While reviewing , I was shown .  I thought it was a good question, and I wanted to ask what the term odr-used means, so I pressed add comment.  For daring to taint a good question with my filthy comment, I was struck down:   Now I cannot make any more reviews.     You have made too many incorrect reviews. For an example of a task you   should have reviewed differently, see:   .      Come back in 2 days to continue reviewing.   Review audits should not fail due to the add comment button.
I just failed these   in First Post, I read the question and thought it seemed reasonable but the user was deleted so to be on the safe side I clicked add comment and I failed the audit.  I'm not sure why adding a comment would be considered a negative action, is the correct option to click No Action Needed or edit?  What was I supposed to do in this situation?  Adding a comment should not be a review audit fail.
I'm trying to understand at a deeper level the ubiquity of log-likelihood (and perhaps more generally log-probability) in statistics and probability theory.  Log-probabilities show up all over the place: we usually work with the log-likelihood for analysis (e.g. for maximization), the Fisher information is defined in terms of the second derivative of the log-likelihood, entropy is an expected log-probability, Kullback-Liebler divergence involves log-probabilities, the expected diviance is an expected log-likelihood, etc.    Now I appreciate the many practical and convenient reasons.  Many common and useful pdfs are from exponential families, which leads to elegantly simplified terms when log-transformed.  Sums are easier to work with than products (esp for differentiating).  Log-probs have a great floating point advantage over straight probs.  Log-transforming a pdf often converts a non-concave function into a concave function.  But what is the theoretical reason/justification/motivation for log-probs?  As an example of my perplexity, consider the Fisher information (FI).  The usual explanation for intuiting the FI is that the second derivative of the log-likelihood tells us how "peaked" the log-likehood is:  a highly peaked log-likelihood means the MLE is well-specified and we are relatively sure of its value, while a nearly flat log-likehood (low curvature) means many different parameter values are nearly as good (in terms of the log-likelihood) as the MLE, so our MLE is more uncertain.   This is all well-and-good, but isn't it more natural to just find the curvature of the likelihood function itself (NOT log-transformed)?  At first glance the emphasis on the log-transform seems arbitrary and wrong.  Surely we are more interested in the curvature of the actual likelihood function.  What was Fisher's motivation for working with the score function and the Hessian of the log-likelihood instead?  Is the answer simply that, in the end, we have nice results from the log-likelihood asymptotically? E.g., Cramer-Rao and normality of the MLE/posterior.  Or is there a deeper reason? Parsing DateTime on Localized Systems I ran into the "mysterious"  \pdfendlink ended up in different nesting level than \pdfstartlink   error.  According to , "this happens when hyperref is used under pdftex and a citation splits across a page boundary".  The given solution is to manual fix the citation to not split across the page boundary.  However, this workaround isn't feasible for me, as the documents are automatically generated on a server with no user interaction.  Is there any solution to the problem known, perhaps an experimental hyperref action or a patch to pdftex?  (Probably, one could use luatex to solve the problem, but for other reasons, luatex is not an option in this project.)  MWE:  \documentclass[%draft               ]{article} \usepackage{hyperref} \setlength{\textwidth}{3cm} \setlength{\textheight}{3cm}  \begin{document} Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna \href{http://www.tug.org/errors}{aliquyam erat, sed diam voluptua.} \end{document} Can Hooke's law be derived? Can we derive  from the theory of elasticity? I know it is not a fundamental law and therefore can be derived from more basic considerations. How to replace one char with another in all filenames of the current directories? What is this noisy shadow overlay that stays with the camera? I am looking for an easy way to create in Illustrator vintage style corners like on the picture provided.  I have some technical ideas, but they are time consuming, there should be an easier way I believe. Prove or show a counter example for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$ I'm working on my Discrete Mathematics homework and they are asking me this:  Prove or show a counterexample for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$  I'm not completely sure how to prove it. I was thinking to find a counterexample like zero but I'm not sure if that it's going to work. Or maybe try to approach it backwards?   I'm a little bit lost Can an inanimate thing lift Mjolnir? Can an inanimate thing can lift Mjolnir without the help of a living being (unworthy)  Scenario 1  Mjolnir in a very light car with a sail attached to it, then a very strong wind blew and moved the car uphill.  It is possible or not?  Scenario 2  Can upward wind alone lift the Mjolnir? If I have Optimize iPhone Storage enabled on my iPhone and my phone storage is completely full, I understand that iOS will only store a low-res thumbnail of many of my photos on the device. (The full high-res version of the image will only exist in iCloud and on devices with Download and Keep Originals enabled.)  But when only thumbnails exist on the device, how does that work in relation to other photo apps on iOS? For example, do third-party cloud-based photo apps (like Google Photos, Dropbox's Carousel, or Amazon Prime Photos) have access to the full high-res images from the iCloud Photo Library? Or will they only see the low-res thumbnails in some cases? Could normal users have an easier way to flag for migration? Problem about a process with bins of balls Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements I am attempting to prove what the title says, that $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements.  I have already proven that for any field $K$ and polynomial $f(x)$ in $K[x]$, $K[x]/\langle f(x)\rangle$ is a field if and only if $f(x)$ is irreducible in $K[x]$. So I know that $\mathbb{F}_p/\langle f(x)\rangle$ is a field for sure. Where I'm lost is figuring out how to know for sure that there are $p^n$ elements. It's fairly clear if $n\in\{ 0 ,1\}$, but I don't think induction is going to help.  I know from a proposition in class that since $F_p = \mathbb{Z}/\langle p\rangle$ and $F_p = \mathbb{Z}/\langle p\rangle$ is an integral domain, $F_p[x] = (\mathbb{Z}/\langle p\rangle)[x] = (\mathbb{Z}[x])/(\langle p\rangle[x])$, but I'm not sure whether or not that's helpful information. Something has changed in server 16.04 LTS, I can't find tty1, but I need to make an auto-login on tty1 (in console mode), in 14.04 LTS I can make this work.  I can't find /etc/init/tty1.conf  How to, or a link? note: This is a question about relativistic effects. I've included some detail about the spacecraft and its orbit for background, but the question is about relativistic effects and their observability.     When the Parker Solar Probe passes within 8.5 solar radii of the Sun, it will be moving really fast.  A perihelion and aphelion of about 6.6 and 109 million kilometers suggests a semi-major axis of 57.8 million kilometers. The standard gravitational parameter for the Sun is:  $$GM_{Sun} \ = 1.327\times 10^{20} m^3/s^2$$  So using the :  $$v^2 \ = \ GM_{Sun}\left(\frac{2}{r}-\frac{1}{a}\right)$$  the orbital velocity at perihelion will be about 195,000 m/s, or about 25 times faster than a satellite in LEO. This is close to one part per thousand of the speed of light! I think this will be a new record for a spacecraft velocity relative to the solar system.  Depth of a gravitational potential well for an object of mass $m$ is approximately given by:  $$u_G \ = \ -GM_{Sun}\frac{1}{r}$$  At 6.6 million kilometers the spacecraft will be 23 times deeper in the Sun's gravitational well than it would be at 1 AU.  Will there be any particularly unique relativistic effects detectable for the Parker Solar Probe during it's close flyby of the Sun?  Just for example, during one close flyby, how much time will its on-board clock gain or lose compared to some convenient standard solar system timescale? I know there are several different choices, "GPS time" might be one but I don't want to arbitrarily choose an inconvenient one.     above: Parker Solar Probe cropped, from .    above: screen shot from NASA's      note: the link seems to be dead now, but there is plenty of related information available at     above: Illustration of the Parker Solar Probe's orbit, from . We're building a feature for a website and trying to think of a hypernym for clients, partners and members so that the feature remains generic enough for re-use later on other websites. Atiyah Macdonald, Exercise 8.3. Let $k$ be a field and $A$ a finitely generated $k$-algebra. Prove that the following are equivalent:   (1) $A$ is Artinian.   (2) $A$ is a finite $k$-algebra.   I have a question in the proof of (1$\Rightarrow$2): By using the structure theorem, we may assume that $(A,m)$ is an Artin local ring. Then $A/m$ is a finite algebraic extension of $k$ by . Since $A$ is Artinian, $m$ is the nilradical of $A$ and thus $m^n=0$ for some $n$. Thus we have a chain $A \supseteq m \supseteq m^2 \supseteq \cdots \supseteq m^n=0$. Since $A$ is Noetherian, $m$ is finitely generated and hence each $m^i/m^{i+1}$ is a finite dimensional $A/m$-vector space, hence a finite dimensional $k$-vector space.  But now how can I deduce that $A$ is a finite dimensional $k$-vector space? Get the real width and height of an image with JavaScript? (in Safari/Chrome) So I'm in Linux and I want to have a program accept arguments when you execute it from the command line.  For example,   ./myprogram 42 -b -s  So then the program would store that number 42 as an int and execute certain parts of code depending on what arguments it gets like -b or -s. Definition of complex number In many situations (problems as well as solutions) I encounter the complex number $i$ which many times is defined as $i^2=-1$ instead of $i=\sqrt{-1}$, since it is "more preferred". Does anyone know why? Is it because there are two solutions to the equation $x^2+a=0, \ \ a&gt;0$?