How do I get "V-shaped" distributed random numbers from uniformly distributed numbers?

Question: I have 1000 uniformly distributed random numbers. How do I manipulate them to get a V-shaped histogram?
Comment: "V-shaped" is not a precise term. There is no way for us to know whether you mean something that looks like $f(x)=|x|$ on $x \in [-1,1]$, or $f(x) = 1-|x|$ on $x \in [-1,1]$, for instance.
Comment: Is this for some subject?
Comment: I mean something like the $f(x)=|x|$
Comment: $f(x) = |x|$ won't work if your data are $\mathcal U(0,1)$. Are your data uniform on (-1, 1)? Have you tried simply subtracting .5, multiplying by 2 & then taking the absolute value? Do you need the actual data to have the 'V-shaped' distribution, or just the histogram?
Comment: I just want the histogram from  uniformly distributed numbers. I don't have an actual data.
Comment: Yes. I need to generate uniformly distributed random variables in excel and then transform them to random numbers from this kind of distribution.
Answer: Search for the "transformation method" or "inverse transform method", which is a way to generate random numbers with an arbitrary distribution. You'll find many lecture notes describing the idea. This is the wikipedia page: Inverse transform sampling.  It has links to more detailed resources at the bottom.
The basic result is this recipe: If you need some distribution $D$, then

find its CDF and invert it.
generate uniformly distributed random numbers between 0 and 1
transform these numbers with the inverse CDF to get numbers distributed according to $D$

The calculation can't be done analytically for every distribution.  For your distribution it can.  If the domain of the "V" is $[-1,1]$, then the PDF is $|x|$, the CDF is $(1+\operatorname{sign}(x) x^2)/2$, and the inverse CDF will be
$$\operatorname{sign}(2x-1) \sqrt{|1-2x|}$$
For example, in Mathematica
Answer: If $X$ and $Y$ are independent uniformly distributed random variables on $[0,1]$, then $X + Y$ has a pyramid or "inverted V" shaped distribution on $[0,2]$.
All we need to do to turn this pyramid into a V is to swap the two halves of the distribution.
Thus, given independent $X, Y \sim \mathcal U(0,1)$, let $$Z = \begin{cases} X+Y & \text{if } X+Y < 1 \\ X+Y-2 & \text{otherwise.} \end{cases}$$
The random variable $Z$ will then have the V-shaped the distribution you want on $[-1,1]$.
Comment: @NickStauner: From the random number generator, same as $X$. I'm not sure I understand your question.
Comment: Where does your $Y$ come from?
Answer: This should really be a comment below the above answer.  But since I do not have enough reputation to make this comment I will post it here.  In the question you originally asked how to do this in "excel".  This should do it,
<code>=SIGN(2*RAND()-1)*(ABS(1-2*RAND()))^0.5
</code>
An interesting note to the previous answer is that it does not change the distribution of the created variable at all if you are using one uniform random variable (the same for both) to generate the V-shaped distribution or two (for the sign function and the abs function).
Answer: You do want to use $U\sim \text{Uniform}(0,1)$. You are looking for something called Probability Integral Transform (PIT).
If $X \sim F$ then, $F(X)\sim \text{Uniform}(0,1)$. Therefore, first you will find the CDF for the distribution you are interested in, then you will transform. For example if you want $f(x)=|x|$, $x\in (-1,1)$, integrate to get $F(x)=P(X\leq x)=\begin{cases} \frac{-x^2}{2}+\frac{1}{2} & x\leq 0 \\ \frac{x^2}{2}+\frac{1}{2} & x> 0 \end{cases}$. Then, $F^{-1}(u) \sim F$
Answer: There are a variety of approaches that might be suitable.
Even with the comments you haven't really pinned it down enough (you give an example of what you want, but not what range of cases you want considered), but here are some examples of approaches:
1) rejection sampling. Generate a uniform on the desired range, and use rejection to obtain the desired distribution. This works quite generally, and can be made reasonably efficient even for fairly general cases. Variants of rejection sampling, such as the ziggurat approach, can be very fast, but may be quite fiddly to set up if you only want a few numbers.
2) For the case of $f(x) =|x|$ on $(-1,1)$. Let $U_1,U_2$ be iid standard uniform. Then $\text{max}(U_1,U_2)$ has a distribution like the positive half of the desired density. Let $Z$ be a random sign - i.e. $\{-1, +1\}$ with equal probability. Then $X=Z\,\text{max}(U_1,U_2)$ has the desired distribution.
3) (following the same set-up as in (2)): Let $V=\sqrt{U_1}$, and attach a random sign to that, $X=Z\,V$. (This uses the probability integral transform to get V of the right form).
There are innumerable other approaches with varying mixes of convenience and speed. For example, the approach in (2) can be used to generate two such variables at a time, and if speed is paramount, the bit required for a random sign may be taken from one of the uniforms used (preferably before normalizing to (0,1), and then bitshifting or a smaller scaling factor used to take what's left to still be uniform); this later approach might be used in (3) for example, or in a modified version of (1).


Active Directory Group Policy: Script Errors

Question: Anyone having issues with AD group policy script errors when enabling VMware Fusion's "Sharing" feature? I've run into this problem in version 2.0 and 3.0. I have a logon script applied on an AD OU. It works fine on all Windows client workstations and in VMware Fusion only when the "Sharing" feature is NOT enabled. Any ideas would be much appreciated. Thanks.
Answer: Can you run the logon script manually once you log in? any error output ? What is failing about the script?
My completely off the wall guess is that the sharing feature is mapping drives that your script then tries to map, causing it to fail.


Free OSX Sound Database programs

Question: Are there any free alternatives to Sound Miner out there?
Answer: you can use the finder and spotlight to do a lot of databasing.
The idea would be to put your metadata in the spotlight comment window - which spotlight can read in its searches.  There are automator scripts out there that can take metadata from spreadsheets and embed them into the spotlight comment fields as a batch process.  I'd imagine you can get good results using waveagent to read the bwav description and moving metadata over that way as well.
If you search for photographer automator actions, you'll find a lot of automater based solutions that the photography community has come up with.
its pretty powerful.
here's a link:
https://apple.stackexchange.com/questions/46614/adding-tags-to-files-in-os-x-how-to-use-where-are-tags-stored-and-will-they-w
deep in that first link is a link to this page, which has 7 file tagging applications for ya.
http://mac.appstorm.net/roundups/utilities-roundups/7-file-tagging-applications-for-os-x/
Answer: I bought AudioFinder for the meagre price of $70. It appears to do most of what SM does and is far far cheaper. I've found most useful and would happily recommend it.
Answer: I'll be honest I have this on my Mac but never really used it haha. Found it randomly thought I'd give it a try, it works. Now I just need figure out how to add metadata to my recordings.
http://www.sound-ideas.com/metadigger-free-metadata-management-software.html
Answer: I know a few people who use Itunes to organize their sound library - not quite sound miner but it's free.
Answer: @stephen: You can use wave agent from sound devices to add metadata.
http://www.sounddevices.com/products/waveagent/videos/

Free OSX Sound Database programs


How do I choose between ionization and photoelectric smoke alarms?

Question: I need to change my smoke detectors but I don't know how to choose between ionization and photoelectric smoke alarms. I guess that there are pros and cons to choose one or the other. Should I buy a combination detector that uses both methods?
Answer: One consideration is where it's going to be installed.
The issue being that some places are more likely to have them go off when they shouldn't.
Ionizing can be affected by steam, so has problems if installed right outside a bathroom.  They also don't work too well if mounted near moving air (forced air systems, ceiling fans, etc.)
Photoelectric are set off by lots of dust, so workshops, laundry rooms (lint) and the like are problem areas for them.
They both have problems in kitchens.
Where you can, you should use combination alarms, but you can also use a mix of types to achieve the same effect, while avoiding areas that might cause them to go off when they shouldn't.
Comment: Good points.  You don't want to keep getting false alarms because then people become inclined to disable them altogether.
Comment: i presently have the problem that my smoke alarm set off when i use my bathroom. It is positioned just outside the room. I thougth it was because of its high age but you've just pointed the real problem. Its probably a unit with an ionization detector that is too near my bathroom!
Answer: I just posted this on a different thread... but it is useful here also.
Ionization detectors are the most prevalent style installed in residences. This is largely due to a lower cost, but they aren't necessarily the best. They have more false positives (nuisance) alarms and are frequently removed or disabled, which does absolutely no good. We had a fatal cooking fire just last year because of this very phenomenon. Couple this with the fact that they take longer to alarm (up to 20+ minutes) in a smoldering fire, illustrates that you are better served by switching to either a dual sensor unit, or a photoelectric style for your home. Here is the text of an email I send out regularly on this subject.

Investigative news footage regarding different types of detectors - Report #1 and Report #2
Interesting program from a father of a fire victim from the OSU fire tragedy in 2003 -(The first several slide are heartbreaking)
The first 10-15 minutes of this presentation are very informative
Position paper from a State Fire prevention association (the Southwest Ohio Fire Safety Council) which recommends photoelectric detectors.

Do yourself a favor and install photoelectric, it may save your life.
Comment: Turned the URLs into links for you. Great information, thank you!
Answer: I would go for a combination detector, or install one of each type. Each method detects different things:
Optical detect smoke and are better as detecting smouldering fires while ionization detect heat and smaller smoke particles. Ionization are more prone to false alarms than Optical.
The Wikipedia article states:

the National Fire Protection Agency recommend installing what are called combination alarms, which are alarms that either detect both heat and smoke, or use both the ionization and photoelectric / optical processes.

Which is a sentiment I agree with.
Answer: I've recently completed research into this topic, in order to buy a set of alarms for my home. I chose Photoelectric detectors for a few reasons:

Ion detectors have a high false-positive rate, leading to disabled detectors. A look around my own home confirms this: the old detectors are all presently disabled due to a nuisance alarm at one point or another.
Combination units are also prone to the "nuisance" issue. If someone in the house is going to take out the battery, then the alarm is no longer useful, even if it would have been better at detecting a smoldering fire. Since it's disabled, it won't detect anything at all.
Ion detectors take 15 to 50 minutes longer to react to a smoldering, smoke-producing, fire, as compared with Photo detectors.

http://www.propertyevaluation.net/Photoelectric%20vs%20Ionization%20Smoke%20Alarms%20-%20Deadly%20Differences.html
http://www.startribune.com/local/yourvoices/146781575.html
Answer: There are two main types of smoke alarms; photoelectric activate when the light beam is broken, and ionization react to heat and dust. The ionization alarms will react to shower steam, so they shouldn't be used near bathrooms. Photoelectric should be used in areas that have steam, and ionization should be used in living rooms, bedrooms, kitchens, near air vents, etc. Some companies label smoke alarms for the appropriate location.


Is it possible to "hack" a MacBook so as to be able to install macOS Mojave?

Question: I know you can hack an iPhone, but is there a way to "hack" a Macbook? I have a late 2010 model that has been upgraded so it has the RAM, hard drive space etc... and it works beautifully, but I would really like to put Mojave on it. I am able to download the developer file, but then I got told by the iTunes Store for Mac that it is not compatible with this model.
Comment: There is a rich community that specializes in installing unsupported (newer) versions of macOS on older hardware.It often requires hacking the installer itself. That is not something that we generally do here.
Comment: First of all, if an iPhone is not compatible with an iOS version, there is no way to install that iOS version on that iPhone.
Comment: I know it sometimes maybe hard to let go but it maybe time to move on to a newer Mac :) MacBook 2010 is considered "obsolete" by Apple.
Comment: Firstly, welcome to Ask Different! :) I hope you come to find this site a valuable resource! If you don't mind me saying, while I understand your desire to install macOS Mojave, it **is** currently a beta product. If you have a MacBook that runs beautifully **and** you depend on it on a daily basis, you really don't want to be taking the risk at this stage. As @SteveChambers mentioned, there is a rich community that does specialise in this type of thing, so if it can be done then a workaround (or "hack") will be available at some point, but I'd recommend waiting for even that to be tested.
Answer: macOS Mojave requires Metal support. Apple is justified to prevent installation on older models because they literally do not have the capability to render the GUI.

Edit: A recent upvote has reminded me about this answer. I'm appending this section to say that an inability to run Mojave is not entirely the case. Mojave still has software rendering for Recovery Mode. AnyOS'll Do's answer is not entirely wrong, despite most of the answer being assumptive.
This answer links to a tool already in existence (that has been brought to my attention before, although I didn't think much of it) to enable installation of Mojave on unsupported Macs. The only catch is that hardware acceleration will be disabled, since hardware acceleration for old GPUs has been dropped.
Answer:
"That is until some genius on github decides to create an opengl wrapper that interrupts metal calls. My opinion is Apples doing to force hardware upgrades and propagate #MeTooGFXLibrary. They literally DO have the capability to render "dark" mode on anything they choose, they have the source code after all. Another opinion is dropping opengl/cl support has nothing to do with performance or stability or engineering effort and purely about is profit. Pure and simple greed explains*"

What you wrote here is a decent synopsis with the information you been reading by others in general as it's trendy and popular to hate everything Apple does without gathering any real research/evidence. You are missing very important details that dismiss almost everything you claimed as it was formulated by a collection of misinformation from people parroting unfounded conclusions based off of other parroters.

The older Macbook's are too old: This is actually completely correct, Apple has rewritten most/all of the GUI, The Quartz 3D Compositor and CoreAnimation in Metal (Basically the whole desktop is now accelerated by Metal and this will only grow in time). Currently older Macbooks with the Intel iGPU don't support the Metal API as they can't even use all the basic Metal API calls in release V1.0. Currently High Sierra does ship with both the old OpenGL Quartz compositor and the new Metal V2 Compositors.
You can instantly see what kind of mess they would be in if they kept both 3D API's around (incompatibilities across all the new advanced features, further upkeep of all the Frameworks that now have to be written twice for each API = Equals more bugs, greater power draw and less stability by means of hardware variation compliance).
Metal to OpenGL wrapper: First of all these components of OSX are not open source so this would never get anywhere and 2nd this is a terrible idea as you're taking an API that directly communicates to the GPU with custom written functions, then would be no possible way a high level API like OpenGL could pass that info directly onto the GPU (that's not how these older API's function). Also since no one is relying on OpenGL anymore it's going to fizzle and rot since Khronos works on the Vulkan API now, they are never going to advance OpenGL anymore, hence it's a bad decision to stay on that API.
"MeTooGFXLibrary" If you researched these low level API's you would find out that Apple's Metal API came around before Vulkan and D3D12. So in this instance "MeTooGFXLibrary" camp would refer to  both Vulkan and M$ D3D12 for playing "The Me too" card by following and copying Apple's new direction in 3D tech*. (In fact, Apple had the Metal API completed and released in devices to the public 1 whole year before Vulkan was even announced. By the time Vulkan was ready to release and be used in games, Apple had already rewrote most of the graphics layers in OSX with Metal acceleration being used in OSX Sierra.

*This blurb focused on the Personal Computer low level API race, in reality it was Sony with their "LibGCM" low level API, included in the PS3 dev kits which had almost all game developers shocked at how much more control, freedom and performance it delivered which made most everything else useless. This event here kick started the movement of this type of API to the Desktop world.

"DO have the capability to render "dark" mode on anything" Yep they certainly can, but this is not the main feature or the motivator.
"dropping opengl/cl support has nothing to do with performance or stability or engineering effort and purely about is profit."
By now I hope anyone reading this has comprehended that I already demonstrated multiple times on how dropping OpenGL will, without a doubt increase performance by a very large margin across all graphical frameworks, and at the very least hold onto their current stability profile.

Beyond the scope of this response to list the entire list of components that rely on Metal, Most people have came to a realization on just how big the upkeep of an API is and just how many other OS Frameworks rely on it to function. It's hooked into most everything you're interacting with, from drawing 2D animations, Anti-Aliasing fonts, drawing transparencies, accelerating video rendering, applying video effects, rendering shapes and layers, heavy mathematical calculations, video compression, allowing your web browser to accelerate rendering it's own canvas...
it's basically everywhere and to keep and use the weak performing/obsolete OpenGL around and manage a massive separate code base for an OpenGL equivalent of everything your OS is accelerating with no support for any of the advanced acceleration additions the keep getting added on the Metal side of things.
No user would rather weak performance and less features, then find out that most 3rd party programs they love and use start to refuse to include OpenGL acceleration due to economics, people stuck on that old hardware will have difficulty just getting around the internet and loading up google maps by that point...
Although I believe these decision were motivated by greed/dev lock-in:
Apple's deprecation of OpenCL and reluctance to adopt the Vulkan API.
Answer: A utility was created by some person called "dosdude1" that downloads a copy of Mojave's installer from apple (Sierra and HSierra versions available), burns the image to a usb thumb, and applies patches into it so that it's bootable on unsupported Macs. any Mac with a penryn CPU is compatible (SSE4.1). since yours is 2010 MacBook therefore it can run Mojave just fine. make sure that you properly read his documentation before attempting to do anything so that you don't waste time being in a cycle of confusion. As for metal rendering. if your Mac does not support metal (clearly). OpenGL still exists in Mojave and you can still use it to render everything through drivers that were possibly copied over from a High Sierra installation: https://www.youtube.com/watch?v=5uyYVCiYFuE
Catalina 10.15.x : http://dosdude1.com/catalina/
Mojave 10.14.x :   http://dosdude1.com/mojave/
H Sierra 10.13.6 : http://dosdude1.com/highsierra/
Sierra 10.12.6 :   http://dosdude1.com/sierrapatch.html/
Comment: There's a rich and active community over on the MacRumors forums dedicated to this topic. The conversation mostly revolves around the _dosdude1_ tool mentioned above. https://forums.macrumors.com/threads/macos-10-14-mojave-on-unsupported-macs-thread.2121473/
Answer: Parallels does exactly what I want. So I created a minimum host and now run everything in parallels vm. SSD makes it quick and the calls from metal to OPENGL! are performed by parallels directly. So it can be done and runs absolutely smooth with large gaming support.
Comment: Not convinced that running Mojave in a VM on a 2010 MacBook is a viable solution to the question. It's only got 2 cores on a Core 2 Duo.
Answer:
literally do not have the capability to render the GUI

"That is until some genius on github decides to create an opengl wrapper that interrupts metal calls. My opinion is Apples doing to force hardware upgrades and propagate #MeTooGFXLibrary. They literally DO have the capability to render "dark" mode on anything they choose, they have the source code after all. Another opinion is dropping opengl/cl support has nothing to do with performance or stability or engineering effort and purely about is profit. Pure and simple greed explains this decision."
I wrote the above at the time in disgust of the perpetual movement to deprecate hardware in this day and age that still has plenty of life left in it. I hope you can appreciate that ageing is a natural part of life, we don't deprecate that, do we?
It may then come as no surprise to some that a person like me could be passionate enough to care about not just my hardware, but the hardware of others. It's what I do, I am good at it. Also, the environment is really the biggest factor here if we must go down the rabbit hole.
Apple are the leaders of where I considered the direction of the operating system to go moving into the future. I am back peddling on this. I am an avid traveller of OS's and, if I were to hate on anything, then it would be the abominations that are Windows 8 through 10.
This need for all operating systems to look samey same (I am looking at you ubuntu) is just off-putting. As for my personal opinion piece above? Pure anecdotal, I own a MBP2011 and can not afford a new one at this time, so there's that. I am turning away from Apple once support for high sierra drops and will go the route of a *nix flavour of the month I wish to try. Staying at the forefront is always the best option for me, rather than to stagnate on an os on this device. I have been burnt by Apples ios 32bit to 64bit deprecation which removed +70% of my "paid"(i.e. not freemium crap) gaming library, because I am the sucker who likes to own things and stay updated, can't go back when one adopts too early.
To answer you about trends? I make my own, thank you. I am smart enough and ugly enough to not be herded by your mentality on such matters. I admit I jumped the gun, but I have a passionate reason to, anecdotally. My opinion may coincide with others, but I am sure the devs of MAME and WINE were under fire from all hurdle turtles jumping up and down all donkey kong like when they were trying to stand on the shoulders of the platforms they were opening up for others at the very beginning. So, yeah, I think your absurdity of running higher cpu/gpu cycles is a challenge to get around, not a spike in the ride to die from.
Comment: I've edited the insults out of this. We welcome criticism and sourced opinions. Can someone put up any reference of open source additions to back port any graphics code going back to the original Mac? Clearly with enough money, anyone can make code run if speed is no issue. Whether it's efficient enough to render one frame per second is the real question.
Comment: More importantly, this is a comment on another answer and not a question. Unless this gets edited to directly answer the question it might need to move to a chat room or be removed. In the interest of fostering a better answer that's politely critical, let's see if this can get beefed up with some concrete examples or citations so the opinions here can be evaluated and voted upon.
Comment: There is no "genius on github" as of now. I understand this is possible, but right now nobody has done it yet.


What are the famous debates in canonical Buddhist texts?

Question: Debate plays an important part of Buddhism. What are famous debate encounters by the Buddha and also by other Buddhist masters like Dharmakīrti, especially with Hindus(exponents of Brahmavāda-Ātmavāda) and Jains?
Comment: Edited your title so that the question can be understood when it appears on the right-hand column.
Answer: A really good look at the sort of debates Buddhists got into is in the Kathaavatthu - translated into English as "Points of Controversy". This is a later text, but outlines the many controversies and associated arguments. Examples of good debates in the suttas are MN 56 and DN 23.
As you say, debate plays an important part in the teaching, so the debates are really too numerous to list. I don't have any information on Dharmakirti though.
Comment: Thanks for your answer. Where could I find an English translation of MN 56 and DN 23? I found an English transliteration though internet search. And Dharmakiriti is a Mahayana master who I've read was involved in a debate with Kumarilla Bhatta of Purva Mimamsa school of Hinduism.


How to interpret the effect of different windows in short time fourier transform?

Question: There are many categories of windows, e.g., rectangular, Gaussian, and triangular. What are their effects on STFT?
Comment: Also have a look [here](https://dsp.stackexchange.com/a/20535/8202).
Answer: A window $w[n]$ truncates and weights (tapers) an input signal $x[n]$, to produce $v[n] = x[n]. w[n]$., for subsequent spectral analysis of $x[n]$. A windows's effect on the input signal's true spectrum $X(e^{j\omega})$ is described by a convolution of $X(e^{j\omega})$ with $W(e^{j\omega})$ (window's Fourier transform);
$$V(e^{j\omega}) = \frac{1}{2\pi} \int_{-\pi}^{\pi} W(e^{j\theta})X(e^{j (\omega -\theta)}) d\theta $$
due to this convolution, two main effects are observed:
1 - smoothing (smearing) of $X(e^{j\omega})$ due to the main lobe width of $W(e^{j\omega})$,  which results in a loss of spectral resolution.
2- spectral leakage due to peak side lobe of $W(e^{j\omega})$, which results in a loss of weak components shadowed by nearby stronger ones.
Main lobe width of any window type is primarily determined by its length. Increasing the length of any window will therefore decrease its main lobe width (hence increase its spectral resolution capability)
A rectangular window has the narrowest main lobe width and the highest peak side lobe, compared to all other windows. And the remaining window types perform a tradeoff between mainlobe width and the peak side lobes.
Peak side lobe is primarily determined by windows's shape. So by changing the shape (type) of the window you adjust its leakage amount.
Answer: The rectangular window is just what, when we have truncated the data, while the
other windows provide some data weighting. From their effects on the frequency
spectra,
The advantage of using a window other than rectangular is to have
lower sidelobes.
However, the disadvantage is a loss in frequency resolution, from
$\Delta \omega = 4\pi / N$ for the rectangular window to $\Delta \omega = 8\pi / N$ and $16\pi / N$ for Gaussian and
Triangular windows respectively.
Answer: In addition to what's already been said, using a rectangular window also results in the minumum possible noise floor, which is desirable in some applications.
With regard to obtaining the best amplitude/magnitudes estimates, you should consider using some of the flat top windows, which are designed specifically for this purpose. However, they have a wide main lobe, and thus poor frequency resolution, so they're not suitable for signals where you have sinusoids that are close in frequency.
Anyway, see here http://zone.ni.com/reference/en-XX/help/371361H-01/lvanlsconcepts/char_smoothing_windows/ or here https://en.wikipedia.org/wiki/Window_function if you interested in the theory.
Answer: [EDIT 2017-11-10: added details one the used of inverses] Their first effect, in the time domain, is to localize, or (weakly) stationarize the data, as a preprocessing before applying the FFT.
Then in the analysis side, their frequency effect is the same as when used for an FFT, ad detailed on other answers.
Last, in  the synthesis side, a different window can be used when  recovering a signal from a selection of chunks in the time-frequency domain.
This is used  in practice, for instance in image compression. One wavelet/window type is used for the analysis or image decomposition, better at compacting information. Then, this information is quantized, and another wavelet/window is used for decompression: it is smoother, and attenuate, visually, quantization artifacts. Here, the whole transform is not redundant, and this is called biorothogonality.
In the redundant setting, certain analysis windows admit a closed-form inverse with the same window, but this is not always the case, as you c an see from the following picture given in Duality for Frames, 2016, with the analysis window on the left, and the synthesis one on the right.
Comment: Isn't using a different window for the synthesis phase undesirable because you're more likely to introduce certain digital artifacts that were not present in the original signal?
Comment: Tough comment for a simple answer. Since the  STFT is redundant, it may admit several inverses. So if you don't change STFT coefficients, those other inverses are just perfect. So you can [design other inverses](https://arxiv.org/abs/0907.3654), that are more optimal in some sense. Those could be useful, for given purposes, but not use for direct inverses. However, when doing processing in the STFT domain, you may want reconstructed data more precise in time, or in frequency, for detection purposes
Comment: Now that you brought this up and since I'm doing some audio manipulations in the frequency domain (which sometimes/often sound bad when inverted back), I think I might give this idea a try.
Comment: The article you linked to looks very theoretical and I suppose it may be useful in certain situations (though I don't pretend to even understand what it involves :)
Answer: Important appendum to Fat32's answer: the standard formulation of STFT,
$$
\text{STFT}_x(\tau, \omega) = \int_{-\infty}^{\infty} x(t) w(t - \tau) e^{-j\omega t} dt
$$
which is what most libraries (including scipy and librosa, I've not checked MATLAB) implement, is not described by $V$. This variant lacks some important properties of time-frequency transforms, e.g. one-integral inverse and zero phase (even if window is zero phase), making it ill-suited for many kinds of operations on complex values - though the modulus (spectrogram) is unaffected.
The better variant, implemented in ssqueezepy, writes
$$
\text{STFT}_x^\text{mod}(\tau, \omega) = \int_{-\infty}^{\infty} x(t) w(t - \tau) e^{-j\omega (t - \tau)} dt
$$
which is described by $V$. n_fft is then a sampling of $V$, assuming hop_size=1. If hop_size > 1, then $V$'s integral must account for aliasing, though I don't think the measure remains useful, except indirectly.


What is a good age to introduce children to a martial art?

Question: I have seen different recommendations for different styles as to what age to introduce a martial art to a child, sometimes as young as 4 years old.  Factors such as attention span and interest of the child definitely affect the individual.  What are the right criteria to measure age appropriateness for a child?
Comment: There is a really good [Parenting.SE answer](http://parenting.stackexchange.com/questions/1425/what-age-is-it-appropriate-to-start-martial-arts) about this.
Comment: Please consider accepting an answer for your question, or rephrasing your question if you feel the answers don't fit your need.
Answer: For myself, the main criteria is not to do damage to the child's growth.
Repeated strains on joints (wrist locks for example) and repeated impacts can have negative effects much later in life. Some aikido dojo will have a syllabus for under 18s, other will just refuse to train anyone under the age of 18. What adults do is not necessarily what a child should do. Having a junior syllabus is a good indication that someone has thought about that.
Psychologically, some children are much more mature than others at the same age.  But all do need good teachers to get discipline and a healthy states of mind in which to approach martial arts -- including western ones like fencing. Competition should be about learning to grow and not crushing your enemies and hearing the lamentation of their women.
In my not so humble opinion, the right criteria is "What will lead to the best development of the child, both mentally and physically, without causing harm?".  The answer to that, will vary between child, parents, teachers and the law of your country.
Some McDojos will be teaching badly and those should be avoided at all costs.
Comment: I agree with all of Sardathrion's points, and I would concur with Patricia that focus AND interest are key.  My son joined my Kung Fu school and had interest for about 9 months, then it waned.  He liked the idea of learning but didn't get into it as much as I did, although he had fun I eventually let him out of his commitment until he is a bit older.  I also spent time looking for a school, and joining, for a year before signing up my son to be sure it was a good environment for him.
Answer: Sardathrion  made some excellent points!
I just wanted to add:  every child is different,  we have had kids as young as 4 in our jiu jitsu program, and some kids as old as 6 or 7 that couldn't handle the class.  Of course we don't teach the small children any joint locks!
Our main criteria for determining if a child is old enough to participate in the class is their ability to pay attention during demonstrations, and to focus on the practice.
Even if the kids are having a hard time with the move, as long as they are not disrupting the class for the other students, or taking up all of the instructors time because they weren't paying attention and now need 1 on 1 attention for a long portion of time, they are welcome in our class.
Answer: This is really a broad question (there are many kind of martial arts).
Speaking of karate, I wouldn't reccommend training to anyone under 9, and even then the training should avoid fight (kumite). It should cover kihon and kata only.
They lack the maturity to understand what they are learning and the consequences of their acts; they usually want to play; they do not control their strength and may easily injure other or themself.
However, it is always up to the teacher to adapt the lesson to the audience.
Comment: Could you say *why* you would not recommend it?
Comment: Done, I edited my answer.
Answer: I'm a co-instructor for classes of younger kids (under 8's) and juniors (8 to 14).
With very little ones (4 to 6 year olds) it's just about safe fun, developing confidence, concentration and improving co-ordination.  I find it does not matter what you do, as long as they are enjoying it.
Along with plenty of games (sumo, wrestling, running, "sock war" etc), we also show them some of the basic rolls and falls was well as throws and sweeps (it goes without saying, nothing that goes anywhere near a joint lock!)
It teaches the child empathy.  (Example, outside "arm twist" - kote gyaku) - the fact the arm gets torqued and moves uke, means that tori has to empathise with uke and help her fall without hurting her.  This can be an important learning point for young kids.
Up to about 8, I don't personally think it should be too serious. Kids are very fickle.  As long as they are doing something active (my daughter does dancing and my son rugby, as well as martial arts) then I'm not too fussed.  From around 10 then they should have developed enough concentration and discipline to be taught properly (safely).
Answer: Back in England at my first Judo club we had a very active pre-junior (under eleven) class. The basic criteria for continuing in the class was interest, attention span and not being disruptive. We had kids as young as five, but most were seven to eleven. Having helped in the teaching of that class, I can tell you it was great fun and the kids that kept coming back seemed to have lots of fun as well.
In British Judo organisations, under sixteens do not get taught or permitted to use armlocks or strangles. This combined with all activity on nice foam mats, kept everything pretty safe from an injury perspective. If there was a Judo club near me, I'd have my daughters enrolled in it.
Answer: My local tae-kwondo club has an excellent juniors program. I started my two eldest at 3 and 5

At that age, the patterns and circuit training, as well as the discipline, are really good for them, teaching core strength, fitness and respect
They would also start and end each session with some games, which helped them enjoy it
From the age of 4 the competed, both in patterns and sparring (which in TKD is very controlled - 90 second bouts, body armour etc) so got used to the competition aspect

Now 6 years on my eldest is almost at black belt, and my daughter is only 2 belts behind him, they have a wide collection of medals and trophies and despite currently spending more time in swimming competitions, they love the core strength, speed and discipline TKD gives them so they don't want to give it up.
Some of that is definitely down to the instructor - a good one will handle the youngsters as well as the transition to older classes well, whereas one who doesn't have the connection with the children may find they leave after a while - but also the way almost all martial arts give the individual a way to measure their own improvement. That challenge keeps them progressing and interested.
Comment: (side topic - my daughter, at 4 years old, on the podium winning a gold after beating all the boys in a county competition, had the **biggest** grin I have ever seen. Kids love competition.)
Answer: My club starts as young as four.  Again, the overriding characteristic is the ability to listen to instructions and then carry them out.  My club has a lot of primary school aged children, from prep (aged 5) and up.  Most all of them do just fine.  There are a few kids that are a little young for the age (if that makes sense) and they struggle and everyone else struggles because of it unfortunately. But hey, we're a family so we help the poor guy out (ADHD).
My daughter started just after she turned 6, mid way through prep, and she performed excellently. She's now nearly 8 and still going strong.


Dual sound output on XP

Question: My computer is equipped with two sound cards, the integrated one on the motherboard, as well as a Soundblaster Live I installed myself. The Soundblaster has a special front panel with midi ports, and a volume control for the output. For some reason unbeknownst to me, the analog output on the back panel of the Soundblaster is only sending left side sound, so what I want to do is send sound from both the integrated card and the Soundblaster, so I can have my headphones plugged in the front of the Soundblaster, and my loudspeakers plugged in the integrated card in the back. Unfortunately, Windows only seems to have support for one sound output device at a time, so I was wondering if there was any other way of doing it.
Comment: have you tried fixing the root problem -- that the SBL rear output is only sending left-side audio?  have you checked whether other rear ports (if any) are set to send right-side audio?  i wonder if you don't have a setting somewhere that is set to one-channel-per-port.
Answer: The problem with onboard audio is that it doesn't always play well with dedicated sound cards. I would recommend that you turn off your onboard sound device in the bios and get some hardware that connects to the soundblaster card to drive both the speakers and your headphones. Many PC speaker systems, like the logitech X-240 -link below #1-, have a little satellite device that sits on your desk. It usually has both volume control for the speakers and a headphone jack.
If you really want to use your current speaker system, you can get a little "Speaker/Headset Switching Hub" -link below #2-. These devices plug directly into your sound card and then run the sound for your speakers. The only down side is that most of them only support 2.1 sound, not surround sound.
A third option would be to get a USB headset. The downside of this option is that you have to change sound hardware settings when you want to use your headphones. I have friends who use this option and it seems to work well.
If you want to use your front panel audio ports, I would look and see if your soundblaster card has audio headers. Look for "Intel HD Audio Compatible Front Panel Header" in the specs. I don't think the cheaper ones have it and the more expensive ones sometimes come with something you put in the drive bay. I think all the X-Fi cards have it.
Keep in mind that you could have some faulty hardware somewhere if you only get sound out of one channel. I would try testing out each port with a known good set of headphones and see what kind of audio signal you get. If you have surround sound, you may be plugging into a rear channel by accident.
Hope that helps

Links (New users can't post multiple links)
#1: Go to logitech's webpage and go to the speaker+audio section. If you look under speaker subheading, the X-240's are at the bottom.
#2: Go to amazon and search for "Manhattan-Speaker-Headset-Switching-Hub" it's the only result at $9.99 .
Comment: you can always comment to your own answer and post links there.  welcome to superuser!
Answer: Only thing I know of that might do this is Pulseaudio.

Support for more than one sink/source

Sink being output.  It's not in version 1 yet so caveat hacker.

Dual sound output on XP


Why do most exchanges still have not implemented segwit bc1 addresses to save block space?

Question: Segwit bech32 bc1 addresses has been out for a good 2 years. Why do most exchanges still refuse to implement such a feature for its users? Exchanges create a bulk of the bitcoin transactions and also can promote the use of segwit bc1 addresses. What are some technical pitfalls to why big exchanges have not implemented this feature?
Comment: The obvious answer is 'cost-benefit ratio', beyond that it is a matter of speculation. Anyways, there are exchanges that have implemented bech32 addresses, so as a user if you expect fees to rise in the future you would be prudent to use one of those exchanges.
Comment: Which exchanges has implemented bech32 addresses?
Answer: The primary reason is the lack of incentives to actually migrate their entire system. Lower transaction fees is the most direct benefit that SegWit provides. I'm not discounting the other myriad benefits that SegWit brings to the table, but for exchanges this is the most rational one. Below is a chart that shows the average transaction fees used by all the pending transactions in the mempool.

As can be seen, the transaction fees isn't that high for the exchanges to get the transactions confirmed. This is because the mempool congestion isn't high enough. Below chart shows the mempool size (aggregate size of the transactions waiting to be confirmed).

The small decrease in transaction fees that can be achieved with the help of SegWit doesn't justify the monetary or time costs required to upgrade all wallets to the new standard. Replacing legacy addresses and migrating them to Segwit is a very cumbersome process for exchanges. For centralized exchanges, the largest cost cutting come from batching (aggregating many outputs into a single transaction) which they do when sending bitcoins from individual account's address to the centralized addresses. This underscores the exchange's decision of not moving to SegWit since the fees for getting transactions are already low. In future, if we see mempool congestion like we saw in latter half of 2017, we are most likely to see migration to native SegWit addresses.
Comment: With your answer in mind, one might think that a prudent exchange operator would upgrade their code now, in order to be prepared for times of high fees in the future.
Comment: @chytrik Fees has been low for almost better part of the last 16 months. Exchanges want to use their resources to list more trading pairs and list new ICOs/IEOs. After doing that if they have resources left then they will improve their programmatic trading via APIs. Given that since these two are the most important drivers of their revenue today, I wouldn't blame them for pushing out SegWit.


How to modulate very smoothly and stealthily from major to minor?

Question: I would like to modulate from G major to c minor in such a way that it would be almost unnoticeable to the listener. I'm composing a piece in a style that's very Arvo-Pärtesque minimalist-sounding, so that does limit the chromatic/enharmonic options. The main difficulty seems to be that it's very hard to introduce the E flat without it sounding ever so slightly jarring. The other way round (going stealthily from minor to major) is much easier, for some reason.
Comment: @Tim it may be the somewhat misleading title. I thought it was about a mode change major I to minor i - of course not a modulation - but it's really about modulating to minor iv.
Comment: I'd be intrigued to find out why this question has attracted 1000 views. It's a great question, but so prolific!
Comment: @Tim My impression is that this question—and it's a good question!—involves a few buzzwords that attract the everyday musician. I know I've heard several self-learned guitarists and composers talk about making modulations that are "smooth" and "stealth" without disrupting the musical surface too much; perhaps this is why the question is so popular? (Again, I'm not denigrating the question at all; it's a good quesiton, and I'm glad it's here!)
Comment: Does this answer your question? [How many types of modulation are there?](https://music.stackexchange.com/questions/27079/how-many-types-of-modulation-are-there)
Comment: @Tim I've been wondering about that as well. It's not like there's a shortage of "How to modulate from X to Y?" questions on this stack.
Comment: @MichaelCurtis Modulating to minor iv is just an example that came up in my own composing. My whole beef with change of mode from major to minor (whether or not it also involves a change of key note) is that it seems hard to do in a stylistically convincing way, especially in a more "white keys" kind of environment, where chromatic/enharmonic chords would be out of place.
Comment: Just want to point out that the minor iv chord is already a chord that sound natural in a major key, as it is very often borrowed from the parallel minor, and can give the the IV chord dominant function. In fact, I'd argue the more difficult part of a key change in those circumstances is to make it where the ear doesn't want to fall back to the G as tonic. You'll need to get that Ab or Bb in there fairly quickly after modulating.
Comment: @Tim it's on the HNQ list.
Answer: Eb is certainly a foreigner in G major.  To help the ear not to be surprised by it, you could use D# a couple of times as a chromatic passing note from D to E (D > D# > E) in preceding melody. This could be part of an innocuous harmonic progression like I-IV. You could then write a melodic fragment D -> Eb -> G, introducing C minor around G. You could tonicise it then and there, or later.
Mozart was a master of musical puns like this.  See how crafty he was in the 24th Piano Concerto:
Comment: Listen to the image: https://youtu.be/2XlLpZ4erlw?t=447
Comment: Thanks for this excellent answer. I think I could jiggle it in as a chromatic passing note. Mozart rocks!
Answer: Within a minimalist sort of setting, one approach I might take would be to boil things down to just the root or root and fifth.  If you have a long enough period of time where you don't have a third in the mix, your ear won't be glued to a given tonality and introducing the minor flavor into the mix shouldn't sound as abrupt.  You can also start adding in the b7 of the original key before hitting the Eb.  Since there is a major mode that has a b7 (Mixolydian), that is the only note that is present in the minor modes that is common with any major modes.
I'm not familiar with Arvo-Pärtesque to be able to say whether or not this approach would be great in that context or not.
Comment: That sounds like the most convincing way (stylistically speaking) I've read here so far. Just fade out the thirds for a while (or treat them like dissonances as it were) and then gradually bring them back in. Definitely going to try that. Thanks!
Comment: No problem! I definitely don't write minimalist music or have a lot of experience there but that makes the most sense to me
Comment: If you're still interested, I've posted a (partial) answer to my own question. It will probably end up at the bottom, and possibly attract its share of criticism, my "modulation" being more a juxtaposition of keys. Whatever. It fits my style, and I'm happy with it.
Answer: I would recommend, as a general approach, looking at Max Reger's Modulation.  C min is relative to Eb Maj, a cadence from GMaj to Eb Maj could be modified to move to C min in a fairly straight forward manner.
Answer: A modulation from G major to C minor would be a modulation to the subdominant.
The most straight forward way to to the subdominant is the lower the leading tone and apply it to the tonic chord. In G major, change the F sharp to F natural and add it to the tonic G chord. So the tonic I chord in G major will become the dominant V7 in C (major or minor.)
The interesting part is your concern about the tone E flat and the possibility it could be jarring.
The vii°7 in G major is F#,A,C,Eb so you could use that to move into G and introduce the E flat. Something like G: vii°7 I Cm: V4/2 i6/3.
Another possibility is to go to the major IV first then just lower the third to make it minor iv. If that is combined with the G7 you will get a nice chromatic descent F,E,Eb plus both work with the notion of altering tones by lowering them.

EDIT
Forgot to load an image yesterday. I added a third example trying out two converging chromatic lines.
Answer: Using the notes that make up Bo works well. Diminished harmonies are often used to move out of one diatonic place to another.
Answer: G major is the dominant chord of C harmonic minor, so I don't think you actually need to do anything special to go from one to the other. G already moves in to Cm easily. Try a progression like G, Am, D7, G, Cm, Fm, G, Cm, for example. (You could of course drop the harmonic minor after the switch, so the 2nd half of that example could as well be e.g. Cm, Fm, Gm, Cm.)
Other, shorter examples, with 3-note voicings:

D7, G, Cm

Am7, G, Cm

G, G7, Cm (also G, Bdim, Cm)

G, C, Cm (a little different)

Some of those work fine, even with just 2-note voicings.
Emphasizing the leading tone resolution (B in to C) somehow can also help make the G, Cm change sound more deliberate.
Comment: I think it just depends on how minimalist they are going for.  Extreme minimalism may not even really have chord progressions.  Ultimately, I'd argue that the answer you've supplied makes sense for a modulation but doesn't seem to satisfy what the OP is asking for, particularly that they are stating that the inclusion of the Eb in the C minor chord feels abrupt.  It's true that G is the dominant in C minor and that it acts as a good pivot chord but ultimately that doesn't help the fact that the modulation to minor is jarring.
Comment: I think the issue here is that the OP is trying to accomplish this in a minimalist setting, so a whole bunch of chord changes isn't likely to help.
Comment: @Basstickler There's no reason they can't use fewer chords than my example. `G, Cm` is the only necessary part, or something like `D, G, Cm` if they want to spend more time setting it up.
Comment: @Basstickler I don't think there's any reason these progressions can't be used in a minimalist composition. [Here's `G, G7, Cm` with two-note voicings, for example](https://onlinesequencer.net/973040). I'm honestly not really understanding your criticism here. Do you think I should try to explain how I would go about voicing these chords?
Comment: I don't think that your answer is wrong in general or that it's impossible to accomplish in a minimalist setting, just that it doesn't seem to address what the OP is talking about with the addition of the Eb sounding abrupt.
Comment: I don't agree that this doesn't address the problem with the Eb. I'd recommend trying some of my examples.
Comment: Fair enough, we can agree to disagree.  I'm just pointing out that nothing specific about your answer seems to address that issue.
Answer: Modulations should make use of pivot chords to make the modulation smooth.
A pivot chord(s) put simply is chords that fit in both the key you are modulating towards and the key you are coming from.
so for instance, if you have a 4 bar phrase in C Major. Let say your phrase ends on an interrupted cadence. Now that six-chord of C major is an a minor chord, this is conveniently also the tonic chord of a minor. Both these chords are a suitable resolution to your cadence.
Now we are in the second chord of your second four bar phrase now you can go to the d minor chord that is again both C:ii and a:iv this is the second pivot chord you can use.
Then finally we would just have an E Major chord with a raised g# tha resolves correctly to now make it clear that we are in a minor. There is nothing that makes modulations as clear as Leading Tones resolving towards a Tonic.
Some modulations lend themselves more towards the use of pivot chords than others but the modulation to the relative minor is an especially easy one to use them with.
Comment: All very well and fancy. But OP wants to get to **C MINOR**.
Answer: The progression I I7 IV iv is quite common.  If you were to establish that as a pattern in G major, but gradually shift the rythmic emphasis away from the I and IV and toward the I7 and iv, then those two chords could come to be perceived as the V7 and i of C minor, without there necessarily having been any clear point where the piece switched key.
Answer: In case anyone's interested: I've solved, to my own satisfaction, the change of mode part of my question, in a rather unexpected way, by transitioning first to F sharp Aeolian. Of course, I'm still way off C minor, but modulating through minor-like modes and keys makes it easier (I hope). I think the main lesson here is that key transition doesn't necessarily involve advanced "chord magic" (although it can). Stylistically speaking, it's more about setting up proper expectations and then refuting those in a convincing way than anything else.
The repeat bars all involve two repetitions instead of the usual one, by the way. The key of G major had been very firmly established beforehand. I want to end with a modulation from C minor back to D minor (hence the key signature), followed of course by a protracted cadence in that key.

Follow-up question (to all you harpists out there): is the stuff I wrote for the harp at all playable, assuming a reasonably competent harpist? (The tempo is very slow, like 45 BPM.)
Comment: Have you looked at my answer?  The repeating sequence G G7 C Cm, with rhythmic emphasis on the G and C, will suggest a G major tone center, but if the rhythmic emphasis is shifted to G7 and Cm, it will suggest a C minor tone center.  If the shift in emphasis is gradual, there may not be any point the listener can identify as a key change.


Is there a difference in the pronuciation of a single vowel or multiple vowels in a row?

Question: There are several phrases, most of which are easily distinguished by context, that have very similar, if not the exact same pronunciation.  The distinction I'm curious about is a single vowel in a word such as "le" or the double vowel in "lee" for example.  Another example would be ¿Qué vas a ser? and ¿Qué vas a hacer? with the single 'a' in the first example and the 'a ha' in the second.  I know in some dialects the 's' in ser and the 'c' in hace would be different, but I'd like to know specifically if there is a difference in the vowels.  Do you draw out the sound a little longer if there is more than one of the same vowel?
Answer: When 2 vowels appear in a row in he same word they belong to different syllables (there's an hiatus on them). So you would pronounce a longer sound but you have to take into account that you should make the stress in the stressed syllable of the word.
For example

"Le" vs "Lee"

Le: one syllable
Lee: 2 syllables (le-e)

In this case "Le" has only one syllable but "lee" has 2. So you have to make the 2 syllables in "lee" stressing the "le" syllable. So the sound will likely sound as a longer "e" sound which starts stressed but finished unstressed.

"Cree" vs "Creé"

Cree (present of verb "creer"): 2 syllables (cre-e)
Creé (past of verb "crear"): 2 syllables (cre-é)

In this case both words have 2 syllables but the stressed one changes. So in "cree" the long "e" sound starts stressed and finishes unstressed but in "creé" it's in the opposite way (starts unstressed but finishes stressed).
The same happens when you have 2 words in a row and one finished with the same vowel sound as the next one. For example the one you give in your question:

a hacer (a ha-cer)

In this case the sound of "a" is linked and you'd usually pronounced them without any pause between them and as both are stressed the sound is the same as "a" sound just a bit longer. When there's no change in stress between the syllables the sound is not as long as when you have to stress one of them.
Answer: Is there a difference in the pronuciation of a single vowel or multiple vowels in a row?
Sí.
Do you draw out the sound a little longer if there is more than one of the same vowel?
Sí, exactamente. Esa es la manera oficial de pronunciarlas. En "lee", pronuncias un sonido "e" de doble duración, y en "a hacer", pronuncias una "a" de doble duración. En este segundo caso, si además estás separando las palabras (porque, por ejemplo, estés contándolas en voz alta), pronunciarás dos sonidos "a" separados. En un ámbito coloquial, o cuando hablas deprisa, o cuando no hay peligro de confusión, o cuando habla alguien que no cuida mucho su pronunciación, puedes perfectamente pronunciarlas u oírlas con duración simple (de una sola vocal).
En general, no hay problema, porque suelen ser únicas las palabras que cuadran con los sonidos pronunciados. Pero en casos como [boialabar], si no hay contexto, puede no quedar claro si estamos diciendo "voy a lavar" o "voy a alabar". Lo habitual es pronunciar [boialabar] o [boi a labar] si estamos queriendo decir "voy a lavar" y [boiaalabar] o [boi a alabar] si estamos queriendo decir "voy a alabar".


Should I add more detail to my story, or just leave it vague and add it all in later?

Question: I am having a hard time with adding detail, I feel it may leave a good chunk of the story out, but I don't know for sure if I should really add it or not. If I do end up with too much detail, my readers can get easily bored and not want to read anymore of my story.
Comment: What type of detail are we talking about? Description of characters, settings, anything? You mention leaving "a good chunk of the story out" which has me thinking about subplot (which, I suppose, can be seen as detail too).
Comment: If you feel like you need details, put them in (you can always strip them later). If you feel like they slow down the pace of your story, omit them (you can always add them later). Plow through your first draft any way you see fit to finish it, then run your story by a circle of readers you trust and listen to what they say.
Comment: what do you mean by "add it in later"? In a later draft?
Answer: It's a very strange question. You're effectively asking if the coffee needs more sugar before anybody has tasted it. And even if we had tasted said coffee we all take varying amounts of sugar.
Personally, I insist any detail be relevant. If you're telling me Brian wore brown shoes I'd need to know why you felt I needed that information. If the killer is revealed as wearing brown shoes then the detail is relevant.
My personal mantra is "Never stop a story to insert a description."
Any statement including a description must also serve other functions.
e.g. "Ever since her divorce Amy had little more than lounge around the house in her old, grey sweatpants."
Answer: There is a huge difference between plot and story. A plot is a sequence of events that happened for a reason. A plot requires only technical detail.
A story is an experience. It is the observation of or an entry into the live of, a particular person in a particularly place and time, who is experiencing the events of the plot.
A plot can be received on a purely intellectual level. Who was the murderer? It was the man with the brown shoes.
A story is received viscerally. It is received by the same set of senses that real life is received by (thought through a different sensory input, obviously). We remember its scenes, not merely (or not only) its words. Thus we have a memory of Rivendell or the Shire or Mordor in our heads that is a visual and auditory and olfactory memory, as if we had actually visited these places. (Peter Jackson obviously received a very different memory of these places than I did!)
Creating a story as a visceral experience obviously requires more detail than the simple recounting of a plot. On the other hand, it does not require that you relate every detail that goes into the reader's visceral experience and ends up in their sense memory of the event. Rather, you rely on what is called the "telling detail", the few scraps of imagery that irresistibly pull a much more complete picture into the reader's head.
This when Prospero says:

The cloud-capp'd towers, the gorgeous palaces,
  The solemn temples

We get a picture in our heads that is much more complex, full of many more details, than anything that is explicit in the scene. "cloud-capp'd" is the telling detail that evokes an image in the mind that pulls all the rest in with it.
This is whe whole art of detail, to find the telling detail that pulls a whole world of detail in its wake.
If you find that you are leaving out most of the detail, it may well be that on first draft you are really just relating the plot. That may work as a writing technique, but on second draft, you are going to have to tell the story, and that is going to require more than just filling in some more details. Creating an experience for the reader is very much about selection of scenes and about emphasis. It is about when to illustrate in detail and when to bridge. But it is also, certainly, about the telling details that transform the reception of words into the reception of images.
The right selection of scenes and the use of telling detail will never be boring to the reader because it is immersing them in the experience. Some experience will require more details than other to create. Don't worry, therefore, whether you have too much detail. Worry about whether you have the telling details. And when you find the telling details, relate those, and then let them do their work of pulling in the rest of the scene. Don't go on with additional detail that may only interfere with the image that the reader is forming based on the telling detail.
Answer: Add details like they cost money.
That being said..
During the race to build the first US transcontinental railroad, both sides operated with the mantra, "Build it first. We'll fix it later." Maybe you should try doing exactly that?
While you're first-drafting, let your story spill out. Just get it down. Later, when you're second-drafting, you'll have the scaffolding in place and a clearer vision. The question of whether to add more detail will likely answer itself under the brighter light.
Something else to consider: Adding content vs deleting and/or reorganizing it. For example..

Delete three paragraphs for every one you add
Try moving things around..
Do you need those adverbs?
Target weak sentences loaded down with "be verbs" and rewrite them using their stronger counterparts, "action verbs".

There's a fair amount of discussion on that last thought.
I agree with your observation that too much detail can bore the reader and push them away. So harness this strength of your writing style—write it first, then fix it later.
Comment: Okay, I'll do that, I just wanted to make sure that I wasn't doing it wrong.
Answer: You're right to be concerned, because there is a fine line between "too much detail" and not enough. Either way, you stand to lose at least part of your audience.
To avoid this, it's helpful to get feedback from your audience. Show your work (or part of it) to five or ten friends and get their reactions. It has been shown that "crowd wisdom" is quite reliable, even though individuals might be far off.
One caveat, and that is that even in the modern day United States, different groups of people may react differently. For instance, the so-called Silent generation (born before World War II) liked lots of detail, while Gen-Xers "cut to the chase" and don't want a story "spoiled" by too many details that they can figure out themselves.
Finally, when you have enough "experience," you may become your own best judge. Many people know that a certain Supreme Court justice said, "I know pornography when I see it." Few know the preceding remarks which went something like this:
"Pornography is something that would be offensive to a man of average sensuality (un homme moyen sensual). I am such a man. Therefore I know it when I see it."
Comment: Oh, that makes sense. Thank you for the input.


investors hold efficient portfolios because generally they are risk averse

Question: I'm trying to find a concept on this question,in my understanding investors differ on risk preference,the question said investors hold efficient portfolios because they are generally risk averse? agree or disagree with some explanation..
Answer: By definition, an efficient portfolio is one that is "best in its (risk) class." That's the main rationale for holding it.
There are some efficient portfolios for risk averse investors (low risk, accompanied by relatively low return), and others for risk loving investors (high risk, highest return). But in either case, they are (by definition) the highest return portfolios available for their risk levels.


One way ticket to India

Question: My son is a US citizen and is travelling to India from USA on a one way ticket. He has a valid visa(entry visa, type X). Please let me know if anybody sees any concerns with this journey with respect to boarding a direct flight and entry into India. Also, if there is anything to keep in mind while performing this journey. Thank you.
Comment: Timatic doesn't note a requirement that I can see to have return travel booked for entry to India even for Americans traveling on tourist visa. I can't imagine they would complain about that for someone in possession of a long-stay visa.
Comment: Be aware that one-way flights are sometimes _very_ expensive - I have seen many cases where they cost _more_ than a round trip ticket. That doesn't hinder you in any way; you might just lose some money.
Comment: I emailed the airline and this is the response I got:

_U.S. citizens traveling to India must have a Valid U.S. passport and may
travel one way as long as the visa is not tourist or business._
Answer: We travelled like this on a one way ticket and the only thing that was checked by the airline was the visa and the one way ticket. Since, it was not a business or a tourist visa, the airline allowed us to board the flight. Further, at immigration in India, no questions were asked.

One way ticket to India


show that Joukowski transform is one-to-one in the upper half outside the unit disk

Question: I have a problem on showing how the Joukowski transform $w=J(z) = .5(z + 1/z)$ takes the upper half plane, $|z| \gt 1$, one-to-one into the w upper half plane. I have shown how the unit disk itself collapses onto the real axis and how points outside it approach $(x,0)$ as $|z| \rightarrow 1$ from above. But I think I am supposed to show that there is a single-valued inverse function, and this is what I'm stuck on. Solving $J(z)=w$ for $z = w±\sqrt{w^2-1}$ and I have a rather larger formula for w in terms of $z = x + iy$, which seems like maybe more what I should be concerned with since after all the other condition is that $Im(z) \gt 0$, but also maybe I should be looking at the branch cuts except I'm not quite sure how to deal with that either. Any thoughts? Thank you.
Answer: One way to prove injectivity is to notice that for any distinct $z_1,z_2$ in your domain
$$
\left|\frac{1}{z_1}-\frac{1}{z_2}\right| = \frac{|z_1-z_2|}{|z_1|\,|z_2|}<|z_1-z_2|
\tag1$$
hence
$$
\frac{1}{z_1}-\frac{1}{z_2}\ne z_1-z_2
\tag2$$
which is equivalent to
$$
z_1+\frac{1}{z_1}\ne z_2+\frac{1}{z_2}
\tag3 $$


Live linux cd's with TOR

Question: I've looked on distrowatch for linux live distros with tor, but not all distros are shown. I know "Birds Linux" live cd has tor, but isn't on distrowatch. Can anyone suggest other distros with tor, which arn't on distrowatch, or a list of linux distros with tor?
Answer: I'm not sure if you would want to use Tails, which is a live version of Linux that runs from a thumb drive that runs Tor by default. https://tails.boum.org. You didn't mention in your question if you had already seen this and discarded it as an option, and I don't want to assume you are are aware of it already.
From the site:

Tails is a live operating system that you can start on almost any computer from a USB stick or a DVD.
It aims at preserving your privacy and anonymity, and helps you to:

use the Internet anonymously and circumvent censorship;
  all connections to the Internet are forced to go through the Tor network;
leave no trace on the computer you are using unless you ask it explicitly;
  use state-of-the-art cryptographic tools to encrypt your files, emails and instant messaging.
Answer: I use tails and tor-RAMdisk distributions.

Live linux cd's with TOR


Where do I find a Buddhist retreat in Asia?

Question: I have had experience in meditation, I want to have experience of living and learning with Buddhist monks.  Where in Asia can I experience this for 8 to 10 weeks to start?
Comment: Which tradition are you interested in? Tibetan? Theravada? Zen? Chinese Mahayana? Etc.
Comment: http://www.meditation.lk
Answer: Speaking from personal experience with stays at Zen monasteries in Japan:
It depends on what you mean by retreat. Many Zen monasteries in Japan offer "retreats" in their web pages, but this is not necessarily what is meant in Japanese Zen by a sesshin (接心). If you want to experience the daily life of Buddhist monks in Asia, I'd advise not joining a sesshin for your first time in Japan, as this is an extremely intense period for the monks, and if you do not fully master the local language and the temple customs you will struggle. First time around, I would advise you stay at one or more temples during a regular period.
If you want to sleep, meditate, eat, and work with the monks you can contact the head temple or administrative office of a Buddhist lineage in Japan and ask for possible periods and places to stay (also, indicate if you need some help with the language and customs, as this will be taken into account proposing possible stays to you).
Here are some links you may find useful:
Shoganji Monastery - Rinzai lineage
Soto Zen monasteries for foreigners in Japan - Soto Lineage
ShinShoJi Temple - Rinzai Lineage
Shunkoin Temple - Mindfullness
Japan Vipassana Association
There's also shukubo in Japan, a kind of pilgrim lodging associated with nearby temples.
Answer: Many Westerners come to here to meditate, some become monks, some as laypeople.
International Buddhasāsana Meditation Centre
https://www.paaukforestmonastery.org/
You might also be interested in this monastery which the abbot has traveled to the deep forests and mountains in Karen State and meditated for many years. It is also common that several monks go to the forest and return only when they achieve a certain level of enlightenment.
https://goo.gl/maps/BgDTUBbbDvQ2
Note: Free of charge. Stay as long as you want. These are in Myanmar, so I am afraid you might end up like Jack Dorsey.
Answer: If you're searching for Theravada Buddhist retreat in Sri Lanka you can visit,

Na Uyana Aranya Senasanaya
Mithirigala Nissarana Vanaya
Rathmalkanda Meditation Centre
Kanduboda Siyane International Insight Meditation Centre
Answer: Well there are plenty of monasteries, so try to find videos by bikkhus online and then go to their website to find the contact info and ask them about retreats
ex in thailand:
the famous http://www.forestdhammatalks.org/en/contact.php
the famous https://www.phrasuchart.com/contact/
the famous http://www.wbd.org.au/visiting/overnight-and-longer/


When did the Roman Empire devalue currency?

Question: I had read some years ago an article describing the decision of an emperor to deal with the empire's economic troubles be devaluating the currency. The devaluation occured by mixing silver with not so precious metals. That policy was continued by the successor emperors but in the end the only thing they managed to achieve was to cause a tremendous inflation. I am trying to find out infos about this incident, the time span in which it happened and the emperor that initiated it.
Any info or links to books about this policy will be most welcome
Comment: Basic economic principle- "Inflation is a tax that nobody has to vote for".  Debasement (effectively the same as inflation for specie currency) creates more money, giving the government more funds and more. Debasement happens all the time - there is no single event or period.
Comment: The answer lies not in creating an inflation but forcing everyone in your "Empire" to find alternative methods of being paid. Horses became a powerful form of Money as a consequence. Emperors became weak. Legions quite often defeated.
Comment: This may not be directly related to the question, but Diocletian's [Edict on Maximum Prices](https://en.wikipedia.org/wiki/Edict_on_Maximum_Prices) is an interesting related thing.
Answer: The correct term for this is Debasement of the currency. The Wikipedia article on Roman Currency has details.
To summarise, the basic coin was the denarius, introduced in 211BC. Its size and the amount of silver in it gradually shrank over time; debasement of the coins was a fairly continuous process. The exact reasons for it aren't clear, but shortages of precious metals, and inadequate state finances probably had a lot to do with it. Debasement usually increased when the empire was weak.
Comment: In the basement of the National Roman Museum - Palazzo Massimo alle Terme, behind a 3'-thick vault door, is a massive display of coins. You can track the fortunes of Rome by looking at the coins -- debased, back to high quality, debased again.
Answer: I wanted to expand on my comment; the traditional formulation of the economic principle is "Inflation is a tax for which nobody has to vote." In an autocracy like the Roman Empire, the maxim would be slightly adjusted, "Debasement is a way of funding the government without generating opposition from strong stakeholders."
Debasement reduces the buying power of the individual and shifts that buying power to the state - it reduces the wealth of everyone who stores wealth in coin.  Like most "flat" taxes, it is regressive and has a greater impact on the poor.  Like most flat taxes, it is also easier for the wealthy and powerful to minimize the impact of the tax.  (when debasement is imminent, shift wealth to non-coin assets such as land or art.)
Infographic summarizing Roman currency debasement  - Note the graphic "Silver content of an individual denarius" - debasement occurred repeatedly and frequently. There was no single event.
Econtrader on currency debasement
Comment: Which concept are you referring to as being too modern to be understood at the time? If you refer to inflation, you are probably right. But the Romans certainly understood tax policy, the distribution of the tax burden and the possibility to cut costs by debasing the silver (Dinarius) and gold (Aureus) coins. (Although they likely did not anticipate the long term effects of currency debasement.)
Comment: This is far to modern a concept to be understood at that time. There was no paper money at the time so hard currency was simply very limited in supply. Greece's silver came from nearby Thrace whereas Rome's silver came from far away Spain (at least by the overland route.) So Rome was always in grave danger of having its physical monies not just debased but eliminated by any "barbarians" who might take Spain. This is certainly what Carthage tried but failed to do.
Comment: The Carthaginians were in Spain before the Romans, not the other way around. Rome conquered Spain (south of the Ebro) only after driving out the Carthaginians in the Second Punic war; the Carthaginians in Spain were never after Rome's silver supply.


Why would the side of the moon that faces earth be as dark as the far side of the moon?

Question: Somebody suggested that the side of the moon that always faces the earth is as dark as the far side of the moon, but is that really the case? Doesn't earth-shine make the earth-facing side of the moon overall brighter? Or does the absence of a moon atmosphere negate any possible gain from earth-shine?
Comment: Your question is unclear. Are you asking about the albedo of the moon on the near and far sides, or are you talking about the amount of illumination received on those sides?  If the latter, then obviously Earthshine only affects the nearside. The amount of Earthshine received by the moon differs according to the phase of the Earth as seen from the moon. A Full Earth will produce more earthshine than a New Earth from the moon's point of view.
Comment: Matter of fact, it's all dark.
Comment: This should be indeed made more clearer as for it can be interpreted in different ways leading to different answers equally correct.
Comment: @Alchimista. thx for the constructive comment. Have tried to make the question clearer. Have learned a lot from the already received answers.
Comment: Question looks good now, has +13/-0 score and has several good answers, so **voting to leave open!** Next time maybe we can just leave a comment about improvement without the close votes?
Answer:
Somebody suggested that the side of the moon that always faces the earth is as dark as the far side of the moon, but is that really the case?

That is not the case.
I'll look at two different wavelengths: visible and radio.

Visible
Doing astronomy from the surface of the Earth when the Moon is full is much more difficult than is doing astronomy from the surface of the Earth when the Moon is new. While much of this difficulty arises due to the Earth's atmosphere, some is the direct result of the presence of a largish, well-lit object that has same angular size as does the Sun. The full Earth as seen from the Moon is, on average, over 40 times brighter than is the full Moon as seen from the Earth. Reading a newspaper on the Moon at night under a full Earth would be a piece of cake compared to reading a newspaper on the Earth at night under a full Moon.

Radio (and microwave)
These are the wavelengths where an observatory on the far side of the Moon would truly shine. The Earth radiates significant amounts of electromagnetic radiation in the radio and microwave wavelengths. There are a few places on the Earth where radio towers and microwave towers are absolutely forbidden, such as the area around the Murchison Radio-Astronomy Observatory in Australia, the area around the Itapeting Radio Observatory in Brazil, and the area around the National Radio Astronomy Observatory (Green Banks, West Virginia) in the US. These Earth-bound radio quiet zones are still plagued with radio and microwave radiation reflected by the atmosphere and by radiation from satellites orbiting the Earth.
Radio telescopes on the far side of the Moon would be shielded from the large amounts of electromagnetic radiation in those wavelengths emitted by the Earth, and possibly even from the electromagnetic radiation in those wavelengths emitted by satellites orbiting the Earth. Moreover, radio telescopes on the far side of the Moon would not be hindered by the Earth's atmosphere. The transparency of the Earth's atmosphere at radio wavelengths ends at the very long wavelengths that would be useful in studying the early universe, and it ends at the upper microwave that would be useful in studying molecular gas clouds.
Comment: +1. It would be good if you could include a few references or links in your answer too.
Comment: The last point about lack of atmosphere of course applies to the whole Moon, not just the far side.  And of course there'd be problems in setting up a telescope on the far side of the moon, in that in order to be of any use, it would need to relay signals off of something else in order to send any data back to Earth.  The ideal place might be somewhere in the belt between the near and far sides, which periodically has a direct line of sight back to Earth to send data home, and in between is shielded from all of our noise.  This would eliminate the need for an orbiter to be the go-between.
Comment: I am sure that there will be an orbiter and possibly even a space station in lunar orbit, but if you want a land based sight you would choose the "peaks of eternal light" at the north and south poles where there is contact with Earth (and the far side) as much as 90 percent of the time (the south pole has nice craters with water ice).
Comment: @JackR.Woods I think if you're putting up a permanent, unmanned telescope on the Moon, you might not bother with an orbiter.  The only reason we needed that in Apollo was because we had to bring the people (and samples) back.  Eliminating the orbiter would greatly simplify things; you don't need fuel, rocket, reentry shielding for the return trip, you don't have to maintain stable orbit (also requires some fuel).  That's a lot of weight (and thus cash) savings.  And I don't think you'd want 90% coms time because of aforementioned radio interference, just enough to send back data periodically.
Answer: In addition to user-LTK's very good answer, it is also true that the mare which we see on the Near Side are largely absent on the far side.  The basaltic flows of the mare are darker than the regolith of other areas, contributing to a higher albedo, brightness, on the Far Side.
https://en.wikipedia.org/wiki/Lunar_mare
Answer: The far side of the Moon has sometimes been called the "dark side of the Moon", mostly because we can't see it from Earth.  Apart from partial libration, we never see most of the far side of the Moon from Earth, we can see about 59% of it as it wobbles slightly as it orbits a somewhat elliptical orbit.
It's more accurate to say "far side of the Moon" than dark side and actually, the near side or Earth side is darker because it has more maria (spelled like the name, pronounced differently).   The near side is darker on average, the far side has more craters and a thicker crust.   The reason for this is because the Earth side of the Moon probably cooled more slowly, warmed by the Earth that was also quite hot after the giant impact, and took more time to cool.  The far side cooled more quickly and as a result, retained more craters.
Article for further details.
Comment: Update: the light from the full (or even half) Earth on the moon is definitely enough to read. Earth is way bigger than the Moon in the sky and has more favorable albedo. And if it is less than half-Earth, you will get direct sunlight as well. It will probably never be dark enough, even in eclipses.
Comment: "libration" not "libation". (I make this same mistake about half the time I use either word.)
Comment: Once or twice a year, when I can't quite finish a six-pack.
Comment: Would it be easier or harder on average to read a newspaper on the near or the far side of the moon, though? (This is also a reasonable interpretation of the question of which side is "darker").
Comment: By day, both sides are equally lit by the Sun. By night, the "near" side has some light from the Earth that may be enough to read. The far side by night is lit only by stars.
Comment: @A.I.Breveleri, now I'm curious: How often do you use the latter? Does it come up much in day-to-day conversation?
Answer: Short answer:  Yes and No.
Long answer:  The question is a little ambiguous.
What do you mean by dark and light? Do you mean that:

the lunar material is lighter or darker on one side of the Moon, or

the lunar surface is illuminated by more light on one side of the Moon?

Part One: The color of lunar surface material on the two sides of the Moon.
The side of the Moon which faces the Earth has a lot more marias than the far side.  Those marias are full of rocks which are much darker than the rocks in the lunar highlands.  People with good eyesight can actually see the darker areas on the near side without telescopes.
So on average, the surface material on the near side of the Moon is darker and less reflective than the surface material on the far side of the Moon.
Part Two: Illumination levels on the two sides of the Moon.
The two sides of the Moon receive almost exactly the same amount of illumination from the Sun.
But the near side of the Moon which faces the Earth is sometmes eclipsed by the Earth.  Two to five lunar eclipses happen each Earth year.  And each time, the near side of the Moon is partially or wholly in the shadow of Earth and the sunlight is partially or wholly cut off from the near side of the Moon for up to almost two hours.
But a lunar eclipse also makes the night on Earth darker, since the Moon in eclipse reflects far less light at Earth.  And overall the length of time the Moon illuminates the Earth is many times as long as when the Moon is in eclipse and does not illuminate the Earth, and so the Moon makes a total positive contribution to the the illumination of the Earth.
And similarly, the Earth makes a total positive contribution to the illumination of the Moon.  Since Earth appears larger in the sky of the Moon than the Moon appears in the sky of the Earth, Earth at a specific phase illuminates the Moon much more than the Moon at the same phase illuminates the Earth.
And overall the length of time the Earth illuminates the Moon is many times as long as when the Earth is in a solar eclipse and does not illuminate the Moon, and so the Earth makes a total positive contribution to the the illumination of the Moon.
As the Earth rotates, different longitudes of Earth are illuminated by the Moon.  But the Moon's rotation is tidally locked, so one side always faces the Earth.  Thus the near side of the Moon is the only side which receives the extra illumination of Earthshine, and thus receives more illumination than the far side.
So the near side of the Moon is darker in the sense that it is made of darker materials on average,and the near side of the Moon is also lighter in the sense that it receives more total illumination due to receiving Earthshine.
Comment: +1. Would it be viable to compare the overall darkness of the two sides by adding together surface darkness and albedo?
Answer: Dark side of he moon is not labeled dark by virtue of poor illumination. All of the moon is exposed to light from the sun. On the otherhand the Moon rotates at such a rate it's fascia is always exposed to View from Earth. Thus being synchronized with it's revolution it never shows it's "Dark side" to line of sight
Answer: The Sun lit far side of the Moon was measured during the Apollo 8 mission and a perpendicular reading of between 160-320 lumens was indicated by the Minolta 1 degree spot meter as they passed over. If the Sun is rated at 130,000 lumens at the Earth/moon distance and the Moon has an albedo of 0.12 then something is wrong somewhere. I have found no measurements for the near side, but NASA tells us that Earthshine on the Moon would provide 76 times more photons than a full moon produces on Earth, so the near side must be brighter than the far side which receives no Earthshine.
See"Lighting constraints on lunar surface operations"
Comment: hmm... interesting answer! "bright" and "dark" can refer to 1) the reflective property of a surface, 2) the quantity of illumination of that surface, and 3) the combination of both together, and can have both absolute and relative interpretations. I think this answer is interesting because it points out that the near side is on average more brightly lit than the far side. Cool! However, I have a hunch that the question really wants to ask about the surface reflectivity or *albedo* and not about illumination.
Answer: The same question could be asked for the Earth. If the moon is full, shouldn't it lighten up the Earth's surface? You can find your way in the light of a full moon, when walking, outside. But it's pretty dark around you. The sky is very dark blue, which already goes to show how little moonlight is coming in. I think that if you walked on the dark side facing us, the surface looks very dimly blueish (because of the Earth looking blue). But this blue won't be bright enough to make the moon shine. Only if you make a time-exposed photograph its true color will show up.


Anal sex between husband and wife

Question: What if married couples didnt know that anal sex is haram and kept doing it from years will Allah forgive them.There are many people who doesn't know that so will Allah forgive them for that ?
Comment: Salam and welcome to Islam stack exchange. I recommend you to make yourself familiar with our site and model by tkaingbthe 2min. [tour] and checking our [help].
Comment: "Verily actions are by intention." [Al-Bukhari and Muslim]

God does not punish one for sins committed without knowledge. But after knowledge has been attained, it is responsibly of the person to abide by the deen and when erred ask God for forgiveness with sincerity and pure heart.
Answer: First of all Allah says:

... And when they have purified themselves, then come to them from where Allah has ordained for you. (2:222)

This verse is regarded as an evidence from the qur'an that anal intercourse is haram. And in the sunnah you may read:

The Prophet (ﷺ) said: He who has intercourse with his wife through her anus is accursed.  (Sunan abi Dawod)

"Allah will not look at a man who has intercourse with his wife in her buttocks." (Sunan ibn Majah)

Assuming the wife was aware of this rule she is held to hinder her husband from doing so -if she can-, as she doesn't need to obey a husband who wants her to do something Allah hates:

...  "No obedience for evil deeds, obedience is required only in what is good ." (See for example in Sahih al-Bukhari and Sahih Muslim)

Nevertheless it might happen that people do this due to lack of knowledge in this case applies:

... And there is no blame upon you for that in which you have erred but [only for] what your hearts intended. And ever is Allah Forgiving and Merciful. (33:5)

Verily Allah has pardoned [or been lenient with] for me my ummah: their mistakes, their forgetfulness, and that which they have been forced to do under duress (See in the 40 hadiths of an-Nawawi or in Sunan ibn Majah and Sunan al-Bayhaqi)

This means that both must repent sincerely and never do this again once they learnt about the truth.
See also -in Arabic- fatwa islamweb #101842

Anal sex between husband and wife