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Comparison between bootstrap percentiles confidence interval and BCa confidence interval? I have generated a nonparametric percentiles bootstrap confidence interval ($32.27143, 51.08571$), and a BCA confidence interval ($33.26, 53.49$) with an initial sample size of $n=7$.  Evidently, the BCA interval is larger than the percentiles interval. Shouldn't the BCA interval be better than the percentiles interval (and by "better" I mean "smaller")? I noticed also that when the sample size is larger, for example $n=40$, BCa confidence interval decreases. Undefined reference to `pow' and `floor' How can I classify data with the nearest-neighbor algorithm using Python? I'm studying for an abstract algebra exam and one of the review questions was this:     Let $X$ be a set, and $\mathcal P(X)$ be the power set of $X$. Consider the operations $\Delta$ = symmetric difference (a.k.a. "XOR"), and $\bigcap$ = intersection.   a) Does $\Delta$ and $\bigcap$ make $P(X)$ into a ring?   b) If so, is it a ring with unity?   c) Is the ring commutative?   d) Is it a field?   For parts a) and b), I think it does form a ring with unity, but I'm not quite sure how to get started on proving it.   For part c), it is a commutative ring since $\mathcal P(X)$ is closed under symmetric difference and intersection, right?  Not even sure how to get started on d).  I'd really like to understand this question fully, so any kind of input would be tremendously helpful. Thank you! Which types of particles are affected by the wave-particle duality? If we take the double slit experiment as a way of demonstrating the wave-particle duality, which types of particles would show an interference pattern?  For example, I know that electrons show such a pattern. But do protons, too? What about atoms? Where is the boundary between "wavey particles" and "classical particles"? Let $V$ be a representation with character $\chi$.  I would like to have a formula for the characters of the representations $\mathrm{Sym}^m[V]$ and $\wedge ^m[V]$ in terms of $\chi$.  Fulton and Harris presents such a formula for $m=2$, but not for general $m$.  Is there a "nice" such expression?  I found a paper by , but this doesn't seem to be what I'm looking for (it doesn't seem to give a general formula in terms of $\chi$).  In case the link does not work, here is the reference:  X. Zhou, P. Pulay. Characters for Symmetric and Antisymmetric Higher Powers of Representations: Application to  the  Number of Anharmonic Force Constants in Symmetrical Molecules. Journal of Computational Chemistry, Vol 10, Issue 7, (1989). Youths can teleport, they are chased by the government Which Python memory profiler is recommended? I want to know the memory usage of my Python application and specifically want to know what code blocks/portions or objects are consuming most memory. Google search shows a commercial one is  (Windows only).  And open source ones are  and .  I haven't tried anyone, so I wanted to know which one is the best considering:   Gives most details. I have to do least or no changes to my code. How to list only JPEG files from root below using the command line? Should we avoid negative words when writing error messages? I'm having a really hard time trying to understand what the differences between a desktop environment and a window manager are?  EDIT: From this :  There are basically three layers that can be included in the Linux desktop: X Windows – This is the foundation that allows for graphic elements to be drawn on the display.  builds the primitive framework that allows moving of windows, interactions with keyboard and mouse, and draws windows. This is required for any graphical desktop. Window Manager – The Window Manager is the piece of the puzzle that controls the placement and appearance of windows. Window Managers include: , , , , , etc. Requires X Windows but not a desktop environment. Desktop Environment – This is where it begins to get a little fuzzy for some. A Desktop Environment includes a Window Manager but builds upon it. The Desktop Environment typically is a far more fully integrated system than a Window Manager. Requires both X Windows and a Window Manager.  Examples of desktop environments are , , ,  among others) Interscholastic Mathematics League Senior B Division #2 8.00GB RAM (3.22GB usable) in Windows 7 x64 I have set up Windows 7 Ultimate 64-bit on my PC. I have 8GB RAM and my BIOS states the correct amount (8192MB), but Windows (System Manager) says I have 8.00GB (3.22GB usable). give me a solution. I'm tried this: Run &gt; MSCONFIG, open the Boot tab &gt; click Advanced Options &gt; make sure that Maximum Memory but this wasn't helpful. My Motherboard Details: CPU Type : DualCore Intel Pentium, 3000 MHz (15 x 200) Motherboard Name : Foxconn G41MXE Motherboard Chipset : Intel Eaglelake G41 System Memory : 3296 MB (DDR3-1333 DDR3 SDRAM) DIMM1: Kingston : 4 GB DDR3-1333 DDR3 DIMM3: Kingston : 4 GB DDR3-1333 DDR3 My BIOS Details: BIOS Type : AMI (03/21/11) Vendor : American Megatrends Inc. Version : 080015 Capabilities : Flash BIOS, Shadow BIOS, Selectable Boot, EDD, BBS System Properties :  Bios File :  What about Bios Update? Converting a system command to python for file search and delete Differences among "It feels...", "It looks...", and "It seems..." I have thus far avoided the nightmare that is testing multi-threaded code since it just seems like too much of a minefield.  I'd like to ask how people have gone about testing code that relies on threads for successful execution, or just how people have gone about testing those kinds of issues that only show up when two threads interact in a given manner?  This seems like a really key problem for programmers today, it would be useful to pool our knowledge on this one imho. Let $m$ be Lebesgue measure and $a \in R$. Suppose that $f : R \to R$ is integrable, and $\int_a^xf(y) \, dy = 0$ for all $x$. Then $f = 0$ a.e. This is a corollary to a proof in Bass, but I don't understand why it follows from the proof he gives. I follow everything up until the last statement. Why is it that proving that the integral is $0$ for all Borel measurable sets guarantees it is true for all Lebesgue measurable sets? Am I missing something vital about the relationship between Lebesgue measurable sets and Borel measurable sets? Statement: Let $m$ be Lebesgue measure and $a \in\mathbb R$. Suppose that $f : \mathbb R \to\mathbb R$ is integrable, and $\int_a^xf(y) \, dy = 0$ for all $x$. Then $f = 0$ a.e. Proof: We prove the conclusion first for intervals, then for unions of intervals, then for open sets, then for Borel measurable sets. For any interval $(c,d)$, we have $$\int_c^df = \int_a^d f - \int^c_a f = 0.$$ By linearity, if $G$ is the finite union of disjoint open intervals, then $\int_G f = 0$. Now, if $G$ is open, then $G$ is the countable union of disjoint, open intervals, $G = \bigcup^n_{i=1}I_i$. We have $$\int_G f = \int \lim_{n\to\infty} f \cdot \chi_{\bigcup^n_{i=1} I_i}$$ and since $f_n$ is integrable for all $n$, and $|f_n| \le f$ for all $n$, by the dominated convergence theorem, $$\int_G f = \lim_{n\to\infty} \int_{\bigcup^n_{i=1}I_i} f =0.$$ Now, if $G_n$ is a decreasing sequence of open sets converging to $H$, since $|f \cdot \chi_{G_n}| \le f \cdot \chi_{G_1}$ for all $n$, we again have by the DCT that $\int_H f = 0 = \lim_{n\to\infty} \int_{G_n}f = 0$. Finally, if $G$ is a Borel measurable set, then we know that there exists a sequence $G_n$ of decreasing, open sets, that converge to some set $H$, where $H \setminus G$ is a null set. Thus, $$\int_G f = \int_H f = 0.$$ We have found that for every Borel measurable set $G$, $\int_G f =0$. Since $f$ is real valued and measurable, $f = 0$ a.e. Testing a UPS by unplugging it from the wall At an Not For Profit/Charity I volunteer for occasionally we were very fortunate to be provided (donated) with a brand new 3Kva APC UPS. This is total overkill for our modest server rack (four mid-range servers and a switch!) but hey, I'll take what I can get!  Pressing the TEST button on the front indicates that yes, the UPS does work. Brilliant. But it only tests it for about 15 seconds.  My question is - will I degrade the UPS by unplugging it from the wall to see how long it will last? My plan is to unplug it, and wait until the battery meter reaches its last LED before plugging it back in, so that I know about how long I will have in the event of a power outage.  Do people do this on a regular basis? I'm guessing no (Lead Acid is very different to Li-Ion batteries)... but what kind of harm would it do if this were to happen (on purpose) every 6 months? I've built a current sense differential amplifier that measures the voltage across a 1 Ohm resistor, to give me a reading for the current through it.  I've connected it as follows, all resistors are matched 10k to give a gain of 1:    (Image source: )  I am powering it from a single rail 12 volt source. The problem is even though this is a rail to rail opamp (Output Low swing from 5-20mV) I'm getting a constant error of 0.62V and it seems the opamp is not able to go below this value.   I have tried to resolve this by connected Vout to ground using a 10k resistor, but that makes no difference whatsoever.  I tried it with dual supply configuration (+8V, -8V) and that seems to resolve the issue. However I want to run this off a single supply rail, so this is not a viable option.  How can I resolve this? I'm trying to measure the voltage drop across a 1 ohm resistor to give me a reading for current through the circuit (0-1V represents 0-1 A) so I can set up a current limit. A better way (or practice) to doing this is also welcomed. The initial (but not ideal) fix I can think of, is to offset the readings by a few volts?  Edit:  Changed R1-R4 from 10k to 100k and I'm down to about 30-50mV! Is it acceptable to insult god in a user profile? Like always I hang around in Stack Overflow's chatrooms. Today, someone posted a link to his new "reloaded" user profile.  Along the lines I read in Arabic "god is a pig". So I asked him to remove it:     Me: I have a lot of respect towards you because of your knowledge but what you wrote there in Arabic is offensive. Could you remove it please?   OP: if it were in English, would it be equally offensive?   I will write it in Dutch because you ask it so kindly.   Me: yeah, I mean what's your goal? You're just seeding hatred   OP: It is an experiment.   After that, the user changed it to Dutch.  My question is: are such statements acceptable by Stack Exchange's standards? If not, should I flag one of his posts like stated ? If yes, could you state why?  My answers to possible questions:   This happened on SO, why don't you post it on MSO?   This happened on SO but I think it's applicable to all SE sites.  Why didn't you link the user or the chat conversation?   I want the user to remain anonymous unless he or she chooses to reveal him/her self. I will give the user a link to this question  Why do you care?   I find it offensive, not only to my religion but to any religion that believes in god. I posted this question to know what you guys and girls think about this. I live by the rules, so if it's acceptable by SE then so be it and I won't bother you again.  If you don't like it then move on.   I know that this is not a mosque/church/temple and that swearing  to a certain degree. But I don't see the point in insulting god, a religion or a race in a public profile. More over, it's not even built on arguments.