Universities recommandations and choices
How does the admissions process work for Ph.D. programs in the US, particularly for weak or borderline students?
Looking for a book with parallel universes like pages, possibly with "maze" in title, and a black Jewish female character Looking for a book. A series,  actually.  The main characters were a Jewish man and a black woman who was his wife. There was a running gag when she would tell people her last name and they thought it was unusual that a black woman would have a Jewish name.    They went on adventures in parallel dimensions. I believe that each book had a word repeated in the title, maybe "mirror?" Or "maze?" Or "page..."  it seems they jumped into worlds through a tool like a mirror or a book.   The parallel universes were like pages, and the pages closest to you were most similar but the further you got the further they were from your life.  One page over might be that you had something different for breakfast and so now you have a tummy ache, a few more pages over you might have become a prostitute, too far and it was theorized that humans had evolved differently altogether, I didn't get that far in the series.  For adults, and humorous.  I read them about 15 years ago, so they are not new. I would love to find them again. Lost/Deleted dpkg (package manager for Debian). How do I get it back? Integral $\int_0^1\sqrt{1-x^4}dx$ I am asked to show $\int_0^1\sqrt{1-x^4}dx=\frac{\{\Gamma(1/4)\}^2}{6\sqrt{2\pi}}$. I know the gamma function is defined by $\Gamma(n)=\int_0^\infty x^{n-1}e^{-x}dx$. I tried to substituted $x^2=\sin(t)$ but couldn't go further. I am really questioned how a radical function can convert to an exponential one? :-0 Thank you. Can "Mr", "Mrs", etc. be used with a first name? Is it correct to use Mr/Mrs with a first name? Symbols instead of numbers as footnote markers How to find the foreach index? What is the definition of a "feature map" (aka "activation map") in a convolutional neural network? Intro Background Within a convolutional neural network, we usually have a general structure / flow that looks like this:  input image (i.e. a 2D vector x)   (1st Convolutional layer (Conv1) starts here...)  convolve a set of filters (w1) along the 2D image (i.e. do the z1 = w1*x + b1 dot product multiplications), where z1 is 3D, and b1 is biases. apply an activation function (e.g. ReLu) to make z1 non-linear (e.g. a1 = ReLu(z1)), where a1 is 3D.   (2nd Convolutional layer  (Conv2) starts here...)  convolve a set of filters along the newly computed activations (i.e. do the z2 = w2*a1 + b2 dot product multiplications), where z2 is 3D, and and b2 is biases. apply an activation function (e.g. ReLu) to make z2 non-linear (e.g. a2 = ReLu(z2)), where a2 is 3D.    The Question The definition of the term &quot;feature map&quot; seems to vary from literature to literature. Concretely:  For the 1st convolutional layer, does &quot;feature map&quot; corresponds to the input vector x, or the output dot product z1, or the output activations a1, or the &quot;process&quot; converting x to a1, or something else? Similarly, for the 2nd convolutional layer, does &quot;feature map&quot; corresponds to the input activations a1, or the output dot product z2, or the output activation a2, or the &quot;process&quot; converting a1 to a2, or something else?  In addition, is it true that the term &quot;feature map&quot; is exactly the same as &quot;activation map&quot;? (or do they actually mean two different thing?)  Additional references: Snippets from :  *The nomenclature is being used loosely here. In particular, I'm using &quot;feature map&quot; to mean not the function computed by the convolutional layer, but rather the activation of the hidden neurons output from the layer. This kind of mild abuse of nomenclature is pretty common in the research literature.   Snippets from :  In this paper we introduce a visualization technique that reveals the input stimuli that excite individual feature maps at any layer in the model. [...] Our approach, by contrast, provides a non-parametric view of invariance, showing which patterns from the training set activate the feature map. [...] a local contrast operation that normalizes the responses across feature maps. [...] To examine a given convnet activation, we set all other activations in the layer to zero and pass the feature maps as input to the attached deconvnet layer. [...] The convnet uses relu non-linearities, which rectify the feature maps thus ensuring the feature maps are always positive. [...] The convnet uses learned filters to convolve the feature maps from the previous layer. [...] Fig. 6, these visualizations are accurate representations of the input pattern that stimulates the given feature map in the model [...] when the parts of the original input image corresponding to the pattern are occluded, we see a distinct drop in activity within the feature map. [...]  Remarks: also introduces the term &quot;feature map&quot; and &quot;rectified feature map&quot; in Fig 1.  Snippets from :  [...] One dangerous pitfall that can be easily noticed with this visualization is that some activation maps may be all zero for many different inputs, which can indicate dead filters, and can be a symptom of high learning rates [...] Typical-looking activations on the first CONV layer (left), and the 5th CONV layer (right) of a trained AlexNet looking at a picture of a cat. Every box shows an activation map corresponding to some filter. Notice that the activations are sparse (most values are zero, in this visualization shown in black) and mostly local.   Snippets from   [...] Every unique location on the input volume produces a number. After sliding the filter over all the locations, you will find out that what you’re left with is a 28 x 28 x 1 array of numbers, which we call an activation map or feature map. I wrote a script to create a big number of heat maps for a given scenario. I would like to save the result of every heat map as an PNG image. I have figured it out doing it with simple Map Rendering but the quality of the result is too low. Furthermore I would like to export to OpenLayers using the same code, which does not seem to be possible with simple rendering.   Now I am trying to do it with QgsComposition instead. Manually in the Map Composer you can just set the paper color to transparent and disable the background of the map canvas.   This is the code that I have so far. I just cannot figure out why it is not working. The result png-file always has a white opaque background.   My OS is Windows 7 and I'm using QGIS 2.6 Brighton.  I hope someone can help me out here.  # PARAMETERS mainPath = 'path/to/folder/' filename = 'filename' imageType = "png" imageWidth_mm = 400 imageHeight_mm = 160 dpi = 300  mapRenderer = iface.mapCanvas().mapRenderer()  c = QgsComposition(mapRenderer) c.setPlotStyle(QgsComposition.Print)  c.setPaperSize(400, 160)  x, y = 0, 0 w, h = c.paperWidth(), c.paperHeight() composerMap = QgsComposerMap(c, x ,y, w, h) c.addItem(composerMap)  # get all items and disable the backgrounds itemList = c.items() c.removeItem(itemList[2]) c.removeItem(itemList[2]) itemList[2].setBackgroundEnabled(False) itemList[3].setBackgroundEnabled(False) # add them to the composition c.addItem(itemList[2]) c.addItem(itemList[3])  c.refreshItems() c.refreshDataDefinedProperty(QgsComposerObject.AllProperties)  c.setPrintResolution(dpi) dpmm = dpi / 25.4 width = int(dpmm * c.paperWidth()) height = int(dpmm * c.paperHeight())  # create output image and initialize it # image = QImage(QSize(width, height), QImage.Format_ARGB32) image = QImage(QSize(width, height), QImage.Format_ARGB32_Premultiplied) image.setDotsPerMeterX(dpmm * 1000) image.setDotsPerMeterY(dpmm * 1000) #image.fill(0)  imagePainter = QPainter(image)  # This part does not seem to have any effect #brush = QBrush(Qt.BrushStyle(0)) # transparent brush # #imagePainter.setBackgroundMode(0) #c.setBackgroundBrush(brush)  c.renderPage( imagePainter, 0 ) imagePainter.end()   imageFilename =  mainPath + filename + '.' + imageType image.save(imageFilename, imageType) print 'image saved' print 'done' If $\mathfrak p \subset R$ is a prime ideal, prove that for every nilpotent $r \in R$ it follows that $r \in \mathfrak p$.   The only hint that my tutor gave me was to use induction. Can someone explain what he means by this?  Thanks for the help! Run a command without making me wait Meaning of syntax $N(\mathbf{y} \mid \mathbf{0}, \mathbf{K})$ (multivariate normal distribution) Multiplying Binomial Terms Prove that $\int_0^{\infty} \frac{\sin x}{x^p}\, dx$ converges for $0<p<2$ For the following block of code:  For I = 0 To listOfStrings.Count - 1     If myString.Contains(lstOfStrings.Item(I)) Then         Return True     End If Next Return False   The output is:  Case 1:  myString: C:\Files\myfile.doc listOfString: C:\Files\, C:\Files2\ Result: True   Case 2:  myString: C:\Files3\myfile.doc listOfString: C:\Files\, C:\Files2\ Result: False   The list (listOfStrings) may contain several items (minimum 20) and it has to be checked against a thousands of strings (like myString).  Is there a better (more efficient) way to write this code? so I stumbled upon this equation/formula, and I have no idea how to prove it. I don't know how should I approach it: $$ \sqrt{2 + \sqrt{2 + \cdots + \sqrt{2 + \sqrt{\vphantom{\large A}2\,}\,}\,}\,}\ =\ 2\cos\left(\vphantom{\Large A}\pi \over 2^{n + 1}\right) $$  where $n\in\mathbb N$ and the square root sign appears $n$-times.  I thought about using sequences and limits, to express the LHS as a recurrence relation but I didn't get anywhere.  edit: Solved, thanks for your answers and comments. Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is... Why does an error appear every time I try to open the Ubuntu Software Center? There is a glitch on the Ubuntu Software Center and whenever I open it an error appears and it keeps loading and never opens.  Why does this happen?  I have installed Ubuntu 13.04 on a disk and partitioned it.  Please help me and ask for excess information if you need it.  If you know of any duplicates please show me them!!  I get the following error in a terminal  SystemError: E:Type '&lt;!DOCTYPE' is not known on line 1 in source list /etc/apt/sources.list.d/medibuntu.list   The /etc/apt/sources.list.d/medibuntu.list file contains a HTML document. How can I make 3D Text in Russian? I've seen a similar question on BSE about entering foreign languages into 3D Text, but it doesn't help. I've tried using two different fonts (both of which support Russian). I've tried enabling International Fonts in Blender's User Preferences, but it doesn't work as well. It either types English text with Greek letters or displays empty vertical rectangles.   If anyone has been able to add text in any foreign language, please let me know.  I actually found out that it can be easily done through Text Editor, which would be probably the best way for me since I would prefer to paste my text. Can anyone perhaps guide me through? How to use GROUP BY to concatenate strings in MySQL? Basically the question is how to get from this:   foo_id   foo_name 1        A 1        B 2        C   to this:   foo_id   foo_name 1        A B 2        C Orange squares appearing on render?