When rain clouds are formed, does the entropy decrease?

Question: Water droplets gathered and formed into cloud which gets heavier then does the entropy of the system decreases? If so why 2nd law of thermodynamics allowed it?
Answer: The second law of thermodynamics says that the entropy of an isolated (or closed) system left to spontaneous evolution cannot decrease with time. A cloud is not an isolated system - it interacts with the surrounding atmosphere, which in turn interacts with the wider atmosphere. So to get to an isolated system that includes the cloud we must at least include the whole atmosphere of the Earth.
But the Earth's atmosphere is not an isolated system either. It interacts with the land, the sea and the ice caps. The sea in turn is influenced by the gravity of the Moon and the Sun. And the Sun also heats the Earth and its atmosphere. So to get to an isolated system that includes the cloud, we must at least include the Earth, the Moon and the Sun.
The entropy of this whole system does not decrease over time, so the second law of thermodynamics is not broken. The entropy of individual components of this system (such as the cloud) may decrease, but this decrease will be matched by a greater increase in entropy elsewhere in the system.
Answer: Clouds are not closed objects, butt rather a part of a dynamic atmosphere, which is far from thermodynamic equilibrium (to which the Laws of thermodynamics/statistical physics apply.) In this sense, there is nothing wrong with entropy being locally reduced, provided that the overall entropy (of the atmosphere or the earth as a whole) increases (see, e.g., Maximum Principle vs. Minimum Principle in Non-equilibrium Thermodynamics.)
Locally, the transition between water vapor, water droplets and ice crystals can be indeed described using equilibrium thermodynamics. Again, these transitions are accompanied by release of latent heat, i.e., the increase of entropy of the surrounding environment (air, kinetic energy of water droplets, etc.)
For more see:  Twelve Lectures on Cloud Physics, A short course in cloud physics
Related:
Why do clouds have well-defined boundaries?
Why are snowflakes flat?


understanding the "chunk size" in context of RAID

Question: Am I correct that chunk size in context of RAID is essentially the same thing as cluster in file-system context? In other words, chunk size is the smallest unit of data which can be written to a member of RAID array? For example if I have a chunk size of 64KiB and I need to write a 4KiB file and cluster size of the file-system is also 4KiB, then is it true that I will use one 64KiB chunk and basically waste 60KiB?
Answer: Given that chunks can be quite big and that the parity information is simple XOR (i.e. does not affect data before or after the piece in question) the assumption that only complete chunks can be written does not make sense to me.
Chunks are the unit in which data is spread over the volumes. One chunk of continuous data is written to a certain volume, the next data is written to another.
Both with file systems and with RAID this is an optimization issue: In a file system too small blocks / clusters would cause metadata overhead, too big blocks waste too much space (as most file systems can use a certain block for a single file only).
With RAID it is similar: If you have tiny chunks then you need accesses to several disks even for very small files (or other data). In most cases the higher latency of the (in this single case) slower drive takes more time than reading from one drive alone. This is not valid for SSDs but they are not the dominant technology for RAID.
If you have very big chunks then even those accesses which could be clearly speeded up by spreading to several drives are done to only one drive.
Answer: The answer to the OP's question is: Yes. In a RAID, a "chunk" is the minimum amount of data read or written to each data disk in the array during a single read/write operation.
In your example, you won't necessarily "waste" 60-KiB as you put it. That depends on the combination of the file system structure and the underlying RAID structure. However, you are raising a very important point, which is that it's ideal if the file system configuration aligns with the RAID configuration with regard to their units of storage.
Continuing with your hypothetical example; if you had a RAID with 64-KiB chunk size and an overlaid file system using 64-KiB block sizes, then yes a 4-KiB file would use an entire 64-KiB area of storage space in the file system all by itself. And at the same time it would eat up an entire 64-KiB chunk in the RAID all by itself. However, that would be because the file system was setup to 64-KiB blocks. Those blocks are the smallest unit of storage data of that file system. Any file size smaller than that block will still use 1 block of file system storage space.
My point is your 2nd question is actually relevant to the file system and not the RAID.
Continuing with my example above, if your RAID used 16-KiB chunks and your file system on top of the RAID used 64-KiB blocks, then each block written to the RAID would require 4 of those chunks (64/16=4).
Now reverse that thought process. What if you had 64-KiB RAID chunks and 16-KiB file system blocks? Now each file system block only uses 1/4 of the RAID chunk. That means 1) your 4-KiB file takes up 16-KiB in the file system; and 2) the RAID will perform a read/modify/write operation when writing that 4-KiB file/16-KiB block because the RAID's smallest unit of storage is 64-KiB. So then your file system is more efficient, but your RAID is less efficient (for that particular file operation).
Answer: The chunk size only defines where the bytes are located. A 512 KB chunk size doesn't require system to write e.g. 512 KB for every 4 KB write or to read 512 KB of device surface for a 4 KB application read.
The chunk size is basically a tradeoff between device first byte latency vs bandwidth of the device for continuous read after receiving the first byte. For a HDD the first byte latency is really bad and trying to sync multiple devices is so slow that you cannot benefit from small chunk size.
Imagine situation where you have chunk size 4 KB and 4 device RAID-0 setup. If an app opens a file and does a 16 KB read, the system will have to move read head of every device in the RAID near the start of the file and read data. Because rotation of the platterns are not syncronized on separate HDDs, one should assume that disks are offset 180 degrees on average, so to get every device to read the same location requires worst case behavior for the HDD latency. This is because at least one of the devices always have a bad offset for the current plattern position vs data position for a single rotation of the plattern so that device must wait maximal time waiting for the correct plattern position to rotate under the read head. This is also why enterprise HDDs have so high rotation speeds but nowadays SSD is already typically cheaper than high RPM HDD.
A single HDD can typically emit 150 MB/s or 16 KB in 0.1 ms. The typical read head latency for a HDD is in range 6–11 ms.
Trying to move read heads on multiple devices doesn't make sense for short reads because reading the rest of the file after getting the first byte is practically free. On the other hand, SATA6 SSD may have first by latency in range 0.1 – 1.0 ms and bandwidth around 400–500 MB/s so the situation is quite different there.
And it also makes a huge difference how much parallel access your workload has. If you have only one process thread accessing the whole RAID setup at once, using a smaller chunk size may improve throughput but typically the chunk size should be set according to following logic:
<code>chunk_size = typical_first_byte_latency ⨯ single_device_throughput
</code>
That is, if your latency is 10 ms and throughput is 150 MB/s (typical HDD), the chunk size should be set around 1.7 MB (!) for optimal throughput. In practice OS often prefers power-of-2 sizes so sensible options are 1 MB or 2 MB. It's typically safe to go with smaller chunk size so 1 MB should be used in practice.
On the other hand, a SATA SSD might have typical latency around 0.2 ms and throughput 450 MB/s and then optimal chunk size should be around 94 KB, or 64 KB in practice. Notice how critical the latency is here because if the typical latency is in actually 0.1 ms, optimal chunk size would be 47 KB already, or 32 KB in practice.
And note that for SSD you have to think about typical random 4KB QD1 latency while considering chunk size, not amortized latency over lots of reads for QD32 load. This is because chunked data MUST be read from multiple devices if the chunk is smaller than the read operation size, so the slowest of all parallel operations limits the response time.


Switching from inner iFrame to the outter (parent) iFrame

Question: I have an iFrame in another iFrame, I´am able to switch to the parent iFrame and then to the child iFrame, but I´am just not able to switch back to the parent one. Is it even possible to switch up top to the parent one, as the driver is in the child iFrame?
Comment: Show your (java?) code in your original post, along with any relevant HTML code.
Comment: Wouldn't driver.switchTo().defaultContent() help you out? As per Java Docs, it selects either the first frame on the page, or the main document when a page contains iframes.
Answer:
No. Its not possible to directly access out side.
As your driver is currently in child iFrame, Then you can access Parent iFrame.
But not directly go for Parent iFrame's top element
Answer: iFrames are nowadays used in almost all professional software companies and having an experience of 6 years in one of the top IT Security Testing Services companies, I have hardly seen any newly developed application without iFrame. So, to handle these iFrames there are multiple ways as mentioned below -

SwitchTo().frame(int frameNumber) - This works based on the frame index.
SwitchTo().frame(string frameName) - This works based on the name of the frame.
SwitchTo().frame(WebElement frameElement) - This works based on frame webElement

and now if you want to switch back to parent frame, you can use default method as - Switch to Default Content method.
This allows you to navigate back to parent method and can be used as -
driver.switchTo().defaultContent();
Answer: Welcome to what I call "frame hell".  I had a very similar situation.

Document

Top frame

navigation frame
content frame

sometimes present iframe

The first thing to note is selenium will always allow you to go back up to the document level (aka defaultContent) regardless of what frame you're currently in.  Moving between frames is like moving between directories without the possibility to jump directly to a frame.
Example: If you're currently on the outermost document level, you can't just jump into content frame, you have to switch to Top, then switch to content frame.
The second problem I ran into is loading states of content and frames. Clicking a button in the navigation frame or content frame might cause the WHOLE page to reload or perhaps just the content frame.
I had to reset to the top and wait for each frame level to load before going into the next level. Here is an example code of switching to content frame regardless of where you are currently:
    def switch_to_frame_content(self, wait: WebDriverWait):
        """moves to the content frame"""
        self.driver.switch_to.default_content()
        wait.until(ec.frame_to_be_available_and_switch_to_it(locators.top_frame))
        wait.until(ec.frame_to_be_available_and_switch_to_it(locators.content_frame))
        return

Here is a use case where clicking a button in the content frame caused the content frame itself to be reloaded within the Top frame.
    self.click(confirm_button)
    self.switch_to_frame_content(wait)
    wait.until(ec.element_to_be_clickable(next_button_to_click))


What is the effect of the filter size in a CNN

Question: I am new in deep learning and I try to understand some details about CNN. Could you explain to me what is the effect of the filter size e.g 5*5 vs 7*7  on features extraction and locality structure ?
Answer: If you work in natural language processing, you can view the filter size in a CNN as the n-gram size.
If you work in computer vision, you can view the filter size in a CNN as the receptive field.
See How to work multiple filter region sizes: 2, 3 and 4 in CNN? to get a better intuition.

how to fix the size of the filter.

The choice of the size of the filter depends on the dataset. I am not aware of any rule of thumb, typically one would start with a size of the filter that has been used in similar works. Some ideas: What are the state-of-the-art methods to determine parameters in CNN, NN, RNN, or any deep learning models . E.g. in {1} we used Gaussian Processes to automatically choose the filter height.

References:

{1} Franck Dernoncourt, Ji Young Lee. Optimizing Neural Network Hyperparameters with Gaussian Processes for Dialog Act Classification, IEEE SLT 2016.
Comment: I mean how to fix the size of the filter. What is the effect on extracting features when we use a small filter size vs big filter size ?
Comment: @BetterEnglish added in answer.


I can't seem to reset the position of the control bone

Question: I have made a foot control rig here, but I try alt-G, and alt-R and it does not reset the pose. I even tried resetting it from the pose menu up there in the top left. Any ideas? I'm just sure it has to do with the bone constraints, but I can't figure it out on my own! Thank you all in advance! You all are the best! Here's a picture if that helps lol.
Comment: hello, please share your file: https://blend-exchange.giantcowfilms.com/
Comment: Okay, I'm working on uploading it. Computer just being slow.
Comment: [](https://blend-exchange.giantcowfilms.com/b/R7vjlOeQ/)
Answer: There's a conflict: the controller controls the foot through several bones parentage, the foot controls the leg through the leg's IK, and the leg controls the controllers through a Limit Distance, so you need to delete the Limit Distance. If it was meant to attach the controller to the leg it is not the right way, I don't know any way to do it but there might be a way though... I personally prefer easier bone setup but I'm not a pro.
Comment: Okay, well thanks for looking at it anyhow. The tutorial I'm following is a older one I suppose. I will try to find a way to get it to stick to the mesh. Thank you moonboots!


Probabilistic interpretation from sigmoid functions

Question: Why do we interpret the results of logistic regression as probabilities? Passing the output of any regression procedure through a sigmoid function results in a probabilistic interpretation with respect to classification. Why is that so? Given that the output is between 0 and 1, is it enough to interpret the results as probabilities?
Comment: Logistic regression is (explicitly) a model for $P(Y=1|\mathbf{X}=\mathbf{x})$.
Comment: Also, if you train the model using some objective function derived from probability theory ( Maximum Likelihood, for example), then the output of the model may be interpreted as a calibrated probability.
Answer: A probability is bounded between 0 and 1 (inclusive), and a sigmoid curve is a convenient curve that can be forced to respect those bounds. It is not the only one, but the sigmoid curve has proven to be the most popular one. So, not all probability models have a sigmoid cure, though many do.
Moreover, not all models with a sigmoid curve model probabilities. For example, models that model a dependent variable that is a fraction also often use a sigmoid curve.
What makes logit, probit, and similar models model a probability is the fact that they model the conditional mean of an indicator variable, which is the conditional proportion of $1$s, which in turn is interpreted as the probability of having a $1$ on that indicator variable.
Answer:
Why do we interpret the results of logistic regression as
  probabilities?

Because the logistic regression model can be viewed as arising from a linear regression latent variable model, where the error term of this linear regression is assumed to follow the standard logistic distribution. See for example this post.

Given that the output is between 0 and 1, is it enough to interpret
  the results as probabilities?

No. The "output" must come from a function that satisfies the properties of a distribution function in order for us to interpret it as probabilities. These properties are:
1) The function $F$ under consideration must be non-decreasing and right-continuous ("cadlag")
2) $\lim_{x\rightarrow -\infty}F(x) =0$
3) $\lim_{x\rightarrow \infty}F(x) =1$
The "sigmoid function" satisfies these properties.
Comment: The latent variable representation is of logistic regression is common in some fields (economics jumps to mind) but not in all fields. I would say that this justification is one of two possible justifications, the other being "the expected proportion of $1$s interpreted as probability" justification.
Comment: @MaartenBuis Certainly, although I don't see them as "alternatives", since the latent-variable repr. being one level deeper, has necessarily to be interpreted eventually as "expected proportion of $1$s...", at the level of the logistic regr. itself. The latent-var. approach is helpful in that it provides a statistical framework for the choice of the upper-level model. Say, if an indicator function is indeed a threshold-signal from a situation where disturbances exist that are believed to be uniformly distributed, then we _should_ use the Linear Prob. model instead of the logit or probit ones.
Comment: The latent varialbe interpretation can indeed be very cute. However, in my applied work I have never been in a situation where it has been worth while. In those cases it is extra baggage that distracts from the real message.


Hot swap debugging with Android

Question: 1) Is there any special setting/configuration required to enable hot swap debugging on Android?
Example case:

Add breakpoint just after entering activity's onCreate method.
Add new line on the fly after the breakpoint (dummy "if (1==1) return;" code)
Step to next instruction
--> Problem: my debugger doesn't break at this line, instead skipping to the next leading me to believe the new line was not hot swapped into the VM.

2) Does only the emulator support hot swap? Are there any handsets which also support it?
Answer: Every time the Android project is built, it's dexed and put into a debug-signed apk that is sent to your phone/emulator. Hence, hotswapping isn't exactly easy to do.
Hotswap is a product of a well-designed JVM, and it makes it possible to exchange classes. On Android, you have Dalvik VM, which does not currently support hot swapping.
I'm guessing the ADT team has this high-ish on their list, though.
EDIT: Even though it has been 2,5 years since this answer, not much has changed. ZeroTurnaround, however, have stuff up their sleeves, and JRebel for Android should give us a much needed method for hot swapping.
http://zeroturnaround.com/software/jrebel-for-android/
EDIT2: With the release of Android Studio 2.0 Instant Run enables you to hot swap. Hot swap will i.e. change a class while your app is running.
They also support warm swap, which is doing a lot more than hot swap in terms of messing with your app. Warm swap still leaves your app running. Resource changes will trigger a warm swap.
Watch this talk from Android Dev Summit 2015 for more info: https://www.youtube.com/watch?v=fs0eira2pRY
Answer: Android Studio 2.0 preview introduced a hot swap feature. You get it by upgrading to:
<code>        classpath group: 'com.android.tools.build', name: 'gradle', version: '2.0.0-alpha1'
</code>
And then setting it from the menu:
Answer: The emulator itself doesn't support code hotswap, but with additional tools like InstaReloader desired action can be achieved. You can use this Android hotswapping tool for free
Comment: What happened to that project?
Comment: Link seems dead - site expired.
Comment: Link is dead, please repost
Answer: Not truly hot swapping but there is a library on Github which emulates that. You can find it here: https://github.com/mmin18/LayoutCast
It has some issues but is active as of the time of writing of this answer.
Also, ZeroTurnaround seems to be working on the problem with JRebel for Android. You can request beta access here: http://zeroturnaround.com/software/jrebel-for-android/

Hot swap debugging with Android


Should the length of the electrodes in the electrophoresis chamber be proportional to chamber's size?

Question: I am trying to build a small horizontal electrophoresis chamber from scratch. I want to use it for comet assay and I will be using only 1 slide, so it's going to be about 3cm wide, 10cm long and 4cm high, just enough to fit the slide and a small amount of buffer. As far as I know such thing is not commercially available, so before I make it I want to make sure that it's going to work. The main issue is the cost of the electrode (has to be platinum wire). I don't want to spent that much money just to realize that it doesn't work.
My question is: is a 3cm electrode in a 60-70cm3 enough? Basically, are there any physical restrictions on the size and the position of the electrodes and the shape of the chamber?
Since I am a biologist and my knowledge in physics are quite limited, I would greatly appreciate any information about this.
Answer: These instructions for building an electrophoresis chamber don't comment on the minimum length of wire, but on the other hand they suggest using something called Monel Seizing Wire (Ni/Cu alloy - £8.95 for 10 m in the UK) or 20-gauge copper wire, so if you follow their advice you probably don't need to worry about cost.
I imagine that alloy electrodes won't last as long, but they would be cheap to replace - in fact you would be looking for opportunities to use up all of your excess wire!
Comment: I had already read these instructions and made a bigger electrophoresis chamber using copper wire. The main issue is that copper reacts with the running buffer and makes it blue. Because of this, I'll have to change the running buffer every time (not a big deal) and change the wire quite often. That's the reason why I wanted to use platinum, everything else wears out. One the other hand, I don't mind replacing it every now and then but I'm worried about the effects on the electrophoresis.


Which type of Xbox console should I get to begin developing games on it?

Question: If I want to start developing small indie-like games with XNA on Xbox (I don't think any game I'd make would need more than 100, maybe 200 megabytes), will the 4gb Slim (I want to get a slim version because of the wi-fi) version of the console be enough, or should I get the 250 gb version? I don't really plan to play actively on the console as I'm more interested in developing on it. Also, will a console and a verified student XBLIG account be enough to set up everything I need to run and debug my game on the console?
Thank you.
Answer: The answer is no.
You'll need an actual hard-drive to use the XNA connect application (upload your game) - but not to play other games.
You'll need a physical hard-drive - NOT flash memory to deploy games.
If you have a AppHub Membership (from DreamSpark, you say yours is from); this is all you need. You will link it with your Gamertag and download the Connect App and and you'll be all set from there.
Comment: You actually need a hard drive to develop with XNA on the 360. You can download and play XBLIG with just the built-in 4GB drive but the XNA connect application that allows you to deploy your own games to the Xbox requires a hard drive. See http://xboxforums.create.msdn.com/forums/p/74847/571243.aspx
Comment: Corrected - odd this isn't actually documented anywhere.
Comment: Thank you very much. So if I would buy the 250gb version (which as I read comes with an actual hard drive), I'd be all set up and I won't have to buy a seperate hard drive, right? Just for clarification :-)
Comment: Yeah, you need at least a 250GB model at that case (if you must get a Slim for WiFi) this is your only feasible choice.


How do d-orbitals interact with molecular orbitals?

Question: I  recently stumbled upon a question asking how iron destabilizes the bonds in a nitrogen molecule. I have searched the web and my textbook for quite a while now and I cannot find a satisfactory answer. The only explanation I could muster was that the d-orbitals of the Iron atom interact with the HOMO and LUMO of the nitrogen molecule, due to the overlap of the molecular orbitals with d-orbitals.
I am not sure if this makes sense. I'd really appreciate any answer or advice!
Comment: Hello and welcome to Chemistry.SE! If you have any questions about how the site works you can visit the [help]. Best of luck solving your problem.
Answer: You are on the right track with your answer.
Notice that the LUMO is a $\pi^*$ orbital, meaning that filling it with electrons would weaken the bonding. When nitrogen and iron interact, electrons from the d-orbitals on iron are well aligned, in terms of symmetry and energy, to fill into $\ce{N_2}$'s $\pi^*$ orbital. This forms a bond between $\ce{Fe}$ and $\ce{N_2}$, but at the cost of weakening the bond between the nitrogens. This is a very important concept in inorganic chemistry referred to as Pi Backbonding.
The classic example given of a ligand that exhibits $\pi$ backbonding in metal complexes is $\ce{CO}$, which is isoelectronic to $\ce{N_2}$ and has the same molecular orbital diagram (though the orbitals themselves look different due to the asymmetry of $\ce{CO}$).
Comment: If $d$ orbitals interact with $\pi^*$ then new molecular orbitals are created and electrons go to the bonding MO. I don't think it makes much sense to talk about bond weakening just because the electrons went into a $\pi^*$. In fact they don't even fill the $\pi^*$ of CO. They fill the MO that result from the combination of $\pi^*$ (CO) and $d$ (metal).


Squat racks and barbells on first floor of home gym: bad idea?

Question: Is it a bad idea to have a home gym on the first floor of a house with a squat rack and barbell? Most home gyms with racks/barbells I have seen are in the basement or garage on concrete. My concern would be the occasional dropped deadlift or bailed clean smashing through the floor. Could mats, plywood platforms, and/or bumper plates mitigate serious damage?
Comment: I spoke with my mother (an architect) and her advice is that you should **definitely** check the house to see how much it can bear; this is quite a lot of weight on a very small area and it can be tricky (not sure how much the plywood would help, either). In my corner of Europe, houses are required to be able to bear 250kg/m^2, but even this might not be enough for a rack (consider what happens when you drop your weights).
Comment: How does the architect check how much the floor is able to bear?
Comment: @Sarah - Load beams. You have to be able to see under the flooring (i.e. the ceiling of the basement), and see what kind of load beams are supporting everything, how all of the other cross beams and support structures are and so forth. A steel beam can support more than a laminated beam can support more than a couple 2x4's nailed together. A contractor can tell you, an architect specifies more than builds.
Answer: It definitely depends on the construction of your house. Some home features require extra care, such as grand pianos and hot tubs.  Essentially, anything that puts a large amount of weight in a relatively small area.
Covering the whole workout area with another layer of 5/8" plywood will help provide additional rigidity and disperse the weight better.  However, if you have an older house, you might have floor joists that are fairly wide apart such as ever 24".  If that's the case, you'll need to add some more floor joists for extra support.
Now, if we are talking a total of 300lbs of weights, you should be fine.  If you are pulling four big plates a side, you should definitely have the home inspected to see if it can handle the weight.  This is true even particularly if you get a proper lifting platform (2" cement base with 2 layers of 3/4" plywood on top).  The weight of the platform itself is enough to warrant caution.
To be absolutely sure, if you have a concrete foundation below you, you should be OK.
Answer: How much weight are you talking about?  A good test is if you bounce on the floor do you go through it?
Seriously, I would recommend a plywood platform to keep your floor from getting messed up, make sure you put padding under it and that it's thick/strong enough for your weight plus the rack plus the max weight you plan on lifting.  Make sure that any drops won't 'rattle' dishes, pictures, etc. in adjoining rooms.  I think the main reason for most home gyms in basesments is due to the need to keep the wife happy OR general space issues.

Here's my workout area (note the cat litter pans adding to the decor)
Answer: It can be achieved if you lay 1 inch ply and use an anti-shock rubber mat which have egg cup feet. 40mm should suffice, but if you're lifting 150kg+, your probably better with 50mm or 60mm or even doubling them up for extra piece of mind.
You can see good pictures with all the different ratings on this website page.
Comment: I believe you forgot to add a link. In any case, how do _you_ know how much OP's house floor can support to give such specific advice? I believe the accepted answer has better advice (check the house structure first).


LIGO: Importance of photons

Question: In LIGO, a photon beam travels in two perpendicular direction and time taken by each beam is noted. Non zero time difference is a signature of GWs here. What if I use electron beam travelling at velocity (say, 0.8c) instead of photons? Will I be able to detect GWs?
I think this will not work since electrons dont travel along null geodesics. But I am not sure.
Comment: Electrons dont always travel at a constant velocity relative to aby observer. The LIGO experiment only works with the constant speed of c.
Answer:
In LIGO, a photon beam travels in two perpendicular direction and time taken by each beam is noted. Non zero time difference is a signature of GWs here.

Not correct, see this description  and this video, at about 27', of the web cast . It is the interference pattern, the phase difference, that generates the signal.

Simplified operation of a gravitational wave observatory
Figure 1: A beamsplitter (green line) splits coherent light (from the white box) into two beams which reflect off the mirrors (cyan oblongs); only one outgoing and reflected beam in each arm is shown, and separated for clarity. The reflected beams recombine and an interference pattern is detected (purple circle).
Figure 2: A gravitational wave passing over the left arm (yellow) changes its length and thus the interference pattern.

The LIGO set up is made so that phases at the light detector cancel out (see video at 27'), no light arrives,  unless the relative distances of the two arms change, then an interference pattern  will appear in the detector.
Electrons do not build up a space wave the same way photons build an electromagnetic wave, due to the charges introducing repulsive forces and magnetic fields attractive, the probability wave describing an electron beam would need a density matrix, not a coherent sinusoidal beam with phases. Thus this experiment could not be done with electrons with any velocity.
Comment: Other than being charged, is there any other reason for which it fails to solve the purpose? Can you please elaborate "why photons only".
Comment: I will repeat : the setup depends on phase differences. One cannot set up an electron beam in a coherent probability wave so as to have the corresponding phase interference.( It is also the magnetic field of a moving electron which will attract the one next to it while the same charge is repulsive, a complex problem)
Comment: I understood why we cant use electrons. But I want to know whether photons moving along null geodesics also plays a role or not? What if our beam is made up of massive but neutral particles?
Comment: To get accurate interference fringes one needs plane waves, which are provided by the lasers in LIGO. A beam of massive neutral  particles will give interference fringes  to the probability distribution on the screen,  but their direction and momentum cannot be controlled for four kilometers, let alone no method of reflection and beam spliting will work , as they are neutral.  The reflections of laser light increase the path length to thousands of kilometers. It is already hard to have four kilometer vacuum for the laser light.
Comment: " a beam of massive neutral particles will give interference fringes" needs a qualification, if it is entangled, i.e. the phases between each neutral particle is fixed in the method of generation of the beam.  I cannot see an experimetal method that can do this. Maybe using magnetic moments.

LIGO: Importance of photons


Why are the officers on DS9 also assigned to the Defiant?

Question: In Deep Space 9, once the war began, the same officers were assigned to the Defiant as were running Deep Space 9. Keeping this in-universe, wouldn't the skill set of officers who run a space station be different than the ones who run a starship, especially at war?
Comment: O'Brien is a decorated helmsman and engineer, Dax is a class-9 pilot, Doctor Bashir is a doctor, etc, etc. Why do you feel that they're under-qualified?
Comment: I'm not convinced the *skillset* is so much the problem. I worry more about who takes care of DS9 while the Defiant is on a mission. Especially since DS9 is such a valuable target for the Cardassians and the Dominion.
Comment: I don't really think that there is an in-universe answer that makes sense; obviously they were the same people because it was the main cast; but in-universe, you need BOTH a crew to man the station and another to man the Defiant; you can't shut one down because your main cast must go to the other, either one of them can't be left without their senior commanding officers, the ones that have everything under control. I don't really have an answer for you.
Answer: Because the ship was assigned to Sisko/DS9 and wasn't autonomous in the same way other starships were.
Even though the Defiant was designed to be a warship, the project was abandoned and the unfinished prototype had never been put in use. Sisko requests it with the sole purpose of deterring a Dominion attack by showing them that DS9 can defend itself if necessary. The Defiant was a flashy ship with a lot of teeth so Sisko thought he could show they were prepared to defend DS9 if they had to.

SISKO: You'll have complete access to the ship evaluation reports but to put it simply, it's overgunned and overpowered for a ship its size. During battle drills, it nearly tore itself apart when the engines were tested at full capacity.
KIRA: And this is the ship that Starfleet sends us to fight off an attack by the Dominion?
SISKO: We're not going to fight the Dominion, Major. At least, not yet anyway. Our mission is to take the Defiant into the Gamma Quadrant and try to find the leaders of the Dominion, the Founders. We have to convince them that the Federation does not represent a threat to them.
BASHIR: What if they don't believe us?
SISKO: That's why I asked for the Defiant. She may have flaws, but she has teeth, and I want the Dominion to know that we can and will defend ourselves if necessary.
DS9: The Search Part I

Given DS9's strategic value to the Dominion, the Federation (and showrunners, of course) felt that it was ridiculous to expect DS9 to be able to defend itself using only runabouts.

At one point, Robert Wolfe and I were sitting around after the 'Jem'Hadar' episode had been filmed. We were looking at dailies and said, 'Jesus, we're blowing up Galaxy Class starships; these guys are tough, and all we have are these freaking runabouts' [....] We had to come up with a ship to combat [the Dominion]."
Captains' Logs Supplemental - The Unauthorized Guide to the New Trek Voyages, p. 79

The Defiant was intended to complement DS9's fleet of runabouts, giving them a faster, stronger ship to perform away missions and protect DS9 from the Dominion. The show's producers even referred to it as "a beefy runabout." (Star Trek: Deep Space Nine Companion, p. 162)
As such, it made sense to be piloted and operated as an extension of the space station in the same way normal runabouts were.
Comment: @Sekhemty - You're right that the Defiant was built to be a warship but the project was abandoned. The ship was a rough prototype and was never officially finished or commissioned as a warship. It was requested by Sisko for the **purposes** I mentioned above. It's because of that purpose that it'd be considered an addition to the fleet of runabouts and why the producers considered it a "beefy runabout".
Comment: The Defiant was something more than a Runabout+++; the quote that you are citing explicitly states that it was a real warship, not a "super shuttle", and was capable to operate also independently of DS9 (see in example when the Cardassians reconquered the station in the first part of Season 6, or during First Contact); Runabouts couldn't do that. To have the same crew man the Defiant and DS9 more or less makes the same sense as having the Space Shuttle manned by the people at the Space Center in Houston
Comment: @TheIronCheek the project was mothballed at the time, but after the design flaws were worked out, the Defiant class did go into production (one is seen in S6Ep22 "Valiant").
Comment: @Sekhemty don't you mean have the Space Shuttle manned by the same people who man the ISS? Oh wait...
Comment: The Space Shuttles were never "assigned" to the ISS, they were based on Earth; astronauts on the ISS did not use the Shuttle to perform "away mission"
Comment: @TheIronCheek It's been a while since I'we watched DS9, I didn't remember these things. Just to be clear, I've upvoted your great answer, it is just that, even with the producers' words, it still doesn't' make much sense to me that a the station and the ship could not have two crews :)
Comment: @Sekhemty - I actually agree with you. My answer is more about the Defiant's use being consistent with their normal runabout use but I actually think that use in general is a bit bizarre. They cram large chunks of their senior staff into tiny, under-powered shuttles for potentially dangerous away missions for days or weeks at a time, leaving their assigned posts abandoned and vulnerable. It does make more sense to have dedicated botanists, security officers, geologists, diplomats, anthropologists, etc. that go on away missions and let the senior staff manage their intended posts.
Comment: Just a bit more nitpicking (towards the producers): https://i.imgur.com/QoBNnXB.png The Defiant size was comparable more to a ship like USS Voyager rather than a Danube class Runabout
Comment: @Irishpanda - That's true but doesn't change the assignment of the original prototype or the fact that it was a scrapped project when Sisko requested it.
Answer: In universe, the Defiant was a prototype, and consequently rather valuable; the Federation would likely prefer that it be crewed and commanded by only the most trusted personnel.
Defiant was "attached" to DS9 for station defense, and had little in the way of on-board living accommodations, so it makes sense that personnel would come from the station. As the commanding officer of the station as well as one of the ship's designers, it's not a huge leap to imagine Sisko would want to captain her himself.
From S3E9, "Defiant":

SISKO:
              Then bring me with you.  I can help
              you stop the Defiant and prove our
              good faith.  I was in charge of the
              shipyard where the Defiant was
              built... I helped design it.  I know
              her vulnerabilities... her
              weaknesses...

The Defiant would likely make regular patrols of the area but we only see the occasions when Sisko and friends are running the ship; it's not clear if there are other patrols run by other crew members.
Out of universe:
It's where the action is, so that's where some of the main characters are going to be.
Comment: I will add the reference to my answer.
Comment: Obviously an in-universe explanation is desired.
Comment: I think the bit I added in postscript is in-universe. The Defiant wasn't just any little ship. I'll clarify in my answer.
Comment: I don't recall Sisko being one the ship's designers. Do you have a reference for that?
Answer: The Defiant was never originally official, it was simply a means for them to hoist the flag to the Dominion, after it's successful shakedown and re-engineering the ship class was put into production. Given the Defiant's small size and minute crew requirements (less than 50) and the size of the DS9 station complement Defiant makes an "Anchor tenant"; one that can stay at station for the majority of it's time under maintenance and only activated when needed. Defiant is in essence an oversized version of a "Runabout". Unlike other starships whose mission parameters are exploration, cargo/utility, logistics, science, transportation. The Defiant is a warship, real world warships spend most of their time either on patrol, deployment or in drydock/berthed. So there's no reason to give it a new crew when DS9 detachment is ideal.


Should the successful philosopher (one who 'does' philosophy) be concerned with having a good reputation, not with being virtuous (correct)?

Question: Too often people are concerned with their reputation at the expense of intrinsic good--virtue.  Virtue and its relation to happiness should be recognized first, even if it means damage to one's reputation.  Aristotle and Aquinas confirm, "Happiness is man's true good."  But, is a good reputation (admiration by others) the way to true happiness?  Conscience is ordinal.  And, from where does conscience, consciousness derive?  No philosopher or scientist, including the neuro-philosophers have come to anything definitive.  The person, truly wise, is not always that person singularly capable of most clearly and quickly grasping the truth of fundamental or experimental reason or logic; but, it is more prudent to be intuitively correct; and--most of all--better to know, indeed, there is a correct solution.  Consider, 'A' is not non-'A'.  There is truth.  And, truth in either philosophy or science is not a matter of synthetic notion but of recognition.
Comment: Do you expect a different answer for philosophers as opposed to any other moderately academic profession?  Do you expect the answer to be about the ideal, or a pragmatic one given the limitations and challenges of our current reality?
Comment: @Joe: Substitute "revelation" for "recognition." Category I questions live on despite the post-modern attempt to expunge the historic record.  Wittgenstein suffered no "god talk"; but, at the end of his life he asked for Last Rites and a Catholic burial. Metaphysics yet endures. The natural cognition tricotomy of description/explanation/experiment (reasoning from an upper story to the lower, most rational) makes more sense if "revelation" is yet placed in the fourth (highest) story: revelation//description/explanation/experiment. The higher 'story' is the consideration of the Creator.
Comment: Depends on whether they have tenure or not. Publish or perish, you know.
Comment: For what it's worth a recognitional modelling of truth is at the very least controversial; and to my mind acutely reactionary
Answer: Your question is miss-specified. You simply played with words, good and virtuous are synonyms, and you haven't specified the difference or the actor and actions clearly.
Do you mean:
"Should someone who philosophizes (loves wisdom) be concerned with having a good reputation or with being correct?"
And not what you wrote:
"Should the successful philosopher (one who 'does' philosophy) be concerned with having a good reputation, not with being virtuous (correct)?."
If so, the answer is self-evident as it is contained within the definition.
If your concern is with success,  - Should one who successfully loves wisdom be concerned with being correct or having a good reputation? - The answer remains clear by definition.
If you have a different definition of success you must specify.
Comment: "Your question is miss-specified." Isn't this like saying, "You are miss-interested"? Exactly, the answer remains clear by definition... Bro-ther!


In the U.S., are major dental procedures considered tax-deductible?

Question: If someone is going to undergo a major dental/medical procedure ($40k+), is there any way to deduct the money paid for the procedure, or at least part of it?
Comment: Is the procedure in question considered medically advisable or necessary, or is it cosmetic surgery?
Comment: @ChrisW.Rea There are multiple points of infection.  I'm not sure if it's "technically" considered medically advisable.  The person is opting for implants over extraction.
Comment: @David IMHO implants are considered "advisable". Verify with your doctor. I had one covered in full by insurance (which means that it would be tax deductible without the insurance).
Answer: If medical, not cosmetic, you can deduct medical expenses to the extent they exceed 7.5% of your adjusted gross income.
Note: it's been announced that starting in 2013 the deduction is for amounts exceeding 10% of AGI.
Answer: Does your company offer a Medical Savings Account? That can allow you to reduce your taxable income. You normally have to join during "open season".
Another option is Medical and Dental Expenses above 7.5% of your adjusted gross income. This is a high hurdle to meet, and only reduces your taxes by the tax rate x the amount your bills exceed 7.5%
Comment: Unfortunately the open season is closed, and 40k+ is a bit too much to add to the MSA.  Plus, the MSA/HSA max is ~3k, which is far less than the $40k+ that will be paid.


Why do radio waves spread out while higher frequency waves travel in beams?

Question: Why is it that radio waves spread out in proportion to the square of the distance, while higher frequency electromagnetic waves, like microwaves, infrared waves, light, etc are able to propagate as beams?  What fundamental property allows higher energy waves to travel differently than lower energy?
Comment: What makes you think that radio transmissions can not be shaped into a narrow beam?  https://upload.wikimedia.org/wikipedia/commons/e/e4/Green_Bank_100m_diameter_Radio_Telescope.jpg
Answer: Due to diffraction, wave effects become more important as the size of the wave source becomes comparable to the length of the wave.  Visible light has micrometer-scale wavelengths, so a millimeter-sized light source is thousands of wavelengths across and diffraction isn't a very big deal.  But radio wavelengths can be many meters, producing similar collimation for a radio "beam" would require an emitting antenna hundreds or thousands of kilometers across.
You can use the same logic to think about shadows.  A hair that's less than a millimeter across can cast a well-defined shadow, while radio waves diffract around buildings.  However larger objects can cast well-defined radio shadows: for instance astrophysical radio sources disappear when they are covered by the Moon or the Sun, which are both very many wavelengths across.
Note that even "collimated" light undergoes dispersion.
Any sort of focusing optical system will produce a beam waist at some finite distance from the final focusing element (mirror or lens or whatever); beyond that beam waist the intensity of the light falls off like $r^2$ just as if a light source were at that location.  A perfectly collimated beam of light is prohibited by the uncertainty principle, unless the beam is infinitely wide.
Comment: +1, but I slightly disagree with the uncertainty principle comments for reasons discussed in my answer. I'm being a bit pedantic, and I think you're quite within rights to make your comments to an "advanced" audience, but it could be a little confusing to someone sorting these ideas out.
Answer: They all spread out, but generally speaking the directivity of an antenna or emitter (assuming optimal design) is proportional to its volume, in wavelengths cubed. So a tiny high-frequency antenna with a volume of five wavelengths cubed has the same directivity as a huge low-frequency antenna also with a volume of five wavelengths cubed. Of course, other things also affect directivity, like temperature, the particular antenna design, etc. That's why I said "generally speaking".
Comment: What do you mean by the antenna volume? Say, I use a straight wire sticking out up from my walkie-talkie. What is the volume in this case?
Comment: This is NOT a precise or scientific measurement, its a "generally speaking" thing. The volume includes a wavelength, or so, in every dimension (i.e. much of the near field).
Comment: I see. A double linear size antenna ($2^3$ volume) would produce the same directional pattern for a doubled wavelength. Makes sense.
Answer: This is simply a question of the beamwidth relative to the wavelength. Unless the transmitter is extremely big, the broadcast "beam" is less than a wavelength across. A small microwave dish is hundreds or thousands of wavelengths across; thus it acts like a huge phased array. On the other hand, the Very Large Arrays used in astronomy do the same for radiowaves; as transmitters they could form collimated beams and as receivers they are superbly directional. A quantity that yields intuition for the phenomenon is the Rayleigh length:
$$z_R = \frac{\pi\,\mu^2}{4\,\lambda}$$
and this is the axial distance a beam of width $\mu$ (as measured by the $1/e^2$ intensity diameter) must propagate before spreading out to twice its beginning diameter. You can see very easily how my comments about relative width and wavelength size are summed up in this equation. The Rayleigh length applies to Gaussian beams, which spread the least possible amount for a given RMS beamwidth. This last assertion is related to the Heisenberg uncertainty principle insofar that the mathematics that lead to it are the same as those that lead to the Heisenberg uncertainty principle, but I disagree slightly with Rob's answer that this is the uncertainty principle, because we're talking simply about a Fourier transform relationship between the superposition weights in the plane wave decomposition of a propagating field, rather than a Fourier transform between co-ordinate systems wherein conjugate quantum observables are multiplication operators (which, by dint of the Fourier transform relationship, leads to the same mathematics). Perhaps I'm being a little pedantic, but to me the HUP is explicitly about quantum measurement and observables. More on this below.

Further Details
On noting that the modes of the Helmholtz equations are plane waves, we can describe diffraction as a scrambling of the wavefront by dint of the different phase delays undergone by the plane wave components propagating in different directions, as I discuss further in my answer here or this one here. Continuing with this line of thought: Because there is a Fourier transform relationship between the field at a given transverse plane and the superposition weight function for the plane wave decomposition, there is a Heisenberg inequality between a beam's divergence angle and its beamwidth, as measured by the RMS spreads of divergence angle as I discuss here. The minimum uncertainty product is realized by a Gaussian Beam, and one should use the equations that describe this special, minimum uncertainty product case to get insight and intuition into your question. The numerical aperture (half the divergence angle) $\eta$ and beamwidth $\mu$, both measured by $1/e^2$ diameters / cones, are related by:
$$\eta = \frac{2\,\lambda}{\pi\,\mu}$$
Answer: There is another level to the question, and it is to do with the intention or purpose of why the different frequencies were put to use in the first place: but first I freely admit that a lot of the discussion in the excellent answers already given are beyond me.
The direct answer is that radio waves, of MW and HF frequencies, were often deliberately broadcast via omnidirectional antennas for specific reasons.  Therefore of course the reduction in field strength with distance followed an easily understood square law.  The other factor was that it is physically difficult and expensive, though always possible, to beam these lower frequency MW and HF frequencies.  Indeed I worked at a complex of about 850 acres of giant rhombic antennas, necessary to make the "radio waves" into beams in the pre-satellite era, for transmission to the other side of the world, rhombic limitations and "broader" diffraction notwithstanding.
The higher frequencies which can be beamed much more cheaply, also, for practical considerations, do actually need to be beamed in order to keep the received field strength up to a reasonable level at the receiving end, many wavelengths away from the transmitter.
The other advantage of beaming VHF, UHF & microwave, etc, besides the great economy and ease of construction of physically small highly efficient beam antennas, is that diffraction at these frequencies also helps to make the beam narrow, hence a low-powered (and much cheaper) transmitter suffices.
I answer this way because implicit in the question was a suspicion (on my part) that some sorts of electromagnetic waves were somehow deemed "different" to others, which isn't really the case.  The developing history of electromagnetic waves almost demanded that the lower frequencies "had" to be utilised first, with their observed omnidirectional capability in practical use - but that capability was not intrinsic, it had much to do with physical antenna sizes and mechanical limitations - and dare I suggest that that this is also a legitimate answer to the question?


Flashing Lenovo Vibe K5 to Stock ROM

Question: Lenovo Vibe K5 is up and running in CM 13. But, I need to flash stock ROM on it. Now, I have tried to flash with TWRP, but that didn't worked for stock firmwares. I have seen multiple tutorials, in that, they are using QPST and flashing it easily. While I am having problem, because my device shows as non Qualcomm device. It shows as RELINK HS-USB QDLoader instead of Qualcomm HS-USB QDLoader. I have installed the Qualcomm drivers correctly.
Answer: Finally i have done it. So i am sharing with all of you, you should turn off your internet while doing all these steps , because when you press and hold vol up + down button and insert usb cable, it automatically downloads Relink driver because of running internet in the background and even if you uninstall and reinstall those drivers it wouldn't work unless you format it .

Flashing Lenovo Vibe K5 to Stock ROM


One word for 'Uncondition Learning'

Question: 'uncondition learning' refers to forgetting the conditioning, society has given us.
Also suggest related words.
Comment: Could you give an example of "uncondition learning," I'm not familiar with that expression? Have you found anything similar but not quite right for your needs?
Comment: no I haven't found anything similar, from our childhood, we are conditioned to be in our limits, taught not to smoke, drink, avoid dangerous situations, some fear of ghosts and all such emotions and habits which wouldn't be in us if we weren't conditioned. I want some word to represent unlearning that conditioning.
Comment: @Ryan can you think of some word like that?? am i clear enough?
Comment: you want something that would imply or mean undoing of that conditioning. did I get that right?
Comment: yes thats correct @vickyace
Answer: Learned behaviors that are unlearned, or that fade over time are said to be extinguished. This is the term used in psychology and learning theory.
http://www.thefreedictionary.com/extinguished
Answer: Conditioning is a term used in Behaviourism for the habit formation caused by repetition and reinforcement. I reckon Unconditioning must be setting oneself free from all those habits introduced and strengthened by the environment. In educational psychology there is Rote learning VS Meaningful learning but I doubt it if Unconditioning could be called a Learning process; however, it can be a part of it since it involves Change in behaviour. It might just be detachment from those engraved-in-stone and taken-for-granted attitudes. I think "unlearning" might be good.
Answer: here is a phrase: wean off.
it means (often wean someone off) Accustom (someone) to managing without something which they have become dependent on.
examples - I tried to wean him off his superstitions.
we are trying to wean ourselves off going to church.
this is the closest one-word thingamajig I have found "that would roughly imply or connote undoing the conditioned ways."
there are several other phrases: abnegate old ways, renounce conventions, reject customs, repudiate the rules...
you can make your own. that is the beauty of the language.
Answer: For anything that is learned, 'unlearn' is the casual word.
For behaviors that are learned, 'extinguish' is the technical word.
For behaviors that are learned by conditioning (whether conditioned by society or other means), there is no word so specific that it applies uniquely to that. But you could play with 'reprogram' or 'decondition' if you wanted to use it that way for this specific context.

One word for 'Uncondition Learning'


can meditation and dharma alone take us to higher levels of consciousness?

Question: I have been practising dharma and meditation now for more than 2 years and i feel a good progress within me. Does these 2 tools dharma and meditation alone can take us through to different levels of consciousness ?
Comment: If by dharma you mean the Buddhist teachings then I'd suggest that just meditation is enough, since the teachings arise from meditation.
Comment: i feel dhamma is common phenomenon in this spiritual process. Astanga Yoga says about dhamma in the terms of iyama and niyama. I come from Tamil language where tirukural literature talks about dhamma in the terms of aram. i strive to walk in the path of dhamma always.
Comment: @SGN:: clarify what u mean by *dharma* in question? Is it dharma or `dhamma` u r asking for as you strive to walk on dhamma?
Answer: The Dharma alone is the true medicine and it alone can cure us of the unsatisfactoriness of samsara. The Buddhas and Sangha are like the best doctors and nurses in the world and can help guide us in the best way to take the medicine - the Dharma - but it is the medicine alone which actually heals!
Theoretically, if we just take the medicine at the right time, in the right way, in the right amount... we do not need doctors and nurses... the medicine is enough.
Practically, we almost always need good doctors and nurses to help us prescribe and apply the medicine and thus we need to take refuge in the Buddhas and Sangha as well.
This is how it has been explained to me.
Answer: Dhamma:: Right Teachings
Meditation:: Tool to establish in dhamma
Different levels of Consciousness:: Comes when one uses tool to establish in dhamma.
Other tools:: Enable one to be able to use Meditation tool.
Answer: There's doctrine which says that a good friend (perhaps "exemplar") is important too: for example SN 45.2.
Apparently the Buddha, having no-one to take as a role-model, used the Dhamma -- Reference request for "the Buddha takes the Dhamma as his superior"


How do you kill Nilfgaardian soldiers?

Question: In Witcher 3 is it possible to kill the Nilfgaardian soldiers? I killed a level 17 soldier when I was still level 3 in the prologue part (White Orchard). Instead of dying and dropping loot he just stayed there like nothing happened. I also can't target/attack him since. Is it a glitch or..?
Answer: They aren't meant to be killed. In the tutorial area they are there to be designed to teach you not to steal from people while guards are around. If they kill you you just wake up after a while and lose some money, you don't even have to reload a save.
If you kill them they simply "respawn" and go about their day.
Answer: I just killed two of them, couldn't loot anything and one of them just got up again and was permanently hostile. No sense in reducing my weapon's durability if I'm not going to get anything out of it.

How do you kill Nilfgaardian soldiers?


What is a person called who makes history

Question: I am doing homework for a newspaper report about Neil Armstrong and i need a word that means "someone who makes history" or "marking a time in history". Please answer so I get a good grade, really confused right now.
Comment: 'Archetypes' 'forerunners' 'pioneers' 'historical figures' are just a few which would be suitable. Welcome to EL&U.
Answer: You might consider using a word history-maker (history maker)

A person who influences the course of history or does something spectacular or worthy of remembrance.

Definition is from here.

The greatest history makers in our time are not politicians and statesmen, but inventors, entrepreneurs, and others who are transforming the technological base of civilization and whose search for new markets is leading us into a more global economy.

Example is from here.
Comment: Probably the best answer, but probably too obvious to give as an answer.
Comment: @Edwin Ashworth, I totally agree that "Archetype" is a much better answer!
Answer: As suggested,  Archetype:

1 : the original pattern or model of which all things of the same type
  are representations or copies : prototype

… the House of Commons, the archetype of all the representative assemblies which now meet … —Thomas Babington Macaulay

; also : a perfect example

He is the archetype of a successful businessman.

Merriam-Webster


port forward http port (80) on virgin super hub

Question: I am currently working on a project to make my apache server live, which is new me so this is the first time I am doing anything like this. basically I have gone in to the router and  requested port forwarding on port 80 for my local IP address, but to no effect. when I test it with a web tool which tells you if a port is open or not it says it's closed. More confusingly when I run a netstsat -a command it shows http as listening. I'm not sure if its a firewall issue or I'm going about it all wrong. any Ideas would be much appreciated. Thanks
Answer: You need to be testing from outside your local network.  If you run netstat on your server, of course it is going to say "listening".  Is your web testing tool being run from outside your firewall?  You should also be able to turn off wifi on your phone and test hitting your broadband IP address:80.  Are you forwarding from port 80 on your router to port 80 on your server?  Is it possible that your provider is blocking port 80 for residential accounts?
Answer: First google for an online port scanner and ask it to scan port 80.
Second if you're using Ubuntu ufw (firewall) is probably running default deny rules so do this: sudo ufw allow 80
To check it's working just plug your WAN IP into your browser URL bar, it should connect to your test page in /var/www/html/index.html


Is there an algorithm that when given a set of axioms, will generate a statement independent of those axioms?

Question: Is there any mechanism or algorithm where one can generate mathematical statements/problems that are undecidable, i.e their proof is independent, from a certain set of axioms?
Answer: Gödel's original proof in effect delivers just such a recipe for  a theory $T$ which is recursively axiomatized, contains (or can implement) at least the minimal amount arithmetic of arithmetic for the incompleteness theorem to apply, and is (omega) consistent. Of course there are complete theories to which Gödel's theorem doesn't apply (and some of them are non-trivial) But -- leaving aside the inconsistent cases -- these exceptional theories will have to be either theories which can't be effectively axiomatized or theories which know (almost) nothing about arithmetic or anything equivalent.
But assuming we are dealing with the right sort of theory, the construction of a Gödel sentence goes in two stages. We first choose some sensible way of "arithmetizing" the syntax of $T$ (i.e. coding up wffs, and proofs by numbers). [There's a lot of freedom of choice here, and different choices will lead to different sentences unprovable in $T$: so this phase is not deterministically algorithmic.]
Then Gödel tells us how to actually produce a wff $Gdl_T(x, y)$ of $T$ which represents the relation "$x$ codes up a proof of the wff that results from putting the numeral for $y$ for the free variable in a wff with code number $y$" [the details of this wff will depend on both $T$ and the chosen coding scheme, but we can give a recipe for producing the wff]. Then he shows how to construct, very simply, an undecidable Gödel sentence $G_T$ for theory $T$ out of $Gdl_T(x, y)$.
The procedure "choose a coding scheme, then apply the recipe for forming a Gödel sentence" applies quite generally (as Gödel stresses in his original 1931 paper), to construct an undecidable sentence for a given $T$ of the (very general) right kind. If you want more of the gory details, any standard text will tell you how the trick is done. Or look at Episode 9 of my online notes Gödel Without Tears
Comment: @Gregory Nisbet: please don't make minor edits to old posts. It sends them back onto the front page of the site, and makes people think the question is active, only to disappoint when they actually look at it.
Comment: @Carl Sorry, didn't realize it would bump the answer.
Answer: It depends on the set of axioms.
Some theories are complete, meaning that every statement (in the given language) can be proved or disproved from them. For example the theory of algebraically closed fields of characteristics $0$.
Some theories are so complicated that such algorithm will have to make appeals to oracles which can access informations we cannot compute on our own. For example the consequences of $\sf PA$ is not a decidable theory, so we don't have an algorithm to compute it.
The incompleteness theorems give us very specific requirements. The theory $T$ must be:

Recursively enumerable.
Strong enough to interpret basic truth about number theory.
Consistent.

In which case the incompleteness theorem[s] give us a mechanism for writing down a statement which is independent of the theory $T$. If the theory does not fulfill these requirement it might be complete, or it might be inconsistent, or we might not have an algorithm (which doesn't make appeals to oracles).
Answer: Yes you can construct such a sentence. Godel's theorem shows how to do it, provided the axioms are appropriate for such a construction. It doesn't work for a decidable complete theory.
To do this using Godel's sentence, it needs the axioms of arithmetic or some subset of them that's sufficient to do the Godel construction. Robinson's arithmetic is sufficient for instance
You can even build a set of rules for constructing such sentences.
But if you formalize the process for constructing those sentences into a formal system - then that system itself has a Godel sentence that it can't construct. And again as a human mathematician using the approach of Godel's theorem you can construct a sentence for that too. But in some sense there has to be a possibility for endless creativity in constructing such sentences.
You can't derive an algorithm to derive all and only true Godel sentences from a theory. If you attempt to do so, it could be made into the basis for a set of deduction rules that you can then use Godel's method to find a sentence it can't produce.
Comment: If the theory is complete it doesn't have a Godel sentence. To have it, it needs the axioms of arithmetic or some subset of them that's sufficient to do the Godel construction. Robinson's arithmetic is sufficient for instance https://en.wikipedia.org/wiki/Robinson_arithmetic
Comment: Oh I see. Oh right then yes, that's correct.
Comment: Just edited it to say this  - thanks!


Apply free shipping coupon code only for spefic shipping method

Question: in project i have two different custom shipping method one for 8 to 15 days delivery and 2 to 4 days delivery.
i have create coupon code for free shipping but i want to allow free shipping coupon code to only  8 to 15 days shipping method.
please help.
Answer: Magento Provide Shipping Method condition it self,
You need to select that shipping method into condition section, For which you want to generate coupen code.
See the screen-sort.
Comment: this will not work for me bcz i am using table rate shipping method and i have create module for custom table rate shipping method
Comment: you can change your custom module development, So that method avilable into this list, so you can select that.
Comment: ok i am trying that one
Comment: Above answer help please accept, so other can get help in community.
Answer: You can change code in your carrier model file  collectRates function check coupon code is applied or not from calling quote object and set custom price if your 8 to 15 days delivery method available and set 0 price for free shipping .
you can get a coupon code from quote object from here

$quote  = $this->session->getQuote();

$address = $quote->getShippingAddress();

$shippingaddress    = $quote->getShippingAddress()->getData();

$coupon     = $quote->getCouponCode();

Before apply this code you have to declare session in construct method like this

protected $session;

public function __construct(

\Magento\Checkout\Model\Session $session, ) {

$this->session = $session;

}

after then you get quote data from session in magento 2.


If you were on a planet orbiting a star that has a black hole companion, could you see light from your host star bent 180 degrees?

Question: I realize that there is a distance from a black hole where photons can orbit. I understand that this orbit is very unstable, but I am concerned with photons just outside this range. Could the black hole cause them to 'u-turn' so that you could see some light from your star when looking at the black hole?
Comment: Related: https://astronomy.stackexchange.com/a/49874/16685 Also see https://physics.stackexchange.com/a/766180/123208
Comment: Oops! I just fixed a typo in the `b` value for 180° deflection in that Physics.SE answer. https://i.stack.imgur.com/LsG0C.png Here are more precise values of those parameters: b = 2.678479315370894344, delta = 0.080403104017578404, r = 1.760308981575963230
Comment: @PM2ring I confirm those numbers. They are also interesting because they represent the maximum radius of a neutron star that you would be able to see the whole surface of in one go. (For the same reason).  https://physics.stackexchange.com/a/350814/43351
Answer: The answer is yes.
Roughly speaking, for a spinless Schwarzschild black hole, light that gets to a closest approach to the black hole of just a little greater than $1.5 r_s$, where $r_s$ is the Schwarzschild radius, can be bent through any angle. The closer the closest approach is to $1.5 r_s$ the bigger the angle becomes, and the light can even loop around the black hole more than once. A 180 degree deflection is caused when inwardly directed light from far away passes a black hole at a closest approach of $1.76r_s$ - see https://physics.stackexchange.com/questions/766132/would-someone-falling-into-or-orbiting-a-black-hole-see-themselves .
Viewing this spectacle from a distance much larger than $r_s$, an observer would see the black hole surrounded by a ring of light that is heading towards them after being bent around the black hole. The apparent radius of this ring would be just a little larger than $3\sqrt{3}r_s/2$.
Comment: also related in Physics SE: [Could a trajectory around a large mass ever deflect by more than 180 degrees due to general relativistic effects?](https://physics.stackexchange.com/q/467144/83380) (thought it asks about a particle's trajectory rather than light)
Comment: The movie *Interstellar* famously paid for actual astrophysicists to do a real physics simulation of light paths to generate the famous black hole image that looks like it's wearing a hat, which shows how you can see every part of the accretion disc due to the bizarre light bending that's going on.  It's not exactly a companion star's light but I think it does a good job of showing that no matter which direction it comes from, the light can reach you where you are. Of course the amount of light that reaches any given observer would be tiny compared to the incident light.
Comment: OK, now I want someone to create a video of life on a planet orbiting at 1 AU around a G2 star orbiting a super massive black hole at 1.76 r_s, where r_s is about 4 AU (or 1 AU is about 1/4 r_s). (The black hole would need to have a mass of a little over 200,000,000 solar masses.) Bah, just realized that the hypothetical planet would be _well_ outside the star's Hill sphere. I'll have to dream up another example...


Whether a given algebra is the algebra of endomorphisms for a vector space.

Question: Let $\mathbb{F}$ be a field and let $A$ be an associative unital $\mathbb{F}$-algebra. Is there a criterion to let me know if $A$ is isomorphic to the algebra $\mbox{End}(\mathbf{V})$ of endomorphisms for some $\mathbb{F}$-vector space $\mathbf{V}$? Generalizations to $A$ being an associative unital ring and $\mathbf{V}$ an Abelian group or similar are welcome. Answers for particular cases $\mathbb{F}\in\{\mathbb{R},\mathbb{C}\}$ are also appreciated. Thank you.
Answer: According to this paper:
BRENNER, S. AND BUTLER, M. C. R., Endomorphism rings of vector spaces and
torsion-free Abelian groups. J. London Math. Sot. $40 (1965), 183-187.$
Every unital associative algebra, E, can be represented as the algebra $\epsilon( U; \mathbb{K})$ of endomorphisms of a vector space $U$ which leave invariant each member of a set $\mathbb{K}$ of distinct proper subspaces of $U$. (The base field $\phi$ is the same for $U$ as for $E$.) This result was proved by constructing a representation of $E$ with $\dim U = 2 \dim E$ and the cardinal |$\mathbb{K}$| of $\mathbb{K}$ equal to $\gamma + 3$, where $\gamma$ is the cardinal of a set of generators of $E$.
Comment: This is interesting, but I don't think it really answers the question. You should post it as a comment (although you are not able to post comments on other people's posts yet). Does the paper indicate in any way when you can take $\Bbb K$ empty? On the face of it, the construction you are describing will never be able to do that.


what あびて means?

Question: Can someone tell me what "あびて" means? i'm trying to read japanese novel "ムーミン谷の冬" and there is sentence "でも, 月の光をあびて, 雪がきれいな青い色に光っていました." I think i understand everything else but not "あびて". Thank you for the answer!
Comment: Well my language is Finnish, but if i translate it into English it would be something like " But the light of the moon ______, the snow shone in a beautiful blueish/blue color." i'm sorry, i'm just a beginner and i'm studying japanese with two different language.
Comment: What is your translation of the rest of the sentence? It helps us if we can judge what your current abilities are. If I said あびて is the te-form of the verb 浴びる does that makes sense?
Answer:
月の光をあびて, 雪がきれいな青い色に光っていました。

This あびて is the te-form of the verb 浴びる, meaning "to bathe in" etc. I don't know how familiar you are with the te-form, but it can have many different functions. In this case it adverbially modifies the verb 光る.  I would translate this sentence as:

Being bathed in moonlight, the snow glittered with a pretty blue colour.

what あびて means?


Spatial graphing, distribution of polygon area over latitudes

Question: Given a polygon in a PostGIS database, what is the best way to create a graph of its distribution over a range of latitudes? I'm picturing a graph of a curve, where the proportion of the total area under the curve that lies between two points on the x-axis (latitude) represents the proportion of the polygon's area between those latitudes. The tools I have at my disposal are PostGIS and R. It seems like this should be a fairly routine exercise for which there are well established approaches that I simply haven't been able to find.
Comment: Create a number of horizontal (or vertical?) slice rectangles that span your polygon. Give each one a latitude attribute. Then do an ST_overlay or ST_union or something, so that your polygon is sliced. Then compute the area of each slice. Would that do it? I've put this in a comment due to vagueness...
Comment: A simple modification of the line-sweep algorithm at http://gis.stackexchange.com/a/33449/664 will do it: you only have to compute the length of the intersection of the sweep line with the polygon at each event, provided you use an cylindrical equal-area projection. The result will be the density function; integrating that will give the requested cumulative function.
Answer: OKay, here in an answer, some R code - uses rgeos, sp:
For p = a single SpatialPolygon or single row of a SpatialPolygonsDataFrame:
slice <- function(p,n=20){
  bb = bbox(p)
  ys = seq(bb[2,1],bb[2,2],len=n)
  ll = list()
  for(s in 1:(n-1)){
    ll[[s]] = Polygons(list(
        Polygon(cbind(
                      c(bb[1,1],bb[1,2],bb[1,2],bb[1,1],bb[1,1]),
                      c(ys[s],ys[s],ys[s+1],ys[s+1],ys[s])))),s)
  }
  SpatialPolygons(ll)
}

where n=number of slices, returns n rectangular slice polygons. Now overlay:
lls = slice(p,40)
ii = gIntersection(p,lls,byid=TRUE)
plot(ii)

should show you the slices. Now get the areas:
a = sapply(slot(ii,"polygons"),slot,"area")

I'm just not sure how correct that will be if the polygons have holes in them. Try some tests first.
Comment: Thanks, that looks like it might work. I just installed rgeos and I'll post back when I have a chance to try it out, unfortunately it might be a few days or more.


How can I turn the outline of this into a path?

Question: I have a profile picture which I have attatched to this post, I want to turn the most major of those white outlines into a path so I can import it into after effects and add some animated neon glow. Problem is, I am horrible at using the pen tool so manually creating a path with that isn't an option. Could I get some help?
Comment: A) There's no picture in your question and B) We're generally happy to help, but more clarity wouldn't hurt. No one is going to create an editable file for you.
Comment: @user287001 The OP says "I have a profile picture which I have attached to this post". It doesn't say the users profile is the picture in question. I think we need clarification here before anything can proceed.
Comment: The question is clear, but the resolution of these white lines https://i.stack.imgur.com/Dyh7o.png is poor and they are so dense that anything which looks acceptable for me needs so much manual fine tuning that as well you practice with the pen so that you become able to redraw the image. Do you perhaps have a high resolution version?
Comment: @user287001 - is that the OPs image they forgot to post?
Comment: Forgot???  It has been there all the time. It's a little difficult to see, but you find it easily  if you see texts Maple38 1 New contributor. It's the profile image as he said.
Comment: I have learned that often people seem to behave in an obscure way and the obscurity is only between my ears. I saw others have already approached this case like I often do, so let's explore another possibility.
Comment: Added the profile image. Also the one I uploaded is only 512x512 because the file size would be too big otherwise, but I have a way higher resolution copy too.
Answer: The new version of your profile image has substantially higher resolution than the stamp with your profile name below the question. The Black&White mixer in Photoshop's adjustments + some contrast boost with curves helped to separate these white lines:

There are still holes because here and there the white was covered by about the same green and blue as the main colors of the image. To convert it to path automatically means tracing it in a vector graphics program like Illustrator or Inkscape or other.
It's generally useful to start tracing attempts from the original, because all preprocessing like converting to BW finally removes information, no matter it may look cleaner.
I pasted your colored image to Inkscape and tried to find a good treshold for tracing as single scan black and white. The result (original is closed in the objects panel):

The white is a hole, because Inkcape thinks white is background, but Boolean operation Path > Difference from a solid red rectangle gave the original lines as red (can be any color) areas:

Activating the node editing tool shows the nodes:

The shape is quite a complex compound path. There's no strokes, only filled areas. But absolutely it is a path as you said you want.
If it happens that you want it as single stroke paths with no filled areas I can recommend only manual tracing. Illustrator and Inkscape have centerline tracing, but they are too dumb to make it right. You'd need so much editing that you as well could trace it manually (=draw on the raster image)
In Inkscape you only click with the pen and then mostly push and pull the curve with the node tool to the wanted forms. There's very rarely a need to drag the Bezier handles, but you may need to delete an excessive node or insert or move one. In Illustrator the manual tracing process is a little trickier, but it's manageable also there.
An opinion: Trying complex path editing in Photoshop or other bitmap image editors is a form of masochism. Their tools are not made for it.
If you decide to trace it manually you may also want the drawn paths to have nicely tapering widths (=resembling brush strokes made by an artist with steady hands). Both Illustrator and Inkscape offer several tools to convert constant width strokes to tapered ones. Just to show what I mean I have inserted in Inkscape one path with a constant width stroke (=blue) and 2 red paths with path effect Power Stroke. They have adjusted taperings.

The variable widths as path effects (or art bushes or width tool effects in Adobe Illustrator) have a drawback: Other programs do not understand them except as expanded to paths. But then the lines are again filled areas and the idea to have simple single stroke paths is lost. Unfortunately I do not have Adobe After Effects nor couldn't use it productively if I had one. It's surely useful to check if AE understands non-uniform width strokes from Illustrator.
Comment: I think he wants centerline tracing.
Comment: I have thought that wish is possible and suggested doing it manually. Automatic tools I have met are so dumb that the result needs more editing work than redrawing all paths manually on the raster image.


REGEX: Capture Filename from URL without file extension

Question: I am trying to create a Javascript Regex that captures the filename without the file extension.  I have read the other posts here and 'goto this page: http://gunblad3.blogspot.com/2008/05/uri-url-parsing.html' seems to be the default answer. This doesn't seem to do the job for me.  So here is how I'm trying to get the regex to work:

Find the last forward slash '/' in the subject string.
Capture everything between that slash and the next period.

The closest I could get was : /([^/]).\w$  Which on the string 'http://example.com/index.htm' exec() would capture /index.htm and index.
I need this to only capture index.
Answer: var url = "http://example.com/index.htm";
var filename = url.match(/([^\/]+)(?=\.\w+$)/)[0];

Let's go through the regular expression:
[^\/]+    # one or more character that isn't a slash
(?=       # open a positive lookahead assertion
  \.      # a literal dot character
  \w+     # one or more word characters
  $       # end of string boundary
)         # end of the lookahead

This expression will collect all characters that aren't a slash that are immediately followed (thanks to the lookahead) by an extension and the end of the string -- or, in other words, everything after the last slash and until the extension.
Alternately, you can do this without regular expressions altogether, by finding the position of the last / and the last . using lastIndexOf and getting a substring between those points:
var url = "http://example.com/index.htm";
var filename = url.substring(url.lastIndexOf("/") + 1, url.lastIndexOf("."));

Comment: This solution fails on filenames with multiple periods, if you need that test see @BGerrissen's solution.
Answer: tested and works, even for pages without file extension.
var re = /([\w\d_-]*)\.?[^\\\/]*$/i;

var url = "http://stackoverflow.com/questions/3671522/regex-capture-filename-from-url-without-file-extention";
alert(url.match(re)[1]); // 'regex-capture-filename-from-url-without-file-extention'

url = 'http://gunblad3.blogspot.com/2008/05/uri-url-parsing.html';
alert(url.match(re)[1]); // 'uri-url-parsing'

([\w\d_-]*) get a string containing letters, digits, underscores or hyphens.
\.? perhaps the string is followed by a period.
[^\\\/]*$ but certainly not followed by a slash or backslash till the very end.
/i oh yeh, ignore case.
Comment: This also captures filenames that have multiple periods, the accepted answer fails on those. (foo.global.js, etc.).
Answer: I did not find any of the answers to be near robust enough.  Here is my solution.
function getFileName(url, includeExtension) {
    var matches = url && typeof url.match === "function" && url.match(/\/?([^/.]*)\.?([^/]*)$/);
    if (!matches)
        return null;

    if (includeExtension && matches.length > 2 && matches[2]) {
        return matches.slice(1).join(".");
    }
    return matches[1];
}

var url = "http://example.com/index.htm";
var filename = getFileName(url);
// index
filename = getFileName(url, true);
// index.htm

url = "index.htm";
filename = getFileName(url);
// index
filename = getFileName(url, true);
// index.htm

// BGerrissen's examples
url = "http://stackoverflow.com/questions/3671522/regex-capture-filename-from-url-without-file-extention";
filename = getFileName(url);
// regex-capture-filename-from-url-without-file-extention
filename = getFileName(url, true);
// regex-capture-filename-from-url-without-file-extention

url = "http://gunblad3.blogspot.com/2008/05/uri-url-parsing.html";
filename = getFileName(url);
// uri-url-parsing
filename = getFileName(url, true);
// uri-url-parsing.html

// BGerrissen fails
url = "http://gunblad3.blogspot.com/2008/05/uri%20url-parsing.html";
filename = getFileName(url);
// uri%20url-parsing
filename = getFileName(url, true);
// uri%20url-parsing.html

// George Pantazis multiple dots
url = "http://gunblad3.blogspot.com/2008/05/foo.global.js";
filename = getFileName(url);
// foo
filename = getFileName(url, true);
// foo.global.js

// Fringe cases
url = {};
filename = getFileName(url);
// null
url = null;
filename = getFileName(url);
// null

To fit with the original question, the default behavior is to exclude the extension, but that can easily be reversed.
Answer: You can try this regex :
([^/]*)\.[^.]*$

Answer: Try this regex. It can even handle filenames with multiple periods.
(?<=\/)[^\/]*(?=\.\w+$)


Is particle entanglement a binary property?

Question: Is the particle entanglement a boolean property? That is, when we consider two given particles, is the answer to the question "are they entangled" always either "yes" or "no" (or, of course, "we are not sure if it's yes or no")? Is there such thing as partial entanglement?
Answer: No, it's not a Boolean property. Entanglement between two quantum systems (could be particles, or anything else) could be partial, and can be quantified using different measures. In the specific example of Bell states, the two systems (each of them with 2 states $|0\rangle$ and $|1\rangle$) are said to be maximally entangled with the entanglement entropy being 1 qubit.
Comment: But without involving multi-particle systems, ie can two photons be partially entangled? Any reference to an experiment where this is achieved?
Comment: @Passiday, two photons *are* a mutli-particle system. More generally, if two particles are entangled, then you have to describe them as a two-particle system.
Comment: I think @Passiday means to ask if _each_ system needs to be multiparticle. If that's the question: There is no such requirement. _Any_ quantum system will do and two or more of them can be entangled. Recall that in quantum mechanics, even a single particle system has multiple states (2 possible photon polarizations, Spin up/down, the many levels of a harmonic oscillator or particle in a box, etc.)
Comment: Yes, I meant the simplest possible particle interaction. Ok, so, let's say, two photon entanglement entropy can be 0.5. Doest that mean that in 50% of measurements, the two such entangled photons behave as fully (=1) entangled?
Comment: @Passiday : No, photons are, or are not, entangled. This has nothing to do with measurements. If you want to have a measure of entanglement for a 2-photon state like $a|0>|0> + b|0>|1> + c|1>|0> + d|1>|1> $, you could use $E = 2* \frac{|ad - bc|}{(a^2 +b^2 + c^2 + d^2)} $. For instance, the state $$|0>|0> + |1>|1> $$ is maximally entangled and has $E = 1$
Answer: Yes, the answer is always either yes or no. Being entangled means that they are not in a separable state. A state is called separable if and only if it can be written in the form $\rho = \sum_i p_i \rho_i^A \otimes \rho_i^B$, where $\rho_i^A$ refer to the state of particle $A$ and $\rho_i^B$ to $B$. This is always either the case or not the case, regardless of how much entanglement precisely we assign to the two particles. All standard entanglement measures satisfy the property that $\rho$ is entangled if and only if $E(\rho) > 0$ (ie. $E(\rho)=0$ for all separable states).
To find out whether given two particles are entangled, people have developed procedures known as entanglement witnesses, and research into the entanglement witnesses has formed a sub-discipline in quantum information theory. Bell inequalities can also be thought of as entanglement witnesses since their violation implies the presence of entanglement.
Comment: Ok, but once the E(ro) is greater than zero, it can be of any value up to 1. Essentially, it is a continuous value characterizing state of entanglement between A and B. The entanglement-ness becomes a yes/no property only because we define it with boolean expression (E(ro) > 0).
Comment: It's the other way around. Entanglement measures are defined so that they are $E(\rho)>0$ if and only if the state $\rho$ is entangled. There are also many measures of entanglement. The form a separable state takes, however, was defined decades before the measures of entanglement were developed. For a nice review I recommend reading http://arxiv.org/abs/quant-ph/0504163


Determining if polygon falls within another polygon using QGIS?

Question: How can I determine if a certain polygon falls within another separate polygon using QGIS?
Comment: Welcome to GIS SE!  As a new user be sure to take the [Tour] to learn about our focussed Q&A format.  Please decide which of the GIS products mentioned you want to ask about.  By asking about more than one you are effectively asking multiple questions which goes against the [Tour]. You should then describe not just what you want to do, but precisely what you have tried and where you are stuck trying that.
Answer: Another option is to use the Spatial Query tool from the Vector menu.

Enter your source layer & reference/ intersect layer, and specify "within" as the criterion. If you want to only run the query using selected features of either layer, select these before running the query.

If you wish, you can then use the button shown below to create a new layer from the resulting selection.

The new layer is then added to the table of contents window. You can then right click on the layer name and "save as" if desired.
Answer: Add your polygon layers and then go to Vector>Research Tools>Select By Location.  Set your parameters accordingly and make sure to check the 'Within' box for the Geometric predicate, and run it.


How can I find out how much toner is left in my printer, which is connected to an Airport Express via USB?

Question: My Samsung ML-2850D printer is connected via USB to an Airport Express. I print to it from my Mac over WiFi. I want to check how much toner is left, so I know if I need to purchase a new cartridge soon. However, when I check the Supply Levels via system preferences, it says "Information Not Available." What is the best way to reliably find out how much toner is left?
Answer: Attaching a printer using Airport does not provide the same capabilities as attaching through USB, and one of the things that will not work is querying the printer for paper/ink levels etc.
When you have the printer attached locally, the driver has the ability to talk over USB for lots of things, including these services, reading from a card reader that may be on the printer etc.  Once the printer is made wireless, these facilities are lost, and it effectively just becomes a dumb queue that you can drop a print into.  About the only feedback it can give is if the printer is offline or not.  If your printer is multifunction, you'll likewise lose the scanning/fax stuff also.
So unfortunately the only way is to hit up the printer direct, walk on over there and take a peek.
Comment: Sure, possibility isn't the issue really, it's whether doing it over USB via an Airport Extreme will yield results for this particular printer.
Comment: It has nothing to do with the airport, and everything to do with the USB protocol.  USB printers are designed as local printers, with a 1:1 relationship to the host OS it is attached to.  Whilst they can be networked via an AE for example, this effectively is merely acheived by turning them into a dumb queue which will accept prints and simple commands like "delete from queue" etc.  Anything further requires  more advanced network print compatability to be baked into the printer, much like your LaserJets, which are designed for multi user and network sharing.
Comment: I can't see any reason this should not be possible. I can check the toner levels on my networked 1998 HP laserjet.
Comment: Ok, wow, The Airport sucks.
Comment: Not sure why this old post comes up as active today, but I don't think that's correct. It works fine with my Canon iP4500 and Airport Extreme. It must depend on whether the manufacturer bothered to implement it or not.