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Does Wasserstein distance require the source and target distributions to have the same mass? If we minimize the Wasserstein loss, $$W_1 (P_S, P_T) = \underset{\gamma \in \Pi}{\text{min }} \sum_{x,y} |x-y|\gamma(x,y)$$ which means we are looking for the coupling $\gamma(x,y)$ that minimizes the cost of moving mass from the source distribution $P_S$ to the target distribution $P_T$,  Do the masses of the source and target distributions have to be identical? If so or not, how are the masses of $P_T$ and $P_S$ accounted for mathematically in, or when minimizing, the shown formula, or what might be missing/overlooked by the Wasserstein approach overall due to the mass differences? Monday morning mistake: sudo rm -rf --no-preserve-root / Please note: The answers and comments to this  question contains content from another, similar question that has received a lot of attention from outside media but turned out to be hoax question in some kind of viral marketing scheme. As we don't allow ServerFault to be abused in such a way, the original question has been deleted and the answers merged with this question.      Here's a an entertaining tragedy. This morning I was doing a bit of maintenance on my production server, when I mistakenly executed the following command:  sudo rm -rf --no-preserve-root /mnt/hetznerbackup /  I didn't spot the last space before / and a few seconds later, when warnings was flooding my command line, I realised that I had just hit the self-destruct button. Here's a bit of what burned into my eyes:  rm: cannot remove `/mnt/hetznerbackup': Is a directory rm: cannot remove `/sys/fs/ecryptfs/version': Operation not permitted rm: cannot remove `/sys/fs/ext4/md2/inode_readahead_blks': Operation not permitted rm: cannot remove `/sys/fs/ext4/md2/mb_max_to_scan': Operation not permitted rm: cannot remove `/sys/fs/ext4/md2/delayed_allocation_blocks': Operation not permitted rm: cannot remove `/sys/fs/ext4/md2/max_writeback_mb_bump': Operation not permitted rm: cannot remove `/sys/fs/ext4/md2/mb_stream_req': Operation not permitted rm: cannot remove `/sys/fs/ext4/md2/mb_min_to_scan': Operation not permitted rm: cannot remove `/sys/fs/ext4/md2/mb_stats': Operation not permitted rm: cannot remove `/sys/fs/ext4/md2/trigger_fs_error': Operation not permitted rm: cannot remove `/sys/fs/ext4/md2/session_write_kbytes': Operation not permitted rm: cannot remove `/sys/fs/ext4/md2/lifetime_write_kbytes': Operation not permitted # and so on..   I stopped the task and was relieved when I discovered that the production service was still running. Sadly, the server no longer accept my public key or password for any user via SSH.  How would you move forward from here? I'll swim an ocean of barbed wire to get that SSH-access back.  The server is running Ubuntu-12.04 and hosted at Hetzner. How much can a grappler with reach move a grappled creature inside its reach? How can I edit my network profile independently? My oldest account on the network is Area 51, followed by Mi Yodeya.  I recently filled out the "about me" section on Mi Yodeya (but nowhere else) and did not choose the "update all sites" option because my blurb is pretty specific to that site.  I intended to have that blurb on exactly one site.  I was surprised tonight to discover that that blurb is now on my network profile, where I see no "edit" link.  Am I stuck with either having a site-specific blurb as my network blurb (because it's my first non-Area-51 site) or rewriting it to be more general?  Or is there some way that I can independently edit the network profile?  (Or designate a different site as the default?)   shows that someone else had this problem too, but I'm asking for support, not for a new feature, so I'm asking this separately. root folder access via gui I'm new to linux and the terminal. As I learn how to use the terminal to navigate through directories, I like to use the gui file explorer to mirror my terminal navigation. The icons and file extension info in the gui file explorer help me figure out what everything is. However, I can't access the root folder via the gui, I can only access it via the terminal. Is there a way to enable access to the root folder outside of the terminal? How do I start Nautilus as root? Where is the denoise option in 2.90? Repeating "to" and "will" in enumerations of verbs Should I use the second "will" in constructions like this one: "it will definitely help you and will make the text more readable"  And should I write "to" before every infinitive in enumeration, or only before the first one, e.g. "it helps to develop and test" or "it helps to develop and to test"? Could this example be influenced by the fact that "help" can go with to-invinitive and bare infinitive, and with other verbs the rule would be different? How do I automatically restart docky after a crash? I'm trying to run this command in the terminal:  sudo apt install software-properties-common   This is the error message I get:  E: Could not get lock /var/lib/dpkg/lock-frontend - open (11: Resource temporarily unavailable)   E: Unable to acquire the dpkg frontend lock (/var/lib/dpkg/lock-frontend),     is another process using it? What are the units of entropy of a normal distribution? I have a random process that follows a normal distribution. It's parameters are mean = 35 units, std.dev. = 8 units. I've seen from the  for the normal distribution that there is a formula to calculate the entropy. So plugging in the figures as:- $$     .5\log\left(2\pi e^1 8\cdot 8\right) $$ I get a value of 1.52, which I take to be  per sample.  My question is what are these units?  What thing do I have 1.52 of?    is (typically) measured in units of bits, after Claude Shannon's definition.  So can I take it that each sample generates 1.52 bits of entropy?  Clearly recording those samples generates information and therefore occupies a real and discrete amount of storage space. Ergo entropy cannot be unit less. Solving multiple congruences by CRT = Chinese Remainder Theorem Training N classifiers for N labels vs one classifier with N labels I have a classification problem which is multi-label with N labels. I would like to know which method would be the better choice? Training N classifiers (1 for each label) or a single classifier which use K-hot encoding. I'm using a neural network for this with a softmax at the last layer. (Is there any chance that the softmax would cause a problem?) I'm using tensorflow for the model. Infinite series for $e$... How do you prove that $e=\sum_{n=0}^{\infty}\frac{1}{n!}$? Here I am assuming $e:=\lim_{n\to\infty}(1+\frac{1}{n})^n$. Do you have any good PDF file or booklet available online on this? I do not like how my analysis text handles this... I am really having trouble working a problem in my course. I will post it and then add what I have thought etc.  Let p be an odd prime, then using the Euclidian Algorithm, calculated the GCD of of $x^{p-1}-1$ and $x^2+1$ in $\mathbb{Z} / p\mathbb{Z}[x]$  Also, how does $p=1 (mod4)$ tell us that  $-1$ is a square in $\mathbb{Z} / p\mathbb{Z}$, infact that $-1$ is a square here if and only if $p=1(mod4)$.  My thoughts:   I know that $$x^{p}-x=(x)(x-1)(x-2)…(x-(p-1))$$ and so that in this sense our roots will be the congruence classes of $1,2,…p-1$  and also that $$x^{p-1}-1=(x-1)(x-2)…(x-(p-1))$$  But I get lost when trying to apply the EA to these polynomials,  like how can I do it when p is arbitrary?  Preferably id like to be able to understand/see how to do the first part first i.e. using division with residue and then move on to the second part. Any insight/hint or solution to this would be great,  Thank you all  Update:  When I try to do division with residue, I just get  $$x^{p-1}-1=(x^2+1)(x^{p-3}-x^{p-5}+x^{p-7}-x^{p-9}...)$$  for example,  $p=7$  $$(x^{6}-1)=(x^2+1)(x^4-x^2+1)$$  for $p=11$  $$(x^{10}-1)=(x^2+1)(x^{8}-x^{6}+x^{4}-x^{2}+1)$$  which for specific cases tells me that 1 is the gcd, but I dont know how to generalize that for the case with arbitrary prime p. A Terms of Service update restricting companies that scrape your profile information without your permission How to restrict a user from accessing a particular application? I want to restrict an application being opened under ordinary privileges. Only root shall run the application, so that contents wont be seen by others and they wont change anything. How to run firefox and firefox ESR simultaneously The main reason I want to use firefox ESR is to use a proprietary database tool for work that only allows oracle-java based web logins for linux (or a windows only thin client). I also want to use the full version of the outlook web application which only works in firefox. I don't want to run the NPAPI plugins for normal web browsing and email.   I have the repo version of firefox installed and firefox ESR installed in /opt/firefox and linked to /usr/local/firefox-esr  When I run firefox any attempt to run firefox-esr either brings up a window without the NPAPI plugins.   If I try running with the --new-instance or --no-remote options I receive the following error:  Firefox is already running, but is not responding. To open a new window, you must first close the existing Firefox process, or restart your system.   Regardless which one I start first, I can only open that one, and get the above error if I attempt to sidestep.  What makes this an especially annoying problem is that I often have to respond to emails that I need to access the database to deal with. So either I close and open many windows. I am stuck with a rather irritating problem I ran into after installing 11.10 on my macbook pro 5,5.  I did a clean install efi booting into the setup using the desktop cd. Upon the first reboot I was presented with the "invalid arch independent ELF magic" and grubs rescue console.  I have read  but the solution is no solution for me since installing grub via live cd only means installing the mbr version and I can't seem to find any manual on how to install grub-efi while booted into the live cd.  So my question is: How can I either edit the grubx64.efi file in my EFI Partition, reinstall grub-efi with a live CD / DVD or use grub rescue commands to fix this issue? SQL Server default collation vs database with different collation - potential problems? I'm struggling with the design of new database that has to use a different collation (Y Collation) than the SQL Server Instance default collation (X Collation). I'm looking for potential problems.  Temp Tables by default will be created with X Collation so any joins on text data types will fail unless I create temp table with Y collations on columns.  What about SQL Server string functions: REPLACE, SUBSTRING, etc.? Will they always be returned in X collation? What about when I use REPLACE(...) COLLATE Y? Do you see any potential data loss or maybe any different problems?