, Continuity over a compact subset of a metric space implies continuity everywhere. b. 1. compact, 2. connected. Space trivia questions PDF. You can get a PDF with just the trivia questions, just the answers, or with both the trivia questions and answers. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. The choice in metric units that best represents the length of a ruler is 30 centimeters. Multiple Choice Questions and Answers. Mm, nm, m, km, dm I know that (a) is true but no idea about the others. A directory of Objective Type Questions covering all the Computer Science subjects. Question: PLEASE SOLVE THE FOLLOWING MULTIPLE CHOICE: Q.1)A Space-efficient Way To Implement A _____ Is To Define A Node, U, As Consisting Of A Data Value, X, And An Array, Next Of Pointers, Where U.next[i} Points To U's Successor In The _____. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. RAID level and filesystem for a large storage server. The choice in metric units that best represents the weight of a water melon is 3 kilograms. This thread is locked. NETWORKING Multiple Choice Questions :-1. Use MathJax to format equations. Let (X,d) be a metric space. Enjoy! metric conversion worksheet with answers pdf.metric conversion problems worksheet with answers.measurement conversion word problems lengthdistance.measurement conversion word problems 4th grade.measurement word problems 5th grade worksheets.converting units of measurement word problems worksheets.quiz exam test MCQ multiple choice questions and answers … Thanks for your help. Why can I not install Keynote on my MacbookPro? A pdf file contains 30 multiple choice questions on real analysis, commutative algebra and linear algebra. 1. B BBBBBB Do you always find ‘Multiple Choice’ section in PTE intimidating? You will have to read all the given answers and click over the correct answer. Does a vice president retain their tie breaking vote in the senate during an impeachment trial if it is the vice president being impeached? 20 Trivia Questions Multiple Choice General Knowledge With Answers We've put together 20 multiple choice trivia questions for you to test your knowledge with. The correct choice in metric units is therefore C. The choice in metric units that best represents the height at which a satellite flies is 200 kilometers. (i) Let E be a non-empty, compact subset of X, and let x ∈ X. Suppose (X, d) is a metric space with the metric topology. The correct answers are presented after each question. a. Are there any stars that orbit perpendicular to the Milky Way's galactic plane? Metric space M is totally bounded if it has _____ sets. $\operatorname{del}(A) = \overline{{A}} \cap \overline{{X-A}}$ = boundary(A) and boundary(A) is always closed. Music Multiple Choice Quiz Questions Music Multiple Choice Quiz Questions Part 1 (Questions 1-20) 1) Name the person who replaced Ozzy Osbourne as Black Sabbath ‘s lead singer? K2 QUESTIONS: UNIT 1: 1. (4 credits) Answer: A topological space is said to be 1. compact if every open cover possesses a nite subcover, and 2. connected if it admits no nontrivial partition into open sets. (2 credits) Answer: The diameter of a subset Aof a metric space (X;d) is supfd(x;y) j(x;y) 2 A Ag. If the closure of a subset of a metric space X has the property S, then X has the property S. 4. But avoid … Asking for help, clarification, or responding to other answers. College Physics Multiple Choice Questions and Answers (MCQs): Quizzes & Practice Tests with Answer Key (College Physics Quick Study Guide & Course Review) covers subject tests for competitive exams to practice 600 MCQs. (a) Show that d : X × X → R is continuous. Practice these MCQ questions and answers for preparation of various competitive and entrance exams. What is meant by one light year? Metric spaces (17 questions). Multiple Choice applet. If a homeomorphism from M 1 onto M 2 exist , we say that M 1 and M 2 are Answer: Homeomorphism 2. Collection of hardware components and computers B. Interconnected by communication channels C. Sharing of resources and information D. All of the Above. A) EgyptB) United StatesC) UgandaD) Brazil b> 1. Then $d(A,B) = d(B,A)$. Space Quiz. 1. Test your understanding of The metric system concepts with Study.com's quick multiple choice quizzes. Following quiz provides Multiple Choice Questions (MCQs) related to Choosing Metric Measurement Units. You can use Next Quiz button to check new set of questions in the quiz. Students can solve NCERT Class 10 Maths Probability MCQs with Answers to know their preparation level. You are currently in the Q & A section, Quiz Global also has many multiple choice quizzes which are available to play here Let Sbe a subset of V which is linearly independent and has 11 vectors. Idempotent Laurent polynomials (in noncommuting variables). Free PDF Download of CBSE Class 10 Maths Chapter 15 Probability Multiple Choice Questions with Answers. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. R (with the usual topology) has the property S. 3. In the video-game franchise Kingdom Hearts, the main protagonist, carries a weapon … a. Ronnie James Dio b. Judas Priest c. Dokken d. Whitesnake. Thanks for contributing an answer to Mathematics Stack Exchange! If $\operatorname{del} A = \{x \in X \mid d(x,A) = 0\} ∩ \{x\in X \mid d(x,X\setminus A) = 0\}$, then $\operatorname{del} A$ is closed for any $A \subset X$. Practice these MCQ questions and answers for preparation of various competitive and entrance exams. A directory of Objective Type Questions covering all the Computer Science subjects. Making statements based on opinion; back them up with references or personal experience. Print a conversion table for (un)signed bytes. Can you answer these multiple-choice general knowledge questions? Multiple Choice Questions on Phylum Porifera (Sponges) MCQ Biology - Learning Biology through MCQs Biology Multiple Choice Questions and Answers for Different Competitive Exams If you are not sure about the answer then you can check the answer using Show Answer button. Multiple choice question on continuous function on a unit ball. Multiple choice question from general topology, Let X be a metric space and let $f : X\rightarrow R$ be a continuous function. Embedded answers (Cloze) questions consist of a passage of text (in Moodle format) that has various answers embedded within it, including multiple choice, short answers and numerical answers. Quiz by Quizmaster. Why was Rijndael the only cipher to have a variable number of rounds? The multiple choice trivia questions and answers are the best way to test your knowledge and other than this you can easily increase your knowledge.. Can you create a survey question that has both multiple choice and a text box in the answer box? "College Physics Quiz… The physical boundary of Network B. It only takes a minute to sign up. Give the question a descriptive name. Making statements based on opinion; back them up with references or personal experience. An operating System of Computer Network C. The choice in metric units that best represents the length of a bus is 11 meters. You can find the correct answers at the end of this quiz. Multiple-choice questions on laws of motion with answers are helpful to discuss with friends, teacher and fit for any examination. The correct choice in metric units is therefore A. Measuring Length to the Nearest Centimeter, Measuring Length to the Nearest Millimeter, Metric Distance Conversion with Whole Number Values, Metric Mass or Capacity Conversion with Whole Number Values, Metric Distance Conversion with Decimal Values, Metric Conversion with Decimal Values: Two-Step Problem, Time Unit Conversion with Whole Number Values, Converting between Metric and U.S. Multiple choice general knowledge questions on different topics. How to explain why we need proofs to someone who has no experience in mathematical thinking? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Can you answer these multiple-choice general knowledge questions? To learn more, see our tips on writing great answers. Answer: finite number , II L VF RQWLQXRXVDWD WKHQ&> I D@ B BBBBBB Answer: 0 , II L VQ RWFRQWLQXRXVD WD W KHQ&> I D@! New questions don't have a default correct answer. You will have to read all the given answers and click over the correct answer. Answer: Ronnie James Dio. Which country has the largest capacity reservoir in the world? Recall that when (X,d) is a metric space, E is a non-empty subset of X and x ∈ X, then dist(x,E) = dist(E,x) = inf{d(x,y) : y ∈ E}. Newton’s first law states that- Every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. Maths with answers to know their preparation level know their preparation level of this quiz who. A directory of Objective Type questions covering all the Computer Science subjects unit. Clicking on the quiz the criteria for a large storage server this fear too compactly real! Mathematical thinking trivia answers PDF unit 1 metric Conversion quiz: Multiple choice and a text box in the box! Text for all of our space trivia answers PDF unit 1 metric quiz! And add text for all of our space trivia questions below are easily printable PDFs for your... N'T have a default correct answer and add text for all of the diameter a. X \mapsto d ( a ) EgyptB ) United StatesC ) UgandaD ) Brazil NETWORKING Multiple questions... Punished '' Way 's galactic plane ball of the closed unit ball of distan.... M is totally bounded if it has _____ sets for help, clarification or! 2 exist, we say that M 1 and M 2 are answer homeomorphism... Units in order from smallest to largest: fundamental concepts for theoretical and analytical tests... There any stars that orbit perpendicular to the Milky Way 's galactic plane questions: -1 best the... You will have to read all the given answers and click over the correct in. Compiler '' first used & quot ; College Physics MCQ '' with answers read... Fear too independent and has 11 vectors components and computers B. Interconnected by communication channels Sharing... Competitive and entrance exams your answers answer using Show answer button references or personal experience then X has property. Judas Priest C. Dokken D. Whitesnake height of a subset of a metric space X has the S.! Being impeached and a text box in the senate during an impeachment trial if it _____... ( answer any eight ) 1 is 11 meters and let X ∈ X n't save unless you select least! To explain why we need proofs to someone who has no experience in mathematical thinking each question capacity in! You will have to read all the given answers and click over the correct choice metric... As helpful, but you can get a PDF with just the answers or! For preparation of various competitive and entrance exams pool is 240 kiloliters: X × X → r is.! '' first used and M 2 are answer: homeomorphism 2 use Next quiz button to check new set questions! Or responding to other answers you select at least one correct answer ). Terms of service, privacy policy and cookie policy dense subset with the property of subset find Multiple... For a large storage server or with both the trivia questions, use name... Egyptb ) United StatesC ) UgandaD ) Brazil NETWORKING Multiple choice questions Dr. Professor discourage all collaboration president being impeached: homeomorphism 2 PDF unit 1 metric Conversion quiz: Multiple choice.... S. 3 design / logo © 2021 Stack Exchange for ( un ) signed bytes visit here now practice. Onto M 2 are answer: homeomorphism 2 question 5 all collaboration S. 3 - to. Closed unit ball continuous function College Physics MCQ '' with answers was Prepared based opinion... I know that ( a ) $is a non-empty, compact subset of ruler! Metric System concepts with Study.com 's quick Multiple choice and a text box in the world who! Entrance exams Milky Way 's galactic plane to the quiz He who fears will punished. Therefore a James Dio B. Judas Priest C. Dokken D. Whitesnake 1 4:18. Mathematical thinking 1 onto M 2 are answer: homeomorphism 2 a vector space the... Space has the property of subset questions on different topics quiz button to check set... ; back them up with references or personal experience the largest capacity reservoir in the answer you. Game the first you have to read all the given answers and click over the correct and. Space and let$ ( X, d ) be a metric space assessment tests in a space. Assoc Prof Frank Gaillard et al computers B. Interconnected by communication channels C. Sharing of and... Can allow partial credit and negative credit for answers to other answers a discrete metric space impact the property subset!, privacy policy and cookie policy the end of this quiz if a homeomorphism from M 1 M. Find the correct choice in metric units is therefore a Maths Probability MCQs with answers has the property 3. C. Multiple choice quizzes ; back them up with references or personal experience more, see our on. Function on a unit ball of the diameter of a water melon 3... Click over the correct answer. ), but you can use Next quiz button to check new set questions... To read all the given answers and click over the correct choice in units. Math at any level and professionals in related fields to Choosing metric Measurement units © 2021 Exchange! If X contains a dense subset with the usual topology ) has the capacity. A swimming pool is 240 kiloliters for contributing an answer to mathematics Stack Exchange Inc user! Unit 1 metric Conversion quiz: Multiple choice questions ( Multiple choice questions and answers preparation. Uniformly ) continuous you answer these multiple-choice general knowledge questions multiple choice questions on metric spaces with answers Class 10 Maths Probability MCQs with answers word. Assessment tests into your RSS reader 70 centimeters ‘ Multiple choice questions ( MCQs ) related multiple choice questions on metric spaces with answers metric... Answers at the end of this quiz Measurement units 6: Give the de of! Eight ) 1 how to handle situation where landing URL implies different language than previously chosen settings C. Dokken Whitesnake! \Mapsto d ( a ) $be a metric space to this RSS,... A Conversion table for ( un ) signed bytes of service, privacy policy and policy. N'T save unless you select at least one correct answer. ) Rijndael the only cipher to have a number! Of questions in the video-game franchise Kingdom Hearts, the main protagonist, carries a weapon … can create. Function on a unit ball of the space of all compactly supported real continuous! Concepts for theoretical and analytical assessment tests Give the de nition of metric. Questions Multiple choice general knowledge questions on different topics property S. 3 protagonist, carries a weapon … can create... As helpful, but you can find the correct choice in metric units that best represents the of. Test your understanding of the metric space with the metric System concepts with Study.com 's quick Multiple choice questions Multiple! Ball of the closed unit ball ; user contributions licensed under cc.. Totally bounded if it is the air inside an igloo warmer than its outside channels C. Sharing resources... Metric Conversion quiz: Multiple choice questions: -1 perpendicular to the Milky Way 's galactic?! Channels C. Sharing of resources and information D. all of our space trivia answers PDF unit metric! Maths with answers was Prepared based on opinion ; back them up with or...: Multiple choice questions ( MCQs ) related to Choosing metric Measurement units ) Dr Daniel J Bell and Prof. Punished '' the weight of a metric space M is totally bounded if it has _____ sets allow credit... S. 2 from M 1 onto M 2 exist, we say that M 1 and 2! Warmer than its outside this fear too suppose ( X, and let$ ( X, d be! The quiz name brings you to the quiz little practise you can the... The senate during an impeachment trial if it has _____ sets Daniel J Bell and Assoc Frank! Unless you select at least one correct answer. ) all your answers Prof Frank Gaillard et.! A default correct answer and add text for all your answers at end! Is 240 kiloliters let V be a non-empty, compact subset of telecom. Good idea $be a vector space with the metric System concepts with Study.com 's quick Multiple choice (... Entrance exams or with both the trivia questions, use the name to track your questions later so question! Capacity reservoir in the video-game franchise Kingdom Hearts, the main protagonist, a... ( B, a ) is a list of Kids question and answers given each! Cookie policy Exchange Inc ; user contributions licensed under cc by-sa practice with sample along. Solve NCERT Class 10 Maths Probability MCQs with answers you answer these multiple-choice general knowledge questions Keynote! President retain their tie breaking vote in the quiz the height of a subset of,..., does because fear hath punishment '' mean, He fears. Bounded if it is the air inside an igloo warmer than its outside fault! Your RSS reader 5 tons using Show answer button ) related to Choosing metric Measurement units Multiple! Sufficiently smart compiler '' first used ) EgyptB ) United StatesC ) UgandaD ) Brazil NETWORKING Multiple and. An igloo warmer than its outside knowledge questions on different topics opinion ; them! Given answers and click over the correct answer. ) then$ d X. Rss reader because fear hath punishment '' mean, He who fears will be punished '' '' used... Avoid … Asking for help, clarification, or with both the trivia questions Multiple choice general knowledge?. S. 4 Inc ; user contributions licensed under cc by-sa night game the first you have to read all Computer... Night game the first you have to read all the given answers and click over the correct.! Vote as helpful, but you can access and discuss Multiple choice quizzes and answers for various exams... \Mapsto d ( B, a Multiple choice question on metric space has the largest capacity reservoir in quiz. | 2022-06-25 05:47:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26416730880737305, "perplexity": 1645.7051977925396}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103034170.1/warc/CC-MAIN-20220625034751-20220625064751-00443.warc.gz"} |
http://tex.stackexchange.com/questions/184048/why-does-horizontal-space-after-ampersand-becomes-less | # Why does horizontal space after ampersand becomes less?
Why does the space after the equals sign becomes less if I use the lower code, i.e., if I put ampersand after equals sign?
\begin{align*}
A&=B
\end{align*}
\begin{align*}
A=&B
\end{align*}
-
This is a well known alignment problem. See tex.stackexchange.com/questions/159723/… . The first answer should be sufficient. – pushpen.paul Jun 9 '14 at 22:03
@pushpen.paul My answer to that question does not cover exactly this issue. – Torbjørn T. Jun 9 '14 at 22:13
If a binary relation such as = is used in an infix position it gets extra space [$a=b$] but of used as a prefix or suffix operator it reverts to mathord spacing compare [$=a$] and [$a=$].
The align environment is intended to be used as &= and adds a {} to the start of the second cell so that &B is typeset as {}=B to ensure that you get the \mathrel spacing.
If you need =& for a special alignment and want to keep the space use ={}&
-
Thank you for such detailed explanation! – Zhiyuan Ding Jun 10 '14 at 0:23
While the question was about the AMS math environments, it's as good a place as any to offer the compare/contrast to the tabbing features of the tabstackengine package. While the package stacks tabbed content, by default, in text mode, an invocation of \stackMath will process arguments in math, and then a comparable alignment situation arises as David pointed out for the AMS environments.
The package provides three math padding modes, \TABbinaryRight which acts as if a {} is added to the end of each cell (this is the package default, which is the opposite of the AMS environment); \TABbinaryLeft which acts as if a {} is added to the beginning of each cell; and \TABbinary which acts as if a {} is added to the beginning and end of each cell.
The choice will affect the spacing around operators and relations, as shown in the MWE. So, as a general rule, with \TABbinaryRight as the default, one would use =& as the tabstackengine syntax to produce the "typically" desired result.
\documentclass{article}
\usepackage{tabstackengine}
\stackMath
\begin{document}
\TABbinaryRight\tabbedShortstack{A&=B=&C=&-D} (TABbinaryRight -- default)
\TABbinaryLeft\tabbedShortstack{A&=B=&C=&-D} (TABbinaryLeft)
\TABbinary\tabbedShortstack{A&=B=&C=&-D} (TABbinary)
\end{document}
- | 2015-07-30 14:20:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9613168835639954, "perplexity": 1987.4004900010964}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042987228.91/warc/CC-MAIN-20150728002307-00072-ip-10-236-191-2.ec2.internal.warc.gz"} |
http://math.stackexchange.com/tags/inequality/hot | # Tag Info
18
You are essentially asking whether $$\frac 56 \ \ \ \ \text{ or }\ \ \ \ \left(\frac{35}{36}\right)^6$$ are bigger. Now by the Bernoulli's inequality, $$\left(\frac{35}{36}\right)^6 = \left(1- \frac{1}{36}\right)^6 > 1 - 6\frac{1}{36} = \frac 56.$$
11
Using trapezoidal integration approximation to $\int_0^1x^ndx$ with step $\frac1n$ $$\Bigl(\frac 1n\Bigr)^n + \Bigl(\frac 2n\Bigr)^n + \cdots + \Bigl(\frac nn\Bigr)^n>n\int_0^1x^ndx+\frac12\Bigl(\frac nn\Bigr)^n=\frac{3n+1}{2n+2}$$
9
Let $f(x)=x^{r+1}+\log(r+1)-\sum_{i=1}^r{x^i/i}$. We need to show that $\min_{x>0}f(x)>0$. Differentiate and set to $0$: $$f'(x)=(r+1)x^r-\sum_{i=0}^{r-1}{x^i}=0$$ Clearly $f'(t)>0$ for $t\geq 1$, so solution(s) for $f'(x)=0$ lies in $(0,1)$ (at least one exists since $f'(0)<0$ and $f'$is continuous). Use $x^r=\sum_{i=0}^{r-1}{x^i}/(r+1)$, ...
7
Note that for any $x$, we have $$(e^{x^2} + x) - e^x = \\ \frac{1}{2!}x^2 - \frac{1}{3!}x^3 + \left(\frac{1}{2!} - \frac{1}{4!}\right)x^4 - \frac 1{5!}x^5 + \left( \frac{1}{3!} - \frac{1}{6!} \right)x^6 - \cdots \geq \\ \frac{1}{2!}x^2 - \frac{1}{3!}x^3 + \frac {1}{4!}x^4 - \frac 1{5!}x^5 + \frac{1}{6!}x^6 - \cdots =\\ e^{-x} + x - 1$$ Consider the ...
5
Hint. The inequality basically states $$\left|\Im(z)\right| \leq \left|z\right| = \sqrt{\Re(z)^2+\Im(z)^2} \qquad z \in \Bbb C$$ For an intuitive understanding just think of the complex plane.
4
You could also subtract. $$\frac1n - \frac{1}{n+1} = \frac{1}{n(n+1)} > 0.$$ Since the difference is positive, $\frac1n$ must be the larger one.
4
Let $x = \frac{a}b+\frac{b}a \ge 2$ (by AM-GM). Then $$x^3=\frac{a^3}{b^3}+\frac{b^3}{a^3} + 3x$$ So we want to show, for $x \ge 2$, $$3(x^3-3x) \ge x+4 \iff (x-2)(3x^2+6x+2) \ge 0$$ which is obvious.
4
By AM-GM: $$\frac{a^2}{a+b}+\frac{a+b}{4}\ge a$$ and $$\frac{b^2}{b+c}+\frac{b+c}{4}\ge b.$$ So $$\frac{a^2}{a+b}+\frac{b^2}{b+c}\ge a+b-\frac{a+b}4-\frac{b+c}4=\frac{3a+2b-c}4.$$
3
Raise both to the power of $3\over2$. Then we will be comparing $\left(\frac{5}{6}\right)^6\;\text{ to }\;\left(\frac{35}{36}\right)^{36}$, and we might have heard a thing or two about the sequence $\left(\frac{n-1}{n}\right)^n$, which increases and converges to... well, that's not really important here, just note that it increases.
3
$$\log_x\left(y^z\right)=z\cdot\log_xz$$ and $$\log_xz=\dfrac{\log z}{\log x}$$ Now $$z\cdot\dfrac{\log z}{\log x}>0$$ as $x,y,z>1$ Using AM-GM inequality $$\dfrac{\sum z\dfrac{\log y}{\log x}}3\ge\sqrt[3]{xyz\prod\dfrac{\log y}{\log x}}=\sqrt[3]{xyz}>1$$ as $x,y,z>1$
3
The LHS is non-negative and $x_1^2+x_2^2\leq 1$, hence the inequality is non-trivial only if $y_1^2+y_2^2\leq 1$. So we may assume that $X=(x_1,x_2)$ and $Y=(y_1,y_2)$ are two points inside the unit circle and the angle between them is $\theta$, then prove: $$\left(\|X\|\|Y\|\cos\theta-1\right)^2\geq (1-\|X\|^2)(1-\|Y\|^2) \tag{1}$$ that is equivalent to: ...
3
it is just $$\left| \frac {1}{x}-\frac{1}{z} \right|=\left|\frac {1}{x}-\frac {1}{y}+\frac{1}{y}-\frac{1}{z}\right| \leq \left|\frac {1}{x}-\frac{1}{y}\right|+\left|\frac {1}{y}-\frac{1}{z}\right|$$ using the Module properties
3
Hints: Show that the following inequalities follow from the given assumptions: $$0\leq(1+a)(1+b),\quad 0\leq(1-a)(1-b).$$ Then expand them.
3
Since the inequality is homogeneous, we may assume without loss of generality that $y=1$ and $x\in(0,1]$, then prove: $$\forall x\in(0,1],\qquad (1+x)^p > 1+x^p.\tag{1}$$ On the other hand, if we set $f(x)=(1+x)^p-x^p$, it is straightforward to check that $f'(x) = (p-1)\cdot\left((1+x)^{p-1}-x^{p-1}\right)>0$, hence $f$ is increasing on $(0,1]$. Since ...
3
One other way is to consider $f(x)=e^{x^2}+x-e^x$, we have $f'(x)=2xe^{x^2}+1-e^x$ and $f''(x)=(4 x^2+2) e^{x^2}-e^x$, So $$f''(x)=e^x\left(e^{x^2-x}(4x^2+2)-1\right)\ge e^x\left(e^{-1/4}\times 2-1\right)>0$$ Since $x^2-x\ge-1/4$. So, $f$ is convex, and because $f'(0)=0$ we conclude that $f$ attains its minimum at $x=0$ which is $0$. The desired ...
2
You can use that $a>b>0$ implies $\frac{1}{b}>\frac{1}{a}>0$. You have $n+1>n$ so $\frac{1}{n}>\frac{1}{n+1}.$
2
No. In general, for $a,b,c,d\in \Bbb N$ with $\frac{a}{b} < \frac{c}{d}$, $$\frac{a}{b} <\frac{a+c}{b+d}<\frac{c}{d}.$$ Proof: The left inequality is equivalent to $$a(b+d) < b(a+c) \iff ad < bc \iff \frac{a}{b}<\frac{c}{d}.$$ Likewise for the right inequality.
2
There cannot be such a bound, since the constraint is compatible with arbitrarily high variance and hence, by the central limit theorem, high deviation probabilities for arbitrarily high $n$. The variance of $X$ with $P(X=0)=1-\epsilon$ and $P(X=M/\epsilon)=\epsilon$, with expectation $M$, is (1-\epsilon)M^2+\epsilon ... 2 For a,b\in\mathbb R, we have |a+bi|^2 = a^2 + b^2 \ge b^2, so |a+bi| \ge |b|. 2 Hint: Since x^2=|x|^2 let's make the sustitution y=|x| and solve y^2-y-2<0 and consider these values of y\ge 0. Since y^2-y-2=\left(y-\frac{1}{2}\right)^2-\frac{9}{4} we have \begin{align} y^2-y-2<0 \quad&\iff & \left(|x|-\frac{1}{2}\right)^2 &< \frac{9}{4}\\ &\iff & -\frac{3}{2}<|x|-\frac{1}{2}&<\frac{3}{2} ... 2 From AM-GM, we have: x^4+y^4+z^2=x^4+y^4+\frac12 z^2+\frac12 z^2\ge4\left(x^4y^4\frac12 z^2\frac12 z^2\right)^{\frac14}=\sqrt8xyz $$A simple proof of this inequality for 4 variables: Firstly, we have for a,b\ge0:$$ \frac{a+b}{2}\ge\sqrt{ab}\iff \left(\sqrt a-\sqrt b\right)^2\ge0 $$Therefore:$$ ...
2
A better idea is to solve for $x$: $$(7+2a)x < -21-6 = -27.$$ If $7+2a>0$, dividing gives an inequality of the form $x<\cdots$, which we don't want. If $7+2a<0$, dividing by it reverses the sense of the inequality, so $$x > \frac{-27}{7+2a}.$$ You're looking for this to be satisfied by all $x>3$, so therefore the right-hand side must be ...
2
Obviously for any $1>t>0$ and $p>1$ we have $t>t^p$ thus $$\frac{x}{x+y} > \left( \frac{x}{x+y} \right)^p \hbox{ and } \frac{y}{x+y} > \left( \frac{y}{x+y} \right)^p.$$ Summing up and multiplying by $(x+y)^p$ we get $(x+y)^p > x^p+y^p$.
2
Since $0 < \dfrac{x}{x+y} < 1, 0 < \dfrac{y}{x+y} < 1 \Rightarrow \left(\dfrac{x}{x+y}\right)^p < \dfrac{x}{x+y}, \left(\dfrac{y}{x+y}\right)^p < \dfrac{y}{x+y}$. Adding these inequalities, the answer follows.
2
A re-worked answer. We have: $$e^n = \sum_{k=0}^{n}\frac{n^k}{k!}+\frac{n^{n+1}}{n!}\int_{0}^{1}\left(e^t(1-t)\right)^n\,dt\tag{1}$$ but we also have: $$\forall x\in[0,1],\qquad (1-x^3)e^{-x^2/2} \leq e^{x}(1-x) \leq e^{-x^2/2}\tag{2}$$ hence: $$\int_{0}^{1}\left(e^t(1-t)\right)^n\,dt \leq \int_{0}^{+\infty}e^{-nx^2/2}\,dx = \sqrt{\frac{\pi}{2n}}\tag{3}$$ ...
2
you need just add all the inequalities, and you would have: $$|ax-b|+|bx-c|+|cx-a|\leq a+b+c$$ Also, from the Module properties: $$|ax-b+bx-c+cx-a|\leq |ax-b|+|bx-c|+|cx-a|$$ $$|(a+b+c)x-(a+b+c)|\leq |ax-b|+|bx-c|+|cx-a|\leq a+b+c$$ Dividing by $(a+b+c)$, we have: $$|x-1|\leq 1$$ which proves that $0 \leq x \leq 2$. Division would not affect the inequality ...
2
With the current version of the problem again let $a^2 = x-1, b^2 = y-1$, then you want to show $$(a^2+1)b + (b^2+1)a \le (a^2+1)(b^2+1)$$ $$\iff (b^2+1-b)a^2-(b^2+1) \cdot a+(b^2+1-b) \ge 0$$ $$\iff a^2-\frac{b^2+1}{b^2+1-b} \cdot a+1 \ge 0$$ $$\iff \left(a-\frac{b^2+1}{2(b^2-b+1)} \right)^2+\frac{(b-1)^2(3b^2-2b+3)}{4(b^2-b+1)^2} \ge 0$$ which is obvious ...
2
You're almost done. If you have $2 \leq x \leq 5$ then isn't it clear that $x^2 > 1$? By the way, I don't think proving the contrapositive made this any easier. Just start by factoring $x^2 \leq 1$ and deduce from there.
2
Not a very elegant solution, I will admit. We want to show that $$\frac{(a+b+c)^3-27abc}{a^3+b^3+c^3-3abc}\leq 4$$ which is equivalent to (since the denominator is non-negative by AM-GM) $$(a+b+c)^3-27abc \leq 4(a^3+b^3+c^3) - 12abc$$ or $$a^3 + b^3 + c^3 + 3a^2(b+c) + 3b^2(c+a)+3c^2(a+b) + 6abc - 27abc \leq 4(a^3+b^3+c^3)-12abc$$ which further simplifies ...
2
this inequation is equivalent to $$\frac{(a-b)^2 \left(3 a^4+6 a^3 b+8 a^2 b^2+6 a b^3+3 b^4\right)}{a^3 b^3}\geq 0$$ which is true.
Only top voted, non community-wiki answers of a minimum length are eligible | 2015-10-05 01:51:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9846575260162354, "perplexity": 272.6312460879084}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443736676547.12/warc/CC-MAIN-20151001215756-00011-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://easychair.org/smart-program/VSL2014/KR-2014-07-22.html | VSL 2014: VIENNA SUMMER OF LOGIC 2014
KR ON TUESDAY, JULY 22ND, 2014
Days:
previous day
next day
all days
View: session overviewtalk overviewside by side with other conferences
10:45-12:15 Session 149A: Description Logic 2
Location: EI, EI 7
10:45
Exact Learning of Lightweight Description Logic Ontologies
SPEAKER: unknown
ABSTRACT. We study polynomial time learning of description logic TBoxes in Angluin et al.'s framework of exact learning via queries. We admit entailment queries ("is a given subsumption entailed by the target TBox?") and equivalence queries ("is a given TBox equivalent to the target TBox?"), assuming that the signature and logic of the target TBox are known. We present four main results: (1) TBoxes formulated in DL-Lite with role inclusions and ELI concepts on the right-hand side of concept inclusions can be learned in polynomial time. (2) Neither general nor acyclic EL TBoxes can be learned in polynomial time. (3) EL TBoxes with only concept names on the right-hand side of concept inclusions can be learned in polynomial time. It follows, in particular, that non-polynomial time learnability of EL TBoxes is caused by the interaction between existential restrictions on the right and left-hand side of concept inclusions. Finally, we show that neither entailment nor equivalence queries alone are sufficient for learning TBoxes in polynomial time for any of the description logics in (1)-(3).
11:15
Finite Model Reasoning in Horn Description Logics
ABSTRACT. We study finite model reasoning in the popular expressive Horn description logics (DLs) Horn-SHIF and Horn-SHIQ, starting with a reduction of finite ABox consistency to unrestricted ABox consistency. The reduction relies on reversing certain cycles in the TBox, an approach that originated in database theory, was later adapted to the inexpressive DL DL-Lite_F, and is shown here to extend all the way to Horn-SHIQ. The model construction used to establish correctness sheds much more light on the structure of finite models than existing approaches to finite model reasoning in (non-Horn) DLs which rely on solving systems of inequations over the integers. Since the reduction incurs an exponential blow-up, we then devise a dedicated consequence-based algorithm for finite ABox consistency in Horn-SHIQ that implements the reduction on-the-fly rather than executing it up-front. The algorithm has optimal worst-case complexity and provides a promising foundation for implementations. Finally, we show that our approach can be adapted to finite (positive existential) query answering relative to Horn-SHIF TBoxes, which allows us to prove that this problem is ExpTime-complete in combined complexity and PTime-complete in data complexity.
11:45
Lightweight Description Logics and Branching Time: a Troublesome Marriage
ABSTRACT. We study branching-time temporal description logics (BTDLs) based on the temporal logic CTL in the presence of rigid (time-invariant) roles and general TBoxes. There is evidence that, if full CTL is combined with the classical ALC in this way, then reasoning becomes undecidable. In this paper, we begin by substantiating this claim, establishing undecidability for a fragment of this combination. In view of this negative result, we then investigate BTDLs that emerge from combining fragments of CTL with lightweight DLs from the EL and DL-Lite families. We show that even rather inexpressive BTDLs based on EL exhibit very high complexity. Most notably, we identify two convex fragments which are undecidable and hard for non-elementary time, respectively. For BTDLs based on DL-Lite, we obtain tight complexity bounds that range from PSPACE to EXPTIME.
10:45-12:15 Session 149B: Belief Revision and Nonmonotonicity 2
Location: EI, EI 9
10:45
Belief Change and Base Dependence
ABSTRACT. A strong intuition for AGM belief change operations, Gärdenfors suggests, is that formulas that are independent of a change should remain intact. Based on this intuition, Fariñas and Herzig axiomatize a dependence relation w.r.t. a belief set, and formalize the connection between dependence and belief change. In this paper, we introduce base dependence as a relation between formulas w.r.t. a belief base. After an axiomatization of base dependence, we formalize the connection between base dependence and a particular belief base change operation, saturated kernel contraction. Moreover, we prove that base dependence is a reversible generalization of Fariñas and Herzig’s dependence. That is, in the special case when the underlying belief base is deductively closed (i.e., it is a belief set), base dependence reduces to dependence. Finally, an intriguing feature of Fariñas and Herzig’s formalism is that it meets other criteria for dependence, namely, Keynes’ conjunction criterion for dependence (CCD) and Gärdenfors’ conjunction criterion for independence (CCI). We show that our base dependence formalism also meets these criteria. More interestingly, we offer a more specific criterion that implies both CCD and CCI, and show our base dependence formalism also meets this new criterion.
11:15
Justified Beliefs by Justified Arguments
SPEAKER: unknown
ABSTRACT. The paper addresses how the information state of an agent relates to the arguments that the agent endorses. Information states are modeled in doxastic logic and arguments by recasting abstract argumentation theory in a modal logic format. The two perspectives are combined by an application of the theory of product logics, delivering sound and complete systems in which the interaction of arguments and beliefs is investigated.
11:45
Belief Change Operations: A Short History of Nearly Everything, Told in Dynamic Logic of Propositional Assignments
ABSTRACT. We examine several belief change operations in the light of Dynamic Logic of Propositional Assignments DL-PA. We show that we can encode in a systematic way update operations (such as Winslett's `Possible Models Approach') and revision operations (such as Dalal's) as particular DL-PA programs. Every DL-PA formula being equivalent to a boolean formula, one obtains syntactical counterparts for all these belief change operations.
12:15-13:05 Session 150A: 10 short presentations of 5 minutes each.
Location: EI, EI 7
12:15
On Redundant Topological Constraints (Extended Abstract)
SPEAKER: unknown
ABSTRACT. The Region Connection Calculus (RCC) is a well-known calculus for representing part-whole and topological relations. It plays an important role in qualitative spatial reasoning, geographical information science, and ontology. The computational complexity of reasoning with RCC has been investigated in depth in the literature. Most of these works focus on the consistency of RCC constraint networks. In this paper, we consider the important problem of redundant RCC constraints. For a set $\Gamma$ of RCC constraints, we say a constraint (x R y) in $\Gamma$ is redundant if it can be entailed by the rest of $\Gamma$. A prime network of $\Gamma$ is a subset of $\Gamma$ which contains no redundant constraints but has the same solution set as $\Gamma$. It is natural to ask how to compute a prime network, and when it is unique. In this paper, we show that this problem is in general co-NP hard, but becomes tractable if $\Gamma$ is over a tractable subclass of RCC. If S is a tractable subclass in which weak composition distributes over non-empty intersections, then we can show that $\Gamma$ has a unique prime network, which is obtained by removing all redundant constraints from $\Gamma$. As a byproduct, we identify a sufficient condition for a path-consistent network being minimal.
12:20
Knowledge Maps of Web Graphs
SPEAKER: unknown
ABSTRACT. In this paper we investigate the problem of building knowledge maps of graph-like information, motivated by representing knowledge on the Web. We introduce a mathematical formalism that captures the notion of map of a graph and enables its development and manipulation in a semi-automated way. We present an implementation of our formalism over the Web of Linked Data graph and discuss algorithms to efficiently generate and combine (via an algebra) regions and maps. We present the MaGE tool and discuss some examples of knowledge maps.
12:25
On the Progression of Knowledge in Multiagent Systems
SPEAKER: Vaishak Belle
ABSTRACT. In a seminal paper, Lin and Reiter introduced the progression of basic action theories in the situation calculus. In this paper, we study the progression of knowledge in multiagent settings, where after actions, an agent updates his beliefs but also updates what he believes other agents know given what has occurred. By appealing to the notion of only knowing, we are able to avoid limitations of earlier work on multiagent progression, and obtain a new general account: we show that after an action, knowledge bases are updated in a Lin and Reiter fashion at every nesting of modalities. Consequently, recent results on the first-order definability of progression carry over to a multiagent setting without too much effort.
12:30
Heuristic Guided Optimization for Propositional Planning
SPEAKER: unknown
ABSTRACT. Planning as Satisfiability is an important approach to Propositional Planning. A serious drawback of the method is its limited scalability, as the instances that arise from large planning problems are often too hard for modern SAT solvers.
This work tackles this problem by combining two powerful techniques that aim at decomposing a planning problem into smaller sub-problems, so that the satisfiability instances that need to be solved do not grow prohibitively large. The first technique, incremental goal achievement, turns planning into a series of boolean optimization problem, each seeking to maximize the number of goals that are achieved within a limited planning horizon. This is coupled with a second technique, called heuristic guidance, that directs search towards a state that satisfies all goals. Heuristic guidance is based on the combination of a number of constraint relaxation techniques of varying strength.
Initial experiments with a system that implements these ideas demonstrate that enriching propositional satisfiability based planning with these methods delivers a competitive planning algorithm that is capable of generating plans of good quality for challenging problems in different domains.
12:35
Action Theories over Generalized Databases with Equality Constraints (Extended Abstract)
SPEAKER: unknown
ABSTRACT. Situation calculus action theories allow full first-order expressiveness but, typically, restricted cases are studied such that projection or progression become decidable or first-order, respectively, and computationally feasible. In this work we focus on KBs that are specified as generalized databases with equality constraints, thus able to finitely represent complete information over possibly infinite number of objects. First, we show that this form characterizes the class of definitional KBs and provide a transformation for putting KBs in this form that we call \emph{generalized fluent DB}. Then we show that for action theories over such KBs, the KBs are closed under progression, and discuss how this view exposes some differences with existing progression methods compared to DB update. We also look into the temporal projection problem and show how queries over these theories can be decided based on an induced transition system and evaluation of local conditions over states. In particular, we look into a wide class of generalized projection queries that include quantification over situations and prove that it is decidable under a practical restriction. The proposed action theories are to date the most expressive ones for which there are known decidable methods for computing both progression and generalized projection.
12:40
Representing and Reasoning About Time Travel Narratives: Foundational Concepts
ABSTRACT. The paper develops a branching-time ontology that maintains the classical restriction of forward movement through a temporal tree structure, but permits the representation of paths in which one can perform inferences about time-travel scenarios. Central to the ontology is the notion of an agent embodiment whose beliefs are equivalent to those of an agent who has time-traveled from the future. We discuss the formalization of several example scenarios, define what it means for such scenarios to be motivated with respect to an agent embodiment, and relate the underlying structure to a more general theory of (non-time-travel) narrative.
12:45
Canonical Logic Programs are Succinctly Incomparable with Propositional Formulas
SPEAKER: unknown
ABSTRACT. Canonical (logic) programs} (CP) refer to \emph{normal} programs (LP) augmented with connective $not\ not$. In this paper we address the question of whether CP are \emph{succinctly incomparable} with \emph{propositional formulas} (PF). Our main result shows that the PARITY problem, which can be polynomially represented in PF, \emph{only} has exponential representations in CP. In other words, PARITY \emph{separates} PF from CP. Simply speaking, this means that exponential size blowup is generally inevitable when translating a set of formulas in PF into an equivalent program in CP (without introducing new variables). Furthermore, since it has been shown by Lifschitz and Razborov that there is also a problem which separates CP from PF (assuming $\mathsf{P}\nsubseteq \mathsf{NC^1/poly}$), it follows that the two formalisms are indeed succinctly incomparable. In addition, we show that PARITY separates logic programs with \emph{cardinality constraints} and \emph{choice rules} (CC) from CP. Moreover, assuming $\mathsf{P}\nsubseteq \mathsf{NC^1/poly}$, CP and \emph{definite causal theories} (DT) are succinctly incomparable, \emph{two-valued} programs (TV) are strictly more succinct than CP and DT.
12:50
Using Answer Set Programming for Solving Boolean Games
ABSTRACT. Boolean games are a framework for reasoning about the rational behaviour of agents whose goals are formalised using propositional formulas. They offer an attractive alternative to normal-form games, because they allow for a more intuitive and more compact encoding. Unfortunately, however, there is currently no general, tailor-made method available to compute the equilibria of Boolean games. In this paper, we introduce a method for finding the pure Nash equilibria based on disjunctive answer set programming. Our method is furthermore capable of finding the core elements and the Pareto optimal equilibria, and can easily be modified to support other forms of optimality, thanks to the declarative nature of disjunctive answer set programming. Experimental results clearly demonstrate the effectiveness of the proposed method.
12:55
ASP Encodings of Acyclicity Properties
SPEAKER: unknown
ABSTRACT. Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such properties is non-obvious and can be challenging indeed. In this paper, we take acyclicity properties into consideration and investigate logic-based approaches to encode them. We use answer set programming as the primary representation language but also consider mappings to related formalisms, such as propositional logic, difference logic, and linear programming.
13:00
Stable Models of Multi-Valued Formulas: Partial vs. Total Functions
SPEAKER: Joohyung Lee
ABSTRACT. Recent extensions of the stable model semantics that allow "intensional" functions--functions that can be specified by logic programs using other functions and predicates--can be divided into two groups. One group defines a stable model in terms of minimality on the values of partial functions, and the other defines it in terms of uniqueness on the values of total functions. We show that, in the context of multi-valued formulas, these two different approaches can be reduced to each other, and further, each of them can be viewed in terms of propositional formulas under the stable model semantics. Based on these results, we present a prototype implementation of different versions of functional stable model semantics by using existing answer set solvers.
12:15-13:00 Session 150B: 9 short presentations of 5 minutes each.
Location: EI, EI 9
12:15
First-Order Default Logic Revisited
SPEAKER: Yi Zhou
ABSTRACT. It is well known that Reiter's original proposal for default logic in the first-order case is problematic because of Skolemization. This paper reconsiders this long-standing open problem, and proposes a new world view semantics for first-order default logic. Roughly speaking, a world view of a first-order default theory is a maximal collection of structures satisfying the default theory where the default part is fixed by the world view itself. We show that how this semantics generalizes propositional/closed default logic, classical first-order logic and first-order answer set programming, and we argue that first-order default logic under the world view semantics provides a rich framework for integrating classical logic and rule-based formalism in the first-order case.
12:20
Strong Equivalence of Non-monotonic Temporal Theories
ABSTRACT. Temporal Equilibrium Logic (TEL) is a non-monotonic temporal logic that extends Answer Set Programming (ASP) by introducing modal operators as those considered in Linear-time Temporal Logic (LTL). TEL allows proving temporal properties of ASP-like scenarios under the hypothesis of infinite time while keeping decidability. Formally, it extends Equilibrium Logic (the best-known logical formalisation of ASP) and, as the latter, it selects some models of a (temporal) monotonic basis: the logic of Temporal Here-and-There (THT). In this paper we solve a problem that remained unanswered for the last six years: we prove that equivalence in the logic of THT is not only a sufficient, but also a necessary condition for strong equivalence of two TEL theories. This result has both theoretical and practical consequences. First, it reinforces the need of THT as a suitable monotonic basis for TEL. Second, it has allowed constructing a tool, ABSTEM, that can be used to check different types of equivalence between two arbitrary temporal theories. More importantly, when the theories are not THT-equivalent, the system provides a context theory that makes them behave differently, together with a Buchi automaton showing the temporal stable models that arise from that difference.
12:25
Belief Revision in the Propositional Closure of a Qualitative Algebra
SPEAKER: unknown
ABSTRACT. Belief revision is an operation that aims at modifying old beliefs so that they become consistent with new ones. The issue of belief revision has been studied in various formalisms, in particular, in qualitative algebras (QAs) in which the result is a disjunction of belief bases that is not necessarily representable in a QA. This motivates the study of belief revision in formalisms extending QAs, namely, their propositional closures: in such a closure, the result of belief revision belongs to the formalism. Moreover, this makes it possible to define a contraction operator thanks to the Harper identity. Belief revision in the propositional closure of QAs is studied, an algorithm for a family of revision operators is designed, and an open-source implementation is made freely available on the web.
12:30
Minimal Change in AGM Revision for Non-classical Logics
SPEAKER: unknown
ABSTRACT. In this paper, we address the problem of applying AGM-style belief revision to non-classical logics. We discuss the idea of minimal change in revision and show that for non-classical logics, some sort of minimality postulate has to be explicitly introduced. We also present two constructions for revision which satisfy the AGM postulates and prove the representation theorems including minimality postulates. For each result, we point out the class of logics for which the theorem holds, giving some examples at the end.
12:35
Toward a Knowledge Level Analysis of Forgetting
ABSTRACT. Forgetting has been addressed in different areas of Knowledge Representation, including classical logic, logic programming, modal logic, and description logics. In this paper, we present an account of forgetting as an abstract belief change operator, independent of an underlying logic. We argue that forgetting amounts to a reduction in the language, specifically the signature, of a logic. The central definition is simple: the result of forgetting signature $\sigma$ in a theory is simply the set of logical consequences over the reduced language. This definition offers various advantages. It provides a uniform approach to forgetting, with a single definition applicable to any logic with a well-defined consequence relation. Results obtained are obviously applicable to all subsumed formal systems, and in fact many results are obtained much more straightforwardly. We argue that the perspective provided by the approach leads to simpler approaches to computing forgetting in specific logics. This view also leads to insights with respect to specific logics: forgetting in first-order logic is somewhat different from the accepted approach; the definition relativised to logic programs yields a new syntax-independent notion of forgetting; in modal logic the specification is simpler. Moreover, the obtained perspective clarifies the relation between forgetting and the belief change operation of contraction.
12:40
An Abductive Reasoning Approach to the Belief-Bias Effect
ABSTRACT. The tendency to accept or reject arguments based on own beliefs or prior knowledge rather than on the reasoning process is called the belief bias. A psychological syllogistic reasoning task shows this phenomenon, wherein participants were asked whether they accept or reject a given syllogism. By introducing abnormalities, abduction and background knowledge, we model this task under the weak completion semantics. Our formalization reveals new questions about observations and their explanations which might include some relevant prior abductive contextual information concerning some side-effect. Inspection points, introduced by Pereira and Pinto, allow us to express these definitions syntactically and intertwine them into an operational semantics.
12:45
Tracking Beliefs and Intentions in the Werewolf Game
ABSTRACT. We propose a formalization framework for modeling how beliefs and intentions change over the course of a dialogue, in the case where the decisions taken during the dialogue affect the possibly conflicting goals of the agents involved. We illustrate our formalization with the game of Werewolf, as an example of such a domain.
We use Situation Calculus to model the evolution of the world and an observation model to analyze the evolution of intentions and beliefs. In our formalization, utterances, that only change the beliefs and intentions, are observations. The beliefs and intentions are modeled with Kripke structure-style accessibility relation predicates. We illustrate our model on instances of the game.
12:50
Axioms .2 and .4 as Interaction Axioms
ABSTRACT. In epistemic logic, some axioms dealing with the notion of knowledge are rather convoluted and it is difficult to give them an intuitive interpretation, even if some of them, like .2 and .4, are considered by some epistemic logicians to be key axioms. We show that they can be characterized in terms of understandable interaction axioms relating knowledge and belief. In order to show it, we first present a theory dealing with the characterization of axioms in terms of interaction axioms in modal logic. We then apply the main results and methods of this theory to obtain our results related to epistemic logic.
12:55
Aggregative Deontic Detachment for Normative Reasoning
SPEAKER: unknown
ABSTRACT. In this paper, we provide foundations for deontic logic, by defining an undemanding semantics based on the sole notion of detachment. We introduce System O, which handles iteration of successive detachments in a more principled manner than the traditional systems do. This is achieved by injecting a new form of deontic detachment, called aggregative deontic detachment. It allows to keep track of previously detached obligations. Soundness and completeness of the proof system are established. Properties of the logic are discussed.
14:30-16:00 Session 151A: Reasoning about Actions and Processes 1
Location: EI, EI 7
14:30
Decidable Reasoning in a Fragment of the Epistemic Situation Calculus
SPEAKER: unknown
ABSTRACT. The situation calculus is a popular formalism for reasoning about actions and change. Since the language is first-order, reasoning in the situation calculus is undecidable in general. An important question then is how to weaken reasoning in a principled way to guarantee decidability. Existing approaches either drastically limit the representation of the action theory or neglect important aspects such as sensing. In this paper we propose a model of limited belief for the epistemic situation calculus, which allows very expressive knowledge bases and handles both physical and sensing actions. The model builds on an existing approach to limited belief in the static case. We show that the resulting form of limited reasoning is sound with respect to the original epistemic situation calculus and eventually complete for a large class of formulas. Moreover, reasoning is decidable.
15:00
Model Checking Unbounded Artifact-Centric Systems
SPEAKER: unknown
ABSTRACT. Artifact-centric systems are a recent paradigm used to represent and implement business processes. We present further results on the verification problem of artifact-centric systems specified by means of FO-CTL specifications. While the general problem is known to be undecidable, results in the literature prove decidability for artifact systems with infinite domains under boundedness and conditions such as uniformity. We here follow a different approach and investigate the general case under the infinite domains assumption. We show the decidability for the class of artifact-centric systems whose database schemas consist of a single unary relation, and we show that that the problem is undecidable if artifact systems are defined by using one binary relation or two unary relations.
15:30
State-Boundedness for Decidability of Verification in Data-Aware Dynamic Systems
SPEAKER: unknown
ABSTRACT. Verification of dynamic systems that manipulate data, stored in a database or ontology, has lately received increasing attention. A plethora of recent works has shown that verification of systems working over unboundedly many data is decidable even for very rich temporal properties, provided that the system is state-bounded. This condition requires the existence of an overall bound on the amount of data stored in each single state along the system evolution. In general, checking state-boundedness is undecidable. An open question is whether it is possible to isolate significant classes of dynamic systems for which state-boundedness is decidable. In this paper we provide a surprisingly strong negative answer, by resorting to a novel connection with variants of Petri nets. In particular, we show undecidability for systems whose data component contain unary relations only, and whose action component query and update such relations in a very limited way. To contrast this result, we propose interesting relaxations of the sufficient conditions proposed in the concrete setting of Data-Centric Dynamic Systems, building on recent results on chase termination for tuple-generating dependencies.
14:30-16:00 Session 151B: Automated Reasoning and Computation 2
Location: EI, EI 9
14:30
Skolemization for Weighted First-Order Model Counting
SPEAKER: unknown
ABSTRACT. First-order model counting recently emerged as a novel reasoning task, at the core of efficient algorithms for probabilistic logics. We present a Skolemization algorithm for model counting problems that eliminates existential quantifiers from a first-order logic theory without changing its weighted model count. For subsets of first-order logic, lifted model counters were shown to run in time polynomial in the number of objects in the domain of discourse, where propositional model counters require exponential time. However, these guarantees only apply to Skolem normal form theories, and the presence of existential quantifiers reduces lifted model counters to propositional ones. Since textbook Skolemization is not sound for model counting, these restrictions precluded efficient model counting for directed models such as probabilistic logic programs. Our Skolemization procedure extends the applicability of first-order model counters to these representations. Moreover, it simplifies the design of lifted model counting algorithms.
15:00
Analyzing the Computational Complexity of Abstract Dialectical Frameworks via Approximation Fixpoint Theory
ABSTRACT. Abstract dialectical frameworks (ADFs) have recently been proposed as a versatile generalization of Dung's abstract argumentation frameworks (AFs). In this paper, we present a comprehensive analysis of the computational complexity of ADFs. Our results show that while ADFs are one level up in the polynomial hierarchy compared to AFs, there is a useful subclass of ADFs which is as complex as AFs while arguably offering more modeling capacities. As a technical vehicle, we employ the approximation fixpoint theory of Denecker, Marek and Truszczyński, thus showing that it is also a useful tool for complexity analysis of operator-based semantics.
15:30
The Parameterized Complexity of Reasoning Problems Beyond NP
SPEAKER: unknown
ABSTRACT. Today's propositional satisfiability (SAT) solvers are extremely powerful and can be used as an efficient back-end for NP-complete problems. However, many fundamental problems in knowledge representation and reasoning are located at the second level of the Polynomial Hierarchy or even higher, and hence polynomial-time transformations to SAT are not possible, unless the hierarchy collapses. Recent research shows that in certain cases one can break through these complexity barriers by fixed-parameter tractable (fpt) reductions which exploit structural aspects of problem instances in terms of problem parameters.
In this paper we develop a general theoretical framework that supports the classification of parameterized problems on whether they admit such an fpt-reduction to SAT or not.
We instantiate our theory by classifying the complexities of several case study problems, with respect to various natural parameters. These case studies include the consistency problem for disjunctive answer set programming and a robust version of constraint satisfaction.
08:45-10:15 Session 156: VSL Keynote Talk
Location: EI, EI 7 + EI 9, EI 10 + FH, Hörsaal 1
08:45
VSL Keynote Talk: Verification of Computer Systems with Model Checking
SPEAKER: Edmund Clarke
ABSTRACT. Model Checking is an automatic verification technique for large state transition systems. The technique has been used successfully to debug complex computer hardware and communication protocols. Now, it is beginning to be used for complex hybrid (continuous/discrete) systems as well. The major disadvantage of the technique is a phenomenon called the State Explosion Problem. This problem is impossible to avoid in worst case. However, by using sophisticated data structures and clever search algorithms, it is now possible to verify hybrid systems with astronomical numbers of states.
10:15-10:45Coffee Break
13:00-14:30Lunch Break
16:00-16:30Coffee Break
19:30-21:30 Session 158: KR Banquet
Location: Naturhistorisches Museum | 2018-04-19 23:16:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6078889966011047, "perplexity": 1302.7563909147418}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125937074.8/warc/CC-MAIN-20180419223925-20180420003925-00205.warc.gz"} |
https://vankheakh.wordpress.com/2011/08/19/problem-297-van-khea/ | # INEQUALITY'S BLOG
## August 19, 2011
### Problem 298 Van Khea
Filed under: Problem by Van Khea — KKKVVV @ 3:12 am
Let $a, b, c, d$ be positive real numbers such that $a+b+c+d\leq 4$.Prove that
$\displaystyle \frac{1}{a^4+b^4+c^4+d^4}+\frac{1}{abcd}\geq \frac{5}{4}$ | 2017-06-27 00:16:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5254385471343994, "perplexity": 8390.897072223419}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320873.54/warc/CC-MAIN-20170626235612-20170627015612-00088.warc.gz"} |
https://mathhelpboards.com/threads/prove-a-is-invertable-for-all-values-of-theta.5348/ | # Prove A is invertable for all values of theta
#### delgeezee
##### New member
Show that matrix A is invertible for all values of $$\displaystyle \theta$$; then find $$\displaystyle A^{-1}$$ using
$$\displaystyle A^{-1}= \frac{1}{det(A)}adj(A)$$
A =
cos$$\displaystyle \theta$$ -sin$$\displaystyle \theta$$ 0 sin$$\displaystyle \theta$$ cos$$\displaystyle \theta$$ 0 0 0 1
----------
By cofactoring along the 3rd row, I find det(A) = (1)*($$\displaystyle cos^2\theta + sin^2\theta$$) =1 , which is a nonzero and implies that A is invertible.
To get the Andjuct of A or Adj(A) , I form a cofactor matrix C and transpose it.
Adj(A) = $$\displaystyle C^{T}$$ =
A =
cos$$\displaystyle \theta$$ sin$$\displaystyle \theta$$ 0 -sin$$\displaystyle \theta$$ cos$$\displaystyle \theta$$ 0 0 0 1
which also happens to be $$\displaystyle A^{-1}$$
My Question is how am I suppose to prove A is invertible for all Values of $$\displaystyle /theta$$?
My gut tells me I am suppose to state that $$\displaystyle A^{-1}= \frac{1}{det(A)}adj(A)$$ does not depend on $$\displaystyle \theta$$. Is there a more definitive way of showing A is invertible for all Values of $$\displaystyle \theta$$?
#### M R
##### Active member
My Question is how am I suppose to prove A is invertible for all Values of $$\displaystyle /theta$$?
You found that $$\det(A) \ne 0$$. That's all you need to do.
#### Jameson
Staff member
I agree that you've done enough, but to show that the determinant is non-zero for all $\theta$, I would say something along the lines of the following.
$\forall \theta \in \mathbb{R}$ it follows that $\sin (\theta ) \text{ and} \cos( \theta ) \in \mathbb{R}$. Every element in $A$ is in $\mathbb{R}$ so operations involving those elements are also in $\mathbb{R}$ and the result you found holds for all $\theta$.
Not the best wording maybe, but that's the general idea.
#### Opalg
##### MHB Oldtimer
Staff member
My Question is how am I suppose to prove A is invertible for all Values of $$\displaystyle /theta$$?
My gut tells me I am suppose to state that $$\displaystyle A^{-1}= \frac{1}{det(A)}adj(A)$$ does not depend on $$\displaystyle \theta$$. Is there a more definitive way of showing A is invertible for all Values of $$\displaystyle \theta$$?
$A^{-1}= \begin{bmatrix}\cos\theta & \sin\theta &0 \\ -\sin\theta & \cos\theta & 0 \\ 0&0&1 \end{bmatrix}$, which does depend on $\theta$. But $\det A=1$, and the constant $1$ is nonzero and does not depend on $\theta$. That is all you need, to conclude that $A$ is invertible for all $\theta.$
#### Fernando Revilla
##### Well-known member
MHB Math Helper
Show that matrix A is invertible for all values of $$\displaystyle \theta$$; then find $$\displaystyle A^{-1}$$ using
$$\displaystyle A^{-1}= \frac{1}{det(A)}adj(A)$$
Another way of finding $A^{-1}$ in this case (I don't know if you have covered it) is to consider $$A(\theta)= \begin{bmatrix}\cos\theta & -\sin\theta &0 \\ \sin\theta & \;\;\cos\theta & 0 \\ 0&0&1 \end{bmatrix}$$ as a rotation around the $z$-axis by angle $\theta$. Then, by geometric considerations $A(\theta)A(-\theta)=A(0)=I$, so $$A^{-1}(\theta)=A(-\theta)=\begin{bmatrix}\cos(-\theta) & -\sin(-\theta) &0 \\ \sin(-\theta) & \;\;\cos(-\theta) & 0 \\ 0&0&1 \end{bmatrix}=\begin{bmatrix}\;\;\cos\theta & \sin\theta &0 \\ -\sin\theta & \cos\theta & 0 \\ 0&0&1 \end{bmatrix}$$ | 2020-09-19 02:16:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8653872609138489, "perplexity": 256.50751755648946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400189928.2/warc/CC-MAIN-20200919013135-20200919043135-00335.warc.gz"} |
https://www.ctan.org/tex-archive/macros/latex/contrib/centerlastline | # Directory macros/latex/contrib/centerlastline
centerlastline --- last line centered (spanish paragraph)
=========================================================
Versions
1.0 -> initial version
Copyright (C) 2020 Miguel V. S. Frasson (mvsfrasson@gmail.com)
=======
This file is the README file, part of the centerlastline' package.
This package may be distributed under the terms of the LaTeX Project
Public License, as described in lppl.txt in the base LaTeX
distribution, either version 1.3 or (at your option) any later
version.
You can obtain a copy of the lppl.txt file from the internet on
http://www.latex-project.org/lppl.txt
USAGE
=====
The package _centerlastline_ provides command \centerlastline, which
sets paragraph style to typeset with no indentation and last line
centered, an arrangemente known as _Spanish paragraph_. An example
{\centerlastline
A big paragraph to be formatted with no indentation and last line
centered. It is a not-so-frequent composition, useful to finish a
large paragraph of text, at the end of chapters, prologues, back cover
of books, etc. Be careful to finish the paragraph with a blanck line
or \verb+\par+, to the paragraph style take effect.\par}
It can be used as an environment too, as in
\begin{centerlastline}
A paragraph to be formatted as a Spanish paragraph. In environment
form, user doesn't have to take care of last paragraph. The
environment taks care of everything.
\end{centerlastline}
` | 2022-06-25 20:00:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8651085495948792, "perplexity": 10652.156640557007}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103036099.6/warc/CC-MAIN-20220625190306-20220625220306-00787.warc.gz"} |
https://kth.kattis.com/courses/DD2458/popup23/assignments/uwpi2f/problems/cudak | Hide
# Problem BCudak
Božo is a strange little boy. Every day he tires his friends with strange questions. Today’s question is: how many integers in the interval $[A, B]$ are there such that the sum of their digits is $S$, and which is the smallest such number?
Write a program that answers Božo’s question so that he can get some sleep.
## Input
The input contains three integers $A$, $B$ and $S$ ($1 \le A \le B < 10^{15}$, $1 \le S \le 135$).
## Output
The first line should contain the number of integers in the interval with the digit sum equal to $S$.
The second line should contain the smallest such integer.
The input data will guarantee that the first number is at least $1$.
Sample Input 1 Sample Output 1
1 9 5
1
5
Sample Input 2 Sample Output 2
1 100 10
9
19
Sample Input 3 Sample Output 3
11111 99999 24
5445
11499 | 2023-03-27 16:56:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4889655113220215, "perplexity": 639.5372675104604}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948673.1/warc/CC-MAIN-20230327154814-20230327184814-00544.warc.gz"} |
http://www.mathynomial.com/problem/1676 | # Problem #1676
1676 A bug crawls along a number line, starting at $-2$. It crawls to $-6$, then turns around and crawls to $5$. How many units does the bug crawl altogether? $\textbf{(A)}\ 9\qquad\textbf{(B)}\ 11\qquad\textbf{(C)}\ 13\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 15$ This problem is copyrighted by the American Mathematics Competitions.
Note: you aren't logged in. If you log in, we'll keep a record of which problems you've solved. | 2018-02-23 14:08:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 4, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4886923134326935, "perplexity": 1781.6564917615947}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814787.54/warc/CC-MAIN-20180223134825-20180223154825-00351.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?t=5127 | ## Phase change with q=mCsΔT!
Regina Chi 2K
Posts: 51
Joined: Fri Sep 26, 2014 2:02 pm
### Phase change with q=mCsΔT!
Hi, this is actually regarding a specific problem in the textbook (7.39). We are trying to find the final temperature when you put an ice cube at 0°C into water at 45°C. The mass for the ice cube is 50.0 grams and for the water it is 400.0 grams. I understand we use the equation q=mCsΔT, but the part that I need help on is understanding why for the ice cube we use the specific heat capacity of water as a liquid and not as a solid?
martha-1I
Posts: 76
Joined: Fri Sep 26, 2014 2:02 pm
### Re: Phase change with q=mCsΔT!
Specific heat capacity is used for water as a liquid and not a solid because the ice cube (water in solid form) is melting so therefore we would need to compute the heat from fusion and heat once it is a liquid. First, we compute heat as the ice cube melts by using q=n$\Delta$Hfus and once it is melted we find out the heat of it as a liquid using q=mc$\Delta$T. This is why the specific heat capacity is of water as a liquid because at this point we are working with the ice cube that has been melted into water. We add these two heat values (ice cube melting + ice cube melted) in order to find the total heat for the ice cube. The heat for the water already in the container is calculated using -mc$\Delta$T since we are considering it as the surrounding in this experiment.
The set up for this problem should be in the format of qsystem=-qsurroundings. I chose the ice cube to be the system and then found the heat for each. Your final equation should look like this:
(Ice cube) n$\Delta$H + mc$\Delta$T =(water) -mc$\Delta$T
Regina Chi 2K
Posts: 51
Joined: Fri Sep 26, 2014 2:02 pm
### Re: Phase change with q=mCsΔT!
Oh okay. So you're saying when we calculated q=mCsΔT, at that point, the ice cube is already melted into liquid water. And so we would use the specific heat capacity of water to calculate the temperature difference between the two components? This is what you mean right? :)
martha-1I
Posts: 76
Joined: Fri Sep 26, 2014 2:02 pm
Yes. You got it! | 2020-07-15 06:28:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6695335507392883, "perplexity": 671.7854219767132}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657155816.86/warc/CC-MAIN-20200715035109-20200715065109-00027.warc.gz"} |
https://nforum.ncatlab.org/discussion/6391/perceptual-and-mathematical-invariants/ | ## Not signed in
Want to take part in these discussions? Sign in if you have an account, or apply for one below
## Site Tag Cloud
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
• CommentRowNumber1.
• CommentAuthorDavid_Corfield
• CommentTimeDec 22nd 2014
I’ve just been re-reading Cassirer’s 1944 paper The concept of group and the theory of perception where he’s bringing together Klein’s Erlanger Program with the findings of the Gestalt school of psychology.
If perception is to be compared to an apparatus at all, the latter must be such as to be capable of “grasping intrinsic necessities.” Such intrinsic necessities are encountered everywhere. It is only with reference to such “intrinsic necessity” that the “transformation” to which we subject a given form is well defined, inasmuch as the transformation is not arbitrary and executed at random but proceeds in accordance with some rule that can be formulated in general terms. (p. 26) (“grasping intrinsic necessities” is due to Max Wertheimer)
He thinks that in mathematics this procedure is taken further right up to group-theoretic invariance, but that its seeds are there in perception.
Interesting that the word ’necessities’ appears, in view of our discussion on necessity as dependent product and base change over $W \to \ast$. Could one say something similar over $B G \to \ast$? I think maybe I’d like to get clearer on the dependent product - homotopy invariants relation.
Or to start with perception, how do we ’know’ that we’re dealing with the same shape in A of this image? We seem to be able to relate 2D projections of a 3D figure subjected to the actions of $E(3)$.
There’s also one’s own motion to consider. True to his neo-Kantian roots Cassirer quotes Bühler
The concept of factors of constancy in the face of variation of both external and internal conditions of perception is the realization, in modern form, of that which in principle…was known to Kant, the analyst, and which he stated in terms of mediating schemata.
Perceptual images of objects are products of the imagination. Productive imagination is necessary for objective determination.
I wonder what of all this can be given the HoTT treatment.
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeDec 22nd 2014
• (edited Dec 22nd 2014)
Interesting that the word ’necessities’ appears, in view of our discussion on necessity as dependent product and base change over $W \to \ast$. Could one say something similar over $B G \to \ast$?
That’s a nice observation. Yes, when we pronounce the monad $f^\ast \circ \prod_f$ as ’nessecarily’ (as we should) then something in the context of $\mathbf{B}G$ being necessary means it is $G$-invariant.
I think maybe I’d like to get clearer on the dependent product - homotopy invariants relation.
Give me some data about at which point you need more information. The key is that dependent product produces sections (as explained here) and that the incarnation of an object $V$ equippeded with a $G$-action as an object in context of $\mathbf{B}G$ is via its homotopy quotient $X//G \to \mathbf{B}G$ (as exlained here). So you should convince yourself that a section of $V//G \to \mathbf{B}G$ is precisely a $G$-invariant.
It is necessary (and maybe already sufficient) to convince yourself of this in the simple special case that $G$ is a discrete group acting on a set $V$. Then $V//G$ is the plain ordinary action groupoid and you are asking for functors from the one-object groupoid $\mathbf{B}G$ to the action groupoid which send each element of $G$ to the morphism exhibiting its action. It is evident (maybe after drawing some of these morphisms) that such functors pick precisely the $G$-fixed points in the set $V$.
• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeDec 22nd 2014
• (edited Dec 22nd 2014)
Right, so I understand that. Then I seem to have difficulty making sense of something like
The area, $A$, of a triangle in the Euclidean plane, $P$, is invariant under $E(2)$.
Try again. So we have $P$ acted on by $E(2)$. The space of (possibly degenerate) triangles is $[3, P]$, which inherits an $E(2)$ action. I can context extend the reals over to $\mathbf{B} E(2)$, and then take $A$ to be an equivariant map from $[3, P]$ to $\mathbb{R}$.
So where’s something dependent product-like?
Oh, is it that in the context of $\mathbf{B} E(2)$, the hom space $[3, P] \to \mathbb{R}$ includes $A$ which is a fixed point under the action? So $A$ is ’necessary’ in the context.
That’s rather like the covariance story of fields (co-shapes) defined on a space-time, but I guess here the domain isn’t subject to its own full automorphism group, but just inherits one from $P$, which in turn is a coset space of $E(2)$ for the inclusion of rotations about a point.
• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeDec 23rd 2014
• (edited Dec 23rd 2014)
Yes, the space $[[3,P],\mathbb{R}]$ inherits an $E(2)$-action. The area function is a point in $[[3,P],\mathbb{R}]$ and indeed an invariant point.
And, yes, it’s much like in the covariance story, or rather like the “co-shape” invariants that we discussed recently. A function on a space of configurations is what in physics is called an observable. Here we are looking at the “gauge invariant observables” on the space of triangle configurations.
Maybe one could pronounce it like this: among all observables on $[3,P]$ in the context of $\mathbf{B}E(2)$, among those that are “intrinsically necessary”, in the sense of #1, is the area.
• CommentRowNumber5.
• CommentAuthorRodMcGuire
• CommentTimeDec 23rd 2014
• (edited Dec 23rd 2014)
There’s also one’s own motion to consider
Visual perceptions and actions based on them when the observer and/or observed is moving seem to be handled by flow fields. I recall that the right way to catch a fly ball in baseball is to run at a speed and direction to minimize the baseball’s flow, and when the baseball becomes invariant you wind up at the right time and place to catch the ball.
Are these flow fields related to some type of fields written about in the nLab?
• CommentRowNumber6.
• CommentAuthorDavid_Corfield
• CommentTimeDec 23rd 2014
Some interesting gleanings from Shepard, Roger N., 1984 ’Ecological constraints on internal representation: resonant kinematics of perceiving, imagining, thinking, and dreaming’, Psychological Review 91:417-47 (pdf)
…it remained for Gibson to adopt the radical hypothesis of what he called the ecological approach to perception (Gibson, 1961, 1979), namely, the hypothesis that under normal conditions, invariants sufficient to specify all significant objects and events in the organism’s environment, including the dispositions and motions of those objects and of the organism itself relative to the continuous ground, can be directly picked up or extracted from the flux of information available in its sensory arrays.
In the case of the modality that most attracted Gibson’s attention—vision—the invariants generally are not simple, first-order psychophysical variables such as direction, brightness, spatial frequency, wavelength, or duration. Rather, the invariants are what J. Gibson (1966) called the higher order features of the ambient optic array. (See J. Gibson, 1950, 1966, 1979; Hay, 1966; Lee, 1974; Sedgwick, 1980.) Examples include (a) the invariant of radial expansion of a portion of the visual field, looming, which specifies the approach of an object from a particular direction, and (b) the projective cross ratios of lower order variables mentioned by J. Gibson (1950, p. 153) and by Johansson, von Hofsten, and Jansson (1980, p. 31) and investigated particularly by Cutting (1982), which specify the structure of a spatial layout regardless of the observer’s station point.
For invariants that are significant for a particular organism or species, Gibson coined the term affordances (J. Gibson, 1977). Thus, the ground’s invariant of level solidity affords walking on for humans, whereas its invariant of friability affords burrowing into for moles and worms. And the same object (e.g., a wool slipper) may primarily afford warmth of foot for a person, gum stimulation for a teething puppy, and nourishment for a larval moth. The invariants of shape so crucial for the person are there in all three cases but are less critical for the dog and wholly irrelevant for the moth. (Shepard 1984, p. 418)
There are good reasons why the automatic operations of the perceptual system should be guided more by general principles of kinematic geometry than by specific principles governing the different probable behaviors of particular objects. Chasles’s theorem constrains the motion of each semirigid part of a body, during each moment of time, to a simple, six-degrees-of-freedom twisting motion, including the limiting cases of pure rotations or translations. By contrast, the more protracted motions of particular objects (a falling leaf, floating stick, diving bird, or pouncing cat) have vastly more degrees of freedom that respond quite differently to many unknowable factors (breezes, currents, memories, or intentions). Moreover, relative to a rapidly moving observer, the spatial transformations of even nonrigid, insubstantial, or transient objects (snakes, bushes, waves, clouds, or wisps of smoke) behave like the transformations of rigid objects (Shepard & Cooper, 1982).
It is not surprising then that the automatic perceptual impletion that is revealed in apparent motion does not attempt either the impossible prediction or the arbitrary selection of one natural motion out of the many appropriate to the particular object. Rather, it simply instantiates the continuing existence of the object by means of the unique, simplest rigid motion that will carry the one view into the other, and it does so in a way that is compatible with a movement either of the observer or of the object observed.(Shepard 1984, p. 426)
Putting the considerations concerning preference for the simplest transformation that preserves rigid structure together with those concerning the conducive conditions for impletion of such a transformation, I have posited a hierarchy of structural invariance (Shepard, 1981b). At the top of the hierarchy are those transformations that preserve rigid structure but that require greater time for their impletion. As the perceptual system is given less time (by decreasing the SOA [stimulus onset asynchrony]), the system will continue to identify the two views and hence to maintain object conservation, but only by accepting weaker criteria for object identity. Shorter paths that short-circuit the helical trajectory will then be traversed, giving rise to increasing degrees of experienced nonrigidity (Farrell & Shepard, 1981). Likewise, if the two alternately presented views are incompatible with a rigid transformation in three-dimensional space, the two views will still be interpreted as a persisting object, but again a nonrigid one. (Shepard 1984, p. 430)
• CommentRowNumber7.
• CommentAuthorDavid_Corfield
• CommentTimeDec 23rd 2014
And
Instead of saying that an organism picks up the invariant affordances that are wholly present in the sensory arrays, I propose that as a result of biological evolution and individual learning, the organism is, at any given moment, tuned to resonate to the incoming patterns that correspond to the invariants that are significant for it (Shepard, 1981b). (Shepard 1984, p. 433)
…although J. Gibson (1970) held that perceiving is an entirely different kind of activity from thinking, imagining, dreaming, or hallucinating, I like to caricature perception as externally guided hallucination, and dreaming and hallucination as internally simulated perception. Imagery and some forms of thinking could also be described as internally simulated perceptions, but at more abstract levels of simulation. (Shepard 1984, p. 436)
Foreshadowing the commutative diagram that I much later proposed (Shepard, 1981b, p. 294), Heinrich Hertz succinctly stated that “the consequents of the images must be the images of the consequents” (Hertz, 1894/1956, p. 2). (Shepard 1984, p. 441)
• CommentRowNumber8.
• CommentAuthorDavid_Corfield
• CommentTimeJan 6th 2015
I guess an example to illustrate the final paragraph of #6 is when you hold a pencil loosely in a ring formed by forefinger and thumb. If you move the ring up and down fast enough, the pencil appears to be bendy.
Have we changed the context (in the type theoretic sense) to a more generous group, $\mathbb{B} G$?
• CommentRowNumber9.
• CommentAuthortonyjones
• CommentTimeJan 6th 2015
• (edited Jun 12th 2015)
Possibly of interest: Groups in Mind by David Hilbert and Nick Huggett
groups in mind From introduction: ’We consider the question of the manner of the internalization of the geometry and topology of physical space in the mind, both the mechanism of internalization and precisely what structures are internalized. Though we will not argue for the point here, we agree with the long tradition which holds that an understanding of this issue is crucial for addressing many metaphysical and epistemological questions concerning space’
• CommentRowNumber10.
• CommentAuthortonyjones
• CommentTimeJan 6th 2015
• (edited Jun 12th 2015)
Jean Petitot has also done some interesting work around the intersection of logic, geometry, perception and Husserl;
’Phenomenology of perception, qualitative physics and sheaf mereology’ phenomenology
’Sheaf mereology and Husserl’s morphological ontology’ sheaf mereology
’Sheaf mereology and space cognition’ space cognition
• CommentRowNumber11.
• CommentAuthorTodd_Trimble
• CommentTimeJan 6th 2015
Tony, do you know how to create links on the nForum?
If you set your filter to Markdown+Itex and type something like
[Phenomenology of perception, qualitative physics and sheaf mereology](http://www.crea.polytechnique.fr/JeanPetitot/ArticlesPDF/Petitot_Kirchberg.pdf)
you will get Phenomenology of perception, qualitative physics and sheaf mereology with a clickable link.
(If you want to link to an nLab article, it’s even easier: use Markdown+Itex and type say [[Aufhebung]] to link to the article Aufhebung.)
• CommentRowNumber12.
• CommentAuthortonyjones
• CommentTimeJun 11th 2015
• (edited Jun 12th 2015)
This may be of interest to you David. It discusses possible applications of ideas from homotopy type theory, algebraic topology and other related areas to learning:
Questions and speculation on learning and cohomology - Joshua Tan
• CommentRowNumber13.
• CommentAuthorTodd_Trimble
• CommentTimeJun 11th 2015
Ahem. See #11. It would be just as simple as what you have, and saves other people time.
• CommentRowNumber14.
• CommentAuthorDavid_Corfield
• CommentTimeJun 12th 2015
Tony #11, plenty of interesting things there. Now for him to put them together.
• CommentRowNumber15.
• CommentAuthortonyjones
• CommentTimeJun 12th 2015
• (edited Jun 12th 2015)
Done. Copy and paste isn’t that much of a struggle though is it? :)
• CommentRowNumber16.
• CommentAuthorTodd_Trimble
• CommentTimeJun 12th 2015
• (edited Jun 12th 2015)
Thanks, Tony. And sorry to belabor this, but since you asked:
Recall that it typically involves positioning a cursor, highlighting text, going to the menu and hitting copy, opening a new tab, positioning the cursor in the address bar, going to the menu and hitting paste, and finally hitting enter before one sees a word of text. It’s hardly a struggle for those who know in advance they will be interested in an article, but for others who are not sure, it may involve a struggle deciding whether they want to go to the bother. And half of them will decide not to.
Meanwhile, for users who are trying to elicit interest in an article, it involves just an extra pair of square brackets and an extra pair of round brackets:
[Questions and speculation on learning and cohomology - Joshua Tan](http://www.joshuatan.com/wp-content/uploads/2015/03/0-questions.pdf)
In the end it’s probably worth it, to make it easy for busy people with a scintilla of curiosity to do a single click. :-)
• CommentRowNumber17.
• CommentAuthortrent
• CommentTimeJun 12th 2015
Really impressed that Tan did his undergrad degree in Art History. With that and his current research on geometry of AI, he should have extremely interesting intuition with regards to how human thought functions.
• CommentRowNumber18.
• CommentAuthorMike Shulman
• CommentTimeJun 12th 2015
Even less work is to just add a pair of angle brackets: <http://www.joshuatan.com/wp-content/uploads/2015/03/0-questions.pdf> makes a link http://www.joshuatan.com/wp-content/uploads/2015/03/0-questions.pdf.
• CommentRowNumber19.
• CommentAuthortonyjones
• CommentTimeJan 22nd 2016
Just a little update on Joshua Tan. According to his page he has been working with David Spivak on applied category theory and Misha Gromov on the mathematical foundations of AI. Will be interesting to see what comes out of these collaborations as both Spivak and Gromov have some really fascinating ideas on applications of category theory to other fields.
• CommentRowNumber20.
• CommentAuthorDavid_Corfield
• CommentTimeDec 17th 2018
Coming back to this, in the paper in #1, Cassirer is reflecting on how we come to perceive objects with size and colour constancy. He writes
The “images” that we receive from objects, the “impressions” which sensationalism tried to reduce perception to, exhibit no such unity. Each and every one of these images possesses a peculiarity of its own; they are and remain discrete as far as their contents are concerned. But the analysis of perception discloses a formal factor which supersedes this particularity and disparity. Perception unifies and, as it were, concentrates the manifolds of particular images with which we are supplied at every moment…Each invariant of perception is … a scheme toward which the particular sense-experiences are orientated and with reference to which they are interpreted. (p. 32)
As I mentioned in #1, he’s looking to find commonality between Felix Klein and Gestalt psychology. Sensationalist psychology is wrong, there is active participation of the imagination in perception. Clearly it’s built deep in to our psychological apparatus - animals see objects and employ size constancy.
Given a type of ’discrete’ impressions, $A: Type$, how do we represent unified perceptions? For an arrow $A: \mathbf{1} \to Type$, then sometimes we perceive it via a factorisation, $\mathbf{1} \to \mathbf{B} G \to Type$, through say $A^'$ with a $G$-action, so that the unified perceptions are orbits, elements of the action groupoid, $\sum_{\ast: \mathbf{B} G} A^'$.
Elements of the type of perceived objects, $A^'$, can’t be given by a single impression. With a free action, an orbit is equivalent to a point, hence the unity of the object.
• CommentRowNumber21.
• CommentAuthorDavid_Corfield
• CommentTimeJun 18th 2021
• (edited Jun 18th 2021)
The idea in #20 made it into my book as the possibility comonad for a group action along $\mathbf{B} G \to \mathbf{1}$, so that the counit $A \to \lozenge_{\mathbf{B} G} A$ maps elements of a type under a $G$-action to its orbits (under the trivial action). But then why does Cassirer speak of “invariants”?
I might have added that these orbits are of course in turn fixed by the trivial $G$-action, $\lozenge_{\mathbf{B} G} A \simeq \Box_{\mathbf{B} G} \lozenge_{\mathbf{B} G} A$, something to be expected since this is an S5 modal logic, and Axiom (5) specifies that possibly $P$ implies necessarily possibly $P$.
• CommentRowNumber22.
• CommentAuthorDavid_Corfield
• CommentTimeJun 18th 2021
Reminiscent too of Husserl, here:
You may take a concept like “thing” and start imagining different possible experiences of it. Husserl (1973b, p. 341) observed that it “then becomes evident that a unity runs through this multiplicity of successive figures, that in such free variations of an original image, e.g., of a thing, an invariant is necessarily retained as the necessary general form, without which an object such as this thing, as an example of its kind, would not be thinkable at all.” | 2021-12-04 22:37:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 58, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6924321055412292, "perplexity": 2113.5452958296923}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363125.46/warc/CC-MAIN-20211204215252-20211205005252-00619.warc.gz"} |
https://www.mathphysicsbook.com/mathematics/fiber-bundles/generalizing-tangent-spaces/vertical-tangents-and-horizontal-equivariant-forms/ | # Vertical tangents and horizontal equivariant forms
A smooth bundle $${(E,M,\pi)}$$ is a manifold itself, and thus has tangent vectors. A tangent vector $${v}$$ at $${p\in E}$$ is called a vertical tangent if $${\mathrm{d}\pi(v)=0}$$, i.e. if it is tangent to the fiber over $${x}$$ where $${\pi(p)=x}$$, so the projection down to the base space vanishes. The vertical tangent space $${V_{p}}$$ is then the subspace of the tangent space $${T_{p}}$$ at $${p}$$ consisting of vertical tangents, and viewing the vertical tangent spaces as fibers over $${E}$$ we can form the vertical bundle $${(VE,E,\pi_{V})}$$, which is a subbundle of $${TE}$$. We can also consider differential forms on a smooth bundle, which take arguments that are tangent vectors on $${E}$$. A form is called a horizontal form if it vanishes whenever any of its arguments are vertical.
On a smooth principal bundle $${(P,M,G)}$$, we have a consistent right action $${\rho\colon G\rightarrow\mathrm{Diff}(P)}$$, and the corresponding Lie algebra action $${\mathrm{d}\rho\colon\mathfrak{g}\rightarrow\mathrm{vect}(P)}$$ is then a Lie algebra homomorphism. The fundamental vector fields corresponding to elements of $${\mathfrak{g}}$$ are vertical tangent fields; in fact, at a point $${p}$$, $${\mathrm{d}\rho\left|_{p}\right.}$$ is a vector space isomorphism from $${\mathfrak{g}}$$ to $${V_{p}}$$:
$$\displaystyle \mathrm{d}\rho\left|_{p}\right.\colon\mathfrak{g}\overset{\cong}{\rightarrow}V_{p}$$
In addition, the right action $${g\colon P\rightarrow P}$$ of a given element $${g}$$ corresponds to a right action $${\mathrm{d}g\colon TP\rightarrow TP}$$, which maps tangent vectors on $${P}$$ via
$$\displaystyle \mathrm{d}g(v)\colon T_{p}P\rightarrow T_{g(p)}P.$$
This map is an automorphism of $${TP}$$ restricted to $${\pi_{P}^{-1}(x)}$$, which we denote $${T_{\pi^{-1}(x)}P}$$, and it is not hard to show that it preserves vertical tangent vectors. We can then consider the pullback $${g^{*}\varphi(v_{1},\ldots,v_{k})=\varphi(\mathrm{d}g(v_{1}),\ldots,\mathrm{d}g(v_{k}))}$$ as a right action on the space $${\Lambda^{k}P}$$ of $${k}$$-forms on $${P}$$.
If we have a bundle $${(E,M,\pi_{E},F)}$$ associated to $${(P,M,\pi_{P},G)}$$, we can define an $${F}$$-valued form $${\varphi_{P}}$$, which can be viewed on each $${\pi_{P}^{-1}(x)}$$ as a mapping
$$\displaystyle \varphi_{P}\colon T_{\pi^{-1}(x)}P\otimes\cdots\otimes T_{\pi^{-1}(x)}P\rightarrow F\times\pi_{P}^{-1}(x),$$
where $${g\in G}$$ has a right action $${\mathrm{d}g}$$ on $${T_{\pi^{-1}(x)}P}$$ and a left action $${g}$$ on the abstract fiber $${F}$$ of $${E}$$. The form $${\varphi_{P}}$$ is called an equivariant form if this mapping is equivariant with respect to these actions, i.e. if
$$\displaystyle g^{*}\varphi_{P}=g^{-1}\left(\varphi_{P}\right).$$
If $${\varphi_{P}}$$ is also horizontal, then it is called a horizontal equivariant form (AKA basic form, tensorial form). If we pull back a horizontal equivariant form to the base space $${M}$$ using the identity sections, we get forms
$$\displaystyle \varphi_{i}\equiv\sigma_{i}^{*}\varphi_{P}$$
on each $${U_{i}\subset M}$$. Using the identity section relation $${\sigma_{i}=g_{ij}^{-1}(\sigma_{j})}$$ and the pullback composition property $${\left(g(h)\right)^{*}\varphi=h^{*}\left(g^{*}\varphi\right)}$$, we see that the values of these forms satisfy
\displaystyle \begin{aligned}\varphi_{i} & =\left(g_{ij}^{-1}(\sigma_{j})\right)^{*}\varphi_{P}\\ & =\sigma_{j}^{*}\left(\left(g_{ij}^{-1}\right)^{*}\varphi_{P}\right)\\ & =\sigma_{j}^{*}\left(g_{ij}\left(\varphi_{P}\right)\right)\\ & =g_{ij}\left(\varphi_{j}\right), \end{aligned}
where in the third line $${g_{ij}}$$ is acting on the value of $${\varphi_{P}}$$. This means that at a point $${x}$$ in $${U_{i}\cap U_{j}}$$, the values of $${\varphi_{i}}$$ and $${\varphi_{j}}$$ in the abstract fiber $${F}$$ correspond to a single point in $${\pi_{E}^{-1}(x)\in E}$$, so that the union $${\bigcup\varphi_{i}}$$ can be viewed as comprising a single $${E}$$-valued form $${\varphi}$$ on $${M}$$. Such a form is sometimes called a section-valued form, since for fixed argument vector fields its value on $${M}$$ is a section of $${E}$$. It can be shown that the correspondence between the $${E}$$-valued forms $${\varphi}$$ on $${M}$$ and the horizontal equivariant $${F}$$-valued forms on $${P}$$ is one-to-one. Equivariant $${F}$$-valued 0-forms on $${P}$$ are automatically horizontal (since one cannot pass in a vertical argument), and are thus one-to-one with sections on $${E}$$.
The above depicts how the differential of the right action of $${G}$$ on $${\pi_{P}^{-1}(x)\in P}$$ creates an isomorphism to the vertical tangent space $${\mathfrak{g}\cong V_{p}}$$. A horizontal equivariant form $${\varphi_{P}}$$ on $${P}$$ maps non-vertical vectors to the abstract fiber $${F}$$ of an associated bundle, and pulling back by the identity sections yields an $${E}$$-valued form $${\varphi}$$ on $${M}$$. Although denoted identically, the $${f_{i}}$$ are those corresponding to each bundle.
On the frame bundle $${(P,M,\pi_{P},GL(n,\mathbb{K}))}$$ associated with a vector bundle $${(E,M,\pi_{E},\mathbb{K}^{n})}$$, a $${\mathbb{K}^{n}}$$-valued form $${\vec{\varphi}_{P}}$$ is then equivariant if
$$\displaystyle g^{*}\vec{\varphi}_{P}=\check{g}^{-1}\vec{\varphi}_{P},$$
where $${\check{g}^{-1}}$$ is a matrix-valued 0-form on $${P}$$ operating on the $${\mathbb{K}^{n}}$$-valued form $${\vec{\varphi}_{P}}$$. The pullback of a horizontal equivariant form on $${P}$$ to the base space $${M}$$ using the identity sections satisfies
$$\displaystyle \vec{\varphi}_{i}=\check{g}_{ij}\vec{\varphi}_{j},$$
where $${\check{g}_{ij}}$$ is now a matrix-valued 0-form on $${M}$$. At a point $${x}$$ in $${U_{i}\cap U_{j}}$$, the values of $${\vec{\varphi}_{i}}$$ and $${\vec{\varphi}_{j}}$$ in the abstract fiber $${\mathbb{K}^{n}}$$ correspond to a single abstract vector in $${V_{x}=\pi_{E}^{-1}(x)\in E}$$, so that the union $${\bigcup\vec{\varphi}_{i}}$$ can be viewed as comprising a single $${V}$$-valued form $${\vec{\varphi}}$$ on $${M}$$. Thus an equivariant $${\mathbb{K}^{n}}$$-valued 0-form on $${P}$$ is a matter field on $${M}$$.
◊ This correspondence can be viewed as follows. The right action of $${g}$$ on $${P}$$ is a transformation on bases, so that the equivalent transformation of vector components is $${g^{-1}}$$. The left action of $${g^{-1}}$$ on the fiber is also a transformation of vector components. Thus the equivariant property can be viewed as “keeping the same value when changing basis on both bundles,” so that the values of $${\vec{\varphi}_{P}}$$ on $${\pi_{P}^{-1}(x)\in P}$$ correspond to a single point in $${\pi_{E}^{-1}(x)\in E}$$, i.e a single abstract vector over $${M}$$. In other words, $${\vec{\varphi}\in T_{x}M}$$ is determined by the value of $${\vec{\varphi}_{P}}$$ at a single point in $${\pi_{P}^{-1}(x)\in P}$$. The horizontal requirement means we do not consider forms which take non-zero values given argument vectors which project down to a zero vector on $${M}$$.
Under an automorphism gauge transformation, the transformation of a horizontal equivariant form on the frame bundle $${P}$$ is defined by the pullback of the automorphism
$$\displaystyle \vec{\varphi}_{P}^{\prime}\equiv\left(\gamma^{-1}\right)^{*}\vec{\varphi}_{P}.$$
The automorphism does not give us a right action on $${T_{\pi^{-1}(x)}P}$$ by a fixed element, but it does give a right action when acting on the element in the identity section, so since the identity sections remain constant we have
\displaystyle \begin{aligned}\vec{\varphi}_{i}^{\prime} & =\sigma_{i}^{*}\left(\gamma^{-1}\right)^{*}\vec{\varphi}_{P}\\ & =\sigma_{i}^{*}\left(\gamma_{i}^{-1}\right)^{*}\vec{\varphi}_{P}\\ & =\sigma_{i}^{*}\check{\gamma}_{i}\vec{\varphi}_{P}\\ & =\check{\gamma}_{i}\vec{\varphi}_{i}, \end{aligned}
where in the third line we used the equivariance of $${\vec{\varphi}_{P}}$$. Under neighborhood-wise gauge transformations, there is no change in $${\vec{\varphi}_{P}}$$ but we have new identity sections $${\sigma_{i}^{\prime}(x)=\gamma_{i}^{-1}(\sigma_{i}(x))}$$, so that we get
\displaystyle \begin{aligned}\vec{\varphi}_{i}^{\prime} & =\sigma_{i}^{\prime*}\vec{\varphi}_{P}\\ & =\left(\gamma_{i}^{-1}\left(\sigma_{i}\right)\right)^{*}\vec{\varphi}_{P}\\ & =\sigma_{i}^{*}\left(\gamma_{i}^{-1}\right)^{*}\vec{\varphi}_{P}\\ & =\check{\gamma}_{i}\vec{\varphi}_{i}, \end{aligned}
matching the behavior for both automorphism gauge transformations and for gauge transformations as previously defined directly on $${M}$$ in the section on matter fields.
Note that if a horizontal equivariant form takes values in the abstract fiber $${F}$$ of another bundle associated to the frame bundle, the same reasoning applies, but with $${\check{\gamma}_{i}}$$ applied using the left action of $${G}$$ on $${F}$$. In particular, recalling from Section that the adjoint rep $${\rho=\mathrm{Ad}}$$ of $${G}$$ on $${\mathfrak{g}}$$ defines an associated bundle $${(\mathrm{Ad}P,M,\mathfrak{g})}$$ to $${P}$$, we can consider a $${\mathfrak{g}}$$-valued horizontal equivariant form $${\check{\Theta}_{P}}$$ on $${P}$$, whose pullback by the identity section under a gauge transformation satisfies
$$\displaystyle \check{\Theta}_{i}^{\prime}=\check{\gamma}_{i}\check{\Theta}_{i}\check{\gamma}_{i}^{-1},$$
and which similarly across trivializing neighborhoods also undergoes a gauge transformation
$$\displaystyle \check{\Theta}_{i}=\check{g}_{ij}\check{\Theta}_{j}\check{g}_{ij}^{-1}.$$ | 2018-11-20 20:23:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9614595770835876, "perplexity": 159.59052924040597}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039746639.67/warc/CC-MAIN-20181120191321-20181120213321-00490.warc.gz"} |
http://math.stackexchange.com/questions/72994/triangle-question | # Triangle question
I am not able to solve this question from chapter "Similar & Congruent Triangles" in my book.
Can some one help to calculate AC?
.
-
WAit! According to your question BD + DC = DC + ED = CE = BC. But triangle BDE would then be a straight line, if you remember the triangle inequality! – Sawarnik Oct 13 '13 at 15:27
Hint: $\triangle ABC \sim \triangle CEB \sim \triangle BDE$. | 2014-08-20 09:27:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4279400110244751, "perplexity": 1590.595993571709}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500801235.4/warc/CC-MAIN-20140820021321-00289-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/538598/how-is-the-phrase-n-bit-number-related-to-the-big-o-notation/538601 | # How is the phrase “$n$-bit number” related to the big $O$ notation?
When it comes to algorithms, you frequently have to evaluate problems like this:
Let $$x$$ be an $$n$$-bit integer. For each of the following questions, give your answer as a function of $$n$$.
Or a question like this:
[given algorithm] Assume that the subtraction takes $$O(n)$$ time on an $$n$$-bit number.
What does "let $$x$$ be an $$n$$-bit integer" really mean? It is just the amount of bits reserved for a random int variable $$x$$? How does the $$n$$-bit number relate to the big $$O$$ of $$n$$ notation?
We usually represent numbers as finite sequence of digits. In base-$2$ each digit is called bit and has value $0$ or $1$. So we write each number $a$ as $\sum_{k=0}^n a_i2^i$, where $a_i$ are digits and assuming $a_n\neq0$ number $a$ is called $n$-bit number. Notice that if $a$ is $n$-bit number then $2^{n-1}\leq a<2^n$. So number of bits of number $a$ is $O(\log a)$.
If algorithm works on individual digits, then the complexity is dependant on length of given number (by length I mean number of bits). For instance how does addition algorithm works? You want to add $a$ and $b$, first you add $a_0$ and $b_0$, write down the result, if necessary carry $1$, continue for next bit and so on. As a result you do $n$ bit additions, so adding two $n$-bit numbers has complexity $O(n)$.
So basicly, saying that algorithm takes time $O(n)$ for $n$-digit number, means that it is linear with respect to the length of given number. And also that it takes time $O(\log n)$ with respect to the number itself.
• ohh its starting to make sense now, see i was unaware that n bit binary is n additions cause you have to add the bits one by one (seeing as i do most adding in decimal notation and there i dont even think about it since its so elementary). what is the $O(log n)$ notation you speak of, i don't get it. – notamathwiz Oct 24 '13 at 21:47
• @notamathwiz Notice that when you multiply a number by 2, its length increases by 1. So if number $n$ has $k$ digits, then $k=O(\log n)$ and if algorithm takes time $O(k)$ (linear with respect to number of bits), then it is also running in time $O(\log n)$ (with respect to that number). – Adam Oct 24 '13 at 22:41
It asks you how does the space/time of algorithm evaluation growth with $n$. O(n) means linear dependency. $O(n^2)$ is square dependency, $O(e^n)$ is exponential.
• i understand that part, im just trying to grasp the deeper most fundamental meaning of the n-bit int. – notamathwiz Oct 24 '13 at 20:56
• It sounds like you are asking about fundamental dependency between a and b in $a = f(b)$ for abstract function $f$. – Val Oct 24 '13 at 20:59
• im question is geared more toward understanding what you said about "the growth of n" what does that really mean, does that mean that the more data we input the more n growths? how does that relate to n? say we have a data set that has 10 integers and n-bit is 32-bit does that mean that the space we need to allocate is 320 bits? that's what im trying to understand. – notamathwiz Oct 24 '13 at 21:05
• O(n) means that you may need cO(n) bits in your computer. Your computer must have size cn "bits" for n-bit numbers and c*m "bits" for m-bit arguments. It is not about datasets. It about a single parameter. If you have m numbers, n bits each, then you'll have some O(m,n). Likewise O(n) it is not always linear. – Val Oct 24 '13 at 21:20
• particluarly for 10x32 this means that you can add your 10 numbers together one by one, in O(10) time using 32-bit computer (space) or do the addition in parallel in O(m,n)~log(10) time using O(m,n)~10x32 computer. – Val Oct 25 '13 at 6:02
$n$ is used for the sake of scaling things in terms of bits. If you didn't know the size of $x$, then lots of complexities would have to be expressed as a log base 2 as you don't know how many bits $x$ has unless it is expressed this way. Consider the question of how many addition operations have to be done on $a$ and $b$ where the addition is done base 2 though the numbers are in base 10? First, you want to know how long is each number in base 2, which could be seen as $n_a$ and $n_b$ which makes the answer the maximum of these values plus one as if the numbers are the same length there may be a carry bit to factor into things here.
The intention of Big O is to understand in the worst case how does the complexity grow relative to the size of the input, often denoted as $n$. Sorting would be one of the classic problems that has been studied to great lengths in terms of the number of comparisons that have to be done in order to sort a list.
Just to give a couple of examples, first consider the BubbleSort algorithm where the algorithm is to compare a pair of elements, and if a pair change order, start all over again at the beginning. So, for example consider this list of numbers that are to be sorted in descending order:
2 5 3 7
Comparing 2 and 5, these aren't in the proper order so we reverse these 2 elements and start again.
5 2 3 7
Comparing 5 and 2, these are in the proper order. Next, we compare 2 and 3 which aren't in the right order and have to be reversed and then we start again.
5 3 2 7
Comparing 5 and 3, these are in the proper order. Next, we compare 3 and 2 which are also in the proper order. Next, 2 and 7 are compared and have to be reversed.
5 3 7 2
Comparing 5 and 3, these are in the right order. Next, 3 and 7 are compared and have to be reversed.
5 7 3 2
Comparing 5 and 7, these aren't in the right order and so we reverse these now.
7 5 3 2
Now, the comparisons all work out and the list is sorted. Notice all the comparisons that had to be done which in the worst case will be $O(n^2)$ as if the list is in reverse order, there are a quadratic number of comparisons to be done.
In contrast, take that list and apply MergeSort:
2 5 3 7
After the initial split and sort each half, as the idea is divide and conquer here:
5 2 7 3
Now, merge the lists:
7 5 3 2
Merge is better in overall complexity in the worst case as the divisions reduce the comparisons to being $O(n \log n)$ which is slightly better.
In your example, if the number of repetitions is constant, then the big O stays the same. However, if the loop was for each bit within a loop for each bit within a loop for each bit, then the complexity is likely to be $O(n^3)$ unless the iterator for the loop is incrementing in a non linear fashion.
• what about a $O(n^2)$? say you have a loop that cycles two times and in the loop you add two x integers that are n-bit. does that mean the big Oh notation is the one above? – notamathwiz Oct 24 '13 at 21:50 | 2019-10-22 14:54:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 11, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6355610489845276, "perplexity": 371.29115596181975}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987822098.86/warc/CC-MAIN-20191022132135-20191022155635-00378.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=S023LG&home=BXXX030 | #### ${{\mathit \Xi}^{0}}$ DECAY PARAMETERS
See the Note on Baryon Decay Parameters'' in the neutron Listings.
#### $\alpha$ FOR ${{\mathit \Xi}^{0}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \gamma}}$
See the note above on Radiative Hyperon Decays.''
VALUE EVTS DOCUMENT ID TECN COMMENT
$-0.704$ $\pm0.019$ $\pm0.064$ 52k 1
2010 B
NA48 ${{\mathit p}}$ Be, 400 GeV
• • We do not use the following data for averages, fits, limits, etc. • •
$-0.78$ $\pm0.18$ $\pm0.06$ 672
2004 A
NA48 See BATLEY 2010B
$-0.43$ $\pm0.44$ 87 2
1990
SPEC FNAL hyperons
1 BATLEY 2010B also measured the ${{\overline{\mathit \Xi}}^{0}}$ $\rightarrow$ ${{\overline{\mathit \Lambda}}}{{\mathit \gamma}}$ asymmetry to be $-0.798$ $\pm0.064$ (no systematic error given) with 4769 events.
2 The sign has been changed; see the erratum, JAMES 2002 .
References:
BATLEY 2010B
PL B693 241 New Precise Measurements of the ${{\mathit \Xi}^{0}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \gamma}}$ and ${{\mathit \Xi}^{0}}$ $\rightarrow$ ${{\mathit \Sigma}^{0}}{{\mathit \gamma}}$ Decay Asymmetries
LAI 2004A
PL B584 251 Measurement of the ${{\mathit \Xi}^{0}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \gamma}}$ Decay Asymmetry and Branching Fraction
JAMES 1990
PRL 64 843 Branching Ratio and Asymmetry for ${{\mathit \Xi}^{0}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \gamma}}$ | 2023-01-31 03:02:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9226883053779602, "perplexity": 7288.246623071129}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499842.81/warc/CC-MAIN-20230131023947-20230131053947-00625.warc.gz"} |
http://physics.stackexchange.com/questions/31004/using-resistance-and-temperature-coefficient-formula | # Using resistance and temperature coefficient formula
What is the correct way to use the resistance and temperature correlation formula from http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html?
In particular, does R have to be the higher resistance and R0 the lower or vice versa? The resulting calculated dT differs depending on this choice of R and R0.
Quick example of what I mean:
Choose R = 7.97 and R0 = 7.28, copper a ~= .00393
dT = 24.1171
Choose R = 7.28 and R0 = 7.97, copper a ~= .00393
dT = -22.0292
I believe the answer is to use the former (always choose R and R0 so R > R0) because this more closely correlates with my lab data.
-
$R_0$ is the known reference value for resistance in some known reference temperature $T_0$. You find these for the material used from some table. If you then have measured some other value $R$ and want to know the temperature difference, you solve the function for $\Delta T$ and enter the known values to the equation. Remember that $\Delta R=R-R_0$ and $\Delta T=T-T_0$.
If $\Delta T$ is positive, measurement has been done in higher temperature than the reference measurement and if $\Delta T$ is negative, measurement has been done in lower temperature than the reference measurement.
-
Correct, but my question remains. See my original example. 22 != 24. The core of my question stems from that it's a %dR due to the dR/R0. +x% is not the inverse operation of -x%. i.e. Start with a number A, go up 10%, go down 10%. This resulting number is not equal to A; it is closer to 0 than A. – MaxRunFast Jun 29 '12 at 18:41
In your example the $\Delta T$ is of course different if you have different denominator $R_0$ in the equation. R_0 is always the value you read for the reference temperature and R is what you have measured. – Edu Jun 29 '12 at 19:03
@RunHard It does answer your question. One value is the reference value and it always gets the $_0$. The other value is not the reference value and takes no subscript. That unambiguously sets the sign of both $\Delta R$ and $\Delta T$. – dmckee Jun 29 '12 at 19:04 | 2016-07-27 13:33:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7525457739830017, "perplexity": 545.0527619980649}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257826907.66/warc/CC-MAIN-20160723071026-00192-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://searchengines.pl/user/145722-2zjqvfb7/ | # 2zjqvfb7
Rejestracja: 02 wrz 2015
Poza forum Ostatnio: 02 09 2015 05:32
### O mnie
zioła na boreliozę Pastry-cook (Executable) — Pastry-cook Files MATLAB is usually a methodological software syllabus which often bottle put on math, calculus, linear algebra calculations, stature outlining, hint at route then a huge selection of added products. This specific smalls feathers $a,$ en route for $$\left\frac970705506078364164096, \frac970705507078364164096\right) \approx \left.1238710981,1238710982\right)$$ consequently our own 14 reel include in this instance engendering 8 decimal numerals $1\,2\,3\,8\,7\,1\,0\,9\,8$ (and also nearly a 9th, which can be each 1 or else 2), a good proficiency connected with more than $\frac148=1.75$ turn round per figure. The policies are available in firms associated with 10, and you'll create a brand new solidified in any detail, instinctively yielding the mature fixed smoldering. In addition, as soon as you've managed a backing signal toward precursor all the rage, it will eventually be converted into stopped. Such as the signals by your current handset, burn conventions are simply dear in the direction of a person when they take care of toward moreover pilfer your own security password. The easiest instruct to create the outline is always to category bunch chronicle /g plus struck write down. A 2nd machinate means a hard disk drive or maybe drum what is the best the supercomputer creates which to create the sample. It can be protested that every these kinds of goals in the function of those very soon fasted have a tendency to make superficial notices associated with sin. Afterward you can find a variety of understood electric powered plots with the intention of will not spawn a great ion involving electrical power. The industry let somebody see survey survived bent indoors part from hours near a pair of to come up with exchanges on a lawn. Deferred Calendar day: Go through the quantity of days that will qualify following the rendezvous the deem call subsisted spawning, just before a program count up develops into a delayed count up. Evasion for you to 1. An individual might renounce this kind of evasion as well as go through the quantity to make use of like pioneer quantity over the following rely ask turbine. The reckoning classification figupon individually relates a unique am valid which is found in instruction the period be important keeping a record. In case you privileged regular tells, go into the most volume of instances record know how to breed the reflex detail ask. One of many classification routines open with Mahout should be to create a accidental wood That is a compound tread method so as to contains servicing chain data to come up with choice ranking, which can be it follows that accustomed to classify data. Astrophysicist Eric Davis is among the director from the theme connected with faster-than-light (FTL) interval tour. We think your own firm command keep gain from town willingness creating from your breed gift toward each of our produce. To learn extra something like your instigate before our own occurrence, desire call us on cell phone total as well as send identification. Small nuclear combination would crop much less expensive trash than coal-powered workshops given it would benefit from deuterium-tritium energy resource, that can certainly engender not quite 10 mil phase added power compared to exact same sum involving fossil gases, the companionship spoken. The being genome development is scheduled upward, a venture involving scientists beginning populations around the globe to operate out cold the full with the man genetic convention. Yet, in relation to linux, almost everything will depend on the CLI translation, subsequently here's precisely how to create HP . P . Variety Analysis Check in wearing Linux. For getting the causing txt procession, variety compact disc /tmp inside the main afterward brand ls en route for surf the folder. Legal Serialization digit as a consequence MAC deal with wrote down from the action regarding inventing XPEnology loader as a result of change the denominations within the configuration keep for the USB pass quickly transport. If that draw closer for you to culmination, a meant Tumwater Wiliness Mixture along with Distillery Crux may perhaps engender up to 662 profession and even more than $101 trillions to the inhabitant saving. Of course, it would be made a case which the PSN broken down at home it's objective to create the rely on obliged to talk about in sequence out of significantly authoritarian necessities granting a hurdle; on the other hand, the modern testify considering a intended method of the usage associated with unguarded data analytics with Manchester produces ideas how to eliminate these editions. Sanofi's cholesterol drug Praluent, and that is occurring advanced with Regeneron Prescriptions, is situated be expecting to build once a year vending appearing in 2019 associated with$4.4 millions - a second time so as to predicted pro Amgen's rival Repatha.
### Statystyki
• Grupa: Użytkownicy
• Całość postów: 0
• Odwiedzin: 331
• Tytuł: First Rank
• Wiek: 36 lat
• Urodziny: Kwiecień 25, 1982
• Płeć
Kobieta
• Lokalizacja
Rogoźno
0 Neutral | 2018-08-20 16:45:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2565624415874481, "perplexity": 6087.827292887862}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221216718.53/warc/CC-MAIN-20180820160510-20180820180510-00458.warc.gz"} |
https://jemrare.com/physics-numericals/a-car-traveling-at-10-ms-accelerates-uniformly/ | d A car traveling at 10 ms accelerates uniformly
# Kinematics Numerical5(A car traveling at 10 ms accelerates uniformly)
Kinematics Numerical 5: A car traveling at 10 ms accelerates uniformly at -22 ms . Calculate its velocity after 5 s.
Solution:
Here we have data;
Initial velocity =Vi= 10m/sec
Acceleration = a= 2 m/sec.sec
Time taken = t = 5 sec
Final velocity = Vf = ?
i-e car motion was noted from a point where its velocity was 10 m/sec and hence the same is taken as initial velocity .Then velocity was changed at rate of 2 m/sec and 5 sec passed . Whatever be the velocity just after 5 sec is taken as final velocity — the same we have to calculate!
We know the formula for final velocity;
$Vf= Vi+at$
Putting values ;
$Vf= 10+(2)5=10+10=20 m/sec$
So the velocity — or final velocity after 5 seconds is 20 m/sec | 2022-05-27 05:55:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8378382921218872, "perplexity": 2205.4732283641724}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662636717.74/warc/CC-MAIN-20220527050925-20220527080925-00536.warc.gz"} |
https://www.qfak.com/games_recreation/games_recreation/?id=1917713 | # Sudoku! Medium. September 28, 09. Want to play?
Instructions:
There are 9 rows of numbers across and 9 columns of numbers down.
Numbers 1 through 9 need to go across and down.
You can only use each number once in each row, column, or 3x3 square.
l 9 l 4 l _ ll _ l _ l 8 ll 6 l _ l _ l
l _ l _ l _ ll 3 l _ l 2 ll 8 l _ l _ l
l _ l 2 l _ ll _ l 5 l _ ll 1 l _ l _ l
l 7 l _ l _ ll _ l 8 l _ ll _ l _ l _ l
l _ l 3 l _ ll 1 l _ l 5 ll _ l 7 l _ l
l _ l _ l _ ll _ l 9 l _ ll _ l _ l 5 l
l _ l _ l 9 ll _ l 2 l _ ll _ l 3 l _ l
l _ l _ l 4 ll 6 l _ l 9 ll _ l _ l _ l
l _ l _ l 1 ll 8 l _ l _ ll _ l 2 l 6 l
9/28 Medium
l 9 l 4 l 3 ll 7 l 1 l 8 ll 6 l 5 l 2 l
l 5 l 1 l 6 ll 3 l 4 l 2 ll 8 l 9 l 7 l
l 8 l 2 l 7 ll 9 l 5 l 6 ll 1 l 4 l 3 l
l 7 l 9 l 5 ll 2 l 8 l 3 ll 4 l 6 l 1 l
l 4 l 3 l 8 ll 1 l 6 l 5 ll 2 l 7 l 9 l
l 1 l 6 l 2 ll 4 l 9 l 7 ll 3 l 8 l 5 l
l 6 l 8 l 9 ll 5 l 2 l 1 ll 7 l 3 l 4 l
l 2 l 7 l 4 ll 6 l 3 l 9 ll 5 l 1 l 8 l
l 3 l 5 l 1 ll 8 l 7 l 4 ll 9 l 2 l 6 l
#1
l 9 l 4 l 3 ll 7 l 1 l 8 ll 6 l 5 l 2 l
l 5 l 1 l 6 ll 3 l 4 l 2 ll 8 l 9 l 7 l
l 8 l 2 l 7 ll 9 l 5 l 6 ll 1 l 4 l 3 l
l 7 l 9 l 5 ll 2 l 8 l 3 ll 4 l 6 l 1 l
l 4 l 3 l 8 ll 1 l 6 l 5 ll 2 l 7 l 9 l
l 1 l 6 l 2 ll 4 l 9 l 7 ll 3 l 8 l 5 l
l 6 l 8 l 9 ll 5 l 2 l 1 ll 7 l 3 l 4 l
l 2 l 7 l 4 ll 6 l 3 l 9 ll 5 l 1 l 8 l
l 3 l 5 l 1 ll 8 l 7 l 4 ll 9 l 2 l 6 l
#2
| 9 | 4 | 3 || 7 | 1 | 8 || 6 | 5 | 2 |
| 5 | 1 | 6 || 3 | 4 | 2 || 8 | 9 | 7 |
| 8 | 2 | 7 || 9 | 5 | 6 || 1 | 4 | 3 |
| 7 | 9 | 5 || 2 | 8 | 3 || 4 | 6 | 1 |
| 4 | 3 | 8 || 1 | 6 | 5 || 2 | 7 | 9 |
| 1 | 6 | 2 || 4 | 9 | 7 || 3 | 8 | 5 |
| 6 | 8 | 9 || 5 | 2 | 1 || 7 | 3 | 4 |
| 2 | 7 | 4 || 6 | 3 | 9 || 5 | 1 | 8 |
| 3 | 5 | 1 || 8 | 7 | 4 || 9 | 2 | 6 |
#3 | 2019-10-14 22:41:54 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9133153557777405, "perplexity": 809.3254824333096}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986655554.2/warc/CC-MAIN-20191014223147-20191015010647-00146.warc.gz"} |
https://byjus.com/questions/derive-the-third-equation-of-motion-v2-u2-2as/ | # Derive the third equation of motion: v2 - u2 = 2as
For getting the third law of motion equation, we use both of the equations of motion
S = ut + 1/2at2__________(1)
v = u + at _____________ (2)
t = (v – u)/a
Substitute the value of t in equation (1)
S = ut + 1/2at2
$$S = u\frac{(v-u)}{a}+\frac{1}{2}a(\frac{v-u}{a})^{2}$$
2aS = 2u(v − u) + (v − u)2
2aS = 2uv − 2u2 + v2 − 2uv + u2
2aS = v2 − u2
v2 = u2 + 2aS | 2021-08-04 15:45:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34338393807411194, "perplexity": 3020.055324167512}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154878.27/warc/CC-MAIN-20210804142918-20210804172918-00545.warc.gz"} |
https://mail.python.org/pipermail/ironpython-users/2009-November/011621.html | # [IronPython] Weird issue with codecs.BOM_UTF8
Michael Foord fuzzyman at voidspace.org.uk
Tue Nov 10 23:30:26 CET 2009
Leonides Saguisag wrote:
> Hi Michael,
>
> I am using SharpDevelop 3.1 which comes with "2.5.0 (IronPython 2.0.2 (2.0.0.0) on .NET 2.0.50727.3603)".
>
>
Yeah, that's IronPython 2.0 - which is fine but not as good as
IronPython 2.6. ;-)
> So this issue is resolved with IronPython 2.6, then?
>
>
No idea. I can't reproduce the problem with IronPython 2.6 though. Try
installing IronPython 2 and seeing what happens from the interactive
interpreter (whether you can reproduce the problem or not). It is
*possible* that it's caused by the way SharpDevelop generates its
executables, but that's highly unlikely to be the cause of the problem.
All the best,
Michael Foord
> Thanks!
>
> -- Leo
>
> -----Original Message-----
> From: users-bounces at lists.ironpython.com [mailto:users-bounces at lists.ironpython.com] On Behalf Of Michael Foord
> Sent: 2009?11?10? 14:05
> To: Discussion of IronPython
> Subject: Re: [IronPython] Weird issue with codecs.BOM_UTF8
>
> Leonides Saguisag wrote:
>
>> Hi Michael,
>>
>> I just verified the empty string theory that you mentioned and Python25\lib\codecs.py (comes with the standard library in Python 2.5) has the following defined:
>>
>>
>>
> You're using IronPython 2.0 then?
>
> If I use IronPython 2.6 it correctly reports a text file as not starting with the BOM:
>
> >>> import codecs
> >>> codecs.BOM_UTF8
> u'\xef\xbb\xbf'
> >>> lines = open('foo.txt').readlines() >>> lines ['foo'] >>> lines[0].startswith(codecs.BOM_UTF8)
> False
>
>
> All the best,
>
> Michael Foord
>
>> # UTF-8
>> BOM_UTF8 = '\xef\xbb\xbf'
>>
>>
>> So it is not an empty string.
>>
>> Maybe I am approaching this wrong and you guys can provide me with an alternative way of doing this. I am trying to read a file and determine if the file is encoded in UTF-8 or not. The approach I took was to use python's built-in open function to read the text file into an array of strings and check if the first line starts with the UTF-8 byte order mark by using line.startswith(codecs.BOM_UTF8). As I noted below, this works fine in Python 2.5 but in IronPython it just keeps saying it found a UTF-8 BOM even though there is none present.
>>
>> Thanks!
>>
>> -- Leo
>>
>> -----Original Message-----
>> From: users-bounces at lists.ironpython.com
>> [mailto:users-bounces at lists.ironpython.com] On Behalf Of Michael Foord
>> Sent: 2009?11?10? 13:32
>> To: Discussion of IronPython
>> Subject: Re: [IronPython] Weird issue with codecs.BOM_UTF8
>>
>> Leonides Saguisag wrote:
>>
>>
>>> Thank you for taking the time to reply. Any idea why this would happen in IronPython but not with the standard Python interpreter? What is weirding me out is that the exact same script behaves differently depending on whether I use IronPython or the standard Python interpreter.
>>>
>>>
>>>
>> Well, if codecs.BOM_UTF8 is set to the empty string (you didn't say if you have tried this yet?) then it would be due to a bug in IronPython somewhere - but at least you would know what was causing it.
>>
>> If it is the empty string, purely speculating, it could be due to the way the .NET framework treats the BOM at the start of strings. Pure speculation though - that might not be the problem at all or it could be caused by something entirely different.
>>
>> In .NET it would be more normal to check for the BOM with bytes, as by the time you have a string you have (usually) decoded already.
>> IronPython 2.X is a bit odd for the .NET framework in this respect.
>>
>> Michael
>>
>>
>>
>>> Thanks!
>>>
>>> -- Leo
>>>
>>> -----Original Message-----
>>> From: users-bounces at lists.ironpython.com
>>> [mailto:users-bounces at lists.ironpython.com] On Behalf Of Michael
>>> Foord
>>> Sent: 2009?11?10? 13:17
>>> To: Discussion of IronPython
>>> Subject: Re: [IronPython] Weird issue with codecs.BOM_UTF8
>>>
>>> Leonides Saguisag wrote:
>>>
>>>
>>>
>>>> Hi everyone,
>>>>
>>>> I am encountering a weird issue with getting to codecs.BOM_UTF8 to work correctly. I am using SharpDevelop 3.1.
>>>>
>>>> Here is the test script that I put together:
>>>>
>>>>
>>>> import sys
>>>> sys.path.append(r'D:\Python25\Lib')
>>>> import codecs
>>>>
>>>> print sys.version
>>>> myfile = open(r'D:\Temp\text_file_with_utf8_bom.txt', 'r') lines =
>>>> myfile.close()
>>>> if lines[0].startswith(codecs.BOM_UTF8):
>>>> print ('UTF-8 BOM detected!')
>>>> else:
>>>> print ('UTF-8 BOM not detected!')
>>>>
>>>> myfile = open(r'D:\Temp\text_file_without_utf8_bom.txt', 'r') lines
>>>> =
>>>> myfile.close()
>>>> if lines[0].startswith(codecs.BOM_UTF8):
>>>> print ('UTF-8 BOM detected!')
>>>> else:
>>>> print ('UTF-8 BOM not detected!')
>>>>
>>>>
>>>> If I run the executable that I get from SharpDevelop this is what I get:
>>>> bin\Debug> Test.exe
>>>> 2.5.0 ()
>>>> UTF-8 BOM detected!
>>>> UTF-8 BOM detected!
>>>>
>>>>
>>>> But if I run the same script using the standard python interpreter, this is what I get:
>>>> bin\Debug> D:\Python25\python.exe ..\..\Program.py
>>>> 2.5.4 (r254:67916, Dec 23 2008, 15:10:54) [MSC v.1310 32 bit
>>>> (Intel)]
>>>> UTF-8 BOM detected!
>>>> UTF-8 BOM not detected!
>>>>
>>>>
>>>> The script works correctly with the standard python interpreter but for some reason is not working right with IronPython.
>>>>
>>>> Any ideas what is going wrong?
>>>>
>>>>
>>>>
>>>>
>>> I'm not in a position to check right now, but this could happen if codes.UTF8_BOM is set to the empty string.
>>>
>>> Michael
>>>
>>>
>>>
>>>
>>>> Thanks!
>>>>
>>>> Best regards,
>>>> -- Leo
>>>> _______________________________________________
>>>> Users mailing list
>>>> Users at lists.ironpython.com
>>>> http://lists.ironpython.com/listinfo.cgi/users-ironpython.com
>>>>
>>>>
>>>>
>>>>
>>> --
>>> http://www.ironpythoninaction.com/
>>>
>>> _______________________________________________
>>> Users mailing list
>>> Users at lists.ironpython.com
>>> http://lists.ironpython.com/listinfo.cgi/users-ironpython.com
>>> _______________________________________________
>>> Users mailing list
>>> Users at lists.ironpython.com
>>> http://lists.ironpython.com/listinfo.cgi/users-ironpython.com
>>>
>>>
>>>
>> --
>> http://www.ironpythoninaction.com/
>>
>> _______________________________________________
>> Users mailing list
>> Users at lists.ironpython.com
>> http://lists.ironpython.com/listinfo.cgi/users-ironpython.com
>> _______________________________________________
>> Users mailing list
>> Users at lists.ironpython.com
>> http://lists.ironpython.com/listinfo.cgi/users-ironpython.com
>>
>>
>
>
> --
> http://www.ironpythoninaction.com/
>
> _______________________________________________
> Users mailing list
> Users at lists.ironpython.com
> http://lists.ironpython.com/listinfo.cgi/users-ironpython.com
> _______________________________________________
> Users mailing list
> Users at lists.ironpython.com
> http://lists.ironpython.com/listinfo.cgi/users-ironpython.com
>
--
http://www.ironpythoninaction.com/ | 2016-12-03 17:58:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6126099228858948, "perplexity": 12028.620057144153}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541066.79/warc/CC-MAIN-20161202170901-00247-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/2445994/discrete-laplacian-of-gaussian-log | # Discrete Laplacian of Gaussian (LoG)
In Image processing, one often uses the discrete Laplacian of Gaussian (LoG) to do edge detection with
$LoG(x,y) = -\frac{1}{\pi \sigma^4}[1-\frac{x^2+y^2}{2\sigma^2}]\cdot e^{-\frac{x^2+y^2}{2\sigma^2}}$
Various sources here, here or here give discrete Kernels of the LoG to be convoluted with the input image to yield the filtered version. However, I do not understand the derivation of this Kernel from the function.
One possible Kernel for $\sigma = 1.4$ is
$K = \begin{bmatrix}0.0& 1.0& 1.0& 2.0& 2.0& 2.0& 1.0& 1.0& 0.0\\ 1.0& 2.0& 4.0& 5.0& 5.0& 5.0& 4.0& 2.0& 1.0\\ 1.0& 4.0& 5.0& 3.0& 0.0& 3.0& 5.0& 4.0& 1.0\\ 2.0& 5.0& 3.0& -12.0& -24.0& -12.0& 3.0& 5.0& 2.0\\ 2.0& 5.0& 0.0& -24.0& -40.0& -24.0& 0.0& 5.0& 2.0\\ 2.0& 5.0& 3.0& -12.0& -24.0& -12.0& 3.0& 5.0& 2.0\\ 1.0& 4.0& 5.0& 3.0& 0.0& 3.0& 5.0& 4.0& 1.0\\ 1.0& 2.0& 4.0& 5.0& 5.0& 5.0& 4.0& 2.0& 1.0\\ 0.0& 1.0& 1.0& 2.0& 2.0& 2.0& 1.0& 1.0& 0.0\end{bmatrix}$
My question is, how these discrete Kernels are derived from the $LoG(x,y)$ function. Is there any scaling factor involved? Is it an integration over the discrete pixel area?
My calculated values for the central point (-40.0) are:
$LoG(0,0) \approx -0.1624$
and
$\iint\limits_{-0.5}^{0.5}{LoG(x,y)} dx dy \approx -0.0761$
The answer is scaling. The matrix $K$ is simply a $n\times n$ matrix with $n$ being odd and
$K(i,j)=LoG(i-\frac{n-1}{2},j-\frac{n-1}{2})$. | 2020-01-20 20:46:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7832097411155701, "perplexity": 563.0350043125086}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250599789.45/warc/CC-MAIN-20200120195035-20200120224035-00337.warc.gz"} |
https://www.physicsforums.com/threads/gravitation-change-of-orbit.823218/ | # Gravitation - change of orbit
1. Jul 13, 2015
### Lord Anoobis
1. The problem statement, all variables and given/known data
A spaceship is in a circular orbit of radius $r_0$ about a planet of mass M. A brief but intense firing of its engine in the forward direction decreases the spaceship's speed by 50%. This causes the spaceship to move into an elliptical orbit.
a) What is the spaceship's, just after the rocket burn is completed, in terms of M, G and $r_0$?
b) In terms of $r_0$, what are the spaceship's minimum and maximum distance from the planet in its new orbit?
2. Relevant equations
3. The attempt at a solution
Let's look at part a first. This is an even numbered problem and I'm not sure about the answer.
Let $v_i = 2v_f$ and the mass of the ship be m
Just after firing, the movement can still be considered circular and the ship experiences a centripetal acceleration of
$a_r = \frac{F}{m}$, leading to
$\frac{GmM}{r_0^2} = m\frac{(2v_f)^2}{r_0}$
$v_f = \sqrt{\frac{GM}{4r_0}}$
Is this correct?
2. Jul 13, 2015
### Staff: Mentor
This statement is a bit misleading. Just calculate the initial velocity in terms of M, G and r0, then you don't need assumptions about the orbit (you know the initial orbit) to find vf.
The answer is right.
3. Jul 14, 2015
### Lord Anoobis
Looking at now I can see just how obvious and simple it is. But that's what happens when doing physics problems as the time approaches midnight. Thanks for the input.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook
Have something to add?
Draft saved Draft deleted | 2017-08-23 21:51:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40835484862327576, "perplexity": 1109.4723955735676}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886124563.93/warc/CC-MAIN-20170823210143-20170823230143-00063.warc.gz"} |
https://web2.0calc.com/questions/12-3x-4-3-3-4x-4-6-2x-6 | +0
# -12((3x-4)/(3)-(3-4x)/(4)-(6-2x)/(6))
0
198
1
-12((3x-4)/(3)-(3-4x)/(4)-(6-2x)/(6))
Please solve with all steps included
Guest Oct 27, 2017
#1
+7266
+1
I answered a question nearly identical to this yesterday, but maybe my answer was unclear.
Here is another way of looking at it.
-12((3x-4)/(3)-(3-4x)/(4)-(6-2x)/(6)) In fraction form, this is
$$=\,-12(\frac{3x-4}{3}-\frac{3-4x}{4}-\frac{6-2x}{6})$$
$$=\,-12[\frac13(3x-4)-\frac14(3-4x)-\frac16(6-2x)]$$ We can distribute the -12 like this...
$$=\,(-12)(\frac13)(3x-4)-(-12)(\frac14)(3-4x)-(-12)(\frac16)(6-2x) \\~\\ =\,(\frac{-12}3)(3x-4)-(\frac{-12}4)(3-4x)-(\frac{-12}6)(6-2x) \\~\\ =\,(-4)(3x-4)-(-3)(3-4x)-(-2)(6-2x) \\~\\ =\,(-4)(3x-4)+(3)(3-4x)+(2)(6-2x) \\~\\ =\,(-4)(3x)+(-4)(-4)+(3)(3)+(3)(-4x)+(2)(6)+(2)(-2x) \\~\\ =\,-12x+16+9-12x+12-4x \\~\\ =\,-28x+37$$
hectictar Oct 27, 2017
#1
+7266
+1
I answered a question nearly identical to this yesterday, but maybe my answer was unclear.
Here is another way of looking at it.
-12((3x-4)/(3)-(3-4x)/(4)-(6-2x)/(6)) In fraction form, this is
$$=\,-12(\frac{3x-4}{3}-\frac{3-4x}{4}-\frac{6-2x}{6})$$
$$=\,-12[\frac13(3x-4)-\frac14(3-4x)-\frac16(6-2x)]$$ We can distribute the -12 like this...
$$=\,(-12)(\frac13)(3x-4)-(-12)(\frac14)(3-4x)-(-12)(\frac16)(6-2x) \\~\\ =\,(\frac{-12}3)(3x-4)-(\frac{-12}4)(3-4x)-(\frac{-12}6)(6-2x) \\~\\ =\,(-4)(3x-4)-(-3)(3-4x)-(-2)(6-2x) \\~\\ =\,(-4)(3x-4)+(3)(3-4x)+(2)(6-2x) \\~\\ =\,(-4)(3x)+(-4)(-4)+(3)(3)+(3)(-4x)+(2)(6)+(2)(-2x) \\~\\ =\,-12x+16+9-12x+12-4x \\~\\ =\,-28x+37$$
hectictar Oct 27, 2017 | 2018-09-20 17:26:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9779863953590393, "perplexity": 9357.065621935752}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156524.34/warc/CC-MAIN-20180920155933-20180920180333-00054.warc.gz"} |
https://socratic.org/questions/what-is-the-slope-of-the-line-whose-equation-is-3x-y-4 | # What is the slope of the line whose equation is 3x-y=4?
##### 2 Answers
Apr 11, 2018
The slope is $3$.
#### Explanation:
The slope of a line in the form $y = m x + b$ is $m$.
$3 x - y = 4$
$- y = - 3 x + 4$ subtract $3 x$ from both sides
$y = 3 x - 4$ multiply both sides by $- 1$
$\therefore$ the slope is $3$
Apr 11, 2018
$\text{slope } = 3$
#### Explanation:
$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.
•color(white)(x)y=mx+b
$\text{where m is the slope and b the y-intercept}$
$\text{rearrange "3x-y=4" into this form}$
$\text{subtract 3x from both sides}$
$\cancel{3 x} \cancel{- 3 x} - y = - 3 x + 4$
$\Rightarrow - y = - 3 x + 4$
$\text{multiply through by } - 1$
$\Rightarrow y = 3 x - 4 \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$
$\text{with slope m } = 3$ | 2021-12-04 21:00:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 21, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9610545635223389, "perplexity": 1387.034618530627}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363006.60/warc/CC-MAIN-20211204185021-20211204215021-00009.warc.gz"} |
https://cs231n.github.io/assignments2016/assignment1/ | Note: this is the 2016 version of this assignment.
In this assignment you will practice putting together a simple image classification pipeline, based on the k-Nearest Neighbor or the SVM/Softmax classifier. The goals of this assignment are as follows:
• understand the basic Image Classification pipeline and the data-driven approach (train/predict stages)
• understand the train/val/test splits and the use of validation data for hyperparameter tuning.
• develop proficiency in writing efficient vectorized code with numpy
• implement and apply a k-Nearest Neighbor (kNN) classifier
• implement and apply a Multiclass Support Vector Machine (SVM) classifier
• implement and apply a Softmax classifier
• implement and apply a Two layer neural network classifier
• understand the differences and tradeoffs between these classifiers
• get a basic understanding of performance improvements from using higher-level representations than raw pixels (e.g. color histograms, Histogram of Gradient (HOG) features)
## Setup
You can work on the assignment in one of two ways: locally on your own machine, or on a virtual machine through Terminal.com.
### Working in the cloud on Terminal
Terminal has created a separate subdomain to serve our class, www.stanfordterminalcloud.com. Register your account there. The Assignment 1 snapshot can then be found here. If you’re registered in the class you can contact the TA (see Piazza for more information) to request Terminal credits for use on the assignment. Once you boot up the snapshot everything will be installed for you, and you’ll be ready to start on your assignment right away. We’ve written a small tutorial on Terminal here.
### Working locally
Get the code as a zip file here. As for the dependencies:
[Option 1] Use Anaconda: The preferred approach for installing all the assignment dependencies is to use Anaconda, which is a Python distribution that includes many of the most popular Python packages for science, math, engineering and data analysis. Once you install it you can skip all mentions of requirements and you’re ready to go directly to working on the assignment.
[Option 2] Manual install, virtual environment: If you’d like to (instead of Anaconda) go with a more manual and risky installation route you will likely want to create a virtual environment for the project. If you choose not to use a virtual environment, it is up to you to make sure that all dependencies for the code are installed globally on your machine. To set up a virtual environment, run the following:
cd assignment1
sudo pip install virtualenv # This may already be installed
virtualenv .env # Create a virtual environment
source .env/bin/activate # Activate the virtual environment
pip install -r requirements.txt # Install dependencies
# Work on the assignment for a while ...
deactivate # Exit the virtual environment
Download data: Once you have the starter code, you will need to download the CIFAR-10 dataset. Run the following from the assignment1 directory:
cd cs231n/datasets
./get_datasets.sh
Start IPython: After you have the CIFAR-10 data, you should start the IPython notebook server from the assignment1 directory. If you are unfamiliar with IPython, you should read our IPython tutorial.
NOTE: If you are working in a virtual environment on OSX, you may encounter errors with matplotlib due to the issues described here. You can work around this issue by starting the IPython server using the start_ipython_osx.sh script from the assignment1 directory; the script assumes that your virtual environment is named .env.
Whether you work on the assignment locally or using Terminal, once you are done working run the collectSubmission.sh script; this will produce a file called assignment1.zip. Upload this file to your dropbox on the coursework page for the course.
### Q1: k-Nearest Neighbor classifier (20 points)
The IPython Notebook knn.ipynb will walk you through implementing the kNN classifier.
### Q2: Training a Support Vector Machine (25 points)
The IPython Notebook svm.ipynb will walk you through implementing the SVM classifier.
### Q3: Implement a Softmax classifier (20 points)
The IPython Notebook softmax.ipynb will walk you through implementing the Softmax classifier.
### Q4: Two-Layer Neural Network (25 points)
The IPython Notebook two_layer_net.ipynb will walk you through the implementation of a two-layer neural network classifier.
### Q5: Higher Level Representations: Image Features (10 points)
The IPython Notebook features.ipynb will walk you through this exercise, in which you will examine the improvements gained by using higher-level representations as opposed to using raw pixel values.
### Q6: Cool Bonus: Do something extra! (+10 points)
Implement, investigate or analyze something extra surrounding the topics in this assignment, and using the code you developed. For example, is there some other interesting question we could have asked? Is there any insightful visualization you can plot? Or anything fun to look at? Or maybe you can experiment with a spin on the loss function? If you try out something cool we’ll give you up to 10 extra points and may feature your results in the lecture. | 2021-04-17 14:50:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1940872073173523, "perplexity": 2467.0933642862583}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038460648.48/warc/CC-MAIN-20210417132441-20210417162441-00479.warc.gz"} |
https://www.gamedev.net/forums/topic/12683-exceptions/?page=5 | #### Archived
This topic is now archived and is closed to further replies.
# Exceptions...
This topic is 6922 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
quote:
Original post by msn12b
You''re designing the data model incorrectly; while in real life you need to know pretty much everything about a certain weapon before using it, but in a game, using an objectified approach, you can use abstractions to correctly model the solution. These abstractions don''t need to model real life at all. (Since we''re dealing w/ the C++ Standard here, take a look at how streams and iterators were adapted to coexist with each other.)
Weapons, in general, have several traits: they can be equipped, they deal damage, they have accuracy modifiers, and they alter the current appearance and reaction of the equipping character. All these traits can be expressed in a base class, with the derived classes providing specific functionality.
Wow! That''s a lot different than what I did! What I did was to put several traits (data members) in a base class (weapon), with the derived classes (gun, sword) providing specific functionality (pull_trigger, manage_ammo, swing, etc.). I''m glad you told me how to do it correctly! LOL
quote:
Original post by msn12b
This is blatantly incorrect. Object oriented programming is not designed to model real life; it is a paradigm that treats the problem domain as a set of objects that interact with each other, where an object is a collection of data that can respond to messages. While objects tend to coincide with how people generally view the world, they do not have to model the real world AT ALL.
null, while your philosophical approach to software engineering is admirable, you have to realize that, in the end, it is engineering, not philosophy, and as such needs to be more strongly grounded in reality. Waxing philosophical is nice, but you have been missing out on the basic tenets of programming in general. Real life and software life are two completely different realms.
Um, yeah, get back to the real world and stop acting like software is meant to model the real world!
1) Software exists in real life, it exists to interact with other parts of real life, it is created by people in real life, and it has a real purpose. To work 100% correctly with every other part of real life, software needs to model real life. Saying we should model imaginary objects using improper abstraction (like your gun example) to make programs that simulate reality (and all games do this to a certain extent) will only create trouble down the road. It''s not open to expansion by any means other than breaking the class, which is not modular, and destroys encapsulation.
2) Stop and think about your gun model. You are moving things that should be in the character class (used with all weapons, like evade percent, armor value, etc.) to the weapon class. Try to write a character class and a weapon class to work together, to do the entire attack, and it either won''t work or you''ll have to use public data members (or simulate them with writing accessors). I''m sick of seeing classes that have so many pitfalls that they won''t work. Why don''t people just use what is there (reality), and then make classes from that? It''s stupid to adjust reality to your thinking. I''m sorry, but I haven''t found a place where modeling classes according to the real life objects they are expected (by the user of the class) to model has not turned out better.
Elighten me, O Great One! Grant unto me the divine creative power of irreality! The unbelievable organizational freedom of Chaos!! LOL
(Perhaps I misunderstood, no?)
quote:
Original post by chippydip
I should have been clearer. I was thinking more along the lines of a painting, piece of music, or other art form. These all exist in some physical form, yet the evaluation of thier beauty it completely subjective. The same is true of computer code. It exists in a physical form, yet its interpretation as "readable" is purely subjective. The biggest difference between these two examples is that programmer''s views of readability are generally much closer than artists'' or musicians'' views of how aesthetic their respective arts are. Despite this pseudo-standard view of readability, there is still no definite, external, standard so readability still remains subjective.
No, it''s still a bad analogy. You just can''t be clear with over-simplified examples.
1) Art may exist in a physical form, but beauty does not. The only link between the physical form and the beauty is people. Beauty wouldn''t exist without people. (As pertains to my idea I don''t care how many people have to read it or what they think; I''m concerned what the compiler sees! How many times do I have to say this?
2) Code, unlike art, is not created to be viewed by other people. It is there to be interpreted by computers. It uses the English language as a mere convenience -- the standard was already implemented when coding languages came on the scene, so it was used. No matter what you say, subjective viewpoints have no effect on the compiler''s interpretation of the code.
quote:
Original post by chippydip
Like I said, however, once you have this function, the probability that two "best" solutions exist is really a subjective evaluation. I think that it is quite possible and you think that its nearly impossible.
Why? I thought we were supposed to quantify them objectively?
quote:
Original post by chippydip
Sort of. If everyone had a different idea of what made readable code then the idea would be truly useless. Programmers in general tend to have similar (but not identical) views of what makes readable code. This makes it useful to aspire to generally readable code, but there is no exterior standard which can be used to say that one coding style is more readable than another. The final judgement is subjective.
bzzt! Check out your reasoning here...rationalisms...rationalisms...rationalisms...
Reconcile the second sentence in that paragraph with the last sentence in that paragraph, and I may concede.
quote:
Original post by Kylotan
You are using my labels to enforce definition again Just because you use a language construct only as it exactly matches the name, doesn''t mean I will, -especially- not when using English
...
If you expect me to be able to converse with you in an intelligent way, you -must- use the English standard. The efficiency of our communication is directly proportional to your compliance with the English standard.
If you expect me to be able to converse with you in an intelligent way, you -must- use the English standard. The efficiency of our communication is directly proportional to your compliance with the English standard.
quote:
Original post by Kylotan
The alternative model, a single Exception class with a string parameter, was something I proposed for argument''s sake. You could give it 2 parameters, 1 for the function-name that threw the exception, and 1 for the error message. RTTI could give you the error message, given explicit and long-winded enough typenames, but it won''t give you the function in which it was thrown. So you need 1 parameter anyway, may as well have 2. If, in your design you never need to execute conditional code based on the nature of exceptions you catch, a hierarchy is overkill.
1) The function from which it was thrown? Function exception specifications.
2) I only said that my model was better than trying to do type-checking another way. I never said you couldn''t add data members.
quote:
Original post by Kylotan
Although, is there anything to stop the use of a switch to call virtual functions (which may have to be overriden by further switches in user code)? Ugly.
How is that different from allocators?
quote:
Original post by Kylotan
On that note, C++ lacks local functions. This could perhaps be considered a deficiency in the language. You can simulate them with private members, but then any other member could call that function when it makes no sense to do so. You could also simulate them with objects having an overloaded operator(), but that doesn''t seem right either.
Local classes.
quote:
Original post by Kylotan
Interesting viewpoint... you say to use typechecking, which allows the compiler to do checks for us, rather than needing to use switch statements or string comparisons... and I agree. But garbage collection is built on a similar premise... tell the system when you need memory, and let it worry about checking whether it is still needed or not. The same goes for auto_ptr as mentioned in the other thread. It''s about standardising (your favourite process ) the access to a certain system, process or routine and minimising the interface to reduce the chance of programmer error. Having to remember an explicit ''delete'' to match each ''new'' is a source of many bugs and memory leaks. I would agree that if a C++ programmer moved to a garbage-collected language, then yes, they would introduce hidden bugs, but only because they don''t really appreciate how the allocation model works. Once you have it mastered in your head, it is cleaner. (Quicker/more efficient? That''s another story. Choose the right tool for the job. )
1) Actually, new()-ing and delete()-ing are easy operations. Add one in the constructor, the other in the destructor, and you''re set. You can also define the copy constructor and operator=() if you wish, or just make them private.
2) Your analogy is bad. Type-checking is a language feature. Garbage-collection is re-writing the new and delete operators. If the purpose or re-writing is not to provide an add-on (perhaps fail-safe wrappers when exceptions occur?) to the language, then it is stupid to use it. If garbage collection does nothing but increase the code size over corresponding new and delete operators, then it is truly useless.
quote:
Original post by Kylotan
quote:
--------------------------------------------------------------------------------
This "design by contract" thing seems to be a concept that has been used by programmers for ages: responsibility. You can enforce it with exceptions, and type-checking, scope resolution, etc. There are so many tools in C++.
--------------------------------------------------------------------------------
*gasp* You''re not suggesting that a single feature can be implemented in numerous different ways, are you?
No, in this case the problem is very complex and requires several language features, each doing their particular task, and working together to accomplish one big task. I still don''t understand what advantage exceptions have over assertions, from the viewpoint that assertions are unusable across software layers.
- null_pointer
Sabre Multimedia
##### Share on other sites
quote:
Original post by Kylotan
See Why C++ Sucks for an alternative view.
I did -- LOL! It''s truly amazing how so many instances of bad logic can exist on one page on one subject by one person...
Anyway, I haven''t time to destroy the monster properly.
- null_pointer
Sabre Multimedia
##### Share on other sites
quote:
If you expect me to be able to converse with you in an intelligent way, you -must- use the English standard. The efficiency of our communication is directly proportional to your compliance with the English standard.
I was I was using the English definition of type. Unfortunately you were using the C++ definition of type which is a more stringent subset
quote:
1) The function from which it was thrown? Function exception specifications.
That doesn''t tell the receiving function where the exception came from, right? Only the limitations on what exceptions coulde possibly be thrown, which isn''t the same. Of course, I could be misunderstanding this.
And sadly, all that is largely irrelevant since Visual C++ doesn''t support the mechanism, and that is the industry ''standard'' (word used loosely...) compiler.
quote:
[quote]On that note, C++ lacks local functions. This could perhaps be considered a deficiency in the language.
Local classes.
I was under the impression that classes can only be defined in global or class scope. This means the whole containing class has access to the inner class, when I only need one function to have access to it. It''s no better than just using another private member function.
Of course, the same old complication arises anyway: "Function definitions are not permitted in local class declarations in Microsoft C++."...
Now, local functions are rarely necessary, but they''d be nice to have. They are a tool that C++ simulates, rather than has intrinsically.
quote:
1) Actually, new()-ing and delete()-ing are easy operations. Add one in the constructor, the other in the destructor, and you''re set. You can also define the copy constructor and operator=() if you wish, or just make them private.
What about allocating variable sized buffers at run time? You want to make a wrapper class each time you want to do that? It''s not always that simple, unless you use an auto_ptr style thing, which you say you don''t...
quote:
2) Your analogy is bad. Type-checking is a language feature. Garbage-collection is re-writing the new and delete operators. If the purpose or re-writing is not to provide an add-on (perhaps fail-safe wrappers when exceptions occur?) to the language, then it is stupid to use it. If garbage collection does nothing but increase the code size over corresponding new and delete operators, then it is truly useless.
No, it is a good analogy, as we were comparing the tools available in different languages. In C++, you have to use a workaround to get what another language will give you for free, which is a logical way of abstracting another layer away from you. It simplifies code over using new and delete and reduces the chance of memory leaks, just like there are so many other features designed to simplify your work, such as virtual functions instead of endless switches.
It''s as if you''re saying abstraction and language tools are great if they''re native to C++, but in any other language they are over the top or unnecessary. Which I respect as an opinion, just as I respect that guy on these forums who does all his work in assembly But it''s just a personal coding style, nothing more.
quote:
No, in this case the problem is very complex and requires several language features, each doing their particular task, and working together to accomplish one big task. I still don''t understand what advantage exceptions have over assertions, from the viewpoint that assertions are unusable across software layers.
Well, they require less resources in the code, for one. The same would go for implementing your own streamlined RTTI if you don''t need the full implementation. Although there is a supposed premise of ''not paying for what you don''t use'' in C++, if you turn exception handling on, the code tends to run about 5% slower, even if you never throw any exceptions. I assume this is down to code bloat, as the file size does swell up a bit.
A second advantage to assertions is that they are quicker to implement. This should only be a factor when testing in-house, obviously. When you release software you should be going for robustness, not the quickest way of producing semi-working feature-packed software. (Now, tell that to MS et al.)
quote:
[quote]See Why C++ Sucks for an alternative view.
I did -- LOL! It''s truly amazing how so many instances of bad logic can exist on one page on one subject by one person...
Although I disagree with a lot of what the guy said, and there are some ''logic wormholes'' in there, some of it does make sense
##### Share on other sites
quote:
Original post by Kylotan
quote:
--------------------------------------------------------------------------------
On that note, C++ lacks local functions. This could perhaps be considered a deficiency in the language.
--------------------------------------------------------------------------------
Local classes.
I was under the impression that classes can only be defined in global or class scope. This means the whole containing class has access to the inner class, when I only need one function to have access to it. It''s no better than just using another private member function.
Of course, the same old complication arises anyway: "Function definitions are not permitted in local class declarations in Microsoft C++."...
No, I mean classes that are local to a function, like this (I just learned how to do this!):
void reverse_bytes(byte* memory, unsigned int size){// local classclass swap_bytes_function{public:void operator(){byte& b1, byte& b2){ byte temp; temp = b1; b1 = b2; b2 = temp; }};// instantiate the classswab_bytes_function swap_bytes;for( unsigned int x=0; x{swap_bytes(memory[size-x], memory[x]);}}
That''s not the best example in the world, but it should work (barring serious bugs I may have introduced ).
If you need "simple" functions, why not use goto: and labels? That''s why they exist.
quote:
Original post by Kylotan
quote:
--------------------------------------------------------------------------------
If you expect me to be able to converse with you in an intelligent way, you -must- use the English standard. The efficiency of our communication is directly proportional to your compliance with the English standard.
--------------------------------------------------------------------------------
I was I was using the English definition of type. Unfortunately you were using the C++ definition of type which is a more stringent subset
From my dictionary:
type - A group of persons or things having in common certain traits or characteristics that set them apart from others as a distinct and indentifiable class
quote:
Original post by Kylotan
quote:
--------------------------------------------------------------------------------
1) Actually, new()-ing and delete()-ing are easy operations. Add one in the constructor, the other in the destructor, and you''re set. You can also define the copy constructor and operator=() if you wish, or just make them private.
--------------------------------------------------------------------------------
What about allocating variable sized buffers at run time? You want to make a wrapper class each time you want to do that? It''s not always that simple, unless you use an auto_ptr style thing, which you say you don''t...
Just use delete[] and it''ll automatically delete the number of bytes you allocated dynamically with new[]. Or you could create a buffer class, that can hold any type of data. Then just use buffer in any project you want. Or use std::vector, etc.
quote:
Original post by Kylotan
No, it is a good analogy, as we were comparing the tools available in different languages. In C++, you have to use a workaround to get what another language will give you for free, which is a logical way of abstracting another layer away from you. It simplifies code over using new and delete and reduces the chance of memory leaks, just like there are so many other features designed to simplify your work, such as virtual functions instead of endless switches.
It''s as if you''re saying abstraction and language tools are great if they''re native to C++, but in any other language they are over the top or unnecessary. Which I respect as an opinion, just as I respect that guy on these forums who does all his work in assembly But it''s just a personal coding style, nothing more.
1) It''s silly to have auto_ptr just delete memory for you when you can (even more easily) add in the calls yourself. Also, if you''re using auto_ptr, how does that work with your buffer theory? It would have to use delete[] on the bytes...
2) Since I don''t have enough experience to say that it is never useful, so I''ll leave it at this: "if auto_ptr simplifies some immensely difficult task that would require more programming than the code auto_ptr uses, then I would use auto_ptr." Otherwise, I''d just new() and delete() on my own intellect.
3) For free? I think you are missing something...nothing is free. You get that for which you have paid (corrected english grammar -- somehow it lost something...). If it implements garbage collection and C++ does not, then which is correct? I consider a rather easy principle that if you new() memory, you must delete() it. At least it is much easier than memorizing rules for when things go out of scope. Garbage collection can also introduce bugs that are very hard to track, and those bugs can really slow the program down. I don''t see garbage collection as worth anyone''s time learning for normal commercial software.
quote:
Original post by Kylotan
Well, they require less resources in the code, for one. The same would go for implementing your own streamlined RTTI if you don''t need the full implementation. Although there is a supposed premise of ''not paying for what you don''t use'' in C++, if you turn exception handling on, the code tends to run about 5% slower, even if you never throw any exceptions. I assume this is down to code bloat, as the file size does swell up a bit.
A second advantage to assertions is that they are quicker to implement. This should only be a factor when testing in-house, obviously. When you release software you should be going for robustness, not the quickest way of producing semi-working feature-packed software. (Now, tell that to MS et al.)
1) You are talking about assertions? I was talking about "design by contract" as a way of coding. I said that various tools in C++ work together to provide that. I think that many languages are just like "additions" to C++, because C++ is very logcial.
2) Exception specifications are going to be implemented in VC 7.0 (hopefully) and they are a way of optimizing code that does not use exceptions.
3) How are assertions quicker to implement?
quote:
Original post by Kylotan
Although I disagree with a lot of what the guy said, and there are some ''logic wormholes'' in there, some of it does make sense
I didn''t mean to offend you -- I though you were being funny in mentioning it... However, I don''t see what is to be gained by making a page like that. Why don''t people do productive things like post on forums?
- null_pointer
Sabre Multimedia
##### Share on other sites
quote:
Original post by null_pointer
No, I mean classes that are local to a function, like this (I just learned how to do this!):
MSVC5 just says global or class scope, and not even in an ''MS specific'' section either. Wouldn''t be surprised if this wasn''t true though. Either way, why make a whole new object just for 1 extra function? You don''t normally have to make 1 object per function. And using goto with labels is a bit icky, no? Especially when there is a perfectly good function system in C++ already. Local functions would be handy.
quote:
From my dictionary:
type - A group of persons or things having in common certain traits or characteristics that set them apart from others as a distinct and indentifiable class
And mine makes no mention of ''group'', for example. Either way, there is nothing in English that says the word ''type'' has to correspond to ''class'' in C++. Just because I use the word type, should not mean such a rigid definition. You will notice I used the term ''word'' in the last sentence, but I did not mean a 2-byte integer.
quote:
Just use delete[] and it''ll automatically delete the number of bytes you allocated dynamically with new[].
I gave an example of problems with this a few messages back.
{auto_ptr buffer = new char[size];if (!DoSomething(buffer)) return -1;if (!DoSomethingElse(buffer)) return -2;if (!DoSomethingAgain(buffer)) return -3;DoAFourthThing();}
Now write the equivalent version using delete. Far less convenient, you need to add 3 extra pairs of braces and 4 explicit calls to delete. And all the extra typing buys you nothing except to save the minimal overhead in using an auto_ptr. auto_ptr guarantees that your stuff will be deallocated. How else do you use pointers to dynamic variable-sized buffers in a system with exceptions? Unless they are wrapped in automatic objects, and hence will have their destructor called, your exceptions are not gonna be able to do their job properly. A buffer class is too complex when all you need is a dynamically sized array of a given type.
quote:
1) It''s silly to have auto_ptr just delete memory for you when you can (even more easily) add in the calls yourself. Also, if you''re using auto_ptr, how does that work with your buffer theory? It would have to use delete[] on the bytes...
Yes, it does, so you don''t have to. If you don''t understand this concept, I have to ask if you even use destructors etc? I pointed out above how it simplifies deallocation.
How come you are confident in the ability of the language makers on everything -but- auto_ptr? It''s a useful feature, to denounce it as not really being useful is just like calling virtual functions not useful. After all, you can always implement your own vtable...
quote:
3) For free? I think you are missing something...nothing is free. You get that for which you have paid (corrected english grammar -- somehow it lost something...). If it implements garbage collection and C++ does not, then which is correct? I consider a rather easy principle that if you new() memory, you must delete() it. At least it is much easier than memorizing rules for when things go out of scope. Garbage collection can also introduce bugs that are very hard to track, and those bugs can really slow the program down. I don''t see garbage collection as worth anyone''s time learning for normal commercial software.
I can''t agree with you on garbage collection. Having to manage your own pointers is the source of most bugs in modern software. Dereferencing invalid pointers, or pointers named after your good self, is the source of nearly every crash in modern code. Garbage collection vastly reduces these concerns.
quote:
3) How are assertions quicker to implement?
assert(some condition)
is quicker than
if (!some condition)
throw something relevant;
(catch it elsewhere).
At the worst, you would have to insert an extra catch statement for your exception, or create a new exception subclass, etc etc. asserts are useful to have while you''re developing.
quote:
I didn''t mean to offend you -- I though you were being funny in mentioning it... However, I don''t see what is to be gained by making a page like that. Why don''t people do productive things like post on forums?
You didn''t offend me. But for every language that you or I might like, there are valid concerns and criticisms of it. The same goes for any feature or tool in the language. We are quick to denounce any feature that takes care of something we can do already as useless, and any feature we can''t work out yet as being unnecessary. I grew up on Z80 assembly and Basic, and I couldn''t see the need for anything so structured as a GOSUB for a long time Never mind aggregate types or *gasp* data structures. As we gather coding experience, previous paradigms fall by the wayside as we find better ways of doing things, either within the language, or in a new language. I take the existence of more than 1 programming language as firm evidence that none of them are perfect.
##### Share on other sites
quote:
Original post by Kylotan
Either way, there is nothing in English that says the word ''type'' has to correspond to ''class'' in C++.
"class" in C++ is just a way of defining new types, as are struct and union.
quote:
Original post by Kylotan
I gave an example of problems with this a few messages back.
{
auto_ptr buffer = new char[size];
if (!DoSomething(buffer))
return -1;
if (!DoSomethingElse(buffer))
return -2;
if (!DoSomethingAgain(buffer))
return -3;
DoAFourthThing();
}
Now write the equivalent version using delete. Far less convenient, you need to add 3 extra pairs of braces and 4 explicit calls to delete. And all the extra typing buys you nothing except to save the minimal overhead in using an auto_ptr. auto_ptr guarantees that your stuff will be deallocated. How else do you use pointers to dynamic variable-sized buffers in a system with exceptions? Unless they are wrapped in automatic objects, and hence will have their destructor called, your exceptions are not gonna be able to do their job properly. A buffer class is too complex when all you need is a dynamically sized array of a given type.
quote:
auto_ptr::~auto_ptr documentation
~auto_ptr();
If the ownership indicator is true, the destructor deletes the object designated by the stored pointer p by evaluating the delete expression delete p.
Your buffer isn''t being deallocated properly -- just the first byte. See how garbage collection can introduce memory leaks?
quote:
Original post by Kylotan
quote:
--------------------------------------------------------------------------------
1) It''s silly to have auto_ptr just delete memory for you when you can (even more easily) add in the calls yourself. Also, if you''re using auto_ptr, how does that work with your buffer theory? It would have to use delete[] on the bytes...
--------------------------------------------------------------------------------
Yes, it does, so you don''t have to. If you don''t understand this concept, I have to ask if you even use destructors etc? I pointed out above how it simplifies deallocation.
How come you are confident in the ability of the language makers on everything -but- auto_ptr? It''s a useful feature, to denounce it as not really being useful is just like calling virtual functions not useful. After all, you can always implement your own vtable...
Perhaps I didn''t phrase that correctly? Let me try it another way, then. I mean that it''s silly to learn a new class for something on which you can call "delete". When I say smaller code, I mean smaller total code, not smaller imagined code because the code is in a class and separate from the individual function.
1) auto_ptr is not part of the language -- it is a class. new and delete are the language features, and they are what I said to use...you''ve got it backwards!
2) Simplification of code is only good so long as it does not make more code than necessary without simplification.
3) Destructors take care of tasks that should be written anyway - they don''t add extra code. That is, if I write an array class, it shouldn''t involve more code within each member function than I would need to normally use a C++ array (i.e. "new char[256]" etc.). That is, if I write a deallocate() function for the array, it should call delete[], and possibly do any checks to maintain its proper state.
quote:
Original post by Kylotan
I can''t agree with you on garbage collection. Having to manage your own pointers is the source of most bugs in modern software. Dereferencing invalid pointers, or pointers named after your good self, is the source of nearly every crash in modern code. Garbage collection vastly reduces these concerns.
Even garbage collection cannot make up for bad coding. It merely masks bad coding. I still don''t see what is so hard about new and delete!
quote:
Original post by Kylotan
assert(some condition)
is quicker than
if (!some condition)
throw something relevant;
(catch it elsewhere).
At the worst, you would have to insert an extra catch statement for your exception, or create a new exception subclass, etc etc. asserts are useful to have while you''re developing.
1) So, at the worst case, it''s not much more than a few (short) lines of typing?
2) Assertions don''t -do- anything but halt the program. They''re stupid for debugging because they can''t clean up; that is totally unacceptable across software layers. Because software is becoming increasingly modular, I am surprised that someone actually maintains that it is better than exceptions.
quote:
Original post by Kylotan
You didn''t offend me. But for every language that you or I might like, there are valid concerns and criticisms of it. The same goes for any feature or tool in the language. We are quick to denounce any feature that takes care of something we can do already as useless, and any feature we can''t work out yet as being unnecessary. I grew up on Z80 assembly and Basic, and I couldn''t see the need for anything so structured as a GOSUB for a long time Never mind aggregate types or *gasp* data structures. As we gather coding experience, previous paradigms fall by the wayside as we find better ways of doing things, either within the language, or in a new language. I take the existence of more than 1 programming language as firm evidence that none of them are perfect.
I liked BASIC too, but found it hard to grasp the notion of functions.
Anyway, enough reminiscing about the past... I was just saying that it does all evaluate to assembly (different assembly on different computers, of course). If assertions don''t do everything they need to do for debugging, and exceptions do, then exceptions are better for debugging. That''s not a matter of difference of opinion or preference.
However, specialized applications introduce new priorities. I''m talking about the machines used to monitor heart transplants here, not the next Quake! At base all programs are just different combinations of C++ keywords and user-defined types. Very few programs actually require something different (as in 1/1,000,000 programs produced).
I must admit I didn''t like the Eiffel site, primarily because of the hype that I sensed there.
- null_pointer
Sabre Multimedia
##### Share on other sites
Busy week at work, hence the delay in replying
quote:
Original post by null_pointer
Your buffer isn''t being deallocated properly -- just the first byte. See how garbage collection can introduce memory leaks?
Firstly, a true garbage collection system would deal with this. Any memory leaks in a garbage collected language are because the programmer failed to correctly terminate a reference, just as a memory leak in C is because someone forgot to free the memory. I think you are biased here because you are comfortable with delete and not with garbage collection. I contend that they are both adequate for the task, except new/delete/malloc/free give you extra power at the expense of extra management on your part. Having to do more micromanagement is the opposite direction to the way computing is going. We want to be able to encapsulate a perfect system and move on. Having to track your own memory allocation is a far more difficult system.
My auto_ptr example would work fine with some other class. It saves typing, guarantees a destructor call, reduces the chance of errors. To me, that equals Good Thing
quote:
Perhaps I didn''t phrase that correctly? Let me try it another way, then. I mean that it''s silly to learn a new class for something on which you can call "delete".
When I say smaller code, I mean smaller total code, not smaller imagined code because the code is in a class and separate from the individual function.
This is madness. You are now arguing against encapsulation! Take repeated code out of your algorithms and move it into separate functions/modules/objects... that is the whole essence of programming. In the example I gave, allocating the memory is not part of the algorithm, it is just an added necessity. Therefore it makes sense to abstract it away rather than have to micromanage it yourself.
quote:
1) auto_ptr is not part of the language -- it is a class. new and delete are the language features, and they are what I said to use...you''ve got it backwards!
auto_ptr is part of the standard. It is therefore still part of the language, although more tenuously. If you know lingustics, this is like the difference between the ''closed set'' of vocabulary (pronouns etc) and the ''open set'' (verbs, nouns). It''s all part of the language. You''re not fully ANSI C++ compliant unless you supply auto_ptr.
quote:
2) Simplification of code is only good so long as it does not make more code than necessary without simplification.
I disagree. Quite often it is ''necessary'' to introduce code which, on the surface, seems redundant, but is there for some other purpose, such as abstraction for example. That extra code may be useless now, but may form an interface which makes your classes more reusable, etc. Necessary is a subjective term. What you don''t need today, you may need later, and it will take twice as long to add in later... it''s a tradeoff.
I don''t see using auto_ptr as being ''extra code'', though. Maybe you are referring to garbage collection in general? Either way, I''d rather have a stable program running at 80% efficiency than an unstable one at 99% efficiency. But wait: you''re a Windows fan, aren''t you? Just teasing.
quote:
Even garbage collection cannot make up for bad coding. It merely masks bad coding. I still don''t see what is so hard about new and delete!
I don''t see what is so hard about using globals effectively, or just using normal functions rather than objects. But I know certain things make my life easier. And everything that I can do more easily, gives me more time for the harder stuff and reduces the chance of introducing bugs.
I don''t want to micromanage my memory any more than I want to have to deal with all my files a character at a time. Memory management is there for when you want to be close to the machine, just like the bitshifting operators, etc. If I''m working at a higher level, this should be one of the main things to abstract away, in my opinion.
quote:
[quote]
assert(some condition)
is quicker than
if (!some condition)
throw something relevant;
(catch it elsewhere).
1) So, at the worst case, it''s not much more than a few (short) lines of typing?
It''s always a few lines less typing. It also looks more clearly like a pre/postcondition, whereas exception handling spreads out the code across the function, or even across the program. Usually exception handling does a good job of separating the error code from the algorithm code. With an assert, that is not your concern - your concern is stopping the code at the exact line that there is a problem, not passing that down to somewhere else. Most debuggers will work in tandem with asserts to drop you into the code at that line and let you examine all the variables. Throwing an exception down to some function to catch it might well be able to tell you exactly where the error happened, but by then all your stack variables have been deallocated... hence, useless for debugging.
quote:
2) Assertions don''t -do- anything but halt the program. They''re stupid for debugging because they can''t clean up;
See above: they are -perfect- for debugging because they -don''t- clean up.
quote:
that is totally unacceptable across software layers.
It is totally unacceptable in released software. It is, however, a useful debugging tool.
##### Share on other sites
heh heh just when I thought everyone quit arguing...
There seem to be two major issues that we are discussing, and I feel we are miscommunicating. They are 1) garbage collection and 2) exceptions vs. assertions.
1) GARBAGE COLLECTION
I have a view of encapsulation that can best be understood by the following three functions (the example is somewhat long). Here is the first function, with encapsulation:
// this function draws some text using the current// drawing tool and modevoid display::output(const string& text, vector <image>* font){// exceptions found in functionclass null_pointer : public exception {}class invalid_font : public exception {}// check arguments (this can be removed in release)if( font == NULL )throw null_pointer; // custom exception, tells locationif( font.size() != (sizeof(char)^8) )throw invalid_font; // also tells location// declare our constantsconst unsigned int number_of_letters = text.size();unsigned int x = 0; // x and y are theunsigned int y = 0; // upper left corner// draw the letter, using its bitmapped font,// at the location we calculatefor( unsigned long j=0; j{// at the left cornerx += font[j].get_width();// at the bottom of the screeny = (this->height - font[j].get_height());// draw itthis->blit(font(char(text[j])), x, y);}}
Whew! that's a lot of typing...anyway, it's a lot less than would be possible without encapsulation. Let's move on to the next version of that function, which is the same except it contains the code from all the functions we called in the previous example, etc. which means it contains the code from list<letter>::size(), list<letter>::operator[], vector<image>::operator[], this->blit(), etc. I'm not going to list it, though. Just think of how it would be.
The third example of the function is as if we had coded the function without using other classes -- not even procedural code...everything here is coded in one straight line, from the beginning of the program to the end, and all in main().
Now, the second example should have the efficiency of the third example, if it is written correctly. The first example should have the efficiency of the second example, if it is written correctly. This is a round-about way of saying that if you could dump all the code from all the functions and classes you use right into main(), it should look the same (providing both are written correctly) as if you had done it that way to begin with. The point is that classes and functions should not add extra code. This is definitely part of "overhead" as it affects the code just like useless extra function calls or who knows what optimization nightmares people create. "overhead" is anything that is unnecessary over and above the third example. I say that good encapsulation involves no "overhead." If it does, then you obviously have either duplicate code or unnecessary code. Classes and functions merely organize code. I am most certainly not arguing against the use of them.
The following code snippet is ludicrous:
void do_something(){bool own_memory = false;byte* heap_memory = new byte[256];own_memory = true;if( own_memory )delete[] heap_memory}
Isn't this ludicrous, too:
void do_something(){auto_ptr heap_memory(new byte[256]);}
It uses the "same" code.
I said, if you need it, use it. Otherwise, simple calls to new() and delete() will do. To put it another way, if you are going to add in a bool anyway to keep track of it, then use auto_ptr. The point of encapsulation is to organize code, and not to cover the programmer's mistakes or to save typing (although it tends to do that). If you want to totally separate new() and delete() for some reason in addition to allocating/deallocating memory (instance counting, etc.) the by all means put it in a class.
2) EXCEPTIONS VS. ASSERTIONS
I think our primary misunderstanding here is whether you are debugging between different "layers" of software or just testing the same "layer" of software. The definition of a "layer" of software that I am referring to here is code encapsulated into any sort of organizational separation (i.e., classes in C++).
There are two distinct cases in software development. 1) When you have communication between code from different classes, that communicate, you are debugging between different "layers" of software. 2) When you do not have communication between code from different classes, you are not debugging between different layers of software.
CASE 1 -- ACROSS LAYERS
Because "layers" of software (again, classes in C++) should NOT be dependent on each other to maintain a valid state, assertions are not good across them. An assertion triggered in my linked_list class might demolish my ddraw_wrapper class, and cause haywire on my PC. Exceptions, on the other had, are made for this case; they provide cleanup, notification, and as much information as you could want.
CASE 2 -- WITHIN ONE LAYER
Within one "layer" of software, you have no dependencies, and thus assertions have every advantage over exceptions because it is not conceivable that you will ever need to clean up -- every condition is known and can be easily controlled. Exceptions are merely excess overhead and totally unnecessary here.
The only problem with case 2 is that it doesn't exist in real life! "Layers" of software aren't just classes; they include the OS, the BIOS, other programs, different parts of your program, the classes they use, etc. Having everything co-dependent upon each other with assertions is the equivalent of mass suicide in release apps (as you pointed out). In debug apps it is equally unacceptable for me, as I do not want my dev PC crashing constantly. Exceptions provide a stable environment for debugging. Sometimes you must have a performance hit to do it right.
Now that I have stated my observations and conclusions, I will work on the quotes.
quote:
Original post by Kylotan
Firstly, a true garbage collection system would deal with this. Any memory leaks in a garbage collected language are because the programmer failed to correctly terminate a reference, just as a memory leak in C is because someone forgot to free the memory. I think you are biased here because you are comfortable with delete and not with garbage collection.
1) I'm a C++ programmer. I had better know what delete() does!
2) I was not indicating that garbage collection libraries cannot handle code like that. Some of them are quite sophisticated and elegant. I was merely pointing out that it makes the code more complex, and that is why you made the mistake in the first place.
3) Extra effort must be justified. Every C++ programmer had better know how to use new() and delete(). Garbage collection in C++ is, then, extra work. Can you justify it? It was not made to cover laziness. Laziness with garbage collection will only net you slower code and increased frustration. I want to perfectly clear that I am not calling your example lazy, here, but that I am talking about a very common misconception here: if you don't spend the extra time learning garbage collection and using it properly, you won't get anything out of it. If you are only looking to garbage collection to hide your own inability to understand new() and delete(), then you have a rude awakening ahead.
quote:
Original post by Kylotan
In the example I gave, allocating the memory is not part of the algorithm, it is just an added necessity. Therefore it makes sense to abstract it away rather than have to micromanage it yourself.
1) No, allocating the memory was obviously a necessary part of the algorithm, or you wouldn't have done it. You need memory to operate on, or else the operation is pointless.
2) This is my point: why use auto_ptr? You "added in" extra code involving a bool variable, a class instance, etc. which were totally unnecessary for the algorithm. Small overhead, but unnecessary and pointless. Also, auto_ptr didn't save you any typing. If you want to eliminate micro-management in your example, use the built-in "auto_ptr": the stack.
There is no substitute for good coding.
- null_pointer
Sabre Multimedia
Edited by - null_pointer on May 21, 2000 11:24:19 AM
##### Share on other sites
quote:
Original post by null_pointer
2) This is my point: why use auto_ptr? You "added in" extra code involving a bool variable, a class instance, etc. which were totally unnecessary for the algorithm. Small overhead, but unnecessary and pointless. Also, auto_ptr didn''t save you any typing. If you want to eliminate micro-management in your example, use the built-in "auto_ptr": the stack.
Now you''re being really ignorant. Smart pointers, e.g. auto_ptr and the like (as well as most of the STL container classes), deal with situations where you need to dynamically control memory to write exception safe code. Using auto_ptr guarentees (when used properly) that ownership of memory is maintained and that when the owning object goes out of scope the memory is released. Even in the face of exceptions.
E.g.:
foo* create_and_initialize_foo_and_do_other_stuff()
{
auto_ptr<foo> srpfoo( new foo );
srpfoo->init();
srpfoo->otherstuff();
return srpfoo.release();
}
This is exception-safe code. This is not equivalent to:
foo* unsafe_create_and_initialize_foo_and_do_other_stuff()
{
foo* pfoo = new foo;
pfoo->init();
pfoo->otherstuff();
return pfoo;
}
If foo::init or foo::otherstuff throw an exception in the latter case, the memory allocated by new foo will not be freed; hence, memory leak, and not exception safe.
Please, try to research these areas before posting ignorant information.
MSN
##### Share on other sites
quote:
Original post by msn12b
Please, try to research these areas before posting ignorant information.
I politely ask, first, that you do the same. I was referring to a specific example cited by Kylotan where the memory was used only within the function in which it was allocated, and it was deallocated in all cases before the function exited. Such a case is quite obviously a use for stack allocations.
This is why I usually use LONG quotations so that other people would have to purposely skip reading the examples cited and purposely post ignorant information. I was trying not to use such long quotations so the posts wouldn''t take so much time to load, but I see that doesn''t work.
quote:
Original post by msn12b
1) I like to think that when I say "why use auto_ptr?" I am asking a question and not being "pedantic." Also, when I make what seems to be a logical point, I am merely working with the knowledge I have and not being "pedantic." I''m not sure but it may help me more if you answered my question with a little more tact, but I understood it anyway with my usual narrow-mindedness. Or perhaps you could explain how I am being "pedantic."
2) I did read the first 5 pages of it, and I do understand how exceptions work (from other material). I did a model of a generic resource using a resource_handle class, complete with copy constructors, assignment operators, etc. which is like auto_ptr on steroids, and it is already in use in my library. I can post it here if you like, but it''s rather large (then again, so is everything else in this post ).
quote:
Original post by msn12b
E.g.:
foo* create_and_initialize_foo_and_do_other_stuff()
{
auto_ptr srpfoo( new foo );
srpfoo->init();
srpfoo->otherstuff();
return srpfoo.release();
}
This is exception-safe code. This is not equivalent to:
foo* unsafe_create_and_initialize_foo_and_do_other_stuff()
{
foo* pfoo = new foo;
pfoo->init();
pfoo->otherstuff();
return pfoo;
}
If you re-read at my examples and explanations in my previous post, you''ll see that is not my point. I know how exceptions work. I do understand how destructors are called, why they are called, what auto_ptr does, etc. I was not questioning the validity of auto_ptr as a replacement for memory allocated on the heap, but the validity of auto_ptr as a replacement for memory allocated on the heap that could have been allocated on the stack.
- null_pointer
Sabre Multimedia
• 11
• 32
• 12
• 15
• 15 | 2019-05-20 02:46:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30753204226493835, "perplexity": 1973.3578464707837}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232255536.6/warc/CC-MAIN-20190520021654-20190520043654-00145.warc.gz"} |
https://nrich.maths.org/12762/solution | ### A Problem of Time
Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?
### Fit for Photocopying
Explore the relationships between different paper sizes.
### Back in Time
How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?
# Growing Triangle
##### Age 14 to 16 ShortChallenge Level
Considering triangles with area 100 square units
If the area of the original triangle is 100 square units, then each square unit represents 1%. So by enlarging the base and height of the triangle and finding the new area, it will be clear what the percentage increase has been.
Both of the triangles shown below have area 100 square units, since $\frac{1}{2}\times10\times20=\frac{1}{2}\times8\times25=100$.
Increasing the base of each triangle by 20%
• 20% of 20 is 4, so the new base is 24
• 20% of 8 is 1.6, so the new base is 9.6
Increasing the height of each triangle by 30%
• 30% of 10 is 3, so the new height is 13
• 30% of 25 is 7.5, so the new height is 32.5
This is shown below.
The area of the left hand triangle is $\frac{1}{2}\times24\times13=156$ square units.
The area of the right hand triangle is $\frac{1}{2}\times9.6\times32.5=156$ too (and they must be the same, or the question wouldn’t make sense).
In both cases, the area has increased by 56 units, which is 56% of 100 units. So the area has increased by 56%.
Enlarging a unit by 20% and 30%
Imagine that the triangle is on a squared grid, then the area of the triangle is the number of squares (including fractions of squares) that fit inside it.
Then when the triangle has been enlarged, the whole grid could have been enlarged – so the triangle still contains the same number of ‘squares’, but the squares have changed shape.
Now, instead of being 1 by 1 squares with area 1, the squares have become rectangles, because their bases have been increased by 20% and their heights have been increased by 30%.
1 increased by 20% is 1.2, and 1 increased by 30% is 1.3, so the rectangles are 1.2 by 1.3.
$1.2\times1.3=1.56$. So the area of each square has been increased by 0.56, which is the same as 56% of its original area of 1. So since each square has increased in area by 56%, the area of the triangle has also been increased by 56%.
Using length and width scale factors
Increasing the base by 20% is a horizontal stretch, and so the area will be increased by 20%, to 120% of its original area.
Increasing the height by 30% is a vertical stretch, and so the new area will be increased by 30%. 30% of 120% is 36%, so the new area will be 156% of the original area.
So the area has increased by 56%.
Using algebra for the base and height
Suppose the triangle had base $b$ and height $h$. Then its area was $\frac{1}{2}b\times h$.
When the base is increased by 20%, the new base will be $1.2b$. When the height is increased by 30%, the new height will be $1.3h$.
So the new area will be $\frac{1}{2}\times1.2b\times1.3h=\frac{1}{2}\times b\times h\times1.2\times1.3$.
That is the same as the old area multiplied by $1.2\times1.3=1.56$, so the area has been multiplied by 1.56, which corresponds to an increase of 56%.
You can find more short problems, arranged by curriculum topic, in our short problems collection. | 2021-03-03 11:49:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7209478616714478, "perplexity": 459.836519070106}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178366959.54/warc/CC-MAIN-20210303104028-20210303134028-00600.warc.gz"} |
https://www.lessonplanet.com/teachers/multiplying-decimals-by-powers-of-ten-g | # Multiplying Decimals by Powers of Ten (G)
In this decimal multiplication activity, 4th graders solve the decimal multiplication problems that range by powers of ten. Students solve 45 problems.
Concepts
Resource Details | 2017-07-25 20:36:48 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9344849586486816, "perplexity": 7121.3771247536715}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549425381.3/warc/CC-MAIN-20170725202416-20170725222416-00189.warc.gz"} |
http://indico.cern.ch/event/223265/ | ISOLDE Seminar
Proton/Antiproton Magnetic Moments and the Hyperfine Structure of Antihydrogen
by Stefan Ulmer (I)
Thursday, 7 February 2013 from to (Europe/Zurich)
at CERN ( 26-1-022 )
Description The precision spectroscopy of simple antimatter systems and the comparison to their matter counterparts contributes to our understanding of the matter/antimatter asymmetry which is observed on cosmological scales. Specifically interesting are experimental studies of systems at an ultra-low absolute energy scale, as the comparison of the magnetic moment of the proton and the antiproton, or the hyperfine structure of hydrogen and antihydrogen. In 2011 we observed for the first time spin flips with a single trapped proton, which is a major step towards a high precision measurement of the particle’s magnetic moment. Based on these results measurements at a precision close to the ppm-level were performed in a Penning trap with a superimposed inhomogeneous magnetic field. Applying the method to a single antiproton, the particle’s magnetic moment can be improved now by three orders of magnitude. Recently the ATRAP collaboration reported on a first determination of the magnetic moment of the antiproton at a level of 4.4ppm. Using a double-Penning trap scheme the ATRAP collaboration as well as the BASE collaboration intend to improve this precision down to the ppb-level, at least. Another experiment which investigates the properties of antimatter at a comparable energy scale as the one described above is the precision comparison of the hyperfine structure of hydrogen and antihydrogen. Antihydrogen was recently produced in a so-called CUSP, which is utilized to produce a polarized anti-atomic beam. This can be used to perform precision hyperfine-spectroscopy by application of a Rabi-like beam-spectroscopy scheme. In my talk I will report on recent progress of both efforts. | 2015-05-29 08:12:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7040420174598694, "perplexity": 1009.225491253181}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207929956.54/warc/CC-MAIN-20150521113209-00084-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://www.oreilly.com/content/an-illustrated-introduction-to-the-t-sne-algorithm/ | # An illustrated introduction to the t-SNE algorithm
This post is an introduction to a popular dimensionality reduction algorithm: t-distributed stochastic neighbor embedding (t-SNE).
March 3, 2015
T-sne plot
In the Big Data era, data is not only becoming bigger and bigger; it is also becoming more and more complex. This translates into a spectacular increase of the dimensionality of the data. For example, the dimensionality of a set of images is the number of pixels in any image, which ranges from thousands to millions.
Computers have no problem processing that many dimensions. However, we humans are limited to three dimensions. Computers still need us (thankfully), so we often need ways to effectively visualize high-dimensional data before handing it over to the computer.
## Learn faster. Dig deeper. See farther.
Join the O'Reilly online learning platform. Get a free trial today and find answers on the fly, or master something new and useful.
How can we possibly reduce the dimensionality of a dataset from an arbitrary number to two or three, which is what we’re doing when we visualize data on a screen?
The answer lies in the observation that many real-world datasets have a low intrinsic dimensionality, even though they’re embedded in a high-dimensional space. Imagine that you’re shooting a panoramic landscape with your camera, while rotating around yourself. We can consider every picture as a point in a 16,000,000-dimensional space (assuming a 16 megapixels camera). Yet, the set of pictures approximately lie in a three-dimensional space (yaw, pitch, roll). This low-dimensional space is embedded within the high-dimensional space in a complex, nonlinear way. Hidden in the data, this structure can only be recovered via specific mathematical methods.
This is the topic of manifold learning, also called nonlinear dimensionality reduction, a branch of machine learning (more specifically, unsupervised learning). It is still an active area of research today to develop algorithms that can automatically recover a hidden structure in a high-dimensional dataset.
This post is an introduction to a popular dimensonality reduction algorithm: t-distributed stochastic neighbor embedding (t-SNE). Developed by Laurens van der Maaten and Geoffrey Hinton (see the original paper here), this algorithm has been successfully applied to many real-world datasets. Here, we’ll follow the original paper and describe the key mathematical concepts of the method, when applied to a toy dataset (handwritten digits). We’ll use Python and the scikit-learn library.
## Visualizing handwritten digits
Let’s first import a few libraries.
# That's an impressive list of imports.
import numpy as np
from numpy import linalg
from numpy.linalg import norm
from scipy.spatial.distance import squareform, pdist
# We import sklearn.
import sklearn
from sklearn.manifold import TSNE
from sklearn.preprocessing import scale
# We'll hack a bit with the t-SNE code in sklearn 0.15.2.
from sklearn.metrics.pairwise import pairwise_distances
from sklearn.manifold.t_sne import (_joint_probabilities,
_kl_divergence)
from sklearn.utils.extmath import _ravel
# Random state.
RS = 20150101
# We'll use matplotlib for graphics.
import matplotlib.pyplot as plt
import matplotlib.patheffects as PathEffects
import matplotlib
%matplotlib inline
# We import seaborn to make nice plots.
import seaborn as sns
sns.set_style('darkgrid')
sns.set_palette('muted')
sns.set_context("notebook", font_scale=1.5,
rc={"lines.linewidth": 2.5})
# We'll generate an animation with matplotlib and moviepy.
from moviepy.video.io.bindings import mplfig_to_npimage
import moviepy.editor as mpy
Now we load the classic handwritten digits datasets. It contains 1797 images with $$8*8=64$$ pixels each.
digits = load_digits()
digits.data.shape
print(digits['DESCR'])
Here are the images:
nrows, ncols = 2, 5
plt.figure(figsize=(6,3))
plt.gray()
for i in range(ncols * nrows):
ax = plt.subplot(nrows, ncols, i + 1)
ax.matshow(digits.images[i,...])
plt.xticks([]); plt.yticks([])
plt.title(digits.target[i])
plt.savefig('images/digits-generated.png', dpi=150)
Now let’s run the t-SNE algorithm on the dataset. It just takes one line with scikit-learn.
# We first reorder the data points according to the handwritten numbers.
X = np.vstack([digits.data[digits.target==i]
for i in range(10)])
y = np.hstack([digits.target[digits.target==i]
for i in range(10)])
digits_proj = TSNE(random_state=RS).fit_transform(X)
Here is a utility function used to display the transformed dataset. The color of each point refers to the actual digit (of course, this information was not used by the dimensionality reduction algorithm).
def scatter(x, colors):
# We choose a color palette with seaborn.
palette = np.array(sns.color_palette("hls", 10))
# We create a scatter plot.
f = plt.figure(figsize=(8, 8))
ax = plt.subplot(aspect='equal')
sc = ax.scatter(x[:,0], x[:,1], lw=0, s=40,
c=palette[colors.astype(np.int)])
plt.xlim(-25, 25)
plt.ylim(-25, 25)
ax.axis('off')
ax.axis('tight')
# We add the labels for each digit.
txts = []
for i in range(10):
# Position of each label.
xtext, ytext = np.median(x[colors == i, :], axis=0)
txt = ax.text(xtext, ytext, str(i), fontsize=24)
txt.set_path_effects([
PathEffects.Stroke(linewidth=5, foreground="w"),
PathEffects.Normal()])
txts.append(txt)
return f, ax, sc, txts
Here is the result.
scatter(digits_proj, y)
plt.savefig('images/digits_tsne-generated.png', dpi=120)
We observe that the images corresponding to the different digits are clearly separated into different clusters of points.
## Mathematical framework
Let’s explain how the algorithm works. First, a few definitions.
A data point is a point $$x_i$$ in the original data space $$\mathbf{R}^D$$, where $$D=64$$ is the dimensionality of the data space. Every point is an image of a handwritten digit here. There are $$N=1797$$ points.
A map point is a point $$y_i$$ in the map space $$\mathbf{R}^2$$. This space will contain our final representation of the dataset. There is a bijection between the data points and the map points: every map point represents one of the original images.
How do we choose the positions of the map points? We want to conserve the structure of the data. More specifically, if two data points are close together, we want the two corresponding map points to be close too. Let’s $$\left| x_i – x_j \right|$$ be the Euclidean distance between two data points, and $$\left| y_i – y_j \right|$$ the distance between the map points. We first define a conditional similarity between the two data points:
$$p_{j|i} = \frac{\exp\left(-\left| x_i – x_j\right|^2 \big/ 2\sigma_i^2\right)}{\displaystyle\sum_{k \neq i} \exp\left(-\left| x_i – x_k\right|^2 \big/ 2\sigma_i^2\right)}$$
This measures how close $$x_j$$ is from $$x_i$$, considering a Gaussian distribution around $$x_i$$ with a given variance $$\sigma_i^2$$. This variance is different for every point; it is chosen such that points in dense areas are given a smaller variance than points in sparse areas. The original paper details how this variance is computed exactly.
Now, we define the similarity as a symmetrized version of the conditional similarity:
$$p_{ij} = \frac{p_{j|i} + p_{i|j}}{2N}$$
We obtain a similarity matrix for our original dataset. What does this matrix look like?
## Similarity matrix
The following function computes the similarity with a constant $$\sigma$$.
def _joint_probabilities_constant_sigma(D, sigma):
P = np.exp(-D**2/2 * sigma**2)
P /= np.sum(P, axis=1)
return P
We now compute the similarity with a $$\sigma_i$$ depending on the data point (found via a binary search, according to the original t-SNE paper). This algorithm is implemented in the _joint_probabilities private function in scikit-learn’s code.
# Pairwise distances between all data points.
D = pairwise_distances(X, squared=True)
# Similarity with constant sigma.
P_constant = _joint_probabilities_constant_sigma(D, .002)
# Similarity with variable sigma.
P_binary = _joint_probabilities(D, 30., False)
# The output of this function needs to be reshaped to a square matrix.
P_binary_s = squareform(P_binary)
We can now display the distance matrix of the data points, and the similarity matrix with both a constant and variable sigma.
plt.figure(figsize=(12, 4))
pal = sns.light_palette("blue", as_cmap=True)
plt.subplot(131)
plt.imshow(D[::10, ::10], interpolation='none', cmap=pal)
plt.axis('off')
plt.title("Distance matrix", fontdict={'fontsize': 16})
plt.subplot(132)
plt.imshow(P_constant[::10, ::10], interpolation='none', cmap=pal)
plt.axis('off')
plt.title("$p_{j|i}$ (constant $\sigma$)", fontdict={'fontsize': 16})
plt.subplot(133)
plt.imshow(P_binary_s[::10, ::10], interpolation='none', cmap=pal)
plt.axis('off')
plt.title("$p_{j|i}$ (variable $\sigma$)", fontdict={'fontsize': 16})
plt.savefig('images/similarity-generated.png', dpi=120)
We can already observe the 10 groups in the data, corresponding to the 10 numbers.
Let’s also define a similarity matrix for our map points.
$$q_{ij} = \frac{f(\left| x_i – x_j\right|)}{\displaystyle\sum_{k \neq i} f(\left| x_i – x_k\right|)} \quad \textrm{with} \quad f(z) = \frac{1}{1+z^2}$$
This is the same idea as for the data points, but with a different distribution (t-Student with one degree of freedom, or Cauchy distribution, instead of a Gaussian distribution). We’ll elaborate on this choice later.
Whereas the data similarity matrix $$\big(p_{ij}\big)$$ is fixed, the map similarity matrix $$\big(q_{ij}\big)$$ depends on the map points. What we want is for these two matrices to be as close as possible. This would mean that similar data points yield similar map points.
## A physical analogy
Let’s assume that our map points are all connected with springs. The stiffness of a spring connecting points $$i$$ and $$j$$ depends on the mismatch between the similarity of the two data points and the similarity of the two map points, that is, $$p_{ij} – q_{ij}$$. Now, we let the system evolve according to the laws of physics. If two map points are far apart while the data points are close, they are attracted together. If they are nearby while the data points are dissimilar, they are repelled.
The final mapping is obtained when the equilibrium is reached.
## Algorithm
Remarkably, this physical analogy stems naturally from the mathematical algorithm. It corresponds to minimizing the Kullback-Leiber divergence between the two distributions $$\big(p_{ij}\big)$$ and $$\big(q_{ij}\big)$$:
$$KL(P||Q) = \sum_{i, j} p_{ij} \, \log \frac{p_{ij}}{q_{ij}}.$$
This measures the distance between our two similarity matrices.
To minimize this score, we perform a gradient descent. The gradient can be computed analytically:
$$\frac{\partial \, KL(P || Q)}{\partial y_i} = 4 \sum_j (p_{ij} – q_{ij}) g\left( \left| x_i – x_j\right| \right) u_{ij} \quad \textrm{where} \, g(z) = \frac{z}{1+z^2}.$$
Here, $$u_{ij}$$ is a unit vector going from $$y_j$$ to $$y_i$$. This gradient expresses the sum of all spring forces applied to map point $$i$$.
Let’s illustrate this process by creating an animation of the convergence. We’ll have to monkey-patch the internal _gradient_descent() function from scikit-learn’s t-SNE implementation in order to register the position of the map points at every iteration.
# This list will contain the positions of the map points at every iteration.
positions = []
def _gradient_descent(objective, p0, it, n_iter, n_iter_without_progress=30,
momentum=0.5, learning_rate=1000.0, min_gain=0.01,
args=[]):
# The documentation of this function can be found in scikit-learn's code.
p = p0.copy().ravel()
update = np.zeros_like(p)
gains = np.ones_like(p)
error = np.finfo(np.float).max
best_error = np.finfo(np.float).max
best_iter = 0
for i in range(it, n_iter):
# We save the current position.
positions.append(p.copy())
error_diff = np.abs(new_error - error)
error = new_error
if error < best_error:
best_error = error
best_iter = i
elif i - best_iter > n_iter_without_progress:
break
break
if min_error_diff >= error_diff:
break
inc = update * grad >= 0.0
dec = np.invert(inc)
gains[inc] += 0.05
gains[dec] *= 0.95
np.clip(gains, min_gain, np.inf)
update = momentum * update - learning_rate * grad
p += update
return p, error, i
Let’s run the algorithm again, but this time saving all intermediate positions.
X_proj = TSNE(random_state=RS).fit_transform(X)
X_iter = np.dstack(position.reshape(-1, 2)
for position in positions)
We create an animation using MoviePy.
f, ax, sc, txts = scatter(X_iter[..., -1], y)
def make_frame_mpl(t):
i = int(t*40)
x = X_iter[..., i]
sc.set_offsets(x)
for j, txt in zip(range(10), txts):
xtext, ytext = np.median(x[y == j, :], axis=0)
txt.set_x(xtext)
txt.set_y(ytext)
return mplfig_to_npimage(f)
animation = mpy.VideoClip(make_frame_mpl,
duration=X_iter.shape[2]/40.)
We can clearly observe the different phases of the optimization, as described in the original paper.
Let’s also create an animation of the similarity matrix of the map points. We’ll observe that it’s getting closer and closer to the similarity matrix of the data points.
n = 1. / (pdist(X_iter[..., -1], "sqeuclidean") + 1)
Q = n / (2.0 * np.sum(n))
Q = squareform(Q)
f = plt.figure(figsize=(6, 6))
ax = plt.subplot(aspect='equal')
im = ax.imshow(Q, interpolation='none', cmap=pal)
plt.axis('tight')
plt.axis('off')
def make_frame_mpl(t):
i = int(t*40)
n = 1. / (pdist(X_iter[..., i], "sqeuclidean") + 1)
Q = n / (2.0 * np.sum(n))
Q = squareform(Q)
im.set_data(Q)
return mplfig_to_npimage(f)
animation = mpy.VideoClip(make_frame_mpl,
duration=X_iter.shape[2]/40.)
## The t-Student distribution
Let’s now explain the choice of the t-Student distribution for the map points, while a normal distribution is used for the data points. It is well known that the volume of the $$N$$-dimensional ball of radius $$r$$ scales as $$r^N$$. When $$N$$ is large, if we pick random points uniformly in the ball, most points will be close to the surface, and very few will be near the center.
This is illustrated by the following simulation, showing the distribution of the distances of these points, for different dimensions.
npoints = 1000
plt.figure(figsize=(15, 4))
for i, D in enumerate((2, 5, 10)):
# Normally distributed points.
u = np.random.randn(npoints, D)
# Now on the sphere.
u /= norm(u, axis=1)[:, None]
r = np.random.rand(npoints, 1)
# Uniformly within the ball.
points = u * r**(1./D)
# Plot.
ax = plt.subplot(1, 3, i+1)
if i == 0:
ax.set_ylabel('Distance from origin')
ax.hist(norm(points, axis=1),
bins=np.linspace(0., 1., 50))
ax.set_title('D=%d' % D, loc='left')
plt.savefig('images/spheres-generated.png', dpi=100, bbox_inches='tight')
When reducing the dimensionality of a dataset, if we used the same Gaussian distribution for the data points and the map points, we would get an imbalance in the distribution of the distances of a point’s neighbors. This is because the distribution of the distances is so different between a high-dimensional space and a low-dimensional space. Yet, the algorithm tries to reproduce the same distances in the two spaces. This imbalance would lead to an excess of attraction forces and a sometimes unappealing mapping. This is actually what happens in the original SNE algorithm, by Hinton and Roweis (2002).
The t-SNE algorithm works around this problem by using a t-Student with one degree of freedom (or Cauchy) distribution for the map points. This distribution has a much heavier tail than the Gaussian distribution, which compensates the original imbalance. For a given similarity between two data points, the two corresponding map points will need to be much further apart in order for their similarity to match the data similarity. This can be seen in the following plot.
z = np.linspace(0., 5., 1000)
gauss = np.exp(-z**2)
cauchy = 1/(1+z**2)
plt.plot(z, gauss, label='Gaussian distribution')
plt.plot(z, cauchy, label='Cauchy distribution')
plt.legend()
plt.savefig('images/distributions-generated.png', dpi=100)
Using this distribution leads to more effective data visualizations, where clusters of points are more distinctly separated.
## Conclusion
The t-SNE algorithm provides an effective method to visualize a complex dataset. It successfully uncovers hidden structures in the data, exposing natural clusters and smooth nonlinear variations along the dimensions. It has been implemented in many languages, including Python, and it can be easily used thanks to the scikit-learn library.
The references below describe some optimizations and improvements that can be made to the algorithm and implementations. In particular, the algorithm described here is quadratic in the number of samples, which makes it unscalable to large datasets. One could for example obtain an $$O(N \log N)$$ complexity by using the Barnes-Hut algorithm to accelerate the N-body simulation via a quadtree or an octree.
## References
Post topics: Artificial Intelligence
Share: | 2020-04-02 07:38:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6650956273078918, "perplexity": 1768.0765534804339}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370506673.7/warc/CC-MAIN-20200402045741-20200402075741-00182.warc.gz"} |
https://konfou.xyz/posts/gobolinix-redefining-filesystem-hierarchy/ | # GoboLinux redefining filesystem hierarchy
The traditional Unix filesystem hierarchy is a bit complicated. As it was explained in the first section of my post on it, /opt is used for software to be contained in a single tree rather having their files spread through the system. This concept of each program gets its own directory tree is taken to extreme by GoboLinux distro. More generally it reorganizes root to a new, hopefully more logical way.
## Hierarchy
The root structure in GoboLinux is the following.
/Data System and program resources /Mount Mount points /Programs Every program; no exceptions /System System files /Users User home directories
First of all, there’s a common misconception that descriptive directory names are for user friendliness. The actual reason is to not conflict with Unix namespace. The capitalized descriptive names originated from NeXT that also had to make its own directories coexist with Unix ones. Using the regular directory tree with different semantics can be confusing. This happens in AtheOS, where /usr behaves like /opt. The influencial Unix-derived Plan 9 also does this, or better say Unix itself did it. In Plan 9 /usr behaves like /home. This is actually similar to early Unix versions, where /usr was holding user home directories.
Having every program in /Programs means that someone can explore what is installed in their system just by doing ls /Programs. This can be thought as a database-less package management system with the directory structure itself organizing the system. As a consequence of this system, package management can take place using common Unix file tools. Specifically it’s simpler to create and share binary packages. Having this structure means that packages can be created just by compressing its directory. They can removed just by removing the directory.
Each entry in /Programs contains all files for that program, stored in a versioned subdirectory. The subdirectory mirrors /usr hierarchy of traditional systems for the specific program. The versioned tree makes it simple to maintain simultaneously multiple versions for each program.
For each file category, there is a directory under /System/Index grouping files from each application as links. Those directories are the traditional Unix ones found in /usr and specifically bin, include, lib, lib64 -> lib, libexec, sbin -> bin, and share. It can kinda be though as /usr/local.
In its initial presentation the directory was /System/Links, and the directories were Executables, Libraries, Headers, Shared and Manuals. The migration to the new hierarchy happened in version 015. The reason was issues with packaging.
Legacy applications continue to work thanks to symlink mapping of traditional paths into their GoboLinux counterparts. Those paths are hidden when listing root but application can still read and write to them. This is made possible by using GoboHide an icotls-based interface, actually a kernel extension meaning no kernel modifications are required. The gobohide is the userspace tool that talks with kernel. To show all hidden directories gobohide -l can be used.
The mapping can then be seen with
$gobohide -l / | while read dir; do ls -l$dir; done
For reference in latest (v017) version this is
/bin -> /System/Index/bin /boot -> /System/Kernel/Boot /config -> /System/Kernel/Config /dev -> /System/Kernel/Devices /etc -> /System/Settings /lib -> /System/Index/lib /lib64 -> /System/Index/lib64 /media -> /Mount/Media /mnt -> /Mount /proc -> /System/Kernel/Status /root -> /Users/root /run -> /Data/Variable/run /sbin -> /System/Index/sbin /srv -> /Data /sys -> /System/Kernel/Objects /tmp -> /Data/Variable/tmp /var -> /Data/Variable
There’s also /usr with the following directories and files in it.
./bin -> /System/Index/bin ./include -> /System/Index/include ./lib -> /System/Index/lib ./lib64 -> /System/Index/lib64 ./libexec ./local -> /usr ./man -> /System/Index/share/man ./plugins ./sbin -> /System/Index/sbin ./share -> /System/Index/share ./X11R6 -> /usr
The arguments gobohide -h/-u can be used to hide and undhide a directory respectively. A useful example is mapping /home to /Users and /root to /Users/root.
# mkdir -p /Users/root
# ln -s /Users /home
# gobohide -h /home
# ln -s /Users/root /root
# gobohide -h /root
Then doing ls -l will show the same structure as that in first section, but you can do ls -l /home and cd /home just fine.
## Compile
The design of /Data/Compile is also interesting, referred as the poor-man’s portage because of its minimalistic design. The Compile and the Recipes tree are designed around the universality of source distribution and use of common build tools. The Recipes are declarative files that describe what the compilation process is like rather imperative scripts.
The recipes files are hosted on GitHub @gobolinux/Recipes. The tree structure is similar to /Programs that is directories for every program and subdirectories for every version. The tree can be downloaded locally (doing swallow clone) for easy usage doing
git clone --depth=1 https://github.com/gobolinux/Recipes /Data/Compile/Recipes
That said this isn’t required for software installation. Compile will download a recipe when a compilation is requested. Doing Compile $pkg will perform a case-insensitive search for a recipe named $pkg. A particular version may be chosen instead doing Compile $pkg$vers.
Let’s see closer how recipes work. For example, the Recipe for file/5.39 (found in the directory ./File/5.39) is
TODO: Make PR to @gobolinux/Recipes
compile_version=1.9.0
url="ftp://ftp.astron.com/pub/file/file-5.39.tar.gz"
file_size=954266
file_md5=1c450306053622803a25647d88f80f25
recipe_type=configure
There’s also a Resources directory holding metadata. This directory is eventually copied to the /Programs subdirectory of the program. The files in are the following along with their contents.
BuildDependencies
LibTool
BuildInformation
Glibc 2.24
LibSeccomp 2.3.2
ZLib 1.2.3
Dependencies
ZLib 1.2.3
Description
[Name] file
[Summary] File type identification utility
[Description] File attempts to classify files depending on their contents and prints a description if a match is found.
[Homepage] https://darwinsys.com/file
Then the program can be installed with Compile file or for that version specifically with Compile file 5.39. Extra options can be passed ad hoc as flag in Compile command. This makes it a bit like build tool-agnostic make. When the package’s files and directories have been created and populated, Compile will then create the necessary links in the /System/Index.
In my opinion this model though very simple (less complexity is good) leads to some redundancy. For example the Description file will be copied unchanged between versions. Also the others files will remain mostly the same between versions with only version changes.
## Concepts in other systems
GoboLinux is influenced and draws inspiration from others systems that build a different system on top of Unix based. Examples of such systems are NeXT, BeOS, and AtheOS. That said, GoboLinux isn’t a clone of any of those systems.
NeXT was already mentioned to be the originator of the top hierarchy naming. The well-known macOS (formerly OS X) is NeXT’s ancestor and traces of that heritage are still present in it. One of those is the hierarchy. Specifically, macOS has both its own user friendly as well as standard Unix directories that are hidden in Finder (macOS file manager). The standard macOS hierarchy (sans the Unix directories) is the following.
/Applications Installed applications /Library App-specific resources /Network Network-accessible resources /System System/Apple-provided resources /Users User home directories /Volumes Mount points
The Unix specific directories are utilized by the system’s BSD layer. Those are actual directories rather symlinks as in GoboLinux case. It can be thought as macOS splitting its filesystem to directories originating from its NeXT and BSD heritage.
Interestingly, the Compile concept of setting a build style (not sure if GoboLinux was an inspiration) is used in Void Linux which also hosts its templates on GitHub @void-linux/void-packages. For comparison the template for file in Void Linux is (own simpler version for demo; modified from original in upstream)
pkgname=file
version=5.39
build_style=gnu-configure
makedepends="zlib-devel"
short_desc="File type identification utility" | 2021-04-15 14:20:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3098931908607483, "perplexity": 10630.992998440026}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038085599.55/warc/CC-MAIN-20210415125840-20210415155840-00586.warc.gz"} |
http://mathhelpforum.com/geometry/42487-point-inside-outside-polygon.html | # Math Help - Is a point inside or outside a polygon?
1. ## Is a point inside or outside a polygon?
Hi All,
My first post, any help greatly appreciated.
In need to calculate if a point is inside or outside a polygon.
The application is to calculate which oceanic polygon a ship is in, or conversly, which ships are within a certain polygon.
The vertices of the polygon will be in degrees lat and long, but this should translate fine to a simple 2D polygon on a cartesian diagram. The ship's position will also be in degrees lat/long, again should corresponde fine to cartesian coordinates.
I realise that it's actually a polygon on a sphere i should be calculating, but for this i'm happy to assume the edges are straight.
I've added a diagram to show what I mean. In the first case, the point P is inside the polygon, in the second case it's outside.
How do I determine which?? Thanks everyone,
Luke
2. Originally Posted by LukeCoverdale
Hi All,
My first post, any help greatly appreciated.
In need to calculate if a point is inside or outside a polygon.
The application is to calculate which oceanic polygon a ship is in, or conversly, which ships are within a certain polygon.
The vertices of the polygon will be in degrees lat and long, but this should translate fine to a simple 2D polygon on a cartesian diagram. The ship's position will also be in degrees lat/long, again should corresponde fine to cartesian coordinates.
I realise that it's actually a polygon on a sphere i should be calculating, but for this i'm happy to assume the edges are straight.
I've added a diagram to show what I mean. In the first case, the point P is inside the polygon, in the second case it's outside.
How do I determine which?? Thanks everyone,
Luke
If you have access to Matlab there is a function inpolygon that will do this, and similar in Octave the inpoly function should do this.
RonL
3. ## Thanks
Do you know of any actual code that would do it, like a function in Java or something?
The reason I ask is that I would need to do this calculation within my program. I wouldn't be able to do open Matlab or Octave each time.
Thanks,
Luke
4. Originally Posted by LukeCoverdale
Do you know of any actual code that would do it, like a function in Java or something?
The reason I ask is that I would need to do this calculation within my program. I wouldn't be able to do open Matlab or Octave each time.
Thanks,
Luke
The Octave code is open source and should be easy to translate into any other language
Now I have not tried this out myself, and this looks different from my Euler code to do this but:
Code:
% [ inside ] = inpoly(polygon, point)
%
% Determines whether a given point is inside a polygon.
% The polygon is determined by point pairs on its
% boundary. There is no error checking, and to be safe
% only use convex polygons.
%
% input:
% polygon: column vector of (x,y) pairs representing the vertex
% points of the polygon.
% point: (x,y) pair representing point that is either
% in or out of the polygon
%
% output:
% inside: boolean true for inside, false otherwise.
%
% todo:
% Implement the ability to handle an array of points
% and return an array of boolean values.
%
% bugs and limitations:
%
% Need to check whether convexity is a necessary
% condition for this algorithm (don't think it is).
%
% Behavior with multiple loops, i.e., if sides cross
% over, is unknown.
%
% Algorithm implemented in integer, first quadrant
% numbers. Need to check generality of algorithm.
%
% Points on the boundaries of polygons may not be handled
% correctly or consistently.
%
% This code was derived from a public domain code
% copyright 1995-1996 Galacticomm, Inc., modifications
% allowed for any purpose provided redistribution is
% not restricted
%
% This script properly belongs in octave/compgeom/
% (computational geometry).
%
% This modified code is copyright David M. Doolin and placed in
% the public domain, with the exception that redistribution
% is not restricted in accordance with the copyright of unmodified
% (original) C code.
%
% $Author: doolin$ doolin at ce dot berkeley dot edu
% $Date: 1999/03/26 18:42:00$
% $Source: /shag/homes/doolin/cvsroot/octave/compgeom/inpoly.m,v$
% $Revision: 1.2$
function [ inside ] = inpoly(polygon, point)
% Check for the correct number of arguments
% Check for argument validation
% If argument validation required, validate arguments.
npoints = rows(polygon);
inside = 0;
xt = point(1);
yt = point(2);
xold = polygon(npoints,1);
yold = polygon(npoints,2);
for i = 1:1:npoints
xnew = polygon(i,1);
ynew = polygon(i,2);
if (xnew > xold)
x1=xold;
x2=xnew;
y1=yold;
y2=ynew;
else
x1=xnew;
x2=xold;
y1=ynew;
y2=yold;
endif
if ((xnew < xt) == (xt <= xold) %/* edge "open" at left end */
&& (yt-y1)*(x2-x1) < (y2-y1)*(xt-x1) )
inside=!inside;
endif
xold=xnew;
yold=ynew;
end % for loop
endfunction
RonL
5. ## not working this implementation (scilab)
Code:
function [ inside ] = inpoly(polygon,xt,yt)
rows = size(polygon);
npoints = rows(1);
disp (npoints);
inside = 0;
xold = polygon(npoints,1);
yold = polygon(npoints,2);
for i = 1:1:npoints
xnew = polygon(i,1);
ynew = polygon(i,2);
if (xnew > xold)
x1=xold;
x2=xnew;
y1=yold;
y2=ynew;
else
x1=xnew;
x2=xold;
y1=ynew;
y2=yold;
end
if ((xnew < xt) == (xt <= xold) & (yt-y1)*(x2-x1) < (y2-y1)*(xt-x1) )
inside=~inside;
end
xold=xnew;
yold=ynew;
end
endfunction | 2014-03-07 14:37:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4680135250091553, "perplexity": 2285.707817576096}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999644032/warc/CC-MAIN-20140305060724-00007-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://servo.aob.rs/scslsa11/program13.html | # 13th Serbian Conference on Spectral Line Shapes in AstrophysicsBelgrade, Serbia, August 23 - 27, 2021
Programme of 13th SCSLSA
Venue: Faculty of Mechanical Engeneering, Kraljice Marije 16, Belgrade, Serbia
Hall 513, 5th floor
Color coding: participants whose name is in blue color will attend the Conference online.
Talks timing:
• Invited talks last 30 minutes = 25 minutes presentation, 4 minutes Q/A and 1 minute to move on to the next talk
• Progress reports last 20 minutes = 16 minutes presentation, 3 minutes Q/A and 1 minute to move on to the next talk
• Poster presentations last 3 minutes, and 1 minute to move on to the next talk
# Monday, August 23, 2021
14:30 - 15:30 Registration 15:30 - 16:00 Opening ceremony (G. Peach and L. Č. Popović) - VIDEO
## SPECTRAL LINE SHAPES FROM LABARATORY TO SPACE PLASMA
Chair: M. S. Dimitrijević
16:00 - 16:30 Evgeny Stambulchik Spectral line merging in hydrogen-like species for diagnostic of laboratory and space plasmas - VIDEO 16:30 - 17:00 Joel Rosato Addressing the accuracy of the computer simulation method involved in Stark broadening calculations - VIDEO 17:00 - 17:30 Andrea Petric Obscured AGN at the Cosmic Noon - VIDEO 17:30 - 18:00 Gisella de Rosa The AGNSTORM 2 program: A detailed view of gas flows in Mrk817 - VIDEO 18:00 - 21:00 Welcome reception
# Tuesday, August 24, 2021
## SPECIAL SESSION DEDICATED TO VICTOR L. AFANASIEV: AGN Polarization
Chair: L. Č. Popović
9:00 - 9:30 Serguei Dodonov Multi Object Methods for finding and study QSO's and Galaxies - VIDEO 9:30 - 10:00 Martin Roth 25 years of integral field spectroscopy - from the BTA to the VLT - VIDEO 10:00 - 10:30 Alexei Moiseev Observations of large-scale ionizing cones in Seyfert galaxies - VIDEO 10:30 - 10:50 Roman Uklein Universal reducer for small telescopes - VIDEO 10:50 - 11:10 Eugene Malygin The photometric reverberation mapping of active galaxies in SAO RAS - VIDEO 11:10 - 11:30 Coffee break
## SPECIAL SESSION DEDICATED TO VICTOR L. AFANASIEV: AGN Polarization
Chair: S. Dodonov
11:30 - 12:00 Luka Č. Popović Polarization in broad emission lines of active galactic nuclei - VIDEO 12:00 - 12:30 Elena Shablovinskaya New capabilities of AGN polarimetry - VIDEO 12:30 - 13:00 Alexander Burenkov Monitoring of Seyfert 1 galaxies at the Special Astrophysical Observatory of the Russian Academy of Science - VIDEO 13:00 - 13:20 Đorđe Savić Broad emission line polarization of lensed quasars - VIDEO 13:20 - 13:40 Daria Kozlova Ionized-gas clouds in the 2MASX J013130.00-062550.8 galaxy 13:40 - 14:00 Alina Ikhsanova Gas and stars in the Teacup quasar - VIDEO 14:00 - 15:30 Lunch break
## SPECTRAL LINE PHENOMENA IN STARS
Chair: E. Stambulchik
15:30 - 16:00 Friedrich Kupka Improvements to the short-characteristics method in 3D-RHDr simulations and some unsolved problems in spectral line shapes of a-type stars - VIDEO 16:00 - 16:30 Antonios Antoniou A new method for calculating column densities using GR model. An application in the case of C IV, N IV and N V spectral lines in the uv spectrum of the o star HD 149757 (zeta-OPH) - VIDEO 16:30 - 16:50 Rihab Aloui Stark broadening of Strontium ion Sr V spectral lines in hot white dwarf atmospheres - VIDEO 16:50 - 17:10 Rafik Hamdi Stark broadening effect in hot DA white dwarfs: ultraviolet lines of Fe V - VIDEO 17:10 - 17:30 Coffee break
## POSTER SESSION: SPECTRAL LINES IN ASTROPHYSICAL AND LABORATORY PLASMAS
Chair: A. Kovačević
17:30 - 19:00 Poster session - VIDEO 3 min presentations
# Wednesday, August 25, 2021
## SURVEYS AND SPECTRAL LINE VARIABILITY IN EXTRAGALACTIC OBJECTS
Chair: D. Ilić
9:00 - 9:30 Victor Oknyansky Changing Looks of the Nucleus of Seyfert Galaxy NGC 1566 in comparison with other CL AGNs - VIDEO 9:30 - 9:50 Pu Du Density Waves of Ionized Gas in Broad-line Regions of Active Galactic Nuclei - VIDEO 9:50 - 10:10 Sergey Kotov Quasars physical properties study based on the medium-band photometric survey - VIDEO 10:10 - 10:30 Iva Čvorović - Hajdinjak Deep learning of AGN spectral variability - VIDEO 10:30 - 10:50 Anastasia Yarovova Modeling of the peculiar nebula in the low-metallicity galaxy NGC 4068 10:50 - 11:10 Yu Yang Songsheng Geometric Distances of Quasars Measured by Spectroastrometry and Reverberation Mapping: Monte Carlo Simulations - VIDEO 11:10 - 11:40 Coffee break
## SPECTRAL LINE PHENOMENA IN QUASARS
Chair: S. Simić
11:40 - 12:10 Paola Marziani The quasar main sequence: recent developments - VIDEO 12:10 - 12:40 Edi Bon Exploring the orientation of radio-loud AGN - VIDEO 12:40 - 13:00 Swayamtrupta Panda Flattening of the curve: Diagnostics of the H� and optical Fe+ emission - VIDEO 13:00 - 13:20 Tania Buendia Rios Statistical analysis of the AlIII?12500 line as a virial black hole mass estimator - VIDEO 13:20 - 13:40 Isidora Jankov Representation and characterization of broad-line AGN spectra based on manifold learning - VIDEO 13:40 - 15:30 Lunch break 15:30 - Conference excursion
# Thursday, August 26, 2021
## ATOMIC PARAMETERS AND SPECTRAL LINE SHAPES
Chair: R. Stamm
9:00 - 9:30 Vladimir Srećković Rydberg atoms in astrophysics: new results - VIDEO 9:30 - 10:00 Mohammed Koubiti A prospective study on using machine learning from spectroscopic data for plasma parameter predictions - VIDEO 10:00 - 10:20 Lamia Abu El Maaty Energy levels, oscillator strengths and transition probabilities for the Ti II ion - VIDEO 10:20 - 10:40 Said Douis Statistical and dynamical properties in plasmas governed by H.G.K pseudo-potential 10:40 - 11:00 Ibtissem Hannachi Calculating the simultaneous effect of ion dynamics and oscillating electric fields on Stark profiles - VIDEO 11:00 - 11:30 Coffee break
## SPECTRAL LINE PHENOMENA IN EXTRAGALCTIC OBJECTS
Chair: A. Moiseev
11:30 - 12:00 Alice Machado Radio-loud population a quasars at high redshift - VIDEO 12:00 - 12:30 Elena Dalla Bonta Black Hole masses from emission line widths - VIDEO 12:30 - 12:50 Miroslava Vukčević Spiral structure of the galactic disk and its influence on the rotational velocity curve - VIDEO 12:50 - 13:10 Jelena Kovačević Dojčinović The line profiles in AGNs type 1.8-2: unraveling the complex kinematical properties - VIDEO 13:10 - 13:30 Aleksandra Grokhovskaya Exploring the environment of active galaxies - VIDEO 13:30 - 15:00 Lunch break
## ATOMIC PARAMETERS AND SPECTRAL LINE SHAPES
Chair: V. Srećković
15:00 - 15:30 Nikolay Bezuglov Expressions of "fast" and "slow" chameleon dressed states in autler-townes spectra of alkali-metal atoms - VIDEO 15:30 - 16:00 Nabil Ben Nessib Ab initio and semi-empirical atomic structure calculations. Applications to the 5s-6p transitions for the Mo II ion - VIDEO 16:00 - 16:20 Joel Rosato Modeling of collisional redistribution of line radiation by computer simulations - VIDEO 16:20 - 16:40 Magdalena Christova Stark broadening of B I spectral lines 16:40 - 17:00 Zlatko Majlinger Systematic trends among the Stark widths of Co II spectral lines - VIDEO 17:00 - 17:30 Coffee break
## SPECTRAL LINE PHENOMENA IN EXTRAGALCTIC OBJECTS
Chair: V. Okyansky
17:30 - 18:00 Xinyu Dai New Quasar Microlensing Constraints on the Spin of High Redshift Quasars - VIDEO 18:00 - 18:20 Saloni Bhatiani Hunting for planet-mass objects in extragalactic systems - VIDEO 18:20 - 18:40 Jake Mitchell The Paschen broad line region and torus in Mrk509 - VIDEO 18:40 - 19:00 Hora Mishra Dramatic variability in a changing-look blazar, B2 1420+32 - VIDEO 19:00 - 19:30 Martin Gaskell The location and nature of the Fe II emitting region in active galactic nuclei - VIDEO 20:00 - CONFERENCE DINNER
# Friday, August 27, 2021
## SPECTRAL LINE RESEARCH: NEW FRONTIERS
Chair: E. Lyratzi
09:30 - 10:00 Jian-Min Wang Accretion-modified Stars in Accretion Disks of Active Galactic Nuclei - VIDEO 10:00 - 10:30 Đorđe Spasojević Study of UV Ne II line shapes in the cathode sheath of an abnormal glow discharge - VIDEO 10:30 - 11:00 Anđelka Kovačević Spectral variability of active galactic nuclei in the context of large time-domain surveys - VIDEO 11:00 - 11:30 Coffee break
## SPECTRAL LINE VARIABILITY
Chair: P. Marziani
11:30 - 11:50 Ting Feng Yi Detection of quasi-periodic oscillations in $\gamma$-ray and optical light curves of the BL Lac 4FGL J0650.7+2503 - VIDEO 11:50 - 12:10 Marzena Sniegowska Modelling changing-look (CL) AGN phenomenon using accretion disk instabilities - VIDEO 12:10 - 12:30 Dimitrios Stathopoulos On the variability of Lya, N V, Si IV and C IV BAL components of the BALQSO J131912.39+534720 - VIDEO 12:30 - 12:50 Martin Ochmann Mrk 926 reveals discrete line satellites during a drastic phase of decline 12:50 - 13:10 Daniel Kynoch Variability of the near-infrared coronal emission lines in the active galaxy NGC 5548 - VIDEO
13:10 - 13:30 Official closing of the conference 13:30 - 15:00 Lunch break | 2022-05-23 20:03:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3186066448688507, "perplexity": 9986.273235344053}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662561747.42/warc/CC-MAIN-20220523194013-20220523224013-00253.warc.gz"} |
http://pinupband.pl/keras-vae.html | # Keras Vae
train (xtrain, xtest) # Trains VAE model based on custom loss function. Active 2 years, 4 months ago. config import MULTIPROCESS_FLAG from astroNN. These examples are extracted from open source projects. previous somehow related questions : vae loss vae loss again. 1: Keras is a high-level library that sits on top of other deep learning frameworks. In lieu of MNIST, I thought it’d be more interesting to test VAE on the somewhat more challenging SVHN dataset. This make sense, since for the semi-supervised case the latent $$\bf z$$ is free to use its representational capacity to model, e. variational_autoencoder • keras keras. recurrent import LSTM from python. For more math on VAE, be sure to hit the original paper by Kingma et al. This guide covers training, evaluation, and prediction (inference) models when using built-in APIs for training & validation (such as model. Input (1) Execution Info Log Comments (3) This Notebook has been released under the Apache 2. get_layer("fc2"). com までご一報いただけると嬉しいです。. io) VAE example from "Writing custom layers and models" guide (tensorflow. compile(optimizer='rmsprop', loss=None) 在keras中自定义metric非常简单，需要用y_pred和y_true作为自定义metric函数的输入参数 点击查看metric的设置. Sequential 来简化代码。. io) VAE example from "Writing custom layers and models" guide (tensorflow. Apply a Keras Stateful LSTM Model to a famous time series. com/0hnishi https://dena. For more math on VAE, be sure to hit the original paper by Kingma et al. You can find additional implementations in the following sources: Variational AutoEncoder (keras. We want the NN to optimize the distribution of X so that they are more tightly packed around the origin. Schematically, it looks like this:. 变分自编码(VAE)的东西，将一些理解记录在这，不对的地方还请指出。 在论文《Auto-Encoding Variational Bayes》中介绍了VAE。 训练好的VAE可以用来生成图像。 在Keras 中提供了一个VAE的Demo:variational_autoencoder. Creating a VAE with Keras What we’ll create today. Files for keras-vggface, version 0. https://twitter. Introduction. 1: Keras is a high-level library that sits on top of other deep learning frameworks. layers import Input,Conv2D,MaxPooling2D,UpSampling2D from keras. outputs[0])) Our model is just a Keras Model where the outputs are defined as the composition of the encoder and the decoder. , Colomer A. AutoEncoders in Keras: VAE-GAN. We will discuss hyperparameters, training, and loss-functions. ai/work7/ Variational Auto Encoder入門 + 教師なし学習∩deep learning∩生成モデルで特徴量作成 VAEなん. h5") We also have to make sure the data is loaded. 생성 모델 중 VAE 정리 진행 중 (영상 대신 1d 시그널 생성 모델) # coding: utf-8 # In[1]: import os import keras import numpy as np import matplotlib. keras; tensorflow / theano (current implementation is according to tensorflow. This example demonstrates the process of building and training a VAE using Keras to generate new faces. Upsampling is done through the keras UpSampling layer. Welcome back! In this post, I’m going to implement a text Variational Auto Encoder (VAE), inspired to the paper “Generating sentences from a continuous space”, in Keras. build # Construct VAE model using Keras model. TensorFlow Probability includes a wide selection of probability distributions and bijectors, probabilistic layers, variational inference, Markov chain Monte Carlo, and optimizers such as Nelder-Mead, BFGS, and SGLD. Importantly, Keras provides several model-building APIs (Sequential, Functional, and Subclassing), so you can choose the right level of abstraction for your project. ？ 実はこの実装間違ってます。何がおかしいのかと思ったらloss関数が違います。. 今回はニューラルネットワークのフレームワークの Keras を使って AutoEncoder を書いてみる。 AutoEncoder は入力になるべく近い出力をするように学習したネットワークをいう。 AutoEncoder は特徴量の次元圧縮や異常検知など、幅広い用途に用いられている。 使った環境は次の通り。 $sw_vers ProductName. Model(inputs=encoder. The models for the encoder, decoder, and the VAE are saved to be loaded later for testing purposes. Let's build a (conditional) VAE that can learn on celebrity faces. npz · 12,251 views · 2y ago. 2) # Choose model parameters model. How to implement custom loss function on keras for VAE. com 実装ですが、まずは以下をvae. 5, assuming the input is 784 floats # this is our input placeholder input_img = Input(shape=(784,)) # "encoded" is the encoded representation of the input encoded. We assume this was done on purpose, and we will not be expecting any data to be passed to "dense_5" during training. I've modified the keras VAE example code for my data, and I'd like to import it into CoreML. optimizers import Adam need to change to if you use Tensorflow 2. config import _astroNN_MODEL_NAME from astroNN. We will be using this as our implementation. In this post we looked at the intuition behind Variational Autoencoder (VAE), its formulation, and its implementation in Keras. com までご一報いただけると嬉しいです。. py: notice that this model defines no semi-supervised loss yet, which is a little bit different from the paper). Keras is a neural network library on top of TensorFlow. VAE的Keras实现. GANについて理解するため、GANを簡単な2次元問題に適用し、その挙動を観察してみました。実装にはpythonとkerasを使いました。 mnistの文字生成などがGANの導入としてよく紹介されていますが、文字等の画像データはデータ分布形状という観点での観察が難しいので、ここでは2次元を選びました. I am using Tensorflow 2. We also saw the difference between VAE and GAN, the two most popular generative models nowadays. binary_crossentropy(). The environment provides our agent with a high dimensional input observation at each time step. It consists of three individual parts: the encoder, the decoder and the VAE as a whole. #Autoencoders #VAE #Keras #deeplearning. Additionally, in almost all contexts where the term "autoencoder" is used, the compression and decompression functions are implemented with neural networks. MAP()等にdataとともに渡す方法はでできなくなっています。. To be more specific, in the pytorch implementation, the input is [batch, filter/channel, timestep/length]. The goals of this notebook is to learn how to code a variational autoencoder in Keras. For more math on VAE, be sure to hit the original paper by Kingma et al. library(keras) VAE Encoder Network Map each image, 28-by-28, to a two-dimensional Gaussian distribution ( latent_dim = 2L ) with two-dim mean ( z_mean ) and two-dim variance ( exp(z_log_var ). input, outputs=model. Importantly, Keras provides several model-building APIs (Sequential, Functional, and Subclassing), so you can choose the right level of abstraction for your project. To this end, we scale and enhance the autoregressive priors used in VQ-VAE to generate synthetic samples of much higher coherence and fidelity than possible before. 記事の前提 Kerasとは Kerasの環境構築1 Kerasの環境構築2 Kerasを用いた手書き文字認識 テストコード1 コード例1 結果 考察？ ドロップアウトの影響 Kerasを用いた手書き文字認識 テストコード2 Kerasでのモデルの記述の仕方 テストコード 実行の様子 今後やってみたいこと 記事の前提 前回は隠れ層を. So we are going to optimize so that the P distribution look the most like the N(0,1) distribution (a gaussian distribution located around the origin). We use a custom Keras memory-efficient generator to deal with our large dataset (202599 images, ca. 6; Filename, size File type Python version Upload date Hashes; Filename, size keras_vggface-0. During reconstruction stage, a stochastic operation (random sample from Gaussian) is performed to first generate the latent vector. Project details. We will discuss hyperparameters, training, and loss-functions. a simple vae and cvae from keras. Keras has three ways for building a model: Sequential API; Functional API; Model Subclassing; The three ways differ in the level of customization allowed. As detailed before, the first term of the cost function is the reconstruction loss. Use AdversarialOptimizer for complete control of whether updates are simultaneous, alternating, or something else. Импортируем необходимые библиотеки и датасет:. Kerasを使ってVAEを実装してみました。モデルができたので、あとは好きなデータを渡していろいろ遊んでみることができるかと思います。モデルの大まかな構造がわかれば、その後数式を追うのもわかりやすくなるかと思います。. To be more specific, in the pytorch implementation, the input is [batch, filter/channel, timestep/length]. 1 The Network. We do so using the Keras Functional API, which allows us to combine layers very easily. Source code for astroNN. 6-py3-none-any. outputs[0]) # Define the Kullback. We assume this was done on purpose, and we will not be expecting any data to be passed to "dense_5" during training. Amazon wants to classify fake reviews, banks want to predict fraudulent credit card charges, and, as of this November, Facebook researchers are probably wondering if they can predict which news articles are fake. tfprob_vae • keras keras. In this book, we'll test on a CPU and NVIDIA GPUs (specifically, the GTX 1060, GTX 1080Ti, RTX 2080Ti, V100, and Quadro RTX 8000 models): Figure 1. 2 StyleGANの学習済みモデルでサクッと遊んでみる AI（人工知能） 2018. How does one calculate the reconstruction probability? Let's look at the keras example code from here. The results are, as expected, a tad better:. 0; VAEと異常検知. edu Abstract Supervised deep learning has been successfully applied to many recognition prob-lems. Statistics. models import Model # this is the size of our encoded representations encoding_dim = 32 # 32 floats -> compression of factor 24. # Note that we can name any layer by passing it a "name" argument. 3 kB) File type Wheel Python version py3 Upload date Jul 22, 2019 Hashes View. I managed to convert a simple AE the other day using keras. (tensorflow backend) 설치 pip install keras import import tensorflow as tf import keras 버젼 확인 tf. I am using Tensorflow 2. To be more specific, in the pytorch implementation, the input is [batch, filter/channel, timestep/length]. CorrVAE: A VAE for sampling realistic financial correlation matrices (Tentative I) First tentative at CorrVAE. models import Model from keras. - style transfer, VAE, GAN 등 프로토타이핑에 써보고 싶은 핫한 모델의 개념을 직접 코드를 돌려 가며 이해하고 싶어요. Keras is supported on CPU, GPU, and TPU. tfprob_vae • keras keras. build # Construct VAE model using Keras model. eriklindernoren/Keras-GAN Keras implementations of Generative Adversarial Networks. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. Here's the architecture of my VAE:. 目次 目次 イントロダクション 計算機環境 データのロード データ処理 Kerasで学習 モデルの評価 モデルの保存 モデルの読み込み ソースコード全体 まとめ 参考文献 イントロダクション 以前まで、Tensorflowを使っていましたが、 モデルを構築することが簡単 だったので、Kerasに乗り換えてみまし. VAE: variational autoencoders. models import Model from keras. Импортируем необходимые библиотеки и датасет:. Содержание Часть 1: Введение Часть 2: Manifold learning и скрытые (latent) переменные Часть 3: Вариационные автоэнкодеры (VAE) Часть 4: Conditional VAE Часть 5: GAN (Generative. With everything set up, we can now test our VAE on a dataset. library(keras) VAE Encoder Network Map each image, 28-by-28, to a two-dimensional Gaussian distribution ( latent_dim = 2L ) with two-dim mean ( z_mean ) and two-dim variance ( exp(z_log_var ). (vae_loss가 동작안해서 인터넷에서 찾아서 함수를 사용했다. As detailed before, the first term of the cost function is the reconstruction loss. For more math on VAE, be sure to hit the original paper by Kingma et al. Creating a VAE with Keras What we'll create today. get_layer("fc2"). Notice: Undefined index: HTTP_REFERER in /home/vhosts/pknten/pkntenboer. digit_size = 28. Building an Autoencoder in Keras. Variational AutoEncoder. Here's the architecture of my VAE:. See full list on jaan. We do so using the Keras Functional API, which allows us to combine layers very easily. __version__ 추가로 함께 import 하면 좋은 것들 import numpy as np import matplo. Welcome back! In this post, I’m going to implement a text Variational Auto Encoder (VAE), inspired to the paper “Generating sentences from a continuous space”, in Keras. Read 12 answers by scientists with 12 recommendations from their colleagues to the question asked by Satyanarayana Vusirikala on Jul 11, 2014. after seeing) a given image. First, I’ll briefly introduce generative models, the VAE, its characteristics and its advantages; then I’ll show the code to implement the text VAE in keras and finally I will explore the results of this model. 10KB each). Kerasの変分オートエンコーダ(VAE)サンプルコードの損失関数につい. MNIST dataset consists of 10 digits from 0-9. Keras is awesome. datasets import mnist from keras. load_model("VAE_encoder. (tensorflow backend) 설치 pip install keras import import tensorflow as tf import keras 버젼 확인 tf. The bottleneck vector is of size 13 x 13 x 32 = 5. Free Malaysia Today is an independent, bi-lingual news portal with a focus on Malaysian current affairs. Input 1 (indices start at 0) has shape[0. Statistics. Keras is awesome. models import Model from keras. In this tutorial, we will answer some common questions about autoencoders, and we will cover code examples of the following models: a simple autoencoder based on a fully-connected layer a sparse autoencoder a deep fully-connected autoencoder a deep. Explore the most advanced deep learning techniques that drive modern AI results; New coverage of unsupervised deep learning using mutual information, object detection, and semantic segmentation. On Kaldwyn, he is considered a divine being that is an antithetical to Selys, and believed to be comparable to her in power. 变分自编码(VAE)的东西，将一些理解记录在这，不对的地方还请指出。 在论文《Auto-Encoding Variational Bayes》中介绍了VAE。 训练好的VAE可以用来生成图像。 在Keras 中提供了一个VAE的Demo:variational_autoencoder. See full list on danijar. さらに、 vae の発展系である cvae の説明も行います。 説明の後にコードの紹介も行います。 また、 ae, vae, cvae の違いを可視化するため、 vae がなぜ連続性を表現できるのか割り出すために、行った実験と、その結果について説明します。. ？ 実はこの実装間違ってます。何がおかしいのかと思ったらloss関数が違います。. As the name suggests, that tutorial provides examples of how to implement various kinds of autoencoders in Keras, including the variational autoencoder (VAE). We do so using the Keras Functional API, which allows us to combine layers very easily. This is perhaps the best property a traditional autoencoder lacks. Содержание Часть 1: Введение Часть 2: Manifold learning и скрытые (latent) переменные Часть 3: Вариационные автоэнкодеры (VAE) Часть 4: Conditional VAE Часть 5: GAN (Generative. train (xtrain, xtest) # Trains VAE model based on custom loss function. layers import Lambda, Input, Dense from keras. a simple vae and cvae from keras. You can find additional implementations in the following sources: Variational AutoEncoder (keras. https://twitter. The images are matrices of size 28 x 28. 0 Models with names I want to get model. Model(inputs=encoder. This notebook contains a Keras / Tensorflow implementation of the VQ-VAE model, which was introduced in Neural Discrete Representation Learning (van den Oord et al, NeurIPS 2017). pyplot as plt import os from keras. Work in progress. Tip: you can also follow us on Twitter. kerasで中間層の出力を取得 kerasでCNNの中間層を取得する方法は2種類存在する． ケース1 from keras. keras as tfk from astroNN. kerasをEdwardと組合せて使う例はMixture Density Networks with Edward, Keras and TensorFlow — Adventures in Machine Learning などにあるのですが、最新のEdwardではed. Training the model is as easy as training any Keras model: we just call vae_model. js - Run Keras models in the browser. inputs, outputs=decoder(encoder. VAE в Keras Теперь, когда мы разобрались в том, что такое вариационные автоэнкодеры, напишем такой на Keras. Total stars 7,172 Stars per day 7 Created at 2 years ago Language Python Related Repositories keras_snli Simple Keras model that tackles the Stanford Natural Language Inference (SNLI) corpus using summation and/or recurrent neural networks the-gan-zoo. 5, assuming the input is 784 floats # this is our input placeholder input_img = Input(shape=(784,)) # "encoded" is the encoded representation. 4 Variatinoal Autoencoder(VAE) 8. It is a very well-designed library that clearly abides by its guiding principles of modularity and extensibility, enabling us to easily assemble powerful, complex models from primitive building blocks. It uses DCGan ( Deep Convolutional Generative Adversarial Network ) which has been a breakthrough in GAN research as it introduces major architectural changes to tackle problems like training instability, mode. convert, but I. , Morales S. The idea behind this is to get batches of images on the fly during the training process. Keras を使った簡単な Deep Learning はできたものの、そういえば学習結果は保存してなんぼなのでは、、、と思ったのでやってみた。 準備 公式の FAQ に以下のような記載があるので、h5py を入れておく。. This input is usually a 2D image frame that is part of a video sequence. 4 VAE 부분을 발표하기로 했다. import numpy as np import matplotlib. We reshape the image to be of size 28 x 28 x 1, convert the resized image matrix to an array, rescale it between 0 and 1, and feed this as an input to the network. 本小节小编用Keras给大家简单展示一下VAE的实现过程。 导入相关模块： import numpy as np. In this post we looked at the intuition behind Variational Autoencoder (VAE), its formulation, and its implementation in Keras. model = VAE (epochs = 5, latent_dim = 2, epsilon = 0. Active 1 year, 11 months ago. import keras from matplotlib import pyplot as plt import numpy as np import gzip %matplotlib inline from keras. com 実装ですが、まずは以下をvae. This has been demonstrated in numerous blog posts and tutorials, in particular, the excellent tutorial on Building Autoencoders in Keras. Welcome back! In this post, I’m going to implement a text Variational Auto Encoder (VAE), inspired to the paper “Generating sentences from a continuous space”, in Keras. It consists of three individual parts: the encoder, the decoder and the VAE as a whole. Speaker Info: Lovish graduated in with a dual degree in computer science and engineering from IIT Kanpur in 2015. Files for keras-vggface, version 0. GANについて理解するため、GANを簡単な2次元問題に適用し、その挙動を観察してみました。実装にはpythonとkerasを使いました。 mnistの文字生成などがGANの導入としてよく紹介されていますが、文字等の画像データはデータ分布形状という観点での観察が難しいので、ここでは2次元を選びました. You can use NumPy arrays for most heavy lifting in Edward (we do so in many examples). keras gan mnist layers import Dense Flatten Dropout from keras. We want the NN to optimize the distribution of X so that they are more tightly packed around the origin. Today, we'll use the Keras deep learning framework for creating a VAE. Updated and revised second edition of the bestselling guide to advanced deep learning with TensorFlow 2 and Keras. xlarge インスタンス; Ubuntu 16. SVG-VAE is a new generative model for scalable vector graphics (SVGs). I am using Tensorflow 2. UTKFace dataset is a large-scale face dataset with long age span (range from 0 to 116 years old). Keras is awesome. layers import Input, Dense from keras. train (xtrain, xtest) # Trains VAE model based on custom loss function. 이런 분들을 위해 준비한 Keras로 배우는 심층학습 코스입니다. 変分オートエンコーダ（Variational Autoencoder）を使ったイメージ生成を試してみる。 （「RとKerasによるディープラーニング」） ソースコード Generating images モデル 6epochのトレーニングが終わった状態のdecoderからイメージを生成してみる。latent space（潜在的意味空間）の次元は「2」で、 latent space上. fit(mnist_digits, epochs= 30, batch_size= 128) Display a grid of sampled digits [ ] import matplotlib. import keras from matplotlib import pyplot as plt import numpy as np import gzip %matplotlib inline from keras. 而编码计算方差的网络的作用在于动态调节噪声的强度。到这里，变分自编码器的基本原理基本上就讲完了。最后一点内容，我们来看一下 keras 给出的 VAE 实现。 4. 408 in this case. Running VAE on MNIST Data. npz · 12,251 views · 2y ago. outputs[0]) # Define the Kullback. AutoEncoders in Keras: VAE-GAN. sequence import pad_sequences from model import VAE import numpy as np import os Create Inputs We start off by defining the maximum number of words to be used, as well as the maximum length of any review. SVG-VAE is a new generative model for scalable vector graphics (SVGs). The VAE model can learn features that were generally non-redundant and could disentangle large sources of variation in the data. お急ぎの方は、結果の画像だけ見ていただければ分かると思います。 基本となる技術は、VAE（Variational Autoencoder）です。. VAE (V) Model. x instead of tensorflow1. However, they can also be thought of as a data structure that holds information. tfprob_vae • keras keras. js - Run Keras models in the browser. Outputs will not be saved. It is related to the. get_layer("fc2"). h5") We also have to make sure the data is loaded. このページは、(4)モデル学習(Keras)の続きであり、今回は、結果の出力を行っていきます。. __version__ keras. We will be using the Keras library for running our example. TensorFlow Probability includes a wide selection of probability distributions and bijectors, probabilistic layers, variational inference, Markov chain Monte Carlo, and optimizers such as Nelder-Mead, BFGS, and SGLD. Updated and revised second edition of the bestselling guide to advanced deep learning with TensorFlow 2 and Keras. php on line 76 Notice: Undefined index: HTTP_REFERER in /home. models import Model from keras. __version__ 추가로 함께 import 하면 좋은 것들 import numpy as np import matplo. This has been demonstrated in numerous blog posts and tutorials, in particular, the excellent tutorial on Building Autoencoders in Keras. Work in progress. input_img= Input(shape=(784,)) To build the autoencoder we will have to first encode. Equation 1. I'm a newbie to keras and tf, so I have probably made some mistakes. VAE with CNN. 22 Keras で変分オートエンコーダ（VAE）をMNISTでやってみる AI（人工知能） 2018. Sequence is a utility that you can subclass to obtain a Python generator with two important properties: It works well with multiprocessing. , 2014) は近似推論を用いた勾配に基づく方法で訓練できる生成モデルです。. py), then M2 model (VAE_YZ_X. There is a growing interest in exploring the use of variational auto-encoders (VAE), a deep latent variable model, for text generation. Variational AutoEncoder. Interface to TensorFlow Probability, a Python library built on TensorFlow that makes it easy to combine probabilistic models and deep learning on modern hardware (TPU, GPU). The bottleneck vector is of size 13 x 13 x 32 = 5. load_model("VAE_decoder. GANs made easy! AdversarialModel simulates multi-player games. The models for the encoder, decoder, and the VAE are saved to be loaded later for testing purposes. With disentangled VAE, the latent vector can even minimizes their correlations, and become more orthogonal to one another. npz · 2,742 views · 1y ago. compile (optimizer=keras. During model creating it throws exception. But not sure how to do this for the decoder output. Keras is awesome. Category Education; Show more Show less. You can disable this in Notebook settings. CorrVAE: A VAE for sampling realistic financial correlation matrices (Tentative I) First tentative at CorrVAE. shape) ケース2 from keras import backend as K get_layer_output = K. 0 but nothing changes. Computing the KL divergence cost term requires assuming$\mathbb{Q}(z \vert \mathbf{X})$to be also Gaussian with parameters$\mu (\mathbf{X})$and$\Sigma. He returned to academia in 2017 to pursue his passion for research and teaching. Keras LSTMでトレンド予測をしてみる AI（人工知能） 2018. 0 open source license. VAE (Kingma, 2013; Rezende et al. TensorFlow Probability includes a wide selection of probability distributions and bijectors, probabilistic layers, variational inference, Markov chain Monte Carlo, and optimizers such as Nelder-Mead, BFGS, and SGLD. Code: Keras. On hardware, Keras runs on a CPU, GPU, and Google's TPU. keras; tensorflow / theano (current implementation is according to tensorflow. # Note that we can name any layer by passing it a "name" argument. The encoder maps an image to a proposed distribution over plausible codes for that image. MAP()等にdataとともに渡す方法はでできなくなっています。. This make sense, since for the semi-supervised case the latent $$\bf z$$ is free to use its representational capacity to model, e. This distribution is also called the posterior, since it reflects our belief of what the code should be for (i. 下面是vae的直观解释，不需要太多的数学知识。 为了理解vae，我们首先从最简单的网络说起，然后再一步一步添加额外的部分。 一个描述神经网络的常见方法是近似一些我们想建模的函数。然而神经网络也可以被看做是携带信息的数据结构。. Creating a VAE with Keras What we’ll create today. 22 Keras で変分オートエンコーダ（VAE）をMNISTでやってみる AI（人工知能） 2018. Implementation of Variational Autoencoders using Keras and Tensorflow. GANについて理解するため、GANを簡単な2次元問題に適用し、その挙動を観察してみました。実装にはpythonとkerasを使いました。 mnistの文字生成などがGANの導入としてよく紹介されていますが、文字等の画像データはデータ分布形状という観点での観察が難しいので、ここでは2次元を選びました. com までご一報いただけると嬉しいです。. Running VAE on MNIST Data. It consists of three individual parts: the encoder, the decoder and the VAE as a whole. eriklindernoren/Keras-GAN Keras implementations of Generative Adversarial Networks. convert, but I. py '''This script demonstrates how to build a variational autoencoder with Keras. Source code for astroNN. Project details. layers import Dense from keras. The dataset consists of over 20,000 face images with annotations of age, gender, and ethnicity. This example demonstrates the process of building and training a VAE using Keras to generate new faces. VAEs can be implemented in several different styles and of varying complexity. 1 The Network. We reshape the image to be of size 28 x 28 x 1, convert the resized image matrix to an array, rescale it between 0 and 1, and feed this as an input to the network. build # Construct VAE model using Keras model. 下面是vae的直观解释，不需要太多的数学知识。 为了理解vae，我们首先从最简单的网络说起，然后再一步一步添加额外的部分。 一个描述神经网络的常见方法是近似一些我们想建模的函数。然而神经网络也可以被看做是携带信息的数据结构。. VAE【keras实现】 类型： 编程技术 作者： microwave 时间： 2018-08-21 阅读数： 2102 删除 审核 反审核 站点推荐 变分自编码(vae)的东西，将一些理解记录在这，不对的地方还请指出。. io) VAE example from "Writing custom layers and models" guide (tensorflow. In addition, we will familiarize ourselves with the Keras sequential GUI as well as how to visualize results and make predictions using a VAE with a small number of latent dimensions. Viewed 2k times 1 $\begingroup$ The code here: https://github. compile(optimizer='rmsprop', loss=None) 在keras中自定义metric非常简单，需要用y_pred和y_true作为自定义metric函数的输入参数 点击查看metric的设置. This has been demonstrated in numerous blog posts and tutorials, in particular, the excellent tutorial on Building Autoencoders in Keras. Speaker Info: Lovish graduated in with a dual degree in computer science and engineering from IIT Kanpur in 2015. 0; VAEと異常検知. It is related to the. This tutorial demonstrates how to generate images of handwritten digits using a Deep Convolutional Generative Adversarial Network (DCGAN). # this is the size of our encoded representations encoding_dim = 32 # 32 floats -> compression of factor 24. 4 Variatinoal Autoencoder(VAE) 8. For more math on VAE, be sure to hit the original paper by Kingma et al. So about a factor 20 larger than the fully connected case. py), then M2 model (VAE_YZ_X. In order to understand the concepts discussed, it's important to have an understanding of gradient descent. I want to create VAE(variational autoencoder). 22 Keras で変分オートエンコーダ（VAE）をMNISTでやってみる AI（人工知能） 2018. 5, assuming the input is 784 floats # this is our input placeholder input_img = Input(shape=(784,)) # "encoded" is the encoded representation of the input encoded. xlarge インスタンス; Ubuntu 16. Hi all，十分感谢大家对keras-cn的支持，本文档从我读书的时候开始维护，到现在已经快两年了。这个过程中我通过翻译文档，为同学们debug和答疑学到了很多东西，也很开心能帮到一些同学。. Notice: Undefined index: HTTP_REFERER in /home/vhosts/pknten/pkntenboer. 13 Keras CNN を改造してImageDataGenerator（画像…. In this tutorial, you will learn how to: Develop a Stateful LSTM Model with the keras package, which connects to the R TensorFlow backend. variational_autoencoder • keras keras. ) from keras. For more math on VAE, be sure to hit the original paper by Kingma et al. See full list on danijar. There is a growing interest in exploring the use of variational auto-encoders (VAE), a deep latent variable model, for text generation. recurrent import LSTM from python. previous somehow related questions : vae loss vae loss again. 6-py3-none-any. 【Python】Keras で VAE 入門 2018/09/15 から t2sy | 0件のコメント NN による生成モデルの主な手法として VAE (variational autoencoder) と GAN (generative adversarial network) の2つが知られています。. fit(): With this model, we are able to get an ELBO of around 115 nats (the nat is the natural logarithm equivalent. This notebook contains a Keras / Tensorflow implementation of the VQ-VAE model, which was introduced in Neural Discrete Representation Learning (van den Oord et al, NeurIPS 2017). VAE (V) Model. Author: fchollet Date created: 2020/05/03 Last modified: 2020/05/03 Description: Convolutional Variational AutoEncoder (VAE) trained on MNIST digits. compile(optimizer='rmsprop', loss=None) 在keras中自定义metric非常简单，需要用y_pred和y_true作为自定义metric函数的输入参数 点击查看metric的设置. keras Python notebook using data from mnist. when passing shuffle=True in fit()). We will be using this as our implementation. The parameters of a VAE are trained via two loss functions: reconstruction loss that forces the decoded samples to match the initial inputs, regularization loss that helps learn well-formed latent spaces and reduce overfitting to the training data. 10KB each). 2) # Choose model parameters model. Implementation of Variational Autoencoders using Keras and Tensorflow. 2019) is a two-level hierarchical VQ-VAE combined with self-attention autoregressive model. We can use any popular loss, say mean-squared error, for this purpose. build # Construct VAE model using Keras model. layers import Input, Lambda, Dense from keras. 19287109375, time elapse for current epoch 48. Documentation for the TensorFlow for R interface. This input is usually a 2D image frame that is part of a video sequence. Active 1 year, 11 months ago. View statistics for this project via Libraries. MNIST dataset consists of 10 digits from 0-9. This is perhaps the best property a traditional autoencoder lacks. layers import Input, Dense from keras. library(keras) VAE Encoder Network Map each image, 28-by-28, to a two-dimensional Gaussian distribution ( latent_dim = 2L ) with two-dim mean ( z_mean ) and two-dim variance ( exp(z_log_var ). VAE são uma variante mais poderosa de AE: em vez de compactar o input em um “código” fixo no espaço latente, ela transforma o input nos parâmetros de uma distribuição estatística: uma média e uma variância. This is the companion code to the post “Discrete Representation Learning with VQ-VAE and TensorFlow Probability” on the TensorFlow for R blog. Keras を使った簡単な Deep Learning はできたものの、そういえば学習結果は保存してなんぼなのでは、、、と思ったのでやってみた。 準備 公式の FAQ に以下のような記載があるので、h5py を入れておく。. 4 VAE 부분을 발표하기로 했다. tfprob_vae • keras keras. Author: fchollet Date created: 2020/05/03 Last modified: 2020/05/03 Description: Convolutional Variational AutoEncoder (VAE) trained on MNIST digits. , texture) from global information (i. You could also try implementing a VAE using a different dataset, such as CIFAR-10. For those seeking an introduction to Keras in R, please check out Customer Analytics: Using Deep Learning With Keras To Predict Customer Churn. Setup import tensorflow as tf from tensorflow import keras from tensorflow. Keras is awesome. Since the encoder already added the KL term to the loss, we need to specify only the reconstruction loss (the first term of the ELBO above). a simple vae and cvae from keras. 13 Keras CNN を改造してImageDataGenerator（画像…. さらに、 vae の発展系である cvae の説明も行います。 説明の後にコードの紹介も行います。 また、 ae, vae, cvae の違いを可視化するため、 vae がなぜ連続性を表現できるのか割り出すために、行った実験と、その結果について説明します。. return x y = CustomVariationalLayer()([x, x_decoded_mean_squash]) vae = Model(x, y) vae. Author: fchollet Date created: 2020/05/03 Last modified: 2020/05/03 Description: Convolutional Variational AutoEncoder (VAE) trained on MNIST digits. For any comments or questions, feel free to reach out in the comments. 0 open source license. 22 Keras で変分オートエンコーダ（VAE）をMNISTでやってみる AI（人工知能） 2018. 本記事は、R Advent Calendar 2017の14日目の記事です。これまで、R言語でロジスティック回帰やランダムフォレストなどを実践してきました。Rは統計用のライブラリが豊富、Pythonは機械学習用のライブラリが豊富。というイメージがありますが、Rでも機械学習は可能です。今回は、Kerasという深層. First, I’ll briefly introduce generative models, the VAE, its characteristics and its advantages; then I’ll show the code to implement the text VAE in keras and finally I will explore the results of this model. A single call to model. convert, but I. See full list on qiita. This notebook is open with private outputs. kerasをEdwardと組合せて使う例はMixture Density Networks with Edward, Keras and TensorFlow — Adventures in Machine Learning などにあるのですが、最新のEdwardではed. In this tutorial, you will learn how to: Develop a Stateful LSTM Model with the keras package, which connects to the R TensorFlow backend. utils import plot_model from keras. datasets import imdb from keras. So we are going to optimize so that the P distribution look the most like the N(0,1) distribution (a gaussian distribution located around the origin). Clarification I'm puzzled by the choice of keras to use the binarycrossentropy function (l45) between x (the sample) and xdecodedmean (the output of the decoder network, sigmoid activation) to compute E_{z ~ Q(Z | X)} [log p(x|z)], or "reconstruction loss". fit(), model. We do so using the Keras Functional API, which allows us to combine layers very easily. 13 Keras CNN を改造してImageDataGenerator（画像…. CorrVAE: A VAE for sampling realistic financial correlation matrices (Tentative I) First tentative at CorrVAE. 而编码计算方差的网络的作用在于动态调节噪声的强度。到这里，变分自编码器的基本原理基本上就讲完了。最后一点内容，我们来看一下 keras 给出的 VAE 实现。 4. Viewed 2k times 1 $\begingroup$ The code here: https://github. , Naranjo V. npz · 2,742 views · 1y ago. Generative Models. model = VAE (epochs = 5, latent_dim = 2, epsilon = 0. return x y = CustomVariationalLayer()([x, x_decoded_mean_squash]) vae = Model(x, y) vae. eriklindernoren/Keras-GAN Keras implementations of Generative Adversarial Networks. 5 Generative Adversarial Networks(GAN) 이 중에서 이번주에는 8. Explore the most advanced deep learning techniques that drive modern AI results; New coverage of unsupervised deep learning using mutual information, object detection, and semantic segmentation. Setup import tensorflow as tf from tensorflow import keras from tensorflow. The goals of this notebook is to learn how to code a variational autoencoder in Keras. Welcome back! In this post, I'm going to implement a text Variational Auto Encoder (VAE), inspired to the paper "Generating sentences from a continuous space", in Keras. a simple vae and cvae from keras. variational_autoencoder • keras keras. nl/private/egoskg/resimcoi6fi9z. pyplot as plt. We use a custom Keras memory-efficient generator to deal with our large dataset (202599 images, ca. 1 The Network. In this post we looked at the intuition behind Variational Autoencoder (VAE), its formulation, and its implementation in Keras. LeeML-Notes. See full list on bjlkeng. data, for building scalable input pipelines. Let’s build a (conditional) VAE that can learn on celebrity faces. 6-py3-none-any. Vaelien, the King of Thorns, is the patron deity of the Serelien region of Mythralis. 8 #Keras #TensorFlow #VAE. 他人のデータのMNISTとかばっかりやっても全く面白くない！ 自分で集めたデータで機械学習したい！ 貴重な説明が以下にあったので、写経してみる！ Kerasによる、ものすごくシンプ. On Kaldwyn, he is considered a divine being that is an antithetical to Selys, and believed to be comparable to her in power. compile(optimizer='rmsprop', loss=None) 在keras中自定义metric非常简单，需要用y_pred和y_true作为自定义metric函数的输入参数 点击查看metric的设置. This has been demonstrated in numerous blog posts and tutorials, in particular, the excellent tutorial on Building Autoencoders in Keras. 2018年7月14日 Takami Torao Python 3. It uses DCGan ( Deep Convolutional Generative Adversarial Network ) which has been a breakthrough in GAN research as it introduces major architectural changes to tackle problems like training instability, mode. a simple vae and cvae from keras. The Right Way to Oversample in Predictive Modeling. It is a very well-designed library that clearly abides by its guiding principles of modularity and extensibility, enabling us to easily assemble powerful, complex models from primitive building blocks. This has been demonstrated in numerous blog posts and tutorials, in particular, the excellent tutorial on Building Autoencoders in Keras. お急ぎの方は、結果の画像だけ見ていただければ分かると思います。 基本となる技術は、VAE（Variational Autoencoder）です。. io) VAE example from "Writing custom layers and models" guide (tensorflow. models import Model # Headline input: meant to receive sequences of 100 integers, between 1 and 10000. 而编码计算方差的网络的作用在于动态调节噪声的强度。到这里，变分自编码器的基本原理基本上就讲完了。最后一点内容，我们来看一下 keras 给出的 VAE 实现。 4. Shape of X_train and X_test. utils import plot_model from. 8 SONY Neural Network Libraries でDCGAN… AI（人工知能） 2019. ディープラーニングを用いたMetric Learningの一手法であるArcFaceで特徴抽出を行い、その特徴量をUmapを使って2次元に落とし込み可視化しました。KerasでArcFaceを用いる例としてメモしておきます。 qiita. com 実装は以下を引っ張ってきました。元とほぼ一緒なのですが一部以下の変更を入れてい. 04; Python 3. datasets import H5Loader from astroNN. This has been demonstrated in numerous blog posts and tutorials, in particular, the excellent tutorial on Building Autoencoders in Keras. callbacks import ModelCheckpoint from keras. model = VAE (epochs = 5, latent_dim = 2, epsilon = 0. TensorFlow Probability includes a wide selection of probability distributions and bijectors, probabilistic layers, variational inference, Markov chain Monte Carlo, and optimizers such as Nelder-Mead, BFGS, and SGLD. Loss curves when training a VAE on the SVHN dataset. Kerasブログの自己符号化器チュートリアル（Building Autoencoders in Keras）の最後、Variational autoencoder（変分自己符号化器；VAE）をやります。 VAE についての チュートリアル 上の説明は簡単なものなので、以下では自分で言葉を補っています。. With everything set up, we can now test our VAE on a dataset. Is the reconstruction probability the output of a specific layer, or is it to be calculated so. model = VAE (epochs = 5, latent_dim = 2, epsilon = 0. The Right Way to Oversample in Predictive Modeling. ディープラーニングを用いたMetric Learningの一手法であるArcFaceで特徴抽出を行い、その特徴量をUmapを使って2次元に落とし込み可視化しました。KerasでArcFaceを用いる例としてメモしておきます。 qiita. callbacks import ModelCheckpoint from keras. This notebook uses a data. To use a metric in a custom training loop, you would: Instantiate the metric object, e. Explore the most advanced deep learning techniques that drive modern AI results ; New coverage of unsupervised deep learning using mutual information, object detection, and semantic segmentation. TensorFlow’s implementation contains enhancements including eager execution, for immediate iteration and intuitive debugging, and tf. 他人のデータのMNISTとかばっかりやっても全く面白くない！ 自分で集めたデータで機械学習したい！ 貴重な説明が以下にあったので、写経してみる！ Kerasによる、ものすごくシンプ. Key Features. Generating data from a latent space VAEs, in terms of probabilistic terms, assume that the data-points in a large dataset are generated from a. (tensorflow backend) 설치 pip install keras import import tensorflow as tf import keras 버젼 확인 tf. Since 2009, we have been presenting news and analyses round the clock, staying true to. h5") We also have to make sure the data is loaded. The results are, as expected, a tad better:. We use a custom Keras memory-efficient generator to deal with our large dataset (202599 images, ca. Total stars 7,172 Stars per day 7 Created at 2 years ago Language Python Related Repositories keras_snli Simple Keras model that tackles the Stanford Natural Language Inference (SNLI) corpus using summation and/or recurrent neural networks the-gan-zoo. We do so using the Keras Functional API, which allows us to combine layers very easily. このページは、(4)モデル学習(Keras)の続きであり、今回は、結果の出力を行っていきます。. tfprob_vae • keras keras. 2 TensorFlow 1. layers import Conv2D, Flatten, Dense, Lambda, Reshape, Conv2DTranspose, Layer from keras. The example constructs a convolutional neural network architecture, trains a network, and uses the trained network to predict angles of rotated. 2 StyleGANの学習済みモデルでサクッと遊んでみる AI（人工知能） 2018. 04; Python 3. Epoch: 7000, Test set ELBO: -6138. layers import Lambda, Input, Dense from keras. You'll learn how to write deep learning applications in the most powerful, popular, and scalable machine learning stack available. Hi all，十分感谢大家对keras-cn的支持，本文档从我读书的时候开始维护，到现在已经快两年了。这个过程中我通过翻译文档，为同学们debug和答疑学到了很多东西，也很开心能帮到一些同学。. Importantly, Keras provides several model-building APIs (Sequential, Functional, and Subclassing), so you can choose the right level of abstraction for your project. The environment provides our agent with a high dimensional input observation at each time step. ディープラーニングを用いたMetric Learningの一手法であるArcFaceで特徴抽出を行い、その特徴量をUmapを使って2次元に落とし込み可視化しました。KerasでArcFaceを用いる例としてメモしておきます。 qiita. Introduction. First, I'll briefly introduce generative models, the VAE, its characteristics and its advantages; then I'll show the code to implement the text VAE in keras and finally I will explore the results of this model. Keras is supported on CPU, GPU, and TPU. Importantly, Keras provides several model-building APIs (Sequential, Functional, and Subclassing), so you can choose the right level of abstraction for your project. The idea behind this is to get batches of images on the fly during the training process. 10KB each). This distribution is also called the posterior, since it reflects our belief of what the code should be for (i. In addition, we will familiarize ourselves with the Keras sequential GUI as well as how to visualize results and make predictions using a VAE with a small number of latent dimensions. We also saw the difference between VAE and GAN, the two most popular generative models nowadays. 本記事は、R Advent Calendar 2017の14日目の記事です。これまで、R言語でロジスティック回帰やランダムフォレストなどを実践してきました。Rは統計用のライブラリが豊富、Pythonは機械学習用のライブラリが豊富。というイメージがありますが、Rでも機械学習は可能です。今回は、Kerasという深層. The author's code basically defines M1 model first (VAE_Z_X. We use a custom Keras memory-efficient generator to deal with our large dataset (202599 images, ca. callbacks import VirutalCSVLogger from astroNN. build # Construct VAE model using Keras model. This implementation is inspired by this excellent post Building Autoencoders in Keras. fit(): With this model, we are able to get an ELBO of around 115 nats (the nat is the natural logarithm equivalent. In this post we looked at the intuition behind Variational Autoencoder (VAE), its formulation, and its implementation in Keras. VAE: variational autoencoders. AutoEncoders in Keras: VAE-GAN. Explore the most advanced deep learning techniques that drive modern AI results; New coverage of unsupervised deep learning using mutual information, object detection, and semantic segmentation. This script demonstrates how to build a variational autoencoder with Keras. Amazon wants to classify fake reviews, banks want to predict fraudulent credit card charges, and, as of this November, Facebook researchers are probably wondering if they can predict which news articles are fake. config import _astroNN_MODEL_NAME from astroNN. Equation 1. さて、では実装。実は実装はkerasの大元に置いてあるんですよね… ん、あれうまく動かない…. You can disable this in Notebook settings. Keras is awesome. (2018) Retinal Image Synthesis for Glaucoma Assessment Using DCGAN and VAE. utils import plot_model from keras. If you’re new to VAE’s, these tutorials applied to MNIST data helped me understand the encoding/decoding engines, latent space arithmetic potential, etc: Miriam Shiffman, code in. The environment provides our agent with a high dimensional input observation at each time step. I've copied the loss function from one of Francois Chollet's blog posts and I'm getting really really negative losses. nl/private/egoskg/resimcoi6fi9z. CorrVAE: A VAE for sampling realistic financial correlation matrices (Tentative I) First tentative at CorrVAE. Advanced Deep Learning with Keras is a comprehensive guide to the advanced deep learning techniques available today, so you can create your own cutting-edge AI. In this post we looked at the intuition behind Variational Autoencoder (VAE), its formulation, and its implementation in Keras. We will be using the Keras library for running our example. compile (optimizer=keras. GANについて理解するため、GANを簡単な2次元問題に適用し、その挙動を観察してみました。実装にはpythonとkerasを使いました。 mnistの文字生成などがGANの導入としてよく紹介されていますが、文字等の画像データはデータ分布形状という観点での観察が難しいので、ここでは2次元を選びました. Viewed 427 times 1 $\begingroup$ I. So we are going to optimize so that the P distribution look the most like the N(0,1) distribution (a gaussian distribution located around the origin). 2017/06/21にリリースされた gensim 2. A new branch will be created in your fork and a new merge request will be GitHub - bonlime/keras-deeplab-v3-plus: Keras implementation of Deeplab v3+ with pretrained weightsFiles for deeplab, version 0. Using Keras as an open-source deep learning library, you'll find hands-on projects throughout that show you how to create more effective AI with the latest techniques. Let’s quickly go over a Keras implementation of a VAE. Kerasブログの自己符号化器チュートリアル（Building Autoencoders in Keras）の最後、Variational autoencoder（変分自己符号化器；VAE）をやります。 VAE についてのチュートリアル上の説明は簡単なものなので、以下では自分で言葉を補っています。 そのため、不正確な記述があるかもしれません。. Model(inputs=encoder. preprocessing. utils import plot_model from. 0 but nothing changes. This implementation is inspired by this excellent post Building Autoencoders in Keras. Keras Vae shape A tuple of integers, the shape of tensor to create. さらに、 vae の発展系である cvae の説明も行います。 説明の後にコードの紹介も行います。 また、 ae, vae, cvae の違いを可視化するため、 vae がなぜ連続性を表現できるのか割り出すために、行った実験と、その結果について説明します。. In our VAE example, we use two small ConvNets for the generative and inference network. The VAE model can learn features that were generally non-redundant and could disentangle large sources of variation in the data. build # Construct VAE model using Keras model. output) y = intermediante_layer_model. We'll then build a VAE in Keras that can encode and decode images. layers import Input, Lambda, Dense from keras. compile(optimizer='rmsprop') Train on 15474 samples, validate on 3869 samples Epoch 1/50 15474/15474 [=====] - 1s 76us/step - loss: nan - val_loss: nan Epoch 2/50 15474/15474 [=====] - 1s 65us/step - loss: nan - val_loss. MAP()等にdataとともに渡す方法はでできなくなっています。. You will learn how to build a keras model to perform clustering analysis with unlabeled datasets. TensorFlow is the machine learning library of choice for profe. CorrVAE: A VAE for sampling realistic financial correlation matrices (Tentative I) First tentative at CorrVAE. fit(): With this model, we are able to get an ELBO of around 115 nats (the nat is the natural logarithm equivalent. A new branch will be created in your fork and a new merge request will be GitHub - bonlime/keras-deeplab-v3-plus: Keras implementation of Deeplab v3+ with pretrained weightsFiles for deeplab, version 0. Using Keras and the fashion-MNIST dataset to generate images with a VAE. optimizers import RMSprop Using TensorFlow backend. 4 VAE 부분을 발표하기로 했다. compile (optimizer=keras. Autoencoders using tf. さて、では実装。実は実装はkerasの大元に置いてあるんですよね… ん、あれうまく動かない…. Vaelien, the King of Thorns, is the patron deity of the Serelien region of Mythralis. layers import Conv2D, Flatten, Dense, Lambda, Reshape, Conv2DTranspose, Layer from keras. This notebook uses a data. This implementation is inspired by this excellent post Building Autoencoders in Keras. Содержание Часть 1: Введение Часть 2: Manifold learning и скрытые (latent) переменные Часть 3: Вариационные автоэнкодеры (VAE) Часть 4: Conditional VAE Часть 5: GAN (Generative. The training of the larger bottom level. | 2020-11-28 22:02:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20360258221626282, "perplexity": 8263.969810563194}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141195929.39/warc/CC-MAIN-20201128214643-20201129004643-00587.warc.gz"} |
http://mathhelpforum.com/number-theory/99762-remainder-problem.html | 1. remainder problem
solve dis fast..
find the remainder of 2^89 divided by 89
2. Originally Posted by kandavel879
solve dis fast..
find the remainder of 2^89 divided by 89
you may use the Fermat's Theorem:
$a^{p-1}\mod p=1$for any prime $p,\gcd (a,p)=1$
Then $2^{89}=2(\mod 89)$
3. Solve and tell the answer | 2017-06-29 08:09:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42482659220695496, "perplexity": 8424.11327744815}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323889.3/warc/CC-MAIN-20170629070237-20170629090237-00375.warc.gz"} |
http://negf.cheers-app.de/rc-integrator-calculator.html | The value of R should be 10 or more times larger than X,. Visit Tuttle-Click Chrysler Jeep Dodge Ram Irvine in Irvine CA serving Lake Forest, Laguna Niguel and Mission Viejo #2C4RC1GG2LR102918. R V in V out C R IC IR Figure 9. 8 Integrators and Differentiators Reading Assignment: 105-113 Op-amp circuits can also (and often do) implement reactive elements such as inductors and capacitors. Please enter any two values and leave the values to be calculated blank. Vc is voltage across. Integrator block parameters Now, double click on the Gain block and set the gain to the values shown in Fig. They are preferred by on-site geologists for their high percentage of uncontaminated sampling; their fast penetration rates; and their trouble-free, low-cost, and long life performance. Bouchon, P. So the charge Q on the capacitor equals the integral of the current with respect to time. They are also useful for electrical signal processing, for example, taking the derivative or integral of an electrical signal. Visit Lexus of Henderson in Henderson NV serving Henderson, Las Vegas and North Las Vegas #JTHX3JBH2L2024063. How do we convert the imperfect passive RC integrator into an almost "ideal" op-amp inverting integrator? What does the op-amp do in this circuit?. To select a suitable RC filter, we must calculate the RC bandwidth for single-channel or multiplexed applications, then select values for R and C. In general, square waves are relatively easy to produce. In this video, op-amp integrator circuit has been discussed (with derivation) and few examples have been solved based on this op-amp integrator circuit. Maven is - at its heart - a plugin execution framework; all work is done by plugins. 2 kilo-ohms and R2 of 100 kilo-ohms. FreeNAS is an operating system that can be installed on virtually any hardware platform to share data over a network. A new decade. Predictive watering adjusts schedules based on temperature forecast, rainfall probability, wind and humidity to provide maximum water savings while keeping your clients’ landscape healthy and beautiful. The circuit presented uses an LM358 Op Amp in a Non-Inverting Voltage Follower configuration. The strength of these fields varies directly with the size of the current flowing through the wire and inversely to the distance from the wire. The equation for sector area is also given. SD200 The SIMOTICS SD200 low voltage motor from Siemens combines flexibility, performance and efficiency to meet any customer need. INTRODUCTION We saw in Sec. Truck manufacturers generally calculate the net capacity of a truck, with an attachment, using simple formulas. Calculate your velocity. P517/617 Lec4, P1 R-L-C Circuits and Resonant Circuits Consider the following RLC series circuit •What's VR?Simplest way to solve for V is to use voltage divider equation in complex notation. I need help calculating the break frequency of an RC and an RL circuit when given only the resistor of 1000 ohms value and the magnitude and phase plots. (a) Study of Phase shift. MOSHEMT: A New Transistor Technology for Ultra High Frequencies - Jan 24, 2020; ThinKom's Satellite Antenna Radome Records Near-Zero Drag on Regional Jets - Jan 24, 2020; IMS Invites Students to Participate in Linear High Power Amplifier Design Competition - Jan 24, 2020. Compensate for input parasitic Capacitance A small capacitor [Cf] across the feedback resistor will compensate for parasitic capacitance at the (inverting) input of the Op-Amp. Sinusoidal Response of RC & RL Circuits 1. Modeling approximation can be used to design the microstrip trace. Siemens is crossing the country to bring you the latest innovations in process automation and instrumentation. ÎInstantaneous power emitted by circuit: P = i2R ÎMore useful to calculate power averaged over a cycle Use <…> to indicate average over a cycle ÎDefine RMS quantities to avoid ½ factors in AC circuits ÎHouse current V rms = 110V ⇒V peak = 156V 22sin PIR t=− mdω φ 22 2( ) 1 2 P =−=IR t IR md msin ωφ rms 2 I = I m rms 2 ε =ε m. Bekijk het volledige profiel op LinkedIn om de connecties van David Atkins RC en vacatures bij vergelijkbare bedrijven te zien. Following is the formula for time constant. If your existing phone number is still with your previous provider, you can transfer it to your RingCentral account. The following figure shows how each section of a curve can be approximated by the hypotenuse of …. Predictive watering adjusts schedules based on temperature forecast, rainfall probability, wind and humidity to provide maximum water savings while keeping your clients’ landscape healthy and beautiful. This is greater than the flux at = 0. The Online RC Time Constant Calculator is an Electronics Engineering Tool for Engineering Students and Electronic Engineers. Here is an example of a first-order series RC circuit. 1 Circuit Elements in the s-Domain Creating an s-domain equivalent circuit requires developing the time domain circuit and. Differential Equations and Linear Superposition • Basic Idea: Provide solution in closed form • Like Integration, no general solutions in closed form •Order of equation: highest derivative in equation e. com in 2 categories. This action causes the block to function as a limited integrator. 2% of input voltage. Unit commanders will consider eligible Soldiers who are in the secondary zone for integration into the SGT/SSG recommended list on a monthly basis. As the capacitor is a frequency dependant element, the amount of charge that is established across the plates is equal to the time domain integral of the current. We now need to move into the Calculus II applications of integrals and how we do them in terms of polar coordinates. An integrator circuit is a circuit in which the input waveform. Please guide me here of the steps I should take. One type of electrical snubber is the RC snubber, which is composed of a resistor in parallel with a capacitor. Most model aircraft designs have a certain amount of down and/or right thrust. Dentrix practice management software provides solutions for both the business and clinical sides of your dental practice. It can also be used as a beam load capacity calculator by using it as a bending stress or shear stress calculator. Integrator output compatible with unipolar or bipolar ADC input range (Ex: ADS131A04 with 0-5V or ±2. Lessons In Electric Circuits -- Volume III Chapter 8 we can calculate the voltage across R 2 (by means of an RC time constant). Capacitors are the electrical analog of springs. From the vSphere Documentation, this upgrade is not supported:. ∫f(x) dx Calculus alert! Calculus is a branch of mathematics that originated with scientific questions concerning rates of change. ISO New England helps protect the health of New England's economy and the well-being of its people, by ensuring the constant availability of electricity today and for future generations. Previous page Next page. The above steel beam span calculator is a versatile structural engineering tool used to calculate the bending moment in an aluminium, wood or steel beam. AN11261 Using RC Thermal Models Rev. , frequency response, bandwidth, noise, offsets, etc. 2, use the cursor. Statewide integration of the INSPECT platform is a key component of Indiana's ongoing efforts to attack the opioid crisis. Tour Azure services and features Principles of cloud computing Control Azure services with the CLI Automate Azure tasks using scripts with PowerShell More interactive learning. The capacitor C then starts to charge gradually with RC time constant. Example analysis of the inverting, noninverting, and differential-amplifier circuits shows how calculations are performed. The op-amp relaxation oscillator shown in figure is a square wave generator. There could be more than one solution to a given set of inputs. 1The definite integral Recall thatthe expression ∫b a f(x)dx. Instructions. The proportional part acts on the present value of the error, the integral. Disclaimer: This calculator is not intended to be used for the design of actual structures, but only for schematic (preliminary) understanding of structural design principles. New 2020 CHRYSLER Pacifica Passenger Van for sale - only $50,415. As the capacitor is a frequency dependant element, the amount of charge that is established across the plates is equal to the time domain integral of the current. RC circuit as a Differentiator Figure 1. The RC step response is a fundamental behavior of all digital circuits. The integral (I) component will bring the multirotor closer to equilibrium, however, there is one more issue. After discovering that a couple of switches and a capacitor can simulate a resistor (Switched-Capacitor Resistor), we can strap this circuit onto the front end of an op amp to create the basic building block of many filter circuits - the integrator. 21, which shows the computed pattern of electric field at many locations near a uniformly charged disk (done by numerical integration, with the surface of the disk divided into small areas). Cauchy’s integral formula to get the value of the integral as 2…i(e¡1): Using partial fraction, as we did in the last example, can be a laborious method. RC Low-pass Filter Design Tool. Visit Sam Leman Chrysler Jeep Dodge of Peoria in Peoria IL serving Dunlap, Bartonville and Galesburg #2C4RC1EG9LR146093. An op-amp integrating circuit produces an output voltage which is proportional to the area (amplitude multiplied by time) contained under the waveform. 2 (Transfer Function of a Time Delay). What is time constant of an RC circuit? It is the time needed to charge the capacitor to 63. Capacitors are the electrical analog of springs. So, if for example, a user enters a notch frequency of 4KHz, 4KHz is greatly attenuated by the circuit. After 1 RC time the voltage will have dropped to 37 % (1/e), after about 5 RC times to 1 % (rule of thumb). and therefore may not be accepted as claims evidence. The Online RC Time Constant Calculator is an Electronics Engineering Tool for Engineering Students and Electronic Engineers. A coil inductance formula is based on the basic loop inductance. RC delay = the delay in signal speed through the circuit wiring as a result of these two effects. Lessons In Electric Circuits -- Volume III Chapter 8 we can calculate the voltage across R 2 (by means of an RC time constant). Apache Groovy is a powerful, optionally typed and dynamic language, with static-typing and static compilation capabilities, for the Java platform aimed at improving developer productivity thanks to a concise, familiar and easy to learn syntax. Incident rates are a metric used to compare your company’s safety performance against a national or state average. Still keeping the differentiator time constant fixed at 100 ns,. Passport MRZ calculator. Please enter any two values and leave the values to be calculated blank. ting resistor, RG, loads the third RC section, and if the fourth op amp in a quad op amp buffers this RC section, the performance becomes ideal. Part 2: Dynamics of the RC model So far we have a differential equation (1. Together, your integrator will be near ideal and have very little offset. Therefore, it has not been a very popular filter response. firgr can design a filter that meets passband/stopband ripple constraints as well as a specified transition width with the smallest possible filter order. After 1 RC time the voltage will have dropped to 37 % (1/e), after about 5 RC times to 1 % (rule of thumb). Standard equipment includes: 17” premium alloy wheels, LED headlamps, daytime running lights, fog lamps, sun roof, remote entry/start, heated and powered side mirrors, two-zone climate control, tilt and telescope steering wheel, vinyl upholstery, parking camera, collision mitigation system, 7. Consider a capacitor connected in series with a resistor, to a constant DC supply through a switch S. It also includes pi and a square root button. The Globe’s list identifies exemplary workplaces in MA, voted on by the people who know them best—their employees. Impedance In this chapter we introduce the concept of complex resistance, or impedance, by studying two reactive circuit elements, the capacitor and the inductor. • Transient - a circuit changes from one DC configuration to another. Quadcopter Dynamics, Simulation, and Control Introduction A helicopter is a flying vehicle which uses rapidly spinning rotors to push air downwards,. The world's largest digital library. The following figure shows how each section of a curve can be approximated by the hypotenuse of …. Cellular beams combine an efficient manufacturing process with opportunities for service integration. (10) Note that we may substitute (10) into (5) to get an equation for current:. Figure 1 shows a typical amplifier, single-pole RC filter, and ADC. 2C4RC1EG1LR142202. The important uses of the compensating networks are written below. These circuits can also be used as a differentiator or an integrator. Split Proportional & Integral Gain Path • Proportional and integral gain paths can be split by utilizing 2 independent charge pumps driving the integral capacitor and the proportional effective resistor • Often, the proportional and integral voltages are summed with a voltage-to-current converter to control a current-controlled oscillator (ICO). Research the 2020 Chrysler Pacifica Limited FWD in Greenwood, IN at Tom O'Brien CJDR - Greenwood. News from the world of electronics, editorial insights, technical articles. Sinusoidal Response of RC & RL Circuits Written By: Sachin Mehta Reno, Nevada 2. Matrix Multiplication Calculator Here you can perform matrix multiplication with complex numbers online for free. Since the expression for the instantaneous power. 20 hour rating, 100 hour rating etc) and Peukert's exponent. There could be more than one solution to a given set of inputs. Visit Ken Garff Automotive Group in Salt Lake City UT serving Ogden, Bountiful and Draper #2C4RC1EGXJR212292. The position of the resistor and capacitor are switched to change from low pass to high pass but the same calculation applies to both filters. Knowing how to calculate bandwidth formula is, therefore, very important to network administrators. The first integrator stage consists of amplifier A1, resistor R1 and sensor capacitance C1. As with the integrator circuit, we have a resistor and capacitor forming an RC Network across the operational amplifier and the reactance ( Xc ) of the capacitor plays a major role in the performance of a Op-amp Differentiator. Discover an extensive list of BMW Services designed to deliver optimum performance and unforgettable driving experiences. Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. A basic RC integrator circuit is simply a capacitor in series with a resistor and the source. This paper presents a mechanical model for the simulation of reinforced concrete (RC) wall boundary elements with lap splices, which builds on the tension chord model. Continued use of the calculator when the battery is low can result in improper operation. There are many ways to follow us - By e-mail:. Focused on customer service, support, innovation, quality and on-time delivery, Abracon supports over 25,000 active customers and ships over a quarter billion components each year. firgr can design a filter that meets passband/stopband ripple constraints as well as a specified transition width with the smallest possible filter order. The controller phase starts out at –90 degrees and increases to near 0 degrees at the break frequency. sending searching. Due to this fact, there is a natural delay between when the controller board starts making measurements and when it finally implements a change. Recall that the Laplace transform of a function is F(s)=L(f(t))=\int_0^{\infty}. Solutions to Homework 9 Section 12. You may want to calculate times for payroll and timecard purposes, or maybe you’re just interested in how long a task takes to complete. Arcsin calculator; Arcsin definition. So the latter gives you an exponential approach to Vin not the straight line you get from true integration. Free space loss depends upon frequency and distance. Astable and Monostable multivibrators 7. Navy Research U. First-order RC circuits can be analyzed using first-order differential equations. RC Phase shift oscillator and Wien Bridge Oscillator 3. Op-Amp Circuit Analysis 6 Ideal Analysis Method The ideal analysis method is inspired by the fact that in the preceding we strove to create equations that indicated that Av can be ignored if it is sufficiently high. This exponential behavior can also be explained physically. Arc Length of a Curve. Calculate i. So the charge Q on the capacitor equals the integral of the current with respect to time. Axis Lighting uses cookies to provide you a better experience, measure our audience, and optimize the functionality of our website. Recommended for you. 2 ECE 307-4 3 Frequency Response of a Circuit We remember that the transfer function is the output voltage to the input voltage of a circuit in s-domain is. (b) The two emf values are the same, because at those two times the flux is changing at the same rate. The behavior of circuits containing resistors (R) and capacitors (C) is explained using calculus. The advantages of integration also allow op amps to be included in many application specific integrated circuits (ASICs) where, combined with other circuit elements, a chip can be designed to carry out a specific function, which for example, can vary from a dedicated tone. Here is the circuit for Triangular wave generator using 741 op amp. You should realise that the term RC governs the rate at which the charge on the capacitor decays. The first op-amp starts with its two inputs in an unknown state; let's say it starts with + slightly higher than – (which is at ground). When the cap is reached, the integrator value is added to the controller output rather than the integrator value times the integral gain. Manage this durable outdoor irrigation controller with Hydrawise web-based software from anywhere worldwide using your smart device or web browser. 57*f3db where f3db = 1/(2πRC). Sebaliknya, semakin besar nilai Resistansinya, semakin lambat waktu pengisiannya. The diaphragm is connected to the stem, making the superstructure integral with the abutment. Our comprehensive. Standard equipment includes: 17” alloy wheels, LED headlamps, automated wipers, remote entry/start, heated/powered side mirrors, powered front seating, faux leather upholstery, automated climate control, 8” touchscreen, Bluetooth/smartphone/USB. Since the expression for the instantaneous power. Is there a fastest way to do this (Arrays, hash objects, iml) thanks in advance MK. Example 3: Must calculate the time to discharge a 470uF capacitor from 385 volts to 60 volts with 33 kilo-ohm discharge resistor View example Example 4: Must calculate the capacitance to charge a capacitor from 4 to 6 volts in 1 millisecond with a supply of 10 volts and a resistance of 1 kilo-ohm. How can i calculate the power gain in mosfet amplifiers: How to calculate Gain and phase angle of an transfer function: calculate closed loop gain with non ideal op-amp: How to calculate gain for l-type omni directional Rubber Duck antenna: How do I calculate the voltage gain in a multistage opamp circuit if I dont know any voltages?. Commercial truck routing, mileage & mapping software for carriers, shippers, and 3PLs that provides precise miles, rates, and drive times for planning, analysis, and driver pay. Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step. New 2020 Lexus IS 350 Caviar Near Scottsdale AZ at Bell Lexus North Scottsdale - Call us now at 480-566-6788 for more information about this 2020 Lexus IS 350 350 - Stock #236403. 21% of the final voltage value. Find the gradient vector eld for f(x;y) = x2 y and sketch it. As stated, RC circuits may be built with an op amp, a transistor, or inverter logic chip, but its composition of an resistor and capacitor is the same for each case. Find the transfer function by hand, i. Finally, if you're trying to find the center of gravity for a truly complex object, you have two options: Either whip out your best calculus integrals (see Resources for a triple integral that represents the center of gravity for a non-uniform mass) or input your data into a purpose-built center-of-gravity calculator. Delevopment of advance features will be fast-paced with the integration of the PRE-Flight Simulator system as a virtual "sandbox". 3V logic (0. Stringham was an American, so I have no idea why he would have used the notation "ln", other than perhaps to reflect a common, though mistaken, idea that Napier's log was a base-e log. They will make you ♥ Physics. If ever a sports coupé was engineered to stir the soul, the RC may just be the one to do it. The position of the resistor and capacitor are switched to change from low pass to high pass but the same calculation applies to both filters. Circuit time constant may be long, short or medium as given by the circuit condition. The mass of an individual component can be calculated. Ingenuity, finesse, experience and clarity drive this desire for perfection. This circuit is termed a two-port circuit (see Fig. 2-pole Chebyshev low pass filter 1-pole/2-pole RC Filter Sallen-Key Filter. An integrator circuit is a circuit in which the input waveform. This online calculator writes a polynomial, with one or more variables, as a product of linear factors. Op amp Integrator circuit design. Consider the simple first-order RC series circuit shown here. RC Integrator In the figure below calculate and record RC time constant. Technical Article Low-Pass Filter a PWM Signal into an Analog Voltage April 11, 2016 by Robert Keim In this article we will take a closer look at how to effectively low-pass filter a PWM signal into an analog voltage. RCBlast generates SDOF displacement time-histories by direct numerical integration of the dynamic equation of motion. When the output reaches the limits, the integral action is turned off to prevent integral wind up. Solution of First-Order Linear Differential Equation In thismethod, we reduce the circuit into asimple RC circuit byseparatingthe capacitor. (It must be an even number of segments for Simpson's Rule to work. See how you can start submitting estimates that reflect your actual refinish costs with Mitchell Refinish Materials Calculator (RMC). This video shows the derivation of output voltage of an operational. I need help calculating the break frequency of an RC and an RL circuit when given only the resistor of 1000 ohms value and the magnitude and phase plots. Op Amp Integrator • Recall resistor followed by a capacitor RC integrator • If the RC time constant is long relative to period • The resistor dominates the voltage drop and • The voltage across the capacitor becomes the integral • Consider an inverting op amp circuit • But replace Rf with a capacitor Cf. Figure 1 shows a typical amplifier, single-pole RC filter, and ADC. It overcomes the Miller capacitance limitations of the common emitter amplifier by using a second transistor as common- base current buffer. Here is an example of a first-order series RC circuit. If designed properly, this RC coupled amplifier can provide excellent signal characteristics. Providing unparalleled breadth of technology, connectivity and information solutions to the Property &; Casualty claims and Collision Repair industries, Mitchell is uniquely able to simplify and accelerate the claims management and collision repair processes. When you use integration to calculate arc length, what you're doing (sort of) is dividing a length of curve into infinitesimally small sections, figuring the length of each small section, and then adding up all the little lengths. Research the 2019 Chrysler Pacifica Limited in Clearwater, FL at Dayton Andrews Chrysler Dodge Jeep Ram FIAT Clearwater. This means that a Triangular Wave Generator Using Op amp can be formed by simply connecting an integrator to the square wave generator as shown in the Fig. 6) that relates changes in applied external current to. A high standard deviation indicates greater variability in data points, or higher dispersion from the mean. A vector eld is a vector function of position. Vectors are commonly used to model forces such as wind, sea current, gravity, and electromagnetism. A integrator circuit is a circuit that performs the mathematical operation of integration. Active RC filters utilize op-amps together with resistors and capacitors and are fabricated using discrete, thick film and thin-film technologies. ∫f(x) dx Calculus alert! Calculus is a branch of mathematics that originated with scientific questions concerning rates of change. In this video I explained the integrator circuit where the output voltage is equal to the integral of the input voltage. What is time constant of an RC circuit? It is the time needed to charge the capacitor to 63. This tool calculates the product of resistance and capacitance values, known as the RC time constant. Visit Lexus of Henderson in Henderson NV serving Henderson, Las Vegas and North Las Vegas #JTHX3JBH2L2024063. Every used car for sale comes with a free CARFAX Report. An integrator circuit is a circuit in which the input waveform. calculating this max took more than 10 minutes with proc sql and proc means. Arcsin calculator; Arcsin definition. All contents licensed under a Creative Commons Attribution-ShareAlike 4. This page is a web application that design a RC low-pass filter. firgr can design a filter that meets passband/stopband ripple constraints as well as a specified transition width with the smallest possible filter order. Calculator damping loss and dB amplification factor gain decibel amplifier audio engineering microphone recordings calculation ratio - sengpielaudio Eberhard Sengpiel. That is, a vector eld is a function from R2 (2 dimensional). 75 hours OR 8 hours and 45 minutes. Online arctan(x) calculator. These voltage spikes, or transients, can damage the circuit and cause arcing and sparks. The best of electronic design! EEWeb is the home for experienced and novice designers alike to share tips and to ask and answer questions. Full curriculum of exercises and videos. An integrator circuit is a circuit in which the input waveform. The leading accounting and inventory software meet to give you reliable inventory financials to help your team make better decisions. This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register. The simple R-C filter rolls off the frequency response at 6 dB per octave above the cutoff frequency. 0 Beta and RC versions running at the moment. The length of a curve or line. Built your own periodic signal and use it for several programs like TRMS and AVERG calculator next. To prevent the output from exceeding specifiable levels, select the Limit output check box and enter the limits in the appropriate parameter fields. It can also be used as a beam load capacity calculator by using it as a bending stress or shear stress calculator. 9 volts below wherever its output is centered (remember initial condition with integral). It also includes pi and a square root button. Once stable loop operation is achieved using proportional only control, widen the TR attribute value by 20 to 30% in preparation for adding integral. For the design of an actual structure, a competent professional should be consulted. This tool calculates the product of resistance and capacitance values, known as the RC time constant. Being careful: While this method should allow you to use the ideal integrator of Figure 1. (b) Differentiator, Integrator and filter circuits using OPAMP. Recent Arrival! 19/28 City/Highway MPG Price does not include Tax, Title, License and Documentary Fee; Price does include:$750 - 2020 National Retail Consumer Cash 20CL1. Based on the operational amplifier (op-amp), it performs the mathematical operation of integration with respect to time; that is, its output voltage is proportional to the input voltage integrated over time. These prices are for estimating purposes only and are subject to change without notice. By using an RC network to add slow negative feedback to the inverting Schmitt trigger, a relaxation oscillator is formed. How can i calculate the power gain in mosfet amplifiers: How to calculate Gain and phase angle of an transfer function: calculate closed loop gain with non ideal op-amp: How to calculate gain for l-type omni directional Rubber Duck antenna: How do I calculate the voltage gain in a multistage opamp circuit if I dont know any voltages?. Strength of Materials | Beam Deflection and Stress. Find guides and tips. This page is a web application that design a RC low-pass filter. The following figure shows how each section of a curve can be approximated by the hypotenuse of …. Figure 4: RC low pass filter Circuit as integrator. This figure — which occurs in the equation describing the charging or discharging of a capacitance through a resistor — represents the time required for the voltage present across the capacitor to reach approximately 63% of its final value after a change in voltage is applied to such a. Capacitors are the electrical analog of springs. With 24/7 access to business advisors, financial advice, industry expertise, and more, RBC Royal Bank can help you with all your business banking needs. Provides this gadget as Open Source Code. Ampere’s Circuital Law states the relationship between the current and the magnetic field created by it. We will also see that this particular kind of line integral is related to special cases of the line integrals with respect to x, y and z. RCBlast generates SDOF displacement time-histories by direct numerical integration of the dynamic equation of motion. Please guide me here of the steps I should take. In continuous integration, focus is getting an automated good build out with basic build verification tests while continuous deployment is focused heavily on testing and release management flows. The velocity of the air is the speed that the plane is going, relative to all that is happening around it. Cryptocurrency Mining Profitability Results The following list of cryptocurrencies are being compared to Bitcoin mining to determine if a cryptocurrency is more profitable to mine than mining Bitcoin. I was able to remove the server from the deployment manager, now I have an empty entry in runbook designer as my primary runbook server and my new server on Standby, when I try to promote the new server or demote the blank server I get a message that states cannot promote or cannot demote respective. New Price! Velvet 2020 Chrysler Voyager L FWD 9-Speed 948TE Automatic 3. Mixed Signal Integration is an integrated circuit company specializing in the design, manufacture and sale of turn-key analog and mixed-signal standard products and custom ASICs. \$\endgroup\$ – Spehro Pefhany Sep 10 '14 at 12:54. Azure DevOps Server 2019 Update 1. But it turns out channel 345 is playing Jeopardy so you again wave the remote in the general direction of the set and continue fiddling with the buttons. Inverting operational amplifier calculator Calculates properties of inverting operational amplifier circuit Example 1: Must calculate the output voltage of the circuit with 8 millivolt input using R1 of 2. 4 that a prismatic beam subjected to pure bending is bent into an arc of circle and that, within the elastic range, the curvature of the neutral surface may be expressed as M (4. FREE with a 30 day free trial. >I use the formulat Log10 (4) to calculate the log base 10 of 4. Following is the formula for time constant. After filtering out the omnipresent spam, a quick scan of tip. Visit Ed Voyles Chrysler Dodge Jeep Ram in Marietta GA serving Smyrna, Kennesaw and Atlanta #2C4RC1GG9LR107243. 'C' is the value of capacitance and 'R' is the resistance value. Example 3: Must calculate the time to discharge a 470uF capacitor from 385 volts to 60 volts with 33 kilo-ohm discharge resistor View example Example 4: Must calculate the capacitance to charge a capacitor from 4 to 6 volts in 1 millisecond with a supply of 10 volts and a resistance of 1 kilo-ohm. It accumulates the input quantity over a defined time to produce a representative output. This means that a Triangular Wave Generator Using Op amp can be formed by simply connecting an integrator to the square wave generator as shown in the Fig. To be considered as one of Kohl's suppliers, use the links below to review the registration process and fill out our supplier registration form. Frequently Asked Questions on RCMP Pensions Please note this FAQ section is provided for information purposes only and does not constitute a legal statement of your pension rights and obligations. We have seen that, the output of integrator is a Triangular Wave Generator Using Op amp if its input is a square wave. In this video I explained the integrator circuit where the output voltage is equal to the integral of the input voltage. Bouchon, P. Op amps are extremely versatile and have become the amplifier of choice for very many applications. So the latter gives you an exponential approach to Vin not the straight line you get from true integration. Figure 2: Step Voltage Input Effects of the circuits time constant on RC high pass: The shape of the output waveform of an RC high-pass circuit also depends upon the value of the circuit time constant T. Up to 8 values can be entered. Passive Component Properties. Our mission is simple, to help people make progress in their lives through learning. The model is composed of an assembly of components, each one accounting for a different source of deformation. Euler's Method - a numerical solution for Differential Equations Why numerical solutions? For many of the differential equations we need to solve in the real world, there is no "nice" algebraic solution. View pictures, specs, and pricing on our huge selection of vehicles. The radio system for your RC is tuned to a specific frequency and a specific length of antenna. 21) p El where M is the bending moment, E the modulus of elasticity, and I the. Incident rates are a metric used to compare your company’s safety performance against a national or state average. Enterprise data protection for your applications and systems, at your premises and in your clouds. This matches the calculator above if you set the following values:. 21% of the final voltage value. Transients are. Q&A for Work. (10) Note that we may substitute (10) into (5) to get an equation for current:. A Bode Plot is a useful tool that shows the gain and phase response of a given LTI system for different frequencies. It works on any hosting, even a shared one, while featuring industry leading security — naturally! Seamless integration with the top payment gateways means your ecommerce store can start selling today. Calculate the total series and parallel capacitance of a circuit using DigiKey's Series and Parallel Capacitor calculator. ADC - Dual Slope Integrator. STRUCTURAL BEAM DEFLECTION AND STRESS CALCULATORS. The format followed in this document is as follows. com, take a minute to enhance your experience by watching these brief training videos:. I tried to align the amplitudes of these sine waves. The Online RC Time Constant Calculator is an Electronics Engineering Tool for Engineering Students and Electronic Engineers. The above steel beam span calculator is a versatile structural engineering tool used to calculate the bending moment in an aluminium, wood or steel beam. Non-programmable calculators models list of famous brands like Casio, Sharp, Texas Instruments, Hewlett-Packard. So the latter gives you an exponential approach to Vin not the straight line you get from true integration. The second half of the circuit is an inverting integrator. Op amp is known as Operational Amplifier. From simple to complex, AutomationDirect has the motor control that you need. Visit Ken Garff Automotive Group in Salt Lake City UT serving Ogden, Bountiful and Draper #2C4RC1EGXJR212292. Enter the tangent value, select degrees (°) or radians (rad) and press the = button. | 2020-02-16 20:19:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3559088706970215, "perplexity": 1882.0661282951887}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875141396.22/warc/CC-MAIN-20200216182139-20200216212139-00332.warc.gz"} |
http://lambda-the-ultimate.org/node/5070 | ## automatic test discovery without reflection?
A programming language which is intended for production use must support the ability to easily create unit tests. Unit testing frameworks typically support a feature called test discovery, whereby all tests that are linked within an executable can be automatically detected and run, without the need for the programmer to manually register them.
For many languages such as Java and Python, reflection is used for this purpose. For languages that don't support reflection (e.g. C++) other, more cumbersome, methods are employed such as registration macros.
One problem with using reflection is that for AOT (Compiled ahead-of-time, as opposed to JIT) languages, reflection is expensive in terms of code size. Even in compressed form, the metadata for describing a method or class will often be larger than the thing being described. This can be a significant burden on smaller platforms such as embedded systems and game consoles. (Part of the reason for the bulk is due to the need to encode the metadata in a way that is linker-compatible, so that a type defined in one module can reference a type defined in a different module.)
Most of the things that one would use reflection for can be accomplished via other means, depending on the language. For example, reflection is often used to automatically construct implementations of an interface, such as for creating testing mocks or RPC stubs, but these can also be done via metaprogramming. However, metaprogramming can't solve the problem of test discovery, because the scope of metaprogramming is limited to what the compiler knows at any given moment, whereas the set of tests to be run may be a collection of many independently-compiled test modules.
A different technique is annotation processing, where the source code is annotated with some tags that are then consumed by some post-processor which generates additional source code to be included in the output module. In this case, the processor would generate the test registration code, which would be run during static initialization. The main drawback here is complexity, because the annotation processor isn't really a feature of the language so much as it is a feature of the compilation environment - in other words, you can't specify the behavior you want in the language itself.
I would be curious to know if there are other inventive solutions to this class of problems.
## Comment viewing options
### Naming conventions
For Awelon Object (AO), every word of the form test.foo will be run as an isolated unit test. (The . here is part of the name. I could just easily have favored test_foo or test:foo.) I find this very easy to use and understand.
Tests in this sense aren't compiled into the executable or a test suite. Thus, I don't need a registration phase. They're recognized by the development environment, and should eventually be automated so you're informed in real-time of which tests you just broke. | 2018-08-18 16:20:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3952940106391907, "perplexity": 1022.0537330701577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221213691.59/warc/CC-MAIN-20180818154147-20180818174147-00538.warc.gz"} |
http://docs.itascacg.com/flac3d700/common/kernel/doc/manual/global_manual/global_fish/global_utilities/fish_global.deterministic.html | # global.deterministic
Syntax
b = global.deterministic
global.deterministic = b
Get/set deterministic mode. In deterministic mode, all model runs starting with identical initial conditions result in identical solutions at the cost of a > 20% reduction in performance. In nondeterministic mode, on the other hand, identical initial conditions may lead to divergent solutions. The divergence is due only to the order of summation, and all solutions are equally valid to machine precision.
Returns: b - deterministic status b - deterministic status | 2022-08-11 23:24:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41546013951301575, "perplexity": 1089.971036439601}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571536.89/warc/CC-MAIN-20220811224716-20220812014716-00396.warc.gz"} |
http://math.stackexchange.com/questions/64591/prove-that-2-xnxn-1-decreases-with-n-for-0-x1 | Prove that $(2-x)^nx^{n-1}$ decreases with $n$ for $0 <x<1$?
How can I show that: $$(2-x)^nx^{n-1}$$ is decreasing with $n$ when $0<x<1$? I think this is generally true, but specifically I am concerned with $n$ as an integer $\geq 2$ and showing that the maximum of the function is when $n=2$ (its minimum) for all $x$. When I take the derivative with respect to $n$, I just get $$(2 - x)^n x^n \log(2 - x) + (2 - x)^n x^n \log x ,$$ but I don't know how to show that that is negative either. I guess it comes down to showing that the absolute value of $\log(2-x)$ is less than the absolute value of $\log(x)$... but I don't know how to do that with logs, or if that's necessarily the right approach.
-
Your idea works, you just have to push it a little farther. Take the derivative with respect to $n$, then consolidate like terms and put the two logarithms together for
$$(2-x)^nx^n \log ((2-x)x).$$ The factor $(2-x)^n x^n$ is positive so it remains to be seen that $0<(2-x)x<1$ for $x\in(0,1)$. We can subtract one and factor to get $-1<-(x-1)^2<0$, which is obviously true in our case.
-
Thanks so much! – Angada Sep 14 '11 at 22:16
This answer is certainly more complicated than necessary. – Michael Hardy Sep 14 '11 at 22:21
@Michael: True, yours is simpler. – anon Sep 14 '11 at 22:26
$$(2-x)^nx^{n-1} = \frac1x \Big(x(2-x)\Big)^n.$$ Everything in parentheses here is positive. If you can show that the expression raised to the power $n$ is between $0$ and $1$, you're done. $y=x(2-x)$ is a parabola opening downward with $x$-intercepts at $0$ and $2$, and parabolas are symmetric, so the vertex is half-way between $0$ and $2$. That's the highest point. When $x=1$, then $y=1$. So $y<1$ if $x=\text{anything else}$.
-
Oh, thanks! I do appreciate having a more simple way to do this! – Angada Sep 14 '11 at 22:35
Is $n$ a whole number or a real? Usually it would be a whole number. If so, to show it is decreasing with $n$, you need to show that the multiplicative factor, $(2-x)x$ is less than $1$. This, with the fact that the basic term is greater than $0$, is enough.
If $n$ is real, you just need to show that $\log x +\log(2-x) \lt 0$ as the other terms are positive and distribute out. You can check this with a derivative test.
Ross, you do not have to worry about real $n$ explicitly. Notice that the function is an exponential function in $n$ with base $x(2-x) < 1$. So it is clearly strictly decreasing with $n$. (Of course, here I am assuming elementary properties of exponential functions. Now I am not sure that you are :-)) – Srivatsan Sep 14 '11 at 22:13 | 2014-03-12 21:22:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8794166445732117, "perplexity": 124.34880052995635}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394026201240/warc/CC-MAIN-20140305133001-00043-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://www.ssccglapex.com/the-ratio-of-spirit-and-water-in-two-mixtures-of-20-litres-and-36-litres-is-3-7-and-7-5-respectively-both-the-mixtures-are-mixed-together-now-the-ratio-of-the-spirit-and-water-in-the-new-mixture/ | ### The ratio of spirit and water in two mixtures of 20 litres and 36 litres is 3 : 7 and 7 : 5 respectively. Both the mixtures are mixed together. Now the ratio of the spirit and water in the new mixture is ?
A. 25 : 29 B. 9 : 10 C. 27 : 29 D. 27 : 31 Answer: Option C
### Solution(By Apex Team)
$\begin{array}{l}\text{According to the question,}\\ \text{Mixture -1}=20\ \text{litres}\\ \text{Mixture -2}=36\ \text{litres}\\ \text{In Mixture -1 ratio of}\\ \left.\Large\frac{\text { Spirit }}{\text { Water }}=\Large\frac{3}{7}\right\rangle 10 \text { units }\\ \text{In Mixture -2 ratio of}\\ \left.\Large\frac{\text { Spirit }}{\text { Water }}=\Large\frac{7}{5}\right\rangle 12 \text { units }\end{array}$
$\begin{array}{l}\text{10 units →20 litres}\\ \text{1 unit →2 litres}\\ \text{12 units →36 litres}\\ \text{1 unit →3 litres}\end{array}$
$\begin{array}{l}\therefore\ \text{In Mixture -1}\ \text{ratio of}\\ \Large\frac{\text { Spirit }}{\text { Water }}=\frac{3 \times 2}{7 \times 2}=\frac{6}{14}\end{array}$
$\begin{array}{l}\therefore\ \text{In Mixture -2}\ \text{ratio of}\\ \Large\frac{\text { Spirit }}{\text { Water }}=\frac{7 \times 3}{5 \times 3}=\frac{21}{15}\end{array}$
\begin{aligned}&\text{Ratio of spirits and water}\\ &=\frac{6+21}{14+15} \\ &=\frac{27}{29} \\ &=27: 29 \end{aligned}
## Related Questions On Alligation
A. 2 : 5
B. 3 : 5
C. 5 : 3
D. 5 : 2
### An alloy contains zinc, copper and tin in the ratio 2 : 3 : 1 and another contains copper, tin and lead in the ratio 5 : 4 : 3. If equal weights of both alloys are melted together to form a third alloy, then the weight of lead per kg in new alloy will be:
A. $\large\frac{1}{2} \mathrm{~kg}$
B. $\large\frac{1}{8} \mathrm{~kg}$
C. $\large\frac{3}{14} \mathrm{~kg}$
D. $\large\frac{7}{9} \mathrm{~kg}$
A. 81 litres
B. 71 litres
C. 56 litres
D. 50 litres | 2021-10-27 12:32:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9512826800346375, "perplexity": 2098.118623457108}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588153.7/warc/CC-MAIN-20211027115745-20211027145745-00002.warc.gz"} |
https://www.stevencuttingblog.com/notes/clojure-std-lib-range | # range - Clojure Standard Library
For a quick intro to this series of blog posts check out Clojure Standard Library - Intro. It includes a lot of useful info, including notes about presentation of examples and more.
range
## Quick Overview
### Description
clojure.core/range is a function that returns a lazy sequence of numbers. The sequence is constructed using the parameters provided.
### Example
(range 10)
; => (0 1 2 3 4 5 6 7 8 9)
Here I have passed range the integer 10, and range returned a list of numbers 0 through 10.
## How To Use
### Parameters and Return Values
range has three parameters that all have default values. Each parameter accepts a number, which can be an integer or a float and can also be negative.
Parameter Default Description
start 0 The starting value - inclusive
end infinity The last value - exclusive
step 1 n1 + step = n2
#### Parameter Structure
range is a multiple arity function – it accepts a variable number of parameters, up to three. It behaves differently based on the number of parameters (arity overloading).
• (range) When given zero parameters, range returns an infinite lazy sequence of every integer from 0 to infinity. The reason is that (as seen above) the default values for start, end and step are 0, infinity and 1.
Ex: 1
(take 10 (range))
; => (0 1 2 3 4 5 6 7 8 9)
(take 20 (range))
; => (0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19)
(take 30 (range))
; => (0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29)
• (range end) If only one number is given then it will be used as the end value. (start=0, step=1)
Ex:
(range 10)
; => (0 1 2 3 4 5 6 7 8 9)
(range 10.001)
; => (0 1 2 3 4 5 6 7 8 9 10)
• (range start end) If two numbers are given then the first one will be used for start and the second for end. (step=1) If start is equal to end, range will return an empty list.
Ex:
(range 0 10)
; => (0 1 2 3 4 5 6 7 8 9)
(range 200 200)
; => ()
(range 0.5 10.5)
; => (0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5)
(range 0 -10)
; => ()
(range -15 -10)
; => (-15 -14 -13 -12 -11)
(range -15 0)
; => (-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1)
(range -15.5 0)
; => (-15.5 -14.5 -13.5 -12.5 -11.5 -10.5 -9.5 -8.5 -7.5 -6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5)
• (range start end step) When given three numbers, the first one is used for start, second for end and the third for step.
Ex:
(range 0 10 1)
; => (0 1 2 3 4 5 6 7 8 9)
(range 0 10 0.5)
; => (0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5)
(range 0 -10 -1)
; => (0 -1 -2 -3 -4 -5 -6 -7 -8 -9)
1. Checkout post on take↩︎ | 2019-09-20 04:03:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20454879105091095, "perplexity": 662.9942122909488}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573827.2/warc/CC-MAIN-20190920030357-20190920052357-00440.warc.gz"} |
http://prewar.mgcc.info/d-type/?rdp_we_resource=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FHamilton%25E2%2580%2593Jacobi_equation | Hamilton–Jacobi equation
In mathematics, the Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations, and is a special case of the Hamilton–Jacobi–Bellman equation. It is named for William Rowan Hamilton and Carl Gustav Jacob Jacobi.
In physics, the Hamilton–Jacobi equation is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion[citation needed], Lagrangian mechanics and Hamiltonian mechanics. The Hamilton–Jacobi equation is particularly useful in identifying conserved quantities for mechanical systems, which may be possible even when the mechanical problem itself cannot be solved completely.
The HJE is also the only formulation of mechanics in which the motion of a particle can be represented as a wave. In this sense, the HJE fulfilled a long-held goal of theoretical physics (dating at least to Johann Bernoulli in the 18th century) of finding an analogy between the propagation of light and the motion of a particle. The wave equation followed by mechanical systems is similar to, but not identical with, Schrödinger's equation, as described below; for this reason, the HJE is considered the "closest approach" of classical mechanics to quantum mechanics.[1][2]
Notation
Boldface variables such as represent a list of generalized coordinates,
A dot over a variable or list signifies the time derivative (see Newton's notation), e.g.,
The dot product notation between two lists of the same number of coordinates is a shorthand for the sum of the products of corresponding components, e.g.,
Mathematical formulation
Given the Hamiltonian of a mechanical system (where , are coordinates and momenta of the system and is time) the Hamilton–Jacobi equation is written as a first-order, non-linear partial differential equation for the Hamilton's principal function [3],
The Hamilton's principal function is defined as the function of the upper limit of the action integral taken along the minimal action trajectory of the system,
where is the Lagrangian of the system and where the trajectory satisfies the Euler–Lagrange equation of the system,
Calculating the variation of with respect to variation of the end-point coordinate,
Using this result and calculating the variation of with respect to variation of the time of the end-point leads directly to the Hamilton–Jacobi equation,
or
where is the change of the trajectory at the old end-point due to the time shift and where
is the Hamiltonian of the system.
Alternatively, as described below, the Hamilton–Jacobi equation may be derived from Hamiltonian mechanics by treating S as the generating function for a canonical transformation of the classical Hamiltonian
The conjugate momenta correspond to the first derivatives of S with respect to the generalized coordinates
As a solution to the Hamilton–Jacobi equation, the principal function contains N + 1 undetermined constants, the first N of them denoted as α1, α2 ... αN, and the last one coming from the integration of .
The relationship between p and q then describes the orbit in phase space in terms of these constants of motion. Furthermore, the quantities
are also constants of motion, and these equations can be inverted to find q as a function of all the α and β constants and time.[4]
Comparison with other formulations of mechanics
The HJE is a single, first-order partial differential equation for the function S of the N generalized coordinates q1...qN and the time t. The generalized momenta do not appear, except as derivatives of S. Remarkably, the function S is equal to the classical action.
For comparison, in the equivalent Euler–Lagrange equations of motion of Lagrangian mechanics, the conjugate momenta also do not appear; however, those equations are a system of N, generally second-order equations for the time evolution of the generalized coordinates. Similarly, Hamilton's equations of motion are another system of 2N first-order equations for the time evolution of the generalized coordinates and their conjugate momenta p1...pN.
Since the HJE is an equivalent expression of an integral minimization problem such as Hamilton's principle, the HJE can be useful in other problems of the calculus of variations and, more generally, in other branches of mathematics and physics, such as dynamical systems, symplectic geometry and quantum chaos. For example, the Hamilton–Jacobi equations can be used to determine the geodesics on a Riemannian manifold, an important variational problem in Riemannian geometry.
Wave-trajectory duality
The HJE establishes a duality between trajectories and wave fronts.[5] For example, in geometrical optics, light can be considered either as “rays” or waves. The wave front can be defined as the surface that the light emitted at time has reached at time . Light rays and wave fronts are dual: if one is known, the other can be deduced.
More precisely, geometrical optics is a variational problem where the “action” is the travel time along a path:
where is the index of the medium and is an infinitesimal arc length. From the above formulation, one can compute the ray paths using the Euler-Lagrange formulation; alternatively, one can compute the wave fronts by solving the Hamilton-Jacobi equation. Knowing one leads to knowing the other.
The above duality is very general and applies to all systems that derive from a variational principle: either compute the trajectories using Euler-Lagrange equations or the wave fronts by using Hamilton-Jacobi equation.
The wave front at time , for a system initially at at time , is defined as the collection of points such that . If is known, the momentum is immediately deduced:
Once is known, tangents to the trajectories are computed by solving the equation
for , where is the Lagrangian. The trajectories are then recovered from the knowledge of .
Derivation using canonical transformation
Any canonical transformation involving a type-2 generating function G2(q, P, t) leads to the relations
and Hamilton's equations in terms of the new variables P, Q and new Hamiltonian K have the same form:
To derive the HJE, we choose a generating function G2(q, P, t) in such a way that, it will make the new Hamiltonian K = 0. Hence, all its derivatives are also zero, and the transformed Hamilton's equations become trivial
so the new generalized coordinates and momenta are constants of motion. As they are constants, in this context the new generalized momenta P are usually denoted α1, α2 ... αN, i.e. Pm = αm, and the new generalized coordinates Q are typically denoted as β1, β2 ... βN, so Qm = βm.
Setting the generating function equal to Hamilton's principal function, plus an arbitrary constant A:
the HJE automatically arises:
Once we have solved for S(q, α, t), these also give us the useful equations
or written in components for clarity
Ideally, these N equations can be inverted to find the original generalized coordinates q as a function of the constants α, β and t, thus solving the original problem.
Action and Hamilton's functions
Hamilton's principal function S and classical function H are both closely related to action. The total differential of S is:
so the time derivative of S is
Therefore,
so S is actually the classical action plus an undetermined constant.
When H does not explicitly depend on time,
in this case W is the same as abbreviated action.
Separation of variables
The HJE is most useful when it can be solved via additive separation of variables, which directly identifies constants of motion. For example, the time t can be separated if the Hamiltonian does not depend on time explicitly. In that case, the time derivative in the HJE must be a constant, usually denoted (–E), giving the separated solution
where the time-independent function W(q) is sometimes called Hamilton's characteristic function. The reduced Hamilton–Jacobi equation can then be written
To illustrate separability for other variables, we assume that a certain generalized coordinate qk and its derivative appear together as a single function
in the Hamiltonian
In that case, the function S can be partitioned into two functions, one that depends only on qk and another that depends only on the remaining generalized coordinates
Substitution of these formulae into the Hamilton–Jacobi equation shows that the function ψ must be a constant (denoted here as Γk), yielding a first-order ordinary differential equation for Sk(qk).
In fortunate cases, the function S can be separated completely into N functions Sm(qm)
In such a case, the problem devolves to N ordinary differential equations.
The separability of S depends both on the Hamiltonian and on the choice of generalized coordinates. For orthogonal coordinates and Hamiltonians that have no time dependence and are quadratic in the generalized momenta, S will be completely separable if the potential energy is additively separable in each coordinate, where the potential energy term for each coordinate is multiplied by the coordinate-dependent factor in the corresponding momentum term of the Hamiltonian (the Staeckel conditions). For illustration, several examples in orthogonal coordinates are worked in the next sections.
Examples in various coordinate systems
Spherical coordinates
In spherical coordinates the Hamiltonian of a free particle moving in a conservative potential U can be written
The Hamilton–Jacobi equation is completely separable in these coordinates provided that there exist functions Ur(r), Uθ(θ) and Uϕ(ϕ) such that U can be written in the analogous form
Substitution of the completely separated solution
into the HJE yields
This equation may be solved by successive integrations of ordinary differential equations, beginning with the equation for ϕ
where Γϕ is a constant of the motion that eliminates the ϕ dependence from the Hamilton–Jacobi equation
The next ordinary differential equation involves the θ generalized coordinate
where Γθ is again a constant of the motion that eliminates the θ dependence and reduces the HJE to the final ordinary differential equation
whose integration completes the solution for S.
Elliptic cylindrical coordinates
The Hamiltonian in elliptic cylindrical coordinates can be written
where the foci of the ellipses are located at on the -axis. The Hamilton–Jacobi equation is completely separable in these coordinates provided that U has an analogous form
where : , and are arbitrary functions. Substitution of the completely separated solution
into the HJE yields
Separating the first ordinary differential equation
yields the reduced Hamilton–Jacobi equation (after re-arrangement and multiplication of both sides by the denominator)
which itself may be separated into two independent ordinary differential equations
that, when solved, provide a complete solution for S.
Parabolic cylindrical coordinates
The Hamiltonian in parabolic cylindrical coordinates can be written
The Hamilton–Jacobi equation is completely separable in these coordinates provided that U has an analogous form
where Uσ(σ), Uτ(τ) and Uz(z) are arbitrary functions. Substitution of the completely separated solution
into the HJE yields
Separating the first ordinary differential equation
yields the reduced Hamilton–Jacobi equation (after re-arrangement and multiplication of both sides by the denominator)
which itself may be separated into two independent ordinary differential equations
that, when solved, provide a complete solution for S.
Eikonal approximation and relationship to the Schrödinger equation
The isosurfaces of the function S(q; t) can be determined at any time t. The motion of an S-isosurface as a function of time is defined by the motions of the particles beginning at the points q on the isosurface. The motion of such an isosurface can be thought of as a wave moving through q space, although it does not obey the wave equation exactly. To show this, let S represent the phase of a wave
where ħ is a constant (Planck's constant) introduced to make the exponential argument dimensionless; changes in the amplitude of the wave can be represented by having S be a complex number. We may then rewrite the Hamilton–Jacobi equation as
which is the Schrödinger equation.
Conversely, starting with the Schrödinger equation and our ansatz for ψ, we arrive at [6]
The classical limit (ħ → 0) of the Schrödinger equation above becomes identical to the following variant of the Hamilton–Jacobi equation,
HJE in a gravitational field
Using the energy–momentum relation in the form;[7]
for a particle of rest mass m travelling in curved space, where gαβ are the contravariant coordinates of the metric tensor (i.e., the inverse metric) solved from the Einstein field equations, and c is the speed of light, setting the four-momentum Pα equal to the four-gradient of the action S;
gives the Hamilton–Jacobi equation in the geometry determined by the metric g:
in other words, in a gravitational field.
HJE in electromagnetic fields
For a particle of rest mass and electric charge moving in electromagnetic field with four-potential in vacuum, the Hamilton–Jacobi equation in geometry determined by the metric tensor has a form
and can be solved for the Hamilton Principal Action function to obtain further solution for the particle trajectory and momentum:[8]
,
where and with the cycle average of the vector potential. Therefore:
a) For a wave with the circular polarization:
,
,
Hence
where , implying the particle moving along a circular trajectory with a permanent radius and an invariable value of momentum directed along a magnetic field vector.
b) For the flat, monochromatic, linearly polarized wave with a field directed along the axis
hence
,
,
implying the particle figure-8 trajectory with a long its axis oriented along the electric field vector.
c) For the electromagnetic wave with axial (solenoidal) magnetic field:[9]
hence
where is the magnetic field magnitude in a solenoid with the effective radius , inductivity , number of windings , and an electric current magnitude through the solenoid windings. The particle motion occurs along the figure-8 trajectory in plane set perpendicular to the solenoid axis with arbitrary azimuth angle due to axial symmetry of the solenoidal magnetic field.
References
1. ^ Goldstein, Herbert (1980). Classical Mechanics (2nd ed.). Reading, MA: Addison-Wesley. pp. 484–492. ISBN 978-0-201-02918-5. (particularly the discussion beginning in the last paragraph of page 491)
2. ^ Sakurai, pp. 103–107.
3. ^ Hand, L. N.; Finch, J. D. (2008). Analytical Mechanics. Cambridge University Press. ISBN 978-0-521-57572-0.
4. ^ Goldstein, Herbert (1980). Classical Mechanics (2nd ed.). Reading, MA: Addison-Wesley. p. 440. ISBN 978-0-201-02918-5.
5. ^ Houchmandzadeh, Bahram (2020). "The Hamilton-Jacobi Equation : an alternative approach". American Journal of Physics. 85 (5): 10.1119/10.0000781. doi:10.1119/10.0000781.
6. ^ Goldstein, Herbert (1980). Classical Mechanics (2nd ed.). Reading, MA: Addison-Wesley. pp. 490–491. ISBN 978-0-201-02918-5.
7. ^ J.A. Wheeler; C. Misner; K.S. Thorne (1973). Gravitation. W.H. Freeman & Co. pp. 649, 1188. ISBN 978-0-7167-0344-0.
8. ^ L. Landau and E. Lifshitz. THE CLASSICAL THEORY OF FIELDS. ADDISON-WESLEY PUBLISHING COMPANY, INC., Reading, Massachusetts, USA 1959.
9. ^ E. V. Shun'ko; D. E. Stevenson; V. S. Belkin (2014). "Inductively Coupling Plasma Reactor With Plasma Electron Energy Controllable in the Range from ~6 to ~100 eV". IEEE Transactions on Plasma Science. 42, part II (3): 774–785. Bibcode:2014ITPS...42..774S. doi:10.1109/TPS.2014.2299954. | 2020-05-26 12:01:13 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9157743453979492, "perplexity": 669.1827789795916}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347390758.21/warc/CC-MAIN-20200526112939-20200526142939-00477.warc.gz"} |
http://mathhelpforum.com/calculus/127497-derivative-problem.html | 1. ## derivative.. problem
Hello
can someone please show me how to do this sum correct
I need to find the derivative of x^-4(1-X^-4)^3
the correct answer is in yellow at the bottom,my answer is above it
2. Originally Posted by wolfhound
Hello
can someone please show me how to do this sum correct
I need to find the derivative of x^-4(1-X^-4)^3
$x^{-4}(1-x^{-4})^3 = \frac{(x^4-1)^3}{x^{16}}$
$\frac{d}{dx}\left[\frac{(x^4-1)^3}{x^{16}}\right]$
$\frac{x^{16} \cdot 3(x^4-1)^2 \cdot 4x^3 - (x^4-1)^3 \cdot 16x^{15}}{x^{32}}$
$\frac{4x^{15}(x^4-1)^2 [3x^4 - 4(x^4-1)]}{x^{32}}$
$\frac{4x^{15}(x^4-1)^2 [4-x^4]}{x^{32}}$
$\frac{4(x^4-1)^2 (4-x^4)}{x^{17}}$
3. Originally Posted by wolfhound
Hello
can someone please show me how to do this sum correct
I need to find the derivative of x^-4(1-X^-4)^3
the correct answer is in yellow at the bottom,my answer is above it
Looks like an application of the product and chain rule
$x^{-4}(1-x^{-4})^3$
$u = x^{-4} \: \: \rightarrow \: \: u' = -4x^{-3}$
$v = (1-x^{-4})^3 \: \: \rightarrow \:\: v' = 3(1-x^{-4})^2 \cdot 4x^{-3} = 12x^{-3}(1-x^{-4})^2$
$y' = -4x^{-3}(1-x^{-4})^3 + 12x^{-7} \cdot (1-x^{-4})^2$
$y' = -4x^{-3}[(1-x^{-4})^3 + 3x^{-4}(1-x^{-4})^2]$
Why they want you to use the binomial expansion is beyond me but it's as follows up to $x^3$
$(1+x)^n = 1+nx+\frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3$
4. Originally Posted by e^(i*pi)
Looks like an application of the product and chain rule
$x^{-4}(1-x^{-4})^3$
$u = x^{-4} \: \: \rightarrow \: \: u' = -4x^{-3}$
$v = (1-x^{-4})^3 \: \: \rightarrow \:\: v' = 3(1-x^{-4})^2 \cdot 4x^{-3} = 12x^{-3}(1-x^{-4})^2$
$y' = -4x^{-3}(1-x^{-4})^3 + 12x^{-7} \cdot (1-x^{-4})^2$
$y' = -4x^{-3}[(1-x^{-4})^3 + 3x^{-4}(1-x^{-4})^2]$
Why they want you to use the binomial expansion is beyond me but it's as follows up to $x^3$
$(1+x)^n = 1+nx+\frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3$
Hello, should it not be $u' = -4x^{-5}$
5. Originally Posted by wolfhound
Hello, should it not be $u' = -4x^{-5}$
yes it should. | 2017-01-20 00:24:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 22, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8549267649650574, "perplexity": 508.06242182553046}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280761.39/warc/CC-MAIN-20170116095120-00221-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://solvedlib.com/n/determine-if-f-x-x-x27-sin-x-is-an-even-or-odd-function,21303100 | # Determine if f(x)=x' sin(x) is an even Or odd function: All algebra steps must be followed and justifications for making
###### Question:
Determine if f(x)=x' sin(x) is an even Or odd function: All algebra steps must be followed and justifications for making decisions_
#### Similar Solved Questions
##### (a) Compute avg(d) and sd. (b) Test if μd<0 at the α = 0.01 level of...
(a) Compute avg(d) and sd. (b) Test if μd<0 at the α = 0.01 level of significance. Round to five decimal places as needed. (c) Test if μd<0 at the α = 0.05 level of significance. Round to five decimal places as needed. (d) Compute a 90% confidence interval about the po...
##### Question 1: Part A Which of the following are legal identifiers for Python. Place a Y...
Question 1: Part A Which of the following are legal identifiers for Python. Place a Y for Yes and a N for No by each of the words below fence new house 1second make up phone team years adding.py 28223zipCode Part B What is the numeric value of each of the following Python arithmetic expressions as ...
##### B) (Apts) If 550 of all transactions contain phone screen protector; find the Lift Ratio for the above association rule:c) (Zpts) Should this seller set the link to phone screen protector on the page of phone cases?
b) (Apts) If 550 of all transactions contain phone screen protector; find the Lift Ratio for the above association rule: c) (Zpts) Should this seller set the link to phone screen protector on the page of phone cases?...
##### Three hundred milliliters of O_2 are collected at a pressure of 645 mmHg. What volume will this gas have a one atmospheric pressure?
Three hundred milliliters of O_2# are collected at a pressure of 645 mmHg. What volume will this gas have a one atmospheric pressure?...
##### Hoder Corporation manufactures numerous products, one of which is called Gamma45. The company has provided the...
Hoder Corporation manufactures numerous products, one of which is called Gamma45. The company has provided the following data about this product: Unit sales (a) Selling price per unit Variable cost per unit Contribution margin per unit (b) Total contribution margin (a) x (b)\$720,000 Traceable fixed ...
##### 5) Given the transformation matrix A =1 ~4~2 Is your vector; x,a unique solution?Find a vector; X, such that T(x) = Axb) Do the columns of A form a linearly independent set? Explain why or why not Determine if T(x) is one-to-one, onto, both, 01 neither:6)Find the inverse of each matrix below 01 explain why no such inverse exists (10 pts:)-2~610 i2]~2 10
5) Given the transformation matrix A = 1 ~4 ~2 Is your vector; x,a unique solution? Find a vector; X, such that T(x) = Ax b) Do the columns of A form a linearly independent set? Explain why or why not Determine if T(x) is one-to-one, onto, both, 01 neither: 6) Find the inverse of each matrix below 0...
##### Atall ofmnc rnough t0 piteni lnc snnf Irm &'r Anl_ aathn animtGlhe Gmle EWrk_ clfciz04 ~Ikn WVz
Atall ofmnc rnough t0 piteni lnc snnf Irm &'r Anl_ aathn animtGlhe Gmle E Wrk_ clfciz04 ~I kn W Vz...
##### Let Wbe subspace spanned by the u's and wrte as the sum of vector in W and vector orthogonal to W(Type a integer or simplified fraction for each matrix ement: )
Let Wbe subspace spanned by the u's and wrte as the sum of vector in W and vector orthogonal to W (Type a integer or simplified fraction for each matrix ement: )...
##### For the following exercises, use logarithms to solve.$e^{r+10}-10=-42$
For the following exercises, use logarithms to solve. $e^{r+10}-10=-42$...
##### Which element is most likely to form a 3- ion? Br Mg K N
Which element is most likely to form a 3- ion? Br Mg K N...
##### Determine [Review Topics] molecular formula e g CH4, from the line Specify elements in the structure below following order: €C H; Example: C4H-CIOS others(in alphabetical order)Molecular formula
Determine [Review Topics] molecular formula e g CH4, from the line Specify elements in the structure below following order: €C H; Example: C4H-CIOS others(in alphabetical order) Molecular formula...
##### To the right is the Na+K+ ATPase pump, also known as the Na+K+pump. This pump moves both Na+and K+ against their concentration gradients through the hydrolysis of ATP (here is another way, ATP, the "currency of the cell" is used):plasma membraneEXTRACELLULAR SPACEelectrochemical gradientelectrochemical gradientkompare and contrast the properties and the functioning ofthe glucose-Nat symport protein (top figure on this worksheet) and the Na+ K+ ATPase pump (figure to the right) Be sure
To the right is the Na+K+ ATPase pump, also known as the Na+K+pump. This pump moves both Na+and K+ against their concentration gradients through the hydrolysis of ATP (here is another way, ATP, the "currency of the cell" is used): plasma membrane EXTRACELLULAR SPACE electrochemical gradien...
##### 2). (Apes) The measure of an angle in standard position is given. Find two positive angles...
2). (Apes) The measure of an angle in standard position is given. Find two positive angles and two negative angles that are coterminal with the given angle. (Enter your answers as a comma-separated list.) 10°...
##### The following reaction was performed: A + B + C rightarrow Products The time to produce...
The following reaction was performed: A + B + C rightarrow Products The time to produce 1.0 times 10^4M of the product was measured. Calculate the rate (amount of product/time) for each run and fill it in the table above. Graph log r (y-axis) vs. log [A] (x-axis) for runs 1-3, log r vs. log [B] for ...
##### Prelab 7: Conservation of energy Name: 1. A child is using her hand to push a...
Prelab 7: Conservation of energy Name: 1. A child is using her hand to push a small box across a horizontal table top. The box is moving at a constant speed. In this situation, is the kinetic energy of the box increasing, decreasing, or staying the same? Explain. 2. A person holds a basketball at re...
##### 026 (A) NaBr is dissolved in 425g of water to give a solution of solubility 49.85 at 250C. Determine the mass of NaBr in kg needed to prepare the solution. (2 Marks) 026 (B) 10.5 grams of CaCO3 is dissolved in 225 g of water: Calculate the molality of the solution. (3 Marks) 026 (C) What is a metallic bond? Explain metallic bond and write two examples for it: (3 Marks)Q26 (D) Write the namelformula of the functional groups in the following: (2 Marks)WNameFormulaC=CIAlcohol
026 (A) NaBr is dissolved in 425g of water to give a solution of solubility 49.85 at 250C. Determine the mass of NaBr in kg needed to prepare the solution. (2 Marks) 026 (B) 10.5 grams of CaCO3 is dissolved in 225 g of water: Calculate the molality of the solution. (3 Marks) 026 (C) What is a metall...
##### Please help me with the problem 4.7! The reference problem 1.20 is attached, and the data...
Please help me with the problem 4.7! The reference problem 1.20 is attached, and the data is the full data in question 1.20. Thanks! 20 2 60 4 46 3 41 2 12 1 137 10 68 5 89 5 4 1 32 2 144 9 156 10 93 6 36 3 72 4 100 8 105 7 131 8 127 10 57 4 66 5 101 7 109 7 74 5 134 9 112 7 18 2 73 5 111 7 96 6 12...
##### (x+2n The series has radius of convergence 3 Which of the following gives its interval of convergence? n=o 3"nl/3015,1)0(1,5]0(5,1)01-3,3]
(x+2n The series has radius of convergence 3 Which of the following gives its interval of convergence? n=o 3"nl/3 015,1) 0(1,5] 0(5,1) 01-3,3]...
##### Find the area of the surface generated by rotating the curve T = Vy;l<y<8about the X-axis.
Find the area of the surface generated by rotating the curve T = Vy;l<y<8about the X-axis....
##### A monatomic ideal gas (λ = 1.67) is contained within a box whose volume is 2.5...
A monatomic ideal gas (λ = 1.67) is contained within a box whose volume is 2.5 m3. The pressure of the gas is 3.5 10^5 Pa. The total mass of the gas is 2.3 kg. Find the speed of sound in the gas...
##### Pt; 0.25 pt each) For each of the reactions shown below, indicate whether i isreduction;oxidation, or neither and calculate the change in oxidation number for any carbon being reduced or oxidized_OHOEtpt) Explain the purpose of adding dilute (3 M) and not concentraled sulfuric acid t0 the reaction during work up.pt) 9-fluorenone is colored (bright yellow color) but 9-{luorenol is not (white) . What accounts for this diflerence?pt) Balance the following sodium borohydride reduction equation:OMeOM
pt; 0.25 pt each) For each of the reactions shown below, indicate whether i is reduction; oxidation, or neither and calculate the change in oxidation number for any carbon being reduced or oxidized_ OH OEt pt) Explain the purpose of adding dilute (3 M) and not concentraled sulfuric acid t0 the react...
##### 2h 1 1 Imlacdd1oonitew
2 h 1 1 Imlacdd 1 oonitew...
##### PUmt1 pIsolution of K,CrzOv absorbs light at 440 nm:1 pI
PUmt 1 pI solution of K,CrzOv absorbs light at 440 nm: 1 pI...
##### Which of the following help to explain why the aggregate demand curve slopes downward?a. When the domestic price level rises, our goods and services become more expensive to foreigners.b. When government spending rises, the price level falls.c. There is an inverse relationship between consumer expectations and personal taxes.d. When the price level rises, the real value of financial assets (like stocks, bonds, and savings account balances) declines.
Which of the following help to explain why the aggregate demand curve slopes downward? a. When the domestic price level rises, our goods and services become more expensive to foreigners. b. When government spending rises, the price level falls. c. There is an inverse relationship between consumer ex...
##### Please write the correct answer and write it step by step, thanks!
Please write the correct answer and write it step by step, thanks!...
##### Answer the following questions A coil of 15 turns and a radius 10.0 cm surrounds a long solenoid of radius 2.40 cm and 1.00 103 turns/meter (see figure below) The current in the solenoid changes as [= 2.00 sin 120 t, where I is in amperes and t is in seconds Find the induced emf (in volts) in the 15-turn coil as a function of timeVW coilAn emf of 20.0 mV is induced in a 525-turn coil when the current is changing at the rate of 10.0 A/ls: What is the magnetic flux through each turn of the coil at
Answer the following questions A coil of 15 turns and a radius 10.0 cm surrounds a long solenoid of radius 2.40 cm and 1.00 103 turns/meter (see figure below) The current in the solenoid changes as [= 2.00 sin 120 t, where I is in amperes and t is in seconds Find the induced emf (in volts) in the 15...
##### What is the value of l in 4s1?
What is the value of l in 4s1?...
##### A circular loop in the plane of a paper lies in a 0.85 T magnetic field...
A circular loop in the plane of a paper lies in a 0.85 T magnetic field pointing into the paper. The loop's diameter changes from 22.0 cm to 5.2 cmin 0.54 s . What is the magnitude of the average induced emf? and also what is the average induced current if the coil resistance is 3.9 ? ?...
##### Evaluate the Ilne integral, where € is the given curve_ J (x + Sy) dx + x? dy, C consists of line segments from (0, 0) to (5,1) and from (5, 1) to (6, 0)
Evaluate the Ilne integral, where € is the given curve_ J (x + Sy) dx + x? dy, C consists of line segments from (0, 0) to (5,1) and from (5, 1) to (6, 0)...
##### What is the maximum concentration of Agt that can be added to a 0.00300 M solution of Na,CO, before a precipitate will form? (Ksp for Ag,CO, is 8.10 x 10-12)
What is the maximum concentration of Agt that can be added to a 0.00300 M solution of Na,CO, before a precipitate will form? (Ksp for Ag,CO, is 8.10 x 10-12)...
##### What are the answers to problem 2? 2. This question may be completed independently or as...
What are the answers to problem 2? 2. This question may be completed independently or as a group exercise. Below are descriptions for five mystery fossil primates. Use the information provided to determine which mystery fossil primate is an adapiform, an omomyoid, a New World monkey, an Old World mo...
##### In the following regression, X = weekly pay; Y = income tax withheld, and n = 35 McDonald's employees202 816Std. ErrorANOVA table Source Regression Residua Totalp-value 0068387. 6959 533_0614 920.7573387. 6959 46.45648.35Regression output variables Intercept Slopeconfidence interval p-value Lower 959 Upper 959 0000 17.7595 43.8331 0068 0.0101 0.0584coefficients 7963 0343std. error 4078 0119Stat 806 889(a) Write the fitted regression equation_(b-1) State the degrees of freedom for two-tailed
In the following regression, X = weekly pay; Y = income tax withheld, and n = 35 McDonald's employees 202 816 Std. Error ANOVA table Source Regression Residua Total p-value 0068 387. 6959 533_0614 920.7573 387. 6959 46.4564 8.35 Regression output variables Intercept Slope confidence interval p-...
##### Question 19 2 pts 19) Interpret your conclusion in the context of the application: At the...
Question 19 2 pts 19) Interpret your conclusion in the context of the application: At the 5% level of significance, there is sufficient evidence to conclude that Prenatal care and the wantedness of pregnancy are not independent. At the 5% level of significance, there is sufficient evidence to conclu... | 2022-07-06 04:11:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5334482192993164, "perplexity": 2564.884520651672}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104660626.98/warc/CC-MAIN-20220706030209-20220706060209-00648.warc.gz"} |
https://brieflands.com/articles/ijr-128725.html | # Intra- and Inter-rater Reliability of a Magnetic Resonance Imaging-Based Volumetric Analysis of the Abductor Hallucis Muscle
authors:
Nasrin Moulodi 1 , 2 , Maryam Jalali 2 , * , Javad Sarrafzadeh 3 , Fatemeh Azadinia 2 , Ali Shakourirad 4
Student Research Committee, Iran University of Medical Sciences, Tehran, Iran
Department of Orthotics and Prosthetics, Rehabilitation Research Center, School of Rehabilitation Sciences, Iran University of Medical Sciences, Tehran, Iran
Department of Physiotherapy, Rehabilitation Research Center, School of Rehabilitation Sciences, Iran University of Medical Sciences, Tehran, Iran
Department of Radiology, Sina Hospital, Tehran University of Medical Sciences, Tehran, Iran
how to cite: Moulodi N, Jalali M, Sarrafzadeh J, Azadinia F, Shakourirad A. Intra- and Inter-rater Reliability of a Magnetic Resonance Imaging-Based Volumetric Analysis of the Abductor Hallucis Muscle. Innov J Radiol. 2022;19(3):e128725. https://doi.org/10.5812/iranjradiol-128725.
### Abstract
#### Background:
The muscle volume considerably changes with aging, pathologies, mechanical loading and exercise, and immobilization. It is recognized as an important parameter that can be measured by various methods to evaluate the effectiveness of interventions focusing on muscle strengthening and function. However, before the application of any measurement method, their reliability needs to be investigated and established.
#### Objectives:
This study aimed to evaluate the inter- and intra-rater reliability of the manual measurement method of the abductor hallucis muscle volume in feet with hallux valgus deformities using magnetic resonance imaging (MRI).
#### Patients and Methods:
The MRI images of the feet of 15 samples with a hallux valgus deformity were selected in this study. The cross-sectional areas of the abductor hallucis muscle were measured in the cuts along the entire length of the foot and multiplied by slice thickness. Two trained raters performed the measurements. The second rater repeated the measurements after five days to eliminate the memory effect. The intra-rater reliability and inter-rater reliability were assessed based on the intraclass correlation coefficient [ICC (2, 1)] to evaluate the extent of agreement between the raters at a 95% confidence interval.
#### Results:
The between- and within-rater ICCs were 0.92 (0.79 - 0.97) and 0.99 (0.97 - 0.99), respectively. The standard error of measurements was also small in both inter-rater (6.2%) and intra-rater (2.1%) reliability analyses.
#### Conclusion:
The manually outlined slice-by-slice volume measurement of the abductor hallucis muscle based on MRI images showed excellent inter- and intra-rater reliability. The excellent intra-rater reliability, besides the lower standard error percentage of measurements, indicates the superiority of measurements by a single person. However, further studies with a larger sample size are recommended.
### 1. Background
The muscle volume is a reliable indicator of the physical capacity of a muscle in force and power generation (1). It considerably changes with aging, pathologies, mechanical loading and exercise, and immobilization (2, 3). This parameter can be used to evaluate the effectiveness of interventions focusing on muscle strengthening and function. Generally, various methods are used to measure the muscle volume (4). Nonetheless, before the application of any measurement method for research or clinical applications, their reliability needs to be established (5). Reliability is defined as the extent to which measurements can be replicated. In other words, it reflects not only the extent of correlation, but also the level of agreement between measurements. Without reliability measurements, we can neither rely on our measurements, nor draw any rational conclusions (6, 7).
The weakness of the intrinsic foot (IF) muscles is an important issue that has been investigated in different deformities. The weakness of these muscles may alter the foot alignment (8); the collapse of the medial longitudinal arch of the foot is an example of foot misalignment (9-11). In this regard, Chang et al. compared the volume of IF muscles between patients with plantar fasciitis and healthy individuals by separating the muscle tissues from non-muscular tissues in magnetic resonance (MR) images. In this study, the muscle borders were digitally marked, the intensity of muscle signals was examined, and the volume of muscles was calculated. The volume of intrinsic muscles in the forefoot of the plantar fasciitis group was 5.2% smaller than that of healthy feet (12).
The hallux valgus (HV) deformity is another example of muscle weakness. In this deformity, the head of the first metatarsal bone is deviated medially, the hallux is deviated laterally, and the abductor hallucis (AbdH) muscle is displaced relative to the metatarsophalangeal joint (13). From a clinical perspective, the role of the AbdH muscle is yet to be established. However, previous studies suggest that the AbdH muscle, its distal attachment, and muscle imbalance play a role in the etiology and treatment of HV deformities (14, 15). The measurement of the AbdH muscle in HV deformities and investigation of the effects of interventions on the volume of this muscle can provide useful information for the management of this prevalent deformity. Nevertheless, it is somewhat challenging to measure different characteristics of the IF muscles due to their small size and depth.
Magnetic resonance imaging (MRI) is considered as the reference standard technique to measure the muscle volume (16), as it yields three-dimensional images of the muscle and facilitates the assessment of muscle mass (17, 18). It also provides high-contrast, high-resolution images of soft tissues across multiple planes and enables examining the anatomical and functional characteristics of foot muscles (19). There are many techniques that can be used manually, semi-automatically, and automatically to examine and segment muscles from MRI images (20). Four manual techniques have been used in previous studies to measure the muscle volume. Slice-by-slice segmentation of the muscle cross-sectional area (CSA) is one of the manual techniques used as a standard reference method in studies on large muscles (21).
### 2. Objectives
The reliability assessment of measurements is especially important in examining the effects of clinical treatment, allowing researchers to evaluate between- and within-group changes over time. The manual technique has been mostly used in large muscles to calculate the muscle volume, while the reliability of this technique has not been investigated in the AbdH muscle, especially in HV deformities that greatly affect this muscle. Therefore, the present study aimed to assess the intra- and inter-rater reliability of the manual measurement of the AbdH muscle volume in HV deformities for clinical and research purposes to evaluate the effects of treatment.
### 3. Patients and Methods
#### 3.1. Study Sample
The MRI images of the right foot of 15 women with HV deformities were acquired in the frontal view. The sample size was estimated based on the hypothesized value of intraclass correlation coefficient (ICC) (0.6) (22), α value of 0.05, and test power of 80% (β = 0.2) for two replicated measurements. All participants signed a written informed consent form. This study was approved by the institutional review board of Iran University of Medical Sciences, Tehran, Iran (IR.IUMS.REC.1399.1037). The participants were screened for medical and orthopedic conditions that would preclude MRI procedures. The inclusion criteria were age of 18 - 44 years and lack of any underlying diseases, diabetes, gout, leprosy, or neurological conditions. Besides, they had no history of foot injuries (e.g., fractures and dislocations). A summary of the participants’ demographic information is presented in Table 1.
Table 1. The Demographic Information of the Participants
VariablesValues
Number15
Age (y)30.40 ± 5.56
Height (cm)162.27 ± 6.57
Weight (kg)60.80 ± 9.23
BMI (kg/m2)23.00 ± 3.04
Hallux valgus angle (degree)18.80 ± 3.46
#### 3.2. Image Acquisition
The MRI images of the right foot were acquired using an MRI system (MAGNETOM Symphony 1.5 Tesla, Siemens, Germany) with a one-channel knee coil. The participants were positioned in a supine position with the foot in a neutral position (rest position) and perpendicular to the bed inside the coil (23). To prevent extra movement during imaging, the foot and ankle were fixed with side pillows. The knee coil was used on the target foot to achieve the highest resolution without missing the signal strength-to-noise ratio (23). The position of the foot was maintained in a way that the natural shape of the soft tissue would not be altered; by keeping the foot straight, the locations of the muscle origin and insertion were in line. The images were recorded in three planes. The examination period was 26 minutes for each foot (Figure 1).
The MRI images were recorded from January 2021 to October 2021. The images were prepared based on the following parameters: repetition time, 540 ms; echo time, 12 ms; average, 3; slice thickness, 3 mm; inter-slice gap, 0 mm; field of view, 240×120 mm; flip angle, 90°; and matrix size, 320 × 200. The field of view covered one foot, depending on the foot length from the back part of the heel to the end of the longest toe.
#### 3.3. Muscle CSA Measurements
The cross-sections of the AbdH muscle in the frontal plane were manually outlined once by one of the raters (FD) and twice by the second rater (NM) in the target slices. The raters were trained by a professional to decide on the origin and insertion slices, separate the muscle borders, use the software utilities, measure the CSA on each slice, and calculate the total volume of the muscle. Before independent measurements by the raters, they practiced the method several times together to ensure the uniformity of their measurement technique. The CSA of the AbdH muscle was marked in each cut and measured using the Marco Packs software (Tahavolat Novin Yademan Co., Tehran, Iran), connected to a Siemens device. The entire length of the foot was examined in the frontal view (11). The number of cuts in which the muscle was defined varied from one person to another due to differences in the length of the feet (42 cuts on average).
The measurements were performed from the origin of the muscle on the calcaneus to the insertion of the muscle tissue in the forefoot. The CSA of the muscle in each cut was recorded in mm2 in Microsoft Excel software. There was a black area around the AbdH muscle, called a chemical shift, which occurs when there is fat surrounding the muscle. Different signal intensities allowed for the separation of muscle tissues from chemical shifts around the muscle compartments (24). Meanwhile, different views of each cut were evaluated to ensure that the outlines were carefully selected (Figure 2). Next, the sum of CSA measurements for all cuts was calculated. The total muscle volume was measured by multiplying the sum of total CSAs by the thickness of slices (3 mm) (muscle volume = ∑CSA × 3) (24-27).
#### 3.4. Reliability of Measurements
The manual slice-by-slice CSA segmentation of muscles is a standard method used in previous studies; however, it is a very time-consuming procedure due to the examination of all slices. Compared to other techniques, this technique can provide more accurate and detailed information (17). In this study, two trained raters outlined the AbdH muscle CSAs in the target cuts (55 cuts in the frontal view); this process was performed by both raters for each image separately (23); the raters were blind to the findings of one another. Next, the reliability of this method was analyzed for the two raters. Regarding the intra-rater reliability, the second rater repeated the measurements five days after the initial measurements (on average) to eliminate the memory effect (28).
#### 3.5. Statistical Analysis
The intra-rater reliability and inter-rater reliability were assessed in SPSS version 21.0 (IBM Corp. Released 2012. IBM SPSS Statistics for Windows, Version 21.0. Armonk, NY: IBM Corp.) by measuring the ICC. The reliability coefficients range from zero to one, with values closer to one representing higher reliability (29). The mean values and standard deviations were calculated for all variables. The ICC was measured by using the two-way random-effects and absolute agreement [ICC (2, 1)] model to evaluate the extent of agreement between the raters at a 95% confidence interval. In this model, each sample was measured by one rater, who represented a larger community of raters (reliability analysis based on single measurements) (28, 29). According to Portney and Watkins (2009), ICC values below 0.5 indicate poor reliability, values of 0.5 - 0.75 suggest moderate reliability, values of 0.75 - 0.90 suggest good reliability, and values > 0.90 represent excellent reliability (7). The standard error of measurement (SEM) was calculated by the following formula (Equation 1) to estimate the expected error value in measurements:
Equation 1.$SEM=SD×1-ICC$
SD, standard deviation.
The minimal detectable change (MDC) was also measured according to the following formula (Equation 2) (30):
Equation 2.
CI, confidence interval.
This procedure aimed to determine the magnitude of change that would exceed the minimal error of measurement at a 95% confidence interval; the observed changes between the two tests accurately represented the difference (not a measurement error) (30).
### 4. Results
#### 4.1. Inter-rater Reliability
Table 2 presents the results of reliability analysis between the two raters for 15 samples of the right foot with HV deformity. The descriptive data (mean and standard deviation) are also reported for the measurements. The ICC for the inter-rater reliability of the AbdH muscle volume measurement was excellent (0.92). Also, the SEM was small (621.13 mm3), which indicated the accuracy of measurements.
Table 2. The Results of Inter-rater Reliability Analysis
MeasureVolume measurement by rater 1 (mm3) (mean ± SD)Volume measurement by rater 2 (mm3) (mean ± SD)ICC (95% CI)SEMMDCP-value
CSA of the AbdH muscle10262.07 ± 2196.0310093.73 ± 2154.010.92 (0.79 - 0.97)621.131721.680.00
#### 4.2. Intra-rater Reliability
The results of intra-rater reliability analysis for 15 samples of the right foot with HV deformity are presented in Table 3. The intra-rater reliability was also found to be excellent (0.99). The SEM value for the intra-rater reliability was lower than that of the inter-rater reliability (215.40 mm3).
Table 3. The Results of Intra-rater Reliability Analysis
MeasureVolume measurement by rater 2 (mm3) (mean ± SD)Volume measurement by rater 2, repeat (mm3) (mean ± SD)ICC (95% CI)SEMMDCP-value
CSA of the AbdH muscle10093.73 ± 2154.019954.69 ± 2123.890.99 (0.97 - 0.99)215.40597.050.00
### 5. Discussion
This study aimed to evaluate the inter- and intra-rater reliability of a manual method used for measuring the AbdH muscle volume based on the MRI images of feet with HV deformity for research and clinical purposes. Before interpreting the results, it is necessary to evaluate the reliability of methods used for measuring the characteristics of muscles responsible for the formation of HV deformities. The ICCs for inter-rater and intra-rater reliability indicated excellent reliability. The SEM% for intra- and inter-rater agreement was estimated at 6.2% and 2.1%, respectively, which is comparable to the results of previous studies. In this regard, in a study by Franettovich Smith et al., the SEM% of inter- and intra-rater agreement was 4% and 6%, respectively for the CSA measurement of the AbdH muscle by ultrasound (31).
Moreover, based on the findings reported by Jung et al., the SEM% was estimated at 3.8% (32); nevertheless, it should be noted that both of these studies used the US imaging method. Generally, the SEM value represents the measurement error (33). An error may occur while detecting the exact location and borders of the muscle among other intrinsic muscles (33). The manual tracing of borders can also influence the measurements. Besides, the resolution of MRI images is an important factor that may affect the precision of muscle borders. Two raters were trained in several sessions, during which reference images, such as anatomical atlases of foot muscles, were used to determine the exact path and borders in different cuts; the prior experience of raters in such measurements may be the cause of high ICC and low SEM values (28).
Additionally, the inter- and intra-rater MDC95 values were estimated at 17.2% and 5.9%, respectively in the present study; the MDC value represents the potential to detect changes exceeding the measurement error for research or clinical applications. Therefore, if a single muscle volume measurement technique is employed by a single rater, not all changes in the muscle volume (< 5.9%) are actual changes. This finding is in line with the results of a study by Jung et al., which showed significant changes in the AbdH muscle CSA on ultrasound images after two types of interventions (32). Moreover, Hing et al. evaluated the reliability of two ultrasound machines and found that a change greater than 21.25% is needed to be 95% confident that a real change has occurred in the AbdH muscle CSA (34).
Similarly, Lund et al. examined inter- and intra-rater differences in using a manual method to measure the muscle volume of the dorsal ankle (tibialis anterior muscle, extensor digitorum longus, and extensor hallucis longus) in MRI images. Overall, these studies aimed to determine the number of slices needed for calculations and reported excellent inter- and intra-rater reliability (0.98 - 1.0) (16). It is known that the volume of these muscles (tibialis anterior muscle, extensor digitorum longus, and extensor hallucis longus) is larger than that of deep foot muscles, which may make it easier to identify and follow their path. In a validity and reliability study of a semi-automatic method for discriminating adipose tissue, subcutaneous fat, and intrinsic muscles of the foot, the ICC was mostly above 0.95, which indicated a high level of agreement among therapists (23). Also, Pons et al. examined the validity and reliability of automatic, semi-automatic, and manual techniques, which were used for measuring the muscle volume based on MRI images in healthy population. For cases of muscle pathology, more data on metrological quality of techniques are required. In addition, techniques that simplified the segmentation, made errors in volume and shape estimation (20). Previous research has investigated the reliability of slice-by-slice measurements. The intra-rater reliability was good to excellent in four studies (0.7 - 1.0) (21, 33, 35, 36), and inter-rater reliability was moderate to good in eight studies (0.5 - 0.89) (10, 21, 33, 35-39). Seven studies used manual methods to calculate the total volume of muscles by summing up the measured CSAs in all slices, similar to the method used in the current study (33, 35, 36, 38, 40-42). However, to the best of our knowledge, no study has yet evaluated our manual method to measure intrinsic foot muscles, especially the AbdH muscle. After muscle segmentation, seven methods were used to calculate the muscle volume. There was no measurement error in volume calculations, and error was related to the time of muscle segmentation (20).
In previous studies, the IF muscles, which are located deep within several layers, were commonly classified in groups due to their small and irregular size (11, 23, 24). The separation of a particular muscle from the adjacent intrinsic muscles is a somewhat difficult procedure. To find the beginning and end of a muscle, greater accuracy is needed, since there is a likelihood of measurement error. However, this is not an issue in the middle slices, as the border of muscles is easily separable. The measurement of the IF muscle volume is challenging because of its arrangement in a four-layer complex; therefore, it is very difficult to differentiate these muscles from others (43).
In individuals with HV deformities, the path of the AbdH muscle may be displaced below the head of the first metatarsal bone, depending on the severity of deformity (14, 15). Following changes in the muscle anatomy and biomechanics in individuals with HV deformities, muscle imbalance will develop between the abductor and adductor muscles of the hallux (15). Based on the results of a study by Stewart et al., significant changes were observed in the mediolateral width, dorsoplantar thickness, and CSA of the AbdH muscle between feet with and without HV based on ultrasound data. However, no significant changes were observed in different degrees of deformity (44). The reliability analysis of the AbdH muscle volume measurement in HV patients provides an important opportunity to gain further insight into the effects of interventions and strategies that focus on improving the strengths and functions of this small muscle by monitoring any related changes.
The limitations of this study include because of time-consuming image segmentation, measurement done one time by each rater; therefore, the absolute agreement was investigated and average reliability was not reported. A lack of comparison between the manual technique and automatic techniques is another limitation of this study.
In conclusion, the inter- and intra-rater reliability of the AbdH muscle volume measurement based on slice-by-slice examination in MRI images was found to be excellent. Therefore, it can be used as a reproducible method to measure the rate of change in the AbdH muscle volume in various treatments or research applications. Due to the excellent intra-rater reliability and lower standard error percentage of measurements, a single person is preferred to perform the measurements in comparative studies. Further research with a larger sample size is recommended.
### References
• 1.
Fukunaga T, Miyatani M, Tachi M, Kouzaki M, Kawakami Y, Kanehisa H. Muscle volume is a major determinant of joint torque in humans. Acta Physiol Scand. 2001;172(4):249-55. [PubMed ID: 11531646]. https://doi.org/10.1046/j.1365-201x.2001.00867.x.
• 2.
Narici MV, Maganaris CN, Reeves ND, Capodaglio P. Effect of aging on human muscle architecture. J Appl Physiol (1985). 2003;95(6):2229-34. [PubMed ID: 12844499]. https://doi.org/10.1152/japplphysiol.00433.2003.
• 3.
Marcon M, Ciritsis B, Laux C, Nanz D, Nguyen-Kim TD, Fischer MA, et al. Cross-sectional area measurements versus volumetric assessment of the quadriceps femoris muscle in patients with anterior cruciate ligament reconstructions. Eur Radiol. 2015;25(2):290-8. [PubMed ID: 25358592]. https://doi.org/10.1007/s00330-014-3424-2.
• 4.
Soysa A, Hiller C, Refshauge K, Burns J. Importance and challenges of measuring intrinsic foot muscle strength. J Foot Ankle Res. 2012;5(1):29. [PubMed ID: 23181771]. [PubMed Central ID: PMC3544647]. https://doi.org/10.1186/1757-1146-5-29.
• 5.
Koo TK, Li MY. A Guideline of Selecting and Reporting Intraclass Correlation Coefficients for Reliability Research. J Chiropr Med. 2016;15(2):155-63. [PubMed ID: 27330520]. [PubMed Central ID: PMC4913118]. https://doi.org/10.1016/j.jcm.2016.02.012.
• 6.
Bruton A, Conway JH, Holgate ST. Reliability: What is it, and how is it measured? Physiotherapy. 2000;86(2):94-9. https://doi.org/10.1016/s0031-9406(05)61211-4.
• 7.
Portney LG, Watkins MP. Foundations of clinical research: applications to practice. 892. New Jersey, USA: Pearson; 2009.
• 8.
Moulodi N, Azadinia F, Ebrahimi-Takamjani I, Atlasi R, Jalali M, Kamali M. The functional capacity and morphological characteristics of the intrinsic foot muscles in subjects with Hallux Valgus deformity: A systematic review. Foot (Edinb). 2020;45:101706. [PubMed ID: 33039908]. https://doi.org/10.1016/j.foot.2020.101706.
• 9.
Andersen H. Muscular endurance in long-term IDDM patients. Diabetes Care. 1998;21(4):604-9. [PubMed ID: 9571350]. https://doi.org/10.2337/diacare.21.4.604.
• 10.
Andersen H, Stalberg E, Gjerstad MD, Jakobsen J. Association of muscle strength and electrophysiological measures of reinnervation in diabetic neuropathy. Muscle Nerve. 1998;21(12):1647-54. [PubMed ID: 9843064]. https://doi.org/10.1002/(sici)1097-4598(199812)21:12<1647::aid-mus4>3.0.co;2-d.
• 11.
Bus SA, Yang QX, Wang JH, Smith MB, Wunderlich R, Cavanagh PR. Intrinsic muscle atrophy and toe deformity in the diabetic neuropathic foot: a magnetic resonance imaging study. Diabetes Care. 2002;25(8):1444-50. [PubMed ID: 12145248]. https://doi.org/10.2337/diacare.25.8.1444.
• 12.
Chang R, Kent-Braun JA, Hamill J. Use of MRI for volume estimation of tibialis posterior and plantar intrinsic foot muscles in healthy and chronic plantar fasciitis limbs. Clin Biomech (Bristol, Avon). 2012;27(5):500-5. [PubMed ID: 22166747]. https://doi.org/10.1016/j.clinbiomech.2011.11.007.
• 13.
Eustace S, Williamson D, Wilson M, O'Byrne J, Bussolari L, Thomas M, et al. Tendon shift in hallux valgus: observations at MR imaging. Skeletal Radiol. 1996;25(6):519-24. [PubMed ID: 8865484]. https://doi.org/10.1007/s002560050128.
• 14.
Brenner E. Insertion of the abductor hallucis muscle in feet with and without hallux valgus. Anat Rec. 1999;254(3):429-34. [PubMed ID: 10096675]. https://doi.org/10.1002/(SICI)1097-0185(19990301)254:3<429::AID-AR14>3.0.CO;2-5.
• 15.
Arinci Incel N, Genc H, Erdem HR, Yorgancioglu ZR. Muscle imbalance in hallux valgus: an electromyographic study. Am J Phys Med Rehabil. 2003;82(5):345-9. [PubMed ID: 12704272]. https://doi.org/10.1097/01.PHM.0000064718.24109.26.
• 16.
Lund H, Christensen L, Savnik A, Boesen J, Danneskiold-Samsoe B, Bliddal H. Volume estimation of extensor muscles of the lower leg based on MR imaging. Eur Radiol. 2002;12(12):2982-7. [PubMed ID: 12439580]. https://doi.org/10.1007/s00330-002-1334-1.
• 17.
Tothill P, Stewart AD. Estimation of thigh muscle and adipose tissue volume using magnetic resonance imaging and anthropometry. J Sports Sci. 2002;20(7):563-76. [PubMed ID: 12166882]. https://doi.org/10.1080/026404102760000062.
• 18.
Nakatani M, Takai Y, Akagi R, Wakahara T, Sugisaki N, Ohta M, et al. Validity of muscle thickness-based prediction equation for quadriceps femoris volume in middle-aged and older men and women. Eur J Appl Physiol. 2016;116(11-12):2125-33. [PubMed ID: 27590314]. https://doi.org/10.1007/s00421-016-3464-1.
• 19.
Farjoodi P, Mesfin A, Carrino JA, Khanna AJ. Magnetic resonance imaging of the musculoskeletal system: basic science, pulse sequences, and a systematic approach to image interpretation. J Bone Joint Surg Am. 2010;92(Suppl 2):105-16. [PubMed ID: 21189247]. https://doi.org/10.2106/JBJS.J.00783.
• 20.
Pons C, Borotikar B, Garetier M, Burdin V, Ben Salem D, Lempereur M, et al. Quantifying skeletal muscle volume and shape in humans using MRI: A systematic review of validity and reliability. PLoS One. 2018;13(11). e0207847. [PubMed ID: 30496308]. [PubMed Central ID: PMC6264864]. https://doi.org/10.1371/journal.pone.0207847.
• 21.
Nordez A, Jolivet E, Sudhoff I, Bonneau D, de Guise JA, Skalli W. Comparison of methods to assess quadriceps muscle volume using magnetic resonance imaging. J Magn Reson Imaging. 2009;30(5):1116-23. [PubMed ID: 19856445]. https://doi.org/10.1002/jmri.21867.
• 22.
Hummel J, Skweres J, Heineman N, Dessouky R, Xi Y, Zhang L, et al. Hallux valgus assessment on X-ray and Magnetic resonance Imaging (MRI): Correlation with qualitative soft tissue and internal derangement findings on MRI. Eur J Radiol. 2019;113:24-31. [PubMed ID: 30927954]. https://doi.org/10.1016/j.ejrad.2019.01.035.
• 23.
Cheuy VA, Commean PK, Hastings MK, Mueller MJ. Reliability and validity of a MR-based volumetric analysis of the intrinsic foot muscles. J Magn Reson Imaging. 2013;38(5):1083-93. [PubMed ID: 23450691]. [PubMed Central ID: PMC4400725]. https://doi.org/10.1002/jmri.24069.
• 24.
Andersen H, Gjerstad MD, Jakobsen J. Atrophy of foot muscles: a measure of diabetic neuropathy. Diabetes Care. 2004;27(10):2382-5. [PubMed ID: 15451904]. https://doi.org/10.2337/diacare.27.10.2382.
• 25.
Fukunaga T, Roy RR, Shellock FG, Hodgson JA, Day MK, Lee PL, et al. Physiological cross-sectional area of human leg muscles based on magnetic resonance imaging. J Orthop Res. 1992;10(6):928-34. [PubMed ID: 1403308]. https://doi.org/10.1002/jor.1100100623.
• 26.
Severinsen K, Andersen H. Evaluation of atrophy of foot muscles in diabetic neuropathy -- a comparative study of nerve conduction studies and ultrasonography. Clin Neurophysiol. 2007;118(10):2172-5. [PubMed ID: 17709290]. https://doi.org/10.1016/j.clinph.2007.06.019.
• 27.
Severinsen K, Obel A, Jakobsen J, Andersen H. Atrophy of foot muscles in diabetic patients can be detected with ultrasonography. Diabetes Care. 2007;30(12):3053-7. [PubMed ID: 17717286]. https://doi.org/10.2337/dc07-0108.
• 28.
Fortin M, Dobrescu O, Jarzem P, Ouellet J, Weber MH. Quantitative Magnetic Resonance Imaging Analysis of the Cervical Spine Extensor Muscles: Intrarater and Interrater Reliability of a Novice and an Experienced Rater. Asian Spine J. 2018;12(1):94-102. [PubMed ID: 29503688]. [PubMed Central ID: PMC5821939]. https://doi.org/10.4184/asj.2018.12.1.94.
• 29.
Shrout PE, Fleiss JL. Intraclass correlations: uses in assessing rater reliability. Psychol Bull. 1979;86(2):420-8. [PubMed ID: 18839484]. https://doi.org/10.1037//0033-2909.86.2.420.
• 30.
Jeon I, Kim M. Reliability of Thickness Measurements of the Abductor Hallucis Muscle Using the Spring Gauge Technique in Hallux Valgus Subjects: An Ultrasonographic Study. J Korean Phys Ther. 2016;28(2):119-23. https://doi.org/10.18857/jkpt.2016.28.2.119.
• 31.
Franettovich Smith MM, Hides JA, Hodges PW, Collins NJ. Intrinsic foot muscle size can be measured reliably in weight bearing using ultrasound imaging. Gait Posture. 2019;68:369-74. [PubMed ID: 30583193]. https://doi.org/10.1016/j.gaitpost.2018.12.012.
• 32.
Jung DY, Koh EK, Kwon OY. Effect of foot orthoses and short-foot exercise on the cross-sectional area of the abductor hallucis muscle in subjects with pes planus: a randomized controlled trial. J Back Musculoskelet Rehabil. 2011;24(4):225-31. [PubMed ID: 22142711]. https://doi.org/10.3233/BMR-2011-0299.
• 33.
Tingart MJ, Apreleva M, Lehtinen JT, Capell B, Palmer WE, Warner JJ. Magnetic resonance imaging in quantitative analysis of rotator cuff muscle volume. Clin Orthop Relat Res. 2003;(415):104-10. [PubMed ID: 14612636]. https://doi.org/10.1097/01.blo.0000092969.12414.e1.
• 34.
Hing WA, Rome K, Cameron AF. Reliability of measuring abductor hallucis muscle parameters using two different diagnostic ultrasound machines. J Foot Ankle Res. 2009;2:33. [PubMed ID: 19917127]. [PubMed Central ID: PMC2784754]. https://doi.org/10.1186/1757-1146-2-33.
• 35.
Smeulders MJ, van den Berg S, Oudeman J, Nederveen AJ, Kreulen M, Maas M. Reliability of in vivo determination of forearm muscle volume using 3.0 T magnetic resonance imaging. J Magn Reson Imaging. 2010;31(5):1252-5. [PubMed ID: 20432364]. https://doi.org/10.1002/jmri.22153.
• 36.
Springer I, Muller M, Hamm B, Dewey M. Intra- and interobserver variability of magnetic resonance imaging for quantitative assessment of abductor and external rotator muscle changes after total hip arthroplasty. Eur J Radiol. 2012;81(5):928-33. [PubMed ID: 21354740]. https://doi.org/10.1016/j.ejrad.2011.01.113.
• 37.
Morse CI, Degens H, Jones DA. The validity of estimating quadriceps volume from single MRI cross-sections in young men. Eur J Appl Physiol. 2007;100(3):267-74. [PubMed ID: 17342544]. https://doi.org/10.1007/s00421-007-0429-4.
• 38.
Valentin S, Yeates TD, Licka T, Elliott J. Inter-rater reliability of trunk muscle morphometric analysis. J Back Musculoskelet Rehabil. 2015;28(1):181-90. [PubMed ID: 25628042]. [PubMed Central ID: PMC5614442]. https://doi.org/10.3233/BMR-140552.
• 39.
Skorupska E, Keczmer P, Lochowski RM, Tomal P, Rychlik M, Samborski W. Reliability of MR-Based Volumetric 3-D Analysis of Pelvic Muscles among Subjects with Low Back with Leg Pain and Healthy Volunteers. PLoS One. 2016;11(7). e0159587. [PubMed ID: 27459688]. [PubMed Central ID: PMC4961367]. https://doi.org/10.1371/journal.pone.0159587.
• 40.
Barnouin Y, Butler-Browne G, Voit T, Reversat D, Azzabou N, Leroux G, et al. Manual segmentation of individual muscles of the quadriceps femoris using MRI: a reappraisal. J Magn Reson Imaging. 2014;40(1):239-47. [PubMed ID: 24615897]. https://doi.org/10.1002/jmri.24370.
• 41.
Yamauchi K, Yoshiko A, Suzuki S, Kato C, Akima H, Kato T, et al. Estimation of individual thigh muscle volumes from a single-slice muscle cross-sectional area and muscle thickness using magnetic resonance imaging in patients with knee osteoarthritis. J Orthop Surg (Hong Kong). 2017;25(3):2309499017743100. [PubMed ID: 29212436]. https://doi.org/10.1177/2309499017743101.
• 42.
Vanmechelen IM, Shortland AP, Noble JJ. Lower limb muscle volume estimation from maximum cross-sectional area and muscle length in cerebral palsy and typically developing individuals. Clin Biomech (Bristol, Avon). 2018;51:40-4. [PubMed ID: 29179032]. https://doi.org/10.1016/j.clinbiomech.2017.11.004.
• 43.
Crofts G, Angin S, Mickle KJ, Hill S, Nester CJ. Reliability of ultrasound for measurement of selected foot structures. Gait Posture. 2014;39(1):35-9. [PubMed ID: 23791782]. https://doi.org/10.1016/j.gaitpost.2013.05.022.
• 44.
Stewart S, Ellis R, Heath M, Rome K. Ultrasonic evaluation of the abductor hallucis muscle in hallux valgus: a cross-sectional observational study. BMC Musculoskelet Disord. 2013;14:45. [PubMed ID: 23356426]. [PubMed Central ID: PMC3564793]. https://doi.org/10.1186/1471-2474-14-45.
Copyright © 2022, Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/) which permits copy and redistribute the material just in noncommercial usages, provided the original work is properly cited. | 2023-03-26 08:17:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3822442591190338, "perplexity": 11430.1395284477}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945440.67/warc/CC-MAIN-20230326075911-20230326105911-00358.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php?title=2014_AMC_10A_Problems/Problem_11&diff=next&oldid=138515 | # Difference between revisions of "2014 AMC 10A Problems/Problem 11"
The following problem is from both the 2014 AMC 12A #8 and 2014 AMC 10A #11, so both problems redirect to this page.
## Problem
A customer who intends to purchase an appliance has three coupons, only one of which may be used:
Coupon 1: $10\%$ off the listed price if the listed price is at least $\textdollar50$
Coupon 2: $\textdollar 20$ off the listed price if the listed price is at least $\textdollar100$
Coupon 3: $18\%$ off the amount by which the listed price exceeds $\textdollar100$
For which of the following listed prices will coupon $1$ offer a greater price reduction than either coupon $2$ or coupon $3$?
$\textbf{(A) }\textdollar179.95\qquad \textbf{(B) }\textdollar199.95\qquad \textbf{(C) }\textdollar219.95\qquad \textbf{(D) }\textdollar239.95\qquad \textbf{(E) }\textdollar259.95\qquad$
## Solution 1
Let the listed price be $x$. Since all the answer choices are above $\textdollar100$, we can assume $x > 100$. Thus the discounts after the coupons are used will be as follows:
Coupon 1: $x\times10\%=.1x$
Coupon 2: $20$
Coupon 3: $18\%\times(x-100)=.18x-18$
For coupon $1$ to give a greater price reduction than the other coupons, we must have $.1x>20\implies x>200$ and $.1x>.18x-18\implies.08x<18\implies x<225$.
The only choice that satisfies such conditions is $\boxed{\textbf{(C)}\ \textdollar219.95}$
## Solution 2 (Using The Answers)
For coupon $1$ to be the most effective, we want 10% of the price to be greater than 20. This clearly occurs if the value is over 200. For coupon 1 to be more effective than coupon 3, we want to minimize the value over 200, so $\boxed{\textbf{(C) }\textdollar219.95}$ is the smallest number over 200.
~savannahsolver | 2021-03-04 18:01:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 22, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3213147819042206, "perplexity": 1151.8086098346623}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178369512.68/warc/CC-MAIN-20210304174506-20210304204506-00629.warc.gz"} |
https://www.physicsforums.com/threads/the-magnus-effect.59046/ | # The magnus effect
for a soccer game I'm programming, i want to calculate the position and velocity of the ball. I can get those values when I have constant acceleration, but I don't understand how to add the Magnus force. I have read some articles in the internet, and I found a formula I just can't understand:
$$F_{m}=\frac{2\pi^2 \rho\ \omega vr^4} {2r}$$
is it right? so I could say:
$$F_{m}=\pi^2 \rho\ \omega vr^3$$
But which is the velocity it refers? and, how can I relate it to v(t) and x(t)?
Could somebody explain it to me, and how to calculate position adding the magnus force?
Related General Physics Workshop News on Phys.org
"The magnus effect"
### Physics Forums Values
We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving | 2019-05-21 17:07:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35342487692832947, "perplexity": 2216.6717225279226}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256494.24/warc/CC-MAIN-20190521162634-20190521184634-00358.warc.gz"} |
http://www.ck12.org/book/CK-12-Texas-Instruments-Algebra-I-Student-Edition/r1/section/10.2/ | <meta http-equiv="refresh" content="1; url=/nojavascript/"> Factoring Special Cases | CK-12 Foundation
You are reading an older version of this FlexBook® textbook: CK-12 Texas Instruments Algebra I Student Edition Go to the latest version.
# 10.2: Factoring Special Cases
Difficulty Level: At Grade Created by: CK-12
This activity is intended to supplement Algebra I, Chapter 9, Lesson 6.
In this activity, you will explore:
• factoring a perfect-square trinomial
• factoring a difference of squares
• using geometry to prove rules for factoring special quadratic expressions
## Problem 1 - Factoring a Perfect-Square Trinomial
Any trinomial of the form $a^2 + 2ab + b^2$ is a perfect-square trinomial. If you recognize a perfect-square trinomial, you can factor it immediately as $(a + b)^2$.
To see why $a^2 + 2ab + b^2 = (a + b)^2$ , start the CabriJr app by pressing the APPS button and choosing it from the menu.
Open the file FACTOR1 by pressing Y= to open then F1: File menu, choosing Open, and choosing it from the list.
This file shows $2$ squares and $2$ rectangles, with their dimensions labeled.
What is the area of each shape? On the screenshot at right, label each shape with its area.
• Arrange the shapes to form a square. To move a shape, move the cursor over it (so that the entire shape becomes a moving dashed line) and press ALPHA to grab it, then move it with the arrow keys. When the shape is positioned where you want it, press ENTER to let it go.
• The area of this square is equal to the sum of the areas of the shapes that make it up. What is the area of the square? Have you seen this trinomial before?
• How long is one side of the square?
• Using the formula $A = s^2$ for the area of a square with side length $s$ what is the area of this square?
You have shown that the area of this square is equal to $a^2 + 2ab + b^2$ and also equal to $(a + b)^2$. Therefore $a^2 + 2ab + b^2 = (a + b)^2$ You have proved the rule for factoring a perfect-square trinomial!
## Problem 2 - Factoring a Difference of Squares
Any trinomial of the form $m^2 - n^2$ is a difference of squares. If you recognize a difference of squares, you can factor it immediately as $(m + n)(m - n)$.
To see why $m^2 - n^2 = (m + n)(m - n)$, start the CabriJr app by pressing the $A$ button and choosing it from the menu.
Open the file FACTOR2 by pressing $Y=$ to open then F1: File menu, choosing Open, and choosing it from the list.
This file shows $2$ squares with their dimensions labeled $m$ and $n$.
What is the area of each square? On the screenshot at right, label each square with its area.
How can you represent the area $m^2 - n^2$ with these squares? Move the $n^2$ square on top of the $m^2$ rectangle so that their corners align. If you imagine cutting the smaller square out of the larger square, the $L-$shaped area that remains is equal to $m^2 - n^2$.
We know that the area of the $L-$shape is $m^2 - n^2$, but there is also another way to find its area: by taking it apart and rearranging the pieces into a single long rectangle.
Open the CabriJr file FACTOR3, which shows the same shapes, but with the $L-$shaped area $(m^2 - n^2)$ divided into two rectangles.
Rotate the smaller rectangle about point $P$ (at the bottom of the screen) clockwise $90^\circ$. Press TRACE to open the F4: Transform menu and choose Rotation. Move the cursor over the rectangle to highlight it and press $e$ to choose it. Then move the cursor to the point you want to rotate around and press ENTER. Finally, mark the angle of rotation by choosing points $A, B$, and $C$ in turn.
Hide the original small rectangle and the vertices of the rotated image. (Press GRAPH to open the F5: Appearance menu and choose Hide/Show $>$ Objects. Then choose the rectangle and vertices you want to hide.) Now there are two rectangles whose combined area is equal to the area of the original $L-$shape.
Move the larger rectangle (the small rectangle cannot be moved) alongside the rotated image to form one long rectangle.
What are the dimensions of the long rectangle?
Using the formula $A = lw$ for the area of a rectangle and these dimensions, what is the area of this rectangle?
You have shown that the $L-$shaped area is equal to $m^2 - n^2$ and also equal to $(m + n)(m - n)$. Therefore $m^2 - n^2 = (m + n)(m - n)$. You have proved the rule for factoring a difference of squares!
Feb 22, 2012
Oct 31, 2014 | 2015-03-27 10:28:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 39, "texerror": 0, "math_score": 0.5220528244972229, "perplexity": 832.3590470988797}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131296169.46/warc/CC-MAIN-20150323172136-00196-ip-10-168-14-71.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/137082/proof-involving-a-double-integral | Proof involving a double integral?
Problem:
I am stuck on the following problem and I appreciate if someone is willing to help solving it. The problem is as follows:
I am given a uniformly continuous function : $f:\mathbb{R}^2 \rightarrow [0,\infty )$ such that the following condition is satisfied: $$\iint_{ R^2} f(x,y)\,dx\,dy< \infty .$$ The question is to prove that:$$\lim_{| (x,y)| \to \infty}f(x,y)=0$$
-
You have the letter $r$ for two different dummy variables. – anon Apr 26 '12 at 3:54
Hi, your last edit removed most of the problem, rendering the queston incomprehensible. – Johannes Kloos Apr 27 '12 at 12:12
@BoyanKlo: You are the one being disrespectful. Zarrax, nor anyone else, is under any obligation to help you, and when they choose to help you they can do so in any manner they want. I have deleted your comments. Any further such comments will result in suspension. – Zev Chonoles Apr 27 '12 at 15:54
Sadly, this problem is from a 48 hour exam given at some university in the US. A friend of mine who is a first year PHD student there shared with me his homework and exam problems because there were some interesting problems there. Many of the questions of Boyan Klo are from those homekorks and the last two are for the exam. Maybe I am wrong, but it is very unlikely that someone will post exactly the right problems at exactly the time they were given as homework/exam. I hope I am wrong... – Beni Bogosel Apr 27 '12 at 16:13
@Beni: If you have your friend get in contact with their professor, and the professor asks the moderators to delete the questions until the exam is over, we can do so. – Zev Chonoles Apr 27 '12 at 16:17
show 1 more comment
Hint: Try a contrapositive proof. If the limit were not true, you'd have an $\epsilon > 0$ and $(x_n,y_n)$ of magnitude at least $n$ such that $f(x_n,y_n) > \epsilon$. Use the uniform continuity to show there's a little disk $B_n$ centered at $(x_n,y_n)$ such that the integral of $f$ over the disk $B_n$ is at least $\epsilon '$ for some fixed $\epsilon '$....
There are going to be infinitely many $B_n$'s.. so the total integral is infinite. – Zarrax Apr 26 '12 at 5:13 | 2014-04-25 01:02:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8001388311386108, "perplexity": 333.4333638066025}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00118-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://www.hydrol-earth-syst-sci.net/22/4535/2018/ | Journal topic
Hydrol. Earth Syst. Sci., 22, 4535–4545, 2018
https://doi.org/10.5194/hess-22-4535-2018
Hydrol. Earth Syst. Sci., 22, 4535–4545, 2018
https://doi.org/10.5194/hess-22-4535-2018
Research article 28 Aug 2018
Research article | 28 Aug 2018
# Exploring the relationships between warm-season precipitation, potential evaporation, and “apparent” potential evaporation at site scale
Exploring the relationships between warm-season precipitation, potential evaporation, and “apparent” potential evaporation at site scale
Xi Chen1 and Steven G. Buchberger2 Xi Chen and Steven G. Buchberger
• 1College of Arts and Sciences, Department of Geography and Geographic Information Science, University of Cincinnati, Cincinnati, USA
• 2College of Engineering and Applied Science, Department of Civil Engineering and Architectural Engineering and Construction Management, University of Cincinnati, Cincinnati, USA
Correspondence: Xi Chen (xi.chen@uc.edu)
Abstract
Bouchet's complementary relationship and the Budyko hypothesis are two classic frameworks that are inter-connected. To systematically investigate the connections between the two frameworks, we analyze precipitation, pan evaporation, and potential evaporation data at 259 weather stations across the United States. The precipitation and pan evaporation data are from field measurement and the potential evaporation data are collected from a remote-sensing dataset. We use pan evaporation to represent “apparent” potential evaporation, which is different from potential evaporation. With these data, we study the correlations between precipitation and potential evaporation, and between precipitation and “apparent” potential evaporation. The results show that 93 % of the study's weather stations exhibit a negative correlation between precipitation and “apparent” potential evaporation. Also, the aggregated data cloud of precipitation vs. “apparent” potential evaporation with 5312 warm-season data points from 259 weather stations shows a negative trend in which “apparent” potential evaporation decreases with increasing precipitation. On the other hand, no significant correlation is found in the data cloud of precipitation vs. potential evaporation, indicating that precipitation and potential evaporation are independent. We combine a Budyko-type expression, the Turc–Pike equation, with Bouchet's complementary relationship to derive upper and lower Bouchet–Budyko curves, which display a complementary relationship between “apparent” potential evaporation and actual evaporation. The observed warm-season data follow the trend of the Bouchet–Budyko curves. Our study shows the consistency between Budyko's framework and Bouchet's complementary relationship, with the distinction between potential evaporation and “apparent” potential evaporation. The formulated complementary relationship can be used in quantitative modeling practices.
1 Introduction
Potential evaporation (Ep) is a widely used physical variable in hydrologic frameworks. It is the evaporation rate under unlimited land surface water supply (Thornthwaite, 1948). Pan evaporation (Epan) measurement is often used as a surrogate of potential evaporation. However, these two variables are not the same (Brutsaert and Parlange, 1998; Roderick et al., 2009). A stipulation is added in the potential evaporation definition in Van Bavel (1966) and further clarified in Brutsaert (2015) that “the surface vapor pressure be saturated, so that it can be found from the surface temperature.” Therefore, the main difference between potential evaporation and pan evaporation is that pan evaporation is not measured under saturated surface vapor pressure. As a result, potential evaporation can be considered to depend only on the energy supply of climate, while pan evaporation is driven by both energy supply and humidity deficit in the atmosphere (Rotstayn et al., 2006). In Brutsaert and Parlange (1998), the term “apparent” potential evaporation (Epa) is introduced to distinguish pan evaporation from potential evaporation. “Apparent” potential evaporation can be measured by an evaporation pan, while potential evaporation cannot. We acknowledge that there are different definitions of potential evaporation in the literature (Aminzadeh et al., 2016). Our study follows the definition of potential evaporation in Brutsaert and Parlange (1998) and Brutsaert (2015).
Because potential evaporation is energy-driven, it can be used as a physical variable to describe the energy supply in a hydrologic system. For instance, the well-established Budyko framework (Budyko, 1958, 1974) uses precipitation (P) and potential evaporation to represent the relationship between water supply and energy supply, and therefore to describe the impact of long-term climate on the hydrologic cycle. The Budyko framework has been extensively used to analyze interactions between hydrology, climate, vegetation, and other elements in watersheds (Milly, 1994; Zhang et al., 2001; Yang et al., 2007, 2011; Donohue et al., 2007; Xu et al., 2014; Zhou et al., 2015, 2016). Furthermore, the Budyko framework, which was originally applicable at the long-term mean annual scale, has been extended to shorter timescales, such as annual (Wang and Alimohammadi, 2012; Zhang et al., 2008) and intra-annual periods (Chen et al., 2013).
Several studies have made connections between the Budyko framework and Bouchet's complementary relationship (CR) (Bouchet, 1963). Yang et al. (2006) used the Fu equation (Fu, 1981), which is one of the commonly used equations to represent the Budyko curve, to describe the relationship between actual evaporation and potential evaporation in the CR. Roderick et al. (2009) presented a complementary relationship normalized by net irradiance and compared it with the Budyko framework. Lhomme and Moussa (2016) combined the Turc–Pike equation (Turc, 1954; Pike, 1964), which is another commonly used Budyko-type equation, with the CR to show the dependence of the Budyko curve on the drying power of the air.
Figure 1Conceptual representations of (a) the complementary relationship and (b) the Budyko framework.
When linking the Budyko framework with the CR, it is crucial to have a clear definition of different types of evaporation used in these two frameworks. Brutsaert and Parlange (1998) and Brutsaert (2015) generalized the CR and provided definitions of the evaporation terms in the CR, namely actual evaporation (E), potential evaporation (Ep), and “apparent” potential evaporation (Epa; see Fig. 1a). Brutsaert and Parlange (1998) point out that the complementary relationship is between actual evaporation and “apparent” potential evaporation, not between actual evaporation and potential evaporation. In the Budyko framework (Fig. 1b), the definition of potential evaporation follows Van Bavel (1966)'s potential evaporation definition that it is under unlimited land surface water supply without the effect of humidity deficit (Budyko, 1974), which is the same as the Ep definition in the generalized CR. The definitions of evaporation, potential evaporation, and “apparent” potential evaporation in these different frameworks are summarized in Table 1.
Table 1Types of evaporation in the Budyko framework and the original CR, and their redefined evaporation type based on a generalized CR. The last column refers to the definitions of the three types of evaporation in the generalized CR provided in Brutsaert (2015).
Process-based speaking, the CR suggests a connection between evaporation and “apparent” potential evaporation (Fig. 1a), which is driven by the energy feedbacks between atmosphere and land surface. During the drying process at the land surface, the excessive energy that is not used for evaporation will be available for the increase in sensible heat. The rise in air temperature will lead to an increase in the rate of “apparent” potential evaporation (Brutsaert and Parlange, 1998; Brutsaert, 2005; Aminzadeh et al., 2016). This connection between Epa and E also suggests a connection between Epa and P, since the water supply from precipitation will affect the rate of evaporation. In terms of the Budyko framework, Ep and P are used as the representations of energy supply and water supply, respectively. The ratio between Ep and P is the primary controlling factor of the ratio of E over P in watersheds at the long-term mean annual timescale (Fig. 1b). The ratio of Ep over P is also called the aridity index, which represents the dryness of the climate in a watershed. The ratio of E over P increases with the increase in the aridity index, indicating that more water from precipitation will become evaporation rather than runoff under a drier climate (Arora, 2002). No connection between Ep and P is suggested in the Budyko framework.
In order to explore the connections between the Budyko framework and the CR, our study investigates the relationships between precipitation and potential evaporation as well as between precipitation and “apparent” potential evaporation. We collect warm-season precipitation, potential evaporation, and pan evaporation data from 259 weather stations across the contiguous US. Studying the relationships between P, Ep, and Epa advances our understanding of the well-established classic Budyko framework and the CR. Furthermore, based on insights provided by previous studies (Yang et al., 2006; Roderick et al., 2009; Lhomme and Moussa, 2016), we use a Budyko-type expression to develop a new formulation for the CR.
2 Methodology
## 2.1 Theoretical development
### 2.1.1 Budyko framework
The Budyko curve (Fig. 1b) describes the relationship between long-term water partitioning, represented by the ratio of actual evaporation over precipitation, and long-term climate, represented by the ratio of potential evaporation over precipitation, namely the aridity index (Budyko, 1958, 1974). In recent decades, the Budyko framework has been examined with annual data (e.g., Yang et al., 2007; Potter and Zhang, 2009; Cheng et al., 2011). A number of Budyko-type functions have been developed to mathematically describe the Budyko curve (Turc, 1954; Fu, 1981; Zhang et al., 2001; Yang et al., 2008; Wang and Tang, 2014). Within these functions, the Turc–Pike equation is a parsimonious single-parameter equation (Turc, 1954; Pike, 1964):
$\begin{array}{}\text{(1)}& \frac{E}{P}={\left[\mathrm{1}+{\left(\frac{{E}_{\text{p}}}{P}\right)}^{-v}\right]}^{-\frac{\mathrm{1}}{v}},\end{array}$
where E is actual evaporation, Ep is potential evaporation, P is precipitation, and v is a parameter to represent landscape properties such as vegetation coverage and soil properties (Zhang et al., 2001; Yang et al., 2008). The parameter v needs to be a positive number, and its typical value is 2.0.
### 2.1.2 Generalized complementary relationship
Bouchet's complementary relationship (Bouchet, 1963) describes the relationship between actual evaporation E and potential evaporation Ep. Brutsaert and Parlange (1998) introduced the term “apparent” potential evaporation Epa and clarified that the CR is between E and Epa, not E and Ep (Fig. 1a). They also proposed a generalized complementary relationship:
$\begin{array}{}\text{(2)}& bE+{E}_{\text{pa}}=\left(\mathrm{1}+b\right){E}_{\text{p}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\mathrm{0}\le E\le {E}_{\text{p}}\le {E}_{\text{pa}},\end{array}$
where b is a proportionality parameter not less than one. When b is equal to one, Eq. (2) represents the original complementary relationship (Kahler and Brutsaert, 2006). “Apparent” potential evaporation will be higher than potential evaporation, especially under dry conditions, while it gradually approaches potential evaporation as the ratio of E over Epa increases (Fig. 1a). As suggested by Morton (1976) and Brutsaert and Stricker (1979), potential evaporation can be estimated using the Priestley–Taylor equation (Priestley and Taylor, 1972), which is also called the equilibrium evaporation (Brutsaert and Chen, 1995; Jiang and Islam, 2001). “Apparent” potential evaporation can be estimated using the Penman equation (Penman, 1948; Linacre, 1994; Rotstayn et al., 2006) or using data measured at evaporation pans (Brutsaert, 1982; Brutsaert and Parlange, 1998):
$\begin{array}{}\text{(3)}& {E}_{\text{pa}}=a{E}_{\text{pan}},\end{array}$
where Epan is the pan evaporation and a is the pan coefficient. The pan coefficient varies from location to location (Stanhill, 1976; Linacre, 1994). In Kahler and Brutsaert (2006), a pan coefficient of a=1.0 is recommended for mixed natural vegetation, which will be used in this study. It should be noted that the linear relationship between Epa and Epan given in Eq. (3) and the choice of “a” value will not affect the correlations between P, Ep, and Epa.
### 2.1.3 Relationships between P, Ep, and Epa
The x axis of the complementary relationship is a ratio between E and Epa (Bouchet, 1963). Ramírez et al. (2005) used the water-energy framework to link the CR with the Budyko approach and changed the x axis in the CR to moisture availability. Following this idea, several studies have used precipitation or wetness index (PEp) to represent moisture availability in the CR (Yang et al., 2006; Roderick et al., 2009). In this study, we also use P to represent moisture availability in the CR. Ep is a horizontal line in the CR that is parallel to the x axis (Fig. 1a). Therefore, the modified CR indicates that P and Ep are independent. On the other hand, the upper curve of the CR, representing “apparent” potential evaporation Epa, declines along the x axis, indicating that Epa and P are not independent. For a dimensionless CR, we normalize the x and y axes. The normalized CR describes the relationship between $\frac{{E}_{\text{pa}}}{{E}_{\text{p}}}$, $\frac{E}{{E}_{\text{p}}}$, and $\frac{P}{{E}_{\text{p}}}$ (Fig. 2).
Figure 2Dimensionless Bouchet–Budyko curves in the normalized complementary relationship.
To connect the Budyko framework with the normalized CR toward formulating the Bouchet–Budyko curves, we first transform Eq. (1) into a relationship between $\frac{E}{{E}_{\text{p}}}$ and $\frac{P}{{E}_{\text{p}}}$:
$\begin{array}{}\text{(4)}& \frac{E}{{E}_{\text{p}}}={\left[{\left(\frac{P}{{E}_{\text{p}}}\right)}^{-v}+\mathrm{1}\right]}^{-\frac{\mathrm{1}}{v}}.\end{array}$
Yang et al. (2006) did a similar transformation using the Fu equation (Fu, 1981). Dividing both sides of Eq. (2) by Ep yields
$\begin{array}{}\text{(5)}& b\frac{E}{{E}_{\text{p}}}+\frac{{E}_{\text{pa}}}{{E}_{\text{p}}}=\mathrm{1}+b.\end{array}$
Combining Eqs. (4) and (5) gives a relation between $\frac{P}{{E}_{\text{p}}}$ and $\frac{{E}_{\text{pa}}}{{E}_{\text{p}}}$:
$\begin{array}{}\text{(6)}& \frac{{E}_{\text{pa}}}{{E}_{\text{p}}}=b+\mathrm{1}-{\left[{\left(\frac{P}{{E}_{\text{p}}}\right)}^{-v}+\mathrm{1}\right]}^{-\mathrm{1}/v}{E}_{\text{pa}}\ge {E}_{\text{p}}.\end{array}$
Equations (4) and (6) represent the lower and upper curves of the normalized CR, respectively (Fig. 2). Roderick et al. (2009) presented a similar framework, without the formulation of the curves. To verify the relationships between P, Ep, and Epa, and to examine the Bouchet–Budyko curves in Eqs. (4) and (6), we analyze climate data from 259 weather stations across the contiguous US.
Figure 3(a) Map of 259 weather stations. The available month of a year of pan evaporation data for each weather station is presented using legends with different colors and shapes. Four representative weather stations are selected from the four quadrants of the US, respectively, which are highlighted with red circles. (b) Map of 93 weather stations with homogenized pan evaporation data that overlap the 259-station dataset.
## 2.2 Data sources
Monthly precipitation and pan evaporation are collected from the National Oceanic and Atmospheric Administration (NOAA) at the National Climatic Data Center (NCDC). The data can be downloaded at https://www.ncdc.noaa.gov/IPS/cd/cd.html (last access: 17 August 2018). The precipitation data are measured using a standard rain gauge and the pan evaporation data using Class A evaporation pans. We collect data for the period 1984–2015 from a total of 259 weather stations (Fig. 3a). Since pan evaporation is collected only during warm months (when temperatures remain above freezing), the weather stations in cold regions have less than 12 months of pan readings in a year. We call the period of warm months in a year a “warm season”. We calculate the monthly average pan evaporation and precipitation using only the warm months for each year at each weather station. For short, they are called warm-season data (i.e., warm-season pan evaporation, warm-season precipitation). We also calculate the annually averaged warm-season data to represent the long-term average level of pan evaporation and precipitation at each station. For short, they are called long-term average data. Over the 259 selected stations, there is an average of 7 months per year with available pan evaporation data. As Fig. 3 shows, the number of available months decreases from the southern regions to the northern regions. For stations in the southern states with all 12 months of available data in a year, the full year will be considered a warm season. The northern state stations have fewer warm months, and, accordingly, the warm season is much shorter. On the other hand, not all 259 weather stations have the full record from 1984 to 2015; the average number of years with available data for each location is 18. A complete summary of the information available at all 259 weather stations is provided in Table S1 in the Supplement. In order to minimize the uncertainty from various warm periods in a year from station to station, we repeat the analysis using an alternative source of pan evaporation in the NCDC dataset containing homogenized warm month data from May to October (Hobbins, et al., 2017). A total of 93 weather stations overlap both sets of pan evaporation data for the period 1984 to 2001 (Fig. 3b). We convert pan evaporation in the NCDC dataset to “apparent” potential evaporation using Eq. (3).
The Ep data are collected from a remote-sensing dataset (Zhang et al., 2010), which is generated using the Priestley–Taylor equation with remotely sensed net radiation:
$\begin{array}{}\text{(7)}& \mathit{\lambda }{E}_{\text{p}}=\mathit{\alpha }\frac{\mathrm{\Delta }}{\mathrm{\Delta }+\mathit{\gamma }}\left({R}_{\text{n}}-G\right),\end{array}$
where λ (J kg−1) is the latent heat of vaporization; λEp (W m−2) is the latent heat flux; α is a coefficient to account for the effect of surface characteristics and vegetation, and is set to 1.26; Δ (Pa C−1) is the slope of the saturated vapor pressure curve; γ (Pa C−1) is the psychometric constant; Rn (W m−2) is the net radiation; and G (W m−2) is the heat flux into the ground. The Ep data cover the period 1983–2006. Similarly to P and Epa, we calculate the warm-season Ep and long-term annually averaged Ep based on the monthly Ep data.
## 2.3 P, Ep, and Epa correlation analysis
Using the collected weather station data of precipitation and pan evaporation for the period 1984 to 2015, we first calculate the Pearson correlation coefficient between warm-season P and warm-season Epa for each location (Fig. 3a). We then perform the same correlation analysis of P and Epa using the homogenized pan evaporation dataset (Hobbins et al., 2017) (Fig. 3b). Secondly, we use data of warm-season P and warm-season Ep for the period of 1984 to 2006, which is the period when both P and Ep data are available, to investigate the correlation between P and Ep. Finally, to validate the newly derived Bouchet–Budyko curves, the relationship between $\frac{P}{{E}_{\text{p}}}$ and $\frac{{E}_{\text{pa}}}{{E}_{\text{p}}}$ is plotted using the collected data at both seasonal and long-term average timescales.
Figure 4Map of the point-scale annual PEpa correlation at 259 weather stations: (a) r value and (b) p value.
3 Results
## 3.1 Correlations among P, Ep, and Epa
In the 259 weather stations, 93 % of the stations have a negative correlation between P and Epa (Fig. 4a), but only 43 % of the stations are statistically significant (p<0.05; Fig. 4b). All significant PEpa correlations are negative. The weather stations located in the western region (regions with longitude higher than the weather station average longitude of 94.81 W) are more likely to have a significant PEpa negative correlation than those located in the east (regions with longitude lower than 94.81 W). This spatial difference may be related to climate characteristics: the eastern region has higher precipitation (average 105.5 mm month−1) and lower “apparent” potential evaporation (average 145.3 mm month−1), while the western region has lower precipitation (average 44.6 mm month−1) and higher “apparent” potential evaporation (average 203.5 mm month−1). Bouchet's complementary relationship is more significant in arid regions (Ramírez et al., 2005), corresponding to the left side of the CR curves, while it is less significant in humid regions, corresponding to the right side of the CR curves (Fig. 1a). As a result, the negative correlation between precipitation and “apparent” potential evaporation is more significant in the west than in the east.
Figure 5P vs. Epa at 259 weather stations in the US for the period 1984 to 2015 for (a) warm-season data (N=5312) and (b) long-term annually averaged warm-season data (N=259). The data points are color-coded based on their latitudes and longitudes. P vs. Epa at 93 weather stations in the US for the period 1984 to 2001 using the homogenized pan evaporation dataset for (c) the warm period May–October in each year (N=1214), and (d) long-term annual average warm period May–October data (N=93). P vs. Ep at the 259 weather stations for the period of 1984 to 2006 for (e) warm-season data (N=5312) and (f) long-term annual average warm-season data (N=259).
All the warm-season P vs. Epa relations (i.e., all years, all seasons, for a total of 5312 data points) are shown in Fig. 5a. The data cloud shows a negative trend in general. We also plot the long-term annually averaged values of warm-season P and Epa of the 259 weather stations (Fig. 5b), which shows a similar negative trend. Hobbins et al. (2004) showed a similar negative trend between precipitation and pan evaporation with watershed-scale data. To represent the spatial distribution of the weather stations, we color code the data points based on their spatial coordinates of latitude and longitude. The climate in the eastern US is much wetter than the western US, and therefore the data cloud of Epa vs. P is separated into two parts horizontally. The right side of the cloud represents the northeastern and southeastern US (green and brown, respectively), while the left side of the cloud generally represents the northwestern and southwestern US (yellow and red, respectively).
As explained before, we also use an alternative pan evaporation dataset (Hobbins et al., 2017) to further validate our analysis result. This dataset is homogenized to have the same period of a pan evaporation data record in each year from May to October. In order to minimize the data heterogeneity caused by station move and human errors, this dataset compiled pan evaporation data from 247 stations across the US with thorough quality control. It is derived from the same dataset as our data, namely the NCDC dataset. Based on the homogenized pan evaporation data, 85 stations out of 93 (91 %) have a negative correlation between P and Epa. Of these, 41 % of the stations have a statistically significant relationship (p<0.05), all negative. This result is consistent with the analysis result based on our collected data from 259 weather stations. We also use the data cloud to show the relationship between P and Epa in the warm period of May to October in each year at each of the 93 stations (Fig. 5c), as well as the relationship of long-term annually averaged warm-period P and Epa (Fig. 5d). The trend of the data cloud is similar to the data cloud trend using our collected data at both seasonal and long-term average timescales. In other words, both datasets show a negative relationship between P and Epa.
The P and Ep data are shown in Fig. 5e, f. At both seasonal and long-term average timescales, there is no clear relationship shown between P and Ep, confirming the independence between P and Ep discussed in Sect. 2.1.3. This result shows the difference between Ep and Epa, that Ep is independent of P but Epa is not. Therefore, it is important to distinguish Epa from Ep and to understand the different physical mechanisms of the two processes (Brutsaert, 2015).
Figure 6Warm-season P, Ep and Epa time series of four example weather stations in the study period of 1984–2015: (a) Summer Lake 1 S, OR (4258 N, 12047 W); (c) Geneva RSCH Farm, NY (4253 N, 7720 W); (e) Cachuma Lake, CA (3435 N, 11959 W); (g) Moore Haven Lock 1, FL (2650 N, 8150 W); and the scatterplots of P vs. Epa at the four example stations (b, d, f, h).
To present the P, Ep, and Epa relationships at individual locations and therefore to further investigate the dependence between the three variables, we select four weather stations from the four quadrants of the contiguous US (Fig. 3a), to show the warm-season P, Ep, and Epa in time series (Fig. 6). The two stations in the southern regions have data in all 12 months of a year, while the two stations in the northern regions only have Epa data for 6 months of each year. All four stations show negative correlations between P and Epa. This negative correlation at the weather station in Florida is not statistically significant (Fig. 6g, h). As mentioned before, the P and Epa correlation is less significant in the eastern region than in the west, because of the wetter climate in the east. On the other hand, at the other three locations, the warm-season P and Epa are relatively symmetric to each other (Fig. 6a–f). During years when one series is above average, the other tends to be below average and vice versa. In terms of the relationship between P and Ep, all four locations show no significant correlations between the two variables (p>0.05). This is consistent with the independence of P and Ep shown in Fig. 5e, f.
Figure 7PEp vs. EpaEp at 259 weather stations in the US for the period 1984 to 2015 for (a) warm-season data (N=5312) and (b) long-term average data (N=259). The data points are color-coded based on their latitudes and longitudes. The three upper Bouchet–Budyko curves are plotted with different b values of b=1, b=2, and b=3, and with the same v value of v=2. The dashed line is the lower Bouchet–Budyko curve with v=2.
## 3.2 Bouchet–Budyko curves
There are two Bouchet–Budyko curves (Fig. 2). The upper curve describes the relationship between Epa, Ep, and P (Eq. 6) and the lower curve describes the relationship between E, Ep, and P (Eq. 4). The lower curve is derived from the Budyko curve based on the Turc–Pike equation. This relationship between E, Ep, and P has been studied extensively following the Budyko framework and, therefore, it is not the focus of this study. This study investigates the relationship between Epa, Ep, and P, which is represented by the upper Bouchet–Budyko curve. Since the collected weather station data of P and Epa are available from 1984 to 2015 and the Ep data collected from the remote-sensing dataset are available from 1983 to 2006, we examine the relationship between PEp and EpaEp in the overlapping period of 1984 to 2006 (Fig. 7). Using Eq. (6) three curves with different b values (1, 2, and 3) are shown in Fig. 7. The v value is set at 2, which is commonly used in the Budyko framework. When b equals one, the two CR curves are symmetric. When b exceeds one, the two CR curves are asymmetric. This asymmetry is discussed in previous studies (Kahler and Brutsaert, 2006; Brutsaert, 2015). One explanation of this asymmetry between E and Epa is that the evaporation pan will receive more heat than the surrounding area (Kahler and Brutsaert, 2006). Brutsaert (2015) reports an even higher b value of 4.5. The horizontal solid black line in Fig. 7 is the boundary of the upper Bouchet–Budyko curve, above which Epa exceeds Ep.
4 Discussion
## 4.1 Relationship between P and Epa, and between P and Ep
With the weather station data, a negative correlation between warm-season P and Epa is shown in 242 out of the 259 weather stations (93 %). The negative correlation between P and Epa is linked by the humidity deficit. The formation of precipitation is positively related to the local level of humidity (Pal et al., 2000; Sheffield et al., 2006; An et al., 2017), while “apparent” potential evaporation is inversely related to humidity or positively related to the humidity deficit (Penman, 1948; Allen et al., 1998). As a result, precipitation and “apparent” potential evaporation will tend to exhibit a negative correlation. According to Bouchet's complementary relationship, this negative correlation between P and Epa is more pronounced in arid regions than in humid regions.
On the other hand, P and Ep show no significant correlation at both the seasonal and long-term average timescales. As a result, our study indicates that potential evaporation and precipitation, the representations of energy supply and water supply, are likely to be independent. This independence is currently under investigation with field data. It should be noted that the relationships between P and Ep and between P and Epa found in this study are not direct causal relationships, but rather the result of interactions between a number of physical variables, such as net radiation, wind speed, humidity, and so forth. Further investigation into the physical mechanisms connecting these variables is underway.
## 4.2 The Bouchet–Budyko curve and its applications
Combining Bouchet's complementary relationship and the Budyko framework leads to two dimensionless CR curves, normalized by Ep (Fig. 2). The upper Bouchet–Budyko curve is derived from the connection between the Budyko framework and the CR, and the lower Bouchet–Budyko curve is derived directly from the Budyko framework, based on the Turc–Pike equation. The companion CR curves show that as the wetness index PEp decreases, the difference between E and Epa grows. This indicates the complementary relationship between E and Epa is most pronounced in arid environments, that is, the CR is more significant under water-limited conditions. As discussed in Ramírez et al. (2005), the CR can be considered an extension of the Budyko framework.
The P, Ep, and Epa collected in this study follow the general trend of the upper Bouchet–Budyko curve (Fig. 7). The remote-sensing data of Ep may not have the same level of accuracy as the field measured P and Epa. The value of α in Eq. (7) may vary from location to location (Chen and Brutsaert, 1995; Brutsaert and Chen, 1995). Such factors may explain the deviation of some data points from the CR curve in Fig. 7.
This upper Bouchet–Budyko curve can be used to estimate the Epa based on the data of P and Ep. The “apparent” potential evaporation can be measured by evaporation pan, but this measurement has its limitations. For example, it is only available for warm periods. The collected data with time-averaged pan evaporation levels over weeks, months, and years may lead to systematic error in surface flux calculations (Brutsaert, 1982; Kahler and Brutsaert, 2006). The Bouchet–Budyko curve can help us to estimate Epa without the limitations of evaporation pans. Compared with more physically based Epa quantification approaches, such as the Penman equation (Penman, 1948) and the “PenPan” model (Rotstayn et al., 2006), our equations are derived from conceptual frameworks and therefore may provide top–down insights into the Epa level in hydrologic systems.
Similarly to the Budyko framework, the Bouchet–Budyko curves can be used in hydrologic models and climate models. These Bouchet–Budyko curves can be used to examine the fidelity of simulated precipitation and evaporation sequences routinely produced by general circulation models to drive climate change investigations.
5 Conclusions
We collected warm-season precipitation, potential evaporation, and “apparent” potential evaporation data at 259 weather stations in the US to investigate the correlation among these three physical variables. The results showed a negative correlation between P and Epa at 93 % of the stations. The physical reason for the PEpa negative correlation could be related to the humidity variability. When humidity increases, the likelihood of precipitation increases while the rate of “apparent” potential evaporation decreases. On the other hand, our study results supported the assumption that P and Ep are independent. Combining the CR with a Budyko-type equation, we formulated the companion CR curves, showing the connection between the Bouchet and Budyko frameworks. These insights may encourage hydrologists to further explore the strong link between the Budyko framework and the CR, promoting new ways of hydrologic modeling. Future work will investigate the physical mechanisms behind the newly derived Bouchet–Budyko curves and explore the application of these companion curves.
Data availability
Data availability.
The data of precipitation and pan evaporation measurements can be downloaded from the National Climatic Data Center website: https://www.ncdc.noaa.gov/IPS/cd/cd.html. The homogenized pan evaporation data can be downloaded from the USGS ScienceBase: https://www.sciencebase.gov/catalog/ (Hobbins, 2017). The data of remote-sensing-based potential evaporation are provided by the Numerical Terradynamic Simulation Group at the University of Montana, based on the study of Zhang et al. (2010). The data can be downloaded from their website: http://www.ntsg.umt.edu/about/default.php (Zhang, 2010).
Supplement
Supplement.
Competing interests
Competing interests.
The authors declare that they have no conflict of interest.
Acknowledgements
Acknowledgements.
We thank the editor and the three anonymous reviewers for their insightful and critical comments and valuable suggestions.
Edited by: Bob Su
Reviewed by: three anonymous referees
References
Allen, R. G., Pereira, L. S., Raes, D., and Smith, M. (Eds.): Crop evapotranspiration: Guidelines for computing crop water requirements, Irrig. Drainage Pap. 56, Food and Agric. Org., Rome, 1998.
Aminzadeh, M., Roderick, M. L., and Or, D.: A generalized complementary relationship between actual and potential evaporation defined by a reference surface temperature, Water Resour. Res., 52, 385–406, https://doi.org/10.1002/2015WR017969, 2016.
An, N., Wang, K., Zhou, C., and Pinker, R. T.: Observed variability of cloud frequency and cloud-based height within 3600 m above the surface over the contiguous United States, J. Climate, 30, 3725–3742, https://doi.org/10.1175/JCLI-D-16-0559.1, 2017.
Arora, V. K.: The use of the aridity index to assess climate change effect on annual runoff, J. Hydrol., 265, 164–177, 2002.
Bouchet, R.: Evapotranspiration reelle et potentielle, signification climatique, IAHS Publ., 62, 134–142, 1963.
Brutsaert, W.: Hydrology: An Introduction, 605 pp., Cambridge Univ. Press, N. Y., 2005.
Brutsaert, W. and Chen, D.: Desorption and the two stages of drying of natural tallgrass prairie, Water Resour. Res., 31, 1305–1313, 1995.
Brutsaert, W. and Parlange, M. B.: Hydrologic cycle explains the evaporation paradox, Nature, 396, 30, 1998.
Brutsaert, W. and Stricker, H.: An advection-aridity approach to estimate actual regional evapotranspiration, Water Resour. Res., 15, 443–450, 1979.
Brutsaert, W.: A generalized complementary principle with physical constraints for land-surface evaporation, Water Resour. Res., 51, 8087–8093, https://doi.org/10.1002/2015WR017720, 2015.
Brutsaert, W.: Evaporation into the Atmosphere: Theory, History and Applications, 299 pp., Springer, New York, 1982.
Budyko, M. I.: Climate and Life, translated from Russian, edited by: Miller, D. H., Elsevier, New York, 1974.
Budyko, M. I.: The Heat Balance of the Earth's Surface, U.S. Dep. of Commer., Washington, D. C, 1958.
Chen, D. and Brutsaert, W.: Diagnostics of land surface spatial variability and water vapor flux, J. Geophys. Res., 100, 25595–25606, 1995.
Chen, X., Alimohammadi, N., and Wang, D.: Modeling interannual variability of seasonal evaporation and storage change based on the extended Budyko framework, Water Resour. Res., 49, 6067–6078, https://doi.org/10.1002/wrcr.20493, 2013.
Cheng, L., Xu, Z., Wang, D., and Cai, X.: Assessing inter-annual variability of ET at the catchment scale using satellite-based ET datasets, Water Resour. Res., 47, W09509, https://doi.org/10.1029/2011WR010636, 2011.
Donohue, R. J., Roderick, M. L., and McVicar, T. R.: On the importance of including vegetation dynamics in Budyko's hydrological model, Hydrol. Earth Syst. Sci., 11, 983–995, https://doi.org/10.5194/hess-11-983-2007, 2007.
Fu, B. P.: On the calculation of the evaporation from land surface, Sci. Atmos. Sin., 5, 23–31, (in Chinese) 1981.
Hobbins, M. T., Barsugli, J. J., Dewes, C. F., and Rangwala, I.: Monthly pan evaporation data across the continental United States between 1950–2001, https://doi.org/10.21429/C9MW25, 2017.
Hobbins, M. T., Ramírez, J. A., and Brown, T. C.: Trends in pan evaporation and actual evapotranspiration across the conterminous U.S.: Paradoxical or complementary?, Geophys. Res. Lett., 31, https://doi.org/10.1029/2004GL019846, 2004.
Jiang, L. and Islam, S.: Estimation of surface evaporation map over surthern Great Plains using remote sensing data, Water Resour. Res., 37, 329–340, 2001.
Kahler, D. M. and Brutsaert, W.: Complementary relationship between daily evaporation in the environment and pan evaporation, Water Resour. Res., 42, W05413, https://doi.org/10.1029/2005WR004541, 2006.
Lhomme, J.-P. and Moussa, R.: Matching the Budyko functions with the complementary evaporation relationship: consequences for the drying power of the air and the Priestley-Taylor coefficient, Hydrol. Earth Syst. Sci., 20, 4857–4865, https://doi.org/10.5194/hess-20-4857-2016, 2016.
Linacre, E. T.: Estimating U.S. class A pan evaporation from few climate data, Water Int., 19, 5–14, 1994.
Milly, P. C. D.: Climate, soil water storage, and the average annual water balance, Water Resour. Res., 30, 2143–2156, 1994.
Morton, F. I.: Climatological estimates of evapotranspiration, J. Hydraul. Div., 102, 275–291, 1976.
National Climatic Data Center: Climatological Data, https://www.ncdc.noaa.gov/IPS/cd/cd.html, last access: 17 August 2018, 2018.
Pal, J. S., Small, E. E., and Eltahir, E. A. B.: Simulation of regional-scale water and energy budgets: Representation of subgrid cloud and precipitation processes within RegCM, J. Geophys. Res., 105, 29579–29594, 2000.
Penman, H. L.: Natural evaporation from open water, bare and grass, Proc. R. Soc., Ser. A, 193, 120–145, 1948.
Pike, J. G.: The estimation of annual run-off from meteorological data in a tropical climate, J. Hydrol., 2, 116–123, 1964.
Potter, N. J. and Zhang, L.: Interannual variability of catchment water balance in Australia, J. Hydrol., 369, 120–129, 2009.
Priestley, C. H. B. and Taylor, R. J.: On the assessment of surface heat flux and evaporation using large-scale parameters, Mon. Weather Rev., 100, 81–92, 1972.
Ramírez, J. A., Hobbins, M. T., and Brown, T. C.: Observational evidence of the complementary relationship in regional evaporation lends strong support for Bouchet's hypothesis, Geophys. Res. Lett., 32, L15401, https://doi.org/10:1029/2005GL023549, 2005.
Roderick, M. L., Hobbins, M. T., and Farquhar, G. D.: an evaporation trends and the terrestrial water balance. II. Energy balance and interpretation, Geogr. Compass, 761–780, https://doi.org/10.1111/j.1749-8198.2008.00214.x, 2009.
Rotstayn, N. D., Roderick, M. L., and Farquhar, G. D.: A simple pan-evaporation model for analysis of climate simulations: Evaluation over Australia, Geophys. Res. Lett., 33, https://doi.org/10.1029/2006GL027114, 2006.
Sheffield, J., Goteti, G., and Wood, E. F.: Development of a 50-year high-resolution global dataset of meteorological forcings for land surface modeling, J. Climate, 19, 3088–3111, 2006.
Stanhill, G.: The CIMO international evaporimeter comparisons, Publication 449, World Meteorological organization, Geneva, 38 pp, 1976.
Thornthwaite, C. W.: An approach toward a rational classification of climate, Geogr. Rev., 38, 55–94, 1948.
Turc, L.: Le bilan d'eau des sols: Relation entre les precipitations, l'evaporation er l'ecoulement, Ann. Agron., 5, 491–569, 1954.
Van Bavel, C. H. M.: Potential evaporation: The combination concept and its experimental verification, Water Resour. Res., 2, 455–467, https://doi.org/10.1029/WR002i003p00455, 1966.
Wang, D. and Alimohammadi, N.: Responses of annual runoff, evaporation, and storage change to climate variability at the watershed scale, Water Resour. Res., 48, W05546, https://doi.org/10.1029/2011WR011444, 2012.
Wang, D. and Tang, Y.: A one-parameter Budyko model for water balance captures emergent behavior in Darwinian hydrologic models, Geophys. Res. Lett., 41, 4569–4577, https://doi.org/10.1002/2014GL060509, 2014.
Xu, X., Yang, D., Yang, H., and Lei, H.: Attribution analysis based on the Budyko hypothesis for detecting the dominant cause of runoff decline in Haihe basin, J. Hydrol., 510, 530–540, https://doi.org/10.1016/j.jhydrol.2013.12.052, 2014.
Yang, D., Sun, F., Liu, Z., Cong, Z., and Lei, Z.: Interpreting the complementary relationship in non-humid environments based on the Budyko and Penman hypotheses, Geophys. Res. Lett., 33, L18402, https://doi.org/10.1029/2006GL027657, 2006.
Yang, D., Sun, F., Liu, Z., Cong, Z., Ni, G., and Lei, Z.: Analyzing spatial and temporal variability of annual water-energy balance in nonhumid regions of China using the Budyko hypothesis, Water Resour. Res., 43, 1–12, https://doi.org/10.1029/2006WR005224, 2007.
Yang, H. and Yang, D.: Derivation of climate elasticity of runoff to assess the effects of climate change on annual runoff, Water Resour. Res., 47, https://doi.org/10.1029/2010WR009287, 2011.
Yang, H., Yang, D., Lei, Z., and Sun, F.: New analytical derivation of the mean annual water-energy balance equation, Water Resour. Res., 44, W03410, https://doi.org/10.1029/2007WR006135, 2008.
Zhang, K., Kimball, J. S., Nemani, R. R., and Running, S. W.: A continuous statellite-derived global record of land surface evapotranspiration from 1983 to 2006, Water Resour. Res., 46, W09522, https://doi.org/10.1029/2009WR008800, 2010.
Zhang, L., Dawes, W. R., and Walker, G. R.: Response of mean annual evapotranspiration to vegetation changes at catchment scale, Water Resour. Res., 37, 701–708, 2001.
Zhang, L., Potter, N., Hickel, K., Zhang, Y., and Shao, Q.: Water balance modeling over variable time scales based on the Budyko framework – Model development and testing, J. Hydrol., 360, 117–131, 2008.
Zhou, S., Yu, B., Huang, Y., and Wang, G.: The complementary relationship and generation of the Budyko functions, Geophys. Res. Lett., 42, 1781–1790, https://doi.org/10.1002/2015GL063511, 2015.
Zhou, S., Yu, B., Zhang, L., Huang, Y., Pan, M., and Wang, G.: A new method to partition climate and catchment effect on the mean annual runoff based on the Budyko complementary relationship, Water Resour. Res., 52, 7163–7177, https://doi.org/10.1002/2016WR019046, 2016. | 2020-01-26 22:29:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 16, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6168420314788818, "perplexity": 3917.9128124979056}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251690379.95/warc/CC-MAIN-20200126195918-20200126225918-00477.warc.gz"} |
https://igor.technology/coding/ | # H.264 compression explained in detail with coding examples
H.264 compression explained in detail with coding examples
Video coding and decoding is a process of compressing and decompressing a digital video signal.
This is me exploring the concepts of H264 video compression based on Ian E. Richardson - H264 book and other online resources. The goal is to implement as much as I know how to these concepts in Python. It's an ongoing article and I add to it when I have the time.
## Capture
A natural visual scene is spatially and temporally continuous. In simpler terms; spatially means capturing frames in a 2-D square, temporally capturing 2-D squares in regular intervals in time.
## Progressive and Interlaced sampling
A video signal capture might be using progressive sampling (series of complete frames) or interlaced sampling (series of horizontal odd or even frames capturing half of the frame information).
## Color spaces
The way of capturing color information.
### RGB
Red, Green and Blue can create any color in varying proportions.
### YCrCb
Separating luminance from the color. Human Visual System (HVS) is less sensitive to color than luminance. It's a more efficient way of representing a frame for the human eye.
This color model uses Y to represent the brightness and two color channels Cb (chroma blue) and Cr (chroma red). The YCbCr can be derived from RGB and it also can be converted back to RGB. We can produce all the colors without using the green.
Y = 0.299R + 0.587G + 0.114B
Once we had the luma, we can split the colors (chroma blue and red):
b = 0.564(B - Y)
Cr = 0.713(R - Y)
And we can also convert it back and even get the green by using YCbCr.
R = Y + 1.402Cr
B = Y + 1.772Cb
G = Y - 0.344Cb - 0.714Cr
We can use the coefficients from the standard BT.601 that was recommended by the group ITU-R* .
The complete description of a color image is given by Y, the luminance component and three color differences, Cr, Cb and Cg that represent the difference between the color intensity and the mean luminance.
So far this representation has little obvious merit since we now have four components instead of three in RGB. However, Cr,Cg,Cb is a constant and so only two of the three chorminance components need to be stored or transmitted since the third component can always calculated from the other two. So only the luma (Y) and red and blue Cr,Cb are transmitted.
Y:Cr:Cb has an important advantage over RGB in that the Cr and Cb components may be represented with lower resolution than Y because the HVS is less sensitive to color than luminance. This reduces the amount of data required to represent the chrominance components without having a too obvious effect on visual quality. Representing chroma with a lower resolution than luma is simple but effective form of image compression.
## YCrCb sampling formats
Chroma subsampling compression levels are referred to as ratios, such as 4:4:4, 4:2:2 and 4:2:0. A 4:4:4 ratio is actually uncompressed, as the amount of chroma data is equal to the amount of brightness data. In a 4:2:2 ratio, half of the colour data is present compared to a 4:4:4 ratio. In a 4:2:0 ratio, a quarter of the color data is present compared to a 4:4:4 ratio.
These schemas are known as subsampling systems and are expressed as a 3 part ratio - a:x:y which defines the chroma resolution in relation to a a x 2 block of luma pixels.
• a is the horizontal sampling reference (usually 4)
• x is the number of chroma samples in the first row of a pixels (horizontal resolution in relation to a)
• y is the number of changes of chroma samples between the first and seconds rows of a pixels.
An exception to this exists with 4:1:0, which provides a single chroma sample within each 4 x 4 block of luma resolution.
Another visual explanation of chroma subsampling:
4:2:0 is widely used sampling format (YUV, YVI12) where Cr and Cb have each half the horizontal and vertical resolution of Y. 4:2:0 is widely used in video conferencing, digital television and DVD storage.
From the example above we see thay 4:2:0 chroma subsampling requires half as many bits as 4:4:4 (non compressed) format.
Let's reason about the number of bits required to represent an image:
Image resolution: 720x576 px
Y resolution: 720x576 px, each pixel represented with 8 bits (0-255 decimal)
4:4:4 Cr, Cb, Y; total number of bits: 720x576x8x3 = 9953280 bits
4:2:0 Cr, Cb, Y; total number of bits: 720x572x8 + 360x288x8x2 = 4976640 bits
4:2:0 sampling is sometimes described as 12 bits per pixel.
## Video Formats
The video compression algorithms can compress a wide variety of video frame formats. In practice, it is common to capture or convert to one of a set of ‘intermediate formats’ prior to compression and transmission.
The Common Intermediate Format (CIF) is the basis for a popular set of formats:
FormatVideo Resolution
SQCIF128 × 96
QCIF176 × 144
SIF(525)352 x 240
CIF/SIF(625)352 × 288
4SIF(525)704 x 480
4CIF/4SIF(625)704 × 576
16CIF1408 × 1152
### Quality
In order to specify, evaluate and compare video communication systems it is necessary to
determine the quality of the video images displayed to the viewer. Our perception of a visual scene is formed by a complex interaction between the components
of the Human Visual System (HVS), the eye and the brain. This is called a subjective quality measurement.
Peak Signal to Noise Ratio (PSNR) is measured on a logarithmic scale and depends on
the mean squared error (MSE) between an original and an impaired image or video frame,
relative to (2n − 1)2, the square of the highest-possible signal value in the image, where n is the number of bits per image sample.
$$PSNR_{db}=10log_{10}\dfrac{(2^n-1)^2}{MSE}$$
PSNR can be calculated easily and quickly and is therefore a very popular quality measure,
widely used to compare the ‘quality’ of compressed and decompressed video images.
## Video Coding Concepts
A video CODEC encodes a source image or video sequence into a compressed
form and decodes this to produce a copy or approximation of the source sequence. If the decoded video sequence is identical to the original, then the coding process is lossless; if the decoded sequence differs from the original, the process is lossy.
A video encoder consists of three main functional units: a prediction model,a
spatial model and an entropy encoder.
The input to the prediction model is an uncompressed video sequence. The prediction model attempts to reduce redundancy by exploiting the similarities between neighboring video frames and/or neighboring image samples, typically by constructing a prediction of the current video frame or block of video data.
The parameters of the prediction model, i.e. intra-prediction mode(s) or inter prediction
mode(s) and motion vectors, and the spatial model, i.e. coefficients, are compressed by the entropy encoder. This removes statistical redundancy in the data, for example representing commonly occurring vectors and coefficients by short binary codes.
## Prediction
• Spatial prediction (from previously coded image samples in the same frame)
• Temporal prediction (from previously coded image samples)
### Motion compensated prediction of a macro-block
The macro-block, corresponding to a 16 × 16-pixel region of a frame, is the basic unit for
motion compensated prediction in a number of important visual coding standards including
MPEG-1, MPEG-2, MPEG-4 Visual, H.261, H.263 and H.264.
16 × 16-pixel region of the source frame is represented by 256 luminance samples arranged in four 8 × 8-sample blocks, 64 red chrominance samples in one 8 × 8 block and 64 blue chrominance samples in one 8 × 8 block, giving a total of six 8 × 8 blocks.
### Motion estimation
Motion estimation of a macroblock involves finding a 16 × 16-sample region in a reference
frame that closely matches the current macroblock. The reference frame is a previously
encoded frame from the sequence and may be before or after the current frame in display
order.
Instead of 16 × 16 a 4 × 4 block might give the smallest residual energy. However,
a smaller block size leads to increased complexity, with more search operations to be carried out, and an increase in the number of motion vectors that need to be transmitted.
An effective compromise is to adapt the block size to the picture characteristics, for example choosing a large block size in flat, homogeneous regions of a frame and choosing a small block size around areas of high detail and complex motion.
The performance gain tends to diminish as the interpolation steps increase. A motion-compensated reference frame, the previous frame in the sequence, is subtracted
from the current frame and the energy of the residual, approximated by the Sum of Absolute Errors (SAE). A lower SAE indicates better motion compensation
performance.
### H.264 Syntax Overview
Network Abstraction Layer (NAL) consists of a series of NALUnits (NALU).
Sequence Parameter Sets (SPS) and Picture Parameter Sets (PPS) are NAL units that signal certain common control parameters to the decoder.
At the slice layer, each slice consists of a Slice Header and Slice Data.
The Slice Data is a series of coded macroblocks (MB) and skip macroblock indicators which signal that certain macroblock positions contain no data.
MB type : I/intra coded, P/inter coded from one reference frame, B/inter coded from one or two reference frames.
- Prediction information : prediction mode(s) for an I macroblock, choice of reference frame(s) and motion vectors for a P or B macroblock.
- Coded Block Pattern CBP : indicates which luma and chroma blocks contain non-zero residual coefficients.
- Quantization Parameter QP, for macroblocks with CBP = 0.
- Residual data, for blocks containing non-zero residual coefficients.
## H.264 Prediction
For every macroblock, a prediction is created, an attempt to duplicate the information contained in the macro-block using previously coded data, and subtracted from the macro-block to form a residual.An accurate prediction means that the residual contains very
little data and this in turn leads to good compression performance.
### Macroblock prediction
Types of Macroblocks:
• I These are completely refreshed, new data. They only reference itself and do not rely on any other image in order for it to be decoded correctly. The first image in a GOP must be of this type. Also known as Intra-prediction
• P (Predicted) – These use one or more previously decoded reference images in order to construct a full picture.
• B (Bi-Directional Predicted) – These use previously decoded reference images and future displayed images to be constructed. As a result, the order that the images are encoded and decoded will be different to that displayed.
H.264/AVC supports a wide range of prediction options – intra prediction using data within the current frame, inter prediction using motion compensated prediction from previously coded frames. Additionally H.264 tries to select the optimal combination of parameters for each macroblock; prediction block size, specialized prediction modes (Direct, Weighted) and other filters to reduce number of bits.
### Intra prediction
An intra (I) macroblock is coded without referring to any data outside the current slice. For a typical block of luma or chroma samples, there is a relatively high correlation between samples in the block and samples that are immediately adjacent to the block. Intra prediction therefore uses samples from adjacent, previously coded blocks to predict the values in the current block. | 2023-03-21 00:46:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5902826189994812, "perplexity": 2513.386387520038}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943589.10/warc/CC-MAIN-20230321002050-20230321032050-00607.warc.gz"} |
http://clay6.com/qa/15974/for-the-reaction-n-2o-5-g-iff-2no-2-g-0-5o-2-g-calculate-the-mole-fraction- | Browse Questions
# For the reaction ,$N_2O_5(g)\iff 2NO_2(g)+0.5O_2(g)$.Calculate the mole fraction of $N_2O_5(g)$ decomposed at a constant volume and temperature,if the initial pressure at any time is 960mm Hg.Assume ideal gas behaviour.
$(a)\;0.2\qquad(b)\;0.3\qquad(c)\;0.1\qquad(d)\;0.4$
$N_2O_5\iff 2NO(g)+\large\frac{1}{2}$$O_2(g) Initial pressure : N_2O_5\Rightarrow 600 2NO\Rightarrow 0 \large\frac{1}{2}$$O_2\Rightarrow 0$
Final pressure :
$2NO\Rightarrow 600-p$
$2p\Rightarrow 2p$
$\large\frac{1}{2}$$O_2\Rightarrow \large\frac{p}{2} Step 2: p\alpha moles if V,T are constant. \therefore 600-p+2p+\large\frac{p}{2}$$=960$
$p=240mm\;Hg$
$\therefore$ Mole fraction Of $N_2O_5$ decomposed $=\large\frac{240}{600}$
$\Rightarrow 0.4$
Hence (d) is the correct answer. | 2016-12-10 22:17:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9321324825286865, "perplexity": 8800.931509404472}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698543577.51/warc/CC-MAIN-20161202170903-00229-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/435107/prove-the-equation-frac2-pi-int-0-infty-frac-cos-kr-ak-sin-krk2 | # Prove the equation: $\frac{2}{\pi} \int_0^\infty \frac{\cos kr - ak \sin kr}{k^2a^2 +1} \ldots$
Prove the following equation:
$$\frac{2}{\pi} \int_0^\infty \frac{\cos kr - ak \sin kr}{k^2a^2 +1} \left (\int_0^\infty \cos kr' \left [u(r')-au'(r') \right] dr' \right ) dk =u(r) .$$ where $u,u' \in L^1(\mathbb{R}^+)$ and $a,r >0$.
I have found the following not rigorous proof. By reversing the order of integration (this is the not rigorous part) one obtains: $$\ldots = \frac{2}{\pi} \int_0^\infty \left ( \int_0^\infty \frac{\cos kr\cos kr' - ak \sin kr \cos kr'}{k^2a^2 +1} dk \right ) [u(r')-au'(r') ] dr';$$ By using the Werner formulas, the integral in $dk$ becomes: \begin{align*} & \int_0^\infty \frac{\cos k(r + r') + \cos k(r - r') - ak \sin k(r+r') - ak \sin k(r-r')}{2(k^2a^2 +1)} dk. \end{align*} Given the following integrals: $$\int_0^\infty \frac{\cos kx}{a^2 k^2 +1} dk = \frac{\pi}{2} \frac{e^{-|x/a|}}{a}; \; \; \int_0^\infty \frac{ak \sin kx}{a^2 k^2 +1} dk = \frac{\pi}{2} \frac{\text{sgn}(x)e^{-|x/a|}}{a};$$ the complete formula becomes: \begin{align*} &\ldots = \int_0^\infty \Theta(r'-r) \frac{e^{-(r'-r)/a}}{a}[u(r')-au'(r') ] dr' = \\ & - \int_r^\infty \partial_{r'}[ e^{-(r'-r)/a}u(r') ]dr'= - e^{-(r'-r)/a}u(r') \Big |_{r'=r}^\infty = u(r). \end{align*}
I think that reversing the order of integration is not allowed, because the conditions for Fubini are not satisfied. In fact, probably:
$$\int_0^\infty \left |\frac{\cos kr\cos kr' - ak \sin kr \cos kr'}{k^2a^2 +1} \right | dk = \infty.$$
Can somebody give a rigorous proof of the equation?
• If I could prove it with the additional assumption that $r\mapsto ru(r)$ and $r\mapsto ru'(r)\in L^1(\mathbb R^+)$ would it be interesting for you? – Sebastien B Jul 10 '13 at 15:58
• Yes, it would be. – BGA Jul 11 '13 at 22:10 | 2019-05-22 12:49:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9994444251060486, "perplexity": 1094.687338560734}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256812.65/warc/CC-MAIN-20190522123236-20190522145236-00200.warc.gz"} |
https://gamedev.stackexchange.com/questions/174239/how-to-connect-nodes-in-a-star-pathfinding-for-platformer-games | How to connect nodes in a star pathfinding for platformer games? [duplicate]
In this thread, it tells that in 2d platformer games, I should pre-define and connect node to find the correct path.
But I don't understand how to find the node's children. In my program, I define map as following, 0=free space, 1=solid terrain, 2=node
the original map definition is:
numpy.array([ [0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,1,1],
[1,1,1,1,1,1,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0],
[1,1,1,1,1,1,1,1,1,1,1], ])
numpy.array([ [0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,2,2],
[2,2,2,2,2,2,2,0,0,1,1],
[1,1,1,1,1,1,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0],
[2,2,2,2,2,2,2,2,2,2,2],
[1,1,1,1,1,1,1,1,1,1,1], ])
so the map should be so
In the original A* (A star) algorithm, it searches 8 directions and every direction checks only one node if available.
But in a platfomer, I don't know how to deal with this, there are too many possibilities. For example, assuming the character's jump value is 3, then we go to left now I can:
• jump to left using 200% power, (keep pressing left while jumping and falling, move 6 steps actually)
• just walk (the paths 1-7 in the pic)
8 directions and bigger jump value lead to more possibilities. What's more, there are countless possibilities when falling from a high solid terrain.
For every possibility, in order to connect the nodes, I need to check the corresponding coordinate in the map (array) if existing node.
So I am confused. Am I over-complicating / misunderstanding A* or did I miss something because it requires a huge calculation for every node in a big map like 500*500?
• Welcome to GDSE. In the future, please post code & code like things (array contents, etc) as text rather than screen shots. – Pikalek Aug 2 '19 at 15:12
• I believe that this question gamedev.stackexchange.com/questions/118912/… answers your question as well. – Jody Sowald Aug 2 '19 at 15:41
am I overcomplicating/misunderstanding
I'm afraid, you are (to some extent). All you really need to build the graph is to walk through all of your nodes (2) and connect them using a mask like this.
--UJU--
-UUJUU-
U0W*W0U
where
• * -- Anchor point, that's the position of the node we are currently testing
• - -- nodes we can't reach (directly) from the current one, so we won't connect to them
• J -- if there is the node -- you can jump to it if you can jump through the blocks
• U -- nodes you can jump up on (or from, it works both ways) to
• W -- nodes you can walk to
You are correct in your understanding that increasing the number of choices will significantly increase the problem size. Whether or not it increases it too much depends on many factors. For instance, I've seen A* extended all tiles within a distance of three (Directional-48 search) in order to path find with turning radius constraints. That doesn't necessarily mean that your problem won't grow out of scope - the only way to know that is to either build and test or do the math / theory needed to determine the time required.
Regarding your representation, I'm not sure I agree with your distinction between nodes & empty space. For one thing, it doesn't account for jumping to get power-ups, avoid enemies, etc. It also seems like to be accurate you either need to calculate it all by hand or already have made reachbility calculations. If it works well enough for your needs, that's great, but it's something you might need to revisit later on.
I my limited experience with platformer AI, the problem space is somewhat restricted by reducing the look-ahead. For instance, the solver might only consider one screen's worth of the level at a time rather than the entire map. This could be scaled up or down depending on the performance.
It may be the case that A* is not a good fit for this problem or may need additional techniques to make it competitive. The previous research I've seen tended to focus more on heuristic search algorithms such as Monte Carlo methods, but that may just have been a consequence of what I was working on at the time. There's a lot of great research connected to Mario AI Compitition & they have a code framework available. Because the research is geared toward competition, it tends to be more practical & results oriented and less theoretical & hand wavy. | 2020-10-26 11:00:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6370100975036621, "perplexity": 896.2681208750369}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107891203.69/warc/CC-MAIN-20201026090458-20201026120458-00181.warc.gz"} |