l1 and l2 regularizations
Why L1 norm for sparse models
Recurrence relation for the determinant of a tridiagonal matrix Let  $$f_n := \begin{vmatrix} a_1 &amp; b_1 \\ c_1 &amp; a_2 &amp; b_2 \\ &amp; c_2 &amp; \ddots &amp; \ddots \\ &amp; &amp; \ddots &amp; \ddots &amp; b_{n-1} \\ &amp; &amp; &amp; c_{n-1} &amp; a_n \end{vmatrix}$$  Apparently, the determinant of the tridiagional matrix above is given by the recurrence relation   $$f_n = a_n f_{n-1} - c_{n-1} b_{n-1}f_{n-2}$$  with initial values $f_0 = 1$ and $f_{-1} = 0$ (according to Wikipedia). Can anyone please explain to me how they came to this recurrence relation?  I don't really understand how to derive it. NullReferenceException in Unity Since many users are facing the NullReferenceException: Object reference not set to an instance of an object error in Unity, I thought that it would be a good idea to gather from multiple source some explanation and ways to fix this error.  Symptoms I am getting the error below appearing in my console, what does it mean and how do I fix it?  NullReferenceException: Object reference not set to an instance of an object Let $f_n(x) : \mathbb{R} \rightarrow \mathbb{R}$ be defined as $\dfrac{x}{n}$. Is $f_n$ uniformly convergent?   With "$(a_n)$ is limited and $(b_n)$ converges to 0 $\Rightarrow (a_nb_n)$ converges also to 0" i would guess that $x\cdot \dfrac{1}{n}$ converges uniformly but $x$ is not limited in this case. So does ist converge uniformly or not? KKT points and nonlinear optimality (theory) I have some questions about Karush Kuhn Tucker conditions. I am not clear about the theory. There are plenty of theorems and I am confused with it. Let us say we have the following problem: We have a general problem, not a convex problem. $$\min f(x)\\g_{j}(x)\le 0,\forall j\in J\\h_{k}(x)=0,\forall k \in K. $$ I will solve it.....Lagrange function, verifying primal feasibility, dual feasibility and complementary slackness and I will get some KKT points. Now what is the conclusion?  If I get no KKT point, can I say that the problem has no solution or what is the conclusion? If I get only one KKT point, is it a local minimum or even a global minimum? If I get more KKT points, what is the conclusion? In which case I will verify SOSC condition? If I get more KKT points or even for one point is it necessary? And the conclusion is what? The KKT points which satisfies the SOSC condition are strick local minimum and the poins which does not satisfy it are not the solution of the problem?  I am so sorry for so many questions, but any help would be very appreciated. Thank you very much in advance. setuid root does not work Objective : Run a program as root (C++ binary). The same as :   And :   ./a.out output:  E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root? psurana  //output for "whoami" Look below for the code.   ls -l output:  -rwsrwxr-x 1 root    root    46136 Jun  7 20:13 a.out  The Code :   #include &lt;string&gt; #include &lt;stdlib.h&gt; int main(int argc, char *argv[]){         std::string input = "apt-get install " + std::string(argv[1]);         system(input.c_str());         system("whoami");         return 0; }   Details: : compiled the program and then did chown root:root a.out &amp;&amp; chmod u+s a.out. Please look above for ls -l output.  I still do not get the root privileges and the output for system("whoami") in the code is my own username on the machine.  Reading the two linked questions did not yield me anywhere. :(. both the creator and the owner of the file are root. The setuid bit is set, so it should work. The filesystem is not external either, it is my own machine. How can I make this work? Is MacBook Pro warming during gaming normal? I have a 2010 MacBook Pro MC371 (Core i5, GeForce 320M, 4Gb RAM).   When I launch a game either new one (i.e. Starcraft 2) or rather old (Unreal Tournament 2004, bootcamped) my MacBook gets rather warm, even hot in the top left corner, around the place where magsafe charger is plugged in. The temperature is more than 40C. The fact that confuses me is that this warming occures even when I play old games.  Is that OK? How do I determine how many spell slots I have if I multiclass into more than one spellcasting class? For example, I have a character that is a level 3 Wizard, a level 5 Eldritch Knight Fighter, a level 4 Arcane Trickster Rogue, a level 4 Paladin, and a 4 Warlock. How many spell slots do I have and how do I determine this? I am looking for some (may be rarely know to nonnative English speakers) synonyms for  "immensely valuable" or "extremely valuable". What does this triangle/diamond schematic symbol represent? How to prepare data for ListVectorPlot[]? Symbolizing layer with graduated colors by date/time field? I've got a layer of polygons where each has a date associated with it.  I want to color the polygons with graduated colors, but I want the colors to start with the newest polygons and fade to the oldest polygons.  So far I haven't been able to find a way to do this in ArcMap (&lt;= 9.3.1) other than to create a new field and calculate some integer or float value based on the date.  Is it possible to use a date or time field directly?   The data is natively a date-time value There are far too many records to use any unique-value renderer Converting the date to a numerical field is an answer for a different question. How to wait in bash for several subprocesses to finish and return exit code !=0 when any subprocess ends with code !=0? I haven't found a similar question on here, though I suspect the question may be rather well-covered.   I want to find a conformal map from the vertical strip $\{z:-1&lt;Re(z)&lt;1\}$ onto the unit disc.  Under the exponential map the region is taken to the annulus with radii $e$ and $e^{-1}$, but I'm not sure how useful this will be.  Can anyone advise on what the conformal map may be?  Thanks. When I add LIMIT 1 to a MySQL query, does it stop the search after it finds 1 result (thus making it faster) or does it still fetch all of the results and truncate at the end? Are estimates of regression coefficients uncorrelated? Consider a simple regression (normality not assumed): $$Y_i = a + b X_i + e_i,$$ where $e_i$ is with mean $0$ and standard deviation $\sigma$. Are the Least Square Estimates of $a$ and $b$ uncorrelated? Norm $N$ on $\Bbb Z[\sqrt d]$ is multiplicative, $N(x)$ prime $\Rightarrow x$ irreducible Use early 2009 20" iMac as external display for 2015 rMBP Metapost label based on variable value I want to label a scale based on a variable value and I wrote a metapost code like this.  $ := 1; for i = -.3cm step .6cm until 3.6cm:     label.bot(str$,(i,-3.7cm));     $ := incr($); endfor;   It just labels "$" instead of its value. How to output the variables value? How to have full bleed between two facing pages Indesign How to adopt SD card as internal storage on Samsung devices?