Running Ubuntu 18.04.3 --------------------- I think the 4.15.0-72 generic kernel is corrupt or perhaps just incapable of working properly on my older laptop - it will freeze on shutdown every time when using the default 4.15.0-72 generic, but will shutdown fine when I interrupt boot-up and select 4.15.0-70 generic to boot instead... or is there something else going on?
I installed a mainline kernel for testing purposes. I would like to set grub to boot from the older kernel by default.  I know I can set the GRUB_DEFAULT=0 setting for the first page of grub but how do I set it to boot by default from one kernel in the second page (Advanced page)?  I would prefer doing this without installing other software (ex. grub-customizer).     Related Questions:
How to find a generator of a cyclic group? How to find $\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}$? Problem was to find $$\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}.$$ My partial progress i tried to motivate such that upper term in binomial terms gets constant rather than variable , so i thought of changing it to form $\binom{n}{n-r}\binom{n-r}{n-2r}$. Now it's of the form $\binom{n}{m}\binom{m}{k}$. We know it is equivalent to $\binom{n}{k}\binom{n-k}{m-k}$. Doing this we get $\binom{n}{2r}\binom{2r}{r}2^{n-2r}$. Now what I need to do as next step as such still nothing the upper or lower terms r any constant values(sum to ) , all are variables still. Now by one answer by Robpratt i got by snake oil , is there any other way to solve this problem ? Why are there so many different ways to measure disk usage? Consider an irreducible but possibly periodic Markov chain on a finite state space with transition matrix $P$. We know there exists a unique stationary distribution $\pi$. If the Markov chain were aperiodic, we would have $P^n_{ij} \to \pi(j)$ as $n \to \infty$. This fails if the chain is periodic, but we have convergence of the Cesaro averages: $$\frac{1}{n}\sum_{k=1}^n P^k_{ij} \to \pi(j) \text{ as } n \to \infty.$$ Can anyone point me to a reference that states this fact? Every reference I've seen only considers convergence for aperiodic chains, or "fixes" periodicity by considering a lazy version of the chain. Alternatively, is there a simple way to obtain this result using the result for aperiodic chains? What invisible flicker do different types of light bulbs have? What waveform does the light coming off different types of artificial light sources have and (of course) what are the underlying physical reason for them?    I was inspired to ask this question because of several things I have been hearing lately.  Firstly, there was a recent TED talk about how .  Researchers have been working on the problem for a little while now and they've made a fairly impressive product, but it was only recently made possible by the LED technology, which has such a fast response that it can easily compare to the transfer rates of electric information condiuits that we normally use.  My understanding is that incandescent bulbs flicker because they have 60 Hz AC power being pulsed through them.  In fact, I think 60 Hz was chosen in the first place because it was a threshold that was unnoticeable to humans.  Looking at a  demonstrates that it has a very significant lag time responding to both the normal electrical phasor and being turned off.  In other words, it flickers but it doesn't go dark at any point in the AC waveform.  Looking for more information, however, I was a little disappointed, since nothing seemed to give a graph of lumens emitted over time for all different kinds of bulbs.  Of course, there isn't just one relevant time scale.  A light could flicker with 60 Hz and also flicker with 2000 Hz (I just made that up).  I'm interested in the complete picture of what lights exhibit what patterns. Cost Distance Analyst In QGIS? Are there any tools, plugins or methods in QGIS which allows for an analysis of the best path between two points using least cost path method? As shown below ArcGIS has several distance tools. How does IPv4 Subnetting Work? Activate physics by keyframe I'd like to have a group of debris fall from a ceiling onto the floor, but not have them drop all at the same time. Is there a way to set a keyframe that dictates when the object enters the simulation? For example, object 1 starts falling on frame 0, object 2 on frame 5, object 3 on frame 24, etc. I have a code that prints a table with 2 rows. I want to keep format of it and change 2 rows into 3.   \documentclass[conference]{IEEEtran}  \usepackage{pgfplots} \usepackage{siunitx} \usepackage{multirow} \begin{document}  \begin{table}[h] \caption{Family data set results} \label{tbl::Fam} \centering \begin{tabular}{|l|l|c|c|c!{\vrule width 2pt}l|l|c|c|c|} %\noalign{\hrule height 2pt} \hline \textbf{Column}&amp;\textbf{Algorithm}&amp;\textbf{min}&amp;\textbf{max}&amp;\textbf{std}l&amp;\textbf{Column}&amp;\textbf{Algorithm}&amp;\textbf{min}&amp;\textbf{max}&amp;\textbf{std}\\\hline \multirow{2}{*}{age}&amp;Original&amp;9&amp;2.8&amp;100&amp;\multirow{2}{*}{employer\_type}&amp;Original&amp;13&amp;2&amp;10\\ \cline{2-5} \cline{7-10}&amp;PrivBayes&amp;2&amp;95&amp;96&amp;&amp;PrivBayes&amp;2&amp;100&amp;100\\\hline \multirow{2}{*}{education\_level}&amp;Original&amp;7&amp;2&amp;98&amp;\multirow{2}{*}{marital\_status}&amp;Original&amp;10&amp;2&amp;100\\ \cline{2-5} \cline{7-10}&amp;PrivBayes&amp;2&amp;6&amp;96&amp;&amp;PrivBayes&amp;2&amp;6&amp;100\\\hline \hline %\noalign{\hrule height 2pt} \end{tabular} \end{table}  \end{document}   In this picture, I have 2 algorithms {Original, PrivBayes}. I want to change 2 algorithms into 3 algorithms with keeping the format of table. Can you please help me to do it? 1) Alex's house      2) Alex' house     When the noun ends with the letter 's' or 'x', do I need to put 's' after an apostrophe or not?  I remember I read some rules related to this in my school grammar book, but now I've forgotten it. Why do diamonds shine? Let's say that there exists some "true" relationship between $y$ and $x$ such that $y = ax + b + \epsilon$, where $a$ and $b$ are constants and $\epsilon$ is i.i.d normal noise. When I randomly generate data from that R code: x &lt;- 1:100; y &lt;- ax + b + rnorm(length(x)) and then fit a model like y ~ x, I obviously get reasonably good estimates for $a$ and $b$.  If I switch the role of the variables as in (x ~ y), however, and then rewrite the result for $y$ to be a function of $x$, the resulting slope is always steeper (either more negative or more positive) than that estimated by the y ~ x regression. I'm trying to understand exactly why that is and would appreciate it if anyone could give me an intuition as to what's going on there. Previously, someone posted his/her proof of "every neighborhood is open" . I am focusing on the same statement, but it seems that my approach is different from his/hers. Could someone comment on my own proof? Here we go:  Let $X$ be a metric space and $p\in X$. Fix $r&gt;0$. Define a neighborhood around $p$ as $N_r (p)=\{q\in X| d(p, q)&lt;r\}$. Now, take $w = \frac{r}{2}$. Then, $N_w (p)\subset N_r(p)$. In other words, every point of $N_r(p)$ is interior. Therefore, $N_r (p)$ is open. Since $r$ is arbitrary, this proves every neighborhood is open.  Update:  Under my definition of "neighborhood," can I prove in this way instead: For all $m\in N_r(p)$, take $w=\frac{r−d(m,p)}{2}$. Then, $N_w(m)\subset N_r(p)$.   Update2  From the hints given in comments, I solve it:  Assume $m\in N_r(p)$ and $q\in N_w(m)$. Take $w=r-d(m, p)$. Then, $d(p, q)\leq d(p, m) + d(m, q)&lt; d(p, m) + r-d(m,p) =r$.   Thanks to @JoséCarlosSantos and @fleablood ! Stack Overflow is getting a Meta of its own Deleting a suspicious malware (imklaunchagent) in Mac I have a MacBook Pro (macOS Mojave) laptop and have recently noticed a suspicious process in Activity Monitor with this name : imklaunchagent    I checked this folder: /System/Library/Frameworks/InputMethodKit.framework/Versions/A/Resources/imklaunchagent and it seems imklaunchagent and its related files cannot be removed. I tried to remove it via Terminal and this message showed up: "Operation not permitted". However, in "Security and Privacy" of "System Preferences", I chose Terminal to have full disk access, still can't delete the file and the same message appears.  I installed the free version of Combo Cleaner and it detected other viruses, none of which are imklaunchagent. Is imklaunchagent a malware? How can it be deleted? If $X$ is measurable space, $f : X\to [-\infty,+\infty]$, function such that $f^{-1}([-\infty,r))$ measurable for all rational numbers $r$,prove than $f$ is measurable  I know that $f$ is measurable iff set $\{x\in X : f(x)&lt;a\}$ is measurable for all $a\in \mathbb{R}$ but for $a\in\mathbb{Q}$ I don't know how to proceed. How to view monitor refresh rate in macOS? I just purchased a Dell P2175Q monitor for my 15" MBP w/Touchbar. I'm connecting with a USB-C to DisplayPort cable, but when I go to Apple > System Preference > Displays, there is nothing about the Refresh Rate. Pressing the Option key does not show any additional options.  I've seen countless screenshots where this information should appear. Is there another way to check the refresh rate?  I'm on macOS 10.13.4  Thanks. How can I install Gimp 2.8's help documentation on Ubuntu 12.04? I have a set of coordinate points. The points are distributed in such a way that some points are clustered around a specific area. 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