This is a simple question but I cant seem to find a concrete definition.  What is the meaning of a time series "season"?  Quoting from  blog on determining the period of a season, "...the “frequency” is the number of observations per season."
I'm using R(3.1.1), and ARIMA models for forecasting. I would like to know what should be the &quot;frequency&quot; parameter, which is assigned in the ts() function, if im using time series data which is:  separated by minutes and is spread over 180 days (1440 minutes/day) separated by seconds and is spread over 180 days (86,400 seconds/day).  If I recall right the definition, a &quot;frequency&quot; in ts in R, is the number of observations per &quot;season&quot;. Question part 1: What is the &quot;season&quot; in my case? If the season is &quot;day&quot;, then is the &quot;frequency&quot; for minutes = 1440 and 86,400 for seconds? Question part 2: Could the &quot;frequency&quot;  also depend on what I am trying to achieve/forecast? for example, in my case, I'd like to have a very short-term forecast. One-step ahead of 10minutes each time. Would it then be possible to consider the season as an hour instead of a day? In that case frequency= 60 for minutes, frequency = 3600 for seconds? I've tried for example to use frequency = 60 for the minute data and got better results compared to frequency = 1440 (used fourier see link below by Hyndman)  (The comparison was made by using MAPE for the measure of forecast accuracy) In case the results are complete arbitrary, and the frequency cannot be changed. What would be actually the interpretation of using freq = 60 on my data? I also think it's worth mentioning that my data contains seasonality at every hour and every two hours (by observing the raw data and the Autocorrelation function)
A teacher wants to randomly form two teams of 5 students from a group of 5 girls and 5 boys for a sports activity. A teacher wants to randomly form two teams of 5 students from a group   of 5 girls and 5 boys for a sports activity. Two of the girls, Ann and   Alice, are selected as team leaders. Find the probability that one   team has exactly 3 girls.   If i do this way $$\dfrac{{3 \choose 2}{5\choose 2}{1\choose 1}{3\choose 3} \times 2!}{{8 \choose 4}{4 \choose 4}} = \dfrac{6}{7}$$  Which turns out to tally with the answer. But i got one big question, is my way correct. Do i really need to times $2$ here? Please see my link below to my previous question cause the previous question make me doubt if i should times $2$. Is it coherent to extend $\mathbb{R}$ with a reciprocal of $0$? I'm sure this is an obvious question, but I'm having trouble finding the right words to type into Google.  I know that the definition of a ring allows that the additive identity not have a multiplicative inverse, but is this a requirement?  Specifically, is something like $\mathbb{R}\!\left[\frac{1}{0}\right]$ such that $\frac{1}{0} \cdot 0 = 1$ a ring, or does some contradiction arise from allowing the additive identity to have a multiplicative inverse? Original  The remainder provided by polynom.sty is NOT complete (as shown in the following figure).      My Objective  When I was in senior high school, my teacher made the diagram like below. :-)  Thus the final step must show the TOTAL remainder and mark it with L-shaped curve.  NOTE  I am sorry. The previous post I forgot to put back -1/4 in the original position. It have made you confused. Now there is no mistake anymore. :-)      Minimal Code  \documentclass{article} \usepackage{polynom,array} \usepackage[table]{xcolor}   \makeatletter \def\pld@ArrangeResult#1{%     \ifx\pld@remainder\@empty         \@tempcnta\pld@maxcol\relax         \pld@InsertItems@do\pld@lastline             {\pld@firsttrue\pld@PLD{\pld@R{0}{1}}}%     \fi     \ifnum\pld@currstage&gt;\z@         \pld@Extend\pld@allines{\pld@lastline\cr}%     \else         \pld@InsertFake\pld@lastline     \fi     \pld@iftopresult         \def\pld@lastline{\pld@PrintPoly\pld@divisor%         %====================================================================================         \quad\smash{{\color{red}\rule[-6pt]{\arrayrulewidth}{17pt}}}\kern-\arrayrulewidth&amp;}%         %====================================================================================     \else         \let\pld@lastline\@empty         \ifx B\pld@style\else             \def\pld@lastline{\pld@leftdelim\strut\pld@rightxdelim&amp;}%         \fi     \fi     \expandafter\pld@AR@col\expandafter\pld@PLD                            \expandafter\pld@lastline#1+\relax+%     \pld@SplitQuotient     \pld@iftopresult         \let\pld@currentline\@empty         \expandafter\pld@AR@col\expandafter\pld@PLD                                \expandafter\pld@currentline                                            \pld@quotient+\relax+%         \expandafter\pld@AR@col\expandafter\pld@XPLD                                \expandafter\pld@currentline                                            \pld@shadow+\relax+%         \edef\pld@subline{%             \noexpand\cline{\tw@-\pld@maxcol}%             \noalign{\vskip\jot}}%         \pld@Extend\pld@currentline{\expandafter\cr\pld@subline}%     \else         \@tempcnta-\@tempcnta         \advance\@tempcnta\pld@maxcol\relax \advance\@tempcnta\@ne         \edef\pld@span{\the\@tempcnta}%         \ifx B\pld@style           \pld@AddTo\pld@lastline{%             &amp;\multispan\pld@span${}=%             \pld@PrintPolyWithDelims\pld@divisor             \expandafter\pld@IfSum\expandafter{\pld@divisor}{}{\cdot}%             \expandafter\pld@IfSum\expandafter{\pld@quotient}\pld@true                                                              \pld@false             \pld@if \pld@leftdelim                     \pld@PrintPolyShadow                     \pld@rightdelim               \else \pld@PrintPolyShadow \fi             \pld@firstfalse             \expandafter\pld@PrintRemain\expandafter{\pld@remainder}$}%         \else           \pld@AddTo\pld@lastline{%             &amp;\multispan\pld@span$\pld@leftxdelim\strut\pld@rightdelim             \pld@div             \pld@PrintPolyWithDelims\pld@divisor=             \pld@PrintPolyShadow             \ifx\pld@remainder\@empty\else                 +{}%                 \setbox\z@=\hbox{$\displaystyle                   \frac{\let\strut\@empty\pld@firsttrue \expandafter                         \pld@PrintRemain\expandafter{\pld@remainder}}%                        {\let\strut\@empty\pld@PrintPoly\pld@divisor}$}%                 \dp\z@=\z@\box\z@             \fi             $}%         \fi     \fi \expandafter\pld@AR@\pld@allines\relax} \makeatother   \arrayrulecolor{red} \arrayrulewidth=0.8pt \def\strut{\rule[-6pt]{0pt}{12pt}}  \begin{document} \polylongdiv[style=A]{\frac{3}{7}x^9+x^2-\frac{1}{4}}{\frac{9}{5}x^4-1}  \vspace{1cm} \polylongdiv[style=A]{x^4-1}{x^2-1} \end{document} Noticing that Newtonian gravity and electrostatics are equivalent, is there also a relationship between the general relativity and electrodynamics? In classical mechanics, we had Newton's law of gravity $F \propto \frac{Mm}{r^2}$.  Because of this, all laws of classical electrostatics applied to classical gravity if we assumed that all charges attracted each other due to Coulomb's law being analogous.  We can "tweak" classical electrostatics to fit gravity.  In modern physics, does the reverse work?  Can we "tweak" General Relativity to accurately describe electrostatics or even electromagnetism? I tried a small experiment. I posted a post on Facebook at exactly: 21:01 and waited to see how many hours ago it will say. When it was 22:50 it still said that my post was posted 1 hour ago.  Though some days back on this forum some people told me that when something started at 21:01 and it is 22:50 that I should say it started 2 hours ago.  So whom should I trust now?  All social networks like Facebook, Instagram and YouTube etc. use the system where it would say 1 hour ago even if it was 119 minutes already, so meaning they will never say it was 2 hours ago unless at least 120 minutes passed.  This was the way I used to express 1 hour ago as well. However, since I heard the answers from many other people I feel unsure about it right now...  I am talking about casual speech with friends etc. In such scenario. What would you say? 1 or 2 hours ago? Is Facebook/YouTube/Instagram wrong or?   if we decide to agree on the theory that if it is more than 1 hour and 40 minutes it is a good idea to round to 2 hours ago.   So what time span would you imagine if something happened let say 10:10, now it is 11:50.  If somebody said to me that something happened 2 hours ago and I looked on time saying 11:50 I would image that it happened some time between. (9:30-9:50)  That is why it feels so weird for me to say 2 hours ago thought it has not been more two hours yet.   I dont know why but more logical for me it feels to say 1 hour ago though it can already be more than 100 minutes  and still just say that it happened an hour ago when talking with friends, teachers, whoever in casual speech unless it is something super important i would say exactly hours and minutes.  How do you say it in your life? How do you express time in such situations? Do you express time the same way as Facebook or?   I know that some of you may think this is some kind of joke, unfortunately it is not and I am going crazy and depressed without knowing system for this... It has been already 2 months and I still feel overwhelmed with this ideas and questions... I cannot help myself, please help me, please.  Thanks for your help. Solving "The ObjectContext instance has been disposed and can no longer be used for operations that require a connection" InvalidOperationException Currently, moderators have the ability to reset a user's username and/or profile text, and propagate that to the rest of the network, resetting it everywhere. However, often, the user's stackexchange.com network profile will also need to be reset, and this is currently only possible to do by either the user in question or staff.  Instead of bothering staff every time, moderators should have something available similar to chat, where moderators can change a user's parent site and have access to a "refresh profile" button, which will fetch updated information such as username and avatar from the parent site.  Currently, the only thing that moderators can do on stackexchange.com is to see hidden accounts. It would make sense for moderators to be able to refresh profiles there, like chat, and avoid pinging CMs every time this comes up. Can you make an unwilling creature willing? In other words, what defines “willing”? Going through the spells, I see the phrase "Willing creature" used to determine who you can cast some spells on. I don't ever see a proper definition of what a willing creature is, but I would assume that it would go something like if you asked them "Can I perform this spell on you" they would answer yes. Is there a more formal definition of what makes a target willing in 5e?  What are the ways I could make an otherwise unwilling creature willing? Suggestion spells, for instance, should probably work but what other options do I have? How do I install OpenStack? I'm starting to do designs meant for printing, but I'm fairly new to this medium so I don't really understand how bleed works and how much bleed should I specify for:   Business cards Large format prints (42 inches and bigger) Magazines   Should I extend the design into the bleed areas? Serial protocol delimiting/synchronization techniques As asynchronous serial communication is widely spread among electronic devices even nowadays, I believe many of us have encountered such a question from time to time. Consider an electronic device D and a computer PC connected with serial line (RS-232 or similar) and required to exchange information continuously. I.e. PC is sending a command frame each X ms, and D is replying with status report/telemetry frame each Y ms (The report can be sent as response to requests or independently - doesn't really matter here). The communication frames can contain any arbitrary binary data. Assuming the communication frames are fixed-length packets. The problem: As the protocol is continuous, the receiving side might loose the synchronization or just &quot;join&quot; in the middle of an ongoing sent frame, so it just won't know where the start of frame (SOF) is. A the data has different meaning based on its position relatively to the SOF, the received data will become corrupted, potentially forever. The required solution Reliable delimiting/synchronization scheme to detect the SOF with short recovery time (i.e. it shouldn't take more than, say 1 frame to resynchronize). The existing techniques I am aware (and using some) of: 1) Header / checksum - SOF as predefined byte value. Checksum in the end of frame.  Pros: Simple. Cons: Not reliable. Unknown recovery time.  2) Byte stuffing:  Pros: Reliable, fast recovery, can be used with any hardware Cons: Not that suitable for fixed-size frame-based communication  3) 9th bit marking - prepend each byte with additional bit, while SOF marked with 1 and the data bytes are marked with 0:  Pros: Reliable, fast recovery Cons: Requires hardware support. Not directly supported by most of PC hardware and software.  4) 8th bit marking - kind of emulation of the above, while using the 8th bit instead of 9th, which is leaving only 7bits for each data word.  Pros: Reliable, fast recovery, can be used with any hardware. Cons: Requires an encoding/decoding scheme from/to the conventional 8-bit representation to/from 7-bit representation. Somewhat wasteful.  5) Timeout based - assume the SOF as the first byte coming after some defined idle time.  Pros: No data overhead, simple. Cons: Not that reliable. Won't work well with poor timing systems like, say, Windows PC. Potential throughput overhead.  Question: What are the other possible techniques/solutions exist to address the problem? Can you point to the cons in the above list which can be easily worked around, thus removing them? How do you (or would you) design your systems protocol? I have an area which is divided into several zones the borders of which I have defined as separate layers.  The layers are defined by sql queries on a postgis table of line segments joined with a table that says which segments are part of which zone boundaries.  What I want to do is produce a set of maps where each map is a zoom to layer extent for each zone and which has standard header, legend and scale (which will preferably vary with the zone but could be fixed across all maps).  My first attempt was to get a new composer for each map -- that worked but was rather tedious.  Next I tried producing one map and printing it and then deleting the map frame and going into qgis to zoom to the next layer extent and make the boundary visible then hopping back into the composer to load it in.  This worked more or less.  Map was fine, legend was OK because it was the same for all the maps and the zone name was easy to edit but the scale needed to be deleted and set up again for each map.  Next I looked at Atlas Generation.  The manual seems to assume that you know how it works and all you need is a reminder about the details (like so many software manuals ;)  It seems to assume that you have something that you are iterating over but I can't see how to make it work -- there is nothing to iterate over to get the layers.  Any suggestions welcome!!  :)  Russell How to find relevant and new open research topics? When I run the logistic regression, two independent variables have VIF values greater than 10 like 13 or so. Logistic regression is the one I will use to measure the overall change in the dependent variable with one incremental changes in every each independent variable. However, when I run the linear regression model version on my same data, the VIF values I get from all the independent variables are either slightly greater than 1 or around 5 or 6. Besides, all the coefficients are highly significant all below 0.01.  If so, is it safe to use my logistic regression model to find out the incremental effect of every each independent variable without dropping out any independent variables?   If my purpose is to find an incremental effect of every each independent variable on the overall dependent value in a logistic regression model, is multicolinearity an important problem to consider? Can I ignore it?   If my p-values are all less than 0.01 which is the same indicator as t-value, will I still need to worry about colinearity issue even though my VIF scores for two variables are around 13-14? Based on what you said, if p-value is safe enough, will this be still a problem?  I am also referring to the following website comment:                                                                     So, in sum, my ultimate goal is to use the final output from the logistic regression model generated from the independent variables and one binary dependent variable. If so, do you think I can ignore the multicolinearity problem? What is the "rootless" feature in El Capitan, really? I have just learned about the "Rootless" feature in El Capitan, and I am hearing things like "There is no root user", "Nothing can modify /System" and "The world will end because we can't get root".  What is the "Rootless" feature of El Capitan at a technical level? What does it actually mean for the user experience and the developer experience? Will sudo -s still work, and, if so, how will the experience of using a shell as root change? Logo Pack - What should I include? What files should i put in a logo pack to give to clients? Should I put small, medium and large version of my logo as well as the vector file. How do you install an APK file in the Android emulator? How do I emit light from inside a object? Exact sequence of sheaves with non exact sequence of global sections Let $X$ be some topological space. By $\mathcal{F}_i$ we denote some sheaves of abelian groups on $X$. The sequence of sheaves and morphisms  $$\mathcal{F}_1\longrightarrow \mathcal{F}_2\longrightarrow \mathcal{F}_3\longrightarrow... $$ is said to be exact if for each $x\in X$ the corresponding sequence of stalks $$(\mathcal{F}_1)_x\longrightarrow (\mathcal{F}_2)_x\longrightarrow (\mathcal{F}_3)_x\longrightarrow... $$ is exact. However if the sequence of sheaves is exact than the sequence of global sections is not necessarily exact! (The most famous example is the sequence of sheaves $$0\longrightarrow\mathbb{Z}\hookrightarrow \mathcal{O}\stackrel{\exp}{\longrightarrow} \mathcal{O}^*\longrightarrow0$$ considered as sheaves on $\mathbb{C}-\{0\}$, where $\mathcal{O}$ is a sheaf of holomorphic functions, $\mathcal{O}^*$ is a sheaf of holomorphic functions with no zeros).  So, could you give me some easy examples of such phenomenon ? Pre-generate Review audits to avoid the lag?