Hi.. I am using latex for my thesis, I need some help in titles pages
Add 'Page' above page numbers in Table of Contents
Is Using Digital Signatures to prove identity a zero knowledge proof? Suppose Alice publishes a book with a public key in it, and later wants to prove that she wrote the book. She could sign challenge messages with her private key, and others could verify those signed messages. Alice is proving she knows a private key without revealing anything about it.  Is this an example of an interactive zero knowledge proof?   Or does this example somehow not apply to zero knowledge proofs? Construction of a Borel set with positive but not full measure in each interval Why is carbon dating limit only 40,000 years? I want to reinstall Ubuntu, but I also want all information and settings to disappear. So everything looks like the first time I installed it. Is it possible to do so via Terminal? Or what are the steps I should follow? I own a Panasonic DMC-G81 (same as G80/G85) with in-body Image Stabilization.  When turned on everything is just fine, but when turned off, the sensor is wobbling around in the body. When no lens attached, it's clearly visible moving about 1/2 cm in the body. I didn't find anything about it in the internet. Shouldn't the sensor be in a kind of parking position, should I worry about the sensor ?  I'm not sure if that is the usual behavior, maybe someone with the same or similar body can have a look. What does $dx$ mean? $dx$ appears in differential equations, such us derivatives and integrals.  For example, a function $f(x)$ its first derivative is $\dfrac{d}{dx}f(x)$ and its integral $\displaystyle\int f(x)dx$. But I don't really understand what $dx$ is. Probability of $p(x_1<x_2<\max(x_3,x_4))$ Run a GUI program at startup I am using Ubuntu 14.04. I wrote a small script named trial. The contents of the script are as follows:   #!/bin/sh SHELL=/bin/sh PATH=/bin:/sbin:/usr/bin:/usr/sbin      sh -c firefox   I copied the script to /etc/init.d, modified permission using chmod +x trial and used update-rc.d trial defaults. The file made link but when I rebooted the machine. It did not run firefox. I tried cron @reboot but with no success. I tried rc.local too again failure. Amongst North Indian Students, the phrase "give an exam" is very popular. These students use the phrase to describe the act of writing the answers to examination questions.  The reason being, in Hindi, it's known as "exam dhena" which translates literally to "to give an exam".  In South India, however, a majority of people use the phrase "to take up an exam".  Which of these usages is more common/appropriate/grammatical? (As a prof I have developed a strange aversion toward the "give an exam" phrase; I find it wrong and ugly.) What is the meaning of the term "linear" After the upgrade I can't figure out how the new shield system works. I have the option to discard the shield, and I notice I have a new potion in the inventory.  More importantly, I got attacked (and lost) twice in a short amount of time and don't have a shield. When do you now get shield? poll() failed, context incorrect? - Example: bpy.ops.view3d.background_image_add() Looking for a command to create the geometry line symbol (\overline with arrows on both ends) I need a way of encoding the geometry line symbol. $\overline{AB}$ gives me the line segment symbol and $\overrightarrow{AB}$ gives me the ray symbol, I need a way to get a bar over the letters that has arrows on both ends. $\overrightleftarrow{AB}$ does not work.   Thanks! Referencing subfigures in main caption (with \subfloat and \subref) I've used subfloat to include subfigures, with their relevant labels but with empty captions. what I'm going to do is to reference these figures with \subref in the main caption of the figure. But what I get is only ?? signs in the caption [main caption]. I can't figure out what's the problem. this is what I have:  \begin{figure} \centering \subfloat[][] { \includegraphics[scale=0.55]{signal} \label{signal_model} } \subfloat[][] { \includegraphics[scale=0.55]{amplitude} \label{amplitude_mod} } \caption{phase noise variability: \subref{signal model} some text \subref{amplitude_mod} some other text} \end{figure} Define additional math operators to be typeset in roman Mathematical operators, such as function names, should be set in roman type, not italics. Latex already has commands for some operators, including \max, \min, and \log.  How can I define additional such commands? Most common method for deciding when to stop training a neural net on a batch I have created my own neural net which is using batch gradient descent. In other words, it trains on batches of examples all at once.  My issue is trying to figure out when to stop the training of the batch. I'll try to make things as understandable as possible since there are so many options, but please comment if you need clarification.  Each batch allows me to compute a list of output errors that correspond to the error the computer has on each example. Each error is a vector with elements equal to the number of output neurons.  Let each error vector be notated by e1, e2, e3, ... so the list of output errors is [e1, e2, ...]. Let an error vector in general be notated by e.  Now there are 2 things we can do to a vector or a list:   Average: average all of the elements in a vector or list. This will be notated by the function a(). For example to find the average error of an example we would do a(e) Check: make sure that each element in the vector or list is below a certain value. If any of the elements are too high, we continue to train on the entire batch. (This function can also be applied to a single value.) This will be notated by the function c(). For example, if we wanted to make sure the average error in e was low enough, we would do c(a(e)) Sum: add up all of the elements in the vector or list. This will be notated by the function s(). For example, s(e) would be totaling the error found in error vector e.   Here are the methods I have determined for deciding when to stop gradient descent:   Iterative: just run the training a certain number of times Average of averages: Find the average error of each example, then find the average of those and make sure it's below a certain amount. This is given by the formula c(a([a(e1), a(e2), ...])) Specific error: Check to make sure the error in each output neuron is below a certain amount. This is given by the formula c(e1), c(e2), ... Specific averages: Check to make sure the average error in each example is below a certain amount. This is given by the formula c([a(e1), a(e2), ...]) Sum of sums: Total up all the error in the entire batch and then make sure it's low enough. This is given by the formula c(s([s(e1), s(e2), ...]) Sum of averages: Find the average error of each example, then add up all those and make sure it's below a certain amount. This is given by the formula c(s([a(e1), a(e2), ...])) Average of sums: Compute the average total error in each example, and then make sure it's below a certain amount. This is given by the formula c(a([s(e1), s(e2), ...])) Specific sums: Check to make sure the total of the error in each example is below a certain amount. This is given by the formula c([s(e1), s(e2), ...])   So my question is this:  Which one of these options is most commonly used when training neural nets? Why? (Is there another option that I've missed?)  (Edit: I have found a very general version of this question , where the answers seem to say there is no specifically good way. If that is still true, please say so in your answer. Note that this is not a duplicate, as I explain the specific methods I would like to use.)  Edit: as A.D pointed out, summing is pretty useless because it depends on how many values are in each list/array/batch. And if you know how many examples there are, you can just use averaging. So, the methods involving "summing" have been cut. Use of "Proper" as a postpositive adjective I have an inkling that the following word usage is grammatically-correct; however, it is immensely difficult to search for confirmation, as all I receive for queries like &quot;Proper as an adjective&quot; are reams of results on &quot;Proper adjectives&quot;. The word itself I am using as a postpositive adjective, similar in form to the phrase &quot;time immemorial&quot;.  The shelter remains in name only; the shelter proper is in another town. Work in theory remained, although operations proper had mostly been outsourced.  Can anyone advise? I have a cheap Chinese made tablet from Dubai called the Crony Dubai (www.cronydubai.com). It has a micro B, mini HDMI and a USB labeled as "Host" as well as a micro SD slot. It came with a micro B to USB adapter in box, and its running Ice Cream Sandwich. Is there a way to load Ubuntu on it? Also the tablet is very buggy and crashes often, would that be due to the tablet or the OS? Html Textarea elements only wrap when they reach a space or tab character. This is fine, until the user types a looooooooooooooooooooooong enough word. I'm looking for a way to strictly enforce line breaks (eg.: even if it results in "loooooooooooo \n ooooooooooong").    The best I've found is to add a zero-width unicode space after every letter, but this breaks copy and paste operations. Anyone know of a better way?  Note: I'm referring to the "textarea" element here (i.e.: the one that behaves similarly to a text input) - not just a plain old block of text. Indian passport holder. Do I need transit visa in Sydney?