Suitable modelling approach to incorporate different signals

Question: I am working with data in the form of content that is being reviewed to decide if it violates the policy standards or not. In the review process there are several methods to increase the chances of making the correct decision. Content might be sent for multi-review in which case it is reviewed additional times to help get to a correct decision. We can also check the historical accuracy scores of the humans reviewing the content, higher accuracy scores indicate a higher likelihood of a correct decision. Similarly, we can check some other factors such as length of review time, the type of the original content etc.
There is a separate audit process which evaluates a subset of decisions and decides on the policy correct decision in that instance. We can compare these policy correct decisions to the original decisions to evaluate the marginal lift in accuracy from the multi-review system, reviewer accuracy etc. The goal is to develop a system which incorporates these signals and outputs a score that represents our confidence that the review decision is correct.
I have done analysis comparing the marginal improvement in accuracy based on the individual signals, I have also calculated the margin of error for these scores depending on the number of samples we have. For example, when content gets multi-reviewed it is x% more like to be the correct decision with a margin of error of 0.5%. Some signals have a higher margin of error since we had less samples.
I'm trying to figure out the best way to incorporate all of the signals into a single score. I am not sure if regular classifiers will apply since only a portion of posts get multi-reviewed and we only have historical reviewer accuracy scores for a portion.
The way I have been thinking about it in my head is in the form of a decision tree, if the content has been multi-reviewed yes/no, if we have an accuracy score yes/no. Perhaps a decision tree / random forest model would be suitable. It would be great if the model was interpretable and the output could be explained. I would also be open to a more straight forward solution without the need for complex modelling.
Thanks for any advice you can provide on this :)
Answer: Combing multiple models together is called typically ensembling.
You are describing hierarchical ensembling. There are simpler methods for ensembling, such as voting and weighted voting.


What happens to a license if the licensor sells the rights?

Question: If party A purchases a software license from party B, and party B sells all of its rights relating to the software, what happens to the license party A has? Must the new owner still honer the agreement? When party B sells the rights, must they inform the purchaser that such a license exists? For example could it happen that party C, the new owner of the rights, finds party A using their software and considers it stolen, but then party A is able to prove they received a license from party B. What's the best way party A can protect itself?
Answer: The overwhelming majority of software licenses are non-transferable. The buyer would need to take out their own licenses with the software owner.
For those that are transferable, the contract selling the business should address this.
Comment: @DaleM: I think you confused who is selling what. This is about say end user A buying software with license from software developer B, and B sells his complete business including all copyrights to another developer C.
Comment: How does making a license non-transferable protect that licensee? Does that just means the licensee can't give it to someone else?
Comment: @swandiving that's exactly what it means


Nerve of category

Question: in my first topology lecture I learned about abstract simplicial complexes which were roughly defined as can be found on wikipedia. Now I am reading up on classifying spaces of (topological) categories which are defined as the geometric realization of the nerve , that is a simplicial set or as it is apparently sometimes called a semi-simplicial complex. Now I am wondering if it's all basically the same, that the nerve of a small category can be identified as a simplicial complex in some way. Another thing is, that the author of the paper I am currently reading stresses he is talking about topological categories, but the definition of the nerve doesn't consider any topology as far as I can see.
Comment: Hi @Blubb91, what is the name of the paper? If I could peruse the paper itself I might be able to give a more helpful response.
Answer: In a simplicial complex an $n$-simplex must have $n+1$ distinct vertices and is completely determined by them, that no two simplices can have exactly the same set of vertices. A simplicial set has neither of these restrictions. The usual definition of the nerve a category has as $n$-simplices strings of $n$ composable morphisms; the vertices of such a simplex are the objects these morphisms go between, so as you can see the vertices need not be distinct, and there can be more than one simplex with precisely the same vertices. Thus the nerve is a simplicial set and not a simplicial complex.
As for topological categories, the nerve is naturally a simplicial topological space, not a simplicial set. Say a topological category has space of objects $C_0$ and space of morphisms $C_1$, then you say the space of $n$-simplices is the subspace of $C_0^{n+1} \times C_1^n$ given by $$\{(x_0, f_0, x_1, \ldots, f_n, x_n) : x_i \in C_0, f_i \in C_1, f_i : x_i \to x_{i+1}\}.$$ Simplicial spaces have geometric realizations too, defined in pretty much the same way as the geometric realization of a simplicial set, and the geometric realization of the simplicial space which is the nerve of a topological category is still called its classifying space.

Nerve of category


How to send data from one webApplication to another

Question: I have two web applications in two different server.I want send some data in header or request to other web application.How can I do that, please help me.
Comment: It is based on the data your are sending, [Refer](http://www.diffen.com/difference/Get_vs_Post)
Answer: You can pass data by many means:

by making http request from your app:
URLConnection conn = new URL("your other web app servlet url").openConnection();
// pass data using conn. Then on other side you can have a servlet that will receive these calls.

By using JMS for asynchronous communication.
By using webservice (SOAP or REST)
By using RMI
By sharing database between the apps. So one writes to a table and the other reads from that table
By sharing file system file(s)...one writes to a file the other reads from a file.
You can use socket connection.
Answer: HttpClient can help
http://hc.apache.org/index.html

Apache HttpComponents
The Apache HttpComponents™ project is responsible for creating and
  maintaining a toolset of low level Java components focused on HTTP and
  associated protocols.
Answer: One web application is functioning as the client of the other. You can use the org.apache.http library to create your HTTP client code in Java. How you will do this depends on a couple of things:

Are you using http or https?
Does the application you are sending data to have a REST API?
Do you have a SOAP based web service?

If you have a SOAP based web service, then creating a Java client for it is very easy. If not, you could do something like this and test the code in a regular Java client before trying to run it in the web application.
 import org.apache.http.client.utils.*;
 import org.apache.http.*;
 import org.apache.http.impl.client.*;

  HttpClient httpclient = new DefaultHttpClient();
  try {
     URIBuilder builder = new URIBuilder();
     builder.setHost("yoursite.com").setPath(/appath/rsc/);
     builder.addParameter("user", username);
     builder.addParameter("param1", "SomeData-sentAsParameter");
     URI uri = builder.build();
     HttpGet httpget = new HttpGet(uri);
     HttpResponse response = httpclient.execute(httpget);
     System.out.println(response.getStatusLine().toString());
     if (response.getStatusLine().getStatusCode() == 200) {
        String responseText = EntityUtils.toString(response.getEntity());
        httpclient.getConnectionManager().shutdown();
     } else {
        log(Level.SEVERE, "Server returned HTTP code "
                + response.getStatusLine().getStatusCode());
     }
  } catch (java.net.URISyntaxException bad) {
     System.out.println("URI construction error: " + bad.toString());
  }


How to replace Nokia Lumia 1520 screen?

Question: Yesterday I drop my Lumia 1520 to the ground in an accident and the screen broken, then I went to the repair shop and it cost really much. Is there anything else I can do?
Answer: Well you could get a replacement screen from eBay or somewhere and put it in yourself. This is probably gonna cost you around $40 to $50 including all the tools you need.
HOWEVER please only do this if you're really comfortable with disassembling your phone and you know what you're doing. Having broken a phone myself this way I can say that this is not easy to do right. Especially since you can't do any screen calibration yourself.
Giving the phone to Nokia services should be around $100, right? For me the difference would be small enough to remain on the safe side.
Comment: ...and consider a protective case to avoid breaking it again...
Comment: I purchased a complete screen assy for my 1520 due to the digitizer giving me random ghost touch issues. The screen received from ebay seller seemed to be exact replacement. Upon doing the swap, which I followed step by step from you tube, the screen did not scroll smoothly. And worse, when the screen timed out, it would deactivate the touch screen altogether, requiring a reboot every time to get it working again. I ended up swapping back to my old screen, which is working the same as it did before the swap. So at least I am back to square one and not square zero with an unusable phone.
Answer: Maybe also the teardown of ifixit.com helps you to disassemble
https://www.ifixit.com/Teardown/Nokia+Lumia+1520+Teardown/23924
there is also a YouTube Video about how to repair:
https://www.youtube.com/watch?v=sIVJxqfW27Q&noredirect=1

How to replace Nokia Lumia 1520 screen?


How to add new Linux user restricted to ssh tunneling with password?

Question: I wanted to create a new user on my linux server so that he can access my postgres database through an ssh tunnel. However, I want him to restrict his access only to the ssh tunnel.
I followed these steps:

login on server as root
Create a new user with useradd new_user -M -s /bin/true
Set a password with passwd new_user
make sure that PasswordAuthentication yes is set and uncomment in /etc/ssh/sshd_config
Restart ssh with sudo systemctl reload sshd
Logout from server and login to server with new user with ssh -p 7822 new_user@my_address.com -N 5433:localhost:5432 (I am using a2hosting as a provider, where I need to use port 7822 for ssh)

However, when I try to login I get the error

Permission denied, please try again.

When I do everything like above but change step 2 into
useradd new_user -m -d /home/new_user
I can successfully login with the new user, however, I then have the possibility to actually access command line, which I try to avoid. What am I doing wrong here?
Answer: Match user foo
    ForceCommand echo 'Only TCP port forwarding to PostgreSQL enabled!'
    PermitOpen 127.0.0.1:5432
    PermitUserRC no
    PermitTTY no


Can't switch compliance level in Eclipse

Question: So after reading another question post I realized my question had changed. It is essentially, why can't I change my compliance level in Eclipse from 1.6 to 1.7 but I'm going to leave the body of my question as it was typed originally.
This is a very specific question but I'm going through a series of Java courses online and one of the lessons deals with switch. The example code uses switch with strings (both the course and I use Eclipse). When I try to run the code it gives me an error stating
"Cannot switch on a value of type String for source level below 1.7. Only convertible int values or enum constants are permitted"
I understand this is because strings can only be used with switch in Java 7. Thus I went about installing Java 7 in terminal using some instructions I found online. Afterwards Eclipse wouldn't run at all. I went to switch back to Java 6 and found I was running Java 7 Oracle but had option to change to Java 7 OpenJDK so I did. Eclipse is working again but I still get the same error as before. Why is this? And is there a way to fix it?
For some added info, here's what terminal returns when I type in  "sudo update-alternatives --config java" to switch between versions.
glitch@glitch-Inspiron-1720:~$ sudo update-alternatives --config java
[sudo] password for glitch:
There are 3 choices for the alternative java (providing /usr/bin/java).

  Selection    Path                                           Priority   Status
------------------------------------------------------------
  0            /usr/lib/jvm/java-7-oracle/jre/bin/java         1062      auto mode
  1            /usr/lib/jvm/java-6-openjdk-i386/jre/bin/java   1061      manual mode
* 2            /usr/lib/jvm/java-7-openjdk-i386/jre/bin/java   1051      manual mode
  3            /usr/lib/jvm/java-7-oracle/jre/bin/java         1062      manual mode

Press enter to keep the current choice[*], or type selection number:"

As you can see I'm currently using java-7-openjdk where as before I was using java-7-oracle (which resulted in Eclipse plain out not working) and before that I assume I was using java-6-openjdk (this is what I run Minecraft in after all but who knows).
More specifically I'm using:
glitch@glitch-Inspiron-1720:~$ java -version
java version "1.7.0_55"
OpenJDK Runtime Environment (IcedTea 2.4.7) (7u55-2.4.7-1ubuntu1~0.12.04.2)
OpenJDK Server VM (build 24.51-b03, mixed mode)

I looked at this question: Can't use Java 7 from Eclipse?
I tried following the instructions given therein all the way up to changing Properties > Java Compiler > Compliance Level to 1.7
I found the location of my JVM was /usr/lib/jvm/ but when I put this in for JRE home in Eclipse it gives me this error: "Target is not a JDK Root. Java executable was not found"
I am quite frustrated. Can anyone help? Also, please forgive my ignorance, I am very new at all this.
Answer: Fixed! I uninstalled and reinstalled Java and changed the location of my JVM to /usr/lib/jvm/java-1.7.0-openjdk-i386. The solution was much simpler than I thought. Now I feel very silly.


Help me identify(separate) voices in a piano score

Question:
Can someone please help me separate the two voices in bass clef. The stem direction doesn't help. The time signature is 4/4. When I try to identify voices, the count isn't right for them. Can a note or a chord belong to two voices at the same time? If notes are beamed do they belong to the same voice? If someone could please reference me a legit book on rules about this?
Answer: The problem is that an eighth rest is missing from the "tenor" voice. It should be on beat 3, vertically aligned between the eighth rest in the upper staff and the F octave in the lower staff.
<code>X: 1
T: Question 113539
K: G minor
M: 4/4
L: 1/16
%%score V1 | V2 | V3
V:V1 clef=treble
V:V2 clef=bass middle=d
V:V3 clef=bass middle=d
[V:V1] [dd'][bb']2[dd'] [gg']d'bg z2 [DBd]2 [CBc]2[DBd]2 | [dd'][bb']2[dd'] [gg']d'bg z2 [D^FAd]2 [Bdb]2[Ada]2 |
[V:V2] z2 g[bd'g']- [bd'g']2 G[dg] z2 z [fc'] z[fc']zf | z2 g[be'g']- [be'g']2 E[Be] z2 z [ad'] z[ad']zd |
[V:V3] [G,G]8 [Ff][Ff]-[Ff]2 F3[Ff] | [Ee]8 [Dd][Dd]-[Dd]2 D3[Dd] |
</code>
* The missing ties from beats 3-4 in the lowest part are a software limitation.
The same problem exists in the second bar (i.e., m. 20).

Regarding a note or chord belonging to two voices: yes, that can happen. It is typically indicated by double-stemming the note/chord. See for example: Why does this note have a stem pointing up and another pointing down?

A generally accepted standard text on notating music is Behind Bars, by Elaine Gould. You will find it frequently referenced on this site.
Comment: The image posted by the OP would make Elaine Gould shake her head sadly.  Ideally the stems of a particular voice would be pointed in a single direction only, and the horizontal spacing in the first bar makes it look like the GD fourth in the "tenor" voice and the first F octave in the "bass" voice are simultaneous.
Comment: I'm always amazed by the reluctance of people to use a third staff.  This is so much more clear on three staves than anything that could be done on two.


why can two random variables be added only when they have the same domain?

Question: I am watching lecture 7 in harvard stats 110 and the professor is teaching distribution of addition of two random variables and in a breadth says that random variables can be added only if their domains are same. Which i don't understand completely. Why can i not see by just addition, how $X+Y$ is distributed if $X \sim Bin(n,p)$ and $Y \sim N(\mu,\sigma)$? $X$ and $Y$ can be random variables on completely different sample spaces like $X$ being the number of heads in N coin tosses and $Y$ being excess return on some index
Comment: I believe the posts in our thread about [what the sum of random variables means](https://stats.stackexchange.com/questions/95993) might clear up this issue quickly.
Answer: You misunderstood the meaning of domain, see Wikipedia which have the following figure:

In that figure the domain is X, and Y is the codomain (or range or target space.) For the sum to be defined it is clear that the codomains (of the $X$ and $Y$ in your example) must be compatible, in being (subsets of) some numerical space where addition is defined, no problem in your example. But that is about the codomains.
The domain for a random variable (which really is a function,  see What is meant by a "random variable"?) is a probability space. The probability space in probability theory is, intuitively, the source of randomness. What should the meaning of $X+Y$ as a random variable be if the sources of randomness in $X$ and $Y$ where distinct?  Or simply look at the formal definition of sum of functions which do not make sense if the domains are distinct.
Comment: What should the meaning of X+Y as a random variable be if the sources of randomness in X and  Y were distinct? You sample event A From domain of X.. record X(A) .. you sample event B from domain of Y ... Record Y(B) ... Add X(A) and Y(B).. this is one realization of r.v. X+Y .. it's sample space is Cartesian product of domains of X and Y..
Answer: For me this quora post seems to answer it
A random variable is a way of labeling the outcomes of an experiment with a real number. You can think of it as attaching every outcome with a label, the label being a real number. For instance, if an experiment has two outcomes ω1,ω2, so that the sample space is Ω={ω1,ω2}, we can 'attach' a label to each of the two outcomes. For example, we could label the outcomes with 1,π. This, in an informal sense, is a random variable. It is completely possible to assign one another set of labels, say −7/8,2–√, for ω1,ω2. This will correspond to a second random variable. The sum of above random variables is another pair of labels, with the label being the sum of original labels. Thus a new pair of labels is 1−7/8,π+2–√, which, again in an informal sense, is the sum of two random variables.
To put this in a formal way, a random variable X:Ω→R is a function from the sample space to the set of real numbers. If X1:Ω→R,X2:Ω→R are two random variables, then their sum X1+X2:Ω→R is a function defined by X1+X2(ω):=X1(ω)+X2(ω). The sum of many random variables is defined in a similar manner. Are we done? Well, not yet! In many cases, the random variables are defined on different sample spaces and we want to add them. How do we do that? Since random variables are functions, they must have same domain to be able to add them. Thus we construct a product space Ω:=Ω1×Ω2, and hence every ω∈Ω can be written as ω=(ω1,ω2) for ω1∈Ω1,ω2∈Ω2. We also define X1(ω):=X1(ω1),X2(ω):=X2(ω2). Now we can add the two random variables just like functions as they have the same domain. Similarly, for n random variables we construct an n−fold product ∏1≤i≤nXi and define their sum. This would be become more clear to you once you construct your own random variables and start playing around with them.
Also, i found the link provided in whuber's comment on question very useful
Answer: Simply put, they need to have dimensional homogeneity (https://en.wikipedia.org/wiki/Dimensional_analysis#Dimensional_homogeneity) but the domain doesn't need to be exactly the same.
Imagine one random variable refers to the position and another to time. Obviously, you can't just add up those in any meaningful manner (even if both share the same domain, namely the real numbers). Another example is to consider the result of tossing a coin (head or tails) and add it to the result of rolling a dice (1, 2, 3, 4, 5 or 6), again meaningless. On the other hand, you can legitimately add two random variables even if the domain differs, for example, if you have 2 uniformly distributed variables with non-overlapping domains (i.e, one in [0,1] and the other in [4,5]). In this case, their domains are different but they can be added as long as they have the same units. In summary, to add up 2 random variables the domain doesn't need to be the same, but the add operation must make sense for which it is required dimensional homogeneity.
Hope it helps.
Comment: I think you are likely using the word "domain" in a different sense than intended in the question.  It would therefore help for you to provide a clear definition of your meaning.


Rule-Based and Tree-Based Statistical Models

Question: I have been doing some research and have been trying to find "Rule-Based" and "Tree-Based" (statistical) models that are capable of overcoming the "greedy search algorithm" used within standard decision trees (e.g. CART, C5, ID3, CHAID).
Just to summarize: The "Greedy Search Algorithm" refers to selecting "locally optimal decisions" - this has certain benefits in terms of computing cost and time, but will very likely lead to missing "globally optimal decisions". Here is an example of (the disadvantage of) greedy search:

The above picture shows a task where an algorithm is required to find the largest number ("99") in this tree structure. The "greedy algorithm" will always pick the larger number at every possible decision : In the middle picture, we see that the greedy algorithm picks "12" instead of "3" (because 12 > 3), and then picks "6" instead of "5" (because 6 > 5) - thus, the "greedy algorithm" concludes that "6" is the largest number within this tree structure. However, we can see that the largest number in this tree structure is actually "99" - but the "greedy algorithm" misses the actual largest number all together.
On the statistical modelling side, common decision tree algorithms (e.g. CART, C5, ID3, CHAID, conditional inference tree, etc.) all use the "greedy algorithm" when constructing the decision tree (e.g. choosing tree splits that optimize Entropy/Gini on the local level) - this almost surely results in any of these decision trees being sup-optimal, as a "better decision tree" (e.g. more accurate) is likely to exist, but was never considered due to greedy search (although I have not seen an exact mathematical proof for this statement). For smaller datasets with few variables and less complicated patterns (e.g. iris flower dataset), the use of the "greedy search" algorithm has not been (anecdotally) reported to significantly hinder the performance of the final decision tree - however, for larger and more complicated datasets, the "greedy search" algorithm has been suspected to produce suboptimal decision trees.
With the advent of newer machine learning and statistical models, I have been trying to research newer tree-based and rule-based models that do not suffer as much from "greedy search" : in general, "tree based" and "rule based"  this is particularly useful when you would like the final statistical model be "easily explainable and interpretable" (while sacrificing predictive power). So far, here is the list of models I have come across:

Evolutionary Decision Trees: Decision Trees can be constructed using genetic/evolutionary algorithms which might result in a more comprehensive search (e.g. https://cran.r-project.org/web/packages/evtree/index.html)

CORELS: Certifiably Optimal Rules List (https://cran.r-project.org/web/packages/corels/index.html)

PRE: Prediction Ensemble Rules - said to perform at times comparable to a random forest (e.g. https://www.jstatsoft.org/article/view/v092i12)

Bayesian Rules : https://rdrr.io/cran/sbrl/

Classification Based Association Rules: https://cran.r-project.org/web/packages/arulesCBA/arulesCBA.pdf

NB Rule Mining : https://cran.r-project.org/web/packages/arulesNBMiner/index.html

Reinforcement Learning Trees: A new variable selection method is used during the construction of decision trees to "learn" important and unimportant variables within the dataset (e.g. https://cran.r-project.org/web/packages/RLT/index.html - note: I do not think it is possible to extract decision rules from these trees?)

Fuzzy Rule Mining: https://cran.r-project.org/web/packages/frbs/index.html

Evolutionary Fuzzy Rule Mining: https://cran.r-project.org/web/packages/SDEFSR/index.html, https://cran.r-project.org/web/packages/SDEFSR/vignettes/SDEFSRpackage.pdf

Evolutionary Rules: https://cran.r-project.org/web/packages/fugeR/index.html

KEEL Algorithm: https://www.researchgate.net/publication/318646414_Mining_association_rules_in_R_using_the_package_RKEEL/link/59ba64a0458515bb9c4c8b24/download

Subgroup Analysis Algorithm:** https://cran.r-project.org/web/packages/rsubgroup/rsubgroup.pdf

Extreme Rule Fit: https://cran.r-project.org/web/packages/xrf/index.html

Quantitative Rule Mining: https://cran.r-project.org/web/packages/qCBA/index.html

Recursive Rule Mining: https://cran.r-project.org/web/packages/RecAssoRules/index.html

Patient Rule Induction (PRIM): https://cran.r-project.org/web/packages/prim/index.html

This was a list of rule-based and tree-based models I was able to find, with available software implementations in the R programming language.
Question: Has anyone used any of these models before? Are there any standard rule-based and tree-based models that are currently being used for overcoming the "Greedy Search" algorithm within common decision trees? I am specifically looking for modern statistical models that provide "explainable and interpretable results" - and not "black box" models like random forest and gradient boosting. In my case, the "model rules" are paramount.
Does anyone have any suggestions?
Thanks
References:

https://en.wikipedia.org/wiki/Greedy_algorithm
https://cran.r-project.org/web/packages/KODAMA/vignettes/KODAMA.pdf
https://arxiv.org/abs/1904.12847 (Globally Optimal Trees - no R package available)
https://link.springer.com/article/10.1007/s10994-017-5633-9 (Optimal Classification Trees - no R package available)
Multivariate Decision Trees: https://cran.r-project.org/web/packages/ROP/ROP.pdf
Multivariate Decision Trees for Survival Data: https://cran.r-project.org/web/packages/MST/index.html
Comment: The [`step` function in R](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/step.html) is not greedy. It is a method to select models based on AIC. It looks like the greedy stepwise model selection (repeatedly adding parameters to the model). But, the standard option has 'both' directions and allows the removal of features as well.... So it is an example of a non-greedy algorithm and many people use it. .... Does this answer your question?
Comment: @ Sextus Empiricus : Thank you for your reply! I will look more into this - I am interested in finding out about "rule based" and "tree based" statistical models, that specifically "output a set of interpretable decision rules". I think the "step function" that you have cited is more for model comparison? I will keep reading about this - thank you for your reply!
Answer: Rule-based classifier cannot by greedy by definition, IMHO, since they involve only 1 "node". Hence, any rule-based classifier should fulfil what you need. Then, it depends what are your data/task. For classification I would suggest arulesCBA as the first choice to try:
https://cran.r-project.org/web/packages/arulesCBA/index.html
Personally, I have very good experience with Sirus (2class classification but very stable results, no problem with minority-class prediction):
https://cran.r-project.org/web/packages/sirus/index.html
Best!
Comment: @ Zdenek: Thank you! I will check this out!


Why does the Boltzmann equation deal with single-particle phase space density?

Question: Why does the Boltzmann equation deal with single-particle phase space density $\rho_{1}(\textbf{r}_1,\textbf{p}_1,t)$ rather than the N-particle phase space density $\rho(\{\textbf{r}_i,\textbf{p}_i,t\})$? How'll deal with Boltzmann equation for a system of $N$ interacting particles?
Answer: That's the whole point. Rather than dealing with the complicated N-particle distribution we try to find an equation of motion for the 1-body distribution
$$
f_1(r_1,p_1,t)=\int d\Gamma_2\ldots d\Gamma_n\, f_N(r_1,p_1,r_2,p_2,\ldots).
$$
Boltzmann brilliantly guessed an equation for $f_1$, and standard textbooks try to at least outline a proof that starts from the Liouville (classical) or von-Neumann (quantum) equation, but obviously there are some subtleties (how do you get the non-reversible Boltzmann equation from reversible microscopic dynamics), and much ink has been spilled discussing these subtleties.


Bike won't shift to 6 or 7 gear because shifter is too stiff

Question: On my bike I have 7 gears at the back and 1,2,3,4,5 are normal and shift fine but some reason I can't shift to 6 the lever or switch won't go and feels stiff I'm unsure what it is I thought it might be a tight cable somewhere or the actual shifter.
Comment: First check the limit screws on the derailer.  Next check that the shift lever isn't already hitting its high limit.
Answer: Check the limit screws on the rear derailleur. Without knowing exactly what kind of derailleur you have, it's difficult to be more specific, but these are probably two small screws coming out the back; one limits the derailleur's inside travel, the other its outside. It may be that one is tightened too much.
There's also (usually) a barrel adjuster, either where the cable enters the derailleur, or where it exits the shift lever; if this is backed out too far, it will tighten the cable, preventing you from shifting all the way through the gears, although it's hard to imagine it could block out two gears.
Answer: Sounds like you are having trouble shifting to the two largest sprockets (lowest gear ratios) because the downshift lever needs to pull cable and can be jammed, whereas the upshift lever releases it.
The jam could be in the shift lever, the cable run to the derailleur, or the derailleur itself. Here's a procedure to track it down:

Disconnect the shift cable from the derailleur
With the back wheel off the ground, turn the cranks by hand and manually push the derailleur inwards by hand (being careful not to catch your fingers in the chain). If the derailleur wont shift to the largest sprockets, the problem is there. Check for any debris in the parallelogram. The issue could also be with the limit adjustments.
Put some tension on the shift cable and try to click up and down through the gear positions. If the shifter will not go to the lowest gears the cable may be jamming or shifter could have debris in it.
Pull the housing back off the cable where it enters the shifter and introduce a little slack, try to click up and down through the gear positions again. If the shifter still wont go to the lowest gear positions the problem is in the shifter.

If the problem is in the cable you can try tracking where the jam is be inspecting the cable run. Sometimes you just need to replace the cable and housing - they are technically wear itms and not very expensive.
A jammed shifter if a bit trickier to deal with. There are some existing questions and answers on this site that deal with that.
Finally, you should go through a systematic rear derailleur setup procedure.  This will sort the limit adjustments out if that was the problem.

Bike won’t shift to 6 or 7 gear because shifter is too stiff


How do I beat the Gaming in the 3rd house

Question: In candy box 2, how do I win the gaming in the 3rd house with the key that I just unlocked from the squirrel. I have tried to buy all the swords and shields to defeat the monsters but it just doesn't make sense!
Answer: I assume that you are talking about the Super RPG game playable on the gaming machine (the one that costs 10 candies to play)
This game has no ending as there is no floor limit


Why does a gas inside a closed container experience atmosperic pressure when the gas itself is not in contact with the atmosphere?

Question: I know this is a very basic (and probably stupid) question, but I have been confused about this for a long time.
Answer: Both Ignacio and Anna's answers are correct, but let me see if I can expand on them a little.
You ask:

Why does a gas inside a closed container experience atmosperic pressure
  when the gas itself is not in contact with the atmosphere?

but actually a gas inside a closed container doesn't necessarily experience atmospheric pressure. If you've ever shaken a bottle of pop then opened it you'll know that the gas pressure inside is a lot higher than atmospheric pressure. This is an example where the pressure inside the closed container is higher than atmospheric pressure, but it can be lower as well.
What happens to the gas in a container depends on how flexible the container is. If I take a glass bottle and pump half the air out, the gas inside will stay at half atmospheric pressure. That's because the glass walls of the bottle are rigid and they take some of the pressure.
On the other hand if I fill a plastic bag with gas then pump some out, the pressure inside the bag stays at atmospheric pressure. That's because the plastic bag is flexible. The atmosphere presses on the bag and the bag transmits the pressure to the gas inside it.
Comment: Just expanding on the question . The concept of the atmospheric pressure being transmitted through the bottle to the air inside  seems correct. But If we close a bottle ( anyhow air tight) at sea level  and take it to Mount Everest ( the material of the bottle is very strong ) , then the atmospheric pressure decreases significantly but the total pressure in the bottle is the same as that at sea level ( this is the principle of a manometer ). So if the external pressure is reduced how can the pressure inside the bottle remain the same if we explain this by transmission of pressur
Answer: Unless the container is perfectly rigid, the atmosphere pressing on the container causes the container to press on the contents. If the contents don't press back, the container will collapse under atmospheric pressure.
Comment: So it's Newton's third law?
Comment: It's more pressure equalization, actually. Newton's laws govern motion, even though the situations are analogous.
Comment: Well pressure is just force over area so if you're equalizing pressure on both sides of the same area it's the same as equalizing 2 forces right?
Answer: How do you define "contact"?
For gases contact does not mean "touching".
Small leaks, as small as molecular sizes of the air molecules, will allow leaking and equalization of pressure with the atmospheric pressure.
It needs good seals to be able to keep a vacuum, i.e. a container where no air exists, but it can be done. If the seals are not good, then pressure equalization takes place.
Comment: Yes, the number will change, according to the directionof  the pressure difference. Gas moves from high pressure to low pressure. Think of a tiny hole in a balloon. The molecules hitting the inside balloon surface (pressure comes from this kinetic energy of molecules http://www.silcom.com/~aludwig/Physics/Main/Molecular_model.html#Temperature ) , when they find the hole, will rush through because the air pressure is lower and cannot push them back. The balloon will deflate so that all the molecules will have the average kinetic energy of air. For strong walls with a leak, the same logic goes.
Comment: What is the mechanism of this pressure equalisation? Are you saying that all the gas molecules in the container will come at atmosphere pressure  because of small influx of gas molecules at atmospheric pressure.Gases moving from high pressure to low pressure until equilibrium is set
Comment: Can the number of gas molecules change in the container because of this process
Answer: Imagine the gas is sealed inside a piston, like this:

The piston head is free to move in the sleeve, which changes the volume of the gas.  We know from experience that the piston head will rapidly find an equilibrium position where it doesn't move any more.  If the piston has stopped moving then that means it's not accelerating, and if it's not accelerating that means that the forces acting on it must sum to zero.
Both the gas inside the piston and the atmosphere outside it exert a force on the piston. The magnitude of these forces is equal to the pressure of the gas (or of the atmosphere), times the area upon which it acts. The two forces act in opposite directions, and the piston has the same area on each side, which means that the two pressures have to be equal. This is the reason that gases inside containers reach the same pressure as the air outside - the volume of the gas will adjust until the forces acting on the container are balanced.
Of course, if there other forces than pressure acting on the container wall then the pressures will not be equal. This is why it's possible to create a (partial) vacuum inside a rigid container. It's also why the air inside an inflated balloon has a higher pressure than the air outside it - the balloon's skin is subject to a tension force as well as the two pressure forces.
Answer: You should realize that momentum is a physical thing--- it is a conserved quantity like energy. Momentum flows from place to place, like electric charge, but because it is a vector quantity, the flow is harder to imagine. If you look only at the x-component of momentum, this flow is easier to visualize.
So, for example, if you push on a block, the momentum is flowing through your hand to the block and builds up on the block, making it go faster. If there is friction, the momentum leaks back through the ground to the earth, and the friction between your shoes and the ground completes the x-momentum circuit. When you have a mass sitting on a table, the y-momentum comes from the Earth to the mass, and flows down through the table to the Earth.
Pressure is when the x-momentum is flowing in the (positive) x-direction only, the y-momentum is flowing in the (positive) y-direction only, and likewise for the z-momentum. This is the intuitive idea, since if you put two y-z plates at x=0 and x=a, you need to absorb as much x-momentum as hits the plate on the left and leaves the plate on the right, which means you need to hold the plates apart with a force proportional to their area, and the proportionality constant is equal to the momentum flow rate.
When you rotate the system, you rotate the x,y,z components, but you also rotate the direction of the flow, and the two rotations together give you a tensor transformation law. The pressure is the only rotationally invariant mometum flow possible, and in fluids, rotational invariance is still a correct symmetry, so they can only have a pressure when they are in equilibrium.
When you have gas in a container, the three flows of momentum are passing right through the walls of the container through the gas and out the other side. So the gas has the same momentum-current inside as out, the same pressure inside as out, since the momentum is passing right through the walls. If you want the gas to be at lower pressure, you need to deflect the momentum currents around the gas on the interior, so you need to make a stiff box that pushes the momentum current around the interior. In this case, the box has to have large shear stresses (deflections of x-momentum in the y and z directions) to get the momentum to the other side without going through the middle.
This point of view is the modern stress-tensor view of Newton's laws, and it makes the answer to this question completely obvious, but it isn't emphasized in elementary books, probably because tensors are considered advanced. A tensor is just a vector of vectors, a vector whose x component, y component, and z component is a vector, and there is no reason to delay learning about it.
Answer: Particles push down on the container and it would collapse, also gravity would have an effect on it.
Comment: Hi Jakob, can you please elaborate on your answer.  Right now it isn't detail enough to really be worth anything.


Is it possible to move from an old mac to a new mac only selected applications and documents?

Question: I would like to move from an old mac book pro to a new one only selected applications and documents. I set my old mac using an older one mac so I have very old applications that I should uninstall. I run migration assistant but with this program is not possible to select the application I want to transfer. Is there another way to do this? Both mac (old and new) run Mojave 10.14.6.
Answer: You can of course select and copy any documents you want: though you will have to select them manually.
For the applications, it will largely depend on where they came from. Apps from the Mac App Store are linked to your Apple ID, and can be re-downloaded from the App Store onto the new Mac.
Third-party software may work just by copying the application: though some apps may need an installer that adds additional support files. Apps may need serial numbers or other protection re-applied.
whether they are App Store downloads, or other software that requires an installer. Some apps can be copied


D2L Per user Content Visibility

Question: Can we unlock or unhide content for particular users or does that apply to all students in a D2L course?
Answer: Hidden applies to all users in roles that do not have a "View Content that is Not Released" permission. The system does not manage hidden on a per user basis.
Not sure your specific application, but, because of this property of the system there are apps that apparently use a couple roles to control visibility of items and then swap between the roles dyanamically with the enrollment api. This is used for items like quizzes that are shown or hidden with role permissions. (Note: This does NOT work for restrictions aka release conditions if you are looking to "withdraw" visibility as you can't "unmeet" a Desire2Learn Content Restriction. But you could use this to progressively reveal content; it just might not be particularly graceful code).
Enrollments often have special meaning for systems, so you will want to check with your operations group to see if changing enrollments works with their plans/policies.

D2L Per user Content Visibility


Paper backup from Armory that requires a password?

Question: I'd like to make a paper backup of my Armory wallet that will still require a password to recover. Right now it seems that the paper backup is not encrypted.
Comment: [This is what the core armory dev had to say about encrypted wallet backup.](https://bitcointalk.org/index.php?topic=140103.msg1509823#msg1509823)
Answer: As the paper backup consists of two simple string you can use any encryption scheme you'd like to implement this.
This can be as simple as manually applying rot13-like encryption, to one-time-pads. Just make sure you keep the ciphertext short in order to still be able to print and, more importantly, type it in eventually.
Answer: As Nick mentioned, I'm not a fan of encrypted paper backups.  Instead, I added "Fragmented Backups" to the new version (0.90-beta, posted a few days ago on the website), to give the user flexibility in balancing physical security & redundancy without the high risk of permanent coin loss.  After all, 95% of the emails we get are users who forgot their password.  Many of them didn't even realize that their paper backup protected them against that.  As far as I'm concerned, that's the number one reason to make it.
Of course, doing it this way does reduce physical security, but that's far from the biggest threat to most users. If you are concerned about physical security, I recommend you explore the fragmented backup system in the new releases, which addresses these concerns in a robust and "responsible" way.


How is white light produced from only Red, Blue and Green?

Question: As far as I have read, visible light refers to the part of the EMR spectrum that our eyes are sensitive to and the presence of all the colours of visible light at a single spot forms white light. Why, then, are digital screens able to create white just from a combination of Red, Blue and Green light waves?
Comment: This is really a biology question. The colour you *perceive* is a result of the degree to which the light cones in your eyes are excited, see [this image](https://qph.fs.quoracdn.net/main-qimg-e9179751b489d7264570ba2c6e37a755). Red, green, and blue light are collectively able to stimulate all three light cones and thus give rise to a white appearance.
Answer: White sunlight is a mixture of a huge range of frequencies (i.e. colours), of which most - but not all - are in the range that are visible to the eye. White is not one single colour, it is a mix of many colours.
The eye has 3 different colour receptors (cone cells). Each type is most sensitive to a certain colour range. Their peak wavelengths are in the red, green and blue regions of the visual spectrum, respectively. The brain then mixes the signals from all three types, to produce the sensation of a "colour".
Because our eyes evolved to see in sunlight, if the red, blue and green levels of the perceived spectrum are approximately those of sunlight, we see that colour as being the same as that of sunlight - something we call "white". Again, white is a mix of colours.
There are other perceived colours that do not appear in the spectrum. A common example is brown. Like white, brown is a mixture of pure colours. No part of the electromagnetic spectrum is brown, but our brain interprets certain mixtures of wavelengths that way. Tree trunks reflect only those parts of the sunlight that make the brain think "brown".
In the same way, if something reflects all wavelengths of sunlight, the brain thinks "white". In artificial lighting, if we mix the appropriate amounts of red, blue and green light, all three types of cone cells get the right stimulation to make the brain perceive it like sunlight, i.e. white. If the mixture is not exactly right, the brain will see it as some other shade, like pink or grey.
In fact, different "white" lights have different colour shades. It is said they have a different "colour temperature". The temperature of the sun is close to 6000K and light of that colour temperature looks like sunlight. Many white LEDs have colour temperatures of around 9000K, and their light will have a bluish tinge. Incandescents globes are closer to 4000K and look reddish - but we call all of these lightsources "white".
Answer: White is not a color. By that, I mean there is not one wavelength of light corresponding to what we call "white color". Instead, white light is what we comprehend as the combination of many colors, namely all the colors of visible spectrum. On the other hand, red, green and blue are well defined colors meaning that they are monochromatic light, i.e. they have one specific wavelength. From what I understand, the RGB are at the proper positions in the spectrum and have enough deviation to neighboring wavelengths so that the resulting combination is approximately white light.
Answer: The eye typically has a number of different "receivers" (not a biologist) that respond differently the different wavelengths, by transmitting for example both red and green colours, the eye measures both and adds them together in the brain, resulting in another colour.
I hope this answered your question.


What glue should I use for permanent LEGO construction?

Question: The incredible precision of LEGO parts makes them attractive for building precise jigs, but the fact that they can come apart fairly easily isn't so helpful for this application. Can anyone recommend methods and materials for gluing LEGO bricks together to create permanent assemblies?
I'd prefer to avoid thick adhesives like epoxy or hot melt glue, as I suspect that those might make it difficult to get the bricks to snap together completely. I think most bricks are made of ABS plastic, so I'd guess that a solvent like acetone might work to weld them together, but I've never tried it. Does anyone have experience gluing bricks together?
Comment: Glued lego? my heart breaks.
Comment: @Kramii I hear you! When LEGO bricks are used as a toy, the ability to take them apart and turn them into something else is an essential part of the experience. When used as a tool, however, the fact that they can come apart pretty easily can be a liability. It's not easy to think about bricks as consumable instead of reusable, but when you do there's a whole other world of things you can do with them!
Answer: The LEGO Group have recently started using solvents to "weld" elements together (notably the Minifigure legs to the magnet blocks), which are fairly heavily controlled in pure forms in most countries under drug legislation.

I have discovered that LEGO is not using glue at all, but a solvent, that actually loosens the surface of the ABS plastic and allows the molecules to combine. Once the solvent evaporates, it leaves behind a cleanly fused surface with no residue at all.
Reading further on the subject, I found that LEGO has been using two types of solvents. One is called MEK (methyl-ethyl-ketone) and at some point they switched to GBL (gamma-butyrolactone). I'm no chemist, so I had no idea what these are, but I read that both of them are water soluble at certain temperatures. So, I thought to try loosening the seal between the minifig and the magnet by hot water.

However, as the opaque LEGO bricks are made from a styrene based plastic (ABS), most "Plastic Cement" or "Polystyrene Cement" glues should work to fix your parts together permanently (as these typically contain the same solvents as TLG use, i.e. MEK/Butanone). As with most other plastic gluing projects, care should be taken around transparent elements, as well as ensuring you don't use too much and have it leak over the exterior of your model.
Comment: This was a nice reference for me-http://www.mp3car.com/fabrication/93247-best-adhesive-for-bonding-abs-to-abs.html
Answer: To summarize from the thread that Major Stackings linked, sounds like Acetone is the best general solution, as it melts the pieces together until they are permanently bonded together as one bit of plastic.

You only need acetone, no need for other products or ABS chips.
  Just brush acetone on both pieces, join them and wait 5 minutes.
  You will find that your two pieces now are literally one piece.
  There is not anything stronger for abs plastic.

For the record grocery store nail polish remover is Acetone, at about 70% concentration (see material safety data sheet citation).

Cutex Regular Nail Polish Remover
  Product code: PN 679 (VIJ)
  Date Prepared: January 14, 2000
Hazardous Components: Acetone, Percent content: 70.0
  CAS number 67-64-1

You can get 100% concetrated acetone at the hardware store, or at beauty supply stores.

If you don't mind a little extra work, using melted ABS is probably your best bet, you just need to chop up some scrap ABS into shavings (I used a big drill bit on some ABS and it made shavings very quickly), and then put them in some acetone. Play with the mixture until it comes out to your desired consistency. Make it in a squirt bottle, use it just like epoxy or whatever. This way, the entire work piece is made of ABS plastic so you shouldn't have problems with thermal expansion leading to cracks or separation like you can have with other materials.

If there isn't a tight fit though, Acetone alone might not be enough, and you can either melt a little plastic in Acetone solution to generate filler, or try other plastic-friendly glues that can both fit gaps and bond:

Right, assuming the parts that need to be glued are already a nice snug fit. Plastic welder and/or ABS sludge come in handy when you need to fill a gap though, as is so often the case in carPC-related fabrication.

I'll be experimenting with a few of these soon and will update with my results. Science!
Comment: Science for the win!
Comment: Jeff, in your experiments, don't forget to test out the [other plastics](http://bricks.stackexchange.com/a/197/56) that are used in the manufacture of LEGO bricks - especially the transparent elements ;)
Comment: Not sure how Jef's experiment(s) turned out, but my first attempt using ordinary nail polish remover was not a success. I did see the plastic disolve, with the cloth with acetone turning green (the colour of the bricks, 614328 and 6353424), but after holding them together for 5 minutes, they were not solidly joined. I did notivce the knobs on the lower brick had deformed significantly. Now trying again with acetone applied on both side.
Answer: My Son and I were at the Legoland Discovery Center in Grapevine, TX yesterday.  We spoke with a LEGO® Certified Master Builder.  We asked him and he says that LEGO® uses MEK to permanently adhere their large Lego sets together (lifesize etc).  We just finished putting together the Volkswagen T1 Camper Van.  It is notorious for the roof coming apart, as is the usual lego problem of the walls around doors often come apart.  Well, the MEK we got from Lowes today TOTALLY fixed it.  In less than 3 minutes a part was VERY secure and won't come apart.  You have to work fast as it is immediately affecting the plastic.  Honestly, at less than a minute it won't come apart, and if you don't seat them securely, they will fuse out of place, so be careful.  It didn't take more than a VERY light glaze with a paintbrush.  I am SOLD and wish we had this years ago!
Comment: While MEK is indeed what LEGOland parks use, keep in mind that it does indeed fuse bricks together (don't even think about disassembling the model, ever); and more importantly that its fumes are dangerous.
Answer: Recently had to glue a lot of LEGO together for work.

Acetone was too time consuming and did not offer a solid bond.
Cyanoacrylate-based hobby glues with thick viscosity seemed the most effective. The only problem was, when immersed in water the clear LEGO windows fogged up. (No solution to that so far.) Zap a Gap hobby glue offered best results.
ABS plumbing glue worked but was difficult to apply. And if too much was applied, plastic disfigured from the inside out.
Cheap hobby glues all failed for strength, and many disfigured the pieces and were often not thick enough to offer piece manipulation before gluing your hands to it or running down your arm.
Hot melt glue was messy beyond all hell. But worked better than silicone for sealing roofs.
Selley's advanced quick grip (water based) worked, was strong but failed under water. Was also far too time consuming and messy.
Also tried Parfix contact glue. Disfigured the pieces.
Epoxy resin in self-mixing and hand-mixing varieties offered good strength, but was too costly for the job.

That's all I have tested so far, going back to Bunnings and Auto pro.
Last one I tried was a plastic welding glue for sheet plastic and acrylics. Melted pieces from the inside out. But once set, it was indestructible.
Answer: MEK is the way to go - it's what the Masterbuilders at the LEGOLAND parks use.
I once brought a miniland sized model from London to the US in my main suitcase that had been glued with MEK and the model was fully intact when I got to the other end!
As others have said, it is VERY nasty when breathed in. Do not even think about using it in confined spaces without a proper extraction system (seriously) and if you get any on your skin wash it off immediately. If you ever spill a bottle of it inside, evacuate the building immediately - believe me, even the LEGOLAND masterbuilders do this if they ever spill it.
Cheapest way to get MEK I have found is go to home depot or somewhere similar and buy some PVC pipe glue - that is MEK (and will say it on the 'ingredients' label).
When gluing - you only need a little brushed onto the brick - easiest to use a syringe of some similar device to put the glue between the studs - then apply the second brick. Wait a few minutes, and it's pretty well welded together.
If gluing a large amount of bricks, do one row at a time and wait a few minutes between rows. Don't rush it or apply too much glue as the bricks will melt.
Answer: I use a small bottle of Gorilla super glue for my lego parts. It only squirts a tiny amount to be sure super glue doesn't get all over your parts, and also dries at a mid-range pace. I use it a lot to glue my Tiny Tactical parts to the guns after they come in the mail (which are insanely small parts) and the glue work like a charm.
Answer: We tried all kinds. Solvents just didn't cut it and only made the bricks stick tighter.  The best we found is actually found at the hardware store in the plumbing aisle.
Oatey all purpose cement is the best we found so far. It contains all the above solvents including MEK (which by the way is either a carcinogen or causes brain damage when absorbed into the body excessively I can't recall)  which works well. It is designed specifically for gluing ABS.
We apply it with a small craft paint brush and so far the bond is permanent and allows for plenty of working time without fear of gluing YOURSELF to the bricks.
And it cleans up easily with 100% acetone (hardware store stuf...not nail polish remover as its not concentrated enough).
Answer: So I've been referring to this post for a long time and I figured it is time to put in my experiences. One thing that many answers don't talk about is that different glues are good for different purposes so my input will revolve around that.
A little background. I've been building Lego for multiple decades though only recently started using glue as I've started making art and design for other people through my side business and almost unanimously they want something permanent. I make small delicate designs (I am being intentionally vague here since I don't want to look like I am advertising), mosaics, and large company logos.
The mosaics are made by taking the large grey baseplate and putting a single layer of plates on it (studs out). For this application I use 100% pure acetone. I take a small brush, dip it in the acetone and brush it on a small section of the baseplate and put the mosaic plates on before it dries. Stays together great and if you don't use too much it won't bleed out and mar the look of the mosaic.
For the logos and the small designs, which are built studs up (showing a smooth surface - like building a brick wall), acetone is terrible. Since it melts ABS plastic and is not viscous, it runs along the edges of the bricks creating smudges that don't come out. The end result looks bad especially in those areas where there is a connection between 2 contrasting color bricks. I also tried hobby glue (Testor's Cement Glue) and the results were not great but for different reasons. This glue is very viscous but what happens is when you apply it, it trails thin strands of glue that you need to clean up before it dries. When you squeeze the bricks together (a very tight fit), the glue squirts out and if you wipe it away it mars the glossy surface of the brick. That and that stuff smells so bad it makes you sick. What I have settled on is what Jay mentioned above: Zap-A-Gap. It is viscous enough to not run, does not thin out to strands, doesn't smell nearly as bad as the other glues, and dries really, really strong. I put on a small amount on the back of the brick so that the front surface looks untouched. I just finished a 30" square logo with a Lego frame and I can pick up the piece from its frame without any give. Still looking for a better solution, but Zap-A-Gap is the best for this.
Sorry for the long post, hope this helps!
Answer: MEK is significantly more aggressive than acetone.  It shouldn't be used in a poorly ventilated area over a prolonged period.
Any of these suggestions should work, but choose carefully according to your working conditions.
Answer: I use Kragle for putting together the Lego kits, but not any of the removeable pieces or the lego figures. I use a medium viscosity kind of Cyanoacrylate hobby glue. Just have to be careful to not get it on your fingers and your eyes.
Answer: I've had some good luck using the Gel Super Glue.  It's really controlled, and doesn't dry to fast.
Answer: Krazy Glue works but I would never glue my lego together unless it was minifigures to keep them good
:)
Comment: Not the Kragle! ;)
Answer: I wonder if E6000 (available at any craft store) would work. They use it a lot in very expensive reborn dolls to indefinitely secure the eyes, etc..


Inductor made out of super conductors

Question: I have been thinking about an inductor made out of superconductors, would it work? How would it affect the total inductance compared to a normal inductor? Would it be possible to calculate such a device with a formula? (I'm not an engineer yet, I'm a student so be considerate of that)
Comment: You're a student, so before asking I would expect you to have studied the basics. Like what makes an inductor an inductor? What is the fundamental difference between a conductor and a superconductor? **Anything** can be calculated with a formula provided you have the formula or can derive it and you have accurate enough input parameters for the formula. Formulas just a tool to **describe things** it is not like there's a formula or there isn't.
Comment: One of the biggest inductors I've come across was the superconducting magnet to an MRI machine. That had timescales of minutes, when you tried to change the current through it by putting a voltage across the terminals.
Comment: If the wire is what is super conducting, you remove the resistive loss, however capacitance and inductance still exists to the same formulas
Comment: ... and inductance is unchanged. But removing the resistance can be a biggie.
Answer: I worked with a rather large superconducting inductor in my early career, the magnet for an MRI scanner. It had a roughly 1m bore, was about 3m outside diameter, and about 4m long, though admittedly most of that was insulation and liquid N2 and He.
A critical part of using it was to 'ramp the current', when you got to see at first hand and at the sort of timescales only usually associated with capacitors, how inductance behaves.
The magnet was normally short-circuited internally, with a superconducting switch, which allowed the current to circulate indefinitely. A probe was put in, to make contacts on either side of the switch, and an external power supply then set to match the current running in the magnet. Then the exciting bit, the superconducting switch was heated to turn it resistive. Once the magnet current was running through the power supply, we could apply a voltage, to slew the magnet current, as dI/dt = V/L. If I recall correctly (it was a long time ago), roughly 75 V applied gave us a slew rate of less than 1 Amp per second for that particular magnet. Estimate the inductance from that. This was a 'low field' 0.15T magnet, present ones are more than 10 times the field strength.
The only difference between superconducting wires and normal resistive wires to make an inductor is whether they have any loss.
Answer:
how would it affect the total inductance compared to a normal
  inductor?

Any formula or rule for inductance does not involve the conductivity of the material that might make the wire good for passing a current with low loss. Inductance is more like a measure of area and "good" areas (those that yield higher values of inductance) are more rounded. "Bad" areas are more like long elongated loops having a high ratio of length to breadth. When you consider a the wider 3D model inductance becomes more like a measure of volume.
EM waves
Consider an electromagnetic wave - it is composed of H field and E field (the physics guys might argue that it's something else). The H-field is measured in amps per metre and the E field is measured in volts per metre and if we dig down it's more like volt-metres per metre-squared (which becomes volts per metre) and similarly for inductors.
Then there is the ether (that thing that EM waves travel through from the sun or stars to our eyes). That has two parts namely \$\mu_0\$ and \$\epsilon_0\$ and they are measured in henries per metre and farads per metre.
They define the speed of light as in: -
$$c = \dfrac{1}{\sqrt{\mu_0\epsilon_0}}$$
Last time I checked the ether didn't use any form of current conducting material.
Comment: Would you rather me call it free-space?
Comment: The ether is not a thing.
Comment: Units was a bad choice.
Comment: Is the permeability of free space a thing? Is dark energy a thing? Were you being rhetoric @user110971? Do we really understand stuff enough to make a limited guess at what it is?
Comment: What I meant is that the ether theories, i.e. a medium necessary for the propagation of EM waves, have all been discredited. The permeability of free space is a relativistic effect of the electrostatic force. So EM waves in vacuum do not travel in something.
Comment: Yes. Also, the permittivity and permeability of free space are constants of nature. They are not units. The units are H/m and F/m. P.S. physicists have no problem with the H field and the E field.
Comment: Why are you repeating (H/m and F/m) what I put in my answer and yes, last time I checked, physicists tend to have trouble with breaking apart an EM wave and regard it as a single entity @user110971
Comment: \$\mu_0\$ is a constant while H/m is a unit. You've written "That has two units namely \$\mu_0\$ and \$\varepsilon_0\$ and there are measured in..." [sic]. As for the physicists, although the EM wave is a single entity, you can break it into the E field and the H field; however, the fields are not independent of each other. I don't think the above is in any way controversial.
Answer: It's already done. I guess you have seen a levitating magnet experiment video where a magnet floats in the air above a piece of superconductor. The superconductor has virtually zero resistance so the current induced by the magnet can stay stable a long time. The eddy current flows in a 1 turn shorted inductor.
Some experiments surely are done to get strong electromagnets which do not generate heat, but the cooling needed for superconductivity still costs more than achieved energy savings, so the effect is not in common use, it's used only where it's really needed. There's material dependent upper limit how strong fields are possible because too strong magnetic field removes the superconductivity, say the physicists.
The lack of resistance only removes one loss mechanism but there's no effect to the inductance. Or actually there is some effect. The skin effect becomes stronger, so there's no inductance caused by the interior of the conductor.

Inductor made out of super conductors


Why was the Star Destroyer flying over Tatooine in A New Hope?

Question: I know it was chasing the Tantive IV, but had it already been there before the Tantive IV arrived or did it chase the Tantive IV to Tatooine? Did it have something to do with Vader ordering the execution of Owen and Beru Lars? Does anyone think that this question will be answered in Rogue One?
Comment: @Politank-Z - The answers to that question doesn't address the question of whether they were chased there, or simply found a Star Destroyer in orbit when they turned up.
Comment: Vader ordered the execution of Beru and Lars because he (or his troopers) tracked the droids to that farm after interrogating - and killing - the Jawas.  That's related to the Tantive IV only in the sense that the droids originally escaped from that ship.
Comment: This may be answered in Rogue One I think.
Comment: Possibly just for [gunboat diplomacy.](https://en.wikipedia.org/wiki/Gunboat_diplomacy) I can see the Empire keeping a star destroyer on semi-permanent station around Tatooine as a gentle reminder to the Huts where the real power lies.
Comment: Sagierian - technically the star Destroyer was not flying over Tatooine it was space travelling by Tatooine.  People often say we went from Kitty Hawk to the first moon landing in 66 years.  Bu there is really no connection between the first airplane and space travel.   Actually we went from Robert Goddard's launch of the first liquid fueled rocket on March 16, 1926 to the first moon landing in 43 years.  Since Goddard was interested in ultimately achieving space flight - and was ridiculed for it - his first rocket launch can be considered the beginning of space travel experimentation.
Answer: The Star Destroyer was evidently able to track them from the system where they stole the Death Star plans, Scarrif, to Tatooine.

But the system had been swarming with Imperials. They'd caught on to Leia's bogus tale about her ship's breaking down, but the cover had helped her stall long enough to download the technical plans for something code-named "Death Star." Despite the Rebels' efforts to lose the Imperials in the jump to hyperspace, the hulking Star Destroyer had caught up to them. And Leia knew, the moment the ship identified itself as the Devastator, there would be no escape.
  It was Darth Vader's ship.
A New Hope: The Princess, the Scoundrel, and the Farm Boy

You may wish to note that tailing a ship at lightspeed should be an extremely tricky affair that relies on guessing which route the ship follows and how fast it can travel, however in the novel Tarkin, we see that Vader has shown a deep ability to use the Force to trail his prey, even through Hyperspace.
Comment: The system was probably Scarrif, actually.
Comment: @scott.korin - We shan't find out until Rogue One opens. The details of Operation Skyhook are [notorious for being contradictory](http://scifi.stackexchange.com/questions/124400/how-many-interpretations-are-there-of-the-acquisition-of-the-death-star-plans-in/124881#comment309256_124400)
Comment: Quick question- why Geonosis? Did you mean Jedha?
Comment: @Sagierian - The Death Star itself was in an '*unnamed system*', according to Tarkin - "*For those in the know, then, it seemed inexplicable that Wilhuff Tarkin should be assigned to a desolate moon in a nameless system in a remote region of the Outer Rim.*". Leia doesn't appear to have actually seen the Death Star during her escapades, which rather suggests that she was near it, but not at it.
Comment: @Sagierian The Death Star was originally designed and developed on Geonosis - we saw a schematic of it on Geonosis at the end of Episode II, and in Rebels we learned that construction of the Death Star had started there, but then been moved elsewhere. It's a logical place to imagine the plans being stolen from.


Are there any reconstructions of possible early religions like Proto-Indo-European mythology for other cultures?

Question: I was reading the Proto-Indo-European mythology Wikipedia page when I started to wonder if there were any similar reconstructions for other related groups of mythology. I'm particularly curious if there's anything for Aboriginal Australians or Polynesians although I'd like to learn about any that exist, and if there are what would be some good sources to read about them? Even some good sources to read more about Proto-Indo-European mythology would be appreciated
Comment: See [list of mythologies](http://en.wikipedia.org/wiki/List_of_mythologies), [Australian Aboriginal religion and mythology](http://en.wikipedia.org/wiki/Australian_Aboriginal_religion_and_mythology), and [Polynesian narrative](http://en.wikipedia.org/wiki/Polynesian_narrative), including their *See also* sections.
Comment: The Polynesian narrative page unfortunately only really gives a very rough overview, more confirming the a proto-mythology could be reconstructed than actually doing it, the references don't look like they'll be much help either. The Australian page is largely the same, only covering a few similarities and pan Australian myths making it seem like some sort of stronger reconstruction could be made, although I hadn't looked at the references before and some of them definitely seems worth checking out, so thanks!
Answer: Reconstruction of Proto-Polynesian mythology
It seems that attempts at reconstructing an overall Polynesian mythology are not as abundant and convincing as in the case of Proto-Indo-European. However, there are many articles which use the comparative approach to study specific mythological themes and motifs. For example, in The First-Order Anthropomorphic Gods of Polynesia
and Was There an Early Polynesian 'Sky Father'? Jeff Marck compares recurring themes in Polynesian religions. Also, in the first section of both articles he gives an overview on previous reconstructions and comparative studies on Polynesian mythologies which you might find useful for further reading.
More recently, Martina Buckova has written several articles on specific recurring motifs in Polynesian mythologies (e.g. 1, 2, 3, 4, 5), and a book on the Polynesian culture hero Māui.
Australian mythology
On Australian mythology, Michael Witzel in section 5.3.2 of his book The Origins of the World's Mythologies (2013), gives a nice overview on the similarities and differences between various Australian mythologies. However, regarding a reconstructed pan-Australian mythology he comments:

[...] have the Australians just preserved a late stage of Pan-Gaean mythology,
which already had, for example, a world tree? To answer this question would
depend on a secure dating of the (so far not yet) reconstructed pan-Australian
mythology [...]

Also it should be noted that, while ambitious (and certainly useful in some respects), the book is quite controversial. See for exemple Bruce Lincoln's review.
Further reading on Proto-Indo-European mythology
In my opinion, the best starting point on this subject is Jaan Puhvel's Comparative Mythology. It's a wonderful introduction to comparative Indo-European mythology. Other recommended reads are definitely Indo-European Poetry and Myth by M. L. West and Death, War, and Sacrifice by Bruce Lincoln.
If you are particularly interested in the reconstructed Proto-Indo-European pantheon, Peter Jackson's article Light from Distant Asterisks. Towards a Description of the Indo-European Religious Heritage is a must read.
Comment: Thank you, All these sources look great from first glance, especially the Martina Buckova articles, I'm a little surprised Polynesian isn't more constructed though, although I'm guessing there's nothing quite as studied or developed as the Indo-European theory is so I may have just had my hopes a bit high. Still thank you for giving me a healthy amount of reading to occupy myself with!


What is the differentiating factor between work and heat?'

Question: Although work and heat do the same thing (increase or decrease the internal energy of the system), There is still a fundamental difference between them. For example, The way in which entropy is defined is a very good way to differentiate between work and heat. But, why is there such a distinction between the two things? Is it the limitation of Newtonian mechanics that it never accounted for something like heat which could also change the energy of the system? Is the word "Thermodynamical work" or "Hidden work" suitable for heat?
Comment: In general heat is kind of considered a loss, especially for friction, so it's a bad thing where work is generally a good thing.  So generally the 2 terms work and heat don't go together.
Answer: This is a very good and fundamental question. It lies at the heart of thermodynamics and related disciplines. There is no general answer for all physical systems, unfortunately.
What we define as work and heat is highly dependent on the system in question. Take the classical example of gas confined by a movable piston, in contact with a heat reservoir. In this case, all energy transferred to/from the gas from the mechanical movement of the piston is work. All energy transferred to/from the heat reservoir is heat. We do not prove that the system only exchanges heat with the reservoir; we define it in this way.
The take-away point here is that we define heat and work at the outset, when we are developing our physical model. Where the concept of heat is useful is in keeping track of changes that result in changes in entropy, so we usually associate heat with entropy. Usually, the definition is of the form 'heat is energy exchanged with the heat reservoir', so we need to have some notion of a heat reservoir in our model, for which a temperature can be defined. Then:
$$
\partial S = \frac{\partial Q}{T}
$$
Unfortunately many common definitions of heat that are given in various sources are circular in nature; for example "heat is the energy that is transferred due to temperature differences", or "heat is the energy that can't be used to do useful work."
Comment: dQ = TdS seems like a perfectly good definition once the macrostates are defined.
Comment: The equation you provided only applies to a reversible path, unless you are referring to the entropy exchanged across the interface with the surroundings.
Comment: @ChetMiller Even in that case, his equation is only valid for closed systems, for open systems there is a contribution due to the flow of matter. $d_e S = dQ/T + s dN$.
Answer: Consider a gas inside a container. Every time a molecule hits the wall of the container there is work being done. If we were able to compute the force it did and the displacement it caused to the wall and then sum over all collisions we would have a macroscopic value for work and we would not need to talk about heat. The first law would be just $\Delta U+W=0$. Since we are not able to compute all those microscopic work we effectively call the missing quantity, $\Delta U+W\neq 0$, heat. Heat work done at molecular level.
Comment: "*Heat is work done at the molecular level*" is the clearest and most concise intutive description of heat that I have seen. I might use it in future teaching. +1 for that.
Comment: This definition is misleading, because not all the "work done at molecular level" produces heat, since a part produces macroscopic work.
Answer:
What is the differentiating factor between work and heat?'

Both heat and work are means of energy transfer. The main differentiating factor is heat is energy transfer driven solely by temperature difference whereas work is energy transfer driven by force acting through a distance.

For example, The way in which entropy is defined is a very good way to
differentiate between work and heat. But, why is there such a
distinction between the two things?

Entropy is only transferred when there is a reversible transfer of heat. However entropy can be generated by irreversible work or by an irreversible transfer of heat. So entropy is not unique to heat transfer.

Is it the limitation of Newtonian mechanics that it never accounted
for something like heat which could also change the energy of the
system?

Newtonian mechanics accounts for macroscopic changes in the energy of a system relative to an external (to the system) frame of reference, such as changes to the kinetic energy and gravitational potential energy of an object as a whole. Heating such an object would not change its velocity (kinetic energy) or its elevation (gravitational potential energy).
Thermodynamics, in contrast to Newtonian mechanics, accounts for changes in the internal energy of an object, i.e., changes in the kinetic and potential energy of the object at the microscopic (molecular) level, which may occur as a result of work or heat transfer.

Is the word "Thermodynamical work" or "Hidden work" suitable for heat?

I wouldn't say that "thermodynamical work" or "hidden work" are suitable terms for heat. But it is true that when one heats an object or does thermodynamics work on an object one can not "see" the molecules of the object speed up or slow down (change kinetic energy) or see the molecules move closer or farther apart (change potential energy) as a result of the energy transfer. On the other hand, when one does Newtonian work on an object we can see its velocity change (change in kinetic energy), or see its elevation change (change in gravitational potential energy). So, in that sense, the effects of heat and thermodynamics work might be considered "hidden".
Hope this helps.
Answer: It turns out that terms representing the kinds of energy in a system generally are products of two factors.  One factor is an extensive variable (depends on how much of the system you consider), and the other is intensive (does not).  For example, $PV$: $P$ is intensive, $V$ extensive, or  $\mu N$: $\mu$ (the chemical potential of a species) is intensive, $N$ (the number of molecules of the species) is extensive, or $VQ$: $V$ (not volume, but electrical potential) is intensive, $Q$ (charge) is extensive.  These pairs are called "thermodynamically conjugate."
An infinitesimal change in energy of the system can occur either with a change of the extensive variable or the intensive one:  e.g. $-PdV$ or $-(dP)V$.  For any extensive variable other than entropy, when the extensive variable changes, work is being done (e.g. $-PdV, \mu dN, V dQ$). This is analogous to (and sometimes equal to) a force acting over some distance. Any additional change of internal energy (e.g. $dU + PdV - \mu dN - VdQ -$ (other changes associated with extensive variables)) is associated with heating, and equals $TdS$.
Answer: Heat is a form of energy. And if we go into the basic definition of energy, It is the capacity to do work. They are interrelated. But mathematically they are one and the same. Their SI units is the same ie. Joules . The only thing that changes is the physical interpretation .
Think of a heat engine in a car. It is ready to do work because it contains a certain amount of stored energy . When work is done, energy is transferred between systems or from one form of energy to another.
Thus Heat energy is what the engine contains ( or possesses) while work is what has happened with that heat energy , is it lost to the surrounding, or is it converted to kinetic energy? If yes, how much is what is Work  . You will be knowing the formulas that work is the difference in potential energy or sometimes difference in kinetic energy.
So finally, Heat is what you already have and Work is what you do with it


Revision letter and grammatical errors

Question: I got a major revision and I will prepare a revision letter. The editor asked me to review my manuscript for grammatical errors, in addition to the scientific comments he made. Should I present all the grammatical changes I made on the manuscript one by one? There are lots of minor changes (i.e addition/insertion of commas, "the", "a/an").
Comment: I recommend providing a red-lined version which shows all revisions. This can be done automatically.
Answer: Since they haven't pointed out what mistakes you have, it is unlikely they have a list of errors they have found; therefore, enumerating your changes is pointless. Also, since you got "major revision", a good chunk of your text should be changed anyway.
Just make sure you double check the language before resubmitting, preferably by someone else (native speaker would be ideal).
Answer:
Should I present all the grammatical changes I made on the manuscript one by one because there are lots of minor changes (i.e addition/insertion of commas, "the", "a/an")?

This seems unnecessary. What I usually do is report all the mentioned grammatical errors, and then just remark that I fixed all of them.
That being said, if there are so many grammatical errors that this is an actual problem for you, you definitely need to tighten up the writing of your paper.
Answer: I very much doubt they care for you to acknowledge every problem they point out to you, they just want you to fix them (and others you might find in the process). If you disagree with some of the suggestions, then it makes sense to speak up and explain your reasoning (should probably do it in the text too, if whoever did the revision didn't understand it, chances are it will confuse other readers too).
Answer: You can submit two versions -- one with Track Changes turned on, showing all the changes as edits, and one with all the proposed edits 'accepted'.

Revision letter and grammatical errors


two aligners combined results

Question: I would like to ask if someone uses two different aligners to produce count matrices and then run the same alogrithm for DEG analysis, would it make sense to find the intersection of the DEGs in order to conclude to the "real" DEGS?
Comment: Never heard of that. Main problem in RNA-seq I see is underpowered experiments, therefore unreliable statistics. Just because one aligner may and the other ma not assign certain reads to genes the intersection does not necessarily increase confidence, it also increases the false-negative rate. I would stick to standard procedures, take the aligner (or pseudo/selective aligner, kallisto or salmon) you like most and then proceed with established statistical pacakges.
Comment: Thank you so much for your feedback!Yes that particular problem I am trying to solve..!
Comment: Any particular reason you try to come up with that? Is the gene you are interested in not showing the behaviour your expect so now you try to tweak results?
Comment: No, I am just trying to understand which algorithm to trust and which approach would give the most reliable results.. I am not trying to tweak results..
Comment: I suggest you read papers that actually benchmark aligners, there is much work already done on this. Currently, the field seems to prefer the pseudo- and selective aligners such as kallisto and (my personal favourit) salmon. I would always read existing benchmarks first before trying to come up with personal solutions.
Answer: This sort of procedure is done in tool papers to benchmark results compared to different aligners/mappers. See the salmon or kallisto papers for examples. Using the intersect of DE results from different mappers will end up yielding somewhat conservative results, not unlike using different differential expression packages and taking the intersect of their outputs. In practice you could just take a more conservative p-value cut-off and save the hassle of using multiple tools, the results would end up being similar.
Comment: Yes, I have read in tutorials that the best approach would be to find the intersection of DEGs produced by different algorithms (deseq2, limmavoom, edger) and that s the reason why I wondered if I should the same with the aligner as well.. Thank you for your answer!

two aligners combined results


How do I add options to a mongodb running on Appfog?

Question: Locally I can call mongod --noprealloc --nojournal to prevent preallocation. I want to configure my mongo database on Appfog the same way. I tried using af tunnel to access the database instance, however it only provides the options
1: none
2: mongorestore
3: mongodump
4: mongo
I also thought of configuring the Appfog mongo database when I connect to it on my Nodejs server, using mongodb node native. Unfortunately this has not given me any luck either.
Answer: I never found a way to do this using mongodb on Appfog. My intent for doing this was to prevent the mongodb running over the 100mb Appfog storage limit. I instead moved my database to MongoLab which is supported by Appfog. They somehow seem to save data differently, so that it takes up very little space compared to saving it on Appfog.


Objectively, what can you do on kali that you can't do on a mac?

Question: What is so special about kali?
Is there some suite that just run on kali and won't on other distros/mac?
Is it just marketed better to the infosec community?
Comment: There are some tools that work better on Linux than a Mac (f.e. if you need additional hardware for them). But the main reason for using Kali is that all the tools are there. Me, I'm quite happy with my Slackware with practically the same toolset as Kali. Haven't needed Kali for anything yet.
Comment: You can do everything on a mac you can do on kali.  If you install all the tools kali has.  If the tools compile at all on a mac vs. on linux.   If you don't mind doing the work of essentially building on your mac what makes Kali its own special distro.
Comment: Well, you are trying to compare a Linux distro to MacOS, but other than that, there is nothing special about kali. It just has a ton of pre-bunded tools.
Answer: Aside from the things Wouter already mentioned in his answer, there are other things, that Kali offers, which "general purpose" operating systems don't:

All pentesting tools are tested to work on Kali by the Kali devs.
While that may not sound like a big deal to you, it is indeed a big deal for professional pentesters. When I start a tool, I can be confident that it works. There are no missing dependencies, which are not available through that distro's package manager, which I will have to compile myself. The configuration will already have been done so that the tool will work on this system. And so on and so forth.
That doesn't mean you can't get those tools to run on other distros, but that may include compiling stuff from sources, wading through cryptic error messages by make...essentially trying random things until it works.
MacOS is also notorious for including command line tools or libraries, which are either outdated or have been modified by Apple in some way, so that they don't seamlessly work with code written for Linux. Yes, there are tools like Homebrew, but installing multiple, incompatible versions of command line tools and libraries is usually not a recipe for success.

Kali includes patched kernel modules for wireless hardware.
This is arguably a minor thing, but Wi-Fi pentesting can be a pain in the ass. Getting a random chipset to work in monitor mode, so that it works with airodump-ng can be an exhausting task in Kali, but it's way worse in an OS, that has who knows what installed to manage wireless devices.
In Kali, I can be confident, that my wireless device will work in monitor mode and that I will be able to capture data from it without having to search why channel hopping isn't working or why I can't inject frames with aireplay-ng.
Since you asked specifically about MacOS, this may actually be one of the things you can't do on a Mac. However, depending on the chip used, it may also not be possible on Kali either.

Developers test their tools on Kali.
It's one of those chicken-and-egg scenarios. Since most pentesters use Kali, developers of pentest tools test those tools to work on Kali. And since those tools are tested to work on Kali, that's what pentesters will primarily use.

However, I would like to stress the point that Kali is not a requirement to be a pentester, security researcher or similar.
If you have a good reason to use a different OS, and that setup works for you, then by all means, use what works for you. For example, all of my regular corporate stuff (Outlook, Teams, Word, etc.) runs on Windows, so I usually use Windows as host for web-based security assessments, because Burp Suite runs just as well on Windows.
Answer:
Objectively, what can you do on kali that you can't do on a mac?

Objectively, nothing. Kali Linux is a Debian-based Linux distribution that comes with a complete toolset, often used in penetration testing, as well as related resources like wordlists. A Mac will most likely run macOS as its operating system. There may be operational differences between these operating systems, yet it can be expected that most tools will be operable on either system.
If required, it would be possible to run a Virtual Machine of the other Operating System on either system as well.

whats so special about kali?

The fact that it has a full pentesting suite pre-installed, along with the most popular resources like wordlists. This is directly usable after install. No extensive configuration is required to set up tools and download resources.

is there some suite that just run on kali and won't on other distros/mac?

No.

is it just marketed better to the infosec community?

It is popular because it can be used directly for pentesting out of the box. There are other distributions available that provide a similar experience, like ParrotOS.


Proof of the multivariate Central Limit Theorem

Question: Casella and Lerner's Theory of Point Estimation (2nd edition) provides a definition of the multivariate Central Limit Theorem, for which no proof is given.

Theorem 8.21 (Multivariate CLT) Let $\mathbf{X}_\nu = (X_{1\nu}, \dots, X_{r \nu}$) be iid with mean vector $\zeta = (\zeta_1, \dots, \zeta_r)$ and covariance matrix $\Sigma = \vert \vert \sigma_{ij} \vert \vert$, and let $\overline{X}_{in} = (X_{i1} + \dots + X_{in})/n$. Then,
$$[ \sqrt{n} (\overline{X}_{1n} - \zeta_1), \dots, \sqrt{n} (\overline{X}_{rn} - \zeta_r)]$$
tends in law to the multivariate normal distribution with mean vector $\mathbf{0}$ and covariance matrix $\Sigma$.

What would be its derivation?
Comment: Please use MathJax to include equations, rather than just pasting images.
Answer: There are many proofs of the (many versions of) the CLT. In the iid case you mention, usual proof is based on characteristic functions.  There is a discussion here Proofs of the central limit theorem.
The proof is basically the same for the multivariate case as the univariate case, mostly some changes in notation. There is basically no new necessary ideas for the multivariate case. Some ideas: If $X_i$ are iid $n$-dim random vectors (such that expectation and covariance matrix exists.) If we know the distribution of $a^T X_i$ for all (constant, non-random) vectors $a$, then the distribution of $X_i$ are characterized by that. So we can use the uni-variate CLT on $a^TX_i$ and reconstruct the limit from that.