I read different articles including .   Why is bias term not included in regularization, in general? I see some of the algorithms such as LinearSVC includes bias term in regularization. Also, is bias term used for only predicting minimum value possible when all weights are zero? What is its significance exactly?
According to , weight decay (regularization) is not usually applied to the bias terms b why?  What is significance (intuition) behind it?
Is this a correct demonstration for why elements above untriseptium cannot exist? With the confirmation that elements 113, 115, 117, and 118 are indeed fundamental elements that are now to be named on the periodic table, the next question is: what is the highest atomic number possible for an element? Feynman had a go at this years ago, and he derived (according to my limited understanding) that above element-137 (informally denoted 'Feynmanium') the electrons in the nearest orbit about the nucleus would be traveling at a velocity greater than the speed of light. (Note I am considering the Bohr model of the atom in this question.) I wished to demonstrate to my friends why this is and I came up with the following explanation.  According to Bohr's quantum condition, the angular momentum of an electron about the nucleus is given by $$ L=m_evr_n=n\hslash \implies r_n=\frac{n\hslash}{m_ev},$$ where $m_e$ is the mass of the electron, $v$ its velocity, $n$ an integer, and $r_n$ the radius of the $n$th possible orbit. Because we are concerned with the nearest orbit to the nucleus, $n=1$; and thus $$r=\frac{\hslash}{m_ev}.$$   Now, according to Coulomb's law, if the electron orbits about the nucleus the centripetal motion can be described by $$\frac{Ze^2}{4\pi\epsilon_or}=m_ev^2, $$ where $Z$ denotes the number of protons in the nucleus (the atomic number), and $e$ the elementary charge. Solving for $Z$ and substituting in $r$ from above yields $$Z=\frac{4\pi\epsilon_o \hslash v}{e^2}. $$ But what is $v$? Well, the maximum velocity an electron could ever have is the speed of light, and we wish to find the atomic number associated with an orbiting electron traveling at this speed, so we set $v=c$ and obtain our final result of $$Z=\frac{4\pi\epsilon_o\hslash c}{e^2}\approx 137.521,$$ which implies that for $Z&gt;137$, the electrons at a position of $n=1$ in the Bohr model would have a velocity $&gt;c$; and thus the highest atomic number achievable on the periodic table is 137.  Again, I just want to make sure this is a correct method for deriving element-137 before presenting. Perhaps one could explain how relativity plays a role here. I know Feynman used the Dirac equation to get this result...so could anyone (subsequently of course) expatiate on this in a simplistic manner? Thanks! What is a simple example of an unprovable statement? I have created the custom setting with the hierarchy type    I have added some fields to the custom settings  phone field is added to the custom settings  custom setting Name:Order_Configuration__c  Phone :12345 - one profile  phone:456798 - another profile   Is it possible to access the different values for different profiles in custom settings using apex trigger code I have a question regarding the two QGIS Versions 2 and 3. When I load exactly the same raster file into QGIS 2 and QGIS 3 I get different min/max values, how is this possible? I have used the same coordination system. Use of each and every Whether and how to thank a girlfriend or boyfriend in the acknowledgements of thesis? How to solve following equation: $x^x = C$ as $x, C \in \mathbb{R}_{&gt;0}$. I tried to use exponent and such that: $x\ln x = \ln C$. Proof of $\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s)$ Let $({\Bbb R},{\mathcal A},\mu)$ be the measure space where ${\mu}$ is the Lebesgue measure.  Assume that $\int_{\Bbb R}|f|^pd\mu&lt;\infty$ ($p\geq1$). There is an exercise for proving that       $$\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s).$$   If one formally let $s=t^p$, then $ds=pt^{p-1}dt$ and one would immediately get the equality above. However, how can I justify it rigorously in the sense of Lebesgue integration?    [Edited] What puzzles me is that I have the "change of variable" theorem for Riemann integration, but all the integrations here are in the Lebesgue sense. Unless one has shown that the integrands are also Riemann integrable, how can I directly use "change of variable"? Contraction mapping in the context of $f(x_n)=x_{n+1}$. I'm interested in convergence of $f(x_n)=x_{n+1}$ and often hear this term referenced.  What does it mean to be a contraction mapping in the context of the sequence of real numbers given by $f(x_n)=x_{n+1}$? And what does it tell us about such sequence?  A search online gives the answer given by Wikipedia, that it is a function $f$ defined on a metric space $(M,d)$ from $M$ to itself with the property that for some real number $k \in [0,1)$,  $$d(f(x),f(y)) \leq k d(x,y)$$  This definition is quite unhelpful because I barely know what a metric space is. I feel like this definition is to generalized, and I'm interested in in the specific case of recursively defined real sequences $f(x_n)=x_{n+1}$ that there should be a more specific answer to my question. I'm using Ubuntu 11.10.  The python 2.7.2 provided has a bug that has been corrected in the latest 2.7.2 sources from the python repository.  What is the recommended way to replace the ubuntu provided python with the python from source? Or put another way, how do I "update" the ubuntu-provided one?  Ideally, I would just be able to create new .deb(s) that "update" the python2.7/python2.7-dev provided by Ubuntu. Show that $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ is rational. Parental controls with different settings for different users Does anyone know of a good way to set up some sort of parental controls so that one user account is subject to them, but not another?  A couple of friends of mine use Ubuntu and have kids (7 to 10 years old) who use the family computer. They'd like to have some blocking of adult sites. They're not going to supervise all the time, which I know might be ideal, but there we go. And they're not particularly technical, so they don't want to have to run scripts to turn the parental controls on and off regularly, but they can cope with having different accounts for different people. I haven't found a great way of doing this. I am pretty technical, so I'm happy to spend some time at the command line to set it up, but then it needs to just work.  Please don't just link to DansGuardian. If your answer doesn't address the different user account aspect, I will vote it down. If you want to talk about general parental controls that apply to all users then please start a new question - I'm sure that plenty of people would be interested in it, and I'll link to it from this question. Let $x_{1},x_{2},\cdots,x_{n}$ be real numbers. Show that     $$\sum_{i,j=1}^{n}|x_{i}+x_{j}|\ge n\sum_{i=1}^{n}|x_{i}|.$$   I think this problem may be solved using nice methods, but I can't find them yet; I know this may be of use: $$|a|+|b|\ge |a+b|.$$ But I can't make it work. Thank you everyone. Sample query/DDL for producing page locks on a clustered index in SQL Server (without hints) We currently have some indexes where ALLOW_PAGELOCKS is set to off. This presumably was done in order to reduce deadlocks. However I doubt that it would really had an effect back then.   Now I am trying to understand WHEN SQL Server actually chooses to start locking pages rather than keys in a clustered index. I asked Jonathan Keyhaisas recently and he told me that this could happen if I am touching rows on several subsequent pages. However I didn't manage to get any exclusive page locks by updating rows in a clustered index with a sample query.   Could you help me understand page locks better with a sample query and table? I am running SQL Server 2008 SP4.  Thanks in advance  Martin kidle_inject causing very high load Whenever kidle_inject starts running on my system the load shoots up. In general it only gets to a load of around this 5.23, 3.65, 2.54 but a lot of the time it jumps up past the 15 mark on each of them. At that point the system grinds to a halt and I have to power it off.  This only happens when the kidle_inject process starts. How can I disable this process so my machine can work and I can get some work done.  Example top:  top - 12:43:48 up  3:02,  3 users,  load average: 6.57, 5.53, 3.33 Tasks: 256 total,   3 running, 253 sleeping,   0 stopped,   0 zombie %Cpu(s):  5.9 us, 16.6 sy,  0.0 ni, 74.7 id,  0.5 wa,  0.0 hi,  2.3 si,  0.0 st KiB Mem:   8080252 total,  7937856 used,   142396 free,   258904 buffers KiB Swap:        0 total,        0 used,        0 free.  4061336 cached Mem    PID USER      PR  NI    VIRT    RES    SHR S  %CPU %MEM     TIME+ COMMAND 13509 root     -51   0       0      0      0 S  54.7  0.0   3:29.47 kidle_inject/1 13511 root     -51   0       0      0      0 S  54.1  0.0   3:30.92 kidle_inject/3 13510 root     -51   0       0      0      0 S  48.8  0.0   3:11.60 kidle_inject/2 13508 root     -51   0       0      0      0 S  47.6  0.0   3:08.47 kidle_inject/0 I need to update a vector layer's data when the visibility is turned back on.  My update does not occur when the visibility is off.  To what signal do I need to connect to catch the visibility change? How do I add a kernel boot parameter? I need to add the boot parameter foo=bar to my kernel. How can I do this once for testing, and permanently if testing was a success? I'm having a bit of trouble proving this with the propositional calculus rules.  $$p \lor (p\implies q)$$ Would someone mind helping me and showing which rules they've used with an explanation! Thanks! Display sheet name in Google Spreadsheets Is there any way to display a sheet name as the result of a function in a Google Spreadsheets (exactly like , except in Google Sheets)? How can I remove the new weather information from the taskbar?