What are continuous distributions that are additive and have finite support

Question: I'm wondering what are continuous distributions that are additive and have finite support. Joint normal distribution is continuous, and is additive in the sense that if $X,Y$ are joint normal, then $X+Y$ are still normal, but they have infinite support (on the real line). I want something that is continuous, additive and has finite support. Thanks!
Comment: Your language is ambiguous because "distribution" in this context could be interpreted to mean *a* distribution or a *set* of distributions.  Concerning the latter, you may begin with literally *any* distribution with finite support.  Create the set of distributions arising from all finite sums of that distribution and *voila,* you have an additively closed family of such distributions.  Is that the sort of thing you are looking for?
Comment: Yes, you are right. I'm looking for additively closed family of such distributions. Thanks for pointing this out. Preferably this family also has a nice closed form pdf.
Comment: I meant preferably the pdf for the sum has the same form as the pdf for each individual random variable. Do you have any suggestions on what distributions to start with?
Comment: Please explain, then, what you mean by "same form"!
Comment: Yeah, you are right, the phrase "same form" is not very rigorous. What I meant is something like the normal family, $X\sim N(u_{x},\sigma_{x})$, $X\sim N(u_{y},\sigma_{y})$  then $X+Y\sim N(u_{x}+u_{y},\sigma_{x+y})$, so that to evaluate the joint pdf I only need to change the mean and variance parameters.
Answer: A minimal example is obtained by taking literally any distribution with compact support on the nonnegative reals.  Letting $F$ be its cumulative distribution function, this means there exist $0\le a\le b$ for which $F(a)=0$ and $F(b)=1.$  Repeated convolution produces the sequence of distribution functions $F_n,$ $n=1,2,3,\ldots,$ for which $F_1 = F$ and for all $n\ge 1,$
$$F_{n+1}(x) = \int_{\mathbb{R}} F_n(x-y)\,\mathrm{d} F(y).$$
Because this corresponds to addition of random variables, the support of $F_n$ is contained in the interval $[na,nb],$ which is compact and non-negative.
When $X_n$ is a random variable with distribution $F_n$ and $X_m$ a random variable with distribution $F_m,$ this ensures that $X_n+X_m$ has distribution $F_{n+m},$ showing this family $(F_n)$ is closed under addition.  Its parameter is $n.$  When $F$ is a continuous distribution, so is $F_n.$  Thus, $(F_n)$ satisfies all the requirements of the question.
At https://stats.stackexchange.com/a/43075/919 I describe such a family explicitly (and in great detail) where $F$ is the Uniform$(0,1)$ distribution.  This shows that the construction of $(F_n)$ is not just an abstraction: it can lead to distributions with computable formulas and concrete applications.

It might be objected that $n$ can attain only integral values.  We can try to fix that.  If there were such a family associated with all positive real $n$ it would be infinitely divisible: for all $n,$ the distribution $F_n$ could be expressed as the convolution of $F_{n/2}$ with itself, or generally the $k$-fold convolution of $F_{n/k}$ for any whole number $k.$  The Wikipedia article on infinite divisibility asserts that apart from atomic distributions (which concentrate all probability on a single value), there exist no infinitely divisible family of distributions with "bounded (finite) support."  It does not prove this, but refers to Sato, Ken-iti (1999), Lévy Processes and Infinitely Divisible Distributions for the details.
The minimal example can, however, be enlarged by adding in other distributions.  For instance, by adding in any atomic distribution supported on a non-negative value $\mu$ we can introduce a location parameter.  In effect, writing
$$F_{n;\mu}(x) = F_n(x-\mu)$$
we create a two-parameter family where the parameter $n$ must be a whole number and $\mu$ can be any non-negative real number.  These distributions are supported on the intervals $[na+\mu,nb+\mu]$ which are non-negative and compact.  For corresponding random variables $X_{n;\nu}$ and $X_{m;\mu},$ clearly $$X_{n;\nu}+X_{m;\mu}$$ has $F_{m+n;\mu+\nu}$ for its distribution.  Thus, the family $$(F_{n;\mu}),\, n=1,2,3,\ldots;\, \mu \ge 0$$ satisfies the condition of the question.
We can generate larger families very generally by emulating this process of combining two families of distributions under addition. When $(G_n)$ is also an additively closed family of distributions with non-negative compact support, then for any pairs of whole numbers $m$ and $n$ let $H_{m,n}$ be the distribution of $X_m+Y_n$ where $X_m\sim F_m$ and $Y_n\sim G_n.$  The family $(H_{m,n},\, m=1,2,3,\ldots;\, n=1,2,3,\ldots)$ satisfies all the conditions of the question.  This process can be repeated as many times as you like.
In a specific sense, all solutions to this problem arise in this way.  When $\mathcal F$ is any set of distributions with compact non-negative support, define the "additive closure" of $\mathcal F$ to be the intersection of all sets of distributions that are additively closed and include $\mathcal F.$  This intersection exists because the set of all distributions is one such set.  All additively closed families obviously equal their own additive closures.  As we noted before, the only distributions in $\mathcal F$  that can be infinitely divisible would have to be atomic.
Comment: Thanks, this is very helpful.
Answer: Let $X$ and $Y$ are from same continues distribution with finite support $(a,b)$.
so $a<X<b$ and $a<Y<b$ , in-hence  $2a<X+Y<2b$. Since the support of $X+Y$ equal to $(2a,2b)$ so I think it can not be happen. at least one of $a$ , $b$ $\rightarrow$ $\infty$ and other should be zero. like Chi-square distribution.
Comment: Thanks, this is helpful. This means we cannot have a distribution family that is closed under addition and is supported on the same interval. Maybe the statement of my problem is not rigorous enough, I actually do not require that the sum having the same support as the original two random variables, and I guess as long as we incorporate the support as part of the parameter for the distribution family (like uniform distribution which are characterized by support parameter) it will fix the problem.
Comment: You should look at https://en.wikipedia.org/wiki/List_of_probability_distributions#Supported_on_a_bounded_interval
Comment: This argument is incorrect: the fact that various distributions in the family must have increasingly large supports does not imply that any distribution in the family must be supported on $(0,\infty).$


Looking for a Perl module to store a Hash structure in shared RAM

Question: I'd like to store a data structure persistently in RAM and have it accessible from pre-forked
web server processes in Perl.
Ideally I would like it to behave like memcached but without the need for a separate daemon. Any ideas?
Answer: Use Cache::FastMmap and all you need is a file. It uses mmap to provide a shared in-memory cache for IPC, which means it is quite fast. See the documentation for possible issues and caveats.
Answer: IPC::SharedMem might fit the bill.
Answer: Mod_perl shares RAM on systems with properly implemented copy-on-write forking. Load your Perl hash in a BEGIN block of your mod_perl program, and all forked instances of the mod_perl program will share the memory, as long as there are no writes to the pages storing your hash. This doesn't work perfectly (some pages will get written to) but on my servers and data it decreases memory usage by 70-80%.
Mod_perl also speeds up your server by eliminating the compile-time for Perl on subsequent web requests. The downside of mod_perl that you have to program carefully, and avoid programs that modify global variables, since these variables, like your hash, are shared by all the mod_perl instances. It is worthwhile to learn enough Perl so that you don't need to change globals, anyway!
The performance gains from mod_perl are fantastic, but mod_perl is not available in many shared hosts. It is easy to screw up, and hard to debug while you are learning it. I only use it when the performance improvements are appreciated enough by my customers to justify my development pain.


Network Manager, create multiple lan connection configuration for the same wired card

Question: How can I create in Network Manager, multiple wired lan connection configuration for the same wired card?
I use to move between a lot of offices where I need to change my network config (IP, Mask, ecc) is it possible to create or save different configurations for the same network card and activate the right one time by time?
Answer: On Ubuntu 11.10 with Gnome 3, you will only get the stripped down version of the gnome control panel's network manager (like when you are running gnome-control-center network from terminal).
If you want to configure a second (or more) wired network connections, run nm-connection-editor. It lets you add new connections.
Answer: Right click on the NetworkManager icon.  In the "wired" tab, open up your existing connection ("Auto eth0") and copy the Device MAC address so you can put it in the new configuration profile. Then select "Add" to create a new connection profile for your wired connection.
After this, I believe all the profiles you've created should show up as options in your network list when you plug in a cable.
Comment: I add a little tip, if you need to connect also in dhcp lan, is better to leave the dhcp config on the "Auto eth0" so ubuntu try this config first by default. but you are able to change connection with one of the other saved configurations when you need it. ;)


How to assign existing objects to has_many relation with Hash

Question: I have such a relations between models
class Post < ActiveRecord::Base
   has_many :documents, :as=>:documentable
   accept_nested_attributes_for :documents
end

class Document < ActiveRecord::Base
   belongs_to :documentable, :polymorphic=>true
end

I have a set of documents already generated, those have documentable_type and documentable_id to NULL, suppose their ids are 1 and 2
Now i want to create a new post with existing documents, i generated the hash like this.
h = {:post=>{:title=>'Post Title', :documents_attributes=>{"0"=>{:id=>1},"2"=>{:id=>2}}}}
and then create the post like @post = Post.new(h[:post])
But after ward it goes for finding the documents with documentable_type='Post' and documentable_id=NULL which it can not found.
What would be the proper way to generate hash for such scenario?
Answer: I finally solved the issue by this hash:
h = {:post=>{:title=>'Post Title', :document_ids=>{1,2}}}


Meaning of S11 performing a clockwise arc circle about the smith chart origin?

Question: I've tested a device with my VNA. It displays S11 in a Smith chart as a plot x(w) + iy(w) (w the frequency). Curiously, as w increases from 50KHz to 600MHz, the plot is an almost perfect 1/3 circle whose center is the origin of the Smith chart.
In particular, this implies that the absolute value of S11 remains constant in the frequency range.
This is not to be confused with the constant VSWR circles since these circles relate the plots to the length of a transmission line at fixed frequency.
I am curious to know what is the physical meaning of these circles (how to interpret them).
Answer: Your reflection factor has constant magnitude at 50kHz...600MHz but its phase angle changes.
Guesses: One possibility is that you have microwave quality cable and a same quality resistive load at the end of the cable. Or the end is open and you have an attenuator at the input.
120 degrees curve suggest your line is a 6th part of the wavelength at 600MHz.
Answer: This is the behaviour of a signal traveling through an (almost) lossless system with constant group delay (linear phase shift).
In reality this can be a short cable or something like this. The actual fraction (1/3 in the example) tells you something about the time how long the signal needs to travel through the cable (or more abstract "system"). If you know the epsilon of the cable (or respective the speed of light within the cable) you can calculate the length of the cable.
In reality this wont be a circle if the cable is longer the losses will show itself as a spiral more than a circle.
Just ask further question and i update my answer.
Comment: Thank you. In fact, the device is simply a banal 50 ohm 1/4W resistor soldered directly across a usual SMA connector. But my question was intentionally theoretical.


Importing comments from Facebook App to Wordpress

Question: I know there is a plugin to put facebook comment app into Wordpress, which automatically merge the comments. The problem is that I installed the plugin hard-code style, so I don't have any plugin page on Wordpress, I just check the comments with the moderator tool at facebook. Now I don't want it anymore, and I'm not finding a way to export the comments to wordpress. Tried this: http://wordpress.org/extend/plugins/facebook-import-comments/ but doens't work, doesn't event my App ID. Any ideas?
Answer: Try Facebook for SEO - it should import them into your database (just noticed that it won't import the user pic with the comment, but it worked on mine). I was using the social media plugin for Facebook comments using the FB developers app.


Player changes size after external SWF is just loaded (but not used)

Question: I have a flash player I am working on (developing in AS3).
The stage (and player) size are 640x979.
At the bottom of the player I have a control-bar, with play-pause buttons etc.
Here is an image of the player (image).

So far so good.
Now - on most external SWFs that I load - they load OK.
But on some - if I try to load them using the Loader class - the player goes crazy !
The control bar dissappears, and the video is stretched in a funky way. You can see this in the attached image (image).

What is really strange here is - this happens even if I don't add the Loader object as a child !
I just do this :
<code>public function PlayerCtor()
{
    swfUrlLoader = new Loader();
    swfUrlLoader.contentLoaderInfo.addEventListener(Event.COMPLETE, onSwfReceived);
    swfUrlLoader.contentLoaderInfo.addEventListener(IOErrorEvent.IO_ERROR, onSwfIOError);
    swfUrlLoader.load(new URLRequest(swfUrl));
}
private function onSwfReceived(e:Event):void
{
   swfUrlLoader.contentLoaderInfo.removeEventListener(Event.COMPLETE, onSwfReceived);
   swfUrlLoader.contentLoaderInfo.removeEventListener(IOErrorEvent.IO_ERROR, onSwfIOError);
}
</code>
.
That's it ! I don't do anything else besides just loading the external SWF !
The only things that I can think about are:

maybe the 'bad' SWF files have some code-behind in them that causes this behavior to happen ?
the 'bad' banners are supposed to be 906x340. I have noticed that
they have animations flying in from 'outside' those boundries ... (I
found this out by decompiling the SWFs using 'Flash Decomplier'
trial).

Here are the SWF banners that are OK and don't do any problems:

Adom-Adom SWF
Mama Off SWF

Here are the 'bad' banners that make my player go crazy:

Cheese SWF
Emek Cheese SWF

Can anyone help me figure out how to prevent this from screwing up my player, please ?
Thank you for everyone who can help !
Answer: it sounds like some of the secondary loads are changing the stageAlign and/or the stageScaleMode.  see if changing stage.stageAlign and stage.stageScaleMode to the values you expect after the load is complete fixes the problem


Why didn't Thor go for the Infinity Gauntlet?

Question: In Avengers: Endgame we see Thor make an attempt at getting the Gauntlet but as Thanos grabs his cape he forsakes it and starts attacking Thanos. Why did he just allow Thanos to tear his cape as in Thor: Ragnarok and go for the Gauntlet? He was clearly very close and had he let Thanos tear his cape he most definitely would have taken the Gauntlet.
Answer: Assuming you mean this scene at the end where they are all struggling over the Infinity Gauntlet and to not let Thanos grab it:

Well quite easily because Thanos actually grabs his neck and pulled him backwards. Thor did the sensible thing and turn to face and fight his opponent instead of taking a hit in the back.


operator invertability and measurment

Question:
In Quantum mechanics, we define for each physical quantity an operator (for example - the position operator)  whose eigenvalues are the possible outcomes of a measurement (different positions in space).
So, if we have a system in the state -
$$\left|\psi\right\rangle = \left| x_0 \right\rangle + \left|x_1\right\rangle$$
after measuring its postition we will get by random either $x_0$ or $x_1$.
So measurement can't be an invertible operator since from the result $x_0$ we cannot deduce the original state was $\left|\psi\right\rangle$ and not just $\left|x_0\right\rangle$. But can a measurement be defined as an operator at all?
Another question is whether the position operator (or any other used in QM) is invertible? It is tempting to say it is not because it has $0$ as an eigenvalue, but it is not defined in a finite dimensional space, so i'm not familiar with this kind of operators.
Answer: ad 1: Measurement can not be defined as an operator on Hilbert space, because after the measurement the system can be in different states (with different classical probabilities) and this can not be encoded in the state vector $|\psi\rangle$.
I'll go into some more detail.
Let's say we are measuring an observable corresponding to the self-adjoint operator
$$ A = \sum_n a_n P_n , $$
where $P_n = | a_n \rangle\!\langle a_n |$ are the projectors on the eigenspaces.

After the measurement, the system will be in one of the states $|a_n\rangle$.
If we don't know which one, this can not be written as a state vector $|\psi\rangle$, as explained above.
However, it can be written as a state matrix $\rho$ which includes classical probabilities.
In fact, measurement of $A$ corresponds to a linear superoperator on the space of state matrices:
$$ \rho \mapsto \sum_n P_n \rho P_n . $$
After the measurement under the condition that we know that the result was $a_k$, the system will be in the state $|\psi\rangle = |a_k\rangle$ (assuming no degeneration).
The function on Hilbert space corresponding to this conditioned measurement,
$$ |\psi\rangle \mapsto |a_k\rangle $$
is not linear and therefore not an operator.
The effect of conditioned measurement on the state matrix is also non-linear,
$$ \rho \mapsto \frac{P_k \rho P_k}{\operatorname{tr}(\rho P_k)} .$$

ad 2: Yes, you can define a (self-adjoint) operator $x^{-1}$. The tricky part is that $x$ and $x^{-1}$ are unbounded operators, their domain is not the entire Hilbert space. For each $\psi \in D(x)$ we get $(x^{-1} \circ x) \psi = \psi$ and for each $\psi' \in D(x^{-1})$, $(x \circ x^{-1}) \psi' = \psi'$. However note that $D(x) \neq D(x^{-1})$. You might find this question and the comments therein interesting.
Answer: In the simplest case, measurements are represented by projection operators $\vert \phi_k\rangle\langle \phi_k\vert$, where $\vert\phi_k\rangle$ is an eigenstate of Hermitian operator corresponding to the observable under measurement.  The projectors must satisfy
$$
\hat 1=\sum_k \vert\phi_k\rangle\langle\phi_k\vert\, . \tag{1}
$$
Each projector $\vert \phi_k\rangle\langle \phi_k\vert$ is idempotent and thus non-invertible, but an operator nonetheless.
For mixed states (or more generally in the density matrix formalism), three are also generalized measurements or POVMs, which also satisfy the sum rule of (1).  An example of POVM used in state discrimination can be found on this wiki page.

operator invertability and measurment


Install sql loader linux

Question: I tried to install Oracle instant client on a redhat machine. I have instantClient basic, sdk, and sqlplus but I could not find any sqlldr. Can some one help me do it?
Thanks
Comment: It's sort of [possible](http://www.nyoug.org/Presentations/2007/200703_Ji_Instant%20Client.pdf) to add SQL\*Loader to Instant Client, apparently - I haven't tried and am not advocating that. But you'd need the full client anyway; you can get that from the [database installer](http://www.oracle.com/technetwork/database/enterprise-edition/downloads/index.html), so you might as well just use that. Before you do, have you considered using external tables instead?
Comment: `sqlldr` is part of the server installation.
Comment: At http://www.oracle.com/technetwork/database/features/instant-client/index-100365.html sqlldr is not listed as being a component of the instant client. It is probably available with the full client install.
Comment: @ShannonSeverance, Where can I find full client?
Answer: Following the information @Alex Poole provided in his comment, I was able to add the sqlldr binary to an Oracle instant client installation on redhat linux.  The key is to have access to a full oracle client (or database) installation from which to obtain the sqlldr binary.
In summary here was the process I took with Oracle 220.127.116.11.0:
Install Oracle Instant Client
Download from oracle instant client rpms:

oracle-instantclient11.2-basic-220.127.116.11.0-1.x86_64.rpm
oracle-instantclient11.2-jdbc-126.96.36.199.0-1.x86_64.rpm
oracle-instantclient11.2-devel-184.108.40.206.0-1.x86_64.rpm
oracle-instantclient11.2-sqlplus-126.96.36.199.0-1.x86_64.rpm

Install:
yum install oracle* --nogpgcheck
Create Oracle Environment Variables
In /etc/profile.d/oracle.sh
export ORACLE_HOME=/usr/lib/oracle/11.2/client64
export PATH=$PATH:$ORACLE_HOME/bin
export LD_LIBRARY_PATH=$ORACLE_HOME/lib
export TNS_ADMIN=$ORACLE_HOME/network/admin

Copy sqlldr and message file from full Oracle client/database
[root@redhat bin]# pwd
/usr/lib/oracle/11.2/client64/bin
[root@redhat bin]# scp root@oracleServer:/OracleHome/db/product/11gR2/bin/sqlldr .

Try it:
[root@redhat bin]# sqlldr
Message 2100 not found; No message file for product=RDBMS, facility=ULMessage 2100 not found; No message file for product=RDBMS, facility=UL

We need to copy over the ulus.msb file from the Oracle database.  But first we need to create the proper directory structure:
[root@redhat client64]# pwd
/usr/lib/oracle/11.2/client64
[root@redhat client64]# mkdir -p rdbms/mesg
[root@redhat client64]# scp root@oracleServer:/OracleHome/db/product/11gR2/rdbms/mesg/ulus.msb rdbms/mesg/

With the message file in place, try again:
[root@redhat client64]# sqlldr

SQL*Loader: Release 22.214.171.124.0 - Production on Tue Oct 20 10:12:55 2015

Copyright (c) 1982, 2011, Oracle and/or its affiliates.  All rights reserved.

Usage: SQLLDR keyword=value [,keyword=value,...]
....

Success!
Comment: Works, but some of the steps are not needed. You can just use the basic client zip file, without needing to install anything: With the instantclient-basic-linux.x64-18.104.22.168.0.zip extracted to ./instantclient/, all that you need to do is to add the folder ./instantclient/rdbms/mesg/ folder and the file ./instantclient/rdbms/mesg/ulus.msb, and then add the ./instantclient folder to both your PATH and LD_LIBRARY_PATH variables.
Answer: Install oracle-instantclient12.2-tools, which has sqlldr; and make sure your PATH includes /usr/lib/oracle/12.2/client64/bin.
Adjust versions accordingly.
Comment: You'll probably also need to ensure that your library path includes a reference to the lib directory as well i.e. export LD_LIBRARY_PATH=/usr/lib/oracle/12.2/client64/lib
Answer: Simpler alternative to the accepted answer that does not require an existing full client install to steal the sqlldr binary from:
You can download SQL loader from OTN in a separate instant client package called "Instant Client Package - Tools: Includes Data Pump, SQL*Loader and Workload Replay Client"
Here is the link for linux: Instant Client Downloads for Linux x86-64
Comment: When adding an answer to an older question with an existing accepted answer it can be helpful to discuss how your answer differs and what new information it brings to the question. For example is the link that you provide a better one that the one that Alex left in his comment?

Install sql loader linux


How to use different versions of PHP?

Question: I am using Ubuntu 16.04.
I have several virtualhosts, and I need to run different PHP versions. I have php-fpm and FastCgi installed, but how can I configure it?
Comment: If one of the answers solved your question, please mark that answer as the accepted one by clicking the gray checkmark next to up/down arrows on that answer
Answer: Maybe not the response that you're waiting for, but it gets painful to manage several php versions in your machine.
I've found that the best approach is to have a newer php version (php7+) as primary, and if I need something older or another specific version, I use a container with apache/php from here or use this as base image and modify it as necessary, it has great instructions to do that.
In the case that I need an older php version (unsupported so be careful), I can just build from an older OS version with support for that particular version.
The advantages of this approach are, first, that you don't mess up your machine with lots of packages and dependencies. Second, you don't pollute your php install with all the dependencies and packages that eventually will conflict with each other due to version-incompatibility. Finally, and super importantly, dockerizing apps will give you a replicable recipe for your production environment.
Even if you don't choose this as your approach, take a look at docker. It will make your like easier and it's "the thing" used in development nowadays.
Answer: With nginx, all you have to do is use sockets via proxy_pass:
server{
    (...)
    location ~ ^/index\.php(/|$) {
            fastcgi_pass unix:/var/run/php/php7.2-fpm.sock;
            include fastcgi_params;
            fastcgi_param SCRIPT_FILENAME $realpath_root$fastcgi_script_name;
            fastcgi_param DOCUMENT_ROOT $realpath_root;
    }
}

With apache you need to use proxy:
<FilesMatch "\.php$">
     SetHandler "proxy:unix:/var/run/php/php7.2-fpm.sock|fcgi://localhost/"
</FilesMatch>

This way, you can use different sockets (each for different version of PHP) by configuring them within each Virtual Host
Comment: I'm new here, where I find the config file to put these? @janmyszkier
Comment: for apache it's /etc/apache2/sites-available and for nginx /etc/nginx/sites-available

How to use different versions of PHP?


SharePoint Designer 2010 does not allow end users to make backups of their sites

Question: SharePoint Designer 2010 does not allow end users to make backups of their sites, so is there any other way we can perform the backup using the same SharePoint Designer 2010.
Answer: It's not the answer you are looking for, but no.
The site is not just made up of the files you see, but also data stored in the database. The 2007 SPD backup feature was able to get that information but 2010 has no way to access it.


If algorithm runs $\theta(n)$ in time T, doubling input size has what effect on time T?

Question: In other words, is there a relationship between the step size and the actual running time? Suppose that the algorithm is run on identical machine.
Comment: A *real* machine? That's a can of worms.
Comment: Let's suppose this machine is from the world of CLRS
Answer: There's no clear relationship, except that bigger inputs will tend to take longer.  What we call the "running time" in complexity theory is the number of basic operations but we just choose some set of basic operations and assume that they all have the same cost.  That's fine for asymptotic analysis but it doesn't correspond to the actual running time, as measured by a clock.
For example, imagine your algorithm consists of an initialization phase that takes one second, regardless of the input, plus a quadratic time loop that takes $n^2$ milliseconds to process $n$ items.  Complexity theory just says that your algorithm has running time $\Theta(n^2)$, so doubling the size of the input multiplies the running time by four.  Asymptotically, this is true but, if you double the input size from $10$ to $20$, the running time only changes from $1.1\,\mathrm{s}$ to $1.4\,\mathrm{s}$, which is nothing like a factor of four (it's less less than $30\%$).
Another problem is that complexity theory doesn't model the sheer... well, complexity of modern computers.  A simple example: suppose your quadratic algorithm runs in half a second on an input of length $\ell$.  Great, it's going to run in just over half a second on a similar input of length $\ell+1$, right? Maybe.  Or maybe it takes ten seconds because your data doesn't fit in the cache any more.
Answer: The answer that your teacher or textbook expects is that doubling the input size doubles the running time. The implicit assumption is that the running time is exactly of the form $T(n) = Cn$. In that case, $T(2n) = C(2n) = 2(Cn) = 2T(n)$. In practice, $T(n) = \Theta(n)$ only implies that $cn \leq T(n) \leq Cn$. Therefore all we can say is that if $n$ is multiplied by some large $D$ then
$$
D \frac{c}{C} T(n) \leq cDn \leq T(Dn) \leq CDn \leq D \frac{C}{c} T(n).
$$
So for large enough $D$, multiplying $n$ by $D$ multiplies the running time by some factor lying in the interval $[(c/C)D,(C/c)D]$.
The simple interpretation is still helpful intuitively. Under this interpretation:

The running time is linear if doubling the input size doubles the running time.
The running time is poylnomial if doubling the input size multiplies the running time by a constant.
The running time is exponential if increasing the input size by a constant multiplies the running time by a constant.
The running time is logarithmic if doubling the input size increases the running time by a constant.
The running time is constant if it is independent of the input size.


How do mods balance a game of Werewolves?

Question: Do they look at win rates and adjust setups to reach a particular number (e.g. 50% village win rate), or is it based on some other assessment of strength of the two sides, and what the two sides SHOULD be able to accomplish if they play well?
Comment: is 'with a dartboard and a blindfold' a suitable answer?
Answer: Hosts/Mods usually access a separate page to create their setup, with role cards provided. Each role card holds a specific score (e.g. Seer is at 9 points, GrandVizier at 8 points, etc.) which then is tallied with the other scores to generate a predicted percentage for each faction that's added into the setup.
At this point, each host/mod builds their setup in their own way. I'll answer by sharing how I build my setups, which should give you some basic insight. Other hosts/mods are encouraged to add their input as well.
When I create my setups, I usually start with a particular theme (e.g. Subfaction war, GY-heavy intel, etc.). Once I've added the roles I want in there, I start tweaking the setup to make sure the balance is slightly more favoured to the village (e.g. Village:Wolf = 55:45). I'll not always achieve that exact ratio, but I'll try to get as close as I possibly can. If the setup has more factions (e.g. coven), then village gets the highest chance, and a bit more leverage to coven over wolves. There will be some setups where I don't try to get the exact ratio down, and the setup is made just to have some light-hearted fun.
Comment: Does the choice of open / semi-open / closed setup affect balance at all; if so, how?
Comment: AFAIK, the numbers don't exactly reflect the effect hiding the setup has on the balance, but it could be argued that the effect is noticeable. Kirschstein or Storm might be better suited to answer here.


Phase space formulation: "Representation" vs "function" vs "quasi-probability distribution"

Question: In the phase space formulation, the terms "representation", "function, and "quasi-probability distribution" (as in Glauber–Sudarshan P representation, $P$-function) seem to be used interchangeably.
I wonder about the semantics of these terms: Do they all really mean exactly the same thing, even mathematically, or might there be some subtleties to be understood?
Answer: These three things all emphasize different properties:

"Function": reminds you you're dealing with a function on phase space. Also the shortest one, so can be used for convenience.
"Representation": reminds you this function represents the content of a particular quantum state.
"Quasi-probability distribution": reminds you this function is like a probability distribution but isn't really one.

These adjectives end up being used interchangably not because they mean the same thing, but because the three most common things they're applied to ($P$-function, $Q$-function, Wigner function) have all three of these properties.
Comment: A small tweak: in that article, "representation" is mostly used to contradistinguish functions derived by different operator-ordering maps. They are equivalent, but different rules for producing different functions (P, Q, and W, and... and...) corresponding to ("representing") the same operators and physical quantities.


Does possessing an enemy count towards chaos?

Question: I want to get the "low chaos" ending in my Dishonered playthrough. I know that killing enemies will count towards more chaos. Does possessing an enemy also count towards the chaos score?
Comment: It is unclear what you are asking.
Comment: @Sumurai8 saw it. As I'm not sure, I'll comment: I think that possessing causes chaos.
Comment: @ardaozkal Perfectly clear to me. Have you actually played Dishonored?
Comment: @Studoku It wasn't clear before edit. I'm stuck in middle of somewhere. I have low hp and it is full of guards. Will finish if I get through there.
Answer: No, possessing guards does not directly increase chaos, as long as the guard survives. If the guard is killed because of possessing him, e.g. falling off a ledge after the possession ends, that counts as a kill.
Chaos is caused by kills and certain quest/side-quest objectives in a dangerous and destructive way.


feedback ammeter vs current probe?

Question: Could anyone please let me know which one is better for low current measurement? I'm going to measure power consumption of MCU and camera module, But it seems I can't use shunt resistor, because current will be less than 300mA and shunt resistor has large error for such low current measurement. However, I can't decide a proper tool to make it. If I could use the feedback ammeter, then I'd like to go for it to avoid bying the expensive current probe.
Comment: Please provide justification for "shunt resistor has large error for such low current measurement". You certainly ought to be able to get 1% accuracy.
Comment: is this for in-circuit measurement? or testing your device?
Answer: I assume the load takes large current pulses but with a low average current.
If you just need the average current you can use a normal ammeter (i.e. measure a voltage across a shunt) but add a large capacitor across the shunt (or across the load).
The capacitor will supply the current during the pulses and will let you use a shunt appropriate for the average current, not the peak.  The capacitor may need to be many hundreds or thousands of microfarads depending upon the particular scenario.
Comment: I've done that by putting a small shunt (e.g 0.01ohm) then using a low offset opamp (10uV) configured as a differential amplifier to multiply it by 100 or so to display on an oscilloscope.  The integral feature on many new DSO (I use an Agilent) then allows you to integrate the current to measure not just how much current is required at different phases of operation but also how much charge would be taken from the battery (this was for circuitry in a cell-phone).
Comment: I need to measure detailed profile including rise and fall shape.
Comment: Thank you for the answer. I think I should try it. But I wonder if the method guarentee good accuracy.
Comment: Agreed it has its limitations but is probably at least as good as a current probe. Probably not as good as a feedback ammeter could be,although I've never used one.
Answer: I would not agree that a sense resistor would have a large error.
A wide range of 1% or better current sense resistors is available from multiple vendors. Here is a typical series of parts.
My approach (for simplicity) would be to use one of these with a good instrumentation amplifier or perhaps a precision amplifier.
You have not stated what frequencies you are trying to capture which would influence my amplifier choice.
There are amplifiers specifically designed for current sensing, and even some with an integrated ADC.
If 1% to 2% accuracy is sufficient, then this is how I would probably measure current.
These types of devices are widely available from Maxim Integrated, Analog devices, Linear Technology and Texas Instruments to name but a few.
HTH

feedback ammeter vs current probe?


Correlation coefficient of noise

Question: A correlation coefficient is computed as $$r=Cov(X,Y)/(\sqrt{Var( X)}*\sqrt{Var (Y)})$$
What is the correlation coefficient of a number with itself then.
I have a noise function,assuming with a known value and variance; and I perform a correlation of noise with itself what should I get as the correlation coefficient. The noise follows a $\chi^2$ distribution.
Answer: No matter what distribution the variable $X$ distributed as, the correlation between $X$ and itself equals 1.
$$r=Cov(X,X)/\sqrt{Var (X)}*\sqrt{Var( X)}=Var(X)/Var (X)=1.$$

Correlation coefficient of noise


More than 4 partitions with Ubuntu & Windows Dual Boot

Question: I would like to install Windows 10 & Ubuntu on my PC. I have done this before on my laptop however my PC is giving me issues. On my PC I have created 2 partitions on Windows, and 2 partitions on Linux, root and home. The system will not let me create a fifth partition for swap because it says it's limited to 4 partitions. How can I avoid this limitation? I am new to  so a thorough answer is appreciated.
Comment: Are you willing to start from fresh? installing windows and then ubuntu again... My question is because both Windows 10 and Ubuntu support GPT disks, and GPT does not have the 4 partition limitation
Comment: Other option is to delete one of your primary partitions and create a logical one, inside the logical partition can reside several extended partitions
Comment: Yes i want to start fresh, i'm just doing backup right now and want to install windows and then ubuntu. Where can i make a logical partition? Can i install Windows and let space for Ubuntu, then in windows with some program change that partition on logical and then install ubuntu on this partition?
Answer:
The system will not let me create a fifth partition for swap because it says it's limited to 4 partitions. How can I avoid this limitation?

The MBR supports up to 4 primary partitions. To avoid this limitation you need to use one of the primary partitions as an extended partition.
Also you can convert your disk to GUID Partition Table (GPT), you will be allowed to create 128 partitions.
On GPT the Windows 10 can boot only with EFI firmware. Linux should boot Legacy and EFI.
Answer: In the Ubuntu installer, when asked how much space do you want for your ubuntu system, choose the option below the slider that says Advanced partitioning, there you will be presented with a tree view of the partition table outlining your already existing partitions for windows, there you must resize one of the windows partitions if you didn't leave any unpartitioned space for ubuntu, to resize just select the last partition and click the edit button, in the edit window just reduce the size leaving the desired space for ubuntu and don't change anything else.
After that in the tree view there will be a free space option in the list, select that and click the '+' button, input the desired size (take in mind the space needed for the home and swap partitions and don't use all the space), select the logical radio button and in the 'Mount point' option select '/' (root) from the dropdown and click OK.
Repeat the previous step for the home partition but select '/home' from the dropdown, and again for swap.
Answer: Just make the logical partition instead of primary. Your problem is solved. You can do this in 2 ways:
1) Make your / root as primary and home and swap as logical.
2)or make everything logical.
Comment: The OP asked for "a thorough answer".   Please provide details — what steps should the user take?    Please do not respond in comments; [edit] your answer to make it clearer and more complete.


Photon polarization transformations

Question: Photon polarization states form a qubit $(\cos \theta ~  \sin \theta)^{T}$ - characterized by a parameter $\theta$. Obviously, such a state can be rotated by some transformation matrix  $R_{\theta} = (\cos \theta, \sin \theta; -\sin \theta, \cos \theta)$. However, I do not understand what a polarization beamsplitter (PB) does to such a vector (probably splits it into two orthogonal vectors). What is the corresponding operator for PB, say $S_{\theta}$? How can one physically implement $R_{\theta}$ and $S_{\theta}$ (if it exists)?
Answer: To discuss polarizing beam splitters you'll need to add another degree of freedom for the photon: its path. Initially, your photon has some polarization state and is incident in some path:
$$|\psi\rangle=(\alpha|H,0\rangle+\beta|V,0\rangle)$$ where I labelled the path as 0. A polarizing beam splitter directs all photons of one polarization (say, horizontal) to one path and all photons of the other to an orthogonal path. For example
$$PBS|\psi\rangle=(\alpha|H,2\rangle+\beta|V,3\rangle).$$ Now, if you inspect the photon in path 2, for example, you'll always find it to have polarization $|H\rangle$, but you'll only find it in that path with probability $|\alpha|^2$.
There are many question here, you can keep reading the quoted Wikipedia page for more answers. For example, you can make a PBS by "tilting a stack of glass plates at Brewster's angle to the beam." To make this into a polarizer that only transmits light of a particular polarization, you can ignore or absorb light exiting one of the two paths. To just change the polarization and do nothing to the path degree of freedom, you can use a waveplate; essentially a birefringent material that transmits different polarizations at different speeds such that they pick up a relative phase.

Photon polarization transformations


What is ExtraNonce2?

Question: I'm reading about the Stratum protocol where miners contribute to pools.  Specifically there is a "mining.submit" method -- https://en.bitcoin.it/wiki/Stratum_mining_protocol, in which I miner will submit a share for consideration.  The details on this doc are a little sparse.  Specifically, what is the "ExtraNonce2" value they describe as being submitted back to the pool?
Answer: The extra nonce is a value in the coinbase transaction which miners will increment in addition to incrementing the nonce in the block header so that there are more possible hashes that can be tried with a given set of transactions.
The ExtraNonce2 is specifically the part of the extra nonce that the miner is changing while performing work for the pool. There is also an ExtraNonce1 which the pool provides to the miner. That ExtraNonce1 is typically used as an identifier.
Comment: ExtraNonce2 is a value that the miner keeps changing in order to produce more block headers that can be hashed. Because this is something that the miner changes, he has to provide it back to the pool when he submits his work. ExtraNonce1, Coinbase1, and Coinbase2 are provided by the pool, so they know what they are and can reconstruct the block from the ExtraNonce2 and nonce that the miner submits.
Comment: Could you elaborate on the "ExtraNonce2" part of your answer?  Maybe with an example.  For isntance, you say its "part of the extra nonce" but I'm reading the extranonce2 is different from extranonce1 in terms of forming the coinbase, which I' reading is (coinbase1 + extranonce1 + extranonce2 + coinbase2).
Comment: So I am understanding that `nonce2` is `ExtraNonce` which is composed of 2 parts `ExtraNonce1` and `ExtraNonce2` where the pool defines `ExtraNonce1` bits but the miner is free to set/redefine during its mining job the `ExtraNonce2` bits.  The pool specifies in bytes (ie 8 bits) how much of `ExtraNonce` the `ExtraNonce2` takes, ie if `ExtraNonce2` is 2 bytes, then `ExtraNonce1` will be 6 bytes because both have to add up to 8 (64 bits)?

What is ExtraNonce2?


Abstract Algebra study methods?

Question: I am currently busy with an introduction to Abstract Algebra (undergraduate module) through distance learning, but I am really struggling to answer the questions in my textbook. I know what all the concepts mean and can name all the properties, but when I get a question I usually have no idea where to start. I can usually only do the first quarter of the questions and then after that I am lost. Any hints or tips on how to approach Abstract Algebra. Please don't judge.Thanks, any tips would help.
Comment: Don't forget to _test_ claims that you are asked to prove. In other words, play "skeptic". Once you see, by testing examples, that the given claim appears to be true, the examples _might_ give a clue as to _why_ the claim _must_ be true.
Comment: You need a supplementary text with _lots_ of worked problems. Try them, peeking a little if you get stuck. Once you understand it, review it to try to get an understanding of _why_ the solution used a given line of attack.
Comment: You probably don't know what the concepts mean as well as you think, so I think the first step is to shake off this belief and look for where your understanding is lacking.
Answer: Here is some advice from Joe Gallian that I found nice when I learned algebra for the first time.  I usually give this to my students at the beginning of the semester and many have said they found this to be helpful.  Much of this is related to his book on Abstract Algebra (which I think is a great first one to learn from) but I think a lot of the advice is good for any book.
http://www.d.umn.edu/~jgallian/advice.html
Hang in there, you start to get the hang of it as you go!  It is like solving a puzzle, the challenge is half the fun :)  Best of luck studying a beautiful part of mathematics.
Answer: A general tip for solving problems is to only consider the things you know about, and possible consequences. Once you start to freely express this creation then you will see that the theorems and questions that are proved are not random, rather are intimately related to the axioms of the abstract group. To be concrete about what I mean is look at the integer(whole) numbers with addition and multiplication, it is a non-trivial consequence that when you multiply any number with zero you get zero, and a non-trivial corollary to this is that you can not divid by zero which mystifies most elementary school students. But when you realize that for any $a\in \mathbb{Z}$ $0\times a= (0+0)\times a=0\times a+0\times a$ the first equality is by axiom of additive identity, the second is because of distribution axiom. If you can prove that $0$ is the unique number such that $0=0+0$ from group axioms then you will immediately see that $0\times a=0$.
In summary I sincerely was baffled by the theorems proved in abstract algebra when I was told them at first, however I learned to accept the nature of abstract algebra being that which writes down a finite set of axioms for the relationship operators and deduce the natural consequences.
P.S. you should be curious why you can't divide by zero, well use the definition of multiplicitive inverse and the fact zero times any number is zero not one.

Abstract Algebra study methods?


How to sync onedrive for business?

Question: At my school we are starting to implement Office 365 for our students. We are working on basis of a bring-your-own-device strategy and will meet all kinds of devices and OS's. Office 365 comes with a built-in cloud feature, which can be synced to a newer Windows machine. Is there a possibility to sync to Ubuntu or Lubuntu machine, as it is possible with fx Dropbox?
Thanks for helping.
Armin
Answer: One Drive business (former Skydrive Business) also used as Sync tool for SharePoint has no native client for Linux. It is based on the Groove tool MS had back in the days.
For now you can only use the web browser to upload/download files.
Your best bet is that for OneDrive a Linux client/tool/daemon (like http://xybu.me/projects/onedrive-d/) will be built and that OneDrive Business support to use the same.
Answer: you can synchronize Ubuntu with oneDrive but not with the busines version. So use the free version and it works well. There is solution for ubuntu 14-04. I use it on 15 and it works fine.
How to sync OneDrive on Ubuntu 14.04?
All what I have to do is some minor adjustment - not reported on other ubuntu machines.
Answer: Here is my working solution: not a sync but a full access is possible with spfilezilla.
Download spfilezilla
Install mono-complete package
sudo apt install mono-complete

Run spfilezilla with mono
mono spfilezilla.exe

Configure it
Download link: https://spfilezilla.codeplex.com/downloads/get/1488499
There you get the source code and binary (in bin/Debug folder).
Be adviced that currently the download feature is in progress due to a missing token.
The problem is in spcomhelper.cs file at line
var fi = File.OpenBinaryDirect(ctx, fileServerRelUrl);

which is not able to generate the temporary token needed to download the single file.
Enjoy
Comment: Added, check above
Answer: A working SPfilezilla has been uploaded here: https://github.com/suoko/spfilezilla
Answer: The Microsoft Office on-line has integration with Dropbox, as you can see in this link: Microsoft Office for Dropbox — Frequently Asked Questions. And there's a Dropbox client available at Ubuntu Software Centre, and also in the official website: https://www.dropbox.com/install?os=lnx.
So, should work fine.

How to sync onedrive for business?


Sub Panel Conduit

Question: I'd like some advice to connect the main panel to the conduit. It's 2" conduit to the outside which connects to a detached garage. The problem I'm not sure of is how do I go from this LB box to the main panel without hogging out the entire 2x4's in between the two. It's 2" conduit because a bunch was given to me. I'm running 3- #4 and 1- #6 through this.
Comment: Can you move your panel two bays to the right, or will it not fit there?
Comment: @ThreePhaseEel technically I think the panel could be moved but if that's the best option I think I'd move the hole and the conduit. I used a old hole from the single branch circuit. Between the panel and my current conduit is the communications stuff (eg ATT & Comcast) so it would require more digging outside around those non electric cables.
Answer: Given  that you're using "free" 2" conduit, you have to pay the other way - by basically obliterating your 2x4s to make room for it.
Another option is to downsize the conduit where you go through the 2x4s. Your wires can fit in 1" Schedule 40 PVC conduit (using Sch 40 is OK here). You might consider bumping to 1-1/4 or 1-1/2 EMT conduit, if your existing holes have the space, because that would allow upsizing your wire - either for more amps or going aluminum wire to save money.  You definitely shouldn't waste money on copper feeder wire, unless aluminum just won't fit.
Comment: Thanks. I already have the mentioned wires in copper. I can use emt. The pvc has such a large oversized that the lb box sticks way out of the wall. I can get a small box and drill holes for  1-1/4 emt. That still takes a lot out of the studs though. But far less than the 2" pvc
Answer: Could you cut back the two 2 inch conduits on the right of the panel and set a PVC junction box (ON THE OUTSIDE) and then run conduit over and LB through the wall inside to the back of the panel?
And if you wanted to add any additional circuits in the future, you would have access to a junction box on the outside to come out of. Remember to seal and close (caulk) all the holes and pipes extruding to the outside.
Or just 90 over both 2 inch PVC conduits and then go through the wall into the back of the electrical panel. You will have to re pull new wiring though because the existing would be to short.
Comment: Welcome to StackExchange. This is not an "internet discussion forum" in the way you are used to. It is a question and answer site. If you prefer the discussion forum style, try diychatroom.com. 99.99% of the time you should have *one* answer per question. You can [edit] your answer when you wish to add content.  Also, you now have enough reputation to **add a comment** below a question or answer, which is where to ask for clarification. If you think you'll stick around for awhile, register an email and set up a password, that way you'll keep your reputation!

Sub Panel Conduit


show georss feed on gmap

Question: I am new to georss. i have my georss feed but i don't know how to check it on gmap.
Is there any way to check geoRss feed on google map.
(I work on php platform)
Answer: This post on the google maps api blog should pont you in the right direction - http://googlemapsapi.blogspot.com/2007/03/kml-and-georss-support-added-to-google.html

show georss feed on gmap


Hardwired WiFi Doorbells

Question: Other than one of the Nest models, are there any other WiFi doorbells which interface to a physical bell (as well as phones)? Obviously, there is the DIY option, but that is not what I'm asking about here (even if it might be reasonably trivial).
Answer: The Ring Pro is a hard wired doorbell, much like Nest's product. It retails for around $250. It also does 1080p video and has motion detection capabilities.
I assume you already have a hardwired doorbell, since you asked for that specifically, but if not and you are thinking of running wires, Ring also has the Elite line which uses power over ethernet. It retails for $500. The advantage here is that you don't have to worry about wireless coverage of your doorbell (at the price of double the cost) because it's plugged directly into your switch and providing power. Your switch does need to provide power over ethernet for this to work.
Ring also has battery powered doorbells - the Doorbell and Doorbell 2.
A word of warning, depending on your geographic location, such a doorbell may not be a great idea. The Ring products claim they only work between -5°F to 120°F (-20.5°C to 48.5°C) while the Nest products offer 5˚F to 104˚F(-15˚C to 40˚C). The low range may be a problem in the winter - and with the Nest there are some areas where the high is common multiple days in the summer.
Comment: 30˚C is generally a cause for celebration here, and I have a sheltered location. Good point though.

Hardwired WiFi Doorbells


Synaptic package manager question

Question: Why does the synaptic package manager display results for applications that have already been removed?
Answer: Synaptic is not what Windows' Add/Remove Programs or Uninstall a program control panel is!
It shows you software packages that are available to install and also the packages that are already installed on your system.
If you want to see only what is installed on your system, click the Status button and select Installed.

Synaptic package manager question


How would TimeMachine work with two external (destination) drives?

Question: I would like to backup my data to two external drives. That way I would like this to work is that both disks should have have a full backup of my internal disk. Is this the way TimeMachine would work?
Comment: Not officially supported without manually choosing a disk in System Prefs. If you want to automate this, hints here: http://apple.stackexchange.com/questions/3096/command-line-method-to-backup-using-two-time-machine-disks plus MarcoPolo would help.
Comment: Update: This is now easier to do with 10.7 / Lion: http://hints.macworld.com/article.php?story=20110906221223743
Answer: I haven't tried it, but since mountain lion, it just works.
Answer: I don't think time machine will backup to two separate disks simultaneously, but I can give you my backup solution:

Time Machine to external drive. Easy and I don't ever have to think about it. Just plug it in and BOOM! backup.
Second, bootable backup to a second external drive using CarbonCopyCloner. This one runs on a schedule and it's a free program.
Dropbox. I have the 50gb account, and I store all of my current projects, important documents, and anything else i may need at any time, whether I'm in front of my Mac or not. Using the Dropbox iPhone and iPad apps along with the web interface, I can always get to important files when I need to.
Finally, I use Arq to backup a copy of my library folder to an Amazon S3 bucket. This one is a paid app, but worth it because I'm paranoid and it makes me feel comfortable that even if both of my backup drives fail, between the S3 Library backup and my documents on Dropbox, I can recover from a disaster quickly and with minimal hassle.
Comment: Thanks for that tip on [Arq](http://www.haystacksoftware.com/arq/)! That is exactly what I'm looking for to do backups to my own S3 space.
Comment: Glad to help. Careful that you remember the password that you set. I forgot mine and didn't save it in my keychain so I couldn't restore the library when I did a system restore. Fortunately I had it on another backup.
Answer: You might consider 1 Time Machine disk and 1 disk that is using CrashPlan. The CrashPlan disk can be offsite too.
Answer: This has always worked well to cycle drives in to back up your files to more than one place. Mountain Lion can now track two drives at once, so you don't need to keep setting up a new preference, but I have used this for several machines since day one with Time Machine.
Before Mountain Lion, you needed to enter the Time Machine preference pane and select each drive as you connected the new drive to break the expectation that the system should back up to a drive that's now not mounted.
I have seen this work well for using multiple drives and cycling them manually for weekly, monthly and more sparse rotation schedules including if you place a drive off-site or keep one drive mostly in a fire safe (in a waterproof container) for enhanced protection in case of a fire (and/or flood).
With Mountain Lion, you can tell the system to alternate between two drives so a simple A/B rotation means you can set it and forget it. If both drives are connected, each backup will alternate between drives, but if only one drive is connected, all backups will go to that drive. When you reconnect a drive that has missed several backups, it's only an hour or two away from being updates.
Of course - you now have two (or more) locations to find any one instance of a file, but again, the longer a file lives - the higher chance it's on both drives. Files you download and delete could only get backed up to one drive, but if a file sits on your mac long enough to get saved to both drives, you'll have at least two copies of it should you delete it and need a recovery later.


Understand Ground

Question: I am confused regarding the attached image due to lack of understanding of ground.
It's a basic question i.e. "How do I setup ground in my bread-board."
 Tried finding it but the confusion prevails due to unavailability of a working setup image.
Answer: Occasionally (particularly in AC power distribution and some radio antenna systems) Ground really does mean "a connection to the earth", but in most electronics "ground" is just a name we give to the point in the circuit we wish to call "zero volts" - the place where we put the black meter lead when measuring voltages elsewhere in the circuit.
This "ground" might better be called "reference" or "common", but we seem to be stuck with the term "ground".  This "ground" has no magic properties.
This "ground"/common/reference is very often the most negative terminal of the power supply, but could be the positive terminal (ECL logic is supposed to operate on -5.2 volts, with the positive terminal of the power supply being "ground"/common).
In many audio and op-amp circuits, "ground" is the mid-point of the power supply, so we have both positive and negative supplies.
Again, there is nothing special or magical about "ground" - it is just what we call Zero Volts.
Comment: Good points about the alternate supply configurations.
Answer: Ground is just the part of the circuit that directly connects to the negative terminal of your power supply or battery. It's the line at the bottom of the schematic. There's not much significance to the "GND" symbol in this case. If you're using a solderless breadboard, usually you'll use the strips marked "-" for ground.
Comment: The concept of ground can be hard to understand at first because it means two different things. One meaning is the point on the circuit we use a reference when measuring voltages. For simple circuits that's usually the negative terminal of the power supply. Anything directly connected to that is ground. The other meaning is actual physical ground, a literal connection to the earth. Most hobbyist circuits are not earth-grounded, so the "ground" symbol just means the negative power supply terminal.
Comment: Thanks @Willis ..But had there been any one of the two(no negative and only the ground or vice-versa) I would not even be asking this question. Having 2 lines :-one for ground and one for -ve foxes me. Is it that ground is mentioned for layman to understand that negative part of the battery means ground
Comment: Some bench power supplies have three terminals: positive, negative, and "ground," which is usually green. In this case, "ground" on the power supply is a literal connection to earth via your home wiring. The negative terminal just connects to the power supply's transformer, which, being a transformer, is *not* directly connected to your home wiring. But you connect your circuit's "ground" to the power supply negative terminal, not to the green "ground" terminal.
Answer: I also once felt that the concept of GND to be confusing. In that schematic GND can actually be removed from it. The GND does not add anything or do anything at all, really. So to answer the question Where should I connect GND to? you shouldn't actually connect it to anything. No extra cable to or from anything to anything else.
A natural question to ask then is Why have that GND symbol at all?. In this schematic it simply shows the point which we consider to be the zero point. As you can see in the schematic the batteries or power supplies are connected in serial. In such a setup there are two common ways to place GND.
One way is to place it at the lowest voltage, in this case the negative terminal of the first/lowest battery/power supply, that makes us consider both batteries/power supplies essentielly as one battery/power supply from zero to 9 volts.
The second common way is to place GND in the middle of the two batteries/power supplies. That makes us consider the point between the batteries/power supplies as the zero volt point. Both the batteries/power supplies then is seen by us not as a supply from zero to 9 volts, but instead a supply from -4.5V to +4.5V!

Where we choose to place GND depends purely upon what makes most sense in the circuit at hand.
Another example. Here the ground i just changed between 3 positions. The positions of GND does not change anything. All what changes is the numbers:

Even more examples
Let's assume that you have the following circuit and you want to know the voltage at the point where it says ? V. A very important thing to understand is that question does not make sense. Because, voltage is a relational concept. There is never simply a voltage but rather a voltage between two points. A multimeter has two leads, one can't just use one of them, one must use both.

So, in order for it to make sense we must measure the voltage in relation to something. The following image makes more sense. We see here that the voltage is 1.5 V in relation to the negative terminal of the lowest battery.

Another notation that could be used for the exact same situation is this:

Depending upon what makes most sense in the circuit at hand (which is sort of another question), we can measure the voltage at the point in relation to some other point, for example the middle between the batteries or the positive terminal of the upmost battery:

I hope that makes it somewhat clearer what is meant with ground being the zero volt point in relation to which all other points in the system is measured against (unless something else is explicitly specified).

Understand Ground


Can't open bitlocker with flash drive

Question: I have activated Bitlocker on my Windows 7-64 bit Ultimate machine.  The system put the key on a thumb drive.  The system will not open with the key on the thumb drive.  It is the same key that printed out; and the same key that is stored in the machine.  Could it be a corrupted .tpm file, or does anyone know how to have the computer regerate all key and tpm file information?
Answer: It's unclear from your question exactly how BitLocker is configured on your computer. For an overview of your settings, open an elevated command prompt and type manage-bde C: -status (assuming your OS drive is C:). You can also use the manage-bde command line utility to add/remove BitLocker protectors.
For a more user-friendly (though less flexible) way of adding/removing protectors, right click your OS drive in explorer and click "Manage BitLocker" to manage your keys via a UI.

Can't open bitlocker with flash drive


Time complexity of norm function in Matlab

Question: What is the time complexity of the "norm" function in matlab?
Answer: If you consider the $\ell^2$ norm of a real vector of size $n\times 1$, it requires $n$ operations to square all the elements, $n-1$ sums and $1$ square root so all in all the complexity is something like $O(3n)$. You can also test this empirically in Matlab with the commands tic & toc and with multiple vector sizes.
With norm 1 and inf you should also have a linear time complexity using the same reasoning.


Is there a word for people who use children to gain sympathy?

Question: For example, beggars use children to get more money. People who think they can get away with things because they have children around.
The word can be an adjective or a noun.
A ______ person.
A ______.
Doesn't matter.
Comment: You should include a sample sentence demonstrating how the word will be used.
Comment: ...in particular, showing whether you are asking for a noun or an adjective; whether the word should be pejorative, neutral or adulatory; formal or informal. We have [lots of help on this sort of question](https://english.stackexchange.com/tags/single-word-requests/info).
Comment: Adjective or noun is fine. Just any word to describe that... Even if it loosely describes it. Close to words are fine too.
Answer: A adjective for taking advantage of others (including but not limited to one's children) is
exploitative (adj.)

Unfairly or cynically using another person or group for profit or
advantage m-w

Making use of a situation or treating others unfairly in order to gain
an advantage or benefit. Lexico

exploit (v.) To make use of meanly or unfairly for one's own advantage m-w

exploiter (n.) A person who takes advantage of something, esp. a person who takes unfair or unethical advantage of another OED

Exploitative parents are focused only on their needs. They view their children as a means of solving their problems. They wish to
reverse roles with their children and to remain forever dependent on
their sons and daughters. A. M. Uhl; The Complete Idiot's Guide to
Coping with Difficult People

Côte d'Ivoire is one of nine countries participating in the ILO-IPEC
project to combat the trafficking of children for exploitative
labor in West and Central Africa... U.S. Dept. of Labor; 2001
Findings on the Worst Forms of Child Labor

Rather than the family being a protective haven, it was the place
where, at best, parents might exploit their children and treat
them as a mixture of expensive nuisance, slave and 'Ideal Cute Child';
at worst, a place where parents could abuse their children in private.
Jane Fortin; Children's Rights and the Developing Law p.8

Young can do whatever they want. Parents support that. Many parents
want to present themselves as modern and open-minded. In reality, they
are disinterested and just care about their ego. They exploit
their children both financially and emotionally. So these people don't
only exploit  their children, but also tie them to themselves. V.
Živković; Return to God
Comment: Thank you for the amazing response. Well written. :)
Answer: Just to be clear, at least in most of Europe, it is illegal to use children as pawns for begging. Passersby might be accosted by nomads or Romani people with infants in their arms and be asked for money but these persons will rarely remain on a fixed spot for a length of time.
This probably explains the absence of a specific word for an adult who panhandles/begs with children as the offenders can risk fines, imprisonment, or losing the custody of their children.
However if one is looking for an umbrella term that loosely fits the definition of an adult who exploits children for monetary gains then  child trafficker could be used.
The Wikipedia page on child trafficking says [emphasis in bold mine]

Trafficking of children is a form of human trafficking and is defined by the United Nations as the "recruitment, transportation, transfer, harboring, and/or receipt" kidnapping of a child for the purpose of slavery, forced labor and exploitation. […]
The objective of child trafficking is often forced child labour. Child labour refers specifically to children under a stipulated minimum age, usually 14 at the lowest, being required to work. UNICEF estimates that, in 2011, 150 million children aged 5–14 in developing countries were involved in child labour.

Child trafficking is a serious crime and an accurate accusation for the act of kidnaping and selling children but used loosely, it could refer to adults who use their offspring for forced labour, as it is abusing and trafficking the services of that child.
The word pawn is appropriate to describe the child whose status is being manipulated.
Source: Longman Dictionary

pawn

someone who is used by a more powerful person or group and has no control of the situation.

The ambassador was being used as a pawn in the struggle between the two superpowers.

Source: Cambridge Dictionary

A pawn is also a person who is controlled by others and used for their own advantage:

She felt she had been used as a political pawn.

From NBC New York

"If it's even possible that parents are using their babies as pawns to get people to give them donations that's horrendous and deeply unfair to those children," de Blasio said at the time, saying he would put his inter-agency children's cabinet and the NYPD on the case. (2015)
Comment: Thank you for the amazing response. Well written. :)


Can no longer rename calendar events in Outlook since update

Question: I used to be able to change the name of a meeting that another person organized in order to better identify the event. In a recent update of Outlook, I can no longer do that and I have to click on the event to see the details. This is really a major productivity killer. I'm on a Mac. My husband who uses a PC can still edit the titles of meetings organized by others. Any ideas?
Answer: What's the detailed version of Outlook for Mac?
I tested this issue on my side(version 16.24). Subject of calendar cannot be changed for attendees.
According to the reply of our MVP in this thread, this feature may be changed and only organizer can edit the calendar items.


What are the differences between men's and women's bike frames?

Question: Why do women's bikes have a diagonal bar in the frame instead of a horizontal frame? Is this the only difference?
Sorry if this has been asked (but I cannot find it by searching) and I also just cannot think of a reason why.
Comment: @WTHarper just casually asking someone, they mentioned it might be dress related...skirts or dresses might be more accommodated with the diagonal bar...but that was a guess...
Comment: @davidsleeps - Way, way, way back in the mists of history women rode horses side-saddle and rode "women's bikes" in dresses.  Hence the slanted top tube.  (However, I happen to know a 50-something woman who frequently rides in a skirt, but rides a "men's" bike.)
Comment: I always compare it to the difference between fiddles and violins.
Answer: Way back when safety bikes were becoming popular, women wore skirts. Skirt lengths were to the ankle. The dropped top bar made getting on possible while maintaining respectability. Women were considered too fragile to risk hitting the top tube, hence the slanted bar. The trend continued even long after women stopped riding in long skirts.
Modern WSD (women specific design) geometry differs from conventional bike geometry. The difference goes beyond just size. Whether it is needed depends on who you ask. While some women may be smaller than the average male, many are as tall; height is not the only issue. Many women have a different leg to torso ratio than the male average and the frames are built to fit that difference. This is not to say that a women needs a female specific frame or that a male wouldn't fit on a WSD frame. It all depends on the individual physical traits of the rider.
Comment: Some of us still bike in long skirts. Just sayin'. :)
Comment: The difference between then and now is now you do it by choice
Comment: Differing leg/torso ratios are handled by top-tube sizing for any given seat-tube length. I think the OP is asking about step-through frames-- not just sloping top-tubes like on compact geometry frames for road bikes.
Comment: mikes: Agreed. I just thought "long after women stopped riding in long skirts" was a tad bit overstated.
Comment: I have seen no evidence that leg to torso ratios actually differ by gender.  It is my understanding that this is a myth and that there is more variation within gender than between gender (i.e., not statistically different)
Comment: @Rider_X do you have a source for this?  Very interesting.
Comment: @William here is a general article http://www.womenscycling.ca/blog/georgena-terry/womens-body-proportions-different-mens/
Comment: Around the time at the end of the 1800s when the "safety bikes" came up (which are often mounted by swinging a leg backwards over the saddle while holding on to the handlebar) women were apparently still wearing [undergarments which were not closed between the legs](https://localhistories.org/a-history-of-womens-underwear/). This makes the potential for indecency fairly serious (and the CanCan more spectacular).
Answer: For MTB I have observed that many bikes marketed as woman specific are almost a scam, they are only the same frame with different colors and lower grade transmission parts (I remember one where the male model was 9 spd while the female was 8 spd, but the frame had pink patches... )
Before any feminist starts pointing out that I'm a male rider, let me state I have built a couple of bike for female riders, and also have shared the trails with many females that got their bikes on their own...
I have studied many models of "women's bikes", and even from reputable brands I often find that the only meaningful difference is in the saddle.
Another difference that can really mean something is that some makers size their frames "Small", "Medium", "Large" and "Extra Large" rather than giving a size in inches, so it may happen that for some brand "Medium" for male means 17" and for female means 15". Outside that, the rest of specifications in the geometry for the same model of frame are usually the same, or small enough that are negligible.
Traditionally, a woman's bike has a very sloped top tube. This applies mostly to classic and urban bikes. This feature was initially created to let women ride while wearing their dresses. It also allows for easy mounting and dismounting without requiring to raise any leg prominently. However, this design is a bit weaker compared to the diamond frame design, so it is less used in mountain bikes.
At least in my country, the people has too many different sizes (because we have such a big mix of races in our ancestors) and while it's true that women have different proportions than men, it is also true that there can be huge differences among males as can be among females. For example, given two people of the same gender and height, one of them can have longer legs than the other, this can hold true both for women or men. These two people clearly can not ride the same bike without some sort of adjustment.
Frame size and geometry is only one step in bike fit, you still have seatpost length, stem length, stem angle, steerer tube length and the corresponding steem spacers, handlebar style and size and saddle fore/aft position and saddle angle. As long as my experience recalls, adjusting these variables is enough to achieve a proper fit (as long as your frame is not too far from the ideal size) regardless of your gender.
However, there are a few tips that usually can narrow your search for components:
Saddle: As I said before, this is the only area where I have seen that there are real differences. First, while it is true that female anatomy is different from male anatomy, it is also true that there can be huge differences from one person of one gender to another of the same, so not every woman will be O.K. just with a woman's saddle.
The female riders I know are usually fine with wider saddles than a man of similar size, remember women usually have wider hips. When the saddle has a cut groove in the center, females usually have a saddle that has a wider groove towards the front, while males are fine with a saddle that has a groove of uniform width. Also, when using a saddle that does not have any grooves, women tend to "nose down" the saddle angle.
This remembers me that the most reasonable "woman's saddle" design I have ever seen, rather than having a longitudinal groove, had a curved depression that begins roughly and inch behind the tip of the nose and ended there the "wings" begin to spread.
Grips: Women tend to have smaller hands, so a thinner grip (resulting in smaller overall diameter) can be more suitable. Also adjust brake lever reach so the lever is closer to the grip.
Handlebar: Its width is related to the rider shoulder to shoulder width, but then you have to account for riding style and technique, so I don't take the bait on women's handlebars. For any rider, if a narrower-that-can-be-bought MTB handlebar is needed, it is fine to simply cut it off (just cut the same length from both sides). I have also seen women's handlebars marketed as such because they have smaller diameter at the ends, but, unless you buy the corresponding grip, you wont be able to use it. That's why I rather recommend to buy thinner grips (or thicker if that's the case) that provide the same final result. And unless there is color and decorative design involved, you don't necessarily need grips to be designed for women to be thinner (smaller outer diameter), there are smaller grips at the same price of regular ones, you just have to find them.
Sources: The wife, the sister, a couple of female rider friends and 3 racer ladies.
Update: A few months after I wrote this answer I saw a trend in certain brand where the frames designed for women are a bit smaller but also have a shorter effective top tube, that is, they have less distance between the seat tube and the head tube. This makes sense for women that have proportionally longer legs and smaller torso + shorter arms, since this design would allow for a handlebar that is "closer to the rider" without using a super-short stem (which can cause a funky steering feeling at first). Funny enough, this difference is visually noticeable only in their 29ers. Side note: This difference also makes for a shorter wheelbase bike (the wheel axles are closer) which makes the bike feel more agile and easy to maneuver for a smaller person whereas a larger person would feel the same bike as "twitchy".
Comment: @Mσᶎ he totally answers it right at the beginning "Traditionally, a woman's bike has a very sloped top tube. This applies mostly to classic and urban bikes. This feature was initially created to let women ride while wearing thir dresses. It also allows for easy mounting and dismounting without requiring to raise any leg prominently. " see?
Comment: I'm not sure how this answers "why the sloped top tube" question.
Comment: So 17 hours after the succinct, accurate answer this one comes along and drops some of that answer into paragraph 5 of 15, the rest being at best vaguely relevant. Not convinced.
Answer: Except for differences in size (because women tend to be shorter than men), women's frames are no different than men's frames, really.
Although "step-through" frames have typically been marketed as women's frames in the USA, they're ridden by both men and women elsewhere. This type of frame is very convenient for utility and commuter bikes in urban areas where one may want to mount/dismount without swinging a leg over the back of the bike.
In other words, the step-through is not really a women's frame. It is just a commuter/city-bike design that is not as sporty looking as a proper diamond frame, but if you're wearing regular trousers or a skirt they're easier to deal with.
Comment: @jm2, you're just saying that the dimensions chosen better fit the dimensions of the distribution of sizes/proportions that women have. There is nothing intrinsically gender-based about that. In other words, there are men who will best fit a 41cm Ruby and women who would best fit a 61cm Roubaix.
Comment: The first point is misleading. There are differences between many women's frames as compared to men's/unisex frames. I suggest you edit your answer to reflect this- especially because I can't un-downvote your answer until you do (as in, the site won't let me until the answer is edited; it was a mistake to begin with, sorry!)
Comment: Traditionally, in the US "women's" frames had the dropped top bar.  It was only maybe in the 60s that women's frames began to disappear, though they weren't immediately replaced by suitably smaller diamond frames.  It wasn't until maybe the late 70s that Terry and a few others started offering frames designed for women.
Comment: @jm2. Can you name some actual differences? frames are available with a range of different geometries (seat-tube, top-tube, angles, wheel-size) to fit different rider measurements. This is correlated with gender only insofar as women tend to be shorter. Unless you're talking about color-preferences, skirt protectors or saddles, there is NO DIFFERENCE in bikes for men and women.
Comment: @jm2, sizing, which includes the length of the top-tube, stem, seat-tube, head-tube and wheel size has nothing to do with gender and everything to do with body proportions and overall height. The specialized ruby is just a range of slightly different tube lengths intended to be more suitable for the distribution of sizes of women. A woman who rides a 61cm will prefer the roubaix and not the ruby, even if the ruby is a "girl's" bike.
Comment: @Angelo yes there is. For an example, check out the specs on Specialized Roubaix vs Ruby.
Comment: @Angelo study the geometry a little closer. If you do, you will notice that the WSD frames have slightly shorter cockpits with slightly more upright positioning than the men's/unisex frames do. This is due to the fact that women typically have proportionally longer inseams and shorter torsos than men. There are differences in the tubesets and components as well, but talking purely in terms of geometry, there is a difference in how the frames fit proportionally. The numbers are there for you to read clear as day if you so choose.
Comment: @Angelo It is not true that modern WSD bikes are no different than men's other than size. As jm2 says, women tend to have a longer leg to torso ratio than men and the geometry is altered to reflect this. A better apples-to-apples comparison of bikes is the Trek FX line. You can compare a standard (men's) 15" 7.6 FX to the 15" WSD 7.6 FX and see that the WSD actually has a slightly *higher* standover than the men's, but a shorter reach.
Answer: Women have different leg/arm/torso ratios, so if a frame truly has a women specific geometry, you're going to typically see a shorter effective toptube and longer seat tube & headtube. For really small women's frames (and men's for that matter), the geometry starts to get really wonky because the wheel size and BB height typically don't change. I won't elaborate any further because I think you're asking more about step-through frames than you are women-specific frames.
Step through frames are thought of as women-specific, although typically these are cheap bikes where there is no difference between the standard and the stepthrough geometry. The only difference is the shape and angle of the toptube which has no effect on the geometry of the frame or the contact points for your body (ie pedals, saddle, handlebars).
Just like with most things there are exceptions to this rule- for instance, Breezer makes nice step through commuters with slightly shorter cockpits for the stepthrough models.
Comment: @Angelo just because you're not aware that there is such a thing doesn't mean it doesn't exist. Most reputable companies are doing women specific geometry frames these days (I've already named two), and yes, there is a difference. Men's vs women's body geometry goes beyond one being taller than the other. So let's lay off the retaliatory downvotes. Like I said, if you'd edit your answer so that it's not misleading I could remove the downvote.
Comment: Some women are tall, some men are short. Each will select a bike that fits them. There is no "male" or "female" frame.
Comment: this is not a "retaliatory" downvote. I simply disagree.
Comment: @Angelo with which part do you disagree? I will gladly explain it to you.
Answer: There aren't more than two things going on here really. One, women are generally shorter. Two, someone probably thought the quickest way to be able to differentiate the women's models was to slant the top bar a little, and it caught on. It's not by any means a standard, and most well built bicycles don't have much difference in shape between the women's and men's beyond size.
Answer: Oy...How about this. Yes, geometries are different in marketed WSD frames vs "unisex frames", BUT...what if they weren't ever called WSD? What if they were just proportionally smaller bikes?  Orbea has done that this year -- TT length/headtube height are proportional to the frames.  It's not about whether a bike is men's or women's...it's "was it designed for a human"?
There are many, many men who have proportions that are "seen as" women's proportions. And many women who are porportioned like men. I wish companies never would've never made WSD frames...it's misleading and leads women (especially new riders) to believe that that is what they need. When in fact, many many women can fit a 50 or 52 cm frame so long as touch points are modified (narrower handlebars, for example). But, truth be told, men modify these touch points also -- shouldn't really be any different for any human.
(been in the industry for 20 years, raced for 25, female)
Comment: Welcome to Bicycles! Please note that this is a Q&A site, not a traditional forum. See the help link above for more info. I am going to let your post stand, but I think you should edit it to more clearly answer the original question, and incorporate Kibbee's comments. If you desire to have a "back and forth" conversation, please try our link above.
Comment: I don't think that most women would shy away from buying a unisex/ments bike if it did fit them right, as you get a much larger selection of bikes in unisex/mens bikes. However, I do agree that the manufacturers are doing themselves a disservice calling them "women's specific bikes" as that means that almost no man will buy one, ever.  They're also not just proportionally smaller. They are generally made to fit a rider who has longer legs, and a shorter torso and arms relative to their total height (which is much more common among women) and not just be a smaller version of the men's bike.
Comment: Hi Dena! Welcome to bicycles. I think @davidsleeps' question refers to women's versions of more casual bikes while your answer seems to refer to road-racing bikes. (where I agree that the woman/man difference is just marketing). As a woman with the amount of industry experience you have, I'm thinking you probably also know a bit about the physical (rather than commercial) reasons for female specific bikes?
Answer: For some types the answer appears to be "just marketing".  I've got a 58cm road bike with 700x23 tires, and 18" wide handlebars.  My wife's old bike (which she no longer uses and is now the one that I can beat around in town with when I don't feel like wearing cycling shoes since it has platforms on 1 side of the pedals) is a 53cm frame, 700x23 tires, and 16" wide handlebars.  Crank lever length is 7" for both of them.  Dimensions on her "women's" bike match smaller "men's" bikes...  And yes, it's a little small for me for a road bike, but actually very closely matches the dimensions on my MTB which I was using to beat around town on...  :-)
Answer: The difference in height between a 5'10" (178 cm) man and a 5'5" (165 cm) woman is 8%.
So if men and women have the same shape, and if their bikes have the same shape, and if the man's bike has 28-inch (700 cm) wheels, then the woman's bike should have 26-inch wheels.
However I've found that small-framed road bikes or hybrid bikes, claimed to be suitable for women, still have 28-inch wheels: which changes their shape, and how well they fit the rider.
26-inch wheels exist but seem to be more standard for "mountain bikes" than for road bikes.
A couple of inches can make a real difference to how well a bike fits the rider.
Instead of or as well as asking the difference between a "mens" and a "womens" bike, it might be accurate/important to ask the difference between bikes for taller and shorter riders.

I also just cannot think of a reason why...

Apart from wearing a skirt, another reason seems to be so that her feet can touch the ground when she hops off the saddle at a stop, because of sitting too high to begin with, perhaps because of the wheels are bit too large.
Comment: I think the wheels are always the same size because there's too many things that must change along with the wheels.  When the wheel/rim size changes, the tire, tube, spokes, forks, stays and probably a couple other things I'm forgetting need to change along with them.  You can get a lot of variation in frame size while leaving the wheels the same size.  It only becomes a problem in very small bikes where you start to have the toe contact the front tire when turning.  On the smaller bikes you'll sometimes see 650c wheels, but even those are uncommon, as its a tradeoff for less tire selection.
Comment: For a while Terry made road bikes with a 27"/700c back wheel and a 26" front wheel.  This seemed to work pretty well, but for some reason the scheme was dropped.


How to disable HTML email from adjusting with Dark mode?

Question: I'm new to HTML codes in general. I'm trying to create an HTML email using this template. Things are working fine except for one thing: the email colors are changing when my phone is on dark mode. How can I disable that?
Answer: Many people desire to have their phones or computers in a dark mode/theme for readability, battery-saving, and/or reduced eye strain. You should not seek to remove this.
Furthermore, the current landscape of email clients is such that you cannot necessarily control this.
Specifically, we cannot change Outlook 2019 (Windows) or Gmail.
See the full writeup on Litmus https://litmus.com/blog/the-ultimate-guide-to-dark-mode-for-email-marketers
Comment: But that's an issue with the graphic, which is much easier to update so that doesn't happen (make it not transparent) than somehow try and disable dark mode for the entire email.
Comment: You make a great point about the benefits of dark mode. And also, there is good reason to disable it: namely if you're emails aren't going to render well when dark mode is forced on for users. For example, I receive coupon emails from some retails that use transparent PNG graphics for the scannable barcode, so every time I go to checkout at the store I must now disable dark mode on my phone at the system level and go back into the app. Many vendors (retail, enterprise software, etc) are just not ready to support dark mode yet.
Comment: From your perspective, that may be true. But not necessarily from the perspective of the people responsible for creating the emails. Not all teams are equipped to easily make changes to their own graphics (whether custom illustrations created by an illustration team, or generated graphics like barcodes which may be sourced from an outside vendor), and for those teams being able to disable dark mode is a much simpler and friendlier solution to the accessibility problem of a forced dark mode.
Comment: Since dark mode/theme is a user system preference, that customers change on their own device, we have no control over that. It may be simpler in concept, but in practice, it's simply not possible! There are techniques, however, in graphics and code, to try and minimise the ill-effects.


Difference between "unlikeable" and "dislikeable"?

Question: Is there a difference between unlikeable and dislikeable? It feels like there is, but I'm uncertain how to explain it.
Comment: The same as the difference between any un-word and dis-word. There is no special significance to likeable in relation to the use of the un- and dis- prefixes.
Comment: @Kris and what is that general difference?
Answer: Assume there are three states of fondness for something.

Like
Neither like nor dislike
Dislike

Disliking something is not the same as not liking something. If I don't like peas, I will eat them with no pleasure. If I dislike peas, I will actually find them nasty.
So, dislikeable is something that's easy to dislike.
Unlikeable is something that's difficult to like.
Comment: My interpretation.  *unlikeable* ... you cannot fall into the first group, "like".  *dislikeable* ... it is possible to fall into the last group, "dislike", but perhaps also possible to fall into the other two groups, instead.
Comment: @slim thanks for the answer. It's useful to point out that 'dislike' is not the same thing as "not like". However, to me the word unlikeable implies that something is impossible to like, not merely difficult.
Answer: According to the definitions of unlikeable:

Adj. 1. unlikeable - (of characters in literature or drama) tending to evoke antipathetic feelings; "all the characters were peculiarly unsympathetic"
   2. unlikeable - difficult or impossible to like; "a disagreeable and unlikable old woman"

and dislikeable:-

Definition: easy to dislike

the difference would appear to be that an unlikeable thing is something you don't or can't like, and a dislikeable thing is something you could quite easily not like (but that you have no particular aversion to at the moment).
Comment: thanks Brian, but sorry it's still a bit unclear to me. On one hand, we have "difficult to like" and on the other "easy to dislike"!
Comment: @BrianFenton, I think slim has put what I was trying to say, rather better.
Answer: At first glance, it seems pretty straightforward.
Unlikeable - 'Not likeable' (Not necessarily negative, just straddling the fence. Infrequent usage)
Dislikeable - 'easily hated' or 'easily vilified'
Unless you mean the new 'unlike'-able, which is a sad result of the FB culture and not a real word.
Comment: Thanks but I don't fully agree with you. Unlikeable to me is a strongly negative term, implying impossibility of liking.


How do I re-authorize Quicktime Player to use the microphone when once it has been denied?

Question: I wanted to use a USB audio input to record a video, and got something I've never seen before having done this 100 times; it asked "Authorize Quicktime to use the microphone?" I clicked no, because I didn't want it to use the internal mic, I wanted it to use a USB input.  Now, it won't let me get rid of the denial.  I've quit QT, quit & reopened it twice and it still won't let me choose ANY input source. It still says it doesn't have access to the microphone.  Is this a new Mojave 10.14.2 bug or what?  How the heck do I get out of this?  Thanks!
Answer: Go to System Preferences > Security & Privacy > Privacy > Microphone, unlock the preference pane by clicking the padlock symbol at the bottom left of the window and tick "QuickTime Player.app", which should be listed without a tick mark in its checkbox.
If QuickTime Player.app is missing, you should be able to reset all decisions you made for the various applications that asked for access to your Microphone by quitting System Preferences, opening Terminal (to be found in /Applications/Utilities/, or search via Spotlight) and running the following command:
tccutil reset Microphone

...then press enter.
This should clear all applications from the Microphone section and after launching QuickTime Player, it should ask for permission to the microphone all over again.
Comment: @ChaimEliyah I added an [answer](https://apple.stackexchange.com/a/384295/18101) that avoids wiping out microphone permissions for other apps.
Comment: It's noteworthy that this erases all of the apps that have already requested access, and depending on the logic of the app, they might not request access again. Use with caution.
Comment: It erased all the microphone permission. But when I start QuickTime player  > screen recording(or audio recording) it doesn't ask permission.
Answer: This new requirement to authorize Microphone was added in macOS Mojave (10.14).
The answer from Redarm is very good, and the best answer for people using macOS Mojave (10.14). But there is a slightly better option for people using macOS Catalina (10.15) or newer. This will reset the privacy settings for QuickTime Player only, without affecting microphone permission settings for other applications.
tccutil reset Microphone com.apple.QuickTimePlayerX

Note that you must quit and restart QuickTime Player after running this command.
Answer: For me QuickTime was not sharing my iphone screen as well. My QuickTime started showing this warning:

can not use Vaibhav's iphone. This app is not authorized to use Vaibhav's iphone quicktime

What I did:
Go to System Preferences > Security & Privacy > Privacy and follow these steps: