I plan on storing data, encrypted with AES256, where the first dozen bytes are known plaintext.  ('Hello World!' for example.)  Does having this known plaintext prefix weaken AES256?  I do not care about modifications being made to the ciphertext, which result in modifications to the decrypted plaintext.  I do care about an attacker being able to decrypt any plaintext beyond the known plaintext prefix.  I expect to use counter mode, as random access is required.  Does GCM have any advantage?
At least it's my understanding that AES isn't affected by known-plaintext. Is it immune to such an attack, or just resistant? Does this vary for chosen-plaintext?
Program does not wait before output Why are the holodecks on Voyager in use if they have energy issues? I'm watching the first two seasons of Voyager and various episodes have commentary on having energy limitations -- but we constantly see crew using extremely complicated holodeck simulations. Why would they allow use of the holodeck if they need to conserve energy? 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? If you have to provide some initial troubleshooting support by phone [or email], and you don't have access to the user's PC itself, what is the easiest and most foolproof question one can ask of the user to find out if the 'dumb' user is using either Windows 7 or Windows Vista?  For example: determining if the user has either Windows XP or Windows Vista/7 is easy. Just ask the user if the button at the left bottom corner is (a) either square with the word 'Start' on it, or (b) it is a round button.   But how do you determine the difference between Vista and 7?  Edit: For all the existing answers the user has to type something, and do it correctly. Sometimes even that is already hard for a computer illiterate user. My XP example just requires looking. If it exists (although I am afraid it doesn't), I think a solution that is just based on something this is visually different between Vista and 7 would stand above all others. (Which makes Dan's suggestion to turn over the box and look at the label" not so stupid). Perhaps the small 'show desktop' rectangle at the right side of the task bar (was that present in Vista)? Obtaining consistent one-hot encoding of train / production data Boy goes insane during space travel I'm trying to remember the name of a short story I read about 25 years ago or so. I'd also like to know of any collections it appeared in.   The details I recall involve a family who are embarking on a hyperspace journey. To undertake this journey you have to be put to sleep. One of the children pretends to be asleep, and when the jump is complete the child has gone insane. From the child's point of view the jump lasted for an eternity while in reality it was only a few seconds. I created a thick glass bottle and duplicated the interior faces to make a new object to create the liquid inside.   I went in the edit mode, selected the faces I wanted to copy and duplicated them with ShiftD. Then I pressed P to  separate the duplicated faces.   Now I try to make a duplicate of that liquid to make it flow out of the bottle, and I simply need the duplicate of one face of it. So I go to edit mode and do as I did to make the liquid from the bottle faces... but as soon as I'm back to the object mode and I want to move the duplicated faces, every thing moves with it...   I played around and tried things, and while doing so I realized that if I dupe the liquid object in object mode using ShiftD and press 0 to place it where the original is, they move together if I duplicate it and place it somewhere else so that they are separated.   Also if I pick one of the two separated objects and make it intersect with the other one, release my left mouse button to place it there, and then try to move it again, they both move together, but not at the same speed.  I really don't understand what is going on and I'm sure it's really badly explained, so what I'll do is make a screen capture of my Outliner and record the behavior of the objects and upload those to help you understand. Why does the sizeof operator return a size larger for a structure than the total sizes of the structure's members? In single-blind peer-review, can you reveal your identity without the editor's consent? In my field (chemistry), review is always done in a single blind process, i.e. the author does not know who the referees were, but the referees do know who the authors are. In ten years, I have never seen a referee breaching this anonymity, e.g. by signing their review, unless they got prior approval by the editor (in order to continue discuss things further with the authors, once the manuscript was accepted for publication).  So, it seemed logical to assume that in single blind peer-review, the reviewer should not disclose his identity without the editor's consent. Yet, some people have told me ( and ; also IRL a friend from human sciences) that they have seen people sign their reviews, or write emails to them after the review but before the paper is published.  So, in single-blind peer-review, can you reveal your identity without the editor's consent? Does it depends on the customs of each field, or is there a hard rule? (in which case, the few anecdotes I heard were outliers) Why is Excel truncating my 16-digit numbers? If I type in a 16 digit number (format: number, no decimals) it changes the number on me. Example: 1234567812345678 changes the view to 1234567812345670.    If I type it in as a general format it changes the numbers above so it displays 1.23457E+15 but if you click on the cell, the display shows the last digit as a 0 instead of an 8 once again.   I opened the file on a different computer and same issue now with it.  I have changed the auto correction and auto formatting all to no avail.  Help! Set up a scheduled job? Google Drive storage mismatch Removing nodes from graphs such that one is dependent on other - ZIO $2010$, P$1$ Greetings Community! The above problem you see is a combinatorics problem I could not solve. :( This problem is from ZIO $2010$, P$1$.     Here is what I did: Observe that every graph can be divided into "sub-groups" which may help in solving. We first remove the empty set. Then the singleton set. Consider the bigger but smaller than the sub-parts example:    The singleton sets are $\{4,5,6\}$ which are at the least position in the graph.   The dual sets are $\{2,4\}, \{3,5\}, \{3,6\}$, the bottom - two portions in the graph. The triplet sets are $\{2,4,5\}, \{4,5,6\}$ which we may manually count but for the bigger graphs in the sub-part, this may prove to be difficult and this is where I am stuck.   Any help would be appreciated. Thanks. How do I resize my current ubuntu partition? I was wanting to initialize some strings at the top of my script with variables that have no yet been set, such as:  str1='I went to ${PLACE} and saw ${EVENT}' str2='If you do ${ACTION} you will ${RESULT}'   and then later on PLACE, EVENT, ACTION, and RESULT will be set. I want to then be able to print my strings out with the variables expanded. Is my only option eval? This seems to work:  eval "echo ${str1}"   is this standard? is there a better way to do this? It would be nice to not run eval considering the variables could be anything. Closure of a Ball is Contained in Closed Ball (usual metric) Let $\overline{B_d (x, r)}$ be the closure of an open ball, and let $\hat B_d (x, r)$ be a closed ball. Show that in any metric space $(X, d)$, $\overline{B_d (x, r)} \subseteq \hat B_d (x, r)$ for all $x \in X$ and $r &gt; 0$.    I used the definition of closure: $\overline{B}$ = $B \bigcup B'$. If $x \in \overline{B}$, then $x \in B$ or $x \in \overline{B}$, or both. If $x \in B$, then clearly $x \in \hat B$ since $B \subseteq \hat B$. But, if $x \in B'$, then $x$ is an accumulation point. Since $\hat B$ is closed, it contains all accumulation points of $B$. Thus, $x \in \hat B$.  Is this approach correct, or at least in the right direction? Should I be using the closure definition, or try another one? Thank you. Convergence in Distribution in Order Statistics Let $X_1, X_2, \ldots$ be iid from Exp$(\theta)$ with density function $f(x) = \frac{1}{\theta}e^{-\frac{x}{\theta}}$. (a) Find the limiting distribution of $M_n = Y_1 - \theta\ln(n)$ and $T_n = nY_n$, where $Y_1$ and $Y_n$ represent the first and last order statistics (among $n$ observations) respectively. Answer: I have obtained the CDF of X to be: $$F_x(x) = 1 - e^{-\frac{x}{\theta}}$$ the CDF of $Y_1$ to be: $$F_{Y_1} = 1 = e^{-\frac{xn}{\theta}}$$ the CDF of $M_n$ to be: $$F_{M_n}(x) = \left[1 - \frac{1}{n}e^{-\frac{x}{\theta}}\right]^n$$ with limiting distribution $$e^{-e^{-\frac{x}{\theta}}}$$ the CDF of $T_n$ to be: $$F_{T_n}(x) = 1 - e^{-\frac{x}{\theta}}$$ which is also the limiting distribution. (b) Show that $M_n$ and $T_n$ are asymptotically independent. Answer: I've tried finding the joint PDF for ordered statistics by using the equation $$g_{ij}(y_i, y_j) = \frac{n!}{(i - 1)!(j - i - 1)!(n - j)!}[F(y_i)]^{i - 1}[F(y_j) - F(y_i)]^{j - i - 1}[1 - F(y_j)]^{n - j}f(y_i)f(y_j)$$ however, it is a mess based on my CDFs. Any suggestions on a different approach? Number of solutions of an arithmetic function's equation Say, an equation is given below \begin{equation} 2\pi(x) - \pi(2x)=\omega(x) \end{equation}  where $x$ is a positive integer, $\pi(x)$ is the prime-counting function, and $\omega(x)$ is the number of distinct prime factors of $x$.  I would like to know if this equation holds for finitely many values of $x$ or infinitely many.  If one uses asymptotic formula (from number theory) it can be written that \begin{equation} \omega(x) \sim \ln x / \ln \ln(x) \end{equation} (from )  and  \begin{equation} \pi(x) \sim x/\ln(x), \end{equation} so the above equation can be rewritten (after simplification) as \begin{equation} 2x\ln(2)=\ln(x)\ln\ln(x)\ln(2x) +f(x) \end{equation}  where $f(x)$ is an error term.  If  I plot left side (which is linear, supposed to be a straight line) and right side(a curve),assuming $ f(x) $ is 100% accurate, then the equation implies(?!) that the right will intersect left side. Since line can intersect a curve ($ln  $ function) finite times, so there are finite intersection point. So, can I say that there are only finitely many values of $x$?  graph example-   here f(x) is assumed as x + sinx  without the f(x)- How to determine which program is making a certain sound in windows 7? I'm experiencing an annoying "female robotic" sound effect saying "loading complete" at uncertain interval in windows 7.  I want to shut down that noise for good. To do that, I have to determine which program is making this sound. I tried to open the "sound mixer" window, only to find to program last made any sound, one is official GTalk client, one is system sound. I tried to close GTalk and the sound still existed.  I started experiencing this issue not long after I installed a "driver" program for Rapoo E9198 wireless keyboard. Small snap loop devices visible in gnome-disk-utility OR what is the function of snap ubuntu-core