Clenbuterol dangers?

Question: Ive recently looked into the bronchial dilator clenbuterol for fat loss and body fat reduction aid. I'm wondering what if any comments anyone here had about this, mainly the dangers of it and long term side effects if could produce? Thank You!
Comment: Using a drug in an off-label use is typically **not** a good idea.  Especially for a drug that has been compared to [Ephedrine](https://en.wikipedia.org/wiki/Ephedrine).  Don't take any shortcuts.  In the long run, it's not worth it.
Comment: Nobody really knows because it's not a widely researched substance for human consumption. Consensus is that you're likely better off dieting better and exercising more. As far I know, the weight loss is secondary on this substance, the primary being better breathing as it's essentially an astma treating substance, not for weight loss - this is a side effect.
Comment: @rrirower Not to sound rude, but the effects of Ephedrine are greatly exaggerated...I mean I'm from Canada and it's legal here. I've done the regular ECA stack without the A, and it works amazing, given that you don't overdo the doses of course.
Comment: @rrirower Clen, is MUCH more dangerous in terms of side effects, I don't think they should even be compared in that regard.
Comment: @Brofessor _"given that you don't overdo the doses of course."_ - exactly why these types of 'shortcuts' should not be used, especially, if one is training naturally.
Comment: There is no fitness related question here.
Answer: "Clenbuterol  is a sympathomimetic that works on the sympathomimetic nervous system. There are several receptors in the body a sympathomimetic can act on. In the case of Clenbuterol, the beta-2 receptor is the area of interest and action. Clen, as it's commonly known, actively stimulates the beta-2 receptor. Through such stimulation, this actively reverses airway obstructions and provides improved breathing for those who need it. This same stimulation can also be used to enhance the metabolic rate of the individual. Clenbuterol does not actively burn fat by attacking fat cells, but rather stimulates the metabolism by increasing the body's temperature. This occurs due to the beta-2 stimulation stimulating the mitochondria of the cells to produce and release more heat. In turn, this heats up the body's temperature (slightly), enhances the metabolism and causes the individual to burn body fat at a greater rate. In reality, the functions and traits of Clenbuterol are very simple and very straightforward.
There are several possible side effects to Clenbuterol use, and the primary will surround its stimulating nature. No surprise, after all, Clen is a stimulant. The side effects of Clenbuterol can be very strong and often very annoying to say the least, and they will generally affect most people in one way or another. The most common side effects surround a jittery or wired feeling, shaky hands and increased sweating. Most all who use Clen will experience such effects to a degree, but they will commonly be very pronounced during the early stages of use. As the individual becomes accustomed to the stimulant, such related effects should begin to subside, but they will be so strong in some people that some will not be able to use it.
When using Clenbuterol, many often inaccurately assume that when the stimulating effects of Clen began to fade that the thermogenic effects are no longer working. Most will find that the stimulating effects will greatly subside after a week or so of use, but assuming the fat burning properties have vanished due to this lessened stimulation is highly inaccurate. The same dose of Clenbuterol Hydrochloride can actually keep the metabolism revved for as much as five weeks. Granted, by the fifth week mark it will be minimal as the body does most certainly adapt. Due to the body's ability to adapt, necessarily adjustments must be made to use.
The aforementioned side effects of Clenbuterol are the most common, but there are other possible effects of note. As with many stimulating substances, some will experience headaches as well as possible nausea. One of the more bothersome possible side effects of Clenbuterol Hydrochloride will be muscle cramps. Cramps are not exceedingly common, but they will affect many people. Athletes are often at the greatest risk due to the hard and often intense training they are already undertaking. Staying well hydrated is often enough to avoid or remedy this problem, but supplementing with taurine can also help. Clen has been shown to deplete taurine, so supplementation may be necessary for some. Some may also have issues with insomnia; in fact, some may find sleep becomes extremely difficult. Again, this is very common with many stimulating substances, but with Clen it can, for some, be impossible to avoid. Clen has an active half-life that stretches to the 34 hour mark, and that can make sleep impossible for some people. Many will, however, find if they take their Clen first thing in the morning they will not have any issues with sleep, but due to the long half-life some will find insomnia occurs regardless of when they take it.
The use of Clenbuterol Hydrochloride also carries with it possible side effects that can be severe; in fact, dangerous would be a more accurate description. Such effects are most commonly associated with abuse through high doses and far beyond recommended extended periods of use. The severe side effects of Clenbuterol include high blood pressure, irregular heartbeat, trembling and even panic. Some studies have also shown that Clenbuterol abuse can also lead to cardiac hypertrophy, which could potentially lead to death. It is very possible to use this compound without such effects, but as with so many things in life it will require responsible use and a thorough understanding of Clen."
Source: various online articles, not my own writing.
BEFORE you start taking such strong supplements to aid in fat loss, PLEASE make sure your diet is down perfect, or one, you will waste the true effects of the drug, and two, you will do more harm than good in the long run. I won't take the same position as some people that strongly advocate against "steroid" like drugs (clen is NOT a steroid) but since you're asking for the side effects of a drug that is WELL documented on the internet and online journals, this gives me the impression that you're a beginner. As a result, I STRONGLY advise you to maximize your fat loss through proper caloric deficit diet and high intensity exercise FIRST, once you do that, then clen can help you lose the last bit of fat very easily. Think of it this way, if you want to get better at math, what is the point of learning calculus, if you don't even know simple arithmetic ? You should have at least a few years experience dieting properly and you should already be relatively lean before you start. You DO NOT need this drug to lose fat if you are already above, let's say 20-30%, that part can easily be lost through natural diet and exercise.
Please note also that, if you don't have your diet down, you are likely to lose way more muscle than fat and therefore end up even unhealthier than when you first began the drug.

Clenbuterol dangers?


Taxes cost basis for 401(k) rollover to Roth 401(k)

Question: Lets say I contributed $18,000 to my 401(k) this year, and my employer matched 50%, so I have a total of $27,000 contributed this year. This money I invested and made $1000, so now I have $28,000. At this point, however, I realized I originally wanted to contribute to my Roth 401(k) and not my 401(k). Is there a way to "roll over" this contribution so I pay taxes on the $27,000, or would I have to pay taxes on the $28,000?
Answer: This is called an in-plan Roth conversion and is discussed by the IRS here. If your 401(k) has a Roth option then it likely also has a provision to convert pre-tax dollars, but you'll have to check with the administrator to be sure. They could also potentially limit the type of money that can be converted. But most likely you should be able to convert any amount you want, and since it's all pre-tax (your contributions, employer matching, and earnings), it doesn't really matter which money is converted because it's all equivalent. One caveat is you won't able to convert any employer matching that hasn't fully vested.
Comment: I don't believe that employer match contributions can be rolled over into the Roth part of a 401(k) plan. Employer match is a pretax contribution and stays in the tax-deferred part of the 401(k); ditto the earnings on the employer match.
Comment: @DilipSarwate I think the IRS says this is allowed [here](https://www.irs.gov/retirement-plans/designated-roth-accounts-in-plan-rollovers-to-designated-roth-accounts).
Comment: @CraigW - nice citation, would you mind adding it into the answer? My inclination is to clean up comments,but that link is great.
Comment: You are correct, but the operative words are "The plan _can_ allow..." and "The plan can specify which of these amounts are eligible for in-plan Roth rollovers and how often these rollovers can be done." and so it is entirely possible that the OP's plan might either not allow such rollovers at all, or permit in-plan rollovers for employee contributions but not for employer match, etc.
Comment: @DilipSarwate I clarified that the employer/administrator could potentially limit what types of money can be converted.


Compact objects and General Relativity

Question: I know that for compact objects (black holes, neutron stars, etc ) the value of the amount of force acting on any particle can be found by solving Einstein's field equations. So my question is that what is the maximum distance up to which Newtonian mechanics is applicable to find the force near such compact objects.  In other words, what is the minimum distance around such objects from where Newtonian mechanics can not longer apply and Einstein's theory of General Relativity comes into action. Please keep the math simple. Thank You.
Comment: On a circular orbit, the centrifugal force normally offsets gravity and the orbit is stable. As you get closer to a black hole, the centrifugal force first reduces (due to the spacetime curvature) and then changes the direction. At this point both gravity and the centrifugal force pull you down. The orbit becomes unstable at 3 times the radius of the event horizon. For the Earth, it is just over an inch. The last stable orbit perhaps is the very last frontier, beyond which the Newtonian gravity is not applicable in any approximation at all.
Answer: The basic answer is that there is no sharp cut off line between where Newtonian Mechanics will fail and where it won't. At any distance, Newtonian Mechanics will fail, it's just that as you get farther and farther away from the compact object, the failure of Newton becomes smaller and smaller. The equation that describes this is the last equation in this answer. Newton's law is (magnitude only): $$F=\frac{GMm}{r^2},$$ the extra factor of $$\frac{1}{\sqrt{1-\frac{2GM}{c^2 r}}}$$ in that answer is introduced by GR.
If you examine this extra factor given in the last equation of the linked answer, you will see that that factor will approach 1 when r approaches infinity. So in the limit that r is very very large (very far away from the compact object), the force law given by Newton is the same as the one given by GR.

Compact objects and General Relativity


Denied PTO AFTER approval

Question: Next week, my family and I take off for a family wedding in Las Vegas. My mother works at a major league baseball field as a retail supervisor. She requested the time off before the baseball schedule had been established, and her time off was approved. However, 7 days before we leave, her PTO has now been revoked due to a very popular opposing team playing those days. She has already paid for the trip. Should she request to be reimbursed for the value of the trip? Should she protest due to the fact that she was approved prior? I feel that as soon as the schedule was established, they should have revoked the time off; not one week prior.
Comment: She should be re-imbursed not only for her costs but the cost of all family members that need to change their plans.
Comment: @Kalen PTO? This is an international forum, so please [edit] and explain. It it also smart to add a country tag to the question, because country-specific rules/issues may apply.
Answer: I do not know if there is applicable labor law here; but if her contract states that she can be called in for such cases, then I'm afraid she cannot do much.
Otherwise, she should definitely raise this issue to her management/HR.

Denied PTO AFTER approval


What does 余裕がない actually mean?

Question: The characters are carrying a heavy object. However, now they are standing in place (with the object) and doing nothing, so one of them asks the other character:

動いてもよいか?俺もそこまで余裕がない

Why is 余裕がない used here?
Comment: Can you add more context? are they in a narrow or cramped place?
Comment: Please always try to explain what you have researched so far since we do not accept direct translation requests. And remember that you're supposed to accept an answer unless you really want to indicate you're dissatisfied.
Comment: No, but the thing is really heavy and he wants to move it
Answer: 余裕がない simply means the speaker does not have much physical capacity left to continue holding the heavy object. I don't know why they're standing still, but he is suggesting that they start moving again to finish the task quickly.
Answer: 余裕がない just means "can't afford", so its interpretation is contextual.
He may simply state that he no longer has enough power and "can't afford" to keep lifting the object. He may have the urge to go use the bathroom and "can't afford" to remain at the place. He may have no longer enough mental leeway to spend time doing nothing and "can't afford" to keep calm and being nice to others. Or he may intend something different. It's all by context.
Answer: '余裕がな' by itself approximates to 'wish I/we/you had time/ability'. 'い' at the end of that approximates to 'I/we/you don't have time/ability, but wish I/we/you did'. This alone answers your question. However, I will derive the full dialogue's meaning below:
The 'そこまで' before that makes the meaning 'I/we/you don't have time/ability to go that far, but wish I/we/you did'. The 'も' before all that makes the meaning 'I/we/you don't have time/ability to go further, but I wish I/we/you did'. The '俺' makes the subject of that part the speaker (I), which makes the meaning so far 'I don't have time/ability to go further, but wish I did'. Finally, The first sentence (the question) means 'Have I/we moved/carried [the object] far enough?'
So, the sentence's full meaning, based on the situation, is "Have I/we moved it far enough? I am unable to go further, but wish I was.", or "Have we moved it far enough? I wish I could go further, but can't." if we take liberties to make it sound like natural English.
Source: I pieced together the full meaning using rikaikun, a browser extension that detects and highlights segments of Japanese text and gives a ton of options for each syllable combination to help determine a text's exact meaning, or at least the root meaning. I have a great amount of experience using it, and have become very good at understanding its syntax and interpreting possible meanings. I commonly use it to translate the lyrics of Japanese music or anime openings by knowing the transcript.
My most recent project is BURN, the opening theme of Yashahime: Princess Half Demon's second 'season' (there are 3 theme songs used throughout the series, with the second one being this song). I do this as a hobby, and haven't worked on it in a while, but have the first 5 lines translated accurately, and just had real life issues preventing me from working on it further.

What does 余裕がない actually mean?


How common are androids in the world of the Alien franchise?

Question: In the Alien franchise androids have played an important role in the story line, from Ash through to David and Walter. However, is it known how common androids are? The names Ash through to Walter suggest only 23 androids in use? Are androids so expensive that they are only used sparingly or are they made use of only in special occasions?
Comment: http://avp.wikia.com/wiki/Synthetic - Extremely widespread.
Comment: The naming scheme is an in-joke out of universe, it's not meant to suggest that there are only 23 androids.
Answer: By 2179, when Aliens is set, it appears that androids are ubiquitous. When Ripley is shocked at the revelation that Bishop isn't human, Burke is visibly confused, noting, "It's just common practice. We always have a synthetic on board." This would seem to indicate that any Company vessel will always include an android among the crew complement.
Ripley's surprise here, along with the Nostromo crew's reaction to Ash being revealed as a robot, indicates this was by no means common practice in 2122, when Alien is set. Their shock seems to demonstrate that they're aware androids exist, but they would not normally expect to see one on a routine ore-hauling job.
This would seem to be contradicted by the prequels, as both Prometheus and Alien: Covenant, both set around 2100, show crews fully aware that there is an android among the crew. It would appear that they're considered a necessary expense for colony ships, but not for freighters.
By the time of Alien: Resurrection, some 300 years later, androids are apparently extremely rare, having been outlawed after a failed uprising. Call's very existence was due to the fact that she wasn't actually built by humans, but rather by other synthetics.
The general timeline would therefore appear to be that synthetics are well known but uncommon in the early 2100s, hit their heyday around the late 2100s, and were nearly extinct by the late 24th century.
Comment: Yes, of course, in Resurrection there was the comment about Cal being an android built by androids


Multiple display connector combo adapter to VGA

Question: I have a crash cart adapter with a VGA input.
I need support for:

DVI-I (full size required, mini would be nice)
HDMI (full size [A] required, C and D would be nice)
DisplayPort (full size and mini [mini displayport covers thunderbolt] required, micro would be nice)

I'm looking for an adapter that takes these as input and converts to VGA output, with all these built into one just to minimize the number of things I need to carry around. Ideally the configuration would be a female VGA output port, then male cables for all the other types sticking out so I don't need to carry a set of cables around either.
Things I don't care about:

It's OK if it has other connectors in addition to those listed above.
I do not care about size or weight, to an extent. It must be reasonably portable, but it's more important to minimize the number of things I carry around rather than the amount of space they take up.

Does a combined adapter like this exist?
Answer: Here are a couple of products:

China 3-in-1 DisplayPort Male to HDMI DVI VGA Female Adapter Cable on Global Sources
Amazon.com: CableDeconn Multiport 4-in-1 HDMI to Hdmi/dvi/vga Adapter Cable with Audio Output Converter (black): Electronics
HDMI to VGA Kit - Monoprice.com


Battery Design using Matlab Simulink

Question: I am new to Simulink software and want to design a battery with 8 cells whoose voltages are 12 Volts. Their capacity is 12Ah. Both have internal resistance of 0.1 Ohms. The aim is to obtain a 24 Volts battery pack by arranging these 8 cells. The load will be 10 Ohms. In the simulink i design the following model. However, i cannot see any result on the current measurement part while i can see the 24V in the voltage measurement part. I have some several questions?
1) Even though there is no load connected to the circuitry there is this internal resistance which cause current in the branches.Why there is no indication of  current in the scope?
2) I know that there should be a ground and a resistance in the circuit. However, since they are from different librarires they are not connected. I try interfaces but nothing changes.
Anyone who have any idea about these issue please answer this question. If you want to propose another model it is also okey. Thank you for your answers in advance.
Answer: The battery's internal resistance is IN SERIES with the battery.  With no load connected, the battery will not deliver any current, and there will be no voltage dropped across the internal resistance.
With a load connected, the battery will deliver current, which will flow through the internal resistance. This current causes some voltage drop in the internal resistance, reducing the effective voltage of the [battery plus internal resistance].
Comment: Thank you for the answer. I understand it and want to ask the following. Do you know how to connect the resistor to this circuitry? They are from different libraries and i cannot connect them. What should i use to implement the resistor in this circuit?
Comment: @GiraySalgır: Sorry - I don't use Simulink, so can't help you with it.
Answer: I think the element you were looking for is the Series RLC Branch in Simscape/Power Systems/Specialized Techonology/Elements, in the Simulink library. That RLC branch can be easily configured as a simple R.

Battery Design using Matlab Simulink


Which corrodes faster at 5% NaCl solution at room temperature: Steel or Aluminum?

Question: Which corrodes faster at 5% NaCl solution at room temperature: Steel or Aluminum? Is it true that Al has high corrosion resistance? Or is it just a myth as stated in this article.
Comment: Come on. At this point it would be better to do the experiments and report. It seems that whatever you are doing you run its virtual version here. I more or less explained to you that Al is a sacrificial anode to iron. Al cannot have a stronger resistance than iron, nor obviously to stainless steel. The point is that aluminium oxide has pretty good mechanical features and does not go away as iron rust. As long the iron (steel) is covered no oxidation can proceed (aluminium is already oxidised and iron is cover protected). Actually it is what you should have found as basically you did the exp.
Comment: Corrosion usually refers to objects. A bar of Al corrodes slower than a bar of iron. But because it gets self passivated. Al it easy to oxidise, tough. It is always the same argument..................
Comment: Actually, as I ask several questions, I am conducting a thorough experimentation. I am asking to verify some of the results, just to know if I am doing the right procedures, since I am very new in this field and my brain cannot comprehend all reasoning behind my project.
Comment: Besides, I didn't specified that the Al is coupled with steel in my question.
Comment: It is not really the number of question... I am nobody here to tell they were too much. But looks like you ignored the previous answer and explanations, as there should be no reason to reask basically the same, and pointing to a link the quality of which is indeed low.
Answer: I've decided to answer only because the confusion about "what is readily/faster oxidised/corroded between..." is quite common.
Given a couple of elements/substances in a given state, than the one with lower oxidation potential is the one which is readily oxidised (this is a rather obvious statement).
If I take corrosion = oxidation, then Al gets easily corroded than Fe or steel.
This will be evident if we were to make a nice dispersion of very very fine particles of the metals and compare their behaviour, for instance weight gain by oxygen intake at given times.
However, although the chemistry underlying is obviously the same, corrosion is not a synonymous of oxidation, in the sense that it refers to the loosing of the integrity (shape, mechanical properties, even electrical properties) of an object.
If  the Al or steel of the question are, instead of very very fine particles, in form of bars, rods, etc., the oxidation process is still easy in case of aluminium. HOWEVER, while iron oxide may take longer to form (at the VERY beginning of the experiment), its mechanical and coating properties are poor. It can continuously detach from the surface it originates from, and so doing lets the underlying iron exposed to the corrosive environment. Things go like this, until the complete object is destroyed - or at least lost is original function.
Conversely, Aluminum oxide has a compact structure and relatively good coating properties. It does not go away. Therefore, as the outer layer of the Al gets oxidised but not detached, an inert passivating layer is formed, and oxidation/corrosion of the object stops.
This may lead someone to say that Al is corroded less than Fe, but now it should be clear that no one means that is indeed harder to oxidise Al as compared to iron.
As the intrinsic properties of Al and Al oxide stay the same, the same happens if we have aluminium coating an inner metal, for instance steel or iron as in the discussion above or in the previous question by the same user. As such, Al is an effective protection layer for steel.
Finally and related: if Al doesn't cover the iron object, but it is merely in contact with it, still it maintains a protective function. A galvanic cell is form, of which Al is the anode.( Look for sacrificial anode).
As still Al can get passivated, a more effective sacrificial anode will be Mg, both in terms of even lower oxidation potential and especially reactivity of the oxide. It gets literally consumed and must be replaced, but meantime you won't have to buy a new boat or engine :)
I hope this makes some clarity.
(Note that the very very fine particles are intended to reduce the mass/surface ratio, little particles can self-passivate, too)
Edited: this is a general picture. Technologically/Material science: I do expect lot of details, much of which shall be on the practical attainment of the passivating layer, its morphology, its resistance to diffusion. It seems well known that aluminium oxide undergoes pitting corrosion upon prolonged permanence in solutions containing chloride ions, such as that of the question.


How common is it for an antivirus program to give false positive?

Question: Often antivirus programs trigger a false alarm that a certain file is corrupted or infected. How common is that and if it is too common, can we really rely on them?
Along with that, how easy it is to corrupt an antivirus?
Comment: *"how easy it is to corrupt antivirus"* - what do you mean with this? Disable antivirus by malware, hijack antivirus by malware to execute code, confuse antivirus by the user due to bad user interface  or even something different?
Comment: by corrupting I mean to make it stop working correctly, and yes, hijacking would be the next level.
Comment: Irfan, do you have any statistics to back that the often trigger a false alarm? I cannot think of many of those alarms during the last 10 years, and in such cases I always used the exception list feature to add the files in question.
I think virus scan vendors to a lot to prevent too many false positives. Also, scan databases are normally signed with a private/public key so you cannot easily fool the virus scanner. In the end, disabling it is the best way to stop it working. There are a lof of infections that were successful with that.
Answer:
... Often antivirus programs trigger a false alarm that a certain file is corrupted or infected. My question is that how common is that

There are detailed tests at https://www.av-comparatives.org/testmethod/false-alarm-tests/.
The results differ between vendors and time but on average can be said that the higher the detection rate (true positive) the higher will be the more false alarms will be triggered (false positive). This is because only parts of the malware is detected by clear signatures, the rest is detected by heuristics which will never be perfect.
These heuristics (or machine learning models) are tuned by the vendor for some specific balance between false positive and false negatives rate. False positives will confuse the user. If there are too much the user will disable the detection completely. False negatives (malware not detected) on the other hand will have a serious security impact too. And models or heuristics can usually be tuned how much false positives and negatives they produce - only the less false negatives they produce (i.e. the more malware they detect) the more false positives they will also produce (i.e. the more innocent files will be detected as malware).

...  and if it is too common, can we really rely on them.

There is no true yes or no. If you mean with "rely on them" that you blindly believe the results then no. If you mean  with "rely on them" that the AV results are true in most cases then then yes.  You are not totally safe from malware if you install an AV (or use the existing AV built into Windows) but the average user is usually much safer than without an AV.

... Along with that, how easy it is to corrupt antivirus.

Not trivial but possible for a determined attacker with enough knowledge and time. In the past there were several cases of AV being vulnerable to code execution attacks, often due to errors in parsing (deliberately corrupted) files. This was especially bad since many of these AV did there analysis as system user. Bypassing AV instead by hiding the malware so that the AV cannot properly see it, is much easier though.
Answer: As a software developer, I can confirm that false positives happen a lot.
I produce a very simple piece of software (less than 200 lines of code) but because it is compiled from Python and involves outgoing network connections it frequently (ie always) gets flagged by antivirus as malware.
Each time I compile a new version (even a tiny minor upgrade) Virustotal will show it as flagged as malware by between 2 and 10 antivirus products. This is despite paying for a signature which I use to digitally sign the executables.
Fixing this as a developer involves submitting the code to each antivirus provider and asking them to review it and whitelist it as a false positive.
Lots of them have really easy and organised processes to submit this and are very pro active (Microsoft and Malwarebytes generally fix within a few hours) but some of them are super painful. McAfee only accepts submission by email and has a bunch of different similarly named virus products which are difficult to work out.
Some distributors require a completely clean scan on VirusTotal which means that even if 69/70 virus scanners deem it clean you need to track down the one random Chinese antivirus provider who has a problem with it, and needless to say only has a website in Mandarin, to try to submit a ticket asking them to fix it.
Even once you're whitelisted that only applies to the specific executable. Want to add an installer option as well as the simple executable? That's new code so you need to whitelist with everyone again. Someone needs it to be distributed as an EXE inside a ZIP rather than just an EXE? Well it's likely that the ZIP will trip someone's algorithm even if they have judged the EXE clean.
It's a real, real pain and honestly puts me off adding new features to my code or releasing new versions. I often spend more time firefighting false malware positives on code than I have on writing the code itself.
Answer: You can probably feel yourself how common the false positive alert can be with VirusTotal.com.
Compile Some Window User form project built in DotNetFramework.
Then obfuscate the code in the project with confuserEx or some other obfuscator.
Now go to Virus total.com and run virus scanning
https://www.virustotal.com/gui/
You will see 2 to 30 AV software raising false positive alert among 70 AV software vendor.
Not having any single harmful code inside the file, this is pretty high false positive alert rate.
It is best to try yourself and see the results with your own eyes.
In my finding, more you obfuscate your code, you will get higher the rate of false positive alert. From my experience, this was even the case, when your project consists with buttons, textboxes, radio buttons, and some mathematical calculation only.
Answer: This is one of the major issues faced by antivirus programs. They can give false positive to anything you can possibly think of, apart from the most famous programs and sites.
In fact, they are some examples when some antivirus programs detected the most trusted sites as malware. Also, they can be corrupted and hijacked as well. A few years back this was easier, but now there have been some improvements in the security flaws.
Answer:
Often antivirus programs trigger a false alarm that a certain file is
corrupted or infected.

You say often antivirus programs triggers a false alarm. You said correct answer by yourself already. In fact, how you feel is correct. Anti Virus software triggers false alarm (aka false positive) frequently. That is probably how most of us feel.

My question is that how common is that and if it is too common, can we
really rely on them.

In fact, many anti virus software are based on similar heuristics. They do make a lot of mistakes raising false alarm for genuinely good and safe software.  If you are looking for statistics, then it would be hard to find one. First reason is that Anti virus software company does not feel comfortable to share such information because it would affect the sales for their anti virus software. You will also find that any negative post about anti virus software is removed from site too even if they are the honest opinion.
Even if you find such statistics, in my own opinion, testing results seems to be far from how we feel from everyday usage of anti virus software. From below link, you will find what anti virus software expert says about the accuracy of anti virus software. According this expert, anti virus software is only accurate around 45%.
https://www.theguardian.com/technology/2014/may/06/antivirus-software-fails-catch-attacks-security-expert-symantec
It means anti virus software is correct at 45% and they are wrong at 55% of time. This is not a direct answer to your question. However, at least, you could figure out some ideas on the frequency of false positive based on this 45% accuracy of anti virus software.

Along with that, how easy it is to corrupt antivirus.

I do not understand your question fully. I rephrased your question like:
"how easy it is to test antivirus false positive at my own computer at home."
I will try to answer. In fact, you can do some simple experiment.

Just create some simple windows form application using c sharp or any other language.

Then use confuserEx or other software to obfuscate to the highest level.

Next, scan the windows form application from virustotal.com.

Then you will see the false positive alert over 90%.
Comment: You can't take the finding from 2014 that AV "misses 55% of attacks" and then make any kind of conclusion about the false positive rate. That entire section of your answer is faulty. And no, your interpretation of the "corruption" question is not correct. Irfan explained what he meant in the comments. So, that entire section doesn't apply. And an AV alerting on the use of confuserEx is not a false positive. It is the job to alert on obfuscated binaries. They will even say that the binary is obfuscated, not that it is confirmed to be malicious.
Comment: And if you read the other answers, you will see that there *are* public tests on flase positive rates. So the first part of your question isn't correct. I think you need to rethink this entire answer.
Comment: If AV software honestly tell that the AV software does not have the ability to tell the obfuscated binaries is virus or not, then it should be fine. But AV software always label the most of obfuscated binaries as Trojan or some other virus type. That is inaccurate detection lowering the reliability of AV software but no AV company correct that. That is the big problem. Check on virustotal.com with some genuine safe application but obfuscated binaries will be often raised as Trojan or other virus. If this is not false positive, then what is false positive ?
Answer: This small program is triggering 5 AV scanners:
<code>int APIENTRY WinMain( HINSTANCE hInst, HINSTANCE phi, char *CmdLine, int CmdShow )
{
   return 0;
}
</code>
Comment: I'm not sure this is useful. There are dozens of AV. Which ones trigger? What techniques do they use? Are they signature-only? The fact that this code creates flags isn't very interesting without context.
Comment: I think he wants to proof that even this harmless code can trigger an AV


What do you call collective intelligence?

Question: Collective intelligence is a form of wisdom of crowds. What together an aggregation knows is often pretty comparable with expert opinions. What is one word (or at most two) that describes this kind of community knowledge?
Comment: Don't expect there to be a possible one-word solution for everything (or even most things). There isn't. That said, my immediate thought when I read the title of the question was ***Borg***.
Comment: commun knowledge or collective intelligence is fine as it is. Why looking for something more complicated ?
Comment: Looking merely for one word that can capture this essence, is all. Even if the word is a combination of two others, or a new one altogether that makes the same sense. Ambitious?
Comment: Of course, we are not always wiser in the aggregate, as recognized in the concept and studies of groupthink. http://en.wikipedia.org/wiki/Groupthink
Answer: You're very close; Wikipedia says the preferred term is collective wisdom:

Collective wisdom, also called group wisdom and co-intelligence, is
  shared knowledge arrived at by individuals and groups.

This rather cuts across a classification I like:
knowledge: knowing what (ie basic factual knowledge)
understanding: understanding why (things inter-relate, work, happen)
wisdom: understanding how (to alter things for the better, and putting these changes into effect).
Comment: Am actually looking merely for a one-word version. Or maybe a invented word, combining two existing ones innovatively so it carries this same sense. Or even root words, maybe.

Co-intel is not bad, but any other?
Comment: "What is one word **(or at most two)**"?
Comment: @Saugata Invented? That would take it off-topic; this website is centred on the English language as it is used.
Comment: Edwin, when I say 'invented', I mean innovative English usage like portmanteau words.
Comment: Perhaps you haven't read nohat's sound comments on meta: Requests for coinage ... this as an invitation to start coining words. I really don't feel comfortable at all with our site becoming a place where people go who want a word invented.
Answer: I believe you are looking for lore.

collective knowledge or wisdom on a particular subject, esp of a traditional nature
Comment: Lore does have connotations of not necessarily being true so if you want to avoid those a quick thesaurus search with lore turns up 'doctrine' which is probably equally suitable in some cases.
Answer: Crowdsourcing or 'Crowd sourcing' is today's common usage, and is so recognized for solving  crimes/mysteries that public officials are directly appealing to enthusiasts

"Simply defined, crowdsourcing represents the act of a company or
  institution taking a function once performed by employees and
  outsourcing it to an undefined (and generally large) network of people
  in the form of an open call. This can take the form of peer-production
  (when the job is performed collaboratively), but is also often
  undertaken by sole individuals. The crucial prerequisite is the use of
  the open call format and the large network of potential laborers." -
Answer: folk wisdom

folk wisdom: knowledge or beliefs associated with or traditional to the common people of a country


Updating variance of a dataset

Question: In an application, I deal will a large number of images from which I successively extract particular values to compute their means and variances. Because storing them all would mean storing Gigas, I'd like to store only things that would allow me to compute the global means and variances. What do I have to store?
Comment: Do you mean that you wish to update the mean and variance - that is, given a computed mean and variance on the first $t-1$ observations you want to compute them on $t$ observations? Are these univariate variances, or variance-covariance matrices? In the univariate case, you only need store a few values.
Answer: In the absence of information to the contrary I assume you want univariate calculations and you want the $n-1$-denominator version of variance.
One useful way is to update the sums of squares of deviations from the mean, which I'll call SSE.
Let's say that at time $t$ you have $\bar x$, $\text{SSE}$ and $s^2$, and an observation, $x_{t+1}$ and you want to have those three computed quantities at time $t+1$.
Here's how you can update them:
$t=t+1\\
e_t = x_t-\bar x\quad\text{     # note that the  } \bar x \text{  term there is the previous mean} \\
\bar x = \bar x + e_t/t \\
\text{SSE} = \text{SSE} + e_t\cdot (x_t-\bar x)\quad\text{     # note that the term there is NOT } e_t^2\\
s^2 = SSE/(t-1)
$
This calculation is much more stable than the raw calculation of $\sum_i^t x_i^2$ version (which you'll find in many old books, and which is not too bad when working by hand, where you can see when you're losing precision). It is not the most stable possible calculation, but is sufficient for almost all purposes. If stability does become an issue for you there are some other things that can be done.
As @January rightly points out, I've given an on-line algorithm and you seem to only want the values at the end. In that case, the above algorithm can be sped up a little, for example, by not calculating $s^2$ each iteration.
Alternatively, the algorithm suggested by @January below can be made much more stable by subtracting an estimate of the mean from each observation before taking the sums and sums of squares. Algebraically it doesn't change the mean, but it makes it substantially more stable. It doesn't need a very good estimate to make a big difference; often the first observation is sufficient (since usually the situations where, say, the first observation is a very bad estimate of the mean are the situations where it really doesn't matter).
See also https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
Comment: Necro 10 years later :D. IMO this is still the best we can do. Lately the only change I've made is using Kahan Summations to fix floating point errors in the SSE and sum for the mean. https://en.wikipedia.org/wiki/Kahan_summation_algorithm
Comment: +1, you are totally right about the stability -- $x_i^2$ can grow very fast. However, that depends on your implementation; keeping track of sum and sum of squares is less computationally intensive.
Comment: @January It's not so much the way the sum of squares grows but when the standard deviation is very small compared to the mean that runs into the big problem. You can get catastrophic loss of precision when subtracting the square of the mean. I am also not so sure your version is actually less computationally intensive.
Comment: Looking at the algorithms as described, mine has one fewer multiplication/division operations and two more addition/subtraction operations. Which is faster depends on the relative speeds of those, which is platform dependent. However, there's a way to save a multiplication/division off January's outline, so that algorithm is potentially faster by two addition/subtraction operations per iteration. (A couple of subtractions is a cheap price to pay for the increase in stability)
Comment: um, yes, but only if you are calculating the SSE and mean in each step, which would not be very clever (if I understand the problem correctly, he only wants to calculate the variance and mean at the end). And then I have a single multiplication, two sums and one increment in each step, vs. your three multiplications, three sums and one increment.
Comment: @January That's a good point; I took him to be wanting them at each step, but it looks it's not the case. In the case where they're only required at the end, I could save some calculations from my algorithm as well, but yours would still be a little faster.
Answer: That is not really a question for CrossValidated, but here it comes: you only need to store three values:

current number of variables,
current sum of squares of the variables
current sum of the variables.

That's because variance can be expressed in terms of $\sum x_i^2$ and $(\sum x_i)^2$.
$var(X) = \frac{\sum (\bar{x} - x_i)^2}{n}$
and
$\sum( \bar{x} - x_i)^2 = \sum \bar{x}^2 - 2\cdot \bar{x} \sum x_i + \sum x_i^2 = $
$= n\cdot\bar{x}^2 - 2\cdot \bar{x} \cdot n\cdot \bar{x} + \sum x_i^2 =$
$=\sum x_i^2 - n\cdot\bar{x}^2 $
The main disadvantage of this method is that the sum of squares tends to grow very fast and might be problematic to store; Glenn's variant (in the other answer) is better in this respect, but computationally (slightly) more intensive.
Comment: Actually I think the question is on topic here, falling under 'statistical computing' but it would also be on topic at SO.
Comment: The biggest problem with this one in raw form isn't storage (though that can be an issue), it's *catastrophic loss of precision* whenever the standard deviation is very small compared to the mean.

Updating variance of a dataset


menu content link in Backend VS menu content link in UI

Question: Goal:
Have a common and same menu content link (for instance Home, about, consumer product, support)  when you are using Angular, NativeScript and Android.
Background:
The menu contain seven different name. Each name is distinguish.
The backend is .net core with SQL server.
Problem:
Two approaches:
First solution:
Should the name from the menu should be located inside of backend? In order words, you retrieve the content of the menu from the backend and display in each UI (angular, android etc.)
Cons:
You use the concept DRY and less maintenance.
Second solution:
The second one is to have the content of the menu in each UI without request for the content of the menu at backend.
The main question is:
What experience have you been through in this situation.
Which of these two solution should I go and why?
Any pros and cons?
Thank you!
Answer: Trying to create a generic solution that loads an UI definition and renders it dynamically sounds like it should save work, but that's usually not the case. At that point, you're effectively creating your own UI framework. Simple platform-specific adaptions (e.g. changing the color of a link but only on Android) will get more difficult.
Sometimes, the effort of creating a generic solution is worth it. That might be the case if these links change very frequently, or are even generated dynamically on the fly. Then you might not want to publish a new version of your Android app, but would rather load a new UI definition from the server. And if you're doing it for one frontend, you might also use the same technique for others.
But if these links change rarely, it will likely be much less effort to update them manually in all places. To keep the different frontends in sync, you might use a traceability matrix instead: a document or spreadsheet where you list all your features, and track where that feature has been shipped or is in progress:
<code>   feature       web      nativescript    Android
------------ ----------- -------------- ------------
     ...         ...           ...           ...
support link  not needed   2020-09-22   (ticket 123)
</code>
So I can't directly recommend what you should do. Instead, consider some guiding questions:

Will either solution make something impossible? E.g. loading links from the backend might slow down the app, or make platform-specific changes more difficult.

Will either solution enable unique capabilities? E.g. hardcoding might make offline support easier, loading links from the backend simplifies updates.

How much does each solution cost? There are immediate costs for the effort of implementing the solution, but there might also be long-term savings if it reduces future work.

How easy is this decision to change? If a design can't be changed later, the design requires much more careful thought. Loading links dynamically makes it easier to change the links, but now you're pretty locked in to keeping this backend service running, or you might break an old version of the app.


Google Sheets - List values if date in corresponding column is the same as the date in Cell D1

Question: In Sheet 1 I have a table of orders due for a delivery. Column A is a list of the order numbers, and column H is the delivery date. In Sheet 2, I want to create a list of the order numbers that have a delivery date that is the same as the date in Sheet 2 Cell D1, which already updates itself as required. I have tried a VLookup, but of course this will only return the first value it finds. I have also tried an IFERROR(Filter formula but am struggling to assign the criteria.
Comment: Welcome to [Web Applications Stack Exchange](https://webapps.stackexchange.com/tour). Please [edit](https://webapps.stackexchange.com/posts/168291/edit) your question and insert a [table](https://webapps.stackexchange.com/editing-help#tables) of sample data together with a [table](https://webapps.stackexchange.com/editing-help#tables) that shows your manually entered desired results. Also consider sharing a sample spreadsheet. There is a [blank sheet maker](https://docs.google.com/forms/d/e/1FAIpQLSeprZS3Al0n7JiVQIEiCi_Ad9FRXbpgB7x1-Wq6iAfdmVbWiA/viewform) that lets you share safely.
Answer: Try this in Sheet2:
=filter(Sheet1!A2:A, Sheet1!H2:H = D1)

Answer: Try with this formula:
=filter(Sheet1!A2:A,D1=Sheet1!H2:H)

Answer: Like the other answers have mentioned, the FILTER() function is a good solution here. However, I would include the use DATEVALUE() for robustness to different date formats. For example, try this:
=FILTER(Sheet1!A2:A, DATEVALUE(Sheet1!H2:H) = DATEVALUE(D1))
Below is an example of this formula on a sheet with various date field formats in both the variable date and the dates in the order list, where the order values that should match are highlighted orange, the variable date in blue and the filter results in green. You can see the actual formula used in the screenshot.
Comment: Oh, perhaps the values are not dates but _text strings_ that just look like dates. That's indeed a use case for `datevalue()`. You can find if the "dates" really are numeric dates with the `isdate_strict()` function.
Comment: The `datevalue()` function will truncate datetimes to dates only, which indeed is often useful. When all values are dates rather than datetimes, `datevalue()` is superfluous. See [this answer](https://webapps.stackexchange.com/a/153710/269219) to see why.
Comment: @doubleunary, thanks for the comment! Any idea why the above won't work on those different formats without DATEVALUE()?
Comment: Ah yeah makes sense, thanks. I didn't know about isdate_strict() either; appreciate the knowledge!
Comment: The date values are generated by a lookup function from a list of set dates in another tab, so should be date values rather than text strings. However I know the people who'll be using this and would not rule out someone overwriting with a text string that looks like a date, so to have this failsafe built in from the start is advantageous


Help with marking keyframes for the timeline

Question: I am trying to work on a 2D animation in Blender, but the markers for the keyframes in the timeline disappeared because I had the express keys for my drawing tablet on. I am trying to make it so the diamond-shaped markers reappear on the timeline. What do I do?
Comment: If you're really talking about frame MARKERS, and not keyframes, float your cursor anywhere in the timeline and press 'm' to add a frame marker at the current position of the playhead.
Comment: Try going in object mode, deselect - reselect the Grease pencil object and return to the draw mode.
Comment: josh sanfelici, I did that, but the markers still aren't there.
Answer: Grease Pencil keyframes are separate from the scene keyframes so they don't show on the timeline nor on the general dopesheet. To see them you have to set a viewport to Dope Sheet then set that dope sheet's mode to Grease Pencil.


Geometric intuition of conjugate function

Question: I am looking for a geometric and intuitive explanation of the conjugate function and how it maps to the below analytical formula.
$$ f^*(y)= \sup_{x \in \operatorname{dom} f } (y^Tx-f(x))$$
Comment: This mini-paper by Bauschke and Lucet does a great job explaining the conjugate with examples and pictures. Link here: https://people.ok.ubc.ca/bauschke/Research/68.pdf
Comment: You can improve this post by asking a more specific question.
Comment: Yes, maybe change the question to "Geometric intuition of conjugate function" or something similar.
Answer: To me the best interpretation is economic. Interpret $f(x)$ as the cost to produce the quantity $x$ of some product and interpret $y$ as the market price per unit. Now notice that $f^*(y)$ represents the optimal profit at given prices $y$. The quantity $xy$ represents revenue from sales and $f(x)$ represents production costs.
Now for the geometrical interpretation. If you sketch the graph of the costs of production $f(x)$ and assume it convex, continuous, and differentiable, you will see that the point of optimal production, given prices $y$, is given by $y - f'(x)=0$, and this can be found graphically with a ruler, looking for the tangent in the cost curve with the same slope $y$. If you place the ruler in that tangent point, it can be seen that the ruler intersection with the vertical axis will give $-(xy - f(x))$.
This is a very useful calculating device. Provided only with the graph of $f(x)$ and a ruler, the analyst is able to turn the ruler and find what is the optimal profit for each possible price. This can be plotted into another piece of paper. Then given any price $y$ he is able to find what was the optimal profit. Without noticing, he has discovered the conjugate function.
Comment: This is actually a really useful explanation, +1
Comment: That comes from the definition: $f^*(y)= \sup_{x \in \operatorname{dom} f } (y^Tx-f(x))$. The function being optimized represents $x$ units sold at given prices $y$ (your revenue) minus the production costs $f(x)$. This optimization is finding the quantity $x$ to produce that gives maximum profit.
Comment: An excellent, intuitive explanation!
Comment: "It is easy to see that f∗(y) represents the optimal profit at given prices y." Not for me. I don't see it. Perhaps I'm stupid. Can you explain this?
Comment: By far the best explanation. Thank you for making me finally understand conjugate function. +1
Comment: What is the "optimal profit"? Is is the smallest selling price for which we are not loosing money?
Comment: This setting assumes that the producer is a price-taker, with the price given by the market. He only gets to choose $x$, how much to produce, and it might be that the 'optimal profit' is negative. In that case, it is a loss, but still the best he can do.
Answer: I found Bertsekas' explanations quite simple and useful to understand many different things in convex analysis and optimization. You may want to check out his book "Convex Optimization Theory", or his notes for the MIT course, which also cover conjugacy.
The short explanation on page 7 of the notes is as follows:

Dual description of convex functions

Define a closed convex function by its epigraph.
Describe the epigraph by hyperplanes.
Associate hyperplanes with crossing points (the conjugate function).

Primal description: Values $f(x)$. Dual description: Crossing points $f^*(y)$.
Comment: "Horrible" seems a bit exaggerated to me. There's no need to go through all 340 pages: reading page 7 is sufficient.
Comment: Great recommendation.
Answer: I'm going to attempt a very basic and intuitively understandable explanation. Of course this will be grossly oversimplifying things but I understand it's what was asked for.
The point of the convex conjugate is to represent a function $f$ as a set of tangent hyperplanes. The parameters of all the tangent hyperplanes are encoded in the convex conjugate function $f^*$.
Let's make things easier to understand by covering the 1D case. In that case our $f^*$ is called the Legendre transformation and our hyperplanes become simple lines. The generalization to multidimensional functionals is then relatively straightforward.
Here's the Legendre transformation:
$f^*(y)=\sup(yx - f(x))$
The domain of $f^*$ is slope values, the co-domain is y-offsets (as in a simple line equation $ax + b$). Hence $f^*$ encodes a set of lines. First we're going to evaluate $f^*$ at a single point $y$.
$f^*$ at a point $y$ is the largest difference value between $f$ and a line through the origin with slope $y$.
Note that this value might be still negative. In plain English, it's the degree to which $yx$ "surpasses" $f(x)$ in value. If your function $f$ goes "above" $yx$ (for example $f(x) = x^2+1$ and $y=0.5$) then the value $f^*(y)$ will be negative. If your function goes "below" $yx$ your value will be positive.
The "surpass value" is important because in the convex case it is one parameter of a tangent line to $f$: the y-offset.
To imagine $f^*(y)$ not just for a single value $y$ but for the entire domain, picture $f(x)$ and a line through the origin that's rotating around the origin, like a propeller. For each incremental rotation we plot the largest difference value between $f$ and the line into a new coordinate system (where $y$ may go along the x-axis and $f^*(y)$ may go along the y-axis). The resulting graph then shows the whole Legendre transformation of $f$.
The Wikipedia Article on Legendre transformations also has some more good information, such as:
If the convex function $f$ is defined on the whole line and is everywhere differentiable, then $f^*(y)$ can be interpreted as the negative of the y-intercept of the tangent line to the graph of f that has slope $y$.
So $f^*$ can be seen as a map where the input is a slope and the output is a y-offset in the coordinate system of $f$. Thus $f^*$ holds the information how much I need to offset a line with a particular slope such that it becomes a tangent to $f$. The set of all the lines offset in y by their respective amounts covers the area at and below $f$.
It's not too hard to imagine why that particular trick only works for convex functions.
PS: If $f$ is convex there is a much easier definition of the Legendre transformation which avoids the whole supremum thing:
$f^*(f'(x))=x*f'(x)-f(x)$
In plain English: For $x$ We compute $f'(x)$ and define $f^*$ at $f'(x)$ as the negative y intercept of the tangent line.
Answer: You can think of conjugate function as an extended infimum function. For $y=0$,$\ f^*(y)$ is simply the infimum of $f$. Here I try to explain what it means geometrically.
Assume:
$x \in \mathbb{R}^n$
, $x_{n+1}= f(x) \in \mathbb{R}$
I denote the axis that measures the output of $f$ as $x_{n+1}$.
Note that we always measure the infimum of a function according to the line $x_{n+1}=0$. Think of finding the infimum of $f$ as finding the supremum of a set $S$:
$ inf(f) = sup(S = \{ 0 - f(x) | x \in dom f\})$
But what if we wanted to measure the infimum of $f$ according to an inclined line that passes through the origin, say, $y^Tx=0$? This is where we can use conjugate function. It takes the slope of the line as its input, and outputs $f$'s infimum according to the line $y^Tx=0$. So its formula should make sense now. It looks like the case above:
$f^*(y) = sup(S = \{y^Tx - f(x)|x\in dom f\})$
As an example of its usage, we sometimes need to measure this extended infimum function in Lagrange dual function for finding a lower bound on the optimal value of an optimization problem.
Answer: Some intuition might come from thinking in terms of support functions. Given a set $A\subseteq \mathbb{R}^n$, its support function is given by
$$h_A(x)\equiv \sup\{x\cdot a: \,\,a\in A\}.$$
The idea is simple: the support function attempts to describe a set by the set of its support hyperplanes. For each direction $x\in\mathbb{R}^n$, we project the set $A$ onto $x$, and look for the largest value of the projection. This will correspond to an hyperplane that has normal vector $x$, and is tangent to $A$. More precisely, $h_A(x)$ tells you that said tangent hyperplane is
$$\{y\in\mathbb{R}^n : \,\, x\cdot y=h_A(x)\}.$$
If $A$ is convex, then it is completely characterised by the set of its support hyperplanes, and thus there is a bijection between $A$ and $h_A$.
Consider now a function $f:\mathbb{R}^n\to \tilde{\mathbb{R}}$, and its epigraph:
$$\operatorname{epi}(f)\equiv \{(x,\alpha)\in\mathbb{R}^{n+1}: \,\, f(x)\le \alpha\}\subseteq \mathbb{R}^{n+1}.$$
Geometrically, this is the set of point that sit above (or on) the graph of $f$. A function $f$ is convex (as a function) iff its epigraph is (as a set).
Because we now have a convex set to deal with, the epigraph of $f$, a natural question is how can we characterise it via its support hyperplanes, i.e., what's its support function. We have
$$h_{\operatorname{epi}(f)}(\mathbf x^*,y^*) =
\sup_{\mathbf x\in\mathbb{R}^n, \,\, \alpha\ge f(\mathbf x)} \left(\mathbf x^*\cdot\mathbf x+y^* \alpha\right).$$
Note that I'm strictly following the definition of $h_A(x)$ I gave above.
But we can now observe something else: for the characterisation in terms of hyperplanes, we don't need to look at $h_A(\mathbf x^*)$ for all $\mathbf x^*\in\mathbb{R}^n$. Rather, it's enough to look at all directions. This can mean all $\mathbf x^*$ such that $\|\mathbf x^*\|=1$. But it can also mean, if we have a subset of $\mathbb{R}^{n+1}$ like we do here, that it's enough to only look at "direction vectors" of the form $(\mathbf x,\pm1)$ for all $\mathbf x\in\mathbb{R}^n$.
But also, $h_{\operatorname{epi}(f)}(\mathbf x^*,1)$ is bound to always be infinite for convex $f$ (think of what the tangent hyperplanes of such functions look like).
It is therefore sufficient to look at $h_{\operatorname{epi}(f)}(\mathbf x^*,-1)$. If we use the definition above, this is
$$h_{\operatorname{epi}(f)}(\mathbf x^*,-1)
\equiv \sup_{\mathbf x\in\mathbb{R}^n} \left(\mathbf x^*\cdot\mathbf x-f(\mathbf x)\right).$$
Note that we could remove the $\alpha\ge f(\mathbf x)$ part of the sup because maximising with respect to such $\alpha$ is trivial: we need the $\alpha$ that maximises $-\alpha$ and is such that $\alpha\ge f(\mathbf x)$, and this is clearly just $-f(\mathbf x)$.
We just found precisely the convex conjugate of $f$.
We conclude that the convex conjugate of $f$ can be given the precise geometric interpretation of the function characterising the set of tangent hyperplanes to the (epi)graph of $f$.
See also Please explain the intuition behind the dual problem in optimization., and Physical interpretation and notions about conjugate function?.


Exclude Random Redirect from caching?

Question:
I have just deployed the W3 Total Cache plugin on my dedicated server (moillusions.com), but am not sure if it works already (server load still high).
I have a very important random link generator: moillusions.com/?random. Yet I am not sure how to exclude this from caching? (so it's always a different link when clicked)
Answer: Use jQuery or Javascript to cycle through and randomly pick one of your links, this way you can bypass the caching?
var messages = ["Good!", "Great!", "Awesome!", "Super!", "Nice!"];
function getMessage() {
   return messages[Math.floor(Math.random() * messages.length)];
}

From https://stackoverflow.com/questions/3419928/how-can-i-return-a-random-value-from-an-array
Answer:
What this plugin is supposed to do about server load, if anything?
This depends on caching setup you use, good caching plugins try to intelligently skip obviously dynamic pages with query arguments in URL.
Comment: @vurdlak make sure that _Performance > Page Cache > General > Cache URIs with query string variables_ is not checked. Although I don't see how this matters since that performs redirect to post which can be cached just fine, has little to do with how user got there.
Comment: sorry, thought it's w3 total cache help forum (mistake)
Comment: anyone knows how to disable the url.com?random from caching with w3 total cache?
Comment: hi, this is because when I click moillusions.com?random it brings me to a page, and when I'm over reading it, click it again, but brings me to same page (as ?random is cached to same page). let me try this what you said
Comment: @Rarst.. this is unchecked by default, yet random doesn't refresh to new page when clicked again (always brings to same page)
Comment: @vurdlak yep, redirect header does seem to stay same... I am not sure about this, you might be better of contacting W3TC developer
Comment: ok, w3 guys are on it, let's see if they can help

Exclude Random Redirect from caching?


Acting with a finite number of rotations on a set of positive measure can you fill almost the whole circle?

Question: Let $E\subset S^1$ have positive Lebesgue measure. Do there exist finitely many rotations
$r_1, r_2, \dots ,r_n$ such that $r_1E\cup r_2E\cup \dots\cup r_nE$  has measure $2\pi$? Or is there a counterexample?
Answer: The answer is no. Take a compact set $E$ with positive measure buth empty interior and assume that $K=r_1 E\cup r_2 E \cdots \cup r_n E$ has measure $2\pi$. Then $K$ would be dense in $S^1$, hence equal to $S^1$, since it is closed. But this is impossible, since $K$ has empty interior, too.
Comment: You can take a Cantor set of positive measure
Comment: @Capublanca Thanks. In that case it is true, by a limit argument, since using a countable dense set of rotations one can cover almost all the circle (see https://mathoverflow.net/questions/358506/acting-with-all-rational-rotations-on-a-subset-of-the-circle-having-positive-mea).
Comment: Do you have an exmple of a compact set with positive mesure but empty interior?
Comment: Of course  I wanted to delete my comment   but to late, you answered already.  Also, your  answer to the main question is very nice!
Comment: Nice answer! What can be said if we relax the condition to: for every $\varepsilon>0$, there exist $n$ rotations such that $r_1E\cup\ldots r_nE$ has measure greater than $2\pi-\varepsilon$?


If every open set is regular open, and every singleton is closed, does it follow that every set is clopen?

Question: I'm new to topology (my main interests are in logic), so forgive me if my question is a bit clumsy. Let $\langle X, A(X) \rangle$ be a topology on $X$. Define a regular open set as an open set which is equal to the interior of its own closure. Suppose that, for every $x \in X$,   $\{x\} \in F(X)$ ($F(X)$ being the set of all closed sets). Does it follow that every open set is also closed? I've been trying to prove this implication for a while, but to no avail; I suspect it's false (i.e. it does not follow that every open set is clopen). However, I haven't been able to construct a counterexample (probably because of my ignorance about those matters). Any ideas?
Answer: Hint.  Suppose that $X$ satisies the given conditions, and let $x \in X$.  As $\{ x \}$ is closed, then $X \setminus \{ x \}$ is open, and therefore regular open. Clearly $$X \setminus \{ x \} \subseteq \overline{ X \setminus \{ x \} } \subseteq X.$$ That fact that $X \setminus \{ x \}$ is regular open allows us to actually determine what $\overline{ X \setminus \{ x \} }$ is.
This will tell you something new about all singletons in $X$, which will then tell you something about all subsets of the space.
Comment: @Nagase: You're making it **much more difficult** than necessary. In particular, we already know what $\mathrm{Int} ( \overline{ X \setminus \{ x \} } )$ is: it's $X \setminus \{ x \}$, since the set is regular open. My hint tells you that $\overline{ X \setminus \{ x \} }$ is either $X \setminus \{ x \}$ or $X$. Can you calculate the interior of either of these sets?
Comment: I'm still struggling a little bit with it. When you say that "the conditions on the space allow us to actually determine what $\overline{X \setminus \{x\}}$ is", do I have to use both conditions (i.e. that every open set is regular and that every singleton is closed) in order to extract the relevant information?
Comment: @Nagase: I've rephrased for clarity. (It was a bit more opaque than I had intended.)
Comment: Hmm. I've been trying to think contrapositively; suppose there is $y \in X$ such that $y \not \in \text{int}(\overline{X \setminus \{x\}})$. This means that there is an open set (say, $V$) such that $y \in V$ and $V \not \subseteq \overline{X \setminus \{x\}}$. On the other hand, suppose there is $y \in X$ such that $y \not \in \overline{X \setminus \{x\}}$. Then there is an open set (say, $O$) such that $y \in O$ and $O \cap X \setminus \{x\} = \varnothing$. This means that either $O = \varnothing$ or $O = \{x\}$ (and thus $y=x$). But I can't go further than this... am I on the right track?
Comment: Ahh, yea, sorry for being dense, I hadn't realized what those set inclusions meant. Well, since both sets are open, they are their own interior. But, if $\overline{X\setminus\{x\}} = X$, then $\mathrm{Int}(\overline{X\setminus\{x\}}) = \mathrm{Int}X = X$, which means that $X \setminus \{x\} = X$, which is absurd. So $\overline{X\setminus\{x\}} = X \setminus\{x\}$, right?
Comment: Got it. So $X\setminus \{x\}$ is closed, which means that every singleton is open. Thus every subset of $X$ is clopen. That's it, right?
Comment: @Nagase: It looks like you've got it!
Comment: Thanks a lot. Me and one of my professors (who knows a lot about logic, but not much about topology) have been struggling with this for weeks! That was very helpful.


Awareness of unconditional positive regard

Question: When Unconditional Positive Regard is in use through several therapy sessions and a client asks about this technique. What explanation should be given?
Comment: To those that voted to close: What is unclear about this question? It is perfectly intelligible, as the answer illustrates.
Answer: Unconditional Positive Regard is one of the core conditions in Person Centered Counselling and so is congruence.
In order for you to provide Unconditional  Positive Regard (UPR), you need to be congruent and in order for you to be congruent you need to be genuine in your responses.  Therefore, you should only provide the truth to any question asked.
You need to tell them what UPR is and that in order for UPR to exist you will be non-judgemental and you would provide a safe and warm environment for them to explore what is troubling them in the here and now.


Deploy to production with git using Acquia like localserver

Question: I'm using Acquia to export my local proyect to production proyect but when I did git push just the code was saved, the changes that I did in UI was not saved for example I created a user in local UI but it did not reflect in production UI, do I have to use drush to do that?
Answer: You're missing the database. git only handles files.
So export your local database, and import it in production.
For that you could use drush sql-sync, but you need to set it up properly.
You could also export the database to an .sql file via phpMyAdmin or your preferred db-tool. and then in aquia devcloud, you import that .sql file.


Extreme case of double jeopardy

Question: I have a very unique and interesting theoretical debate I'm trying to find the answer to. Suppose that I am accused and found guilty of murder of a person (ex. Bob). I serve my time for the murder and am released from imprisonment. Suddenly, Bob is found alive (therefore I didn't murder him). At this point, I've done my sentencing for the murder of Bob and he's still alive. Since this has happened, am I able to "murder" Bob and not be charged with his murder (since I have already done a sentencing for his murder)? Or would I still be charged with his murder since it's a different criminal instance?
Comment: Very similar to https://law.stackexchange.com/questions/15277/can-double-jeopardy-be-a-loophole-for-murder?rq=1 (and not actually so unique).  The short answer is no, you can still be tried for the "second" murder.
Comment: You would still be charged as the instance is indeed different, but the more interesting question is whether the previously served sentence (which should not have been imposed) would temper (or even negate) the new one.
Comment: @Greendrake nah. Actually in the contrary... the law might actually by default make you a repeat offender unless the first conviction is overturned first.
Answer: canada

Or would I still be charged with his murder since it's a different criminal instance?

Yes, this is the correct intuition. Different instance/wrong; different basis for the charge; not precluded by double-jeopardy.
In Canada, the term of art is autrefois convict. Section 609 of the Criminal Code lays out the standard for what it means for the count to be the same:

the matter on which the accused was given in charge on the former trial is the same in whole or in part as that on which it is proposed to give him in charge

The later charge for murdering Bob would be a wholly different circumstance or "wrong" or "delict" than the first conviction was based on. The later charge would not be precluded.
Answer: Facts

You were convicted for the death of Bob that happened on YYYY-MM-DD
Your sentence is not for life or a death sentence
You are released from prison and have served your time
You meet Bob and stab him to death on ZZZZ-MM-DD

Double jeopardy?
After your new arrest your lawyer attempts double jeopardy, pointing to the prior conviction and release. The Police laugh, the state attorney laughs and then threatens the lawyer with referencing them to the bar, because the argument is more than frivolous: You are not for arrest for the murder of Bob on YYYY-MM-DD but for the one on ZZZZ-MM-DD! You will face trial for this separate instance of murder.
This is not the 1999 film Double Jeopardy, which is founded on the same misconception!
The trial
The state will only have to prove that you killed Bob in year ZZZZ, and may use your wrongful conviction in year YYYY as evidence for a motive. The jury will be instructed that the time served between YYYY and ZZZZ is to be disregarded. The state can show beyond a reasonable doubt that Bob is dead this time and you serve for life this time.
Comment: @NeilMeyer the first conviction will be overturned *at some point* but the second conviction will stand.
Comment: @NeilMeyer Imagine someone else killed Bob after your sentence expired. Do you think the court would have to say "no, Alice was falsely convicted of Bob's murder 25 years ago, so now Carl was free to kill Bob without punishment?" Because this situation would pose exactly the same "you can't be murdered twice" problem as the original question.
Comment: I dont see how the same person can be held to be murdered twice.

Extreme case of double jeopardy


What can I do about qadha for a Ramadan from over a year ago?

Question: Brothers and sisters, I am 14 years old, and about two years ago, I hit puberty, and unfortunately started masturbating. And all of Ramadan I masturbated and broke most of my fasts.at that point of my life,
I didn't really care for religion, and I didn't even consider making them up. Is it permissible for me to make them up NOW, 2 Ramadans later?
Comment: Yes, think of it like a debt or money you owe. Regardless how much time passes, the debt is always with you until you repay.
Answer: It is obligatory on you to fullfill your missed fasts and breaking your fasts both of them if you are able to do so
It is narrated in Muwatta Malik that Yahya related to me from Malik from Abd ar-Rahman ibn al-Qasim that his father used to say,
"If someone has to make up for days not fasted in Ramadan and does not do them before the next Ramadan comes although he is strong enough to do so, he should feed a poor man with a mudd of wheat for every day that he has missed, and he has to fast the days he owes as well."
if a person is fasting and he intentionally breaks his fast (without any valid reason) by eating, drinking or engaging in sexual intercourse intentionally then not only will it be compulsory for him to do qada of that fast, it will also be compulsory for him to observe kaffara. The kaffara for intentionally breaking the fast in Ramadan is to fast for two consecutive months. This is if he starts on the first day of a lunar month. Otherwise (if he doesn't start on the first day of a lunar month), he must fast for 60 consecutive days. In this duration (of 2 months or 60 days), the days when it is prohibited to fast (i.e. the 2 Eid days and 3 days of Ayyam al-Tashreeq) must not come. If a person does not have the strength to fast for two consecutive months then he must feed 60 poor people with two meals (or alternatively he can give each one of them the value of sadaqa al-fitr).
It is better if you could ask any Mufti or talk to your Imam of mosque directly
so he could guide you if you are not mature enough to understand this.


migrate list with lookup filed from sharepoint 2010 to sharepoint online

Question: How can I migrate list with lookup fields from sharepoint 2010 to sharepoint online
Answer: First, we need to have an inventory of all lookup lists in the environment - probably we can use the ShareGate tool for this reporting purpose.
Then, using any of the third-party migration tools ShareGate, Metalogix, etc. migrate the parent list (dependent list) first then migrate the main list.
Answer: Consider using SharePoint Migration Tool, which allows you to migrate lists with lookup fields.
You will need to migrate all lists at once so that it carries the lookup connection from SharePoint on-premises to Online.
Individual migration for lists with lookup fields is not supported for the time being.


How do I test for TrueCrypt?

Question: I'm fairly certain my Ubuntu 11.10 install has truecrypt for my home directory, but how can I check. Preferably without rebooting into a live disk install?
Answer: The command
mount | awk '$3 == "'"$HOME"'"'

would give you an output line if your home is a mounpoint, with information about the type of filesystem. This should also allow to detect a truecrypt home folder.
Answer: If your home directory is encrypted (not truecrypted, there is difference), you can tell by looking for ~/.Private and ~/.ecryptfs in ls -la: ls -la | grep ".Private" for example.

How do I test for TrueCrypt?


Why does the wheel size affect the cars gearing?

Question: Using online gearing top speed calculators I realized that the bigger the diameter of the wheels, the higher the theoretical gearing top speed is. Why is that? Why does bigger wheel act as increasing the gear ratio and thus increasing the theoretical gearing top speed, does bigger wheels also reduce the torque going to the ground because it makes the gearing taller?
Comment: You use the word "wheel" in both the title and the body text. Wheel size isn't determinative. Instead, it's the size (diameter and therefore circumference) of the **tire** that affects the car's gearing. Because tires can have different aspect ratios, same-size wheels with different aspect ratio tires will result in changed gearing. The overall tire diameter is what matters.
Comment: yes thats what i meant with wheel. doesnt wheel mean both rim + tire combined?
Comment: I agree that the word "wheel" is sometimes used to indicate the wheel + tire combination, but that use is imprecise because of "sometimes." Your question addresses the exterior dimensions of the tire; because you don't define what you mean by the word "wheel," you risk the reader getting off track. It would be more accurate here to use "tire."
Answer: The answer lies in the rpm conversion to ground travel. Any gearing in a motor vehicle is designed to provide sufficient torque to begin moving (with load, of course) and to keep the engine in the appropriate rpm range.
Consider one thousand engine revolutions. The transmission converts that through the cogs and shafts and belts (CVT) and torque converters (automatic transmissions/locking) into a different value on the output shaft. Depending on the vehicle design, this revolution is then passed through a differential, which is going to change the value again.
Allowing for the incredibly high revolutions per minute of an internal combustion engine, the ratio will be substantial. As an example, Car & Driver magazine, November 2022, p.53, lists 5.2 miles per hour per 1000 rpm for the 2023 Toyota GR Corolla Circuit. This would represent the speed on the tested tires, Michelin Pilot Sport 4, 235/40ZR18. Sixty thousand revolutions during that hour traveling five point two miles calculates to about six inches for each engine revolution. An increase in tire diameter of approximately one-third of an inch adds an inch of travel.
Changing the tire size to something smaller would result in less distance traveled during that one hour and conversely, a larger tire would result in a greater distance traveled.
As you suggest, the effective gearing is also changed. The last mechanical conversion of the power train is the distance from the center of the wheel to the ground. A lever with a greater length (larger tire), pivoting from one end (wheel hub) requires more force to move the equivalent mass at the end (entire motor vehicle) than a smaller lever (smaller tire) does.
Small tires = more torque, less speed. Large tires = less torque, more speed.
This is obviously a simplification, but does factor in when one allows for the necessity to either re-calibrate one's speedometer or determine the speed change with a tire change.
Comment: Actually, small tires don't increase torque compared to large tires. They increase force. With a small tire, the torque is the same but the force that torque creates is larger. So the tire is the device that converts rotational movement and force (torque) to linear movement and linear force.
Comment: @juhist - What fred is stating about small tires and the increase in torque is not inaccurate, just simplistic. A smaller tire does increase the torque applied (ie: force) in changing the twisting motion to linear force. The [Khan Academy](https://www.khanacademy.org/science/physics/torque-angular-momentum/torque-tutorial/a/torque) states, "*An increase in torque comes with a proportional decrease in rotational speed.*", which is pretty much what fred is stating. The tire is a cog in the system between the engine and the road. Reducing radius increases the applied torque.


set variable of flow from class apex through button in visualforce

Question: is it possible set a value of variable of flow thanks apex class using a button in the visualforce?
I try to explain myself better,
I have a flow and a custom button in a visualforce, i would like that after click of button the field of flow is populated with a value that I defined in apex class.
Answer: You can set variables of flow from its' url.
There are various types of Flow variables. Use Input and Output variable in your case. You can use such variable in url and pass its' value to the flow from apex. Your method can be something like this.
<code>public Pagereference openMyFlow() {

    String myVariableValue = 'some value';
    String flowUrl = '/flow/My_test_Flow?myIOvariable=' + myVariableValue;
    Pagereference pr = new Pagereference(flowUrl);

    return pr;
}
</code>


Advantages Using Principal Component Analysis

Question: What are the advantages using Principal Components as input for neural networks compared to using "normal input" for neural networks?
Comment: a) variable selection to reduce overfitting (assuming largest PCs preserve 'signal' b) improved gradient descent (if sphered input data, ie covariance of input is identity)
Answer: You can read a nice description of PCA here.
The advantage of PCA (one method of dimension reduction) in the context of ML (ie. neural networks) would be to reduce the risk of over fitting and reduce computational complexity.
You could also phrase your question as: what are the alternatives to PCA?
For PCA vs Partial Least Squares, see this Cross Validated post
For PCA vs random subspace projection see this Cross Validated post
Answer: I think this question has been asked countless number of times here... You want PCA because you want to reduce your input size and thus improve training time and less likely to overfit.


Can I see the currently checked out revision number in Tortoise SVN?

Question: I'd like to know what the currently checked out revision number is for a file or directory. Is there a way to do this in TortoiseSVN on Windows ?
Answer: Right-click on the working directory in windows explorer, and select "Properties" (Not TortoiseSVN->Properties).  You will see the Properties dialog, which will have a tab called "Subversion".  Click on it, and you will see the version number, and other info.
Comment: "Properties" is not the TortoiseSVN properties but the usual Windows explorer properties.
Comment: Strange...  I have used in on Windows Server 2003 and 2008, both 64-bit.  Are you sure that you have Tortoise installed?  Can you see the Tortoise icons showing the status of the versioned files?
Comment: To my understanding the displayed version number corresponds to the last svn update (or svn checkout if there was no svn update afterwards). Any svn commit which has been applied on the local directory afterwards is ignored. In order to see the 'last' revision number of any update or commit see the answer of @nishantcop: Bold line in TortoiseSVN Log. (Tested on Windows 10, TortoiseSVN 1.13.1, Subversion 1.13.0)
Answer: Not in tortoise but in command line.
<code>svn info
</code>
will return what rev you are checked out on.
Comment: I'll +1 on this answer because this SO-answer is returned by google when I searched for "svn currently checked out revision". And you answered at least that ;-)
Comment: It tells you a revision number, but not whether that revision is the HEAD or not.  For that I think you need to use `svnlook youngest /var/svn/xyz` on the raw repository path... surely an easier way to see whether you are at HEAD?
Answer: TortoiseSVN -> Show log: The line in bold marks the current revision in your working copy.
Comment: while the accepted answer is the fastest one, this seems to be the "canonical TSVN answer" ;)
Comment: To do the same thing from command line use: `svn -r HEAD info --show-item last-changed-revision`
Answer: If you are using XP, change your Explorer windows to Details View. Navigate to an SVN-controlled folder then go to View > Choose Details and select the SVN columns for status/rev/etc.
Comment: Unfortunately, this doesn't work in Vista or Windows 7 Beta. http://tortoisesvn.net/docs/release/TortoiseSVN_en/tsvn-dug-wcstatus.html
Comment: Working on Windows Server 2003 64Bit.
Answer: Thanks John, that's very useful but doesn't show the revision for the root folder of a project.
Now that you've pointed me in the right direction, I have found that I can right-click the folder, select properties and a TortoiseSVN tab appears which contains the revision number.
Comment: Add this as a comment to his question then. You don't need to pretend this is an answer.
Comment: It is an answer. John's answer was not quite what I was looking for. This is.

Turns out that Dima submitted the same answer so I'll accept his.
Answer: Before
"Change your Explorer windows to Details View. Navigate to an SVN-controlled folder then go to View > Choose Details and select the SVN columns for status/rev/etc."
you have to change your Windows Registry settings, adding this DWORD value
HKCU\Software\TortoiseSVN\ColumnsEveryWhere
and setting it to 1, as stated in the TortoiseSVN documentation.
Answer: nice one John Sheehan. I always just right clicked on the root folder and selected tortoise-svn | view log
.


Assign "remainder" weights to bone?

Question: I have a face mesh with a number of detail bones (e.g. eyebrows, lips). The latter have all been weighted accurately, but some vertex weights, whether they are contributed to by one or more bones, may not add up to 1.0. I would like to assign the remainder (missing, 1 - current sum) weights to their parent bone, "head". How can I do this? Currently, all accurately-weighted bones' VGs are locked (only the "head" VG, which is currently empty, is unlocked).
Answer: Through the use of locking vertex groups and the "normalize all" operation.
In weight paint mode, select all vertices for which you'd like to do this.  In properties/object data/vertex groups, select your head group, make sure your weight is set to 1.0 (the default), and click "assign" to assign all selected verts to your head group.
Next, using the dropdown to the right of the list of vertex groups, use a "lock all" vertex groups operation, then unlock your head group, so that it is the only unlocked group.  (You've already done this, but future readers need to understand that this is an important part of the process).
Now, in the 3D viewport, use a "normalize all" operation (from the searchbar or weights menu.)  In its operator panel, uncheck "Lock Active".
The normalize all operation will calculate proper, normalized values for all vertex groups, for each vertex.  Because all vertex groups except head are locked, only the head group will be normalized, and it will be normalized around the existing weights-- ie, the head group for each vertex will become equal to 1 - current (non-head) weight.
Comment: @Nintendraw No, if the weights are 0, or unassigned, the normalize all operation will leave them with 0 weights (or unassigned weights.)
Comment: Without having opened Blender again to check: Would this work even if no vertices were assigned to the target group (or all vertices removed)? I had left the head VG completely empty, as in 0.000 weights when I wrote the question.

Assign "remainder" weights to bone?


Can you tell me the difference between 'all over the world' and 'throughout the world'?

Question: Could you tell me the difference between these phrases: 'all over the world' and 'throughout the world' as well as give me some examples?
Answer: They mean the same thing.
As a British person, there's a very slight difference in what the phrases make me visualise but it's subjective. And it only really matters for descriptive language, because the two phrases have the exact same definition. Just think about other times you would use 'all over' and other times you would use 'throughout' and how that affects the mental image for the reader.
Comment: Thank you so much. Hope you have a nice day!
Comment: While their message is the same, you might prefer one or the other in a certain context. For example, I would say; **Her songs were sung all over the world.** and **The virus spread throughout the world.** This choice is not correct or wrong, it's merely personal. It's what sounds best to you.


parametric polar equation of a circle

Question: I discovered that Mac's Grapher has a parametric polar mode, i.e. where $r$ and $\theta$ can be specified in terms of a parameter, usually $t$.  I am attempting to convert the generic equation for a circle into this format, i.e. from $(x-h)^2+(y-k)^2=g^2$.  (I randomly chose $g$ as the radius to avoid $r$ collisions.)  It is not going well.  I keep making cardioids or weirder shapes.  How can you specify equations for $r$ and $\theta$ in terms of $t$ for a circle of radius $g$ and Cartesian center of $(h,k)$?

[https://i.stack.imgur.com/YvfNv.jpg ]
Comment: https://en.wikipedia.org/wiki/Polar_coordinate_system#Circle gives the general equation of a circle in polar coordinates. Parametrize away! If you want to work it out for yourself, I suggest starting with the cartesian equation and converting it to polar.
Comment: Isn't that just $x=h+rcos(t)$ and $y=k+rsin(t)$?
Answer: One possibility (not very pretty) is to take a parametric form of the cartesian equation and convert that to polar coordinates. Starting from your suggested $x=h+g\cos t$, $y=k+g\sin t$ you can get $$\begin{align} r&=\sqrt{(h+g\cos t)^2+(k+g\sin t)^2} \\ \theta &= \arctan{k+g\sin t\over h+g\cos t}.\end{align}$$ You'll need to use the atan2 function in Grapher so that $\theta$ ends up in the correct quadrant.
Comment: I fear that is as good as it gets.  The polar form ($r=...$) of a circle $g$ about $(h,k)$ is pretty nasty, so that makes sense.  You have my vote!
Answer: A cross between polar and cartesian will lead you nowhere.
A two parameter annular ring of eccentric circles  of radius $R$ is:
$$  x = \sqrt { e^2  + R^2 + 2 e R \cos \phi} \, \cos \theta ; \, y= \sqrt { e^2  + R^2 + 2 e R \cos\phi} \, \sin \theta , $$
out of which choose a single value of desired polar angle $\theta$ for  radius vector of circle centre.

parametric polar equation of a circle


Combining information from two point layers based on the nearest neighbour relationship

Question: I have two layers: One a modeled dataset with points on a 1x1km grid across the globe. I also have another layer which is my own data points which are scattered across the globe. What I want to do is find the nearest modeled value from the 1x1 grid data and append that to my table for my data points.
I thought it would be a join function but as the points are not from the exact same coordinates I need some way of extracting the nearest point to my sample point.
Can someone help me with which tool to use and how best to use it?
I am using ArcGIS and Windows 10.
Answer: You can use spatial join in the toolbox, or join based on spatial location (see the first drop down menu in the "join" form (right click > join and relate > join).