I was reading a  published on Dropout. What I find difficulty in understanding that, In the training phase, a unit is present with a probability p and not present with a probability 1-p. In the test phase, all units are present, but we multiply each of them with the probability.   Now, is it like, let we have 4 input units originally named a,b,c,d. In the training stage, after applying dropout, with a dropout rate of 0.5, we are left with units a and c. So, As in the test stage, all the units are present, so, is it like, we multiply each of the units with 0.5? Also, Is p defined for each of the units in the network, or for the entire Neural Network?  Also, In doing so, how is the result same for training and test stage?
When applying dropout in artificial neural networks, one needs to compensate for the fact that at training time a portion of the neurons were deactivated. To do so, there exist two common strategies:   scaling the activation at test time inverting the dropout during the training phase   The two strategies are summarized in the  below, taken from .  Which strategy is preferable, and why?    Scaling the activation at test time:    Inverting the dropout during the training phase:
Converting MultiLinestring to Linestring with PostGIS I have a multiline string and want to convert it to a linestring in order to use some functions that only work with linestrings. I used ST_Dump() and got a collection of my geometries. If I merge them back together, I still get the multilinestring. Should I get the Npoints and combine them together or something, in order to end up with a simple linestring? ST_LineMerge() also does not work on my multilinestring, it returns the same. my example,  MULTILINESTRING((-3.16420835153456 55.9269166007097,-3.164222 55.926918),(-3.1642070167833 55.9269296196706,-3.16421351659546 55.9268662214904),(-3.16421351659546 55.9268662214904,-3.16421636372824 55.9268384509897),(-3.16421636372824 55.9268384509897,-3.16422182573761 55.9267851753802),(-3.16422182573761 55.9267851753802,-3.16422870102352 55.926718114886),(-3.16422870102352 55.926718114886,-3.16423309121073 55.926675293667),(-3.16423309121073 55.926675293667,-3.16423565148822 55.9266503211093),(-3.16423565148822 55.9266503211093,-3.16424103159897 55.9265978443265),(-3.16424103159897 55.9265978443265,-3.16424680776317 55.9265415044985),(-3.16424680776317 55.9265415044985,-3.16425267254583 55.9264843002995),(-3.16425267254583 55.9264843002995,-3.16425541048045 55.9264575949012),(-3.16425541048045 55.9264575949012,-3.16426111146586 55.9264019883556),(-3.16426111146586 55.9264019883556,-3.1642667032531 55.9263474469124),(-3.1642667032531 55.9263474469124,-3.16426957768543 55.9263194101362),(-3.16426957768543 55.9263194101362,-3.16427488261739 55.9262676666359),(-3.16427488261739 55.9262676666359,-3.16428009893088 55.9262167875066),(-3.16428009893088 55.9262167875066,-3.164282741107 55.9261910161221),(-3.1642875546472 55.9261440655823,-3.164282741107 55.9261910161221),(-3.1642875546472 55.9261440655823,-3.16429466890915 55.9260746741522),(-3.16429466890915 55.9260746741522,-3.16430092974527 55.9260136069079),(-3.16430092974527 55.9260136069079,-3.16430822838418 55.9259424170929),(-3.16430822838418 55.9259424170929,-3.16431547242401 55.925871759829),(-3.16431547242401 55.925871759829,-3.16431448732505 55.9258328901507),(-3.16431770120536 55.9257327846001,-3.16431547242401 55.925871759829),(-3.164339 55.925777,-3.16431770120536 55.9257327846001)) How to reset KDE desktop to default on Ubuntu 14.04? KDE and Gnome Desktops were looking awesome on my Ubuntu 14.04 LTS, today everything seemed ugly. Slim long font, arabic letters in Chromium/Firefox are barely readable no matter how big I made them on system font settings. How can I get back to my previous looks settings, without compromising other settings and tweaks?  Here are my versions:  kde4-config -v:  Qt: 4.8.6 KDE Development Platform: 4.13.3 kde4-config: 1.0   kded4 --version:  Qt: 4.8.6 KDE Development Platform: 4.13.3 KDE Daemon: 4.13.3 Understand the meaning of `$_` Could you explain the following sentences from Bash manual about $_, especially the parts in bold,  maybe with some examples?      At shell startup, set to the absolute pathname used to   invoke the shell or shell script being executed as passed in the environment   or argument list.      Subsequently, expands to the last argument to the previous   command, after expansion.      Also set to the full pathname used to invoke each   command executed and placed in the environment exported to that command.     When checking mail, this parameter holds the name of the mail file. I am trying to find examples of maps between topological space which are local homeomorphism but not covering maps. Especially, how twisted has to be such a counterexample : can it be a local diffeomorphism between connected manifolds which is not a covering map ?   I found here() a nice proposition which state that a local homeo from a compact space to a connected Hausdorff space is a covering map.   I am interested in all type of counterexamples, from non-Hausdorff spaces to surfaces, to get a better picture of the differences between covering maps and local homeomorphisms.  Thank you ! We walk or ride on our vehicles to our destinations daily. Does our movement have any effect on the rotation of the earth according to Newton's law? What will be the effect if we move all the peoples along with their vehicles at their maximum velocity in one line in one direction along the equator? How much effect will it make? could you help me on this integral ? $$\int \frac{1}{\cos(x)}\,\mathrm dx$$ Here's what I've started : $$\int \frac{1}{\cos(x)}\,\mathrm dx = \int \frac{\cos(x)}{\cos(x)^2}\,\mathrm dx = \int \frac{\cos(x)}{1-\sin(x)^2}\,\mathrm dx$$ Now, I did : $u = \sin(x)$, so $\mathrm du = 1$. Now I have : $$\int \frac{\text{???}}{1-u^2}\,\mathrm du$$ But at this point, I think I did the most of the job but I'm stuck. Could you help me to solve this integral please (to the integration by substitution at the end) ? Thanks EDIT : Now I follow the steps and I got : $$\int \frac{1}{1-u^2}\,\mathrm du$$ Doing the partial fraction I got $A = 1/2$ and $B = 1/2$. So basically I have : \begin{align} &amp; \int \frac{1}{1-u^2}\,\mathrm du = \int \frac{1/2}{1+u}\,\mathrm du + \int \frac{1/2}{1-u}\,\mathrm du \\[8pt] = {} &amp; \frac 1 2 \left(\int \frac{1}{1+u} \, du - \int \frac{1}{1-u} \, du\right) \\[8pt] = {} &amp; \frac 1 2 \ln\left(\frac{1+u}{1-u}\right) = \ln\left(\left(\frac{1+\sin(x)}{1-\sin(x)}\right)^{1/2}\right) \\[8pt] = {} &amp; \ln \left(\frac{\sqrt{1+\sin(x)}}{\sqrt{1-\sin(x)}}\right) = \ln\left(\frac{\sqrt{1+\sin(x)}}{\sqrt{\cos(x)^2}}\right) \\[8pt] = {} &amp; \ln\left(\frac{\sqrt{1+\sin(x)}}{\cos(x)}\right) \end{align} Here's what my teacher got :  What's wrong with what I did ? Did I miss something ? How to find architecture of my PC and Ubuntu? How to install packages to external drive (and run them)? I am running Xenial 16.04 and looking to install packages to an external drive - my computer has a 32gb SSD so it would be very useful to me to be able to use an external drive.  In a quick search I found a framework called  which seems to be designed to package all dependencies for a program (chromium, GIMP, some python packages, etc), but haven't had time to look into it.   seems to be looking for the same solution I am.   Thanks, Chris How to reset evolution settings to defaults? I have not used Evolution for long time now and I would like to reset all the settings and start from scratch. How would I be able to do this? Does any skill have a global cooldown? I am new to this game, and will try to optimize my game-play as much as possible. I will do this by making macros for my spells and abilities.  Are there global cooldown on spells and abilities in League of Legends?  Since this is important regarding macros to trigger spell and ability combos.  A Global Cooldown(GCD) is a cooldown which affect most if not all abilities, spells or items when using an ability, spell or item.   In most games it is there to prevent macroing/spamming of multiple instant abilities, spells or items, and usually has a set short duration independent of the ability, spell or items normal Cooldown. What are the 'types' of parametric down conversion? PGFPlots: Understanding how to draw plots on different layers and arrange them Do you get Hex Warrior's Cha bonus with a two-handed Pact Weapon? Hex Warrior says:     you can touch one weapon with which you are proficient and that lacks the two-handed quality. When you attack with that weapon you can use your Charisma for attack and damage rolls.   later the ability says:     This benefit extends to every weapon conjured with the Pact of Blades feature, no matter the type.   (emphasis mine)  Does this allow me to use my charisma with 2 handed weapons(provided it is my Pact Weapon and my Hex Warrior Blade)?  This question is not the same as . That one is asking how many weapons, I'm asking if type means 2 handed or something else(Slashing or Ranged for examples). enclosing a lstlisting environment inside my own environment using matlab-prettifier Why do liquids boil when their vapor pressure equals the ambient pressure? Given that the boiling point of a liquid is the temperature at which the vapor pressure is equal to the ambient (surrounding) pressure, what significance does a liquid's vapor pressure have in the formation of bubbles that happens at and above the boiling point?    The definition of boiling point seems to imply that the pressure inside of the bubbles must be at least as great as the liquid's vapor pressure in order to balance the outside pressure, but is there any particular reason why the pressure inside of the bubbles is related to the vapor pressure?    The vapor pressure seems to be a measurement describing the tendency of the molecules to escape from the surface of the liquid, but I don't see how that relates to bubble formation within the liquid.  This question has bothered me for a while, so any help would be much appreciated. I already have the "Edit Questions And Answers" privilege. Yet, if I approve someone else's edit, I'm told that more votes will be required before the edit is accepted.  This seems a bit peculiar to me, since I could just copy the edited version and paste it myself. Possible Beamer bug: Frame number has different color than date in infolines footer What is the best way to copy a folder and all subfolders and files using c# I am unable to understand what exactly is critical value.My question here is why do we fail to reject a null hypothesis when the test statistic is within the range of critical value.  What i am trying to ask is what is the property of the critical value that makes the hypothesized value to fall within the range implied by the critical value.  Thanks in advance Installing QGIS with ECW support on Mac?