Can you train yourself to sleep fewer number of hours forever, nightly, while remaining at least as  fit and healthful (without harming or impairing yourself in any way) ?  This question was inspired by  on Columbia Professor Jeffrey Sachs:     As far as I can tell, the only time Sachs slows down is when he sleeps, never more than four or five hours a night. His wife, Sonia Ehrlich, a pediatrician and the mother of his three children, has been quoted saying (more than once), "I'm a happily married single parent."
In the past month, I've been really busy with the university and stuff, and I don't sleep as much as I used to. I usually sleep 4-5 hours a night.  I haven't been doing that extensively ( I always kept a good sleeping routine), but can the lack of sleep affect my health on the long term ?
Apologies if this has been asked somewhere before, but I didn't see what I was looking for after several pages of Google results.  I was reading Jech's The Axiom of Choice and was introduced to the equivalence of the ultrafilter lemma and the compactness theorem for FOL. I gather that these are also equivalent to the completeness theorem. I am primarily interested in trying to understand the "ultrafilter lemma $\implies$ completeness/compactness" direction. Jech's own proof takes an odd route through "binary messes" and I don't really follow the last couple of steps. (It's on pp.17,18 of the 2008 Dover reprint, if one is interested).  I'm wondering if anyone knows a good reference for, or can provide, a readable proof that the ultrafilter lemma implies completeness or compactness, with a preference for completeness. Alternatively, if you have Jech's book on hand, helping me bridge the concluding paragraph of his $\textrm{(ii)}\implies\textrm{(iii)}$ step with the preceding steps would clear up much of my puzzlement. (Though in this case I can't offer any help in saying what, specifically, is missing in the way of a bridge). Import error when opening empty notebook Significant predictors become non-significant in multiple logistic regression When I analyze my variables in two separate (univariate) logistic regression models, I get the following:  Predictor 1:    B= 1.049,    SE=.352,    Exp(B)=2.85,    95% CI=(1.43, 5.69),    p=.003    Constant:    B=-0.434,    SE=.217,    Exp(B)=0.65,                            p=.046  Predictor 2:    B= 1.379,    SE=.386,    Exp(B)=3.97,    95% CI=(1.86, 8.47),    p&lt;.001    Constant:    B=-0.447,    SE=.205,    Exp(B)=0.64,                            p=.029   but when I enter them into a single multiple logistic regression model, I get:  Predictor 1:    B= 0.556,    SE=.406,    Exp(B)=1.74,    95% CI=(0.79, 3.86),    p=.171 Predictor 2:    B= 1.094,    SE=.436,    Exp(B)=2.99,    95% CI=(1.27, 7.02),    p=.012    Constant:    B=-0.574,    SE=.227,    Exp(B)=0.56,                            p=.012   Both predictors are dichotomous (categorical). I have checked for multicollinearity.  I am not sure if I have given enough info, but I cannot understand why predictor 1 has gone from being significant to non-significant and why the odds ratios are so different in the multiple regression model. Can anyone provide a basic explanation of what is going on? How to vertically align underbraces I am trying to balance underbraces in the equation below, how can I ensure that both underbraces at the same depth?  \begin{equation} y = \underbrace{ \left [ x^2 + r^2 (a^2+\frac{a^{0.3}}{b}) \right]}_\text{growth rate} \times  \underbrace{ C_0}_\text{initial} \end{equation} So I have a generic list, and an oldIndex and a newIndex value.  I want to move the item at oldIndex, to newIndex...as simply as possible.  Any suggestions?  Note  The item should be end up between the items at (newIndex - 1) and newIndex before it was removed. Solve the recurrence relation:$ T(n) = \sqrt{n} T \left(\sqrt n \right) + n$ $$T(n) = \sqrt{n} T \left(\sqrt n \right) + n$$  Master method does not apply here. Recursion tree goes a long way. Iteration method would be preferable.  The answer is $Θ (n \log \log n)$.  Can anyone arrive at the solution. Definition of $\mathbb{R}^\infty$ Question: Why is the topological space $\mathbb{R}^\infty$ defined to be the subset of $\prod_{i=1}^\infty \mathbb{R}_i$ consisting of sequences $(a_i)_{i=1} ^{\infty}$ such at most finitely many $a_i\neq 0$? Why does one insist on the condition that $a_i\neq0$ for at most finitely many $i$? How to animate noise texture "seed"? It's possible to animate a change noise texture by animating the texture coordinates with a mapping node or by animating the texture space, however this only works on one axis at a time (on the other axes the texture will appear to be sliding across the object's surface).  For example, the top face has the desired effect but the other faces appear to be moving/sliding upwards:    Even with all three axes location and rotation animated it still appears to be sliding rather than statically changing.    Is there some way to make each face appear like the top face in the first gif but still be seamlessly blended with the other faces? This should work for other shapes as well.  In other words, I'm looking for a way to animate the "seed" of the texture. Displaying layout marks in a document set with different layouts Is there any package that allows for the display of layout marks within a document where the layout changes several times throughout? I'm using the geometry facilities to issuing \newgeometry commands throughout my document, but it doesn't update the displayed layout and neither does the showframe package or the facilities of the memoir class.  EDIT: As Werner has pointed out, the showframe option of the geometry package displays correctly any updated page layout set by issuing \newgeometry commands.   My trouble came out of the fact that I'm issuing also \pagecolor commands and the page color seems to be hiding the layout lines typeset according to the geometry package. My confusion only worsened because the showframe package layout lines were not hidden by the page color (the package got the layout wrong on some pages, though). So, it all boils down to a conflict with the page color.   Even though I'm using geometry's showframe option for "debugging" ends, and I don't mind to have no page color at that stage of development, is it possible to override this problem and have at the same time both the page layout displayed by geometry as well as the page colored?   Btw, should I open a new question given that the problem is actually different from the originally posted one? Search functionality in lightning:datatable? Is there a way to search across all rows/columns in a lightning:datatable to narrow down the list, just like jQuery DataTables? If so, how do implement that?  Can I somehow do it all on the client-side to make it super fast (some sort of DOM manipulation)  I'm having some issues with the lightning:datatable not updating. I have attached my code below, maybe you can help me spot the issue:  Markup:  &lt;aura:component extends="c:Base" controller="AccountBrowserForm"&gt; &lt;aura:handler name="init" value="{! this }" action="{! c.doInit }"/&gt; &lt;aura:attribute name="selectedAccountId" type="Id" access="public" /&gt; &lt;aura:attribute name="accounts" type="Object"/&gt; &lt;aura:attribute name="mycolumns" type="List"/&gt; &lt;aura:attribute name="sortedBy" type="String" /&gt; &lt;aura:attribute name="sortedDirection" type="Boolean" default="true" /&gt;  &lt;aura:registerEvent name="AccountFilterChange" type="c:AccountFilterChange" /&gt;  &lt;aura:attribute name="backingdata" type="List" /&gt; &lt;aura:attribute name="filter" type="String" /&gt; &lt;lightning:input type="text" onchange="{!c.filter}" value="{!v.filter}" label="Filter" /&gt;  &lt;lightning:datatable aura:id="lightningTable"                      data="{! v.accounts }"                      columns="{! v.mycolumns }"                      keyField="Id"                      onrowaction="{! c.handleRowAction }"                      onsort="{!c.updateColumnSorting}"                      sortedBy="{!v.sortedBy}"                      sortedDirection="{!v.sortedDirection}"                      hideCheckboxColumn="true" /&gt;     Controller:  doInit: function (component, event, helper) {     helper.callServer(component, "c.getAccounts", $A.getCallback(function (response) {         component.set("v.accounts", response);         component.set("v.backingdata", response);         console.log(component.get("v.backingdata") + " /// BACKING DATA INSIDE ")         console.log(component.get("v.accounts") + " // ACCOUTN DATA INSIDE")          component.set('v.mycolumns', [{                 type: "button",                 typeAttributes: {                     label: '',                     iconName: 'utility:add',                     name: 'selectRecord',                     title: 'selectRecord',                     disabled: false,                     value: 'edit',                     variant: {                         fieldName: 'variantValue'                     },                 }             },             {label: 'Name', fieldName: 'Name', type: 'text', sortable: true},             {label: 'Street', fieldName: 'BillingStreet', type: 'text', sortable: true},             {label: 'Postal Code', fieldName: 'BillingPostalCode', type: 'text', sortable: true},             {label: 'City', fieldName: 'BillingCity', type: 'text', sortable: true},             {label: 'Country', fieldName: 'BillingCountry', type: 'text', sortable: true},         ]);          console.log(component.get("v.backingdata") + " *** BACKING DATA OUTSIDE *** ")         console.log(component.get("v.accounts") + " *** ACCOUNT DATA OUTSIDE *** ")     })) },  filter: function (component, event, helper) {     var data = component.get("v.backingdata"),         term = component.get("v.filter"),         results = data,         regex;     try {         regex = new RegExp(term, "i");         // filter checks each row, constructs new array where function returns true         results = data.filter(row =&gt; regex.test(row.name) || regex.test(row.age.toString()));     } catch (e) {         // invalid regex, use full list     }     component.set("v.accounts", results); },   For some reason the filter function is completely unresponsive. Also, does it matter that I'm populating the component with a response from a callback function. @sfdcfox, I noticed in your example that you simple created an array with dummy data. My "myaccounts" attribute is of type object Understanding minipages - aligning at top I would like to be able to align two minipage at the top, without worrying about what is in the minipage.  I am aware of the optional [t] parameter, but still have some confusion as to how this all works.  I tend to think of a minipage as a regular page in that whatever is placed on it starts at the top and fills the page going across and then down the page, but this does not appear to be the case.  In the MWE example below, I have color coded the sections for reference purposes.   The first case (black) works just as I would expect. The two minipages are aligned exactly as I want with the [t] specifier.  No question here.  The next case (red) only works if the inner minipage also has the [t] specifier. Why is that necessary?  I would have thought that any content would be placed at the top of this page, and since both the outer minipage had a [t] things should have aligned at the top. I would like to place a graphic in the second mini page, and still have the two aligned at the top.   The simple case (blue) of using \includegraphics directly does not result in the content being aligned at the top.  So, then I attempt to put this in a \parbox (green) and this too does not yield the desired results.  I also try to place the graphic inside an inner minipage (brown) and specify the [t] alignment, and even though this worked in the red section, it does not here.  The only difference between the red and brown being that the red section had text, whereas the brown section has a graphic.  I am aware of question regarding  which suggests to place \vspace{0pt} at the top of the minipage, and that does provide the desired alignment (cyan), but adds vertical space at the top.  So, my second question is why is the \vspace{0pt} necessary when a graphic is included, but not when it is text.  This appears to be a hack and wondering if there is a replacement for minipage that works better without having to worry about exactly what is in the minipage?  Also, why did wrapping the figure in a parbox (green) or another minipage (brown) not solve this problem?   Here is the MWE:  \documentclass{article} \usepackage[demo]{graphicx} \usepackage{lipsum} \usepackage{xcolor}  \begin{document} \section{This Works - Aligned at top as desired} \begin{minipage}[t]{0.6\linewidth}     \lipsum[1] \end{minipage} \hfill \begin{minipage}[t]{0.3\linewidth}     \lipsum[2] \end{minipage}  \color{red} \section{Why does inner mini page required the [t]?} \label{Minipage-in-minipage} \begin{minipage}[t]{0.6\linewidth}     \lipsum[3] \end{minipage} \hfill \begin{minipage}[t]{0.3\linewidth}     \begin{minipage}[t]{\linewidth}% Why is [t] required here         \lipsum[4]     \end{minipage} \end{minipage}  \color{blue} \section{Why are These not aligned at top?} \begin{minipage}[t]{0.6\linewidth}     \lipsum[3] \end{minipage} \hfill \begin{minipage}[t]{0.3\linewidth}     \includegraphics[width=\linewidth]{foo} \end{minipage}  \color{green} \section{Why are These not aligned at top?} \begin{minipage}[t]{0.6\linewidth}     \lipsum[3] \end{minipage} \hfill \begin{minipage}[t]{0.3\linewidth}     \parbox{\linewidth}{\includegraphics[width=\linewidth]{foo}} \end{minipage}  \newpage \color{brown} \section{Why does this not work with the [t] as it did in red section?} This worked fine in Section \ref{Minipage-in-minipage}  \begin{minipage}[t]{0.6\linewidth}     \lipsum[3] \end{minipage} \hfill \begin{minipage}[t]{0.3\linewidth}     \begin{minipage}[t]{\linewidth}% Even with [t] here, this does not work         \parbox{\linewidth}{\includegraphics[width=\linewidth]{foo}}     \end{minipage} \end{minipage}   \color{cyan} \section{Adding a \textbackslash{}vspace\{0pt\} works} \begin{minipage}[t]{0.6\linewidth}     \vspace{0pt}% Hack!! But does do the job     \lipsum[3] \end{minipage} \hfill \begin{minipage}[t]{0.3\linewidth}     \vspace{0pt}% Hack!! But does do the job     \begin{minipage}[t]{\linewidth}% Why is [t] required here         \parbox{\linewidth}{\includegraphics[width=\linewidth]{foo}}     \end{minipage} \end{minipage} \end{document} Does anyone know how to remove this dead bolt that has no screw heads to use a screw driver? Here's a picture below. What's in a name: hyperparameters So in a normal distribution, we have two parameters: mean $\mu$ and variance $\sigma^2$. In the book Pattern Recognition and Machine Learning, there suddenly appears a hyperparameter $\lambda$ in the  regularization terms of the error function.  What are hyperparameters? Why are they named as such? And how are they intuitively different from parameters in general? How to show similar display of codes of different programming languages in LaTeX I am very new to LaTeX and I am writing my thesis. In a chapter, I want to show my codes, which are in Mathematica.   I use the listings package as follows:  \documentclass{article}   \usepackage{listings}   \begin{document}   \lstset{language=Mathematica}    \begin{lstlisting}   Do[i^j,{i,1,10},{j,1,10}]   \end{lstlisting}    \end{document}   However, the output is much different to what the code looks like in the Mathematica IDE (even if I use other languages in \lstset{language=&lt;name&gt;}):    I read some questions on the site but, in some of them, the font or color of the codes were not the same. Could you please help me to display something like the picture below in LaTeX?  If it is important, I am using the BiDi package. windows command prompt change directory is now changing directory What would be a good term for continuous testing post-deployment? More than once I've accidentally run a number of commands and polluted my bash history. How do I close my terminal without saving my bash history? I'm using Fedora. Using contracted forms ("don't", "let's") in a formal text How compelled should I feel to use non-contracted forms (do not rather than don't and so on) when writing in a rather formal text, say an academic paper? In one case I am afraid to seem too stilted, in the other, too casual. Are there good guidelines?  And are there differences in this regard between British and American English?  (In this  there was not much more than "Contractions are more frequent in informal than formal contexts".) Under what conditions does loot despawn? I have found that when my bags get full and I need to vendor loot I can sometimes leave loot on the ground and return to it.  Other times it seems to disappear almost instantly once I leave the area.  Is the loot despawn time based, based on my distance from the dropped loot, or some other factor(s)? Declare IDisposable for the class or interface?