What is the purpose of dimension reduction in classification?
Is dimensionality reduction almost always useful for classification?
bash script – for i in {x..y} i am writing a script in bash and I would like to give the two numbers in the brackets, x and y to be precise, as variables.  I wrote the script this way:  echo "x?" read x echo "y" read y  for i in {$x..$y}   but it does not work.  How could I set it up to make it function?  Thanks a lot in advance. Injective functions also surjective? Is it true that for each set $M$ a given injective function $f: M \rightarrow M$ is surjective, too?  Can someone explain why it is true or not and give an example? My prof gave us this definition of an Echelon system:     A system of m linear equations in n variables is called an echelon system if         m ≤ n.   Every variable is the leading variable of at most one equation.   Every leading variable is to the left of the leading variables of all lower equations.   Every equation has a leading variable.      I don't understand this definition at all.  Q1)If you have this system of equations:  $ax_1 + bx_2 + cx_3 = z$  $dx_1 + ex_2 + fx_3 = z$  its not an echelon system because of multiple equations having the same variable as the leading variable and therefore violating rule #2.  But if you switch around variables and rewrite the equation as:  $ax_1 + bx_2 + cx_3 = z$  $ex_2 + dx_1 + fx_3 = z$  It becomes an echelon system! Why would the way you write a system of equations affect its definition?  Q2)Why would point number three matter? Can't you just move around the equations so that they are in order of variables?  Q3)Why would point number four matter? If you have a equation in the system that doesn't have a leading variable can't you just disregard it? For example if you have the equation $0x = 0$ in the equation can't you just ignore it to have a echelon system since it doesn't affect the solution of the system? Cannot dismiss scrollbar in code box, blocks view This question is a duplicate of  (but this question can't be marked as a duplicate because that question is on meta.stackoverflow.com, and this question is on meta.stackexchange.com).  I'm seeing a bug on stackoverflow.com. I'm not sure if the culprit is Stack Overflow, Google Chrome, or macOS.  (Below I refer to a "code box". By that I mean some text that begins with 4 spaces when editing a question or answer.)  When I hover over a code box that contains one long line of code, a horizontal scrollbar appears. When I stop hovering over the code box, very frequently (maybe 3 out of 4 times) the scrollbar does not disappear. Clicking elsewhere on the page also does not dismiss the scrollbar. The only way to dismiss it is to refresh the page.  ...After experimenting more, it appears to always happen if I enter the box from below, but not always when I enter from above. It seems to be triggered by hovering over the lower half of the box.  Also if I enter from the top and scroll to the right, then until I refresh the page again that scrollbox will behave normally (only show a scrollbar when scrolling, and disappear after). In that case the scrollbar also has a different appearance, being much less tall (maybe a quarter of the height of the code box rather than half as tall).  Further, if I get a box and scrollbar into that functional state and then hover over the lower part of the box for a bit, then sometimes eventually it will break and stay broken until refresh again.  And in any case hovering over the lower part of the box causes the scrollbar to get taller.  Here is a screenshot of the issue:        Google Chrome 71.0.3578.98 (Official Build) (64-bit)  macOS High Sierra 10.13.6  Here is a code box that repros the issue for me:  fooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo   Here is another:  foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo Show that the function $f: S \to \mathbb R$ given by $$f(x,s,t):=-\ln(st - ||x||^2)$$ is convex on $$S := \left\{(x,s,t) \in \mathbb R^n \times \mathbb  R \times \mathbb R: \frac{\|x\|^2}{s}&lt;t, s&gt;0, t&gt;0 \right\}$$   $-\ln(x)$ is a convex monotonic decreasing function, hence we can use composition by showing the inner part is concave. Also we know $-||x||^2$ is concave and $st$ is neither convex nor concave on $S$. Also in $S$ we have $st&gt;||x||^2$ but I was unable to show the convexity of the function as a whole Variation of the Kempner series – convergence of series $\sum\frac{1}{n}$ where $9$ is not a digit of $1/n$. It is easy to argue that the  converges:  $$  \sum\limits_{\substack{n \text{ s.t. 9 is}\\\text{ not a digit} \\\text{ of } n}}  \frac{1}{n} &lt; \infty$$  Let $E \subset \Bbb N_{&gt;0}$  the subset of the positive integers  such that $9$ is not a digit of the decimal expansion of $1/n$ (the decimal expansion is not allowed to have a trailing infinite sequence of "$9$"s. For instance $0.24999...$ is not allowed).  Here are the  that don't belong to $E$ : $11,13,17,19,21,23,29,31,34,38,41,…$ (not known by the OEIS, by the way).  My question is:     Does the series    $$ \sum\limits_{n \in E} \frac{1}{n} \tag 1$$ converge?   My attempt is :   Let $1/n = 0,a_1 a_2 \dots a_k \overline{b_1 b_2 \dots b_m}$ with $n \in E$. Since $1/n$ has no digit "9", we have at most $9^{k+m}$ possibilities for the $a_i$'s and $b_j$'s. Moreover, $1/n ≥ 0,00...0\overline{00...01}≥1/10^{k+m}$. But then I can only bound my series $(1)$ from below, by some real number. So, this is not a clue for the divergence of the series. Apparently, the numbers of the form $n=10k+1$ don't belong to $E$. Maybe we can find sufficiently many numbers that have $9$ in the decimal representation of their reciprocals, so that $(1)$ could converge...   Any comment will be appreciated ! Sorting hashmap based on keys How did Bill and Percy get 12 OWLs? In Prisoner of Azkaban, Hermione took 12 subjects, and needed a Time-Turner to do so. However, it is mentioned in the series that both Bill and Percy Weasley got 12 OWLs, so would have taken 12 subjects as well, so both would have needed Time-Turners for three years to do this. Doesn't this seem a little unusual, given how strict the Ministry is over the use of Time-Turners,  that they would give them to several Hogwarts students? Missing Schengen entrance stamp Last night I took a night train from Romania to Hungary. I shared a compartment with another American backpacker (and others.) The border crossing on the Romanian side was normal -- all of our passports were stamped and the border officer recorded our data in his notepad. On the Hungarian side, some sort of commotion broke out further down the train car while we were being processed. The officer who was scanning and stamping our passports left and never came back. As a result, the other American backpacker never had her passport scanned or stamped.  What sort of difficulties might she run into since her passport has not been recorded as entering the schengen zone, nor does she have an extra stamp? What might get options be now, from within Schengen, to get her entrance recorded?  (When I say "scanned", the officers had hand-held devices that read the passport biometrics and I assume, recorded some sort of data somewhere.) iMac with 8GB RAM -- memory always almost full I have a 27'' iMac (Late 2012, OS X 10.9.2) with 8GB RAM. The usage of memory is always above 7GB, even though I don't think I am running that much stuff. This leads to the occasional hanging of a program and occasional feeling of the computer being lagged.  The heaviest thing I am running is a Parallels virtualization of a defunct Windows laptop (for my Windows-only programs; work-related). Then I mostly surf with Chrome (10-20 tabs, some with youtube videos). Of course I have other things opened, like Mail, Evernote and a few more. But I don't think a 8GB RAM computer should be overwhelmed by that. I could be wrong.  I am willing to provide an export of processes from the Activity Monitor. I tried looking into it, of course, and I am running A LOT of small processes (unknown to me) -- system stuff I presume. I am a long-time PC user and I know my way around process management in PCs, but not on Mac.  What do you think? Do I just need more RAM or it doesn't feel like it?  Regards, What Hogwarts classes are taught to two houses at once? I remember from my mumble about nine mumble rereads of the Harry Potter series that the following classes Harry took were taught to more than one house in the same lesson:   Potions with the Slytherins  Herbology with the Hufflepuffs  Care of Magical Creatures with the Slytherins  broomstick riding with at least the Slytherins (maybe other houses, too?)    I don't remember any student from a house that isn't Gryffindor being mentioned in the sections on Transfiguration, Charms, Defense Against Dark Arts, History of Magic, or Divination. That would mean McGonagall had to teach twice as many classes as Snape, if both subjects got the same number of lessons (which I think I recall).   Were any subjects other than Potions, Herbology, and Care of Magical Creatures taught to more than one house in the same lesson? And do we know why some subjects are taught to more students at the same time than others? Adding a Link to a Field in a Field Set? String queryFields = null;              for(Schema.FieldSetMember field : SObjectType.Task.FieldSets.Activity_Detail_Page.getFields()){                  queryFields = (queryFields == null ? field.getFieldPath() : queryFields+', '+field.getFieldPath());               }                String query = 'Select '+queryFields+' from Task where Id=\''+activityId+'\'';               task = Database.query(query);   i'll creating a field-set,now how do i add link on any field?  above code is  for dynamically query creation . below code of page   &lt;apex:pageBlock title="Activity" id="Block1"&gt;       &lt;apex:pageBlockSection title="Activity Detail"&gt;         &lt;apex:repeat value="{!$ObjectType.Task.FieldSets.Activity_Detail_Page}" var="field"&gt;             &lt;apex:outputField value="{!Task[field.fieldPath]}" /&gt;         &lt;/apex:repeat&gt;     &lt;/apex:pageBlockSection&gt; &lt;/apex:pageBlock&gt;    As per the image attached, I want to add a link in Rounded field that liks to account. Can any one help me? What's the canonical way to check for type in Python? What is the best way to check whether a given object is of a given type? How about checking whether the object inherits from a given type?  Let's say I have an object o. How do I check whether it's a str? Is it possible to get the sheetname? Why am I allowed to turn my focusing ring beyond infinity? I'd like to run a .sh file using bash on logout and shutdown of Ubuntu. I have searched up and down the web and have found only fixes for KDE and GNOME. The script is simple, I just need to know if I can add the line of code to the "logoff/shutdown" file or if I need to reference it in another script. How can I get another application's installation path programmatically? Could the missing antimatter lie outside the observable universe? Determine all $f: \mathbb{R} \rightarrow \mathbb{R}$ such that, for all $x, y \in \mathbb{R}$, $$f((x + 1) f(y)) = y (f(x) + 1).$$    Source: Vuong Lam Huy, on a Facebook group. In most electrical circuits with a relay, a diode is connected in parallel to the coil of the relay. Why? Is it always a good practice?