What happens with the beta-binomial distribution, when n approaches infinity?

Question: Short question: What happens to the beta-binomial distribution, when n increases to infinity? Is there a count distribution arising like it's for the classical binomial distribution?
Answer: Consider the urn model for the beta-binomial:

... imagine an urn containing α red balls and β black balls, where random draws are made. If a red ball is observed, then two red balls are returned to the urn. Likewise, if a black ball is drawn, it is replaced and another black ball is added to the urn. If this is repeated n times, then the probability of observing k red balls follows a beta-binomial distribution with parameters n,α and β.

When both $\alpha$ and $\beta$ are very large, the additional balls introduced do not appreciably change the chances of red or black.  This is just a binomial experiment (with fixed probabilities $\alpha / (\alpha + \beta)$ of red and $\beta/ (\alpha + \beta)$ of black).
Comment: Right; without additional scaling the beta-binomial won't converge to a proper probability distribution as $n\rightarrow\infty$ if $\alpha, \beta$ are fixed (I think). From his phrasing ("count distribution") I think the OP may be looking for the analogue of a binomial approaching a Poisson as $n\rightarrow \infty$ if $p\rightarrow 0$ and $np$ is constant. Probably there is a similar result if you send $\alpha/(\alpha+\beta)$ to zero at a proper rate or something, but I don't know it.
Comment: I think $\alpha, \beta$ are fixed and he's sending $n\rightarrow\infty$
Comment: @JMS If that's the case, you recover the underlying Beta distribution if you divide by $n$.


Non convex quadratic problem with complex variables

Question: I am trying to solve a non convex optimization problem with the help of sequential quadric programing. My optimization variables are complex and I have expressions for gradients, hessian etc but all these are in complex form. Let's say I am solving this problem using quadprog toolbox and inputs to this toolbox takes only real values. So what should I do about this
Answer: If x is the optimization complex vector variable, instead make the real variables, x_real and x_imaginary, the variables. Form the original complex variable problem in terms of those. This formulation only involves real variables.
If you directly use quadproog, rather than a more flexible front end such as YALMIP, you will have to "stack" x_real and x_imaginary into one vector variable. if you use YALMIP, you can specify the problem directly in terms of the complex variables, and YALMIP will do this transformation for you under the hood, saving you rime and reducing error propensity.


Google Chrome cast to Google Home on different network

Question: Is there a way to cast to Google Home from Chrome browser, if the smart speaker is on the different network? I know Google says devices should be on the same network, but maybe there are some hacks?
Answer: Okay, figured it out.
To make devices to appear on the same subnet, you may create a network bridge. This way devices, even connected to separate physical interfaces of the server, may be actually in one subnet.
But there is not only a requirement for devices to be in the same subnet.
I've investigated that the Google Home not just merely accepts packets from a casting device. It also wants to be able to ping the caster (ICMP) and send packets to the multicast address 184.108.40.206, over UDP protocol, to port 5353.
Google casting support page says that traffic to Google Home should be unrestricted, but says nothing about the fact that the smart speaker should be able to send some packets over the network, too.
I've unfirewalled this traffic and now casting to Google Home works.
Answer: When you say a different network, are you saying on a different physical network, different subnet, or separated by VLAN?
If you are different physical networks, I don't think it's going to work without creating using VPN. If you're on separate subnets or VLANs you could create static routes between them.
Comment: Well, the Chrome is on a PC on a wired network, and the Google Home is on a Wi-Fi.
Comment: Okay, I would say that you're on the same subnet and, therefore, network. Verify that with a wired device and wireless device. Get their IP addresses make sure they are both in the same /24 block, so 192.168.1.XXX.
Comment: No, devices are actually on different subnets, the PC is 192.168.10.2 and Google Home is on 192.168.150.9. Both devices have common gateway/server, so static route is possible.


Hide VPN from ISP?

Question: We know that when you use a VPN, your ISP can't see what data is going inside the tunnel, but they can see that you are visiting the VPN server. Is it possible for the VPN to somehow configure your internet so that your ISP can't even see that you are using a VPN?
Comment: Your ISP needs to route your traffic to the VPN.
Comment: Additionally, instead of your ISP spying on you, now you have a VPN spying on you.
Comment: There are various ways to obfuscate VPN traffic. I believe you can use obfsproxy with OpenVPN.
Answer: There's a few things that will allow your ISP to know you are using a VPN:

The protocol that VPNs use: UDP. An ISP can filter your traffic and see if you move any data via this protocol; if you are, odds are you are using a VPN, although it could also be VoIP or a Google Meet, since they also use UDP.

VPN clients have default ports: OpenVPN uses 1194, WireGuard uses 51820, L2TP uses 500 and 4500, and so on.

The IP addresses of commercial VPNs, such as Mullvad or TunnelBear, are publicly known. If you make requests to these IPs, your ISP will know you are using a VPN.

You could make your own VPN server on a VPS, which would allow you to bypass known IPs, but 1. and 2. would still apply.
Comment: This does not answer the question, which already acknowledged an ISP could infer that someone was using a VPN. The question is about how to prevent them from being able to. The answer should be to reconfigure default port, to not use commercial VPN (and set up your own), etc. even though I doubt this would be enough.
Also, *many* protocols uses UDP, and VPN certainly are not restricted to UDP.
Comment: So .... the answer you *almost* got to was "use an IP that isn't known to be a VPN and don't use default ports", but you kinda breezed right past that. And UDP is a non-starter.
Answer: When strictly just trying to hide it from the ISP then it is possible with some work: Tunnel the VPN connection through something else, like an SSH connection, to an endpoint under your control and establish the VPN from there.
Of course, the traffic identification issue is not gone but just moved from the ISP to whoever owns the infrastructure of the endpoint used as they can see the VPN traffic.
Obfuscating steps like the ones mentioned by @foreverska can be used here as well to lower the likelihood of routine detection. A targeted investigation will not be fooled.
Answer: One could use DNSSEC to hide lookups, obfsproxy to try and trip up DPI, self managed VPNs hosted in a cloud using nonstandard ports and regularly changing IPs.  Likely would fly under automated flagging.
The brightest of bots would likely determine a home network which only ever connects to a single ip/port at a time for the bulk of it's traffic is using a VPN no matter the ip/port.  One could set up small computers to idly browse the internet and make the signal a bit noisier.  Might trip up all but human review.
Answer: The ISP will know the IP address of the initial receiver. That's unavoidable, because the ISP has to deliver your message somewhere. If your VPN uses one known IP address, then your ISP can know that you are sending to a VPN IP address (99.99% likelihood for VPN traffic, 0.01% that your own computer is sending to the wrong IP address). If the VPN server has multiple IP addresses, your ISP could know them all.
If your ISP doesn't recognise the IP address, they can look at the structure of your message. They shouldn't be able to gain any knowledge about the real message other than the size, but they may be able to conclude that your message is a VPN message sent to an unknown VPN server and be right very often.
Last, if all your traffic goes to one IP address only, then that fact alone makes it likely that you are using a VPN. And if the ISP cannot make sense of the message because it is encrypted, and it doesn't look like https, then it is likely to be VPN.
So what can you do? Pick a VPN server that doesn't use a known IP address and a protocol that can be recognised. (So nothing technical, just pick the right VPN server). And the protocol should be such that it doesn't look like anything encrypted. For example, you could map an encrypted message to grammatically correct sequence of English words and back. Or wrap the VPN message into something that looks like SSL. That's something the VPN server would have to support. And use different IP addresses throughout the day.

Hide VPN from ISP?


How to check for Inconsistent Respondents in System Usability Scale (SUS)?

Question: I'm trying to evaluate the validity of the SUS responses- I think it's also called internal reliability or Response bias.
How is this done for SUS?
Comment: I really think this is a question for http://stats.stackexchange.com/. It has little to do with user experience.
Comment: I'm voting to close this question as off-topic because it belongs to Cross Validated
Comment: It depends- if it's just a calculation, then yes it's more of a stats question. But if it requires to know which pairs of SUS questions ask for the same thing it's more UX.
Comment: @mmatti It's currently unclear exactly what you're asking, and the focus of your question will determine whether it's on topic or not.  In the mean time, I'm closing it, but if you improve the question, you can ask to have it reopened.
Comment: It is totally related to hci!!! Not offtopic to me. Maybe we need more context but it is interesting
Comment: I can see there are pairs of questions in SUS that try to measure the same thing, e.g. questions 2 and 3:
"2. I found CRR unnecessarily complex."
"3. I thought CRR was easy to use."
I'm sure these questions were designed to test for inconsistent answers. (User can't be agreeing with both these statements at the same time).
Answer: When analyzing survey data you need to separate validity from reliability.

Validity is a measurement of how correct the answer is.
Reliability is a measure of how consistent the answer is.

Here's a graphical representation of the concept (from Wikipedia):

In general, SUS has been found to be highly reliable and there is some strong support that it produces valid conclusions [1].
But you are probably more interested in determining if your survey results are valid for your problem. To answer this, my advice is to find some other measure of usability to correlate your results with (this is referred to as "convergent validity"). For instance, you could compare the results of a similar survey or expert evaluation of the interface with the SUS scores. Or you could compare task completion time (or some other quantitative measure of performance) of a user with previously gathered SUS scores, if they correlate then SUS has "predictive validity", which would be pretty convincing.
If you are interested in reliability, I suggest you use Chronbach's alpha. It is a combined measure of all correlations between questions and essentially means how likely is it that respondents answer questions in a similar way. Alternatively, you could rerun the test with the same participants and see if you get similar answers.
[1] Bangor,  A.,  Kortum,  P.  T.,  Miller,  J.  T.:  An  Empirical  Evaluation  of  the  System Usability Scale.  International Journal of Human-Computer Interaction.  24, 574--594 (2008)


MQ shared subscription not working with multiple instances of micro services

Question: I am trying to use MQ shared subscription, which is not working when I have multiple instances of my micro-service up and running.
My DefaultJmsListenerContainerFactory configuration is as mentioned below, where I am using factory.setSubscriptionShared(true).
<code>  @Bean
  @Qualifier("subscriberListenerContainerFactory")
  public DefaultJmsListenerContainerFactory subscriberListenerContainerFactory(@Qualifier("subscriberConnectionFactory") ConnectionFactory subscriberConnectionFactory) {
    DefaultJmsListenerContainerFactory factory = new DefaultJmsListenerContainerFactory();
    factory.setConnectionFactory(subscriberConnectionFactory);
    factory.setDestinationResolver(new MyDestinationTopicResolver("Topic-JNDI-Name", "Topic-Name"));
    factory.setSubscriptionShared(true);
    factory.setPubSubDomain(true);
    factory.setSessionTransacted(true);
    factory.setSubscriptionDurable(true);
    factory.setConcurrency("1-1");
    return factory;
 }
</code>
My listener config is shown below:
<code>@JmsListener(subscription = "My-Test-Subscription", destination = "dummy", containerFactory = "subscriberListenerContainerFactory", selector = "message_sub_type = 'MY_EVENT'")
public void onMessage(Message message) throws JAXBException { ... }
</code>
When I try to run multiple instances of this service, I get following error in all instances:
<code>Caused by: com.ibm.mq.MQException: JMSCMQ0001: IBM MQ call failed with compcode '1' ('MQCC_WARNING') reason '2429' ('MQRC_SUBSCRIPTION_IN_USE')
</code>
I want to use shared subscription so that only one instance of the service gets the message from topic.
NOTE: Previously we had same subscription but it was not shared and not durable. Then we made it shared and durable. After that first time, it worked fine. Now when we are trying to change the subscription name or client id, we are getting above error.
I understand that if it is durable subscription, then the subscription will be present in IBM MQ Server, and due to that, when we are trying to make any change in durable subscription, we are getting error: '2429' ('MQRC_SUBSCRIPTION_IN_USE').
But we are not able to see the durable subscription in MQ explorer, still we are getting MQRC_SUBSCRIPTION_IN_USE error.
Is there a possibility that the previous durable subscription is in some inconsistent state (like stale or uncommitted)?
Comment: What version of MQ are your IBM MQ jar files from?
Comment: Can you confirm the version of the jms.jar?
Comment: MQ version is 22.214.171.124 - @JoshMc
Comment: javax.jms-api-2.0.1.jar
spring-jms-5.3.25.jar
Comment: ibm.mq.allclient-220.127.116.11.jar
Comment: Is our possible the subscription was already created as a unshared subscription?
Comment: You would need to delete it by opening it unshared and removing it. Try runmqsc with `DIS SUB(*)` and see if you see it,  you can use `DELETE SUB` from runmqsc to remove it.
Answer: Please see Sharing Subscriptions.
Comment: This is just theoretical document, which I am already aware off. This does not help in solving the problem I am facing.
Answer: The thing with durable subscriptions is that they are durable. So if it was created it as unshared, it needs to be removed, EG. by unsubscribing, before it's possible to recreate it as a shared durable subscription.
From the link that Doug shared :

If a subscription is created as shared it cannot later be changed to
unshared, or vice versa.


Left and right triggers for xbox elite controller 2 not working on android

Question: I have a galaxy note 9 plus. A new elite controller series 2. I have connected the controller through Bluetooth. Loaded into fortnite. The game accepts the controller and gives me options to configure the controller. I load into a match. I can not aim nor shoot. I downloaded gamepad mapper apps. Which all display lt and rt as throttle and brake keys. Basically they do not seem to be recognized as buttons for shooter games, but rather as throttle and brakes for racing games. I then went to a site for android developers where they are working on updating elite controllers and regular xbox controllers keymapping with the left and right triggers set as buttons instead of an axis. Yet there is nowhere to download the files to my phone. Basically I have zero knowledge with android systems as far as where files are located, how to access them and reconfigure them or else I would have tried to change the values myself. Can anyone help me with this.
Side note: I am 70 percent sure I saw on Microsoft and Fortnites websites that the Elite Series 2 would work for android fortnite and is supported. Yet the left and Right triggers do not work.
Comment: What version of android are you running?
Answer: You might try  buying a whole new remote. You could also try to use the a b x y buttons instead.


second derivative of solutions to ODE with Lipschitz coefficients

Question: Just the simple ODE with Lipschitz coefficient $a$
\begin{align}
&\frac{d}{dx}h(x)=a(h(x))\\
&h(0)=x_0
\end{align}
We know that the existence and uniqueness holds and the solution is in $C^1$. Does the second derivative of the solution exist (in distributional sense perhaps)? How do I show it? So the solution is in $W^{2,p}$, what's $p$?
Answer: Since $h$ is $C^1$, the composition $a(h(x))$ is Lipschitz. Hence $h' $ is Lipschitz. We can write this as $h\in C^{1,1}$. Or, if you prefer, $h\in W^{2, \infty }$ which says the same thing. All of this applies to finite time intervals, of course.


one of my colleagues is difficult to deal with

Question: My colleague is very difficult to deal with. I was recently provided the task of managing my colleagues and it is very difficult to gain their attention and ask to fulfil a task as they do not like being assigned tasks from my end. Often they find it easy to assign the blame and neglect the task being assigned by me. My post is not official but the task of managing is real and is being carried out and there is literally no concern from anyone except this one guy who is supposed to be my friend.
Comment: This seems to be more of a people management problem than a project management problem. Maybe it's better suited for Workplace.SE.
Comment: @nvoigt No, I think this could be on-topic for pmse, but it's lacking enough details and a clearly defined goal. I'm VTC as needs clarity, not as off-topic.
Comment: There may be a good PM.SE question under the hood here, but as it stands, there's lack of minimal context so that it can be more useful. More details, better questions, richer answers.
Answer: Frame challenge: You're difficult to deal with, not your colleague. (I'm assuming. Don't have enough details to see the whole picture, so this answer is a stab in the dark.)
If I were in your colleague's shoes, with you coming in to manage me (without my input, and apparently even without an official position granting that authority), and then you decide to start imposing management techniques top-down onto me, without any of my input... I'd be pretty annoyed.
Top-down assignment specifically is one of my biggest peeves. The moment I read:

they do not like being assigned tasks from my end

I though "Yeah... neither would I." What problem are you actually trying to solve, by assigning tasks to them rather than telling the team as a whole what needs to be done and letting them self-assign?
My advice?

Throw away everything you assume you know about what managing a team means.
Talk to the team to learn from them the biggest pain points.
Talk to the team to tell them what the overall goals are.
Talk to the team to collaboratively estimate the biggest roadblocks to reaching those goals.
Talk to the team to collaboratively come up with possible solutions.
Go from there.
Comment: To give you a brief on the colleague mentioned. He is a developer and possesses an attitude of superiority. Providing timelines and not completing the task within that time frame is a regular character. Besides the points already mentioned by you to ask the team and move ahead which has been tried and tested. Should I accept that not everyone can be managed and some are just the way described.
My problem is this one guy for whom ive been a friend and he takes this liberty for granted when it comes to work.
Comment: @MahanGupta Well, if you're sticking to the stance of "I'm not doing anything wrong with the project management, the problem is entirely this guy", then I take back my earlier comment - this question is off-topic for pmse.
Answer: I can very well relate to this. If you are delivering for a role without being assigned "official" authority and designation, this is going to be an issue especially if you are younger in age and experience.
So, how I had dealt with it?
(It is completely situational-based. There will always be ifs and buts. I am sharing my experience so it can help you to get an idea of solving the problem on hand. Forget anyone being your friend in the corporate world.)
Mostly such a person needs to be tamed for their ego and make sure that they are the most important in their team. I took the help of my manager and asked him for a favor. All my manager had to do was tell him some good words, make him feel as if the project revolves around him. The last blow was asking him to cooperate since each team member is doing their job. Once he gets involved, everything mentioned above will become redundant :)


How can I execute a call from a contract using another contract?

Question: I own a contract (contract A), which in turn, when deployed, created a secondary contract (Contract B).
I have funds trapped in contract B, contract B, has a function that allows its owner to withdraw funds in the contract, but with the OnlyOwner modifier.
The owner of contract B is contract A, I cannot execute the call because a contract cannot sign the transaction, is there any possibility of resolving this?
I need use this function:
function processAccount(address payable account, bool automatic) public onlyOwner returns (bool) {
    uint256 amount = _withdrawDividendOfUser(account);

    if(amount > 0) {
        lastClaimTimes[account] = block.timestamp;
        emit Claim(account, amount, automatic);
        return true;
    }

Or even, it would solve the problem if I could change the owner of contract B, moving it to a wallet.
but only the owner can do that, and unfortunately it's another contract.
Or even, it would solve the problem if I could change the owner of contract B, moving it to a wallet.
but only the owner can do that, and unfortunately it's another contract.
It is a contract for an ERC20 token with dividends in BNB.
We published it in 2021 and we did not have full knowledge, so perhaps we failed to foresee some situations.
The logic of the contract is,
Wallet deploy the Contract A (ERC20) Token, automatically contract B (dividends) was created and published as owner of contract A.
I have a relevant amount of BNB within contract B and would like to try to redeem it.
The calls provided for in contract A to interact with B do not include transferring ownership of contract B or calling the processaccount() function.
If I could call the transferownership() of Contract B (Dividends) easily I would transfer it to a wallet and then I could successfully use the ProcessAccount() function and then I would be able to redeem the BNB in the contract. Or at least calling the processaccount() function directly from Contract A would also work.
The problem is:
TransferOwnerShip() and ProcessAccount() are set to OnlyOwner, that is, only contract A can call, but there is no function in contract A specifies to do this.
Neither contract A nor contract B have delegate or upgradeable functions.
One of the few things that I have at my disposal to use to my advantage is that contract A has an upgradedividendTracker() function that results in incorporating a new contract within contract A replacing the current dividend contract, and this occurs without changing the ownership of the original dividend contract.
Comment: Provide the entire contract code or at least a link to the deployed contracts on a block explorer, this way, users will be able to help you to the best of their abilities.
Answer: Unfortunately, if you have already deployed both contracts without implementing a method to change the owner or call the processAccount() function, then the funds are lost forever.
For future reference, always test your contract code prior to deploying to a real network such as Ethereum mainnet, because smart contract code is immutable by design, meaning it can never be altered.
Comment: Couldn't I solve my problem by creating a third contract that I had delegated, assuming that I can include a third contract within my main contract to command?

In this case, could I implement the third contract that had a delegate function to call the transferownership function in contract B, while preserving the message.sender from contract A?
Comment: So contract A would make a call to the intermediate contract and the intermediate contract would make a delegatecall to contract B, passing msg.sender from A?


What class besides rogue makes a good criminal?

Question: I'd like to have my next PC be a pirate who fences stolen goods and who is effective at her job because she can defeat her rivals in direct combat (as opposed to hiding and stabbing them or ruining their reputations). What class would be best for such a concept?
Comment: Welcome to the site! Take the [tour]. I edited this question to bring it closer to the site's guidelines, but without more information, this question will likely be put on hold as too broad. Were the question to provide even more detail—perhaps what you imagine the character doing, mechanics that interest you, and some campaign background—, the site *may* be able to help, but the question still might be better posed on a [forum](https://rpg.meta.stackexchange.com/q/5449/8610). No matter what though, thank you for participating and have fun.
Comment: @HeyICanChan I think that turned it into an "idea generation" question, but I'll remove the comment.
Answer: Use the Criminal background, not a class
Instead of focusing on a particular class to play, you can simply select the Criminal background (PHB 129):

You are an experienced criminal with a history of breaking the law. You have spent a lot of time among other criminals and still have contacts within the criminal underworld. You're far closer than most people to the world of murder, theft, and violence that pervades the underbelly of civilization, and you have survived up to this point by flouting the rules and regulations of society.

This background gives you the skill and tool proficiencies that are relevant to being a criminal, as well as personality traits and features that befit a criminal.
Because backgrounds can apply to any character, you can play as any of the martial classes, given that any of them could defeat an enemy in direct combat.


What's the geometric explanation of Lie Derivative and Covariant Derivative?

Question:
What's the geometric explanation of Lie Derivative and Covariant Derivative?
For my understanding, covariant derivative somehow explain/ provided a way for determine the invariance or for coordinate transformation. While Lie Derivative somehow showed the changes caused by the metric. But it's still a little bit fuzzy to see how to explain them in a more intuitive way.
Notation Check: I was reading Hamilton's Ricci Flow by AMS GSM series Volume 77, where on page 11 it stated that  $L_X f=Xf $. Just to check that this was a typo and $L_X f = X \bigtriangledown f$, right?
Comment: Personally I would more or less agree with your understanding of covariant derivative. I personally view the $\Gamma_{ij}$ terms as correctional terms. For the Lie Derivative (of a vector field), I just see that "change in the flow" I don't have the paper you are referring to for Q2 on hand, so I'll just leave it to someone else more qualified to answer.
Answer: For your first question, it is somewhat abstract. However, there are two useful concepts.

Both derivatives are defined independent from metric.
Both derivatives are assigned artificially, but in different senses.

If you like, both derivatives could be taken as directional derivatives, yet how to understand this "directional" needs further clarification.
For a covariant derivative $\nabla_XY$, it defines the rate of change in $Y$ as you move it along the geodesic determined by $X$. If the connection $\nabla$ has special properties, say, it is a Riemannian connection which preserves the Riemannian metric and is torsion-free, then $\nabla_XY$ corresponds to the rate of change in $Y$ as you move it along the geodesic determined by $X$ by keeping the norm of $Y$ and the angle between $X$ and $Y$ unchanged.
By contrast, a Lie derivative $L_XY=\left[X,Y\right]$ corresponds to the rate of change in $Y$ as it changes along the flow induced by $X$; in particular, it does not define this rate, because the change of a vector along the flow induced by another vector has its own definition. It is hard to explain this "flow" since it involves much more abstract information. Intuitively, you could imagine this: a drop of ink will immediately be deformed and translated by a water flow. Similarly, for two given vector fields $X$ and $Y$, how $Y$ would be "deformed" and "translated" by $X$ is everywhere well-defined. It is in this sense that you compare $Y$ before and after it changes at each location.
For your second question, recall that $X_p:C^{\infty}(M)\to\mathbb{R}$ is called a tangent vector at $p\in M$, where $M$ is a differentiable manifold, if

$X_p(\lambda f+\mu g)=\lambda X_p(f)+\mu X_p(g)$ for all $\lambda,\mu\in\mathbb{R}$ and $f,g\in C^{\infty}(M)$, and
$X_p(fg)=fX_p(g)+X_p(f)g$ for all $f,g\in C^{\infty}(M)$.

As you can see, while we call $X_p$ a vector, it is actually an operator acting on smooth functions on $M$. Further results have shown that, locally, $X_p$ observes the representation
$$
X_p=X^{\mu}(p)\frac{\partial}{\partial x^{\mu}}\bigg|_p,
$$
where each $X^{\mu}\in C^{\infty}(M)$, while $\partial_{\mu}$ acts as a basis vector in linear algebra. For one thing, it is called a basis, because all tangent vectors are linear combinations of them. For another, they each are differential operators in the usual sense.
With this understanding, you may see that $L_Xf$, the directional derivative of $f$ with respect to $X$, is exactly $X(f)$, because
$$
X(f)=X^{\mu}\partial_{\mu}f.
$$
Of course, you may still adopt notations in linear algebra and put
$$
X(f)=\mathbf{X}\cdot\nabla f=\frac{\partial f}{\partial\mathbf{X}}.
$$
Nevertheless, these notations are not conventional in differential geometry.
Comment: How are you saying that the covariant derivative is defined independent of the metric? Are you thinking of some abstractly defined non-metric linear connection? In your discussion, you use geodesics, which are certainly dependent upon the metric.
Comment: I'm a differential geometer, so I'm fully aware of all this. I just thought your exposition was odd and perhaps confusing to a non-expert.
Comment: @TedShifrin: Thank you for your comment. Yes, I was talking about the abstract definition for connection (covariant derivative) and geodesic. Let $M$ be a differentiable manifold. Let $TM$ be its tangent bundle (the set of all of its tangent spaces on $M$). $\nabla:TM\times TM\to TM$ is called a connection if (1) $\nabla_{fX+gY}Z=f\nabla_XZ+g\nabla_YZ$, (2) $\nabla_X\left(Y+Z\right)=\nabla_XY+\nabla_XZ$, and (3) $\nabla_X\left(fY\right)=X(f)+f\nabla_XY$ for all tangent vectors $X$, $Y$, and $Z$ and all continuously differentiable functions $f$ and $g$.
Comment: @TedShifrin: (cont'd) You may see that this definition does not involve metric. With this definition, let $\gamma:\mathbb{R}\to M$ be a curve on $M$. Let $t$ be its parametrization, i.e., $\gamma=\gamma(t)$. Then a vector field $X$, when restricted on $\gamma$, is called parallel to $\gamma$ if $\nabla_{\dot{\gamma}}X=0$. Here $\dot{\gamma}\in TM$ is the derivative of $\gamma$ with respect to $t$. Further, a curve $\gamma$ is called a geodesic if $\nabla_{\dot{\gamma}}\dot{\gamma}=0$, i.e., its tangent field is parallel to itself.
Comment: @TedShifrin: (cont'd) You may see that this definition is also independent from metric. When talking about metric, there are two essential points: (1) there are many Riemannian metrics on $M$, and (2) there are many connections on $M$. For a given Riemannian metric $g$, a geodesic $\gamma$ locally minimizes $\int_{t_0}^{t_1}\sqrt{g(\dot{\gamma},\dot{\gamma})}\,{\rm d}t$ only if the connection is chosen as the Levi-Civita connection (i.e., it is torsion-free and preserves $g$). In this case, you may show that $t$ is a constant multiple of the arc-length of $\gamma$.
Comment: @TedShifrin: (cont'd) One last comment: a geodesic does not necessarily locally minimize its length even if $M$ is equipped with a Riemannian metric $g$, if the connection $\nabla$ is not a Levi-Citiva connection with respect to $g$. A simple example could be that there are two distinct metrics $g_1$ and $g_2$ on $M$, with $\nabla_1$ being the Levi-Civita connection with respect to $g_1$. In this case, the geodesic defined under $\nabla_1$ might well not locally minimize its length in the sense of $g_2$.
Comment: @TedShifrin: Oh thank you very much for your kindness! May I ask how I could improve my interpretation? I would really appreciate it if you could provide some suggestions or even edit my answer for necessary clarifications. Thanks a lot!


Is there an astronomy exam I can take?

Question: I am currently living in Bangkok and I love astronomy. However, I haven't been able to find an official astronomy exam that I can do to gain college credit. Could someone help me out please?
Comment: @LocalFluff I am actually a high-school student and I was asking if there was something similar to IGCSE that offered the subject Astronomy.
Comment: A master in physics followed by a PhD when you can start to specialize in astrophysics. That's the normal way, and it only takes eight years or a little more normally. And I don't think it would be good to do all of it in Bangkok.
Answer: There is a Dantes Standardized Subjet Test (DSST) in astronomy. I have no idea if and how widely colleges give credit for these exams. Typically, you will start with physics and choose to specialize in astronomy. Therefore, most standardized exams are for physics which may have a handful of astronomy questions.
Answer: There is a GCSE in astronomy offered by Edexcel: https://qualifications.pearson.com/en/qualifications/edexcel-gcses/astronomy-2017.html
The assessment has two parts, an exam, and a series of two observation task (aided and unaided).
The course is suitable for 14-16-year-olds.
Answer: I know this is an old question, but if someone is still wondering ... your country regularly sends teams to the International Olympiad on Astronomy and Astrophysics. I am also certain there are Thai teams at the International Astronomy Olympiad as well as other International Astronomy Olympiads. I know there are people who "discovered" astronomy competitions and then got involved with them. Although they are not standardized tests per se, I think astronomy competitions/Olympiads ought to be mentioned.

Is there an astronomy exam I can take?


Add a built-in app to Fire Kids profile?

Question: I have a bunch of Fire tablets for my kids and we are using the FreeTime locked profiles for them. I can download 3rd-party apps and then share them on my kids profiles. But I can't do this with the built-in apps, like Clock. Do you know how I can do this?
I've chatted with Amazon support and they were no help. Here are the Amazon instructions for more details on how this works for 3rd-party apps: https://www.amazon.com/gp/help/customer/display.html?nodeId=202119930
Answer: At least as a substitute for the Clock app, this app seems to be good, allowing multiple alarms. Plus it is Fire compatible and free:
https://www.amazon.com/MacroPinch-Alarm-Clock/dp/B00EPG51Z4


Can I point my domain name to an Azure web site?

Question: In the current technical preview, Azure lets you create 10 ASP.NET websites. They are given domains such as http://yourappname.azurewebsites.net. Is there currently any way to point a domain name to this website? Or are there any plans to support this in the future?
Comment: @ThunderRabbit: For the new Windows Azure Web Sites, this is simply unavailable right with *shared* model. With *reserved* model, custom domain names are available.
Comment: update 2015: Custom domain names cannot be used with Free websites. Only for Shared, Basic, or Standard mode. http://azure.microsoft.com/en-us/documentation/articles/web-sites-custom-domain-name/
Answer: Update 18-sep-2012: Windows Azure Web Sites tiers:

Free: Allows you to test the Web Site Features
Shared: Cheap hosting (with 5 GB/month free) that supports both CNAMEs, A-Records and naked domains.
Reserved: Same as shared, but you get a dedicated VM

Read all about it in Scott Guthrie's post: Announcing: Great Improvements to Windows Azure Web Sites
Original Answer:
At the moment this is only possible for reserved instances (using a CNAME), this means it's not possible for the free sites you can create (which are shared):

You can only used custom domains in reserved mode. You can't set a
  CNAME like you can in Web Roles because multiple sites share the same
  IP address. Switch to reserved mode and set your CNAME in the
  configuration and it should work.

http://blog.ntotten.com/2012/06/07/10-things-about-windows-azure-web-sites/
Microsoft confirmed that they will add support shared sites in the future:
https://twitter.com/scottgu/status/210972290719031298
Answer: Fast forward two years, it is still not possible to have CNAME directed to Azure free website.  The reasons are commercial and not technical.  MS says that it is not possible because multiple sites share a same IP.  But don't know why I have this dedicated server at GoDaddy that has one IP but hosts 7 different domains :-)  So it can't be a technical reason.  Of course, if they start allowing it, nobody would want to subscribe to paid versions.
Answer: For what it's worth, it's now (finally) available for about $10/month, in shared and Reserved modes). I've tested it and it's working perfectly, after the little DNS dance for the naked domain. This was the missing piece to Azure for some small sites I run.
The Gu has all the info: http://weblogs.asp.net/scottgu/archive/2012/09/17/announcing-great-improvements-to-windows-azure-web-sites.aspx
Comment: $10/month just to use your own domain seems kinda steep. Is anybody looking to use Azure in place of Godaddy Hosting which is only like $7/month including a SQL DB, Web site hosting and a lot of bandwidth.  I really want to move my small web biz and db to Azure, but it would appear I'm looking at 500% price increase compared to my home solution even with Static IP cost.
Comment: For me, having a BizSpark subscription with some free traffic etc., this is the perfect solution. Thanks!
Answer: You will soon be able to use Custom Domain without having to upgrade your plan to RESERVED. We are introducing a new Shared mode. The new Shared mode will have some cost, but it is a lot less than reserved mode, and it will support Custom Domain. Please check back at the http://www.windowsazure.com/en-us/ soon for more info.
Answer: As mentioned by Sandrino, this is possible only for reserved instances.
Not sure about Scott Guthrie answer. Check this thread.
It is stated that at this time there is no plans to support custom domains for shared instances.
It also contains a request to comment on Scott's answer.
Update:
It might be available for a fee (same thread)


How Can I fix this ACF Repeater Block code to render on from end

Question: I am using the ACF Pro Repeater Fields for a project with the location as a Block. The block successfully loaded on the edit page but it not being rendered to the front end.
Here is the code I used to test the page Template:
`//Register a Building Projects Block
add_action('acf/init', 'my_acf_init_block_types');
function my_acf_init_block_types() {
<code>// Check function exists.
if( function_exists('acf_register_block_type') ) {

     // register a building project block.
    acf_register_block_type(array(
        'name'              => 'building_projects',
        'title'             => __('Building Projects'),
        'description'       => __('A custom block for Building Projects.'),
        'render_template'   => get_template_directory() . '/template-parts/blocks/building-projects/building-projects.php',
        'category'          => 'formatting',
        'icon'              => 'building',
        'keywords'          => array( 'building', 'nodaco' ),

    ));
}
</code>
}
// Load values and assign defaults.
$sub_text = get_sub_field('project_descriptions') ?: 'Detail Project here...';
?>
I also echoed with this line of code: echo($sub_text);`
Answer: The issues were much more beyond the ACF plugin. I simply debugged with
define( 'WP_DEBUG', true );
define( 'WP_DEBUG_LOG', true );
which revealed the true the coding issues in both the function.php file and then the template file. It took me several hours to clean up the codes and the fields began to display as expected.


Set control panel site link to open in new window

Question: Is there a way to set the upper right hand website link in the CP to open in a new window or tab?
Thanks!
Answer: You could use the CP CSS & JS add-on (download link) to inject JS to add the attribute to the link?
<code>$('#navigationTabs .msm_sites a').attr("target", "_blank");
</code>
Tested on EE v2.9.2 & v2.5.3. Don't worry about the msm reference - it's marked as that even if you don't have MSM installed.
Comment: That addon hasn't had a commit in 4 years, which makes me weary, but if you've tested it and it works, than your answer is cleaner than mine. Upvote!
Comment: It's not a complex add-on, so no need to fix or improve. Pixelandtonic are a good development agency too.
Answer: I would suggest downloading a custom theme, and modifying the Javascript includes for that theme. All you should need to add to that file is this line:
<code>$( '.first_level:last-of-type' ).attr('target', '_blank');
</code>
And that should hit the last button on your top level menu, which will be the redirect link to your site. Good luck!
ps this was tested in EE 2.5, not 2.9+, but I doubt they've changed class names in the CP when still in the same version. Subversion changes like that would break theme compatibility too badly.
Answer: Simple.
You could edit menu.php file.
It's located in system/expressionengine/libraries folder.
You must go to the line 321 and change it so:
$menu_string .= $this->_process_menu(array('help' => $this->generate_help_link()), 0, TRUE, '', 'external');
Byez


Why is my avocado tough and rubbery?

Question: This is the second avocado from the same bag that is tough and rubbery. The pit won't come out without leaving a skin, and it won't peel out of it's skin without cutting the skin off. I made sure it was soft and was at room temperature before I cut it open. How can I de-rubberize them?
Answer: It's simply not ripe yet.
Don't buy avocados or any other fruit and vegetable in pre-packed bags, because you cannot tell what state they are in.
Buy from a local grocer whom you can trust, and therefore can get honest answers on the state of the produce.
Avocados are usually sold unripe for shipping reasons. Buy ahead of need, and let them ripen at room temperature (2 to 7 days). They will keep in the fridge if you need them later than that.
To recover a peeled unripe avocado, you can cube it, and then cook it in the microwave in short bursts to soften it. It's only good for salsa or sauce at that point though. One advantage of slightly cooking avocado is that the green colour becomes more intense; I suspect this explains the guacamole colour from many fast food vendors. :-)
Answer: If it was transported in a chilled container or even at the store before it's ripe will cause only the skin to blacken even peeling away at the meat. I don't know who started telling people to freeze their avocados either. Refrigerated after ripening yes. You will ruin your avocado experience. My family grew avocados.. And yes also an early pic or a freeze will also do that . If your avo was smaller than norm then that was probably the deal picked early. The smooth avocados Fuertes do that alot.
Answer: Avocado varieties with thin skin tend to have this problem. The hard rubbery lump will not soften with time even when surrounding area begins to rot. It is said that when the tiny young fruit is developing, certain insect can puncture the skin causing a calcified tumor in the flesh which continue to grow as the fruit mature. Some farmer spray pesticide or horticulture oil to control the problem. Spraying calcium containing products like calcium nitrate - the same application to prevent bottom end rot on tomato - will toughen and defense the tender skin against attack. I have a Jim Bacon tree with this problem.
Answer: If avocados that you buy at the store have been picked too soon by the grower and the avocado has less than eight percent fat it will never ripen. If avocados that you buy at the store do not ripen, return them, because it's not something you did, it's because they were picked incorrectly with less than 8% fat.
According to this video California law states that you cannot pick and sell avocados with less than 8% fat because they will never soften.
Comment: There's no such thing as authority. Authority is a myth. The info about the 8% limit was interesting though. At $2 a pop, I will take them back.

Why is my avocado tough and rubbery?


Can't remember email for account

Question: I have another Stack Exchange account, which I had been using for years from my mobile phone, but my mobile phone got lost, and I cannot remember the email associated with my account, I only know the username. How can I retrieve my email (the email associated with the user name of the old account) so that I may merge my old stack exchange account with the new one I accidentally created when trying to reset my password?
Answer: If you know the username I think it should be straightforward for you to get a link to that profile and then use the Contact button to contact and describe your situation to SE staff.
The I accidentally created two accounts; how do I merge them? instructions in the Help of every site may also be useful to you.

Can't remember email for account


Global catalog server and primary domain controller

Question: I have a domain, and a child domain. The child domains domain controller is a Global Catalog server. I know i can use queries to access the partial attribute set inside the global catalog server, and the attributes like bad password count on the PDC using powershell. Is it possible that i can access the attributes of global catalog server and primary domain controller using the GUI of Active directory? If yes, how? If not, what is the reason?
Comment: Are you talking about accessing the properties of the *domain controllers* in ADUC or are you talking about accessing properties of user accounts from each domain? You can view nearly all properties you like from a console in either domain. You can set the console to bind to a specific DC if you want to see per-DC attributes (such as LastLogon). You need to use the Advanced Features view to see attributes in ADUC, or use Active Directory Administrative Center
Comment: Thank you for the reply @Trix, I am new to the active directory so maybe you could dumb it down a bit for me? I am trying the access the attributes on the DC, i know the attribute editor shows the individual attributes of the user but how do in view the attributes stored on the GC and PDC? How do i set the console to 'bind to a specific DC?
Comment: You can connect to any Domain or DC by going to Action > Change Domain or Change Domain Controller in the console. By the way, given fast networks today, all your DCs should be GCs, so that avoids any confusion there.
Comment: Thank you! That solves my issue. However, how do I query the PDC for the attributes such as badpwdcount? I mean from the GUI and not from powershell? I can access the GC, by changing the domain controller but how do i access the PDC? Do i access the DC that has the PDCe role? If yes, how do i find the attribute badpwdcount? I am sorry for the confusion here, feel free to ask me to elaborate if you dont understand my question @Trix
Answer: Active Directory is a multi-master database. As a general rule they will all have the same information. Some attributes are special and not replicated or replicated at very long intervals; badpwdcount is one of those special attributes and you're right to check the PDC.
Open Active Directory User and Computers, right-click the domain and open Operations Masters and go to the PDC tab for the server name. Connect directly to that server then enable Advanced Features from the View menu. After that, you need to find the object in the hierarchy, the Attribute Editor tab will not show if you open the account from the search box. Once you find the object in the hierarchy, go to the Attribute Editor tab and you'll see the badpwdcount attribute.


Path Of Current In A Wire

Question: Why does current follow the path of least resistance? Will all  current pass through a wire with $0$ resistance in a junction leaving other resistive wires with no current?
Answer:
Why does current follow the path of least resistance?

Current doesn't follow the path of least resistance.  Please forget that you ever heard that and if you hear someone else say that, respond with something like this:
If there are two parallel connected resistors with resistance $R_1$ and $R_2$ respectively, the current divides between the two paths such that the path with smallest resistance has largest current through.
This is simply due to Ohm's law and, in particular, the fact that parallel connected circuit elements have identical voltage across (by definition!).
With voltage $V$ across, the current through each resistor is given by Ohm's law:
$$I_1 =  \frac{V}{R_1}$$
$$I_2 =  \frac{V}{R_2}$$
and now it's clear that the smaller resistance has the largest current through.  Denoting the total current $I = I_1 + I_2$, we easily derive the current division formula:
$$I_1 = I\frac{R_2}{R_1 + R_2}$$
$$I_2 = I\frac{R_1}{R_1 + R_2}$$
which again shows that the smaller resistance has the largest current through.  Note that if (just) one of the resistances is zero, then all of the current is through the zero ohm resistor.  For example, if $R_1 = 0$ then
$$I_1 = I\frac{R_2}{0 + R_2} = I$$
Answer: Yes. Think of it like a pipe system with water.
If the pipe splits in two, one having a "squeezed" constriction and the other being much wider, then most water will go through the wide one. Infinite resistance corresponds to fully closing the constriction (no water passes), and 0 resistance corresponds to having the wide pipe infinitely wider than the other (all water would go there).

Path Of Current In A Wire


Why do I have missing keybindings for magit in spacemacs?

Question: I am trying to use magit in spacemacs. When I read instructions to use magit, I am instructed to hit spc + g + s. However, when I push spc + g I see only one shortcut which is spc + g + f + s, which is "helm-ls-git-ls". Why do I not have any of the other keybindings? I have checked to make sure magit is installed, and also I have reinstalled the package, but I still not get any of the keybindings.
I am at a loss. Any ideas on how to troubleshoot this?
Answer: I figured out the problem. In my spacemacs dotfile, under my layers function, I had the line git commented out. I have since enabled the git layer and I now have all the associated magit commands.


Does a Convolutional Layer in a Neural Network learn the correlation between its input signals via its kernel?

Question: I am interested in the theory behing what a convolutional neural network learns with its convolutional operations. I think it learns (useful) kernels which measure the correlation between its input signals. Moreover, on a technical perspective: the convolution operation is implemented as "cross-correlation". So, is my assumption right?
Answer: In a convolutional neural network (CNN), a convolutional layer has several channels, each of which has one convolution kernel, often written down as a matrix. This convolution kernel is nothing more than a collection of weights used to compute a linear combination of elements of the input.
While both "traditional" dense layers and convolutional layers compute a linear combination of their inputs, convolutional layers have the added structure of preserving spatial information. Additionally, the output of a convolutional layer, called a feature map, can be understood as the result of sliding the kernel along the input.
For instance, take a simple kernel $K = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}$ and a small input "image" $I = \begin{bmatrix} 9 & 8 & 7 & 6 \\ 5 & 4 & 3 & 2 \\ 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \end{bmatrix}$. We take an input with only one channel for convenience: if it's the first layer of the CNN, we can assume the values of $I$ represent a grayscale image. Let us look at how the convolution is performed if no padding is added to the image, in which case the output will be a 2 by 2 matrix.
Starting at the top left corner, we convolve $K = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}$ with $\begin{bmatrix} 9 & 8 & 7 \\ 5 & 4 & 3 \\ 1 & 2 & 3 \end{bmatrix}$. To do so, we multiply the two matrices element-wise, then sum up all the elements of the resulting matrix: $1 \cdot 9 + 2 \cdot 8 + 3 \cdot 7 + 4 \cdot 5 + 5 \cdot 4 + 6 \cdot 3 + 7 \cdot 1 + 8 \cdot 1 + 9 \cdot 3 = 146$.
Doing the same three more times yields the following feature map: $\begin{bmatrix} 146 & 157 \\ 200 & 233 \end{bmatrix}$.
Depending on the kernel of a layer, the feature map will look different, and the information extracted from the input has a different "meaning". The idea behind a CNN is to make the coefficients of the kernel learnable parameters. Often, multiple "meanings" must be extracted from a single input, so a convolutional layer has multiple channels.
However, CNNs didn't invent convolution, they merely made the kernels learnable. Indeed, such methods have been used in "traditional" computer vision (CV) for a long time. In traditional CV, the kernels are hand-crafted to fill specific roles, extract specific types of information.
For edge detection or line detection, you might use a Prewitt filter which is the discrete equivalent of a derivative operator or a slightly more complicated Sobel filter.
In fact, it is not uncommon for a CNN to learn approximations of well-known hand-crafted convolution kernels from traditional CV on the first layer. Also, by visualizing feature maps on deeper layers, as the training of a CNN progresses, gives you good insight into what the specific convolution channels are learning to detect.
Comment: Thanks for your nice answer! Really helpful to understand convolutions in general. However, can you elaborate your answer w.r.t. my question if I can say that the kernels measure the correlation between its input signals? Thanks a lot in advance!
Comment: I'm not certain what you mean by "correlation between input signals". If you're asking whether a convolutional layer measures the correlation between different, distant patches of the input, then no, although a dense layer close to the output layer might indirectly measure it. It does, however, measure the cross-correlation between one patch of the input and the convolution kernel.
Comment: Thanks for clarification. This means a cnn learns useful cross-correlations with its kernel's weight w.r.t to the traning data. If the test data does not contain these cross-correlation, the network will not work as expected?
Comment: If, for instance, your CNN has been trained on human faces, it will probably have a convolution which has learned to respond strongly to a human eye, another one which has learned to respond strongly to a human mouth, etc. If you then feed it a test set of bicycles, those convolutions will not register strong activations, which might be good if you expect your network to discriminate between human faces and bicycles. If instead you expect your network to "recognize" monkey faces, and it's been trained on human faces, it probably won't perform very well. Depends on what you expect out of it.


Cutting Ceiling Molding Wihtout Removing It?

Question: I want to put up a stud wall to make a walk in wardrobe. I want to get a flush joint against the wall but I have some molding across the top. I was wondering if there is an approach to cutting a grove/slot in it without removing it, it's quite a long piece 15+ foot so ideally I want it to stay where it is.
Comment: When you say "flush" do you actually mean "tight"? They aren't the same.
Answer: One approach to this problem would be to use an oscillating tool, of which there are many brands available. Different blade options are provided with the tool, including a toothsome flat blade with a square face.
Home Depot is one source of these tools and blades:

It won't necessarily be fast, but it will be a clean cut (depending on operator skill). If you need a cheap solution, Harbor Freight is likely to be a good source. They have a twenty dollar (US) tool that does not specify that it comes with the cutter, but those are seven bucks each in the same location.
Comment: Thanks for the info, might be a long trans Atlantic flight to pick up a small cutting tool :). I might look for something similar here in the UK.
Comment: Yes, it is likely that you will find what you require locally. The photos are representative of products you would purchase. I understand that there are Chinese product outlets in the UK.


How can I insert rows in a table while filling out an infopath form

Question: I am creating form in InfoPath. I am trying to setup the form with 3 columns per row, and the user needs to be able to add rows a needed.
Comment: @ErinL I think InfoPath [questions](http://sharepoint.stackexchange.com/questions/tagged/infopath) are valid.  OP, you're looking for a repeating table/section.
Comment: How does this relate to SharePoint?
Comment: @wjervis InfoPath questions are valid if they relate to SharePoint. http://sharepoint.stackexchange.com/help/on-topic. It's also important to know because repeating table/sections are more complicated if being used in SharePoint.
Comment: @ErinL My experience with InfoPath is rather limited, so if there's a way to use it outside the context of SharePoint, I don't know that.
Comment: @wjervis Let's continue this conversation in chat http://chat.stackexchange.com/rooms/44160/wjervis
Comment: May be you can look into the embedded code on button click.
Answer: MWilson – If your question relates to an InfoPath form saved to a Form library on SharePoint, and you want to create new rows and promote these new fields as columns in SharePoint, you won't be able to.
To achieve similar functionality, you would need to use a List Form.  List Forms are out of the box list forms that have been opened, edited, and display in an InfoPath template.  These are just a few of the gotcha's with List Forms:

As a best practice for a list where a List Form will be designed, the column limit is approximately 60.  If you require more than 60 fields in your form, a straight InfoPath form is your best answer.
There must be a one-to-one relationship for data entered in a List Form, therefore you cannot use repeating tables and repeating sections, which is what you refer to in your question.  You must:  1) set a cap for the number of additional "rows" a user can add (for example three "rows" only), 2) create duplicate columns such as "Option 1 – Hotel," Option 2 – Hotel," Option 3 – Hotel," 3) and use InfoPath Rules to show options 2 – 3 as "Add another row."
Managed Metadata fields cannot be used in List Forms, or InfoPath forms.


resource file not regenerating when rebuilding (hello world tutorial)

Question: I downloaded monodriod yesterday and was following the hello world tutorial, and came across a problem in monodevelop with resources i couldnt figure out.
When i changed the names of the two string resources in String.xml, the partial String class in Resource.designer.cs wouldnt update when i rebuild the solution. I tried building cleaning restarting the solution, but nothing worked. I then tried removing the partial String class hoping that might force itself to regenerate, but no luck that just brought a compile error.
\HelloM4A\HelloM4A\Resources\layout\main.axml(0,0): Error: No resource found that matches
the given name (at 'text' with value '@string/hello'). (HelloM4A)

can anybody give me a pointer to what i have been doing wrong.
thanks
tut:
http://docs.xamarin.com/android/getting_started/hello_world
Answer: It seems that you have not updated main.axml to use the new string name:
Use: @string/<SOME_NEW_NAME_HERE>
Main.axml:
<?xml version="1.0" encoding="utf-8"?>
<LinearLayout ... >
    <Button ...
            android:text="@string/<SOME_NEW_NAME_HERE>" />
</LinearLayout>

Strings.xml:
<?xml version="1.0" encoding="utf-8"?>
<resources>
    ...
    <string name="<SOME_NEW_NAME_HERE>">Hello Mono for Android</string>
</resources>


Notifying The User When Something Changes

Question: What are some general UX best practices when notifying the user that something in your app has changed?
Comment: I'm voting to close this question as off-topic because it does not provide enough specificity to the problem. There are a multitude of ways to address the universal issue of "notifying the user" which is dependent on a number of factors including, but not limited to: (1) platform, (2) environment, (3) impact of change, (4) severity of change, (5) task being performed.
Comment: The question is quite vague, do you mean the app has had new features added, or do you mean that there is new data for the user?
Answer: There are two ways of doing it.
Force to action. Redirect user straight to the information you want to to read. Examples: Google, PayPal, Barclays Bank terms and conditions.
Call to action. Throw a little message at the top of the page or even on the top of the header inviting users to read "what's new".
Your practice should depend on the situation you are in. Google, PayPal and my bank can tho something like that because no matter what they wrote there I want to get to my emails, money, ability to pay bills quickly. People like myself agree to new term without reading.


Does a 3rd-Party Cable cause any harm when charging your Phone with the original Power Brick?

Question: When using the original Power Brick the Smartphone came with to charge it, does a 3rd-Party cable cause any harm to the device or is there no difference to using the original cable?
Answer: Typical connector theory applies.
In order for a smartphone cable to function it needs the following properties:

Proper connector within spec, otherwise it has bad contact or will damage the socket.
Enough copper wire to handle the current. Otherwise voltage drop will cause charging to abort. This is especially a problem since USB cables were not intended to do >500 mA, until smartphones came around.
In case of iPhones: A valid ID chip. Otherwise the iPhone will say: "Accessory incompatible".

Damage will only occur when there is a physical problem with the cable, or a polarity problem of course, but those are rare.
Most damage will happen when the cable or socket has wear. After many mating cycles, cheap cable contacts wear out causing higher resistance, with more heat. Sometimes the phone melt and causes fire.
This is because the springiness of the contacts degrades over time, and degrades faster when heated.  When you often use a slightly off-spec cable, it might cause damage in the long run.
Don't be stingy on a 10$ cable for your hundreds of dollars device.
Comment: For the last line alone plus one !
Comment: I'm not trying to be stingy or safe some money. I'm actually intending buying a cable with higher quality from a good 3rd-Party. But since I have no idea of such things, I was worried about damaging my phone.


Does Shikamaru have a summoning animal?

Question: What is the summoning of Shikamaru?
And also, can I get some explanation of his chakra nature? I don't get it, as Kakashi skips it during Naruto's training for rasen-shuriken.
Comment: who need summon if you can make shadow tentacles :D
Comment: Please try to refrain from asking more than one question in your question. As it can lead to split answers.
Answer: It is nowhere mentioned the summoning animal of Shikamaru Nara.

A mythological mosnter called "Inoshkacho" had the body of a boar, a deer's antlers, and butterfly wings.
So it could be assumed that
Ino = Boar
Shikamaru = Deer
Chouji = Butterfly
The Nara clan's forest is located on the outskirts of Konoha, it is a unique forest within the Land of Fire. Many deer reside here as the clan looks after them and often times use their antlers in medicines
Answer: Nowhere is it ever shown that the Nara family have been using a summoned animal in the anime. So it can only be speculated that they don't use/have a summoning animal. The deer that belong to the Nara clan can be taken as a rearing of their clan.
As far as your answer for the chakra type of Shikamaru Nara is concerned, it refers to the Yin form of release. Now basically, to mould chakra one needs to mould the physical and spiritual energies within ourselves in the right combination. The spiritual energy is the Yin form (or Yin release) and the physical energy the Yang release.
Hence, the Yin release is nothing but the spiritual energy that Shinobis use, can be used in a wide variety of forms. Good examples of it are (all) the Genjutsus used and also the shadow manipulating jutsu of the Nara clan.
The Yin release can be based on our imagination and also be used to create form out of nothingness. It is the same concept coupled with the Yang release (used to give life into an object or form) that led to the creation of the the Nine-Tailed Beasts from the chakra of the Ten-Tails by the Sage of Six Paths (called as the Creation of All Things Technique).
If you want more information, I suggest you go through the Naruto Wiki articles on Yin release, Yang release and Yin-Yang release.

Does Shikamaru have a summoning animal?


codenameone:We want to show the exact seconds of system on each seconds

Question: we are working on progress bar.we want to display exacts seconds of system on each seconds over progressbar.
 currently we are using java.util.Calendar cal=Calendar.getInstance(); for getting system time .
 but its not working .
Can you please let me know how to resolve it. My application needs to be supported on all platforms (Andriod, IOS, windows) and I don't want to write native code for all platforms separately.
Comment: ...What language? Java? What code isn't working? Post more details and code. Also properly tag the question.
Comment: That gets you a Calendar object, how are you using the object to display time?
Comment: time=Calendar.getInstance().SECOND;                System.out.println("Display time"+time);
Comment: this is my code. i want to display time in each seconds on progress bar label and want to set progress dynamically grow with seconds.
Answer: SECOND is a static final value in Java and the same is true for Codename One so you are effectively trying to get the value of a constant that will never change...
System.currentTimeMillis() returns the system time from GMT in milliseconds.
Calendar c = Calendar.getInstance();
int currentSecond = c.get(Calendar.SECOND);

Also check this demo of a live clock with animation and code.


How do satellites accelerate in space?

Question: We are told right from childhood that space is just vacuum and so I wondered if the space is empty then how come satellites accelerate in space. Newton's third law is applied, to accelerate any body but if there is no matter in space then what gives an equal and opposite force to satellites?
Comment: Related: [Will a rocket produce more thrust if fired in air, rather than vacuum?](https://physics.stackexchange.com/questions/122176/will-a-rocket-produce-more-thrust-if-fired-in-air-rather-than-vacuum) The answer to that question is a resounding "No". Contrary to the popular notion that rockets work by thrusting against something, rockets work best when there's no obstruction at all (i.e., in vacuum).
Answer: Satellites accelerate in space mainly

through the action of gravity, both from the Sun as well as the planets, and
by firing rocket engines or other similar means of propulsion.

In the first case, Newton's third law demands an equal and opposite reaction, and this is exerted on the Sun (or planet / moon / whatever), where its effect is negligible. In the second case, the reaction is exerted on the rocket exhaust, which ends up moving much faster (but with lower mass) in the opposite direction.

How do satellites accelerate in space?


Silverlight reflection

Question: With ASP.NET, for instance, we could reflect on the assemblies in an AppDomain, or using the type we could get the metadata about the class (props, methods, etc.).  What is the technique used to extract metadata on a class, extract dependency properties, etc., in Silverlight?
Answer: Reflection exists in Silverlight, with a subset of the APIs provided in the full .NET Framework.
One notable difference is that you can't reflect onto private members in Silverlight (or maybe you can inside your own assembly, but the boundaries should become apparent pretty quickly).  This is a security feature to ensure you don't go messing with the internals of the framework itself.
Other than that (admittedly, rather large) limitation, Reflection should be basically the same.
Comment: You can reflect on private members but you cannot modify or invoke them. I have tried for example to call GetValue for a FieldInfo but was not able to call SetValue, it throws an exception.
Answer: In addition to what Austin said, the rule with Reflection in Silverlight is that you can only access via reflection whatever you could access via normal code. So it's not just about private members. You can reflect over protected members only in the class itself or in any class inheriting it.
There are numerous missing pieces of the API but in general most things should be possible, even if they require a bit more work than in full .NET
Answer: Security Considerations for Reflection
Reflection provides the ability to obtain information about types and members, and to access members. In Silverlight, you can use reflection to perform the following tasks:
Enumerate types and members, and examine their metadata.
Enumerate and examine assemblies and modules.
Access public members.
Access internal members (Friend members in Visual Basic) in the calling code's assembly. (In reflection, this is referred to as assembly-level access.)
In Silverlight, you cannot use reflection to access private types and members. If the access level of a type or member would prevent you from accessing it in statically compiled code, you cannot access it dynamically by using reflection.

Silverlight reflection


What is a good example of a project to use to demonstrate how to build a Microsoft Project Schedule

Question: I want to train a few new team members in the use of Microsoft Project. All are familiar with the basics but I want to explain WBS hierarchy and predecessors. I am trying to think of an 'every day life' example of a project that most people would agree on the contents and logic so we can use this to build a plan together.
I have used 'cook a meal' previously, but would prefer something over longer timescale.
Comment: Although this is a potentially list-generating question, I think it's an interesting one, since a good supporting example is essential for people to focus on the concepts being explained without the structure used to explain them getting in the way.
Answer: I think the best example would be building a house (image source):

Although people might not have built houses before, they have seen it happen at some point or another, and there is a good familiarity with the concept since we all live in houses :).
And it's also a good model to use because it allows you to go in as wide or as deep as necessary to explain various concepts. There are also dependencies between each part (since you can't build the walls without a foundation, or the roof without the walls, etc), you might need to add buffers to your schedule (because of the weather, for example). There is also procurement of materials, if you want to throw that in the mix too,  and so on.
Answer: I suggest you choose an example that is relevant to the business domain that your team are expected to deal with. WBS and schedule makes sense for some kinds of work but not so for others. For example it's not usually a good idea to use WBS for software products; Product Breakdown Structure makes much more sense.
Comment: Thanks for the suggestion. As new team members may be new to the business are (IT projects) and may also be new to project management, i want to use a 'real word' example that all trainees may be familiar with.
Comment: "IT Projects" could mean a lot of things. If it means software development projects then I suggest you avoid WBS and scheduling based on constraints. Try using an agile-style product backlog with deliverable-based epics and stories instead.
Answer: Pick an example in your business domain with all different task dependency types
You said:

I want to explain WBS hierarchy and predecessors

Pick an example in your business domain, but make sure you bring in all different task dependency types.

FS (Finish-To-Start) Dependency: This is the most common dependency found in any project. Task A must finish in order for Task B to start. So, you don't have to think hard to find this one.
FS (Finish-To-Start) Dependency with a lag: This is not that common. For example, you can't paint a wall immediately after plastering. You have to wait until the plaster is dry.
SS (Start-To-Start) Dependency: For example, the writing of a business proposal must have begun in order for review/editing of the proposal to start.
FF (Finish-To-Finish) Dependency: For example, electrical work cannot finish until drywalling is complete.
SF (Start-to-Finish) dependency: This is a very rare one. For example, start of the next shift of the security guards has to happen for the previous shift to end. If the next shift security guards don't turn up, the previous shift security guards have to continue their duty.
Comment: Thanks Ashok. As its an introductory training session i'll probably use FS, SS and FF, ignoring SF for this session. I would also suggest to the attendees to create an activity that explicitly details the lag, so in your example i would create a 'Drying time' task.
Answer: Modernization of a bathroom or kitchen. Easy to visualize.


What is the female equivalent for "handsome"?

Question: In the first days in a relationship, a girl welcomes a guy with "hey handsome". Would be "hey honey" an appropriate response?
Comment: You could try _handful_ :) You might be interested in our sister site, http://ell.stackexchange.com , which specifically caters to English Language Learners.
Comment: [Related](http://english.stackexchange.com/q/17108/2303).
Comment: I have seen the question before created this one. That one checks if you can say "handsome" as well to a woman. But, as far as I know, it is not the "normal" response for which I wanted ask here.
Answer: The feminine equivalent to (usually, facetious) "Hey, handsome!" is...

"Hey, gorgeous!"
Comment: Men can be gorgeous too :)
Answer: Pretty or beautiful are the most common words.
Handsome can be used for women, but is somewhat old-fashioned.
Answer: There is a Hank Williams song in which he says the following:

"Hey, good looking, what you got cooking?  How's about cooking something up with me?"

While these sentences may confuse you with their idiom concerning food, and in answer to your question, the way Hank Williams addresses his girlfriend is still used today:  good looking, or good lookin'. It means simply you are looking good (i.e., attractive, pretty, lovely, pulchritudinous, beautiful, easy-to-look-at, easy on the eyes, appealing, and  so on).  In everyday speech you could also say, "Hey, beautiful!" but not "Hey, pulchritudinous" or "Hey, pretty (or lovely, or easy-to-look-at or appealing)"  .
As for the cooking metaphor, Williams is saying simply "What's going on?  What are you doing now?  Let's do it together and create something pleasurable. "
Comment: +1 for *Hey, pulchritudinous!* Imma have to try that one out.
Answer: In terms of words between a couple you are right that a girl can tell the boy "hey, handsome" and he can say "hey, honey."
If he was not her boyfriend, and he wanted to call a stranger girl "honey," then that wouldn't make sense because "honey" is an endearing (usually romantic) term for girls he knows.
If you wanted an equivalent word for "handsome" then "handsome" for girls can be used, but it is rare nowadays. You could use "pretty," "cute," or even "charming" when describing good-looking girls that you do or don't know personally; these terms are not romantic if you don't want them to be.


Understanding section on electromotive force in Purcell and Morin's Electricity and Magnetism

Question: I am following the book Electricity and Magnetism by Purcell and Morin.
There is a section on the electromotive force that I would like to understand better. I will write out the snippets from the book and my interpretation of what they are saying.
First there is an explanation about how a lead-sulfuric acid cell works, that we can visualize below

They then say

The cell will remain indefinitely in this condition if there is no
external circuit connecting its terminals. The potential difference
between its terminals will be close to 2.1 volts. This open-circuit
potential difference is established "automatically" by the chemical
interaction of the constituents. This is the electromotive force of
the cell, for which the symbol $\epsilon$ will be used. Its value
depends on the concentration of sulfuric acid in the electrolyte, but
not at all on the size, number, or separation of the plates.

Open-circuit means there is no wire connecting the terminals of the battery. The cell in the picture above is charged, meaning there is charge on the terminals, hence an electric field between them, and hence a potential difference between the terminals.
Electromotive force (emf) is not actually a force. It is actually this potential difference between the terminals and it represents work done by a force per unit charge that has magnitude equal to the electric field between the terminals (at least inside the battery near the terminals).
Question: What does it mean that the potential difference between the terminals is established automatically by the chemical interaction of the constituents?
We have an electrolyte (liquid or gel containing ions) between the terminals. My interpretation of the charged state depicted above is that there is some kind of "equilibrium" (where this is not well-defined by me) where no net charge is being added to the terminals. I don't know exactly why this is, but is seems it might be because if we were to write out the chemical reaction equation at each terminal it would be a reaction happening in both directions simultaneously at the same rate. Ie, something being added to the positive plate and removed from the positive plate at the same rate. Not sure if this is correct.
Now let's close the circuit.

We can think of charge moving between the battery terminals through the circuit external to the battery. We can think of negative charge moving from the negative (lower potential) terminal to the positive (higher potential) terminal. If nothing else were to happen, then the potential difference (and hence the current, by Ohm's law) would fall until it reached zero.
However, something does happen: the battery keeps the potential difference constant, or at least tries to because it can't do this forever. It does this by taking electrons flowing into the positive terminal and having them participate in a chemical reaction with the lead dioxide on the positive plate, and increasing the concentration of lead sulfate in the electrolyte a a result. This lead sulfate participates in another chemical reaction, this time on the negative terminal, which releases electrons into the external circuit.
About this whole situation of closing the circuit, the book says

Now connect the cell's terminals through an external circuit with
resistance $R$. If $R$ is not too small, the potential difference $V$
between the cell terminals will drop only a little below its
open-circuit value $\epsilon$, and a current $I = V/R$ will flow
around the circuit.

I don't really understand this. As far as I do understand, we have the relationship
$$V_a-V_b=IR=\epsilon$$
Let $V_b=0$. Then
$$V_a=\epsilon=IR$$
The smaller $R$ is, the more current will flow. The larger $R$ is, the less current will flow. As far as I can see $V_a$ is fixed given $\epsilon$ which I think is determined by the characteristics of the battery we are using.
Question: So why does the book say "the potential difference $V$ between cell terminals will drop only a little below it's open-circuit value $\epsilon$"?
Comment: For your second question, maybe he's referring to the effect of the internal resistance of the battery?
Answer:
Electromotive force (emf) is not actually a force. It is actually this potential difference between the terminals

Correct, and it represents a work done if a charge is brought from one end to the other.

Question: What does it mean that the potential difference between the terminals is established automatically by the chemical interaction of the constituents?

We do not need to do anything to the system, it will maintain this voltage by itself. Automatically. Just putting these objects together will be enough.

there is some kind of "equilibrium" (where this is not well-defined by me) where no net charge is being added to the terminals. I don't know exactly why this is, but is seems it might be because if we were to write out the chemical reaction equation at each terminal it would be a reaction happening in both directions simultaneously at the same rate.

It does not have to start out at the same rate, but because the whole system will end up at thermal equilibrium (and in the case of flow, a steady state), the final rates must be the same, and then it will obviously no longer change when that happens.
Look, each electrode only cares about the electrolyte nearby it, and all of these interactions are happening at multiples of Avogadro's number! It is all probability and statistical, and at equilibrium, the tendency of the acid to eat away at the electrodes must be balanced by the already accumulated charges repelling more of the reaction, calculated by the voltages that have accrued. That is why the open circuit voltages would be what they are—just enough to cancel out the tendency for the electrolyte to be used up.

This lead sulfate participates in another chemical reaction, this time on the negative terminal, which releases electrons into the external circuit.

IIRC, it is some other chemistry. Not the same thing. The acid should become weaker as the battery charge level is used up, and the acid should become stronger as you charge the battery back up. But this is a detail that you definitely can just look up.
Remember that the ``equilibrium" is due to probability and statistics, that the net rate of chemical reactions depends upon the voltages. If you continue to supply precisely the open-circuit voltage $\epsilon,$ then the rate of chemical reaction ought to be precisely zero, which means zero current. In order to sustain a certain current $I,$ the voltage must thus drop a little to let the rate of chemical reaction be equal to the circuit current $I.$
It is this that we crudely model as an internal resistance, so
$$\epsilon=I\left(R+r\right)\qquad\implies\qquad V=IR=\epsilon-Ir$$


Create individual wallet for each user

Question: I am working on a platform where users can register and can have wallets with multiple addresses (one address for each coin/network). I found something in Binance APIs where you're able to create sub-accounts and for each subaccount, you can set the coin and so for each one, you can get a unique address. I don't know if this is the best practice to generate new addresses for the users
Comment: why do you need binance?
Comment: @user253751 Not necessarily Binance, I am new in crypto and only have some experience in binance APIs, I can use any library to create the addresses for each user after they register in the platform so they must be able to receive crypto to that addresses, do you have any suggestions please?
Comment: Look up how e.g. hierarchical deterministic wallets work. In very simple terms, they generate a series of addresses based on the same private key. But that's only useful if you want to only have one private key (and e.g. generate more public addresses without knowing the private keys). If you don't have special requirements then you can just generate new addresses the same way you generated the first one.
Comment: @user253751 Yes that's exactly what I need, the idea is that each registered user must have a wallet to use it for deposit and withdraw bitcoin, ethereum, litecoin,... so for each coin he must have an address that's generated after success registration on the fly. Can you please help about the best way to do this
Comment: how did you generate the first address?
Answer: It is not. It will be safer, easier, and reliable, to use a library designed for address creation.
https://www.binance.com/en/support/faq/360020632811

What is a Sub-Account?
Sub-account allows you to trade through multiple accounts. You can use it to clearly divide responsibilities and manage transactions ...

It is not the intended design of Binance for your use case.
Comment: Thank you @Gerschel, can you please share some examples for libraries used in address creation?
Comment: I have not tried out any libraries. I had written my own; because I didn't know which would be "better" or "safer"; so I wanted to understand the process. Security is a big issue, who's managing the server security, who has access to do so, backups. This topic is just beyond my scope at the moment.
Comment: @MarwanAswad I can share some knowledge with you on how to do it, make the bips less dense.
Do go and continue with your homework, it's going to be a bit, I need to write it up between work. What's your programming language preference?
Comment: it's highly appreciated if you can guide me with the needed steps, my project is written in PHP, and I think I can use any programming language to handle the addresses creation and call the needed web services from my PHP project, what do you think?

Create individual wallet for each user


Fitting to data with a Bernoulli (I think) distribution

Question: I have a series of data to which I want to fit my model. The model predicts the probability of success at a given value of x. I have a single data point at a number of points in this space. As I have a single point which is either pass or fail with a certain probability I believe I should fit using a Bernoulli maximum likelihood fit, is this correct? So i have a likelihood function which looks something like
$$L(\theta,x) = \Pi^{n}_{i} \theta^{x_i}(1-\theta)^{1-x_i}$$
where n are my data points? This is just different enough to the usual Binomial likelihood case to have completely thrown me.
Comment: Isn't $\prod_i^n\theta^{x_i}(1-\theta)^{1-x_i}$ the same as $\theta^{\sum_i x_i}(1-\theta)^{n-\sum_i x_i} = \theta^y(1-\theta)^{n-y}$ where $y = \sum_i x_i$ is a binomial $(n,\theta)$ random variable?
Comment: Wouldn't $y$ have the distribution ${n \choose k} \theta^y (1 - \theta)^{n-y}$ if $y = \sum_{i=1}^n x_i$
Comment: @SachaEpskamp What is the relationship between $y$ and $k$?  In any case, the _probability mass function_ of $y$ is irrelevant.  The _likelihood_ of the _observation_ or data $$x = (x_1,x_2,\ldots,x_n)$$ is exactly what Bowler stated it to be, and it _is_ essentially a binomial likelihood.  The extra constant factor $\binom{n}{y}$ (remember that $y$ is a function of the data $x$ and is thus fixed) that you have included makes no difference: the value of $\theta$ that maximizes $\theta^y(1-\theta)^{n-y}$ is the same as that which maximizes $\binom{n}{y}\theta^y(1-\theta)^{n-y}$.
Answer: I think what you want is logistic regression (or at least the likelihood that is maximized in logistic regression). If the wiki isn't enough, search for MLE fitting of logistic regression on Google.
Comment: Thanks, logistic regression looks interesting its definitely a possibility.
Answer: If $x$ is a vector with independent measurements of a single variable which can be pass or fail, then this is the likelihood indeed, except that I think $L(\boldsymbol{x} \mid \theta)$ would be the proper notation.
EDIT: the binomial distribution is based on the sumscore. It would be the proper distribution if you were using $y = \sum_{i=1}^n x_i$.
Comment: Thining about it I asked a yes/no quesiton so this does actually answer it. Thanks.


closest equidistant point to N points in M dimensions

Question: Is there a formula/algorithm/etc. to find the closest equidistant point (assuming it exists) to a set of points, allowing that the number of dimensions of the space is independent of the number of points? Any help would be greatly appreciated.
Comment: a necessary condition for this to be possible is $N\leq M+1$, if I'm not mistaken; for a sufficient condition you also need to exclude $p+2$ points on a $p$-dimensional subspace (no three points on a line, no four points on a plane, ...); I'm guessing that this special point is the [geometric median](https://en.wikipedia.org/wiki/Geometric_median), for which an efficient algorithm exists.
Comment: It might not be too big an issue, but "assuming it exists" is doing a lot of heavy lifting for me here. N could be bigger than M... 8 points around a circle in 2-dimensional space have a closest equidistant point. The issue of whether such a point exists for me is only a step to finding what the point is IF it exists.
Answer: Let $p$ be the closest equidistant point to your set of points, $\{p_1,\dots,p_N\}$. Then $p$ is in the affine subspace $X$ generated by the points: if not, the orthogonal projection of $p$ in $X$ is also at the same distance to all the points and closer to the points than $p$, which is a contradiction.
$p$ is the unique point of $X$ at the same distance from $\{p_1,\dots,p_N\}$: if there was other such point $p'$, then all the $p_i$ would be in the intersection of two spheres of centers $p$ and $p'$, which is impossible because the $p_i$ affinely generate $X$ and the intersection of two distinct spheres in $X$ is always contained in a hyperplane of $X$.
So you can compute $p$ as the intersection of the affine subspace $X$ generated by $p_1,\dots,p_N$ and the bisector hyperplanes $H_{p_1,p_2},H_{p_2,p_3},\dots,H_{p_{n-1},p_N}$. Moreover, if your set of points is not affinely independent, you can change it by a maximal affinely independent subset. All of this assuming the existence of $p$, of course.
Comment: Thank you! I'm sorry this explanation is a bit beyond my current math knowledge to know how to evaluate or implement. I'll do some research.
Comment: Okey. I suppose you have some program to calculate intersections of hyperplanes (?), so would the problem be obtaining the equations of the affine subspace generated by the points?
Answer: If such a point exists, then it is the center of a sphere on which all $N$ points lie, so I think your question is equivalent to asking, do all $N$ points lie on some sphere?  Since $M+1$ points determine a sphere in $\mathbb{R}^M$, I think it would be enough to first use $M+1$ points to determine that sphere (for example, as described in a/the answer here: https://math.stackexchange.com/questions/2611326/how-many-points-define-a-sphere-of-unknown-radius), and then check whether the remaining $N-(M+1)$ points are located at the given distance from the given center.
In short: the formula/algorithm merely involves solving a linear system of $M+1$ equations, and then checking distances of the remaining points $N-(M+1)$.
Comment: I like this solution very much for cases where N >= (M+1)! But not sure if I could expand it to cases where N < (M+1)... where there are more than one equidistant points, but one of them is closest?
Comment: If three distinct points lie on a line, then no point is equidistant to them. If they don't lie on a line, then a unique circle passes through them; its center is the unique equidistant point.

The same is true in general. We need to check that the $N$ points are in "general position", i.e., that they don't lie on a hyperplane of dimension lower than $N-1$. Three points shouldn't lie on a line, four points shouldn't lie in a plane etc. If the $N$ points are in general position, then a unique hypersphere passes through them; its center is the equidistant point.
Comment: More concretely, I think the algorithm referenced above, that involves solving a system of linear equations, will work just as well for the $N < M+1$ case, though the matrix is no longer square. Assuming the system has a solution, then the point $p$ obtained is the center of the (translated) sphere, and hence the equidistant point you seek.
Comment: The algorithm you mention only uses that the distance from your point to the rest of the points is equal, so it will obtain infinitely many solutions if $N<M+1$. This is the case when you are given three non-colinear points in $\mathbb{R}^3$, then there will be a whole line of points at the same distance of the three points. But only one of them is closest to the three points: in this case it can be obtained by intersecting the line of points equidistant to the three given points with the plane containing those points (this is what my answer generalizes).
Answer: An algorithm that works at least for dimensions $2$ and $3$ is:

calculate a spanning tree of the $n$ points
calculate the bisector planes of the spanning tree's edges
the sought poiint is in the intersection of the affine subspace defined by the intersection of the bisector planes and has least distance to any of the given ones.

that algorithm can be generalized to arbitrary many points by taking the least squares solution to the intersection of the bisector planes with the subspace that is orthogonal to these intersections and contains the $n$ points.
For numerical reasons the maximum weight spanning tree seems preferable over the minimum weight spanning tree; it is also recommended to move the $n$ points center of gravity to the origin to  prior to the calculations.


Simulate GPS IMU With Quadcopter Swarm?

Question: I have multiple drones work in swarm formation, i made the quadcopter model and the swarm one. Until now i have the swarm moving in a formation leader-follower and track a predefined trajectory based on PID Controller. What i need help is how to add GPS, IMU sensors model to my model?
Comment: Did you look at PX4 or Ardupilot frameworks ?
Comment: Can you describe what you are doing / trying to do in more detail?  This is a fairly broad ask...  You want a *simulated* GPS and IMU?
Comment: I have multiple drones ,swarm of drones lets us say 5,one leader and 4 follower. i made the simulation in Matlab, for now the swarm follow a pre-defined path , what i want to do is how can add gps and imu to my simulation? how can put then into my design, i know it maybe be done by Kalman filter, but i need some ideas of the schematic or flow diagram?
Comment: @jackabraham: On stack exchange, it is better to edit your question to add information requested in comments, rather than adding more comments. Comments are for helping to improve questions and answers, and are distracting, so we try to keep them to a minimum. If all of the information needed to answer the question is contained within it, the comments can be tidied up (deleted).
Answer: It depends on what you are trying to achieve.
If you want to see how your path following / formation tracking etc. works under non-ideal conditions, then you can simply give it a position that is slightly wrong.  Perhaps some kind of Gaussian around the actual location.  It is kind of pointless to be in a simulation environment with perfect localization, then simulate multiple noisy sensors, then use a complicated algorithm to fuse the sensors to try to get back out good localization.  Why not just simulate the output of all that mess?  i.e. "good" not "perfect" localization.
To reiterate, it is totally reasonable to not want to use perfect localization in your simulator.  But there are easier ways to go about it.
If you want to make your simulation more closely match your real hardware, I would highly recommend looking at the noise, error, and other characteristics of your actual sensors, then adding those to the simulator.  Every sensor, platform, and application is slightly different, so it will be difficult for anyone else to provide this data for you.
But in general, from what I've seen, GPS usually has some constant offset from the actual position, then in a little while, it will jump to some other offset.  Acclerometers usually have a scale error, or axis misalignment.  And gyros have drift.
If you want to test out your kalman filter or whatever sensor fusion algorithm you have, then that is probably better served in a different question.
Answer: I don't know Matlab, but if you are trying to simulate GPS data you might get some inspiration from Gazebo.  It lets you simulate GPS data with varying degrees of accuracy.  The plugin definition might look like this:
<code><gazebo>
    <plugin name="rtk_gps_plugin" filename="libhector_gazebo_ros_gps.so">
        <updateRate>10.0</updateRate> <!-- Higher update rate for precision -->
        <topicName>/rtk_gps</topicName>
        <frameId>gps_link</frameId>
        <noiseMean>0.0</noiseMean>
        <noiseStdDev>0.05</noiseStdDev> <!-- About 2 inches of noise -->
    </plugin>
</gazebo>
</code>

Simulate GPS IMU With Quadcopter Swarm?