In the neural network community, is a tensor pretty much always just a multi-dimensional array?
In the neural network literature, often we encounter the word "tensor".  Is it different from a vector? And from a matrix? Have you got any specific example that clarifies its definition?  I'm a bit confused about its definition. Wikipedia doesn't help and sometimes I have the impression that its definition depends on the specific machine learning environment used (TensorFlow, Caffee, Theano).
"Most importantly" or "more importantly"? Which of the following two sentences is more correct?   "A picture says a thousand words, more importantly in a fraction of a second"    OR   "A picture says a thousand words, most importantly in a fraction of a second"   Nothing important, just my own quotes! Do also suggest, if I can put it in a better way to express what I want to. Can an integrated HDMI port work both ways? Say I had a laptop [Correction: notebook, don't want my thighs medium rare], any OS, and it has an HDMI port built into the side. Would it be remotely possible to hack it into an input, provided it wasn't already designed for that? I would figure all video ports operate straight off the graphics chip, however, are there ways to override that functionality on the driver level? Driver hacks already exist for plenty of things such as the classic example: Bluetooth adapters (so we can play with our PS3 controllers and save a buck) However, is HDMI one of these tamperable interfaces? As far as the interface standard is concerned, are HDMI ports designed to be either way or are they Input/Output specific? How to simulate data that satisfy specific constraints such as having specific mean and standard deviation? Are there any studies on the use of justified text in web apps? How does justification affect screen legibility?  Example of justified text: How to tell if a site is using Drupal 7 I know how to check , but is there a way to tell if a site is built with Drupal 7? It would be a very useful idea to be able to import PEAR projects that somebody maintains to their careers.stackoverflow.com profile. Most of what is required could be gleaned from the user specific rss profile URL; this takes the form of {username}.rss I'm reading the proof of the multiplicative property of $$s_k(n)=\sum_{d|(n,k)}f(d)g\bigg( \frac kd\bigg)$$ The book wrote that in order to understand the proof, we need to know if $a,b,k,m$ are integers such that $(a,k)=(b,m)=1$, then $$(ab,km)=(a,m)(b,k).$$  I have written proof, but I don't know is it consistent, and this seems used more tools than it necessarily has to.   My proof: Let $$S_1=\{d: d|(a,m), d&gt;0\}\\S_2=\{d: d|(b,k), d&gt;0\}\\S=\{d:d|(ab,km), d&gt;0\}.$$ I will prove the statement by showing that the function $\phi:S_1\times S_2\to S$ defined as $$\phi(d_1,d_2)=d_1d_2$$ is bijective, and complete the proof by connecting the maximal elements from these partial ordering sets.  Obviously, for $d_1\in S_1, d_2\in S_2$, this tells us $d_1 $ is both divisor of $a$ and $m$, and $d_2$ is both divisor of $b$ and $k$, hence $d_1d_2$ is both divisor of $ab$ and $km$, so we can tell $\phi(S_1\times S_2)\subseteq S$.  To show one-to-one, if we have $c_1,d_1\in S_1$ and $c_2,d_2\in S_2$ such that $$\phi(c_1,c_2)=\phi(d_1,d_2)$$ then $$c_1c_2=d_1d_2$$  In particular, $c_1|d_1d_2$, we need to show $c_1|d_1$. Indeed, if $(c_1,d_2)&gt;1$, this implies $a,k$ have common factor larger than $1$, contradicts the assumption. Therefore $c_1|d_1$. A similar argument implies $d_1|c_1$, therefore $c_1=d_1$. Again a similar argument implies $c_2=d_2$, which shows one-to-one.   To show onto, let $d\in S$, since $d|ab$, we can split $d$ into $d_1d_2$ such that $d_1|a$ and $d_2|b$. Since $(a,k)=1$, we see $(d_1,k)=1$, by property of $S$ we see also $d_1|m$, therefore $d_1\in S_1$, a similar argument implies $d_2\in S_2$. So every number in $S$ has a preimage in $S_1\times S_2$  This completes the proof. Is there any mistake in the proof?     Edit: A proof about the statement: If $d|ab$ then there are $d_1,d_2$ such that $d=d_1d_2$ and $d_1|a, d_2|b$.  Let $ab=p_1^{e_1}\cdots p_r^{e_r}$ for distinct prime factors $p_1,\cdots,p_r$, then we can write $$a=p_1^{x_1}\cdots p_r^{x_r}\\b=p_1^{y_1}\cdots p_r^{y_r}$$ where some of $x_i, y_i$ can be zero, and $x_i+y_i=e_i$ for all $i=1,\cdots,r$.  Since $d|ab$, we can write $$d=p_1^{f_1}\cdots p_r^{f_r}$$ with $f_i\leq e_i$ for all $i=1,\cdots,r$. Then since $$f_i\leq x_i+y_i$$ Split into two cases:   Case 1: $f_i&gt; x_i$, then we can choose $g_i=x_i$ and $h_i=f_i-x_i$.  Case 2: $f_i\leq x_i$, then we can choose $g_i=f_i$ and $h_i=0$.  Then the choice $$d_1=\prod_{i=1}^r p_i^{g_i}, \quad d_2=\prod_{i=1}^r p_i^{h_i}$$ will prove the statement. 9-speed system to 11-speed drivetrain upgrade? How to count the number of set bits in a 32-bit integer? 8 bits representing the number 7 look like this:  00000111   Three bits are set.     What are algorithms to determine the number of set bits in a 32-bit integer? Is it possible to have two Win 10 user accounts running simultaneously, with one used locally and one used via RDP? I need to allow someone to remotely connect to my windows 10 computer, and am wondering if this is possible:  I have two user accounts right now on my computer, one for me to work on and one for my friend remotely. I want to use my user account locally for myself, and I want to allow him to RDP and log into the other account when he needs to work without disturbing my computer experience.   In other words, I don't want to have to stop what I am doing and log off of my user account when he needs to access his account remotely. Can two user accounts run simultaneously in this regard, with one being connected to via RDP?  If so, can you please explain how to set it up properly?  Thanks for your help! Getting secondary citations right I have some questions regarding secondary citations (in an computer-science research paper that should be published in a journal). I know that they should be avoided when possible, but it is not always that easy. More specifically, my situation is this:  Article A says:     The average value of ... in ... is ... [B]. [C]’s study says that in ... the value is ...   This statement is exactly what i need for my paper. If I read [B] and [C], I see that [A] cited them correctly and if I would have found these two other articles myself, I would have written the same.  Now how to cite this in a correct way?      [B] and [C] say (cited in [A]) ...   and do a “bad” secondary quote;    [B] and [C] say ...   and neglect the investigation done by [A] and peform citation plagiarism;    [A] says ...   and neglect that the data was the achievement of [B] and [C].    [A] says based on the findings of [B] and [C] ...   and do a secondary quote again. Before upgrading to macOS Sierra, I really liked the Character Accent Menu by doing a long press on a key (for example, the character e) and being able to add an accent on it.   However, this functionality seems to not work anymore, and so far, I can't find out why?   Also, before, doing a long press on the delete button, would repeatly delete characters. Now, it is doing only one character deletion disregarding how long I'm pressing the key. So if I want to erase 10 characters, I need to press the delete button 10 times...  Also, I am not able to log off or shut down. When doing it, all applications are closed, status bar disappears but nothing happens. The dock remains here. I have no way to shut down or log out without doing a long press on the power button.  Is someone facing the same issue?  EDIT : Logging with a new user account or guest account fix all the problems. But I still would like to know what, in my user account, became corrupted during the upgrade. How can I install Oracle 11g R2? The title itself is more than self explanatory. I simply need a way to install Oracle's 11g R2 in the latest version of Ubuntu, I'm using a 32-bit OS, and I need to know how to install the x86 version. I also have a 64 bit desktop and I need the install the x86_64 version. Can anyone help me? Possible Duplicate:          As a English non-native speaker it is difficult for me to understand when I must use present perfect or past simple because in my official language there isn't the present perfect tense. I know that present perfect is related to something that happened in the past but its result is important now. But for instance:        The message has been sent.   The message was sent.      Please help me point me out any examples/contexts where I should use 1. instead of 2. Is there implementation of tri-planar mapping in Cycles renderer? Is it possible to have tri-planar mapping in cycles?  Like in corona renderer or fstorm? Automatically Locate Included Images Do you think it's possible to include images into LaTeX without specifying the exact path to them. So instead of:  \includegraphics{path/to/image/myfig.pdf}   It would be:  \includegraphics{myfig.pdf}   While the image would still reside in the path/to/image/ directory. Basically, I'm asking if there is a macro that can recursively search for the image.  An alternative for me is to write a script outside of LaTeX that determines all the images that are included, performs the recursive search and copies those files temporarily in the same directory as the .tex file. I have taken three fields from case object called AccountName, IntegrationTo__c and SfType__c (checkbox).  I have created one case record with a specific combination of three fields.  For the second time I create a record with that combination, then  display error message only if SfType__c is true in first record otherwise allow  for record creation.  trigger AvoidDuplicate on Case(before insert)  {          set&lt;string&gt; newNameSet = new set&lt;string&gt;();     newNameSet = new set&lt;string&gt;();      set&lt;string&gt; newEmailSet = new set&lt;string&gt;();      set&lt;string&gt; dbNameSet = new set&lt;string&gt;();      set&lt;string&gt; dbEmailSet = new set&lt;string&gt;();      for(Case newLead : trigger.new){          newNameSet.add(newLead.Account.Name);          newEmailSet.add(newLead.IntegrationTo__c);      }      for(Case dbLead : [select id, Case.Account.Name, IntegrationTo__c from Case where IntegrationTo__c IN: newEmailSet OR Case.Account.Name IN: newNameSet]){          dbNameSet.add(dbLead.Account.Name);          dbEmailSet.add(dbLead.IntegrationTo__c);      }      for(Case newLead : trigger.new){          if(dbNameSet.contains(newLead.Account.Name) &amp;&amp; dbEmailSet.Contains(newLead.IntegrationTo__c))              newLead.addError('You are inserting Duplicate Case');      }  }   i wrote this this not checking the account field name and integration__c values only with combination of account and integration__c shows error Increasing Letterspace for words in caps or small caps Some typographers say it's a good habit to increase the letterspace when writing words in caps or small caps. So my question is, how to do it with pdflatex and/or xelatex? And while we're at it, which words would you alter this way? Acronyms like USA, NATO, IBM, GNU, etc.? How about words like PCs, UdSSR, FreeBSD or TV-Station? RSA leak bits to factor N Entire function and the series of its successive derivatives I recently came across the result that if $g$ is holomorphic in a neighbourhood of a point $z_0$ and  $$\sum_{n=0}^{\infty }{g^{(n)}(z_0)} $$ converges then $g $ is an entire function. Now, my doubt is if the above series is absolutely convergent then can we say something more about $g$, like say $g$ is a polynomial? I could not find any non-polynomial  entire function( I tried with functions like $e^z$, $\sin z $, et al), whose successive derivatives converge absolutely as series. Any help please?