Number of Umbilical points

Question: Studying umbilical points on a surface, I wonder if for a convex surface there will be some similar formula to the four vertex theorem, ie will exist some minimum number of umbilical points for $ S $ convex?
Answer: Caratheodory conjecture
This was proven between 1940 and 1959 by different authors (Hamburger,
Bol, Klotz 1959 [798]) for surfaces which are strictly convex and real analytic.
Answer: The works by Hamburger, Bol, and Klotz are concerned only with the very special case where the surface is analytic. A solution to the smooth case was announced by Guilfoyle and Klingenberg in a paper posted on the arXiv in 2008. That paper has been revised twice since then, but does not appear to have been accepted for publication yet. Some other references related to Caratheodory's conjecture may be found here.

Number of Umbilical points


Name of a circuit element. Switch or toggle?

Question: What's correct name of this circuit element — switch or toggle?
Comment: This seems more a question about circuitry terminology than English. The image does not convey anything useful to those who are not already familiar with the domain. You can improve your question by providing a description of the diagram and giving a sample sentence which illustrates your desired use of "switch" or "toggle".
Comment: "Toggle" implies that the switch latches when operated.
Comment: The diagram is clear to those with even a basic scientific or electrical education such as accompanies a basic education in the use of English. The question is clear and a unique answer exists (a switch may select one of many positions whereas a toggle alternates between only two positions). The question therefore should not be closed.
Answer: The name of the symbol is "switch". See BBC Bitesize Electrical Circuit Symbols.
Comment: A *toggle* is a switch, but it's a particular **type** of switch, generally with a [lever which is moved up and down](https://www.google.com/search?q=electrical+toggle+switch&tbm=isch).
Answer: A switch is a circuit element which is intended to connect or disconnect an electric current, so what you show is a switch.  In UK usage the word 'switch' is often combined with another word to show what sort of physical switch is meant, so a toggle switch is operated by a lever (as stated by Andrew Leach). In my fifty-plus years of electrical engineering I have not come across 'toggle' on its own in this context.
There are also rocker switches, push switches, tilt switches and many others.


Any subring of $K[X]$ that contains $K$ is noetherian; not all of such subrings are UFDs

Question: Let $K$ be a field. Show that any subring of $K[X]$ that contains $K$ is noetherian.  Give an example that demonstrates not all of these subrings are UFDs.
Comment: Were you asking for help with these questions? Could you say how far you've gotten so far in considering them?
Comment: This has been asked before, by the way. Have you tried searching before asking?
Answer: Let $K\subset R\subset K[X]$. There exists $f\in R$ such that $\deg f\ge 1$. Since $R[X]=K[X]$ and $X$ is integral over $R$ the extension $R\subset K[X]$ is integral and finitely generated, so it is finite. But $K[X]$ is noetherian, and the Eakin-Nagata theorem implies that $R$ is noetherian.
Now take $R=K[X^2,X^3]$. This is not an UFD since $X^2$ is irreducible and not prime ($X^2\mid X^6$, but $X^2\not\mid X^3$.)
Remark. An elementary argument for showing that $R$ is noetherian can be found here.
Answer: Let $R$ be the $k$-subalgebra of $k[x_1,x_2]$ generated by all the monomials of the form $x_1 x_2^i$ for $i \in \mathbb{Z}_{\geq 0}$ (so a $k$-linear basis of $R$ is the set of monomials $x_1^i x_2^j$ such that $i \neq 0$ if $j \neq 0$). The ideal of $R$ generated by these monomials is not finitely generated, so $R$ is not Noetherian and the first claim is false. This kind of thing can't happen in just one variable (details upon request).
Here is an example that shows that even for a finitely generated subring, the UFD property isn't inherited: Let $R$ be the subring generated by $K$ and $x_1 x_2$, $x_3 x_4$, $x_1 x_4$, and $x_2 x_3$. Then $x_1 x_2 x_3 x_4=(x_1 x_2)(x_3 x_4)=(x_1 x_4)(x_2 x_3)$ shows that $R$ is not a UFD.
Comment: It's amusing that someone has downvoted this for no apparent reason. This was posted before the original post was edited down to the one-variable case; maybe the down-voter thought that my answer was a non-sequitur, when in fact it gives a perfectly valid answer to the original question?


Schichttorte; a 20 layer German broiled cake

Question: I am making the cake named above, which I found on a British baking site. It call s for 5 1/2 oz of reg flour-sifted, and 2 1/4 oz of sifted corn flour. ? Does anyone know if this recipe in this context is calling for actual corn "flour" or is it cornstarch?
  Hope someone has the correct answer for me.  Thanks so much!
Comment: @Johannes_B in most places around the world, corn flour and cornstarch are not synonyms.
Comment: It is the very same thing. There is no difference (except the name)
Comment: Hi Sandy, it is not "in this context", it is standard British terminology.
Answer: Actual corn "flour" is not a traditional ingredient in Schichttorte. The common translation of corn flour translates to the German equivalent of "corn starch".
To be sure, you can have a look at different recipes for "Baumkuchen". It's the same batter as for Schichttorte, but baked on a stake instead of a flat surface.
Comment: The OP states that the recipe was from a British source. That means it uses what's known in Britain as corn flour. The same product happens to be called corn starch in other places.


Is it possible to connect your phone to the computer and use the PCs' headset?

Question: I've got a splendid headset for my computer and I want to use it with my phone. The connection between headset and the PC is via USB 2.0. I wonder if it is possible to connect your phone to the computer and use the PCs' headset?
Answer: Sorry, but that isn't going to work. The audio is only delivered over the headphone jack; not USB.
Maybe you can find a USB to 35mm headphone adapter, and try that. I can't promise it would work, but is should be at least worth a try.
Answer: You can connect via Bluetooth and play music from the phone and make calls. By USB un can only use Computer Internet Connection.
Edit: Sorry I think I misunderstood what you whant. Since you can connect Windows Phone in PC via bluetooth I think you can use PC headset instead of PC speacker.
Comment: @BennySkogberg Good to hear that. If it really solve the puzzle please remember to mark as answer. ;)
Comment: Count on it :-)


Best career record vs par

Question: I read a USA Today article that talked about how Tiger Woods is nearly 2000 under par* for his career.  I've tried searching, but how does this compare to others all-time?
Obviously this is a rolling score since Tiger could end up shooting over par for the rest of his career and end up at 1500 under or something, but is this the lowest in history?  I'm just looking for some comparable stat to compare against the other all time greats' career scores.
Comment: I'm interested in these statistics as well, but the article does explicitly state that they have compiled such information. I would assume (given if golf has comprehensive records in previous eras compared to golf today. eg, "[strokes gained putting](http://www.pgatour.com/stats/academicdata/shotlink.html)") that this is doable with a tedious amount of work.
Answer: In regards to the score versus par number referenced, it's difficult to ascertain a specific answer about how it compares against other greats.  However, I think we can safely say that Tiger's number is the lowest in history for the following reasons.
Yearly Scoring Average
Looking at the list of Vardon Trophy winners shows a list of the lowest scoring average for golfers each year as far back when Jimmy Demaret averaged 69.90 for the year in 1947.  Viewing these numbers, Tiger Woods won this award and subsequently held the lowest scoring average 9 times (1999 - 2004, 2005, 2007, 2009, 2013) with an average over those 9 years of 68.39.  Only 14 other golfers won the award more than once.  Additionally, no other golfer on the list even scored as low as the AVERAGE of Tiger's 9 years in a single year.  Before 1988, there were only 10 years in which the lowest yearly scoring average was lower than 70.
This strongly suggests that no one in history has come close to touching Tiger's historic low scoring records.
Scoring In Majors (versus Jack)
The widely-regarded top 2 golfers in history are, of course, Tiger Woods and Jack Nicklaus.  Jack is the most likely to have a chance to match Tiger in this career score versus par considering his long-term success in majors and the PGA Tour in general.  This link from 2014 sought to compare Jack and Tiger over their first 14 major tournament wins.  The stats near the bottom of the page tell the tale quite well.

Scoring Average: Jack 71.41, Tiger 70.82
Score Versus Par: Jack +78, Tiger -109

Even in a small sample of 14 wins each, Tiger outscores probably the second best in history by 187 strokes -- or an average of more than 13 strokes better per major. It's hard to imagine a scenario that Jack finished with a better career scoring total versus par considering these numbers.

Prior to 1947, stats are somewhat harder to come by, but a quick look at some of the greats from that era show that scores were much higher during those times.  Additionally, match play was much more common in the majors during those times so an accurate number would be impossible to measure.  However, Walter Hagen and Bobby Jones are the best regarded golfers of that era and looking at even a few of their winning scores shows that they were nowhere near the level of low scoring seen in today's Tour.

Best career record vs par


Sync desktop application with android application

Question: I want to raise an event from my Android application to my desktop application which is in Java. Can I do so? If yes, which API to use? Any examples or code snippets?
Comment: Can you add more details? What is your use case? What's your intended way of communication? What have you already done/tried?
Answer: Both android and desktop applications are clients. Two clients can talk to each other via server or at least initialize their connection via server that is running on pre-defined location (IP address). So, you need some server that allows to do this.
You can probably use (or abuse) some 3rd party servers for this. For example if your desktop application "knows" the phone number it can send SMS via one of available web services. The android application will catch the SMS and take information from its text. You probably can use Skype installed on your machine or email to send messages among applications too. But better way is to develop your own server that exposes RESTful API and use it for the negotiation.
Comment: can i use sockets in android to trigger my desktop application??


Not able to see the standard User lookup field for custom object in a tab, even as System Administrator profile

Question: I have created a custom object with several fields in which one of the field is of type lookup to the reference to the User object. When I created a tab to add records to this object, I can only see all the other custom fields except this User lookup field. I ma logged in as System Administrator which should have access to that User object.
Comment: You switch between terminology a few times here. Is your relationship field a standard field (like, say, `CreatedById` or `LastModifiedById`), or is it a custom field (with an API name ending in `__c`)? If it's a custom field, is this issue something you see in the org that you created the custom field in, or in an org that you _deployed_ this custom field to?
Comment: My relationship field is custom field something like Release_Manager__c which is of type User. I have only one org where I deployed my DX project which I locally developed.
Answer: I'm not 100% sure if this is how things work (because I haven't used sfdx in this capacity), but...
When you create a new field on an SObject, and deploy that field to another org, the permissions for that field are generally not transferred to the receiving org.
Long story short, unless you know for a fact that you're deploying profile data too1, you'll need to at the bare minimum set the Field Level Security (FLS) for the new field in your receiving org.
By default, a field2 deployed to a new org has the FLS set to disallow everyone (even sysadmins) from reading or writing the field. You'll be able to see the field in the object manager (in the setup menu) but not be able to see it on layouts (or even query it, for that matter).
I have a feeling that this also applies to fields created in a scratch org and then deployed to another org, as well as fields created "directly" as xml files in an SFDX project (if you're crazy enough to do that).
One more time for clarity:

If you create a field via the web UI of Salesforce, you have the chance to set FLS when you create the field
If you deploy a field to an org, setting the FLS is something you need to do as well (and is typically a separate step from deploying the field)

1: or a PermissionSet, and you've already assigned the permission set to users in the receiving org
2: With the possible exception of formula fields
Comment: My object is a brand new custom object which was created through web UI only with 6 fields in which one of it is a lookup field which is reference to User object. When I create a tab for this custom object to insert data, I am able to see only 5 fields as shown in the above image, but the lookup field which is referencing User object is not rendered in the form. Hence I cannot proceed with creating data. This is all happening in single org. There is no context of multiple orgs here.
Answer: Check your Field visibility and after that, if that field is added on the corresponding page layout!!!!


How to enable multi-touch gestured with Apple Magic Trackpad on Ubuntu 16.04

Question: I've successfully paired my Apple Magic Trackpad (first revision) by Bluetooth. The cursor movement, single/double-click and two-finger scroll - works great.
But I'd like to enable other gestures, like zooming, change desktop-workspaces with a swipe, etc.
I googled the problem and found two packets that could help me: touchegg and mtrack, but neither did help on my Ubuntu 16.04.
Does anyone have experience with configuring Apple Magic Trackpad?
Answer: A good way to swipe with the Magic Trackpad or similar good touchpad, is to use and configure libinput-gesture (https://github.com/bulletmark/libinput-gestures) to convert gestures to xdotool compiz windows arrangements.
Touchegg is good for a touchscreen. Both work well together on a laptop with both input touch devices.
My Full example here :
https://ubuntu-mate.community/t/touch-input-with-touchpad-libinput-and-touchscreen-synaptics/12931
Answer: I had this same question a while ago and as @xlinbsd said, Touchegg seems to be the most highly recommended package to use to configure multitouch gestures for Magic Trackpad.
Now that you know about Touchegg, there are a ton of resources available explaining how to use it with the Magic Trackpad, e.g. here, here, here (if you just search touchegg magic trackpad in this forum you'll get tons of results)
If touchegg doesn't work for you I've seen other packages recommended, like libinputgestures
Good luck! Let us know how it works out!
Comment: @SorenA This appears to be an attempt to answer the question to me.
Comment: This does not really answer the question. If you have a different question, you can ask it by clicking [Ask Question](https://askubuntu.com/questions/ask). You can also [add a bounty](https://askubuntu.com/help/privileges/set-bounties) to draw more attention to this question once you have enough [reputation](https://askubuntu.com/help/whats-reputation). - [From Review](/review/low-quality-posts/820372)


ifilter for search in sharepoint 2010

Question: We ahave scenario hwere we configured our sharepoint 2010 search to a folder which is having xml files and when we try to find the results for example if we are searching for japan  we are getting as 180-12.xml but we need as in wording as japan to show in results.So is there any way to make the xml files internally crawled so that we can get the desired reults.can we use ifilter to crawl intenal elements of xml files to show up in results.How to use ifilter in that case please provide some useful links and information.Please help me out with suggestions.Thanks in advance.
Answer: It sounds as if search is correctly crawling the XML content if it is returning appropriate values in the results.  In your case, you probably need to customize the search results web part to display the information you desire.
Comment: Hi Eric thanks for the response but is there any way to make our search to hit the internal property of xml file  to show up in results..what would be the best ways to do so..please suggest on this thanks
Answer: you would need a 3rd party iFilter, there are plenty on google, but I have never seen on that is free sorry.
You could set out to write you're own but the only Microsoft article I can find is this

ifilter for search in sharepoint 2010


What is your liability if you hit a super expensive car?

Question: Assume you get in an accident that is your fault and cause $300,000 damage to a $1,000,000 Lamborghini. Your insurance pays up to $100,000 in property damage. Are you responsible for the remaining $200,000? What if it was a rare $10 million dollar car that was totaled (you just dented it, but the car is very fragile)?
Answer: Liability
The concept of liability for damages is to place the wronged party in the same position that they would have been in but for the wrongful act.
If restoring their car costs $300,000 then you are liable for $300,000. If the car is a total write off then you are liable for the cost of them getting an equivalent replacement, usually assessed at market value of the asset.
Insurance
Insurance is a different concept. An insurance company agrees to indemnify you for liability for your negligence within the limits of your policy: these usually include a deductable and a limit and sometimes a co-payment.
You are liable to the wronged party - your insurer indemnifies you. If your insurance doen't cover all of your liability, you are responsible for the balance.
Comment: This isn't actually universal. There are jurisdictions (e.g the Netherlands) where the insurer is liable towards the owner of the damaged car. The insured party can still be liable for damage in excess of the limit, but that's a liability towards his insurer.
Answer: You are responsible for whatever property damage you cause, and if you do not have sufficient liability insurance to cover that damage, the injured party may sue you for the rest. None of the $10 million cars are very fragile and would not be totalled by tapping it at 10 mph, but let's say you creamed a 1961 Ferrari 250 GT California SWB Spider by plowing into it at 200 mph, then you could be liable for a large chunk of change. There is no provision in the law that says a person can only be held responsible for e.g. the first million dollars of property damage. Since it is impossible to extract blood from a turnip, you might not actually have to pay the whole cost.
Comment: If you plow into a car at 200MPH, it's more likely that your estate is going to be liable for the damage.
Comment: @ohwilleke: I don't think that high-speed rail has level crossings at all. A bit more on-topic, in general the design of transport infrastructure is aimed at preventing massive, expensive accidents. Speed limits are one way to achieve that, and violating those liits can definitely affect insurance payout.
Comment: @cpast Unless, of course, you are driving a high speed train (e.g. in Japan) and are liable, for example, because a design flaw caused the tracks to be crossed by a road without a crossing gate.
Comment: @MSalters " I don't think that high-speed rail has level crossings at all." That it why having one would be considered a "design flaw" although the example wasn't terribly serious.


Audio file playing in background once button is clicked

Question: I have tried to get a audio file I downloaded as an mp3 to play on a webpage once a button is clicked. When I open my html with live server it is working fine. Something with connecting through heroku isn't recognizing the audio file. I've tried many tips from the internet but nothing is working. The file is in the same folder as everything else.
<code>let button = document.querySelector('button')
let audio = new Audio("trash_Kid.mp3")

const buttonAlert = () => {
    audio.play();
    alert(`Get good kid!`)
}

button.addEventListener('click', buttonAlert)
</code>
Answer: Try to upload your .mp3 file in some another server and then just reference it with an absolute/external URL. Could be a Heroku limitation with audio files.


Big O Proof , f(n) = 2n + 1 and I have to prove f(n) is O n^2

Question: If I have $f(n) = 2n + 1$ and I  have to prove $f(n) \in O(n^2)$, by proving there exists positive constants $c$ and $n_0$ such that $f(n)<cn^2, \forall n\ge n_0$, can I do this all in one step by putting in values of $c$ and $n_0$ at once or do I have to put in values of c first and then get n on one side and put in values for $n_0$, the for all $n \ge n_0$ confuses me.
Answer: It all depends on the case and how easy it is to search $n_0$ or use $c$, in your case you can show that $2n + 1$ belongs to $n^2$, taking the constant $c = 1$, so that in the proof of BigO, $g (n)$ dominates $f(n)$, what is the same $2n + 1 \le c (n^2)\to  2n + 1 \le n^2$; now you can search a $n_0$.
Answer: equation here is f(n) < c(n^2), here we have 2 unknowns,
a mathematical equation with one unknown can be solved in 1 step,
but with two unknowns you have to substitute one with some value to find another one. the number of steps increase with number of unknowns.
So No its not possible to do all this in one step.
Also definition of big O is intuitive, by proving f(n) < cg(n) we are proving that f(n) does not grow faster than g(n),
in our case f(n) is a linear equation, while g(n) is quadratic, its obvious that a quadratic equation will grow faster than any linear equation(meaning linear equation grows like 1,2,3,4,5 while quadratic will grow like 1,2,4,8,16 so on i hope you get my point).
Answer: You have to demonstrate that there is one c and one $n_0$ such that 2n+1 <= c $n^2$ for all $n >= n_0$. In this case, 2n+1 <= $3n^2$ for n >= 1, 2n+1 <= 1.25 $n^2$ for n >= 2, 2n+1 <= 7/9 $n^2$ for n >= 3 etc, so there are many combinations for c, n_0.
To prove this, you usually go the easiest way possible. For example 2n+1 <= 2n^2 + n^2 = 3 n^2, so c = 3 and $n_0$ = 1 works. There is no need to find the smallest possible c or $n_0$.


Group operation is well defined

Question: One of the most common manipulations performed when working with group equations is left or right multiplication, i.e. if you have a group $G$ with $a,b,c \in G$ and you have something of the form $a = b$, we can then say that $ac = bc$ and $ca = cb$. How can one prove this statement from the basic axioms of group theory? I have proved it under the assumption of left and right cancellation properties, but the only proofs I have seen of those properties relies on this fact.
Comment: The definition of a group requires a set $G$ and a binary operation $\cdot$ on $G$ — i.e., a function $f\colon G \times G \to G$, $(a,b) \mapsto f(a,b)$, which we denote by $a \cdot b$ or $ab$. By definition, a binary operation is a well defined function, so if $a = a'$, then $f(a,b) = f(a',b)$ (or $ab = a'b$). This is a matter of definition. You can't "prove" it from the axioms.
Comment: The left and right cancellation properties follow from the fact that every element in a group has an inverse, one of the defining properties of a group. So you can't really ask for something more basic than that.
Comment: @M.Vinay Thank you, this is the level of scrutiny I was looking for.
Comment: @EthanAlwaise : The question isn't about proving cancellation.  The question is about justifying simultaneous left- or right-multiplication of a pre-existing equation.
Comment: Adding to Eric Towers' comment: if $a=b$, that means that $a$ and $b$ are "the same" (without getting into philosophical discussions), so you do something to it (namely, multiply by $c$ on the right or on the left) and you end up with the same result. That is a first principle from equality.
Comment: @EthanAlwaise If one could prove cancellation from basic principles, I would be satisfied. However if I have something along the lines of $ax = ay$, the only way I know how to deduce that $x = y$ is rely on right multiplication by $a^{-1}$, which is what we want to prove...
Comment: @LuizCordeiro I agree and that makes sense to me, however I am looking for a concrete proof of this fact.
Answer: I'm not sure what part of other answers are not satisfying, so let me break this down to basic set theoretic concepts and see if that helps.
Formally, a group is defined to be a set $G$ together with a function $\phi : G \times G \to G$ (the group operation) satisfying some axioms (which won't be used for this problem). We usually use the shorter "binary operation notation"
$$ab = \phi(a,b), \quad a,b \in G
$$
but let me stick with the function notation for the moment.
Suppose we are given $a,b,c \in G$.
If $a=b$ then we have equality of the ordered pairs $(a,c)=(b,c) \in G \times G$ (this is one of the basic properties of ordered pairs, part of set theory).
Since $\phi$ is a function, we therefore have equality of the following values of $\phi$, namely $\phi(a,c)=\phi(b,c) \in G$ (this is one of the basic properties of a function, also part of set theory).
Returning now to binary operation notation, it follows that $ac=bc$.
Comment: The *ordered pair* comes to the rescue once again! For a much less trivial example see [this answer](http://math.stackexchange.com/a/2658/242) for the role that the ordered pair played in rigorizing the idea of complex numbers.
Comment: This is what I was looking for and actually how I convinced myself after M. Vinay's comment. It might be worth mentioning that this came up when working through a model theory exercise, which is why I was looking for such a high level of scrutiny.
Answer: Let $G$ be a group, and for all $c \in G$ define $\phi_c$to  be the function $\phi_c:G \rightarrow G:a \mapsto ca$.  Starting with the equation $a=b$, we apply $\phi_c$ to both sides and equality still holds: $ca = cb$, because functions are well-defined: given a specific input, the output is fixed.  When we say $a=b$, we guarantee that we provide the same input to both copies of $\phi_c$:  \begin{align}
    a &= b & &\text{given} \\
    \phi_c(a) &= \phi_c(b) & &\text{definition of function} \\
    ca &= cb & &\text{definition of $\phi_c$}  \text{.}
\end{align}
A similar argument applies to right-multiplication.
In short, we define "function" so that equal inputs give equal outputs.
Comment: Incorrect.  That's a group axiom.  Every row and every column of the multiplication table is a permutation of the elements of the group.  This is a consequence of inverses existing.  I.e. $\phi_{c^{-1}}$ is well defined by axiom, but every $c$ is someone else's $c^{-1}$.
Comment: This assumes that $\phi_{c}$ is well-defined, which is what we are trying to prove.
Comment: You merely asserted that $\phi_{c}$ is a function, and all functions are well-defined by definition. However based on the basic group axioms (identity, associativity, closure, and inverses), I fail to see how every row and every column of the multiplication table is a permutation of the elements of the group (though I know this to be true). The comments of the original post is more what I was looking for.
Comment: @Oiler a function doesn't have to be a permutation. The cancellation property tells you that multiplication by an element *does* permute the group, but that's not necessary to manipulate equations. You can do that whether multiplication is invertible or not. All it requires is that it be defined at all. If it's not a function, then it doesn't even make sense, so there isn't really a situation where what you're asking could ever fail. It's practically tautological. +1, I think the downvote is unjustified.
Comment: @Oiler : It occurs to me that you are incorrect for an even more fundamental reason.  A group is a set with a binary relation (called multiplication).  Consequently, $\phi_c$ is well defined by definition.
Answer: The $=$ generally implies that the two sides are in fact equal. In that case there's nothing to justify; since the two sides are identical, you can do whatever you want to one side as long as you do the same to the other side.
You can come up with a "proof" by saying that left multiplication by $c$ is a function from the group to itself, and "when two elements of the domain are equal then the value of the function is the same on each of them". But in that case "two" does not count the number of unique elements, since there really is only one.
It's possible to learn so much math you forget that some things are obvious. As you progress this will pass.
Edit: This concept is not really obvious in the broadest sense of the word. It was one of the most brilliant breakthroughs in mathematics and it is the basis of all algebra. But anyone studying group theory has most likely been familiar with this concept for years.

Group operation is well defined


What is the time complexity of Lasso regression?

Question: What is the asymptotic time complexity of Lasso regression as either the number of rows or columns grows?
Answer: While @JacobMick provides a broader overview and a link to a review paper, let me give a "shortcut answer" (which may be considered a special case of his answer).
Let the number of candidate variables (features, columns) be $K$ and the sample size (number of observations, rows) be $n$. Consider LASSO implemented using LARS algorithm (Efron et al., 2004). The computational complexity of LASSO is $\mathcal{O}(K^3 + K^2 n)$ (ibid.)

For $K<n$, $K^3 < K^2 n$ and the computational complexity of LASSO is $\mathcal{O}(K^2 n)$, which is the same as that of a regression with $K$ variables (Efron et al., 2004, p. 443-444; also cited in Schmidt, 2005, section 2.4; for computational complexity of a regression, see this post).
For $K \geqslant n$, $K^3 \geqslant K^2 n$ and the computational complexity of LASSO is $\mathcal{O}(K^3)$ (Efron et al., 2004).

References:

Efron, Bradley, et al. "Least angle regression." The Annals of Statistics 32.2 (2004): 407-499.
Schmidt, Mark. "Least squares optimization with l1-norm regularization." CS542B Project Report (2005).
Comment: Richard, can you comment on iteration complexity for the GLM approach here https://stats.stackexchange.com/questions/280304/how-does-lasso-scale-with-the-design-matrix-size ?
Comment: @moodle, I cannot without digging deep into that (which I do not have time for at the moment), but +1 for your question.
Comment: I had a look, but it is not clear - would be good to get a second pair of eyes on it. So there is iteration complexity and full convergence complexity, and I think the literature somewhat is vague sometimes over the definitions. Basically I have an algorithm that use a lasso solver in a very critical position such that my algorithm's complexity is strongly dependent on the solver. Would be good to nail this. Cheers! I'll put a bounty on it for your input
Comment: @rnoodle, I strongly doubt I will be able to help you there any time soon, but a bounty may certainly attract other people who know better. Good luck!
Answer: Recall that lasso is a linear model with a $l_1$ regularization.
Finding the parameters can be formulated as a unconstrained optimization problem, where the parameters are given by

$\arg \min_\beta ||y - X\beta||^2 + \alpha||\beta||_1$.

In the constrained formuation the parameters are given by

$\arg \min_\beta ||y - X\beta||^2 s.t.||\beta||_1 < \alpha$

Which is a quadratic programming problem and thus polynomial.
Almost all convex optimization routines, even for flexible nonlinear things like neural networks, rely on computing the derivative of your target w.r.t. parameters. You cannot take the derivative of $\alpha||w||_1$ though. As such you rely on different techniques. There are many methods for finding the parameters. Here's a review paper on the subject, Least Squares Optimization with L1-Norm Regularization. Time-complexity of iterative convex optimization is kind of tricky to analyze, as it depends on a convergence criterion. Generally, iterative problems converge in fewer epochs as the observations increase.
Comment: Several things: saying that a problem is "polynomial" is not particularly helpful, unless perhaps you are looking at some sort of combinatorics problem (which is usually exponential). Second, calculating the derivatives is pretty much always **not** the limiting step. Third, usually when discussing time complexity of an iterative algorithm, one typically looks at the cost *per step*, and thus does **not** depend on convergence criteria. Finally, it's not typically the case that more observations = less iterations.


Converting MGRS to Lat/Lon or UTM

Question: How can I convert Military Grid Reference System (MGRS) to lat/lon or UTM?
Answer: I had to write code to convert MGRS to LL last year, however, I am unable to post the code. What I can post though are the two main resources I utilized while writing the code:
US Military Grid Reference System description, published by NGA and the related Appendix and an Online MGRS to LL Converter to check your results as you are coding.
There is also GeographicLib, an open-source library that has code for MGRS conversions and is licensed under MIT. You'll need to look at the GeographicLib::MGRS class, and the MGRS.hpp and MGRS.cpp files if you need to look at the code.
If you can elaborate more on whether you are looking for code, a library, or a utility to convert one or more coordinates, you'll get better answers.
Comment: My suggestion then is to look at GeographicLib and either compile the code as a DLL and use the DLL + PInvoke to access the methods from C#, or convert the relevant C++ code to C# (2nd option would be my preferred route).  Of course, assuming your project is compatible with a MIT style license.
Comment: Thank you for the quick response! Basically I am looking for some formula/code to convert MGRS to lat long or UTM. I am working with Silverlight API and I want to locate the point based on MGRS input.
Answer: If someone needs this in JavaScript...
Probably worth linking to this question, which includes a link to a GPL'd (unfortunately; LGPL would have been more universally useful) JavaScript lib that'll do this.
I should probably add that the library is, more accurately, USNG, which is apparently very closely related to MGRS but not exactly the same.

When referenced to NAD 83 or WGS 84, USNG values are equivalent to
Military Grid Reference System (MGRS) values. The difference in these
two systems is that USNG referenced to NAD27 uses the MGRS WGS 84
scheme of 100,000m Square Identifications...

(from the above link to The American Surveyor)
It looks like OpenLayers lets you do it as well -- an example of it in a production environment (with an MIT-flavor license) can be found here.
That link is now (Mar 2023) dead and is not archived at archived.org. This project may be a decent replacement and is also MIT licensed.:
https://github.com/codice/usng.js/
Answer: GDAL has a silent implementation of MGRS.
You can find the source code here:
https://svn.osgeo.org/gdal/trunk/gdal/frmts/nitf/mgrs.c
Answer: There is a nice online coordinates converter for WGS84, UTM, CH1903, UTMREF(MGRS), Gauß-Krüger, NAC, W3W: https://coordinates-converter.com/en/
Answer: You could also use Python to convert MGRS to lat/long and vice versa. Using the library pyproj you can convert a given MGRS tile (say, WGS84) as follows:
import pyproj

geod = pyproj.Geod(ellps='WGS84')

lat_min, lon_min = mgrs_object.toLatLon(mgrs_id)

x_var = geod.line_length([lon_min, lon_min], [lat_min, lat_min + 1])
y_var = geod.line_length([lon_min, lon_min + 1], [lat_min, lat_min])

lat_max = lat_min + mgrs_tile_edge_size / x_var
lon_max = lon_min + mgrs_tile_edge_size / y_var

lat_min, lon_min, lat_max, lon_max then give the corners of the tile in lon/lat coordinates.
For more background information you can have a look at this blog post.
Comment: The mgrs Python module is needed in order to convert to/from MGRS coordinates, not the pyproj module.

Converting MGRS to Lat/Lon or UTM


Cross Compile the Kernel

Question: I am trying to achieve something similar to this
https://github.com/volatilityfoundation/volatility/wiki/Android#initialize-the-android-build-environment.
Below is the environment I am using:
Ubuntu 14.04, Android Studio 2.3, Android NDK r14, emulator -api22.
I am facing difficulties at step Cross Compile the Kernel.
I am targeting the goldfish kernel 3.10
following are the step I followed. Any help would be really appreciated.
method 1:
export ARCH=arm
export SUBARCH=arm
export CROSS_COMPILE=~/android-ndk/android-ndk-r14/toolchains/arm-linux-androideabi-4.9/prebuilt/linux-x86_64/bin/arm-linux-androideabi-

The tutorial suggesting that we have to run the next command as
make goldfish_armv7_defconfig

but when I checked the directory "android-source/arch/arm/configs/" there is no such config file there. Some tutorials suggesting that we can just copy and paste the file from kernel 2.6, so I did the same thing, and after that add
CONFIG_MODULES=y
CONFIG_MODULES_UNLOAD=y
CONFIG_MODULES_FORCE_UNLOAD=y

But futher
$ make

results in error:
arch/arm/mm/mmu.c: In function 'build_mem_type_table':
arch/arm/mm/mmu.c:470:18: error: 'L_PTE_MT_VECTORS' undeclared (first use in this function)
   vecs_pgprot |= L_PTE_MT_VECTORS;
                  ^
arch/arm/mm/mmu.c:470:18: note: each undeclared identifier is reported only once for each function it appears in
arch/arm/mm/mmu.c: At top level:
arch/arm/mm/mmu.c:637:23: warning: 'early_pte_alloc_and_install' defined but not used [-Wunused-function]
 static pte_t * __init early_pte_alloc_and_install(pmd_t *pmd,
                       ^
make[1]: *** [arch/arm/mm/mmu.o] Error 1
make: *** [arch/arm/mm] Error

methos 2:
Everything is same as in method 1, I just changed single variable
export ARCH=arm64

And run
make ranchu_deconfig

But I got the same error.
method 3:
$ export ARCH=arm
$ export SUBARCH=arm
$ export CROSS_COMPILE=~/android-ndk/android-ndk-r14/toolchains/arm-linux-androideabi-4.9/prebuilt/linux-x86_64/bin/arm-linux-androideabi-
$ make ranchu_defconfig
$ vim .config # added this to .config file

CONFIG_MODULES=y
CONFIG_MODULES_UNLOAD=y
CONFIG_MODULES_FORCE_UNLOAD=y

$ make

This command run successfully: zImage found.
But when I run the emulator using the below command
root@ubuntu:~/Android/Sdk/tools# ./emulator -avd Nexus5x22 -kernel ~/android-source2/android-source/arch/arm/boot/zImage -show-kernel –verbose

I am getting the error of "Linux kernel too old to run ram disk":
    ram disk error
Comment: Be sure your `CROSS_COMPILE=arm-linux-androideabi-` and your `PATH` contains `$HOME/android-ndk/android-ndk-r14/toolchains/arm-linux-androideabi-4.9/prebuilt/linux-x86_64/bin`. (This is just first step)
Answer: Google's Android Kernel is messed up. They forgot to define L_PTE_MT_VECTORS when they back ported this patch.
The solution is to just add it here.

Cross Compile the Kernel


Why and how can TCAS and SSR transponder work at the received frequency of each other?

Question: The TCAS sends interrogation pulses at 1030 MHz and receives replies at 1090 MHz. And the transponder replies interrogations at 1030 MHz receiving at 1090 MHz. There could be interference between them, right?
Comment: Just like TCAS, the transponder receives interrogations at 1030 and replies at 1090.
Comment: "There could be interference between them" -> do you mean a transponder replying to its own TCAS interrogation?
Comment: @Bianfable yess, is there a connection between them to inhibit each other while transmiting??
Answer: To clarify:

A transponder replies on 1090 MHz to ATC interrogations received on 1030 MHz.

A TCAS elicits nearby transponders replies by sending interrogations on 1030 MHz, and listens for replies on 1090 MHz.

So each one transmits on the reception frequency of the other. This is what allows a TCAS to detect threats, even when there is no TCAS on the other aircraft. As you assumed, both transmitters need to be synchronized to prevent the saturation of the receivers.
For TCAS able to coordinate with the other TCAS, continuous data exchange occurs on 1090 MHz using the mode S transponder datalink, thus this transmission is not performed by the TCAS itself.
Radio equipment global synchronization
There is a dedicated avionics mutual suppression bus/line used to report radio equipment status (transmit/receive), to allow different units to be synchronized.

Source.
Interference prevention specific to TCAS
Several techniques are used, both to limit local radio interferences, and spectrum occupancy.

"whisper/shout mode" used by TCAS on 1030 MHz, to use the lowest possible transmission power to not interfere with aircraft which are too far to be threats (to lessen FRUIT on ground stations)

Beam-steering for top antenna in order to elicit replies only from transponders in a certain azimuth, and adapt the transmission power for this azimuth.

Number of active interrogations limit based on the number of TCAS in the vicinity, to not increase FRUIT beyond limits defined by ICAO equations. This reduces the detection range.

This limit also prevents transponders from being suppressed a too long time. Transponder inhibition occurs after transmission, to reduce the spectrum occupancy. Suppression can also be explicitly triggered by a mode S interrogation from a TCAS.

For a detailed view of the interference limiting procedures, see ICAO Doc 9863)
The next two sections are more about TCAS use of frequencies than a direct answer to your question.
TCAS-to-TCAS coordination on 1090 MHz
In order to coordinate resolution advisories, in particular the vertical rates, both aircraft must be equipped with a TCAS implementing ACAS II protocol (i.e. a TCAS 7.1 or higher), this implies a mode S transponder.
A TCAS sends interrogations on 1030 MHz and listens for replies on 1090 MHz. For this phase the TCAS is relatively independent.
But as soon as a thread is detected, the resolution is coordinated by exchanging data messages between TCAS on 1090 MHz. The TCAS prepares the data to be sent on 1090 MHz, the transponder performs the transmission.
ADS-B Out also uses the transponder datalink the same way.
Overview of ACAS II protocol
We assume the aircraft looking for intruders uses ACAS II.
Observation phase

The TCAS passively listens to transponder replies to ATC (in modes A/C and S) and to DF17 messages (ABS-B broadcast), transmitted by potential intruders on 1090 MHz.

TCAS also elicits direct transponder responses by broadcasting interrogations on 1030 MHz (modes A/C and S). Aircraft in the vicinity reply, and a TCAS can determine each aircraft range and azimuth, and for replies in mode C and S, altitude and vertical rate, identifying possible threats.

Threat detection and resolution

When an intruder enters the closest protection envelope, the TCAS elaborates a resolution advisory, based on its maneuvering possibilities at the moment, and pushes the advisory parameters into register 30 (hexadecimal) of the aircraft SSR transponder.

The transponder sends the resolution advisory in a DF16 message (on 1090 MHz), this message is received by the TCAS of the intruder, and, assuming the intruder has an operational TCAS, is used to  determines a complementary maneuver.

If the intruder TCAS implements only ACAS I, the process cannot be coordinated and stops here. Else a coordinated TCAS-to-TCAS exchange continues on 1090 MHz via the transponders. The resolution advisory may be adjusted by each TCAS, until the threat is cleared.

More

ACAS protocol in ICAO Annex 10, vol 4.
Mode S in ICAO Doc 9688.
Mode S messages in The 1090 Megahertz Riddle.
My answer to Why is a Mode S transponder required to be installed and working for TCAS II to be operational?


From where can i get complete AES encryption source code?

Question: I have been searching many websites for source code of AES whether it is ECB, CBC, CTR or any other method but can't find any. Can anyone please help me in getting the source code? I have to implement timing analysis on that code to see whether the code is leaky or non-leaky.
Comment: There are quite a few AES implementations out there, and some will have timing side channel leaks, and some won't.  Which implementation are you interested in?
Comment: Do you have a specific target? Without it this is a broad question, with it, it may be off-topic!
Comment: AES with ECB, CBC, CTR is [here](https://github.com/kokke/tiny-AES-c) and many other places. There's a simple 1-block AES-128 encryption in [this answer](https://crypto.stackexchange.com/a/55899/555). It will be leaky, or not, depending on platform and compilation parameters.
Comment: there are literally thousands of code samples for AES out there, possibly millions, openssl, wifi, and the linux kernel are the most common, and that code is everywhere
Answer: As already mentioned in the comments to your question, implementations of AES are aplenty on Github, depending on the language you want to use and on the type of requirements you have, including the original ANSI C reference implementation.
However, if you are interested in timing analysis of AES implementations, you might as well want to take a look at the Dudect code.
Dudect comes from a paper named "Dude, is my code constant time?", it is a tool meant to detect timing discrepancies using Welch's t-test. It compares actual runs of a given source code against the null hypothesis that the code running is constant time.
It notably features as an example of variable time code a T-tables implementation of AES, which is a typical example of variable-time AES implementation.
But it also bundles another example, which is a bitsliced constant-time AES implementation, to show the differences between variable time and constant time code.
Answer: I just wrote a Post on stack overflow;  about AES
There I step-by-step explaining how to compile them, use them, and where to get them.
https://stackoverflow.com/questions/38975695/aes-aes-cbc-128-aes-cbc-192-aes-cbc-256-encryption-decryption-without-openss/64228925#64228925


Detecting surface intersection in lispbuilder-sdl

Question: I am working on making a game in Common Lisp, using Lispbuilder-SDL. I am currently writing a function to check for collision between two surfaces. I need to find out if a surface A intersects with another surface B. I haven't yet seen anything that fits the bill on https://lispbuilder.googlecode.com/svn/trunk/documentation/lispbuilder-sdl.html - is anyone aware of a simple, built-in way of doing this?
Answer: The math for the line that forms when two planes/surfaces intersect is not difficult.  See Intersecting Planes, Plane Geometry or generally Googling.  If there is no intersection, then the planes/surfaces are parallel - there are simple tests for that.
A plane is defined by a point and a normal.  If the dot-product of two plane normals is one, then the planes are parallel.  In your game, if the dot-product is close enough to one, then the intersection is outside of the play area.
Comment: Perhaps you meant the vector-product? If the dot-product is 0, then the normals are orthogonal or one normal is zero.


Can I get a job offer in the US?

Question: I live outside of the US and I study at a branch of American university in my country. The university has a platform to connect students and employers. Through this platform several employers text me inviting to apply for a job in their company. However, they require US job authorization, which I do not possess at the moment. To get a visa to work and live in the US, I may need a job offer from the companies in the US, so can I count on those messages to help me to get a visa?
Comment: Do the employers *require* authorization, or *provide* help in acquiring it? You can't get a work visa without an employer who's willing to sponsor you for it and assist you in getting it.
Comment: Have you asked the companies who have contacted you if they would sponsor you? They are the only ones who can answer your question
Answer:
can I count on those messages to help me to get a visa?

No.  These messages are not job offers; they are merely soliciting you to apply for a job (and, from your description, only if you are already authorized to work in the US).  As you note,

To get a visa to work and live in the US, I may need a job offer from the companies in the US.

"Job offer" means that you've applied and the company has decided to respond favorably to your application and seek to employ you.  But it seems that none of these companies are willing to do this.  If they were, they would not require work authorization; they would instead be willing to sponsor you for authorization.
Note that such companies will normally still ask whether you have authorization because sponsoring someone for a work visa is fairly costly, so they will take that cost into account in deciding whether to hire you.

Can I get a job offer in the US?


NicEdit + Selenium IDE

Question: Lately me and my QA buddies are trying to find a way to make Selenium IDE (v2.2 with FireFox v22) type a text into NicEdit's textarea, but without success.
We took a look on the internet for the past few days, and so far we discovered, among other things, that NiceEdit is not an iFrame (I think many here already know that).
We're not using code nor any other webdrive, just Selenium IDE, which makes things a bit harder, I guess.
We've tried xpath, class, id etc... no success.
But in these cases, the Find button in Selenium highlights the area.
So, is there a way to make Selenium IDE type in the NiceEdit's textarea without code?
Here's the html code of NicEdit's textarea provided by FireBug.

And the rest before it:

EDIT: I've found out that NicEdit turns the textarea into a div, so Selenium is not able to focus on the area.
Anyone has any sugestions about how can I make Selenium put some text on NicEdit?
Thanks!
Answer:

    storeEval
    this.browserbot.findElement("id=someID").innerHTML='fillerText'

Does the above work for you?

NicEdit + Selenium IDE


Why is the drift velocity directly proportional to the electric field?

Question: If I double the electric field, that should double the acceleration of electrons inside the conductor in the general direction of the electric field. But why does that double the drift velocity, and in turn, double the current? Normally when we have a fixed path length the velocity ends up getting multiplied by $\sqrt{2}$ when we double the acceleration. Thanks!
Comment: Related https://physics.stackexchange.com/q/323959/104696
Comment: There is no "fixed path length" that an electron travels through between collisions. In the Drude model,  there's a fixed amount of TIME in between an electron's collisions with atoms. And if the acceleration of the electrons gets doubled, but the time between collisions doesn't change, that doubles the average velocity of the electrons as they move between one atom the other, thus doubling the drift velocity and the current overall.
Comment: There is not a fixed time between collisions in the Drude model.  There is however an average time between collisions. In my answer I have called this average time $\tau$.  It is all to do with averages.
Comment: Thanks, @Farcher just saw and upvoted your answer - for some reason I hadn't seen it before. My comment was more a response to my past self than a response to you!!
Answer: Recall that Ohm's law relates the three physical objects namely the electric field $\vec{E}$, the conductivity $\sigma$ and the current density $\vec{J}$:
$ \vec{J} = \sigma \vec{E} $.
Assuming that the electrons will flow in a direction perpendicular to some surface in the direction of $ \vec{J}$ we can find the current using the following equation:
$I = J A$ , where $J = |\vec{J}|$ and $A$ the surface area.
Another useful thing to note is that the current of some electrons with electron density $n$ and  some velocity which we define to be the drift velocity $v_d$ then we can also write:
$I = n A v_d e$ where $e$ is the charge of an electron.
This equation could best be derived using for example a cylinder with cross section surface area $A$ and electrons moving with a speed $v_d$ a time $t$ in the direction perpendicular to the surface. Then by definition of the current we have that $I = Q/t = \frac{A n v_d t e}{t} = A n  v_d e$.
Now we take these equations together.
$ I = n A e v_d = J A = \sigma E A $ and solving for the drift velocity we get:
$ v_d = \sigma E / (n e) $.
This shows that the drift velocity is indeed proportional to the applied electric field. How to check this? Do an experiment, I just did a basic derivation of the drift velocity that consist of a lot of assumptions.
As a final note mark that a drift velocity is the average velocity of the electrons. Please also note that since the acceleration is constant we have that $v_d = a \tau$ with $a$ the acceleration and $\tau$ the mean free time. This is always the case, could you give an example where the velocity changes quadratically with $a$ ? Hope it helps, I am not an expert in this subject and I also had to look it up.
Comment: I understand, but the reason Ohm's law is true is because the drift velocity is proportional to the electric field. Imagine if it wasn't. Then doubling the electric field for a certain distance (aka doubling the voltage) would not mean doubling the current.
Comment: Hey Dani. Thats all good and it works out mathematically, but the reason that the current density is proportional to the electric field is that the drift velocity is proportional to the electric field in the first place (as you said yourself, I=nAvde, which means J = nvde). But from basic concepts, why is that in the first place? Thank you!!
Comment: The reason that the current density is proportional to the electric field is due to Ohm's law. Ohm's law is very general and does hold for other situations. Now since we are dealing with a flow of electrons we can define a drift velocity and talk about a electron density. Then you use a definition of the current $I$ and try to relate it to the current density $J$ and therefore the electric field $E$. The two $\textbf{definitions}$ of classical electromagnetism that I used are: $J=\sigma E, I=Q/t $ and I applied it to this situation, that's it.
Comment: I do not know whether you have difficulties with these definitions (which could be measured in lab) or the notion of drift velocity. For the latter I cannot help you further, since my knowledge is not good enough on that subject.
Comment: $I$ is just how many electrons pass per second. Therefore you could look at how much charge is transported from one place to another, this is $Q=nAtv_d e=nAle=nVe=Ne$ where $V$ is the volume and $N$ is the total number of electrons contained in that volume and $l$ is the path length. And this you relate to the two definitions given in the first comment.
Comment: True, I am a theoretical person, so to be honest with you I don't know in which order it is determined. It could be that Ohm's law follows from such an experiment.
Comment: @Dani Have a look at this answer about [the drift velocity in the drudge model](https://physics.stackexchange.com/questions/323959/drift-velocity-in-drude-model).


Is there a lower bound on the number of facets of a full-dimensional convex polytope

Question: As the title say's: Imagine a full-dimensional convex polytope. Is there a lower bound (or even exact formula) for the minimum number of facets the polytope has?
Answer: The lower bound is realized by a simplex, so the answer would be $n+1$ in dimension $n$.
You should be able to prove it by taking $n+1$ extreme points of the convex polytope.  That gives you a simplex.  Show that adding points to that, you are adding faces.
Comment: Thank you. Wouldn't it suffice to say that a full-dimensional polytope needs at least 2 extreme points which in turn means that we need to have at least n+1 irredundant inequalities (since each extreme point sets n inequalities to equalities). Each of these corresponds to one facet. Are there any arguments missing?
Comment: Sorry, I don't quite follow.  2 extreme points seems too few to me to fix anything -- in theory there is a continuum of inequalities that 2 extreme points satisfy.  But maybe I don't quite understand your argument.
Comment: Okay, once again :-)

We need at least two extreme points: If the polytope consisted of only one extreme point, it would have dimension 0 and thus wouldn't be full-dimensional. On the other hand, an extreme point is determined by setting a set of n irredundant inequalities to equality (face of dimension 0). So we need 2 different sets of inequalities while each set contains n elements. Thus, the minimum number of inequalities is n+1. Each of these inequalities determines in turn a facet when it is set to equality. That's my argument. Are there any mistakes?


Conflicting Terms after Post-Merger of Companies

Question: Company A has a contract to produce widgets for the State for $5 per widget. The State also has a contract with Company B to produce the same widgets for $4.50 per widget. Company A acquires Company B. What is the price per widget following the acquisition?
Answer: It depends
There are two possibilities when company A acquires company B:

Company B continues its existence with a new owner. In that case the state is in exactly the same position as it was before the acquisition.
Company B ceases to exist and it's assets, including the contract with the state, become the property of Company A. Both contracts still exist and have full legal force.

Notwithstanding, in either scenario, both contracts continue.
It's unclear from the question if these contracts are for a fixed amount of the goods or for goods to be supplied as and when ordered.
If the former, then both contracts will need to be fulfilled with payment being $5 per unit for those produced under contract A and $4.50 per unit for those under contract B.
If the latter, then the state may be able to place orders under either contract subject to any limitations. For example, one or both of the contracts may have minimum or maximum order amounts or "take or pay" clauses or different delivery times etc.


What's the relationship between smart contract and NFT collections?

Question: I am new to web3 and block chain. I have learned that NFTs are just the tokens stored in a smart contract. But then I see another concept -- NFT Collections. I really wonder what's the relationship between them. Is a contract and a collection one-to-one correspondence or anything else
Answer: As you know NFTs are just ERC-721 token, as single NFT token stored in NFT contract same like more than one token also stored in contract also. You can check your balance of tokens by "balanceOf" method. these tokens can be stored in Metamask.
Answer: This is just terminology and it varies a bit. An NFT Collection means all of the NFTs which are inside one contract. I guess "collection" is a sexier term than "contract".


Apache Jakarta (Tomcat) Connector to forward traffic to specific Tomcat

Question: There is one use case I am unable to solve so far with the Apache Jakarta (Tomcat) Connector load balancing feature.
I have one IIS site which has one Apache Tomcat Connector attached to it.  I need to "forward" the traffic to a different Tomcat depending on the URI that is requested.  It is pretty simple to do when you only have apps with a specific context (like /app1, /app2, etc).  My problem is that I have one app (in one Tomcat) that is at / (ROOT) and one other app (in another Tomcat) that is at /app1.
I have tried the following config in uriworkermap.properties:
<code>/*=loadBalancer1
/app1/*=loadBalancer2
</code>
But this doesn't work, because "loadBalancer1" takes all the traffic.  "loadBalancer2" is being ignored, which make sense, since /app1/* matches /* (regexp wise).
I also tried adding a exclusion as so:
<code>/*=loadBalancer1
!/app1/*=loadBalancer1
/app1/*=loadBalancer2
</code>
But that doesn't work either, because "loadBalancer1" is still taking all the traffic, but just ignoring that "/app1/*" URI pattern.  "loadBalancer2" is simply ignored again.
Any suggestion, keeping in mind that I cannot have 2 IIS sites, nor can I move the app that is at / (ROOT) to a different context path in Tomcat?
Thank you
Edit:
Instead of using just one Apache Tomcat Connector, I use 1 connector for each Tomcat on the same IIS site.
uriworkermap.properties #1: for Tomcat with app at / (ROOT)
<code>/*=wlb
!/app1/*=wlb
</code>
uriworkermap.proerties #2: for Tomcat with app at /app1
<code>/app1/*=wlb
</code>
Connector #1 will ignore traffic on URI "/app1/*", but connector #2 will catch it (and vice versa).
Now I can set different VM options and memory allocation to my apps!
I am open to comments or better solution..
Answer: Does it work when you reverse it as such ?

/app1/*=loadBalancer2
/*=loadBalancer1
Comment: Nope, doesn't work.  I tried it.  Seems that the regexp (if this is what they use) has priority over the ordering of elements in the config file. That said, a coworker probably found the solution. I will post it as soon as I can.


Customise entity reference autocomplete

Question: How do I override the look up on an entity reference autocomplete field? I would like to limit the look up to nodes of a certain type that have been created by the user that is creating the current node.
Answer: The Entity Reference module integrates with the Views module in a few ways.  One of these is a new display called Entity Reference.
Create a view, and filter it to your needs.  Then, add a new Entity Reference display.  Configure this.
Then, on your content type(s), edit the entity reference field.  Make sure you are using the AutoComplete widget.  You should see a fieldset called Entity Selection.  Change this from "Simple (with optional filter by bundle)" to "Views: Filter by an entity reference view".  You should then see a dropdown appear which will have all of the views you have created that have Entity Reference displays.  Pick your view and save.
Keep in mind, though, that views with large datasets can cause dramatic performance problems with autocomplete fields.
Comment: It is possible to set this up instead with autocompletepath setting on the field, and a hook_menu() callback?
Comment: The `entityreference_autocomplete` widget is a normal FAPI `textfield` with `#autocomplete_path` (see `entityreference_field_widget_form()`.  In theory I guess you could form_alter and change the path to something you define yourself, but I have never tried this.

Customise entity reference autocomplete


Mail encoding issue

Question: I have a problem with Mail. My name is Oğuz and there is a Turkish character in my name. I set up a 'live' email address in Mail. When I send an email from a web browser my name appears as "Oğuz", but when I send one from Mail my name appears as "O?uz". Also, other Turkish characters in my last name do not appear correctly. How do I fix this issue?
Answer: I have solved this issue.
1-) Create a new contact using name which you want to use as e-mail sender name.
2-) Add email account that contact.

Mail encoding issue


Installing windows 10 again on a pre-installed system

Question: I have purchased a HP laptop with Windows 10 home single language OEM pre-installed on it,However I've formatted my system without making recovery disks.I've downloaded Windows 10 ISO from Microsoft's site and burn it on a dvd and did a fresh install on my system.It gets activated digitally on my system.Is it legal to use this type of fresh installation or do I have to face problems in updates from HP and Microsoft.I went through superuser post Reinstall Windows 10 using ISO onto new SSD without losing activation status I've not changed the hard disk.It's all about a fresh install.
Comment: Questions about this have been answered many times before. https://www.google.com/search?q=superuser+windows+digital+activation+site:superuser.com Using a digital license for Windows is by design. It's "how it's done." It's how Microsoft expects you to do it. No there is nothing wrong with it.
Comment: If the system wasn't legal to use, the installation wouldn't have activated, the reinstallation of Windows 10 is as simple as the actions you have performed.  There is nothing else to it.
Answer: It's not legal or illegal, as there are no laws involved.
 The correct question would be, are you acting within in the bounds of the license agreement, and within your rights to install the software on your device? The answer is yes - absolutely.  You shouldn't face any problems whatsoever.
Comment: License agreements are dependent upon law and legality. Without law, a license agreement is unenforceable.
Answer: This is a question for a lawyer, but if the Windows does not complain that it requires the activation, I'd assume it's OK to continue using it.
You could use one of the method desrcribed here to make sure there are no problems with activation.


Reopen windows when logging back in does not work

Question: I have just performed a fresh re-install of El Capitan on my MBP 2014 and have found that this setting is not working at all. When I log out, I leave the check box ticked (so I DO want to open all applications and  my open terminal sessions to be restored, which also used to always work). When I log back in, nothing is restored, and my previous terminal sessions are lost. So how do I fix this? In general settings, I have un-ticked "Close windows when quitting an app", but I'm not sure if this is related to logout issue.
Answer: Well, all of the information for the restoration is kept in ~/Library/Saved Application State, so maybe looking there would lend a clue.  You should see a whole lot of folders ending in .savedState.
Comment: I've just checked that and the only file I see is for Dropbox (com.getdropbox.DropboxMetaInstaller.savedState), there is nothing else, so what cam I do? Thanks
Comment: Some apps (such as the ones downloaded from the Mac App Store) store their information in an isolated container separate from other apps, so why don't you check those just to be sure?  Those are in **~/Library/Containers/com.companyname.AppName/Data/Library/Saved Application State**.  If you don't see anything there, it could be that apps are simply not recording any information to be restored, which seems wacky but I can't think of any other reason why nothing would appear in Saved Application State.


In which reference can I find a definition for the equivalence of DFAs?

Question: How is the equivalence of DFA defined?  I found the equivalence of states --- James Hein, section 5.3, page 301.  But he doesn't define equivalence between entire automata.  (Ullman and Hopcropft seem to define neither.)
Answer: You can find a definition in Automata Theory, Languages and Computation by Hopcroft, Motwani, Ullman, in the fourth chapter.
Here's a link : HMU, the section begins at page 171 of the pdf
Two DFA are said to be equivalent if they accept the same language, and (an equivalent proposition) if they have the same minimal automaton (which is unique).
Comment: Since you know HMU, any idea why they used the word "madness" in the first chapter's title?  I didn't read every word of the first chapter, but I couldn't find any sign of an explanation.  This word is not present in the first edition.
Comment: No real idea, sorry!


promoting diet products is haram or halal

Question: I want to know that is permissible to promote diet products in Islam like keto diets and resurge. Resurge is a product that helps to lose weight. Because I want to promote that product and I will get some commission.
Answer: If the contents is halal, you can promote it. Diet seems to become almost a religion for some people but it isn't. Muslims can make a diet, too.
Answer: It all depends on whether the products that you are promoting are Haram or Halal. You also have to clarify if it has halal ingredients or not.
And yes you can surely earn a commission out of it too until you don't lie or hide anything from the customers.


Blue card employer change within six-seven months

Question: My zusatzblatt (green paper got along with blue card) has no employer name mentioned on it.(Location-Berlin)
I am planning to change or look for new opportunities , It is only 6 months now after I received the physical blue card.If I want to change the employer .
Heard that I need to notify the authorities about the change ,My question is do I just need to inform them with the new employer contract and start working already for the new company
Or should I need to wait till I get approval/reply from them and can only join the organisation after that
Answer: According to https://www.bamf.de/EN/Themen/MigrationAufenthalt/ZuwandererDrittstaaten/Migrathek/BlaueKarteEU/blauekarteeu-node.html a permit from the competent immigration authority is required for any change of job within the first two years of employment. The conditions for granting the Blue Card will then be re-examined. Approval is subject to the same preconditions as initial issuance, so that it is necessary, amongst other things, to prove the currently valid minimum gross salary again.
So you should wait for approval before changing employer.


What's the best tool to support Behavior Driven Development in Python?

Question: Cucumber seems to be the go-to tool for BDD in Ruby, and through rubypython it could test Python code as well, but it's experimental. There are some Python tools out there like Pyccuracy and Freshen, but they seem to be in an early stage. What is the best tool to use for Python projects?
Answer: Have a look at lettuce. It strives to be the analogue to Cucumber in the Python world. It's quite early in its development, though.
Answer: Some interesting libraries I have come across for Python testing: factory_boy(https://factoryboy.readthedocs.org/en/latest/), which is like Ruby's FactoryGirl gem. And there is a fairly new testing framework for python called Sure(http://falcao.it/sure/intro.html) which is based on Ruby's RSpec. I started out with Python but now work for a Ruby based company. I've found Ruby's testing libraries to be really fantastic to use, especially RSpec. Sure looks pretty similar to RSpec and could be worth a look.
Answer: Well, I'm biased but I prefer pyspecs:

from pyspecs import spec, given, when, then, the

class simple_addition(spec):
    @given
    def two_numbers(self):
        self.first = 2
        self.second = 3

    @when
    def we_add_them(self):
        self.result = add(self.first, self.second)

    @then
    def the_sum_should_equal_5(self):
        the(self.result).should.equal(5)

def add(a, b):
    return a + b

Note: as the author of pyspecs I would welcome any feedback/collaboration...


If slavery is immoral, why did Yudhishthira donate slaves to Brahmins?

Question: So, I was browsing here and found a post which supposedly said that Yudhishthira gave female slaves to a bunch of Brahmins. Slavery is obviously immoral and is even condemned in several scriptures so I struggle to think why Yudhishthira would do this. Can someone help me out?
Answer:
Slavery is obviously immoral and is even condemned in several scriptures...

It seems like the rest of the world, the dharma śāstra writers of Ancient and Medieval India, did not consider slavery to be immoral. I don't know which Hindu scriptures you are referring to, but I'm yet to find a single one which condemns slavery outright.
The Manusmṛti lists 7 kinds of slaves:

dhvajāhṛto bhaktadāso gṛhajaḥ krītadattrimau |
paitriko daṇḍadāsaśca saptaite dāsayonayaḥ || 8.415 ||
There are seven kinds of slaves—(1) captured under a banner, (2) slave on food, (3) born in the house, (4) bought, (5) presented, (6) hereditary, and (7) slave by punishment.—(8.415)
bhāryā putraśca dāsaśca traya evādhanāḥ smṛtāḥ |
yat te samadhigacchanti yasya te tasya tad dhanam || 8.416 ||
The wife, the son and the slave,—these three are declared to have no property; whatever they acquire is the property of him to whom they belong.—(8.416)

The Nāradasmṛti lists 15 kinds of slaves and the work usually assigned to them:

2. The sages have distinguished five sorts of attendants according to law. Among these are four sorts of labourers; the slaves (are the fifth category, of which there are) fifteen species.
...
5. Know that there are two sorts of occupations; pure work and impure work. Impure work is that done by slaves. Pure work is that done by labourers.
6. Sweeping the gateway, the privy, the road, and the place for rubbish; shampooing the secret parts of the body; gathering and putting away the leavings of food, ordure, and urine,
7. And lastly, rubbing the master's limbs when desired; this should be regarded as impure work. All other work besides this is pure.
...
25. Thus have the four classes of servants doing pure work been enumerated. All the others do dirty work and are slaves, of whom there are fifteen kinds.
26. One born at (his master's) house; one purchased; one received (by gift); one obtained by inheritance; one maintained during a general famine; one pledged by his rightful owner;
27. One released from a heavy debt; one made captive in a fight; one won through a wager; one who has come forward declaring, 'I am thine;' an apostate from asceticism; one enslaved for a stipulated period;
28. One who has become a slave in order to get a maintenance; one enslaved on account of his connection with a female slave; and one self-sold. These are the fifteen classes of slaves as declared in law.
29. Among these, the four named first cannot be released from bondage, except by the favour of their owners. Their bondage is hereditary.
30. Should any one out of them (however) save his master's life, when his life is in peril, he shall be released from slavery and shall take a son's share (of his master's wealth).

So, Yudhiṣṭhira's actions (owning, inheriting and gifting of slaves) were consistent with the dharma śāstras.
Also, as I discuss in this answer, even Rāma and Bharata gifted slaves to brāhmaṇas during their time.
Comment: I mean, Now I am very sure that it was mistranslation of Dasa and dasi which means servant not slave.
Comment: @123456789 Have you ever hired someone for work? If yes, have you tried 'gifting them' to someone else? You can only gift something you already own. You can read [this](https://hinduism.stackexchange.com/a/40062/2995) answer to understand the difference between प्रेष्य/भृत/भृतक/servant (who works for wages) and slave (dāsī/dāsa).
Comment: Again, dasa dasi is translated it servant, not slave. Rama is a king who has servants it is most likely him assigning them to the riches and not 'gifting them'. It is better to read it in Sanskrit.
Comment: FYI, [Arthaśāstra](https://archive.org/details/Arthashastra_Of_Chanakya__Other_Books/page/n259/mode/2up) has a whole chapter devoted to the humane treatment of slaves. If dasa/dasi are simply paid servants, why would anyone create these rules for them? Even if you are a king, you cannot donate servants to others without their permission because servants are not your property. Whereas slaves are one's property, so you can donate/give them away freely. In [this](https://www.sacred-texts.com/hin/m02/m02060.htm) chapter of Mahābhārata, Yudhiṣṭhira can be seen betting male/female slaves. @123456789
Comment: "If yes, have you tried 'gifting them' to someone else?" Managers/Owners might not use the terminology of "gifting", but hired workers are often "given" to other owners to work on other contracts, projects, etc. And this is more so in the military where troops are given to other commanders to assist in other battles, etc. So yes, even today people give/gift their workers.
Comment: And slavery in Hinduism is not like the chattel slavery of North America that you and I learned about where slaves were permitted to be raped, tortured, etc. as their master sees fit, but all those things are sinful in Hindu servitude system.


Can I implement my own authentication process in force.com or it is against terms of service?

Question: I am just wondering if it is permited to implement my own authentication process in force.com or it is against terms of service or any rules. Link to official documentation will be appreciated.
Comment: You may want to review this question - http://salesforce.stackexchange.com/questions/418/is-it-okay-to-use-a-single-admin-user-when-logging-into-the-api-or-do-i-need-to
Answer: I think it depends on what you're planning to do once you've authenticated someone, it may also depend on which exact edition you're looking at. All the agreements are available here http://www.salesforce.com/company/legal/agreements.jsp
Comment: I'd think the relevant parts are the definition of "Users" and section 4.3.
Comment: What to do next would be access the app and manipulate force.com custom objects using the guest profile.
Comment: I think that would be considered user concentration, which i thought was only allowed for database.com editions, but i haven't reviewed the MSA in a really long time.
Answer: By rolling your own users, you wind up losing advantages like individual auditability, password management, and user security - all of which you would essentially need to build into your user management.
http://www.sfdcstatic.com/assets/pdf/misc/salesforce_MSA.pdf
3.2. User Subscriptions. Unless otherwise specified in the applicable Order Form, (i) Services are purchased as User
subscriptions and may be accessed by no more than the specified number of Users, (ii) additional User subscriptions
may be added during the applicable subscription term at the same pricing as that for the pre-existing subscriptions
thereunder, prorated for the remainder of the subscription term in effect at the time the additional User subscriptions
are added, and (iii) the added User subscriptions shall terminate on the same date as the pre-existing subscriptions.
User subscriptions are for designated Users only and cannot be shared or used by more than one User but may be
reassigned to new Users replacing former Users who no longer require ongoing use of the Services.
Comment: Thanks Adam!  Sometimes the line of violation vs. non-violation doesn't seem as clear cut, specifically in questions involving api integration such as [Can I use a single admin user when logging into the api or do I need to use the individual user accounts](http://salesforce.stackexchange.com/questions/418/is-it-okay-to-use-a-single-admin-user-when-logging-into-the-api-or-do-i-need-to)?
Answer: If you are doing it to purposely avoid paying for portal licenses then my understanding is you are violating the TOS.
How much of Salesforce do you need?  Database.com is extremely cost effective if you need to authenticate a number of users and have them own the data but are providing your own UI.  (Although it does have some architectural considerations, database.com is not going to offer you local relational database level latencies).
Answer: If you just want separate authentication would a SAML-based single sign-on solution work for you? You could setup and maintain your own Identity Provider (IdP) and configure Salesforce to use it for authentication purposes. Salesforce would still handle the authorization side, though.

Single sign-on Implementation Guide
How to Implement SSO with Force.com
Comment: Idea is to have my own set of users and passwords to login into my app and communicate to force.com custom objects just using the guest profile. Is that acceptable or completely out of context?
Comment: Please see the link I added to your main question. This is probably a case of "ask your account rep."


Do plants on Roshar that move use nervous systems?

Question: In The Way of Kings, many plants, such as grass, retreat into the ground when disturbed for protection form highstorms. Have the books or Brandon said anything about how this works? Do Rosharan plants have nervous systems, or are they like Venus fly traps?
Comment: fairly certain they are like fly traps
Comment: Are you talking about centralized nervous systems like a mammal would have?  Almost certainly not.  Something simplistic or decentralized?  That might work.  But it's probably some kind of chem/bio trigger like with a flytrap.
Answer: This explanation by Sanderson (At JordanCon, April 2016) seems to strongly imply there is no nervous system (as such a tissue would imply animals).

Questioner I get the impression after reading Stormlight 1 and 2 that a lot of what you would consider to be flora, plant-life, is actually something like coral in the ocean which is actually an animal. So is there actually any flora on Roshar outside out of, like, Shinovar?
Brandon Sanderson Yeah, yeah, like almost all the things you see as flora are actual flora. Like, rockbuds are flora, trees are flora, shalebark is not, and some of the things like that-- haspers are not, and some of these things are more-- are animal life, are fauna. But grass is actually a flora, and trees.

As an extra-point, none of the shema shown in the stormlight seem to show a nervous system.

With that said, we can't completely compare the phisiology to that of earth plants as there are, at least, two very important phisiology differences:
1. Roharan plants can make use of crem to compensate for the weak soil-

..."lot of the trees that you'll find on Roshar, they will be using crem that falls and you use this to create shells, you use this to infuse your bark, they use this in a lot of different ways, the minerals there are very important because they're not getting from the soil what plants on our world get from soil"...
Sanderson At JordanCon, April 2016

2. Rosharan plants can use stormlight.

QuestionerFor Words of Radiance, could you put a comment about something in the upcoming books, something not too specific, just something I can think about? Something like "Renarin has a spren" you wrote for somebody else in The Way of Kings?
Brandon Sanderson [written] Stormlight makes plants grow.


What is the universe and the multiverse and how do you use them in the synaptic package manager

Question: I have recently installed the synaptic package manager and there are various options  related to the universe and the multiverse in it. what exactly are they and how do you you use the Synaptic package manager with them
Answer: Here is a screenshot of the 'Software & Updates' window (part of Ubuntu's default software setup):

The main repository is the main software for Ubuntu, and is officially supported by Canonical (Ubuntu's parent company)
Universe has open-source programs that can be used in Ubuntu, supported by the Ubuntu & linux community.
Multiverse includes video codecs, encrypted DVD streamers etc, which may not be open-source, and/or may cause legal problems.
Restricted - Closed-source drivers

You can also add other repositories/PPAs to download packages from (though please check if you can trust the source of the compiled software!!). Sometimes these are included in packages for updating them - e.g. for Google Chrome, Spotify.
More information can be found on here.


iPhone development on PC: Best Option?

Question: I keep reading things about Airplay SDK and Dragonfire SDK.  Are these legitimate options for iphone development without a Mac?  Anyone have any better solutions?
Comment: "Anyone have any better solutions?" Yes, a Mac
Comment: I know this doesn't really answer your question, but a Mac Mini is an affordable way to get started, and it even works with two monitors. I use one.
Answer: You're not going to get away from the need of OSX regardless of framework due to signing etc.
Before I bought my epic 2007 MacBook at €300 I used VmWare to run OSX and as such access Xcode.
No promise on legality of the procedure, but it's pretty much that, Hackintosh or buying a Mac.
In terms of Legal iOS development it's OS X or nothing. Plain and simple.
Answer: Life is too short.
A Mac Mini is an affordable option and it will hold it's resale value on eBay well.
Answer: DragonFire SDK is an easy way to get started if you own a PC and don't want to get a mac. I had it up and running in a few minutes.  Was learning off the tutorials in a few hours.  Seems if you want a more comfortable/non workaround then you will need to get a Mac.  The price tag for a Mac is what pushed me to DragonFire for now.  A little cheaper option is looking at the refurbished macs.  Save a few hundred and  still get the warranty.

iPhone development on PC: Best Option?


DC Motor/Generator current flow

Question: So I am in the midst of learning circuitry, and cannot for the life of me understand what dictates the direction of current in a DC Motor/Generator. I understand that a charge applied to the negative and positive of a DC motor will be converted to mechanical energy. Conversely, it is also easy to understand that applying mechanical energy to the shaft will result in an electrical charge available via the positive and negative leads. What i don't understand however is if you were to hook a dead battery to the leads and applied mechanical force to the shaft, would it charge the battery? And furthermore, what would prevent any accumulated charge from backflowing and turning the generator into a motor?
Answer: Back EMF and internal resistance are the main things that determine the direction and magnitude of the current flow in a DC brushed motor or generator
Back EMF comes from the speed that the motor shaft is turning, spin it faster and the back emf will have more volts.
in normal runiong the motor will reach a speed where the back emf mostly cancels the supply voltage and the difference in voltage divided by the internal resistance will get you the current through the motor (Ohm's law).
If you spin it fast enough that the back EMF exceeds the supply voltage the the
motor will act as a generator pushing current into the supply.
A third thing that determines the current is the strength of the magnetic field, this sets an upper limit on the current that a generator can produce, no matter how fast you spin it.
To answer your second question nothing would stop the generator from becoming a motor, but if the spinning speed is fast enough it will be acting as a generator.
You could add a diode to prevent current from flowing the wrong direction.
Answer: A DC motor, when run as a generator, would charge a battery.
With the drive taken off, the battery would run the motor in the same direction, were it to be free to run. Otherwise, the battery current would damage it's winding.
This possibility existed in vintage cars having a 'dynamo' (DC generator). It was taken care of by a relay unit known as a 'cutout'.
Comment: The motor would not run in the reverse direction - it would rotate in the same direction but the current flow would reverse. going into the motor rather than out of the motor (when acting as a generator).
Comment: Hi Kevin, Thank you very much for pointing out the blunder. 'Back EMF' totally slipped  my mind.

DC Motor/Generator current flow


What is the time axis array after we convolve two functions in Matlab after sampling it with frequency \$f_s\$?

Question: Suppose we have a continuous time function \$f(t)\$ , we sample it at frequency \$f_s, (t = -5:1/f_s:5)\$, and store it in an array \$a\$ in Matlab. Now we convolve it with itself using \$b = conv(a,a)\$. What is the new time axis array for the convolved function stored discretely in array \$b\$ ?
Answer: the new x-axis should be the lag between the signals.
Since your signal is a digital signal, the x-axis is N, where N is the number of samples ahead or behind the the original signal.


What is the continuous depth concept in Neural ODE paper by David Duvenaud?

Question: I read the ever so celebrated -https://arxiv.org/abs/1806.07366 paper. I am still confused. Does the concept of continuous depth neural network correspond to the fact that the ODEint or the integrator block takes into account the value of the derivative to decide the step size and then performs an "integration"? Or does it refer to something else?
Answer: I wouldn't read into the term "continuous depth" too much. It's just that since the ODE allows you to evaluate the neural network at any layer (for example we could compute $h(\pi)$ to obtain the value of the network at $\pi = 3.14\ldots$, the concept of depth and number of layers is not meaningful. You could say there are an infinite number of layers, but that's not a helpful description.
The authors use NFE (number of function evaluations) as a proxy for "depth" because just as we expect model expressivity and complexity to increase with depth in a typical network, we expect more powerful neural ODEs to require a larger NFE to solve. I think this is what you were getting at. While this definition of "depth" is useful for comparing model capacities and computational efficiency, it's very distinct concept from my usual conception of network depth.
Comment: Thanks for your super helpful reply. Which block do you think is doing this NFEs? Is it the integrator(Euler or RK that gets called eventually)? I do understand that there are adaptive solvers in the system. If the gradient value is very large, the "step size" is reduced for integration (and the number of evaluations or NFEs increase?). And vice-versa when the gradient is small. Is this the correct understanding?
Or these NFEs is for every call made to the entire network (consisting of the neural net, integrator , loss function and the optimizer?)
Comment: NFEs are how many times the ODE solver calls the function. As im not an expert in ODE solvers, I can't say much more.
Comment: Thanks for your help @shimao!