Is it wrong to substitute $u=\sqrt x$ when integrating?  Here's what I mean, I have to integrate: $\int x \sin \sqrt x dx$.  I defined $u=\sqrt x$ so it's: $$\int u^2\sin u du=2u{\cdot}\sin\left(u\right)+\left(2-{u}^{2}\right){\cdot}\cos\left(u\right)+{C}$$  But when placing back $\sqrt x$ I get a totally different result from the integration of the original expression:   $$2{\cdot}\left(\cos\left(\sqrt{x}\right){\cdot}\left(6{\cdot}\sqrt{x}-{x}^{\frac{3}{2}}\right)+\sin\left(\sqrt{x}\right){\cdot}\left(3x-6\right)\right)+{C}$$  Shouldn't both expressions be equal and why aren't they?
I tried using integration by parts twice, the same way we do for  $\int \sin {(\sqrt{x})}$ but in the second integral, I'm not getting an expression that is equal to  $\int x\sin {(\sqrt{x})}$.  I let $\sqrt x = t$ thus, $$\int t^2 \cdot \sin({t})\cdot 2t dt =  2\int t^3\sin(t)dt = 2[(-\cos(t)\cdot t^3 + \int 3t^2\cos(t))] = 2[-\cos(t)\cdot t^3+(\sin(t)\cdot 3t^3 - \int 6t \cdot \sin(t))]]$$  which I can't find useful.
As far as I understand, one of the main claimed problems with initializing e.g. a feed-forward neural network (with several $\text{tanh}$ or $\text{ReLU}$ layers) with $W=0$ is that it doesn't break "network symmetry", meaning, backpropagation would propagate the same error through all such units (i.e. "nudging all weights in the same direction"). This is, I presume, undesirable because we would not be learning "different" calculations through different paths of the network.  However, I'm confused why that even matters in this case given the fact that if $W$ ever drops to 0, we will effectively be propagating no gradients at all through the network, since W=0 would multiply all errors from the output and prevent any learning.  Put another way, even if $W=0$ does not break network symmetry (wasting calculations and paths in the network) is it correct to say that if $W=0$ (e.g. by initialization) we are effectively killing gradients in a neural network, and thus no learning can take place? I'm an Egyptian citizen, who holds Schengen visa and stay permit in Italy. Can I go to UK for some days with my stay permit and Schengen visa? SQL Server 2016 memory optimised table: Precreated files constantly growing I have a memory optimised table in SQL Server 2016, with file durability enabled. The table is only 100MB. SQL Server is constantly creating new files on disk, which start off at a few hundred MB, but then grow constantly until the drive runs out of space then they clear down and the process starts again. The files are growing at about 900MB an hour. Running the SQL below shows that all the space is in Precreated Data - so it's not even actually storing large amounts of data, just allocating space to use later.  SELECT state_desc, file_type_desc, COUNT(*) AS [count],    SUM(file_size_in_bytes) / 1024 / 1024 AS [on-disk size MB]    FROM sys.dm_db_xtp_checkpoint_files   GROUP BY state, state_desc, file_type, file_type_desc   ORDER BY state, file_type     File growth on the file group is set to unlimited, so I'm assuming I can set a value on this and stop it growing, but I can't find anything to say why it's allocating so much space in the first place. The data in the table does change very rapidly (a lot of inserts and deletes as the data is constantly processed, but it the data that isn't Precreated never gets over 4GB.  Is there a setting in SQL Server that controls this file precreation? Is it safe to set a limit on the autogrowth for the file group? If $f:[0,1]\to\mathbb R$ is continuous and $\int_0^x f(t)dt = ∫_x^1f(t)dt$ then prove that $f(x)=0$.  I suppose that $f(x)$ isn't zero, set $g(x)= \int_y^xf(t)dt$ with $y\in[0,1]$ and use Bolzano but I don't know if it's right. Ubuntu 14.04 Wireless not working: no network interface. Atheros [168c:003e] device Get referenced node fields in twig In Drupal 8, I have a content type, that has an "entity_reference" field and I wish to access the referenced node's fields in twig template. the kint() output for the field is:   In this list I can't find the referenced node's field values. How can I (if at all possible) load the node or node fields/values in twig?  Best,  Alari What is this yellow and white mass inside my red cabbage? When I dock my Windows 7 laptop, I want it to prefer the wired ethernet connection over WiFi.  This is a pretty straightforward thing to do on my Mac - I just reorder my network preferences, and it "does the right thing." I just can't figure out how to achieve the same thing on my Win7 laptop.  So, when I'm docked, it connects to WiFi, and then fails to connect to servers on the local wired network. How do I fix this? \begin{eqnarray*} M&amp;=&amp; \max{\left \{a,b,\frac{a+b}{2},\right}\\ &amp;&amp; a+b,a+b/2\Bigg\} \end{eqnarray*} If $f(x)$ is differentiable at x, I need to prove that $\lim_{h\to0}\frac{f(x+h)-f(x-h)}{2h}$ exist and is finite.  so if $f(x)$ is differentiable at a $x$, the difference quotient exist for this point, and also $f(x)$ must be continuous at x as well  so that mean that:  $\lim_{h\to0^+}\frac{f(x+h)-f(x)}{h} =  \lim_{h\to0^-}\frac{f(x+h)-f(x)}{h}$  and that: $\lim_{x\to x_0^+}=\lim_{x\to x_0^-}=f(x_0)$  I know I should probably use arithmetic limit laws to prove this but I can't see how what I figured out could help me. any help with that?  Thanks! How do I identify an airport’s official free Wi-Fi network? While traveling in the Berlin Tegel airport (TXL), I wanted to get on Wi-Fi. I found three unsecured networks in addition to a number of password-protected networks.   _Free_TXL_WiFi airberlin Berlin Tegel Airport WiFi   I had no idea which of these were an official Wi-Fi network provided by the airport and which were provided by other people, potentially for malicious purposes like capturing my network traffic. Presumably the official one uses a captive portal to allow internet access.  Is there any way to determine which Wi-Fi network is the official one provided by the airport? Would airport staff such as at the ticketing booths know? Are there official lists available somewhere?  I’d like an answer that is applicable to airports generally, rather than specific to the Berlin Airport. Also, please don’t just give a blanket “don’t use any public Wi-Fi network” answer; I know there are risks associated with it, but sometimes it is a necessity and so I want to know how to identify the airport-provided one.   suggests there are no official Wi-Fi networks, but the answers are six years old, so it’s not clear if things have changed or if none of the networks I saw were official. What is the difference between Reduce and Solve? Why does demand for stock rise when a company appears to have high future value? So a company decides to raise money by selling shares of its stock. The stock is offered at an initial price of their determination. The stock is then traded in a market where forces of supply and demand, as well as speculation, affect its price.  When a company performs well (or makes decisions that will likely increase the company's earnings in the future), more people want to buy that stock than do people wanting to sell it. This creates demand for that stock which causes its sell/bid prices rise. When a company performs poorly, the opposite occurs; more people want to sell the stock than want to buy. This creates a surplus that causes sell/bid prices to fall.  Understanding this, people speculate over company performance to determine the future behavior of a stock, and attempt to "buy low, sell high" or "borrow high, return low" in order to make a profit.  But my question is regarding the first part of that process. What is it about company performance that causes the perceived value of its stock to rise? This is especially perplexing since I would guess that most people don't exercise their voting rights, and many stocks don't pay dividends.  It's not like a shareholder has any direct financial gains from increased company earnings (speculative stock pricing notwithstanding).  What is the intrinsic value of the stock?  It seems to me that all participants in a stock market tacitly agree that stock price will have a direct correlation with company performance. So another way of asking the question is, would an opposite agreement hold? What financially (this isn't a question about logistics, communication, or feasibility) stops all participants in a market from agreeing to value a particular company's stock inversely with respect to the company's performance?  Since I feel like I can't quite nail down my question, another form of it would be, why is stock market behavior driven by company performance? Is there a way to Inset in the opposite direction (not Outset)? Is there an operation similar to inset that creates faces in the opposite direction? That is, instead of creating faces inwards, they create faces outwards? A normal inset operation:  What I would like: My keyboard doesn't have an Fn key so I can't get the coordinates to show up. I don't know how to get into the multiplayer settings and Shift + F3 doesn't work either.  How can I fix this? I am trying to use squared loss to do binary classification on a toy data set. I am using mtcars data set, use mile per gallon and weight to predict transmission type. The plot below shows the two types of transmission type data in different colors, and decision boundary generated by different loss function. The squared loss is $\sum_i (y_i-p_i)^2$ where $y_i$ is the ground truth label (0 or 1) and $p_i$ is the predicted probability $p_i=\text{Logit}^{-1}(\beta^Tx_i)$. In other words, I am replace logistic loss with squared loss in classification setting, other parts are the same. For a toy example with mtcars data, in many cases, I got a model &quot;similar&quot; to logistic regression (see following figure, with random seed 0).  But in somethings (if we do set.seed(1)), squared loss seems not working well.  What is happening here? The optimization does not converge? Logistic loss is easier to optimize comparing to squared loss? Any help would be appreciated.  Code d=mtcars[,c(&quot;am&quot;,&quot;mpg&quot;,&quot;wt&quot;)] plot(d$mpg,d$wt,col=factor(d$am)) lg_fit=glm(am~.,d, family = binomial()) abline(-lg_fit$coefficients[1]/lg_fit$coefficients[3],        -lg_fit$coefficients[2]/lg_fit$coefficients[3]) grid()  # sq loss lossSqOnBinary&lt;-function(x,y,w){   p=plogis(x %*% w)   return(sum((y-p)^2)) }  # this random seed is important for reproducing the problem set.seed(0)  x0=runif(3) x=as.matrix(cbind(1,d[,2:3])) y=d$am opt=optim(x0, lossSqOnBinary, method=&quot;BFGS&quot;, x=x,y=y)  abline(-opt$par[1]/opt$par[3],        -opt$par[2]/opt$par[3], lty=2) legend(25,5,c(&quot;logisitc loss&quot;,&quot;squared loss&quot;), lty=c(1,2)) Comment deletion notification I think you should be notified if anything of yours is deleted or even flagged, preferably with some explanation (even if it's a simple categorisation like #rude, #irrelevant, #incorrect) and who did it.  Recently, a couple of comments of mine vanished without warning or evidence afterwards. I'm fine with deletion, but I think it should be used sparingly and be based on democratic decisions. What's the harm of letting a comment simply sit with no up-votes or responses rather than outright removal? Or allow downvoting and then negatively voted comments are hidden by default?  I get the impression that anything I post could be deleted. Very few people want to be unpopular or do the wrong thing. It takes time to understand what something is about and how best to use it (this site). Whether or not what I posted deserved to be deleted is irrelevant because I got no feedback. No-one can learn without feedback. The number of frivolous comments with many upvotes I've seen shows how inconsistently the rules are applied. A community that gives too much power to highly rated users won't grow but turn stagnant.  Sorry if this was rude, inappropriate or pathetic. I'm aware that similar discussions have occurred. In any case, I'll continue to use the site and move on... Why does C# disallow readonly local variables? Cardinality of a set that consists of all existing cardinalities What is the mysterious stranger doing in my vault?