Timing method duration: always showing zero seconds?
How do I write a correct micro-benchmark in Java?
Should I use Named Pipes, or .NET Remoting to communicate with a running process on my machine? Is there any relation between the chromatic number of a graph $G$ and its complement $G'$ that are always true?  I saw these ones: $\chi(G)\chi(G')\geq n$ and $\chi(G)+\chi(G')\geq 2n$,  but I'm not pretty sure about them. How does quantization solve the ultraviolet catastrophe? The banner ads are in the wrong format for the right-hand ad slot:    These kinds of ads are not useful (because most of it is cropped) and should be excluded from being shown in that spot. Is it wasteful to use a heating element, instead of doing useful work? Consider a computer CPU consuming electrical energy to perform calculations and consequently emitting heat.  Assumption: That a CPU consuming x Watts of power, emits the same amount of heat as an incandescent heating element which consumes the same amount of power.  The rest of the question assumes that this is true: the energy has to go somewhere, and I can't see that the outcome of the calculations counts as "somewhere".  I've long repeated the claim that "wasteful" appliances such as incandescent lightbulbs, over-full kettles, computers left running, etc. are not wasting power if we make the assumptions:   the appliance is in a room which we aim to maintain at above a certain temperature, warmer than the external temperature (cf a home in winter) the room leaks heat to the outside faster than the "wasteful" appliances emit heat. the room contains an electric heater the electric heater is regulated by a thermostat   In these circumstances, I think (?), if a light bulb produces excess heat, its only effect is to cause the thermostat to switch off sooner, so what energy you've "wasted" in the light bulb, is "saved" at the heater.  I don't think that's controversial.  But my question is:   If a CPU does useful work, and emits all the input energy as heat as a side effect But a heating element emits the same heat, without doing useful work Is it therefore wasteful to use heating elements? Is it more efficient to (for example) run  on a CPU, to get "free" computation as a side-effect of heating?   One reason to heat a room with a heating element, rather than with CPUs, is that the heating element is much cheaper to produce. But ignoring the initial cost of the hardware, would a "heater" made out of 20 CPUs, each running at full capacity and consuming 50W each, output less thermal heat than a 1KW element that does nothing else useful?  To be useful, of course, the CPUs would need to output the result of their computations, which would account for a tiny amount of energy. Let's assume that's negligible.  I'm sure there's a flaw in there somewhere; probably that the assumption above is false. What have I missed? Customizing titlesec-etoc (further question) I need some help in relation to this exercise    "Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$."  I'm not allowed to use quotient groups in the proof, because the exercise is in the chapter before.   I tried by induction on $n$. The case $n=1,n=2$ are obvious, but even  the case $n=3$ is giving me trouble so I give up studying the general case of the inductive step.  My other approach was studying left or right coset of $G$. But I only proved that if $g \in aH$ then $g^2 \notin aH$ if $a \notin H$, and I can't find a way to demonstrate that $g^n \in H$. (my starting idea was to prove that every power of $g$ is in a different coset but then I realize that in this way I don't handle several case, for example $g$ has period strictly lesser than $n$ and in conclusion it doesn't prove the exercise)  Maybe I'm missing something about indexes, and this is why I asked here for some help,  (I can't use quotient groups because they are introduced later than this exercise, forgot to add this info in the beginning) Thanks in advance :) Removing nodes from an XmlDocument Why wave theory cannot explain photoelectric effect and provides evidence for particle nature of light? Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$ I'd like to show that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$ for all $x,y \ge 0$ and $p \in [0,1]$. I started out by defining a function $f(x,y)=(1+x)^p(1+y)^{1-p}$ and checking for critical points, but there are none in the domain I'm interested in. I think I'm probably missing a slick application of Jensen's or Holder's inequalities, but so far a proof eludes me. Any suggestions would be appreciated. Why did sampling boost the performance of my model? I have an imbalanced dataset with 88 positive samples and 128575 negative samples. I was reluctant to over/undersample the data since it's a biological dataset and I didn't want to introduce synthetic data. I built a Random Forest Classifier with this original dataset. I got an F1 score of 0 for the positive class. Zero precision. Zero recall. I cross-checked the predictions and test data. The model predicts some positives none of which are actually positive. Worst performance.  So, I tried to oversample the positive class. I upsampled the positives to 1000 samples. To my surprise, the F1 score for this dataset was 0.97, for the positive class. Then I tried lesser samples. I was able to achieve an F1 score of 0.83 with 200 positive samples, which is just 2.25 times of the original positive samples.  I would like to know why this occurs. For 88 samples, F1 score is 0.00 (rounded off to two digits). For 200 samples it's 0.83. There is no data leakage. All the features are engineered. I used imbalanced-learn module for oversampling. Can someone explain why is this difference in performance? I've googled and also searched the answers here but couldn't find my problem so here goes:  I know how to bevel a curve using another object and when I try it with a normal circle it's fine. But I'm trying to use this flat oval shape to bevel a larger curve of the same shape and it's not following the curve at the correct rotation. I've tried everything, rotating the bevel object, clicking random options in the object data menu.. I can't seem to budge it from looking how it is in the screenshot. In the screenshot you can see the curve I've failed to bevel correctly and also the bevel object in the bottom right.  Basically, I want the flat part of the oval to be above and below the curve, not on the sides as it is. I hope that makes sense. Anyone know what I need to do? I'm trying to run multiple Nodejs applications on Nginx server running on CentOS 7. I noticed that when I run a Nodejs app on some ports I get an 502 Bad Gateway error in the browser so I checked the error logs:  [notice] 12806#0: signal process started [crit] 12807#0: *13 connect() to 127.0.0.1:7777 failed (13: Permission denied) while connecting to upstream, client: **.**.99.58, server: myapp.com, request: "GET / HTTP/1.1", upstream: "http://127.0.0.1:7777/", host: "myapp.com" [crit] 12807#0: *13 connect() to [::1]:7777 failed (13: Permission denied) while connecting to upstream, client: **.**.99.58, server: myapp.com, request: "GET / HTTP/1.1", upstream: "http://[::1]:7777/", host: "myapp.com"   when I change the app to listen to 8008 for example everything is working fine. I checked permissions and if the process is running as root and everything seems ok. I played with the timeouts as well but no result. Can anyone help? How can I manage computers using my Firefox Sync account? I`m using Firefox Sync on a bunch of computers.   I would like to manage my account, by removing some computers. I can't find the place to do this, it should be on the Firefox Sync page, but the official page only has the privacy and download information. I'm looking to get the result of a command as a variable in a Windows batch script (see  for the bash scripting equivalent).  A solution that will work in a .bat file is preferred, but other common windows scripting solutions are also welcome. I have been reading Men With Brooms for a few days. I read a sentence which did not make any sense to me, so I landed here to get some help on it. I have pasted the sentence from the novel. Please go through it and let me know your valuable feedback on it.  An excerpt from the novel (Men With Brooms: A Sweeping Epic, paperback 2002, a novelization by Diane Baker Mason):     Gordon was about to walk away from the Impala when he saw it stop and his son get out. So it was real the boy had come.   As per my opinion it should have been:     Gordon was about to walk away from the Impala when he saw it stopped and his son got out. So it was real the boy had come.   I have two questions here:   Why did the writer use stop and get instead of stopped and got? As she is telling us a story which happened in the past. Let's say the writer is telling us her mind's situation and she used the present tense for it but why did she use stop and get instead of stops and gets? I would like to know: How come that  $$\sum_{n=1}^\infty n x^n=\frac{x}{(x-1)^2}$$  Why isn't it infinity? Let $f:\Bbb{R}\to\Bbb{R}$ be a function given by  $$f(x)=\begin{cases} \exp\left(\frac{1}{x^2-1}\right) &amp; \text{if }\vert x\vert\lt 1\\  0 &amp; \text{if }\vert x\vert\geqslant 1  \end{cases}$$  I would like to prove that $f\in C^\infty$, that is, $f\in C^k$ for all $k\in \mathbb{N}$. I think that it can be done by induction on $k$. If $\vert x\vert\gt1$, the problem is trivial. On other points, the base case is the simplest and the only that I'm be able to do. Can someone help me?  Thanks. I read this sentence in a book:     I just took part in a study over in the Psychology Department.   Why do we add over in front of in the here? Close and flag links do nothing on mobile site