Perceptron learning rate irrelevant in convergence Via this  i studied the single layer Perceptron convergence proof (= maximum number of steps).  In the convergence proof inside this document , the learning rate is implicitly defined as 1 . After studying it, by myself i tried to re-do the proof inserting this time a generic learning rate $\eta $.  The result is that the result remains the same:  $k\leq \frac{R^{2}\left \| \theta ^{*} \right \|^{2}}{\gamma ^{2}}$  that is the learning rate $\eta$ cancelled out in the proof.  Is it possible , or i make mistakes in my proof ?
Normalizing the final weights vector in the upper bound on the Perceptron's convergence The convergence of the "simple"  says that:  $$k\leqslant \left ( \frac{R\left \| \bar{\theta} \right \|}{\gamma } \right )^{2}$$  where $k$ is the number of iterations (in which the weights are updated), $R$ is the maximum distance of a sample from the origin, $\bar{\theta}$ is the final weights vector, and  $\gamma$ is the smallest distance from $\bar{\theta}$ to a sample (= the margin of hyperplane).  Many books implicitly say that  $\left \| \bar{\theta} \right \|$ is equal to 1. But why do they normalize it ?
Dropping z dimension programmatically It seems there is no geoalgorithm to drop z values in the QGIS processing toolbox. Can this be done programmatically using the Python console? At the moment I have to save the layer with unchecked 'Include z-dimension' checkbox (non automatic geometry type): Unable to start Oracle database We have an Oracle database, one data file (users tablespace) of the instance got corrupt and another data file (containing application data) was deleted due to some issue.  The database is in ARCHIVELOG mode, but we neither have data file backup of both data files nor the pertaining archive logs. Hence, I guess we cannot go ahead with the recovery of data files. I am unable to open the database as the data files are not available and face.   ORA-01589: must use RESETLOGS or NORESETLOGS option for database open    I am just able to STARTUP MOUNT the database  I wanted to ask if we can somehow we can open the database by taking both the tablespaces offline after STARTUP MOUNT the database instance. Or if there is any other way I can start the database.   There was a power issue and the  server got abruptly shutdown. When we tried to restart the database and found that we were facing ORA-01589: must use RESETLOGS or NORESETLOGS option for database open. On further analysis we found that 2 of datafiles were creating problem as one got corrupt other deleted as mentioned. As of now if I try to restart the database it says one datafile which belongs to users tablespace need recovery. I wanted to confirm as if we can start the instance by bringing the tablespace offline.  I tried:  SQL&gt; select open_mode from v$database;  OPEN_MODE ---------- MOUNTED  SQL&gt; alter database open resetlogs; alter database open resetlogs * ERROR at line 1: ORA-01194: file 1 needs more recovery to be consistent ORA-01110: data file 1: '/flowsystems/oradata02/flsta02/system01.dbf'   I don't have any archive logs. com.mysql.jdbc.exceptions.jdbc4.CommunicationsException: Communications link failure Multiple workspaces on Ubuntu 18.04.1 LTS and later with GNOME Shell How to check that a cubic polynomial is irreducible? I want to argue that argue that $\pi(\alpha)=\alpha^3+3\alpha+3$ is an irreducible polynomial over the finite field with 5 elements $\mathbb{F}_5$. My approach was just to check that $\pi$ has no roots in $\mathbb{F}_5$. Is this right? Monty hall problem extended. E:Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages I am not sure what caused this error, but here is what the whole error says, and also this is sitting as a notification, and preventing me from updating any software using Update Manager - Please provide some assistance or tell me how to figure out what to do to fix it.  Could not calculate the upgrade  An unresolvable problem occurred while calculating the upgrade.  Please report this bug against the 'update-manager' package and include the following error message: 'E:Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages.' Minimal polynomials and cyclic subspaces I'm trying to make my way through two problems in Curtis's Linear Algebra, chapter 25.  One of the two problems is this one, #5:     Prove that $V$ is cyclic relative to a linear transformation $T \in \mathcal{L}(V)$ if and only if the minimal polynomial of $T$ is equal to the characteristic polynomial.   Part of the issue is that I'm not really sure what it's asking. The statement that $V$ is cyclic seems to suggest that the entire vector space (say it has dimension $n$) is generated by some vector $v \in V$, along with $Tv, T^2v, \ldots T^{n-1}v$; Curtis's definition of a cyclic subspace (as opposed to a space, though I can't see why there should be a difference) seems to reinforce this:     A $T$-invariant subspace $V_1$ of $V$ is called cyclic relative to $T$ if $V_1 \neq 0$ and there exists a vector $v_1 \in V_1$ such that $V_1$ is generated by $\{ v_1, Tv_1, T^2v_1, \ldots T^kv_1 \}$ for some $k$.   However, I've seen several examples that seem to directly contradict this interpretation. For example, we recently had a take-home midterm that required we find elementary divisors, rational canonical form, etc., of a $6\times 6$ matrix; a classmate who received a perfect score on her test found that her matrix's characteristic polynomial was equal to its minimal polynomial &#151; it was $(x+8)^2 (x+14)^2 (x^2+61x+80)$ &#151; and yet the vector space could be written as $\left&lt; v_6 \right&gt; \oplus \left&lt; v_4 \right&gt; \oplus \left&lt; -v_2+v_3+v_6 \right&gt;$ &#151; i.e., as the direct sum of three cyclic subspaces, not as one cyclic subspace.  So that suggests that "$V$ is cyclic" might mean the direct sum of cyclic subspaces. However, while working on the exercise that follows (#6), I came across this:  $$S= \left(\begin{array}{ccc} -1 &amp; 0 &amp; 0 &amp; 0\\ 0 &amp; 1 &amp; 0 &amp; 0\\ 0 &amp; 0 &amp; 1 &amp; 0\\ 0 &amp; 0 &amp; 0 &amp; 2 \end{array}\right)$$  Here, the characteristic polynomial is not equal to the minimal polynomial, which is $m(x) = (x-1)(x+1)(x+2)$. The eigenspace associated with $\lambda = 1$ has dimension $2$. And so it seems as though, if $V$ has basis $\{ v_1, v_2, v_3, v_4 \}$, we can write $V = \left&lt; v_1 \right&gt; \oplus \left&lt; v_2 \right&gt; \oplus \left&lt; v_3 \right&gt; \oplus \left&lt; v_4 \right&gt; $. This would seem to contradict my second interpretation of the original question.  Obviously I'm missing something. Could someone fill me in on what it might be? (I've tried to be thorough, but I'm also trying not to make this ridiculously long; if I've left out necessary information, I'll be happy to append it.) This is tricky. I would like to install Ubuntu on a machine that is intended to work as server, and for some reason I do not have an option to connect a screen to it.  I expect this may be similar to remote installation. However, there is currently no OS on that machine, so I will have to set up everything from scratch.  On the other hand, I do have a physical access to that machine. Therefore I can get it to boot from a CD/USB. But that's not enough.  Is there a way to do such installation remotely? Is there a version of Ubuntu image that comes with a SSH server preinstalled, and starts it once booted, so that I can boot the machine with such image, connect to it via SSH and process the installation from a different computer?  If not, what other options do I have? Why does sstatic.net serve cookies? According to :  This is a fast, cookieless domain intended for static content delivered to the   However, all responses from the server set a cookie anyway: $ http https://sstatic.net/ HTTP/1.1 200 OK CF-RAY: 162b88245bc406be-LHR Cache-Control: max-age=604800 Connection: keep-alive Content-Encoding: gzip Content-Type: text/html Date: Sun, 31 Aug 2014 19:11:04 GMT ETag: W/&quot;d5474fdfb5c3cf1:0&quot; Last-Modified: Fri, 29 Aug 2014 18:20:12 GMT Server: cloudflare-nginx Set-Cookie: __cfduid=db60cc6f3e7f6482e37f1f2b85c9dc5881409512264375; expires=Mon, 23-Dec-2019 23:50:00 GMT; path=/; domain=.sstatic.net; HttpOnly Transfer-Encoding: chunked Vary: Accept-Encoding [...]  Is this intentional, or just funny? Edited to add: I understand that the cookie is used to track visiting browsers so that cloudflare can distinguish them from misbehaving hosts using the same or a nearby IP address. However, if the policy is intentionally to serve cookies, then the self-documentation of sstatic.net as a &quot;cookieless domain&quot; is incorrect. Let: $P(x) = a_nx^n + a_{n-1}x^{n-1} + ..... + a_1x + a_0$ where $a_0a_n &lt; 0$ I have to prove that the Polynomial $P(x)$ has at least one positive root how can I prove it? Any ideas? Vandermonde identity corollary $\sum_{v=0}^{n}\frac{(2n)!}{(v!)^2(n-v)!^2}={2n \choose n}^2$ I am trying to prove this identity:  $$\sum_{v=0}^{n}\frac{(2n)!}{(v!)^2(n-v)!^2}={2n \choose n}^2$$ I think this identity (corollary of Vandermonde identity): $${n\choose 0}^2+{n\choose 1}^2+{n\choose 2}^2+\cdots+{n\choose n}^2={2n \choose n}$$ is applicable for solving it. Please give me some hints. thank you In $Sets$, the initial object is $0 = \emptyset$. We have $C \times \emptyset = \emptyset$ for any set $C$. As there are no maps to the empty set, we don't get much of the universal property of the product.  I am now wondering what is special about arbitrary categories $\mathscr{C}$ with $C \times 0 \cong 0$ for all objects $C$ of $\mathscr{C}$, where $0$ is the initial object of $\mathscr{C}$.   From Sheaves in Geometry and Logic by MacLane (p.194), in any topos $\mathscr{C}$, any arrow $k:C \to 0$ is an isomorphism. The universal property of the product would then also not yield very much.   Are there any categories of higher interest? If the order of all nontrivial elements in a group is 2, then the group is Abelian. I know of a proof that is just from calculations (see below). I'm wondering if there is any theory or motivation behind this fact. Perhaps to do with commutators?    Proof: $a \cdot b = (b \cdot b)  \cdot (a \cdot b) \cdot (a \cdot a) = b \cdot (b \cdot a) \cdot (b\cdot a) \cdot a = b \cdot a$. Making Map Book of pages with same area shown but different layers turned on/off In ArcMap a Map Book is best suited for a series of features that each get their own page. It allows you to pick a feature and generate a Map Book Page for each feature including any additional information you wish to add to each page via dynamic text, charts, etc. Is there an alternative for say a series of pages showing the EXACT same area but with different layers turned on and off? We have a Capital Improvements document that I have to create showing the City Boundaries on every page. One page has all police and fire stations listed, another shows proposed water systems, another shows expressways and highways and work being done near or on them... etc., ad nauseum. Is there some way to set this up so that I DON'T have to created a separate MXD for each Map Page of this document? Disable all software installation I have a scenario. (Windows Forms, C#, .NET)   There is a main form which hosts some user control. The user control does some heavy data operation, such that if I directly call the UserControl_Load method the UI become nonresponsive for the duration for load method execution. To overcome this I load data on different thread (trying to change existing code as little as I can)   I used a background worker thread which will be loading the data and when done will notify the application that it has done its work.   Now came a real problem. All the UI (main form and its child usercontrols) was created on the primary main thread. In the LOAD method of the usercontrol I'm fetching data based on the values of some control (like textbox) on userControl.    The pseudocode would look like this:  CODE 1  UserContrl1_LoadDataMethod() {     if (textbox1.text == "MyName") // This gives exception     {         //Load data corresponding to "MyName".         //Populate a globale variable List&lt;string&gt; which will be binded to grid at some later stage.     } }   The Exception it gave was     Cross-thread operation not valid: Control accessed from a thread other than the thread it was created on.   To know more about this I did some googling and a suggestion came up like using the following code  CODE 2  UserContrl1_LoadDataMethod() {     if (InvokeRequired) // Line #1     {         this.Invoke(new MethodInvoker(UserContrl1_LoadDataMethod));         return;     }      if (textbox1.text == "MyName") // Now it wont give an exception     {     //Load data correspondin to "MyName"         //Populate a globale variable List&lt;string&gt; which will be binded to grid at some later stage     } }   BUT BUT BUT... it seems I'm back to square one. The Application again  become nonresponsive. It seems to be due to the execution of line #1 if condition. The loading task is again done by the parent thread and not the third that I spawned.  I don't know whether I perceived this right or wrong. I'm new to threading.  How do I resolve this and also what is the effect of execution of Line#1 if block?  The situation is this: I want to load data into a global variable based on the value of a control. I don't want to change the value of a control from the child thread. I'm not going to do it ever from a child thread.   So only accessing the value so that the corresponding data can be fetched from the database. We need a profanity filter I searched SE.Meta and was unable to find such question.  Someone just swore at us in a  as an  (warning: profanity, may be NSFW), sure, Arqade (profanity in phrases in games) or some SE (ELU, ELL or Anime.SE maybe?) can sometimes contain profanity as a small parts of question.  I think that a part should be added to the review system that will automatically hide questions/answers with profanity, just like the close vote system, the question/answer will be on hold and will be voted to be shown or be deleted.  Tip, if this gets implemented, u can be typed as \/ or v, and most other can be written as leet (l = 1 etc). Maybe it can be called "suspicious activity", and can be triggered when there is too many number or Unicode characters. (I can write hi as |-| |, |-|I, |-|l, l-li, hî, 1-1i, H1 and many more) SF Short Story about resetting the world every day Trying to identify a short story. I recall it was quite short, shorter than a novella. I read it within the last few years, but my impression is that it's from the second half of the twentieth century, maybe the sixties. I can't recall if I read it online, in an anthology, or collection. Set in America, a middle-aged man stumbles on a team (maybe like dwarves or gnomes) whose job it is to set up the world for the next day by removing all the previous day's &quot;stuff&quot;, like street furniture? (I know that makes no sense). He disrupts this process and somehow prevents progressing to the next day. I also remember the story was quite lighthearted with the team behaving in a very grumpy way like interrupted workmen. I thought the title was something like &quot;What happened to Tuesday&quot; or similar. For some reason, I thought it was by Keith Laumer, but a search doesn't reveal anything. The trope was similar to &quot;The Tunnel Under the World&quot; by Pohl, and &quot;The Adjustment Team&quot; by Dick, in that reality was constantly changed and controlled by an organisation of some kind. Areas versus volumes of revolution: why does the area require approximation by a cone? Suppose we rotate the graph of $y = f(x)$ about the $x$-axis from $a$ to $b$.  Then (using the disk method) the volume is $$\int_a^b \pi f(x)^2 dx$$ since we approximate a little piece as a cylinder.  However, if we want to find the surface area, then we approximate it as part of a cone and the formula is $$\int_a^b 2\pi f(x)\sqrt{1+f'(x)^2} dx.$$  But if approximated it by a circle with thickness $dx$ we would get $$\int_a^b 2\pi f(x) dx.$$  So my question is how come for volume we can make the cruder approximation of a disk but for surface area we can't.