I'm reading  by Rokach, and i've got to a chapter about ensemble methods (using multiple classifiers) and this is where I can't wrap my head around this concept of Plurality Voting (PV).    $$\operatorname{class}(x) = \operatorname{argmax} \left (\sum g(y_k(x), c_i)  \right)$$  Where $$g(y_k(x), c_i) = \begin{cases}1 &amp;\text{if } y = c\\                                 0 &amp;\text{if } y \neq c\end{cases}$$  Most of the other metrics in the chapter weight classifiers, yet this seems to just essentially pick the one which has the highest chance of returning the class you want.  Which seems useless? If thats the case how would this be helpful?
I'm reading . Then I'm not able to figure out the difference between hard voting and soft voting in context to ensemble based methods.  I quote descriptions of them from the book. The first two images from the top are description for hard voting, and last one is for soft voting.        In my view hard voting is majority decision, but I don't understand soft voting and the reason why soft voting is better than hard voting. Would anyone teach me these?
I started thinking about the number of associative (binary) operations on a set with $n$ elements today.  Looking online I found  which indicates only $113$ of the possible $19,683$ operations on a three-element set satisfy association.  So, $50\%$ of binary operations on a two-element set satisfy association, and less than $0.6\%$ of all binary operations on a three element set satisfy association.  For an $n$-element set, where $n$ denotes a natural number, is the ratio $R_{n}=A_{n}/B_{n}$, of the number of associative binary operations $A_{n}$ to the number of all binary operations $B_{n}$, in general small?  I don't mean the following questions as equivalent, but since they seem more concretely answerable in principle, does   $$ \lim_{n \to +\infty} \frac{A_{n}}{B_{n}} = 0 ? $$       Also, is $F : n \to R_{n}$ a monotonically decreasing function?  Some Background of the Question: In his Linear Algebra Problem Book 1995 on p. 6 Paul Halmos writes "The commonly accepted attitudes toward the commutative law and the associative law are different.  Many real life operations fail to commute; the mathematical community has learned to live with that fact and even to enjoy it.  Violations of the associative law, on the other hand, are usually considered by specialists only."  For all I know, Halmos might only have written that to motivate the study of Linear Algebra and doesn't quite literally mean what he appears to say.  But, if he means what he appears to say, and if $F : n \to R_{n}$ is monotonically decreasing, or $R_{n}$ is generally small, I think there's something amiss with what Halmos says, since non-associative operations seem so common that one may as well enjoy them. Is division of matrices possible? Is it possible to divide a matrix by another? If yes, What will be the result of $\dfrac AB$ if $$         A = \begin{pmatrix}         a &amp; b \\         c &amp; d \\         \end{pmatrix},         B = \begin{pmatrix}         w &amp; x \\         y &amp; z \\         \end{pmatrix}? $$ How to influence the name of the pdf file created with pdfLaTeX (from within the source code)? I have a source file called 2011-05-27_Myfilename.tex and I'd like to create a PDF file from it called only Myfilename.pdf.  Can this be configured from within the .tex file itself?  (It seems to be possible with    pdflatex -jobname=Myfilename.tex 2011-05-27_Myfilename.tex   However, as many different files are concerned, It would be easier to have an option like output=Myfilename in the LaTeX source code.) I can't seem to access instance members of the surrounding class from inside an enum, as I could from inside an inner class. Does that mean enums are static? Is there any access to the scope of the surrounding class's instance, or do I have to pass the instance into the enum's method where I need it?  public class Universe {     public final int theAnswer;      public enum Planet {         // ...         EARTH(...);         // ...          // ... constructor etc.          public int deepThought() {             // -&gt; "No enclosing instance of type 'Universe' is accessible in this scope"             return Universe.this.theAnswer;         }     }      public Universe(int locallyUniversalAnswer) {         this.theAnswer = locallyUniversalAnswer;     } } How can I suppress the year from appearing in the bibliography for entries of type @inproceedings?  In my specific case the year is implied in the booktitle (e.g. FOCS '09) so it is redundant when I need to save space.  I found  and the "second solution" looks promising but I am not sure how to translate it to only suppress the year for one type of entry. I am guessing \ifentrytype might be helpful. I am using biblatex+biber. Registered Apple Developer Agreement when under 18 Is it ok to have mixed grounds and neutrals on bars in a breaker box? So to continue my line of electrical questioning (and perhaps narrow down my ), I took a look through the two panels in this house.  There is a 200amp main service in the basement, which then feeds up to a 100amp sub-panel for the main floor.  This 100amp sub feeds a kitchen (fridge, microwave, dishwasher, gas range), a bathroom, 3 bedrooms, and a living room.  The 200amp main feeds the 100amp sub, 2 bedrooms, a living room, a washer/dryer (gas dryer), a utility room (well pump, pressure tank, gas water heater, gas furnace), and an A/C.  My first concern is that the main service panel has the bare ground and neutral wires mixed on the two bus bars.  Reading around, some say this is OK, other's say it is bad.  Any thoughts?  The sub-panel is wired with grounds and neutrals on separate bars.  My second concern- is a 100amp sub sufficient for the main floor? What's the term for using the wrong word because it sounds the same? I was reading about various terms for incorrect words, but they didn't seem to fit.  I saw a post where someone said "what do you like to do when you're board?".  That kind of thing.  Also, would that be considered a mistake in grammar?  I didn't think so, but my friend insists it is.  I'm not sure if there even is a word for that kind of mistake, but was just curious about it.  Thanks! From what I know, it is unknown whether $x_n=x_{n-1}^2 + 1$ has a closed form. Is there a recurrence relation which is known to have no closed form with a proof of inexistence?  Assuming a closed form is a non recursive description using the elementary operations of addition multiplication and power, or, assuming any other good definition of "closed form".  Edit  There are similar questions out there, but the answers are a little bit going around the question.   So is there one with proof or is it unknown? And if it depends on the definition of a closed form, then what are the (or some) options? How strong can a closed form definition be to still have a recursive relation that can be proved to not being able to have its form?  Update  Because it is a big question, and I don't want to open a new small one, I think a good representative small question about this subject is:  Is there a recurrence relation with a domain of the natural numbers, described by elementary functions, which has no closed form defined as:  A closed form of a recurrence relation with a domain of natural numbers is a function $f$ that can be described as a composition of a constant number of elementary functions without reccursion. i.e, $f(n) = f_1(f_2( \dots (f_k(n))) \dots) $ where $f_i$ is elementary for all $1 \leq i \leq k$   I think this definition is the most intuitive and basic.  For example, the relation $x_n = x_{n-1}+1$ has a closed form in this sense: $$f(n) = f_1(f_2(f_3(f_4(n))))$$  Where $f_1$ is division, $f_2(n)=(n,2)$, $f_3$ is multiplication and $f_4(n) = (n,n+1)$   Is there a recurrence relation which has no closed form in this sense? If a function has a finite limit at infinity, does that imply its derivative goes to zero? I've been thinking about this problem: Let $f: (a, +\infty) \to \mathbb{R}$ be a differentiable function such that $\lim\limits_{x \to +\infty} f(x) = L &lt; \infty$. Then must it be the case that $\lim\limits_{x\to +\infty}f'(x) = 0$?  It looks like it's true, but I haven't managed to work out a proof. I came up with this, but it's pretty sketchy:  $$ \begin{align} \lim_{x \to +\infty} f'(x) &amp;= \lim_{x \to +\infty} \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} \\ &amp;= \lim_{h \to 0} \lim_{x \to +\infty} \frac{f(x+h)-f(x)}{h} \\ &amp;= \lim_{h \to 0} \frac1{h} \lim_{x \to +\infty}[f(x+h)-f(x)] \\ &amp;= \lim_{h \to 0} \frac1{h}(L-L) \\ &amp;= \lim_{h \to 0} \frac{0}{h} \\ &amp;= 0 \end{align} $$  In particular, I don't think I can swap the order of the limits just like that. Is this correct, and if it isn't, how can we prove the statement? I know there is  already, but I think this is different in two aspects. First, that question assumes that $\lim\limits_{x \to +\infty}f'(x)$ exists, which I don't. Second, I also wanted to know if interchanging limits is a valid operation in this case. Named blocks to limit variable scope: good idea? Ideal of the twisted cubic The twisted cubic is the image of the morphism $\phi : \mathbb{P}^1 \to \mathbb{P}^3 , (x:y) \mapsto (x^3:x^2 y:x y^2:y^3)$, it is given by $X = V(ad-bc,b^2-ac,c^2-bd)$. Now I would like to compute $I(X)$, which equals by the Nullstellensatz the radical of the ideal $I := (ad-bc,b^2-ac,c^2-bd) \subseteq k[a,b,c,d]$. I think that that $I$ is already a radical ideal, even a prime ideal. Namely, I suspect that  $$\phi^* : Q:=k[a,b,c,d]/I \to k[s,t] , a \mapsto s^3, b \mapsto s^2 t , c \mapsto s t^2 , d \mapsto t^3$$ is an injection. If this is true: How can we prove that? I've already tried to find a $k$-basis of the quotient, but this turned out to be a big mess. Even the representation of the quotient as a monoid algebra doesn't seem to help. Another idea is the following: A formal manipulation of generators and relations implies $Q_a \cong k[a,b]_a$. Thus it suffices to prove that $Q \to Q_a$ is injective, i.e. that $a$ is not a zero divisor. Getting all files that have been modified on a specific date Is it possible to find all php files within a certain directory that have been modified on a certain date  I'm using   find /var/www/html/dir/ -mtime -28 | grep '\.php'    to get files modified within the last 28 days, but I only need files that have been modified on the following date: 2011-02-08 I'm running Bash scripting, but sometimes I get confused which of these commands I use belong to who. Sometimes man xxx works, sometimes doesn't, so I use --help or info, mostly one of these works to show description of the command. Can anyone tell me how I would know what command belongs to what? Bash builtin, GNU utility, etc. Rm can't delete file I'm building a quick csv from a mysql table with a query like:  select DATE(date),count(date) from table group by DATE(date) order by date asc;   and just dumping them to a file in perl over a:  while(my($date,$sum) = $sth-&gt;fetchrow) {     print CSV "$date,$sum\n" }   There are date gaps in the data, though:  | 2008-08-05 |           4 |  | 2008-08-07 |          23 |    I would like to pad the data to fill in the missing days with zero-count entries to end up with:  | 2008-08-05 |           4 |  | 2008-08-06 |           0 |  | 2008-08-07 |          23 |    I slapped together a really awkward (and almost certainly buggy) workaround with an array of days-per-month and some math, but there has to be something more straightforward either on the mysql or perl side.   Any genius ideas/slaps in the face for why me am being so dumb?    I ended up going with a stored procedure which generated a temp table for the date range in question for a couple of reasons:   I know the date range I'll be looking for every time The server in question unfortunately was not one that I can install perl modules on atm, and the state of it was decrepit enough that it didn't have anything remotely Date::-y installed   The perl Date/DateTime-iterating answers were also very good, I wish I could select multiple answers! Undergraduate classical mechanics introduces both Lagrangians and Hamiltonians, while undergrad quantum mechanics seems to only use the Hamiltonian. But particle physics, and more generally quantum field theory seem to only use the Lagrangian, e.g. you hear about the Klein-Gordon Lagrangian, Dirac Lagrangian, Standard Model Lagrangian and so on. Why is there a mismatch here? Why does it seem like only Hamiltonians are used in undergraduate quantum mechanics, but only Lagrangians are used in quantum field theory? I'm trying to write a program in C (on Linux) that loops until the user presses a key, but shouldn't require a keypress to continue each loop.  Is there a simple way to do this? I figure I could possibly do it with select() but that seems like a lot of work.  Alternatively, is there a way to catch a ctrl-c keypress to do cleanup before the program closes instead of non-blocking io? XmlInclude : List and array How critical are macOS Mojave compatibility requirements? As per Apple support document, :     1. Check compatibility      You can upgrade to macOS Mojave from OS X Mountain Lion or later on   any of the following Mac models. Your Mac also needs at least 2GB of   memory and 12.5GB of available storage space, or up to 18.5GB of   storage space when upgrading from OS X Yosemite or earlier.         MacBook introduced in early 2015 or later   MacBook Air introduced in mid 2012 or later   MacBook Pro introduced in mid 2012 or later   Mac mini introduced in late 2012 or later   iMac introduced in late 2012 or later   iMac Pro (all models)   Mac Pro introduced in late 2013, plus mid-2010 or mid-2012 models with a recommended Metal-capable graphics card.      I am currently running macOS High Sierra on my Early 2011 MacBook Pro.  What does Apple's requirements mean for my ability to install Mojave? Is it possible or worthwhile to do so?