Can someone explain the following modular arithmetic?
How do you find the modular inverse of $5\pmod{\!11}$
"Effect" vs. "Affect" I've noticed that some people use effect and affect interchangeably. What are the differences between these two and when are the proper situations to use each of them? Create an instance of an object from a String in Dart? Why is an object stuck to another? So I created a Cube in Blender and then I created an Empty beside the Cube (in object mode). Now, when I move the Empty around, the Cube follows... Why? I think I've got it down to the most basic case:  int main(int argc, char ** argv) {   int * arr;    foo(arr);   printf("car[3]=%d\n",arr[3]);   free (arr);   return 1; }  void foo(int * arr) {   arr = (int*) malloc( sizeof(int)*25 );   arr[3] = 69; }   The output is this:  &gt; ./a.out   car[3]=-1869558540  a.out(4100) malloc: *** error for object 0x8fe01037: Non-aligned pointer                          being freed  *** set a breakpoint in malloc_error_break to debug &gt;   If anyone can shed light on where my understanding is failing, it'd be greatly appreciated. Wired connection not working Ubuntu 12.04 ARIMA equation interpretation I'm trying to replicate ARIMA (1,0,1)(1,0,1) equation in excel as a formula but I am not able to understand the interpretation of white noise residual e(t) or u(t).If could help me understand the interpretation and how to derive it from raw data it'll be really great.  Thanks Notation for intervals I have frequently encountered both $\langle a,b \rangle$ and $[a,b]$ as notation for closed . I have mostly encountered $(a,b)$ for open intervals, but I have also seen $]a,b[$. I recall someone calling the notation with $[a,b]$ and $]a,b[$ as French notation.   What are the origins of the two notations?  Is the name French notation correct? Are they used frequently in France? Or were they perhaps prevalent in French mathematical community at some point? (In this  Bourbaki is mentioned in connection with the notation $]a,b[$.)      Since several answerers have already mentioned that they have never seen $\langle a,b \rangle$ to be used for closed intervals, I have tried to look for some occurrences for this. The best I can come up with is the article on , where these notations are called Czech notation and French notation. Using $(a,b)$ and $[a,b]$ is called English notation in that article. (I am from Central Europe, too, so it is perhaps not that surprising that I have seen this notation in lectures.) I also tried to google for  or . Surprisingly, this lead me to a  where this notation is used for open interval. When changing fields, should I focus more on describing past research or connecting it to the new area in my statement of purpose? I want to change my field from molecular biophysics to theoretical ecology. While they are basically required some same basic background (physics, math, programming), the rest is quite irrelevant. In my current draft of this part, about a half is about this the problem and the result of the work, another half is for my contribution and what I've learnt. Having said that, should I focus less on describing the work and leave space for the thing that will be useful for the next research?  Below is copy from .     What have you already done? What problems have you solved, or at least worked on? What independent projects have you been part of? What were your key contributions? What did you learn? What did you teach the world? How do your results compare to what was already known? What original ideas are you most proud of? Be specific, technical, credible, and confident (but not arrogant). Refer the reader to your web page for more details. Have a web page with more details: preprints, project reports, source code, videos, etc. I have been reading Hamilton Chapter 13 and he has the following state space representation for an ARMA(p,q). Let $r = \max(p,q+1)$.Then the ARMA (p,q) process is as follows: $$ \begin{aligned}  y_t -\mu &amp;= \phi_1(y_{t-1} -\mu) + \phi_2(y_{t-2} -\mu) + ... + \phi_3(y_{t-3} -\mu) \\ &amp;+ \epsilon_t + \theta_1\epsilon_{t-1} + ... + \theta_{r-1}\epsilon_{t-r+1}.  \end{aligned} $$ Then, he defines the State Equation as follows:   $$  \xi_{t+1} = \begin{bmatrix}      \phi_1 &amp; \phi_2 &amp; \dots &amp; \phi_{r-1} &amp; \phi_r \\      1 &amp; 0  &amp; \dots &amp; 0 &amp; 0  \\      \vdots &amp; \vdots &amp; \dots &amp; 0 &amp; 0 \\      0 &amp; 0 &amp; \dots &amp;1 &amp;0 \end{bmatrix} \xi_t  +  \begin{bmatrix}      \epsilon_{t+1} \\     0\\\vdots  \\     0       \end{bmatrix}  $$  and the observation equation as:  $$y_t = \mu + \begin{bmatrix}      1 &amp; \theta_1 &amp; \theta_2 &amp; \dots &amp; \theta_{r-1} \\     \end{bmatrix} \xi_t. $$  I do not understand what the $\xi_t$ is in this case. Because in his AR(p) representation it is $\begin{bmatrix}      y_{t} - \mu \\     y_{t-1} - \mu\\\vdots  \\     y_{t-p+1} - \mu       \end{bmatrix}  $ and in his MA (1) representation it is $\begin{bmatrix}      \epsilon_{t} \\     \epsilon_{t-1}      \end{bmatrix}  $.  Could someone explain this to me a little bit better? Is there an international taxonomy of academic titles/ranks? Looking at the  on Wikipedia shows that the same academic rank/title can mean quite different things in different countries. For instant, a "research assistant" in the US can stand for an undergrad student doing an internship, while in the UK it can stand for a postdoc. Similarly, the term "lecturer" might stand for a permanent position (e.g. in the UK) or for a teaching assistant position, open to graduate students.   However, when thinking about it, there are not so many kind of possible positions (permanent or not, with teaching or not, with research or not, with PhD supervision or not, with team responsibility or not, etc), and having a clear title could help a lot (for instance, in my case, I've been working in four different countries, with a different job title each time!).    Is there some kind of official taxonomy that one could refer to?  If not, who could be in charge to create it? (the EU, if only for intra-Europe mobility?) How to fix Permission Denied (Public key) error? While trying to communicate between my desktop Ubuntu 12.10 and Fedora 19 desktop, I am facing the error of Permission Denied (Public key). I am able to login through ssh from fedora to Ubuntu, but not vice-versa. I even performed telnet on both machines via port 22 and both machines are listening, but not through ssh. What to do? Any idea?  My sshd_config file is as follows:  # Package generated configuration file # See the sshd_config(5) manpage for details  # What ports, IPs and protocols we listen for Port 22 # Use these options to restrict which interfaces/protocols sshd will bind to #ListenAddress :: #ListenAddress 0.0.0.0 Protocol 2 # HostKeys for protocol version 2 HostKey /etc/ssh/ssh_host_rsa_key HostKey /etc/ssh/ssh_host_dsa_key HostKey /etc/ssh/ssh_host_ecdsa_key #Privilege Separation is turned on for security UsePrivilegeSeparation yes  # Lifetime and size of ephemeral version 1 server key KeyRegenerationInterval 3600 ServerKeyBits 768  # Logging SyslogFacility AUTH LogLevel INFO  # Authentication: LoginGraceTime 120 PermitRootLogin yes StrictModes yes  RSAAuthentication yes PubkeyAuthentication yes #AuthorizedKeysFile    %h/.ssh/authorized_keys  # Don't read the user's ~/.rhosts and ~/.shosts files IgnoreRhosts yes # For this to work you will also need host keys in /etc/ssh_known_hosts RhostsRSAAuthentication no # similar for protocol version 2 HostbasedAuthentication no # Uncomment if you don't trust ~/.ssh/known_hosts for RhostsRSAAuthentication #IgnoreUserKnownHosts yes  # To enable empty passwords, change to yes (NOT RECOMMENDED) PermitEmptyPasswords no  # Change to yes to enable challenge-response passwords (beware issues with # some PAM modules and threads) ChallengeResponseAuthentication no  # Change to no to disable tunnelled clear text passwords PasswordAuthentication yes  # Kerberos options #KerberosAuthentication no #KerberosGetAFSToken no #KerberosOrLocalPasswd yes #KerberosTicketCleanup yes  # GSSAPI options GSSAPIAuthentication no GSSAPICleanupCredentials yes  X11Forwarding yes X11DisplayOffset 10 PrintMotd no PrintLastLog yes TCPKeepAlive yes #UseLogin no  #MaxStartups 10:30:60 #Banner /etc/issue.net  # Allow client to pass locale environment variables AcceptEnv LANG LC_*  Subsystem sftp /usr/lib/openssh/sftp-server  # Set this to 'yes' to enable PAM authentication, account processing, # and session processing. If this is enabled, PAM authentication will # be allowed through the ChallengeResponseAuthentication and # PasswordAuthentication.  Depending on your PAM configuration, # PAM authentication via ChallengeResponseAuthentication may bypass # the setting of "PermitRootLogin without-password". # If you just want the PAM account and session checks to run without # PAM authentication, then enable this but set PasswordAuthentication # and ChallengeResponseAuthentication to 'no'. UsePAM yes   This is sshd_config of ubuntu system. How to get a list of monomials of a polynomial without coefficients? I know that I can create/burn bootable CD/DVD or live USB and can boot/install from it. But suppose I am currently running GNU/Linux and I've ISO file of another GNU/Linux that I want to install on my hard disk, then Can I directly boot from ISO from hard disk and try/install that GNU/Linux operating system? I have video tutorials that I want to show in my presentation with beamer class. I don't want the video files get embedded to the PDF because they will make the PDF size very very huge.  If you know how the videos can be played on the HTML with a reference rather than embedding the video file to the HTML file, I want something like this to be applied to my PDF presentation. I just want to reference the video URL from my PDF presentation.   Shortly speaking, can we use media9 to show a video on a PDF but the video is not embedded to the PDF?  Uploading those videos to a web server might be difficult for me because internet connection is very slow and sometimes not available in the presentation room. :-) How to request a random row in SQL? Current  enables one to upgrade to macOS Mojave from a stable release, but I want to try out a fresh installation instead of upgrading with previous data, so that I can assess it better.  I've downloaded an application named "macOS Mojave Beta" from the App Store, and running it would presumably result in an upgrade. Now I wonder what to do next. Would  and booting from it be a good idea, when I'm working with a Beta version? I want to use an old drive as a secondary hard drive without reformatting. But this old hard drive contains my old Vista installation which takes up gigs of space.  I tried changing ownership and it works to some extent but I can not delete anything in Windows/System32 folder.  Is there an easy way to change permissions so I can delete everything?    The solution is to use Takeown as Wil suggested and use cacls to take full control of the files. Since cacls doesn't seem to be recursive, I fired up cygwin and ran this command to recursively change all the files:  for d in $(find directory-of-interest -type d);do   cacls $d'/*' /e /G username:F; done   where directory-of-interest is in my case /cygdrive/g/Windows and username is my username.  I had to manually run it on directories that had spaces in its name. But after all this, I can now delete the directory. Warning: it seems to me that cacls can potentially royally screw things up if improperly used. Counting overlapping polygons in GeoJSON to result in new set of polygons? Counting set for generating functions Give  a  proof  of  the  following  identity  by  counting  two  sets  of  partitions  in  two  different ways.  \begin{equation*}  \prod_{i\geq 0}(1+x^{2i+1})=1 + \sum_{n\geq 1}x^{n^2}\prod_{j=1}^n\frac{1}{1-x^{2j}}  \end{equation*} To prove this inductively, i only successfully complete the base cases, however the counting set for the left side i concluded that would be the number of partitions of n with distinct odd parts and for RS the product part would be the number of partitions of n with even parts, how would the summation of $x^{n^2}$ come into play with counting set. How would i initiate my proof? Sometimes when you're downloading an image and the connection breaks mid stream, you are left with a half downloaded image. If you try to view it you get the upper part of the image and the bottom part is usually coloured grey or green or some other color.  In other words, it is corrupted.  Is there a way to check whether the image is damaged in that way or otherwise corrupted?