The graphical intuiton of the LASSO in case p=2
Graphical interpretation of LASSO
$\lim_{n\to\infty}((\frac94)^n+(1+\frac1n)^{n^2})^{\frac1n}$  Here's what I did:  $\lim_{n\to\infty}((\frac94)^n+(1+\frac1n)^{n^2})^{\frac1n}\\ =(\lim(\frac94)^n+\lim((1+\frac1n)^{n})^n)^{\frac1n}\\ =(\lim(\frac94)^n+\lim e^n)^{\frac1n}\\$  Any hints on how to continue?  PS: no logs/integration/derivation because we haven't covered it. Prove that a set in $\mathbb R^3$ is not an algebraic set I want to prove that the set $\{(\cos(t),\sin(t),t)\in A^3(\mathbb R); t\in \mathbb R \}$ is not an algebraic set.   I already proved that the set $\{(\sin(t),t)\in A^2(\mathbb R);t\in \mathbb R \}$ is not algebraic but the method that I used doesn't seems to be general. Are there concerns with doing a generalized additive model with a smoothing term of multiple variables? In R, usually one performs a generalized additive model like so:  library(mgcv) x &lt;- gam(depvar ~ s(indvar1) + s(indvar2) + parametricvar)   Say I want to explore the non-parametric interaction of indvar1 and indvar2.  Is the following kosher?  x &lt;- gam(depvar ~ s(indvar,indvar2) + parametricvar) is there a way to get the option "Organize Desktop by Name" in Ubuntu 19.10 same as in 18.04? The limit of a sum $\sum_{k=1}^n \frac{n}{n^2+k^2}$ as $n\rightarrow\infty$ What levels-up Psi-abilities? Sufficient conditions for $x, Ax, A^2x, ...$ being linearly indepedent How to increase battery life on Ubuntu 20.04 and what power saving software should I install, if any? I recently installed Ubuntu 20.04 LTS on my Lenovo Ideapad Flex 5 and realized that battery life in Ubuntu is not as good as Windows. The battery drains faster in Ubuntu. I have seen the questions in Ask Ubuntu about this, but I haven't found anything that regards Ubuntu 20.04 LTS. I've done some research and found out that the battery drain is because most vendors optimize their drivers for Windows and with Linux, you have to hope that the kernel drivers do the job (which they usually do). After that, I researched how to increase my battery life and almost all sources I found recommended installing tlp or powertop or something similar to these. But I have a few questions.  Does tlp, powertop, and similar software actually affect battery life?  If the answer to 1 is yes (in a positive way), what would you recommend I install (such as whether I should  install tlp or powertop by itself or in a combination)?  Are there any other ways to increase battery life in Ubuntu 20.04?   Note: I am a beginner to Linux and Linux distros and do not want to mess with anything advanced that may negatively affect the system. I may not be able to immediately know how to tweak any of the aforementioned software, so please suggest any tweaks if they are needed to get results. And if it helps to know, here are my system specs: OS: Ubuntu 20.04.1 LTS x86_64 Host: 81X2 IdeaPad Flex 5 14ARE05 Kernel: 5.7.17-050717-generic CPU: AMD Ryzen 7 4700U with Radeon Graphics (8) @ 2.000GHz GPU: AMD ATI 04:00.0 Renoir (These were given by neofetch) P.S: If you need anything else, just ask. Thanks in advance! WCF - Faults / Exceptions versus Messages We're currently having a debate whether it's better to throw faults over a WCF channel, versus passing a message indicating the status or the response from a service.  Faults come with built-in support from WCF where by you can use the built-in error handlers and react accordingly. This, however, carries overhead as throwing exceptions in .NET can be quite costly.  Messages can contain the necessary information to determine what happened with your service call without the overhead of throwing an exception. It does however need several lines of repetitive code to analyze the message and determine actions following its contents.  We took a stab at creating a generic message object we could utilize in our services, and this is what we came up with:  public class ReturnItemDTO&lt;T&gt; {     [DataMember]     public bool Success { get; set; }      [DataMember]     public string ErrorMessage { get; set; }      [DataMember]     public T Item { get; set; } }   If all my service calls return this item, I can consistently check the "Success" property to determine if all went well. I then have an error message string in the event indicating something went wrong, and a generic item containing a Dto if needed.  The exception information will have to be logged away to a central logging service and not passed back from the service.  Thoughts? Comments? Ideas? Suggestions?  Some further clarification on my question  An issue I'm having with fault contracts is communicating business rules.  Like, if someone logs in, and their account is locked, how do I communicate that? Their login obviously fails, but it fails due to the reason "Account Locked".  So do I:  A) use a boolean, throw Fault with message account locked  B) return AuthenticatedDTO with relevant information Why is spawning threads in Java EE container discouraged? One of the first things I've learned about Java EE development is that I shouldn't spawn my own threads inside a Java EE container. But when I come to think about it, I don't know the reason.  Can you clearly explain why it is discouraged?   I am sure most enterprise applications need some kind of asynchronous jobs like mail daemons, idle sessions, cleanup jobs etc.  So, if indeed one shouldn't spawn threads, what is the correct way to do it when needed? Let $X$ and $Y$ be independent $N(0; 1)$ random variables. Let $Z = \sqrt{X^2+Y^2}$.  (a) Derive the marginal pdf of $Z$ and then using the marginal pdf to compute ${\rm E}[Z^2]$  (b) Can you propose a different way other than that in (a) to compute ${\rm E}[Z^2]$  (c) Compute ${\rm E}[Z]$.  This is the whole question that I was asked. I can do (c) but I don't know how to find the marginal pdf of $Z$ with the given information and can't seem to find any formulas. Any help would be appreciated. Wireless disabled by hardware switch Lenovo Y40 I recently got a lenovo Y40 laptop and after i installed ubuntu 14.04 (also in the live usb) Wireless doesn't work. It says that it is disabled by hardware switch, however the hardware switch doesnt work (its intention is to put on airplane mode but does nothing when pressed in ubuntu) wireless works in windows and the BIOS has it enabled. I tried resetting the BIOS but it still doesn't work. Here are some command outputs  lspci:  03:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 10) 04:00.0 Network controller: Intel Corporation Wireless 3160 (rev 93)   rfkill list all:   0: ideapad_wlan: Wireless LAN     Soft blocked: no     Hard blocked: yes 1: ideapad_bluetooth: Bluetooth     Soft blocked: no     Hard blocked: yes 2: hci0: Bluetooth     Soft blocked: no     Hard blocked: no 3: phy0: Wireless LAN     Soft blocked: no     Hard blocked: no   lswh:     *-network         description: Ethernet interface         product: RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller         vendor: Realtek Semiconductor Co., Ltd.         physical id: 0         bus info: pci@0000:03:00.0         logical name: eth0         version: 10         serial: f8:a9:63:31:2e:b6         size: 1Gbit/s         capacity: 1Gbit/s         width: 64 bits         clock: 33MHz         capabilities: bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation         configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl8168g-3_0.0.1 04/23/13 ip=192.168.1.4 latency=0 link=yes multicast=yes port=MII speed=1Gbit/s         resources: irq:64 ioport:4000(size=256) memory:c0604000-c0604fff memory:c0600000-c0603fff *-pci:3      description: PCI bridge      product: Lynx Point-LP PCI Express Root Port 4      vendor: Intel Corporation      physical id: 1c.3      bus info: pci@0000:00:1c.3      version: e4      width: 32 bits      clock: 33MHz      capabilities: pci normal_decode bus_master cap_list      configuration: driver=pcieport      resources: irq:59 memory:c0500000-c05fffff    *-network DISABLED         description: Wireless interface         product: Wireless 3160         vendor: Intel Corporation         physical id: 0         bus info: pci@0000:04:00.0         logical name: wlan0         version: 93         serial: a0:88:69:90:0a:38         width: 64 bits         clock: 33MHz         capabilities: bus_master cap_list ethernet physical wireless         configuration: broadcast=yes driver=iwlwifi driverversion=3.13.0-32-generic firmware=22.24.8.0 latency=0 link=no multicast=yes wireless=IEEE 802.11abgn         resources: irq:66 memory:c0500000-c0501fff Inequality: $x^2+y^2+xy\ge 0$ I want to prove that $x^2+y^2+xy\ge 0$ for all $x,y\in \mathbb{R}$.  My "proof":  Suppose wlog that $x\ge y$, so $x^2\cdot x\ge x^2\cdot y\ge y^2\cdot y=y^3$ (because $x^2\ge 0$ so we can multiply both sides by it without changing the inequality sign) giving $x^3\ge y^3$. Substracting we have $x^3-y^3\ge 0$ or $(x-y)(x^2+xy+y^2)\ge 0$. Since $x\ge y$ we can divide by $x-y$ to get $x^2+xy+y^2\ge 0$.  Is it right?  Thanks for your help! When I search for my address on Google Maps it cannot be found which means I can't order takeaway etc.  Is there a way of adding my address to Google Maps or even add a street address?  I want the address to be publicly available so others can search it. Put the book back on the table.   I'm having trouble. I think it is a preposition. Handling very large numbers in Python I need to find a way of proving that the square roots of a finite set    of different primes are linearly independent over the field of    rationals.    I've tried to solve the problem using elementary algebra  and also using the theory of field extensions, without success. To  prove linear independence of two primes is easy but then my problems  arise. I would be very thankful for an answer to this question. Java, Cannot reduce the visibility of the inherited method from object Gaussian-like integral : $\int_0^{\infty} e^{-x^2} \cos( a x) \ \mathrm{d}x$ Does flying to Panama from the US reset the ESTA time counter?