If we consider a CNN that takes in $32 \times 32$ grayscale images and has a single convolution layer with 3 different $3 \times 3$ convolution filters (without or with boundary padding). I wonder whether we can treat this CNN as a feed-forward NN with each pixel as input and posting constraints on the weights in the hidden units? If so, what could be the constraints?
I understand that the architecture of Convolutional Neural Networks (CNN) and Feed forward (FNN) are quite different. And that CNNs use pooling and filters of shared weights over a patch of the image. I am not so clear on the core convolution operator (1):   If anyone could link me to an explanation, I have looked at the Colah blog and Nielsen's online book, and I understand what it is doing but don't understand the convolution operator.  Also, it looks quite similar to the the core FNN function is there and difference? (2).  (1) convolution operator is $a^1 = \sigma(b + w*a^0)$ which is equivalent to:  $a^1 = \sigma(b + \sum^4_{l=0}\sum^4_{l=0}w_{l,m}a_{j+l,k+m})$  (2) feed forward operation:  $a^1_i = \sigma(\sum^n_{j=1}w_{ij}x_j +b_i)$  Many thanks  Sources: functions taken from:
Let $G$ be a group and $c\in G$. Define $*$ on $G$ by: $x*y=xdy$ for all $x,y\in G$, where $d$ is the inverse of $c$. Prove $(G,*)$ is a group. Let $G$ be a group and $c$ be a fixed element of $G$. Define a new operation $*$ on G by:   $$x*y=xdy$$   for all $x$ and $y$ in $G$, where $d$ is the inverse of $c$. Prove that $G$ is a group under the operation $*$.    If you want to check, this problem is in the book “A Course In Group Theory”, by John F. Humphreys (problem $3$, page $28$)   I know what are the axioms that $(G,*)$ must obey in order to be a group and I did show that all the axioms where obeyed except the inverse axiom.  My problem is that, whenever I try to verify what would the inverse be for some element $x$, I get an equation where the $x$ is cancelled in both sides.  Can please someone guide me?  Thank you!  (P.S.: This is NOT a homework assignment, I’m studying Group Theory by this book and got problems solving this question) How to create a timeline with LaTeX? Most textbooks introduce differentiable manifolds via . This has the advantage of being concrete, but the disadvantage that the local coordinates are usually completely irrelevant- the choice of atlas and chart is arbitrary, and rarely if ever seems to play any role in differential geometry/topology.  There is a much better definition of differentiable manifolds, which I don't know a good textbook reference for, via . This definition does not involve any strange arbitrary choices, and is coordinate free. Paragraph 3 in Wikipedia (which is the actual definition) states:   A differentiable manifold (of class $C_k$) consists of a pair $(M, \mathcal{O}_M)$ where $M$ is a topological space, and $\mathcal{O}_M$ is a sheaf of local $R$-algebras defined on $M$, such that the locally ringed space $(M,\mathcal{O}_M)$ is locally isomorphic to $(\mathbb{R}^n, \mathcal{O})$.   This confuses me, because I don't see why such a sheaf should be acyclic, or where conditions like "paracompact" or "complete metric space" or "second countable Hausdorff" are implicit. So either:   The wikipedia entry has a mistake (I would want to sanity-check this before editing the entry, because this is such a fundamental definition which thousands must have read). Somewhere in that definition, the condition that $M$ be paracompact is implicit.   Question: Should the definition above indeed require that $M$ be second-countable Hausdorff or paracompact or whatever? Or is it somehow implicit somewhere, and if so, where?    Also, is this definition given carefully in any textbook?  Update: I have editted the Wikipedia article to require that $M$ be second-countable Hausdorff. But I'm still wondering if there is a textbook covering this stuff, and whether requiring the sheaf to be acyclic might have worked instead as an alternative. How to rename multiple files by removing the extension? Types in MySQL: BigInt(20) vs Int(20) Note: The legacy Skype for Linux application (v4.*) is now discontinued and was removed from Canonical’s partner repositories, so this question and its answers are obsolete. Please refer to  of our .  Skype 4.3 is just released with considerable improvements. As a regular Skype user I want to use the latest Skype on my Ubuntu 14.04, but there is no updates from Update Manager. Even in Skype website only Skype 4.3 is available only for Ubuntu 12.04. Is there anyway to use this latest Skype on Ubuntu 14.04 or how much we have to wait for the update? which of the following is NOT a possible value of $(e^{f})''(0)$?? Let $f$ be an analytic function on $\bar{𝐷} = \{z \in \mathbb{C}: |z| \le 1\}$. Assume that $|𝑓(𝑧)| ≤ 1$ for each $z\in \bar{D}$. Then, which of the following is NOT a possible value of $(e^{f})''(0)$??  $(A) 2$  $(B) 6$  $(C) \frac{7}{9}e^{\frac{1}{9}}$  $(D) √2 + 𝑖√2$  So I take a look at Cauchy Integral Formula and then $$(e^{f})''(0)=\frac{1}{\pi}\int_{|z|=1}\frac{e^{f(z)}}{z^3}$$  Taking modulus on both sides we have $$|(e^{f})''(0)| \le \frac{e}{\pi}2\pi=2e$$  Hence (b) cannot be the choice.   Is this alright!!  Thanks for the help! \documentclass[]{phstyle} \usepackage{latexsym,amsfonts,amssymb, undertilde} \usepackage[fleqn]{amsmath} \usepackage{makeidx}  %Preamble  \numberwithin{equation}{chapter} %\renewcommand{\theequation}{\thesection.\arabic{equation}}  \begin{document}  %\include{chapI}   these 2 lines are because the chapters are different tex files  %\include{chap1}  \renewcommand{\thechapter}{\Roman{chapter}}  %\setcounter{chapter}{0} %\renewcommand{\theequation}{\thechapter.\arabic{equation}}  \chapter{Introduction}  \section{Chap I Section1}  \begin{equation} this is equation I.1 \end{equation}  \begin{equation} this is equation I.2 \end{equation}  \section{Chap I Section2}  \begin{equation} this is equation I.3 \end{equation}  \chapter{Chapter 1}  \section{Chap 1 Section 1}  \begin{equation} this is equation 1.1.1 \end{equation}  \begin{equation} this is equation 1.1.2 \end{equation}  \end{document}     I have been typing Chapters 1-5 that contain sections and subsections and equations. The equations were numbered globally, i.e. if I had 3 equations in section 1 of Chap 1, they were numbered 1.1.1, 1.1.2, 1.1.3 and for Section 2, the equations were 1.2.4, 1.2.5, etc.  Recently I had to change Chap 1 and everything in it to Chapter I (roman number) and Chap 2 were renumbered to Chap 1, etc.  My problem is that LaTeX started numbering the equations in Chap I (the other chapters did not have this problem) according to the sections and not globally anymore. That is, the 3 equations in Chap I were I.1, I.2, I.3, and the equations in the second section of Chap I became I.1, I.2, etc instead of I.4, I.5, etc  I needed the prefix to be the chapter and not the sections. I don't understand why there is a change. I have never used \numberwithin in my book  Here are some of my codes  \documentclass[]{phstyle} \usepackage{latexsym,amsfonts,amssymb, undertilde} \usepackage[fleqn]{amsmath}   for the equation numbering in Chap I  \renewcommand{\thechapter}{\Roman{chapter}} \renewcommand{\theequation}{\thechapter.\arabic{equation}} **   Previously when Chap I was Chap 1, ** was  \renewcommand{\theequation}{\thesection.\arabic{equation}}   I have also tried the line below but it didn't work  \renewcommand{\theequation}{I.\arabic{equation}}   Thank you in advance Is there a way to configure pdflatex to make all but the .tex and .pdf files hidden files? I have asked a  about how to manage all the files generated when my LaTeX files are compiled but the approach in the answer I accepted is still unsatisfactory for the many small documents I generate.    I realize the LaTeX  all the files it generates so I can't prevent their creation.    However is there a way to configure pdflatex to make all but the .tex and .pdf files hidden files (i.e., preceded by .)?   (Edit: The two main systems that I use are tex live on Ubuntu Linux and BasicTeX on OS X) I'm trying to insert data from an external table. INSERT /*+ ignore_row_on_dupkey_index ( consruct ( construct_id ) ) */ INTO construct        (construct_id,       n_term ,       enz_name,       c_term,       cpp,       mutations,       mw_kda) SELECT *     FROM EXTERNAL ((       construct_id NUMBER(10),       n_term VARCHAR2 (50),       enz_name VARCHAR2 (50),       c_term VARCHAR2 (50),       cpp VARCHAR2 (50),       mutations VARCHAR2 (50),       mw_kda NUMBER (7,3))      TYPE ORACLE_LOADER     DEFAULT DIRECTORY data_to_input     ACCESS PARAMETERS (         RECORDS DELIMITED BY NEWLINE         SKIP 1         BADFILE bad_files:'badflie_insert_into_construct_from_construct.bad'         FIELDS TERMINATED BY ',' OPTIONALLY ENCLOSED BY '&quot;'         MISSING FIELD VALUES ARE NULL          )      LOCATION ('CONSTRUCT.CSV')     REJECT LIMIT UNLIMITED) ext          WHERE NOT EXISTS (         SELECT * FROM construct c         WHERE c.n_term = ext.n_term         AND c.enz_name = ext.enz_name         AND c.c_term = ext.c_term         AND c.cpp = ext.cpp         AND c.mutations = ext.mutations     );  But now i get this error: Error at Command Line : 171 Column : 7 Error report - SQL Error: ORA-00957: duplicate column name 00957. 00000 -  &quot;duplicate column name&quot;  Line 171 is the last line of this part INSERT /*+ ignore_row_on_dupkey_index ( consruct ( construct_id ) ) */ INTO construct        (construct_id,       n_term ,       enz_name,       c_term,       cpp,       mutations,       mw_kda)  Which is clearly not a duplicate column. If I do: INSERT /*+ ignore_row_on_dupkey_index ( consruct ( construct_id ) ) */ INTO construct      (construct_id,      n_term,      enz_name,      c_term,      cpp,      mutations,      mw_kda) SELECT *     FROM EXTERNAL ((       ext.construct_id NUMBER (10),       ext.n_term VARCHAR2 (50),       ext.enz_name VARCHAR2 (50),       ext.c_term VARCHAR2 (50),       ext.cpp VARCHAR2 (50),       ext.mutations VARCHAR2 (50),       ext.mw_kda NUMBER (7,3))      TYPE ORACLE_LOADER     DEFAULT DIRECTORY data_to_input     ACCESS PARAMETERS (         RECORDS DELIMITED BY NEWLINE         SKIP 1         BADFILE bad_files:'badflie_insert_into_construct_from_construct.bad'         FIELDS TERMINATED BY ',' OPTIONALLY ENCLOSED BY '&quot;'         MISSING FIELD VALUES ARE NULL          )      LOCATION ('CONSTRUCT.CSV')     REJECT LIMIT UNLIMITED) ext          WHERE NOT EXISTS (         SELECT * FROM construct c         WHERE c.n_term = ext.n_term         AND c.enz_name = ext.enz_name         AND c.c_term = ext.c_term         AND c.cpp = ext.cpp         AND c.mutations = ext.mutations     );  I get Error at Command Line : 174 Column : 10 Error report - SQL Error: ORA-00902: invalid datatype 00902. 00000 -  &quot;invalid datatype&quot;  Line 171 is ext.construct_id NUMBER (10), How do I enumerate the properties of a JavaScript object?  I actually want to list all the defined variables and their values, but I've learned that defining a variable actually creates a property of the window object. According to the documentation  in order to retrieve a list of picklist values for an object we need to pass in a Record Type Id which can be retrieved using the getObjectInfo method.   The issue is that these are both wire functions and I cannot figure out how to chain these methods.  If I try code like the following:  getObjectInfo({ objectApiName: ACCOUNT_OBJECT })             .then(result =&gt; {                 return getPicklistValues({recordTypeId: result.defaultRecordTypeId, fieldApiName: TYPE_FIELD});             })             .then(result =&gt; {                 this.picklistValues = result.data             })             .catch(error =&gt; {                 this.error = error;             });   I get an error      render threw an error in 'c:getpicklistexample' [Imperative use is not   supported. Use @wire(getObjectInfo).]   If I try something like   @track rtId;      @wire(getObjectInfo, { objectApiName: ACCOUNT_OBJECT })     handleResult({error, data}) {         if(data) {             this.rtId = data.defaultRecordTypeId;         }     }      @wire(getPicklistValues, {recordTypeId: this.rtId,fieldApiName: TYPE_FIELD})     picklistValues;   Then it throws an internal server error. Anybody have an idea as to how I could retrieve the record type Id and then call to get the pick list values like the documentation suggests?  FYI my imports are:  import { LightningElement, wire, track } from 'lwc'; import { getPicklistValues, getObjectInfo } from 'lightning/uiObjectInfoApi'; import TYPE_FIELD from '@salesforce/schema/Account.Type'; import ACCOUNT_OBJECT from '@salesforce/schema/Account'; Is it possible to install an earlier version of Skype on Windows 8? Windows 8 skype is terrible.  They've removed many buttons, most of the preferences, and have in general made it impossibly oversimplified and difficult to use.  Old Skype was fine when I had windows 7.  Is there any way to get it back on Windows 8? What role does "spontaneously symmetry breaking" played in the "Higgs Mechanism"? In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneously  symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of local gauge symmetry, some people says that we can formulate Higgs mechanism in a gauge invariant way, some people also says that we need only a non-zero vaccum expectation value... I am confused about this different or maybe same point of views.  In this post:  , the most highly voted answer, I still can't feel how SSB worked in Higgs mechanism. It seem that the validity of last part, the appearance of a mass term for $A$, is guaranteed if we have a non-zero equilibrium value $\phi_0$ to expand around. I do not see that the requirement that the phase of the field $\phi$ need to be fixed at some particular value to generate mass term. Thus it seems to me it is not true that SSB is really indispensable for Higgs mechanism.  To put it simply:  The spontanously breaking of what is attributed to Higgs mechanism?   local gauge symmetry global symmetry, since breaking of a "gauge symmetry" should not have any effect on physics. In higgs mechanism, the really broken symmetry is a global one. Mathematically, it is similar in looking as fixing a gauge, but one should not think it as a spontanously breakdown of local gauge symmetry. other.   Is SSB really indispensable for Higgs mechanism?    yes, Higgs mechanism is relied on the SSB of some symmetry (above question), the other approches of description eventually has spontanously broke some symmetry. No, the SSB is just one way to describe Higgs mechanism (or even not a complete way), what is really need is the non-zero vaccum expectation value, for example in the linked post the requirement for the mass term to occur is to have some non-zero expectation value of $\phi$ to expand around, we do not need the phase of the field to be fixed, thus the symmetry is not broken. Other.   some reference materials:    States that SSB of local gauge symmetry is impossible.  in the abstract states that:       gauge symmetries merely reflect a redundancy in the state description   and therefore the spontaneous breaking can not be an essential   ingredient. Indeed, as already shown by Higgs and Kibble, the   mechanism can be explained in terms of gauge invariant variables,   without invoking spontaneous symmetry breaking     In the introduction it says:      In particular, we emphasize that global U(1) phase rotation symmetry,   and not gauge symmetry, is spontaneously violated, and show that the   BCS wave function is, contrary to claims in the literature, fully   gauge invariant biblatex: separator for citing multiple sources, some of them with page, some not I'm using biblatex for my references.  Normally, if I use \cite{source1, source2, source3}, I get a citation like  [3, 45, 98]   If I now want to give a page number for one of them, it looks confusing imho, as I should get (did not try it out up to now, honestly)   [3, 45, 78, p. 23f, 98]   So imho it would make sense to change one of the separator from a comma to e. g. a semicolon like:  [3; 45; 78, p. 23f; 98]   Question 1: Does that make sense, or are there other conventions for citing sources with and without page numbers together?  (Up to now I collected the citations without page number in one cite command and added singular \cite[][p. xy]{} commands for those with page numbers., so I'd get:   [3, 45, 98][78, p. 23f]   )  the \cites[]{}[]{}[]{} could also do that, but it also uses the same separators for entries and postnotes.  Question 2: How could I change the separator globally for those number-citations from comma to semicolon in biblatex? Which Mac is suitable for Blender 2.8? I am considering purchasing a Mac for my godson who will be using it to run Blender 2.8.  I know very little about this program.  All I can find are requirements for a Mac that will run earlier versions of Blender.  Would someone please recommend a list of requirements for a Mac (or a link to a list of requirements) that I could use to find a model that can run 2.8?  Thank you in advance for all your help! Sincerely, M. Lap What does the number in parentheses shown after Unix command names in manpages mean? For example: man(1), find(3), updatedb(2)?   What do the numbers in parentheses (Brit. "brackets") mean? 90's book about children climbing a tree and visiting different worlds from there In the 90's I read a book about two children (I think they were siblings, boy and girl) who climbed a tree. At the end they found a door to another world. After some time the (fantasy) worlds switched to another one. Once they got stuck in a world, because the world went on traveling and therefore the door couldn't be reached anymore. They met many curious individuals during their adventures.  It's a completed novel for kids. I've read it in German, but I can't remember if the author was a German one, so it might've been available in English as well. It was a fairly thick book.  EDIT: After some thought I remember a pancake kind of person Organize desktop icons on Windows into categories or sections Sufficient condition(s) for $f'$ to be Riemann integrable