Does Anivia still retain unique item effects while in egg form, such as Thornmail? Can she activate items like Deathfire Grasp? What summoner spells can she use, if she can use any at all?
In League of Legends, there are a number of effects which revive a champion upon death.  The item  is the most well-known and widely used of these.  I was wondering, however, whether its effect would come before or after other revive effects?  I have two examples.  First, Zilean's ultimate  will provide a champion with a Guardian Angel -like buff for a limited time.  If a champion has this buff in addition to a Guardian Angel, which effect will happen first?  Second, Anivia's passive  allows her to come back to life if her egg is not destroyed after she is killed.  If she has a Guardian Angel, will her passive be triggered before or after it? How does this compare to  and ?  It seems like in one case it is more beneficial to have Guardian Angel's precedence be greater, and in the other it is more beneficial to have it be less.  In the first scenario, if the Guardian Angel was triggered first, then Zilean would have a good chance of simply wasting his ultimate.  On the other hand, if it is triggered after these revival effects, then Anivia could not get the full benefit of her passive.  Is there a set order of precedence, or does each revival effect have their own unique "priority level" that is explicitly detailed for each ability?
I computed the homology groups of the torus, can someone tell me if this is correct? The calculation, not the result that is. Thanks!  The cells of $T^2$ are $e^0, e^1_a, e^1_b, e^2$  The chain groups are  $$ C_0(T^2) = \{ k e^0 |&#160;k \in \mathbb{Z} \} = \mathbb{Z}$$  $$ C_1(T^2) = \{&#160;k_1 e^1_a + k_2 e^1_b |&#160;k_1 , k_2 \in \mathbb{Z} \} = \mathbb{Z} \oplus \mathbb{Z}$$  $$ C_2(T^2) = \mathbb{Z}$$  $$ C_k(T^2) = \{ 0 \} , k &gt; 2$$  Now the homology groups:  $$ H_0(T^2) = \ker \partial_0 / im \partial_1 = \mathbb{Z} / 0 = \mathbb{Z}$$  where $im \partial_1 = 0$ because there is no chain in $C_1(T^2)$ whose boundary is a zero-chain in $C_0(T^2)$. (Is this reasoning correct?)  $$ H_1(T^2) = \ker \partial_1 / im \partial_2 = \mathbb{Z} \oplus \mathbb{Z}$$  where $\ker \partial_1 =  \mathbb{Z} \oplus \mathbb{Z} $, i.e. again everything maps to zero because there is no element in $C_1$ whose boundary maps to an element in $C_0$.  $im \partial_2 = 0$ again because there is no element in $C_2$ whose boundary is an element of $C_1$.  I don't want to use Hurewicz to do $H_1$.  $$ H_2(T^2) = \mathbb{Z}$$ using similar arguments as above.  Thanks for your help.  Edit  I posted the computations as an answer below. I got two up votes but I don't know by who so I'm not yet sure I can trust them... I am trying to find a book (young adult) where the devil is the protaganist, and other gods appear as characters I believe it was written by a teenager, and might have a sequel.   It has been many years since I read it, but I believe it had the devil acting like a regular human. He wasn't evil. I think it incorporated a lot of (gods/characters) norse, roman, Christian, and pagan. I accidentally opened Orca Screen Reader from the Dash when I was trying to open Screenshot. Now everything I type or click on is spoken out loud.  How do I make it stop?  For reference, here is a screenshot of Orca Screen Reader running: Is there a standard and accepted method for selecting the number of layers, and the number of nodes in each layer, in a feed-forward neural network? I'm interested in automated ways of building neural networks. I have two cameras, a 6mpix Panasonic FZ8, and 14mpix Canon A2200.  When I compare shots from two cameras, one of differences I notice is dpi number that camera reports in JPG info:   FZ8 reports dpi=72 A2200 reports dpi=180   What physical meaning can these numbers have? I am at loss for guesses.    I am fairly familiar with notion of dpi in scanning and printing. I can calculate density of pixels on the sensor of the camera. But then, the linear density of pixels on the sensor will be hundreds times larger than number above. So what, if anything, does it mean? Connection between rank and matrix product I have a problem understanding the following:     Let $A$ be an $m \times n$ matrix and let t $\in \mathbb{N}$. Prove that   $\operatorname{rank}(A)\leq t$ if and only if there exists an $m \times t$ matrix $B$ and a $t \times n$ matrix $C$ so that $A = BC$.   I know what a rank is but I can't make a connection between the rank and the existence of two matrices such that $A = BC$. Disclaimer: I'm pretty novice at sysadmin stuff.  I'm trying to set up port forwarding in an AWS EC2 instance, this has to be done in the command-line because I don't want to go in and edit anything, it has to be automatic (it's part of a build process).   sudo echo "net.ipv4.ip_forward = 1" &gt;&gt; /etc/sysctl.conf      Permission denied   The weird thing is I've been (successfully) using sudo for pretty much every command that required su privileges. If I do sudo su before the command (trying it out by hand in an ssh session), then it works.  Reasons behind this? Possible solutions that don't involve sudo su or manual edits? Is $\sin^2(z) + \cos^2(z)=1$ still true for $z \in \Bbb{C}$? Is $$\sin^2(z) + \cos^2(z)=1$$ still true for all $z \in \Bbb{C}$? I've tried rewriting it using complex definitions of $\sin$ and $\cos$, and I don't see why it wouldn't, but the text I'm reading asks this question as if it shouldn't hold? A set with a finite integral of measure zero? Will my 320W PSU handle a Asus GTX 750Ti I've got a 320W PSU as far as I know and it's a Chinese PSU because I've seen the Chinese letters on it. I just had a question if I can upgrade my pc to Asus GTX 750Ti 2 GB OC.  My pc specs are:   4GB DDR3 RAM Intel Core 2 Duo E8400 3.0 GHZ 250GB HDD Onboard graphics card Games like Super Metroid and Aquaria present the terrain with the other facing parts having rocks and stuff while deeper behind them (i.e. underground) there's different detail or just black.      I would like to do something similar using polygons. Terrain is created in my current level as a set of overlapping square boxes. I'm not sure if this rendering method will work such a system for creating terrain but if anyone has ideas I'd love to hear them. Otherwise I'd like to know how I should re-write the terrain rendering system so it actually works to draw terrain in this manner... Does an Echo Knight fighter's echo provoke an opportunity attack when it moves? How to increase JAVA Heap Size? Can the Ubuntu logo be used for a commercial website? Is there an Ubuntu logo that can be used on a commercial website to indicate that Ubuntu can be installed for customers? Where's the summary of your own suggested edits? Recently I had a bunch of my own scripts for the thumbnails in Nautilus: , , office documents and so on.  Seems like either I’m doing something wrong (thumbnail generation behavior changed), or custom thumbnailes don’t work in latest GNOME at all, even my previous scripts, which worked smoothly on previous versions of Ubuntu.  I’ve done some research, tried to run a simple script (see below) and it didn’t work out.  My test thumbnailer in /usr/share/thumbnailers/z.thumbnailer:  [Thumbnailer Entry] Exec=/home/maximal/thumb.sh %s %i %u %o MimeType=image/webp;image/x-webp   Where /home/maximal/thumb.sh is:  #!/bin/bash echo $0 &gt;&gt; /home/maximal/thumb.log echo $1 &gt;&gt; /home/maximal/thumb.log echo $2 &gt;&gt; /home/maximal/thumb.log echo $3 &gt;&gt; /home/maximal/thumb.log echo $4 &gt;&gt; /home/maximal/thumb.log   Then, when I remove thumbnail cache rm -rf ~/.cache/thumbnails and restart Nautilus nautilus -q, my log file doesn’t contain anything and ~/.cache/thumbnails/fail/gnome-thumbnail-factory contains all the failed thumbs (looks like corrupted/empty PNGs):    So, apparently, Nautilus even didn’t try to execute my thumbnailer script. When I try to run thumb command itself, it works perfectly. For example convert through cwebp|dwebp package:  convert -thumbnail 256x256 file.webp png:file.webp.png   When I wrap this command to a thumbnailer, it looks like it wasn’t even requested to run by Nautilus.  [Thumbnailer Entry] Exec=convert -thumbnail %sx%s %i png:%o MimeType=image/webp;image/x-webp;   Exactly the same situation occurs with other my thumbnailers: audio waveforms, office documents, photoshop files and so on.  Could anyone help? Can the Hubble constant be measured locally? The Hubble constant, which roughly gauges the extent to which space is being stretched, can be determined from astronomical measurements of galactic velocities (via redshifts) and positions (via standard candles) relative to us. Recently a value of 67.80 ± 0.77 (km/s)/Mpc was published. On the scale of 1 A.U. the value is small, but not infinitesimal by any means (I did the calculation a few months ago, and I think it came out to about 10 meters / year / A.U.). So, can you conceive of a measurement of the Hubble constant that does not rely on any extra-galactic observations?  I ask because, whatever the nature of the expansion described by the Hubble constant, it seems to be completely absent from sub-galactic scales. It is as though the energy of gravitational binding (planets), or for that matter electromagnetic binding (atoms) makes matter completely immune from the expansion of space. The basis for this claim is that if space were also pulling atoms apart, I would naively assume we should be able to measure this effect through modern spectroscopy. Given that we are told the majority of the universe is dark energy, responsible for accelerating the expansion, I wonder, how does this expansion manifest itself locally?   Any thoughts would be appreciated. Dropping Internet connection on Realtek Semiconductor Co., Ltd. RTL8821AE I have continuous problems of network dropping connections on wifi with ubuntu 16.04, I have an ASUS R510J, this is my network card:  ##### lspci #############################  03:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8821AE 802.11ac PCIe Wireless Network Adapter [10ec:8821]         Subsystem: AzureWave RTL8821AE 802.11ac PCIe Wireless Network Adapter [1a3b:2161]         Kernel driver in use: rtl8821ae  04:00.1 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller [10ec:8168] (rev 12)         Subsystem: ASUSTeK Computer Inc. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller [1043:200f]         Kernel driver in use: r8169   sudo service network-manager restart doesnt's help, as I never regain internet connection after it drops, and I have to restart the PC. On Ethernet cable I have no problem.  What do you think is the issue? drivers?  thank you Gradient Boosting for Linear Regression - why does it not work? I'm learning Neural Networks and I grasped the algebra behind them. I'm now interested in understanding how normalization and centering of the input data affect them. In my personal learning project (Regression with NN) I've transformed my input variables to a range between 0 and 1 using the following function:  normalize &lt;- function(x) {return((x - min(x))/ (max(x) - min(x)))}   The NN model fits well and has an acceptable out-of-sample prediction error.   However, I read in other  that scaling the inputs to have mean 0 and a variance of 1 is advised for NN. I don't fully understand:   how this transformation works better for NN against the min-max normalization between 0 and 1. how can I assess which transformation to apply in my data?