Do State-of-the-art and Cutting edge have the same meaning?

Question: Do state-of-the-art and cutting edge mean the same thing or do they have different meanings? If they have different meanings, which is used when?
Comment: (There's also the phrase *bleeding edge*, which connotes something even ... edgier? ... than *cutting edge*. Again, these shades of meaning derive from the imagery employed: certainly something which has *blood* on it is both super sharp and very *risky*.)
Comment: I am not a native speaker of English, so please excuse me for grammatical mistakes,punctuation mistakes etc.
Comment: There is no sharp distinction here, but just based on the metaphor, one could argue CE is somewhat more advanced than SotA, albeit riskier. The phrase SotA describes the best *generally available* technology; where the world has advanced to, to date. By contrast, the metaphor CE evokes the image of the sharp, extreme *edge* of the knife. The outermost perimeter. In my mind this conjures notions of extremity and therefore experimental, less well-established (and therefore riskier) technology. By way of example: I'd happy take a SotA medical treatment .... less so a CE one.
Comment: As stated, the meanings are slightly different. "State of the art" is the best and most recent of well-established practice.  "Cutting edge" implies something that is not yet well-established and hence may not work right or may be completely discarded for something better before it achieves "state of the art" status.
Comment: It seems to me that a craftsman might produce a manually operated butter churn whose high-quality materials, sturdy design, and adoption of the best features of various nineteenth-century models qualified it as "state of the art" ("best of breed," as some technology magazines put it) today, without its being in any practical sense "cutting edge" ("ahead of the competition in technology or design").
Answer: "State of the art" is used to describe the best in the specified field.
"Cutting edge" is the newest, and mostly likely still has problems to be worked out.
Answer: 'State-of-the-art' is 'the best already produced', something that is the best and implemented. The term usually describes a product.
'Cutting edge' is 'leading', latest trend and achievement. The term is used to describe technology.
Answer: "state-of-the-art": the latest and most sophisticated or advanced stage of a technology, art, or science.
"cutting edge": the leading position in any field; forefront
They can be used interchangeably in most circumstances, but the difference is "State of the art" is generally the most advanced of all the technology, while "cutting edge" would connotate brand new technology.


Can I use pressure-treated 2x2 posts as a base for an aluminum arbor?

Question: I plan on building an arbor with 2" square, white, tubing ( the sort used for screen rooms).
I read that aluminum should not be set in concrete. What if is used 2" X 2" PT wood set in concrete and put the aluminum post over them?
Any comments appreciated
Answer: Wood that thin doesn't offer much in the way of strength or stiffness. Even if you built your arbor as a completely self-supporting structure and only needed the posts to anchor it, 2x2s would offer relatively little in the way of storm resistance, for example.
A better approach is to design your arbor so that it's self-supporting and rigid, and mount stainless steel brackets to the slab using suitable anchors. Your arbor's legs would attach to the brackets. They won't offer torsional stiffness, but they'll keep the arbor in place.
You could also embed pipes in the slab, into which you'd insert your aluminum legs. These could be PVC. You'd then use shims to secure the legs of your arbor into them. The pipes should be open at the bottom with a drainage basin of sand or washed rock.
Answer:
First: Answers are the goal here not comments. Please phrase your post to have a clear question that can be answered, not just say "Any comments appreciated"

2x2 ( 1 1/2" x 1 1/2" ) are not very strong. Cladding them with metal will trap moisture.
Two suggestions.
1: Use steel in the ground, ( square post anchor ) stubbed out just above ground level like stop signs, and slip the aluminum over or into the steel and bolt it on.

2: Use the expanding foam products that are now available to replace concrete for fence post installation. The one website i looked at said it could be used with "metal".  Do some research.


Using Wolfram to Play Functions

Question: As a blind person, I am curious as to whether or not I can use Wolfram to play functions. For example, if I were to plugg in y = x squared from -10 to 10, I would expect to hear a decreasing tone as the function flattens out, then a normal tone at the origin, then tones of increasing pitch as the function moves towards positive infinity.
Answer: Using the play function and sine you can create a function that does what you want mostly ( using amplitude instead of frequency).
sinPlay[f_, { start_, end_},  baseFreq_] := EmitSound[ Play[Sin[x *baseFreq]* f[x], {x,start,end}]]

This function maps the height of the function to amplitude. Note that because it scales sound to from silence to moderately loud, y=1 sounds the same as y=5, likewise y=2x sound the same as y=5x.
It is called like this (the x^2 function):
sinPlay[#*#  &, { 0, 2}, 1000]

#*# & is an anonymous function (into to them) that takes one number and squares it. {0, 2} is the part of the function you want to listen to in seconds. So {0, 2} generates a two second clip.
This is the square root function:
sinPlay[Sqrt[#] &, { 0,10}, 1000]

And this is the sine function:
sinPlay[Sin[#] &, { 0,10}, 1000]

Note the silence is because those are bottoms of the sine function which have been scaled to silence.
Using Frequency Instead
In theory is would be possible to use frequency instead. The function would look something like this:
 sinPlay[f_, { start_, end_},  baseFreq_] := EmitSound[ Play[Sin[x *baseFreq* f[x]], {x,start,end}]]

But then changes in frequency would also cause changes in time from the sine function. Perhaps something could be done using derivatives to fix this problem, but I have haven't worked it out. Wolfram supplies a function to calculate derivatives for you
Answer: You may use Play.  However, you would not get much of a sound with that function.  You should try a sine or cosine function to start.
Comment: Would it then be possible to track the function based on the codomain and change the pitch of the sound as the values change? I.e. higher tones for going up the y axis, lower for going below zero to negative infinity?

Using Wolfram to Play Functions


How long do I need to be in my country for a B2 visa?

Question: I have a question. I spent 6 months in New York City and I came back to my country. I can travel for 10 years. How long do I need to stay in my country before I can come back to NYC? Is 1 month enough?
Comment: Not exactly a duplicate, but the answers to the following question answer your question as well: https://travel.stackexchange.com/questions/67415/is-leaving-the-us-for-a-couple-of-days-enough-to-get-another-3-months-in-the-cou
Comment: It's essentially up to the discretion of the immigration officer.  If you come back a month later for a two-day visit, they're much more likely to let you in than if you come back a month later for another six-month visit.
Answer: There is no specifically stated limit as far as how long you have to stay out of the US before returning - by the letter of the law you could stay out for 1 day (or even 1 hour) and then return.
However your re-admission to the USA is at the discretion of the immigration officers - even though you have a Visa they have no need to admit you to the country.  If they believe you are attempting to either "live" or "work" in the US, then you can expect to be refused entry, or at a minimum granted a shorter stay than the allowed 6 months.
The general rule of thumb is that you must spend as much time out of the country as you have spent in the country.  So if you've been in the country for 6 months, then you should spend 6 months out of the country.  That said, this is NOT a law, just a rule of thumb, so it will depend on the exact situation.  For example, if you can show proof that you will only be in the US for 2 weeks on your second stay then there is a higher chance of being readmitted than if you were planning to stay another 6 months.
Regardless of how long you are out of the country, be ready to answer a number of questions about what you did in the US on your previous stay, what you intend to do on your next stay, and how you are funding your time in the US.


Order/disorder and complexity

Question: What is the relation between order/disorder and complexity ? Sometimes I found the terms confusing and ambiguous.
And higher entropy implies low complexity, does not implies low entropy implies higher complexity.
Comment: See e.g. [Complexity](https://en.wikipedia.org/wiki/Complexity)
Answer: What I think others miss here is that entropy has a precise, exact definition relative to models of physical phenomena. Indeed, the answer by CriglCragl seems flatly wrong on the basis of my statistical mechanics classes.
Entropy is defined in a thermodynamic contexts: ones where the interesting "motion" your physics studies is primarily not that of individual particles but of a very large number of particles as a whole, and the changes in aggregate quantities characterizing the collective behavior of the system (opposed to the variables characterizing the individual behavior of the particles). Of course, the collective is composed of parts, but there is information about the parts that is irrelevant to the behavior of the whole (particle 2 is at position P at time t), and information about the whole that is not informative or even well-defined for any one of its parts (the standard deviation of the velocities of particles in the system is 0.3 m/s).
This dichotomy is expressed in the notion of a microstate in contrast to a macrostate: the former is a particular configuration of a system, with omniscient knowledge of individual behavior of all particles it's comprised of, whereas the latter is a particular configuration of a system with respect only to its collective behavior. Exactly what a microstate is is a matter of the ambient physical theory: in classical mechanics, a microstate is a particular choice of every degree of freedom of every particle in the system; in quantum mechanics, it'd be the composite wavefunction of every system. A macrostate is simply all microstates that are "macroscopically the same," according to some particular macroscopically-measurable quantity (usually total internal energy).
The entropy of such a system, is a specific, well-defined, number that measures how many microstates could have caused a particular macrostate: in general, it is defined to be proportional to the sum of the product of the probability that a particular microstate is occupied with the logarithm of the same (really, Stack Exchange Philosophy, no MathJax? How is any good philosophy to be done without LaTeX?). In systems where all microstates are equally probable, and there are a finite number of total states, this can be simply expressed as being proportional to the logarithm of the number of microstates per macrostate.
How does this correspond to the colloquial notion (using Gibbs' neologism: "mixedupness")? Well, taking the multiplicity definition, system energies with fewer possible microstate configurations tend to have all particles congregating in a particular state (e.g. "all particles stopped," "all particles moving at 5 m/s equally-spaced along the circumference of a 1-meter-radius circle") that seems heuristically "more ordered." Precisely: high-entropy states yield less information about their microscopic configuration than low-energy ones (which leads to Shannon's definition in information theory). A high-school chemistry teacher, to shut up my foundational questions, once defined it as "local, spatial homogeneity;" this is not a definition of any sort, but clarifies how the colloquial notion tends to present itself in practice.
Many intuitions at this level tend to break down. I'm not sure of counterexample systems to the "disorder = high-entropy" notion, but an instructive one comes in the case of temperature: once one defines temperature in terms of entropy, there exist negative-temperature systems that are hotter than any known systems. Since the notion of "disorder" is indeed poorly-specified, I don't know how to search for such an example, though.
Answer: We consistently find that complex dynamics occur at points between a system being at the high entropy end of it's options, and the low end. Like when you mix cream into coffee, it's the intermediate state before full mixing has occurred that you get interesting swirls. Discussed here: How can nature without self-awareness and intelligence create living beings with self-awareness and intelligence?
Entropy is an interesting topic, not so much because it is difficult, but because it challenges our intuitions and requires scrupulous and clear thinking to interpret in practice. For instance, even many physicists think of entropy as a property a system has, but it's actually relative, a system only has an increase or decrease relative to itself at a different time. This is important because not all the dynamics of a system may be visible, for instance at a given energy level.
Order, disorder and complexity, are ordinary words with intuitive meanings in ordinary conversation. But in physics, they have proved key to thinking about thermodynamics, and the arrow of time, and complexity and chaos have special more precise definitions in their own theories, and have helped lead to the powerful idea of emergence, and of emergent dynamics.
See
How does entropy explain consciousness and the forward direction of time?
Have philosophers speculated on how chaotic forces meeting together can result in order?
Why is a measured true value "TRUE"? (about Shannon or signal/message entropy)
Answer: I'm no good at math, but I feel I can convey the meanings of the pairs order-disorder and simplicity-complexity via numbers.

Order: 1, 2, 3, 4, 5, ... There's some kinda rule that determines this sequence (+1 in this case). We're able to, if you notice, predict the next number.

Disorder: 3, 2.0073, -3089, ... ? Randomness essentially. We can't predict the next number in the sequence

Simplicity: The sequence in 1 (vide supra) is simple (just add 1 to the preceding number)

Complexity: What about a sequence such that the nth term, Tn = (n^2 + 3^(n + nth prime)/(sqrt(2.3078 + ((n + 2/n)th Fibonacci number)
Answer:
And Higher entropy implies low complexity, does not implies low entropy implies higher complexity.

I think @MarcoOcram has provided a clear distinction between order/disorder andsimplicity/complexity pairs. However, the entropy refers to neither of them, but rather to certainty/uncertainty - where high/low entropy means respectively high/low level of uncertainty. Information results from the reduction of uncertainty - it is the negative entropy.
E.g., if I have tossed a coin, without showing you whether it landed with the head or the tails up, your uncertainty about the result is 1 bit. Once I you learn the result, the uncertainty vanishes, and we say that you gained 1 bit if information.
Answer: Classically, the world was thought to divide into a binary of orderly-and-simple (squares, circles, Greek architecture) and chaotic-and-complex (the ocean, the weather, war). But we now have a more nuanced understanding of the world.
A good way of understanding complexity is as a measure of meaningful information.

Order: A circle is simple and orderly. We can describe it using very little information (a set of points in a plane, all at the same distance from the center point), but that information is highly significant.

Randomness: Now consider a group of random dots. They take a lot of information to convey (you have to individually describe the position of each dot, since there's no pattern) but that information is not very significant. There's nothing that knowing the exact position of the dots gains you over knowing that they are randomly distributed.

Complexity: Complexity is a large amount of significant information. A photograph is complex. You can't describe it easily, but the position of each dot makes a significant difference.

Chaos: The new(ish) mathematical science of "chaos" describes a special kind of complexity that can often include elements of both randomness and order. A chaotic system is typically unpredictable at one level of scale, and highly predictable at another. The weather is a archetypal example of a chaotic system.

So what's the relationship with entropy? Entropy can be conceptualized as a loss of meaningful organization. When entropy is high, randomness is high, but complexity is low.
For some good beginning primers on the subject I recommend Chaos (Gleick) and Complexity (Waldrop).
Answer: Complexity refers to the degree to which a system or subject has many parts interacting in a variety of ways. Orderliness refers to the extent to which the parts of a system or subject or organised in some meaningful way. Simplicity and complexity are therefore not correlated in a fixed way with order and disorder.
Take a relatively simple system such as a set of Lego blocks. If you have children who scatter them on the floor, you will consider the blocks to represent a disordered system. If your children assemble the block to form a passable model of the Parthenon, you will consider the set to be in a more orderly form, although its complexity will not have changed.
Your observations about entropy are somewhat misguided. Entropy refers to the extent to which energy is dissipated through a system, rather than to states of order and disorder per se.
Comment: Is 'meaningful' the right word? The Parthenon model will have a higher level of complexity than scattered pieces, in ways that are quantifiable & have measurable impacts. Distinguishing one mix of rubble from another, would imvolve specifying each piece, whereas the model could be described in simpler terms
Comment: Wouldn't that be "entropy production" as opposed to entropy?
Comment: @CriglCraglb Parthenon is an example of high level of order (as opposed to rubble) - composed of symmetrically arranges symmetrical parts. Order is actually less complex, as it can be summarized by simpler rules than disorder (Kolmogorov complexity.)
Comment: @RogerVadim: That's a picture of complexity that equates it to or makes it a proxy for entropy. That is not the Complex Systems Theory picture: https://en.wikipedia.org/wiki/Complex_system#Features
Comment: @CriglCragl entropy is a measure of uncertainty. A pile of bricks may have high complexity, but there is nothing uncertain about it or the bricks position in space. *Complex systems* that you linked are not really complex - not in the sense of having *high complexity*
Comment: @RogerVadim: David Krakauer from the Santa Fe Institute which focuses on the study of complex systems, describes complexity as about systems that take information from the environment & record it, which he calls 'telelogical matter'. He gives that & a compelling account of the history of complexity theory in the this Mindscape episode 'Complexity Agency & Info' https://youtu.be/Cq0i4u4DMb0 Susskind defines complexity in relation to capacity to build logic gates, towards his statement of the 'second law of quantum complexity' - that does link to entropy, but it's not uncontested.

Order/disorder and complexity


Does your ISP know your router's name?

Question: If you named your router "A" then changed it to "B", would they know / be notified
Comment: Could you explain what you mean by "name"?
Answer:
Does your ISP know your router's name

By Name I'm assuming you either mean the name of the WiFi SSID (wireless network name) or the hostname assigned to the router on your LAN.
In either case there is no need for the ISP to know this. There is no reason for either of them to be broadcast to the WAN side of the router.
However many ISP provided routers do gather large amounts of information about your settings. These are usually for diagnostic and usage monitoring purposes. I would imagine that for some ISPs everything the router can "see" can be read remotely - including both of these names. The ISPs argument for why would be for phone support - i.e. you've changed the router name to something different from what is printed on the back of the router and now you're phoning them asking why you can't find your network on your phone.
If you would rather they could not do this use your own custom router / access point.
Comment: Also if your router uses DHCP (connected using Ethernet to a Cable Modem for example) there is a hostname on the WAN side. The provider can know this.
Comment: @Josef - Hostname is not a required DHCP field its an option. So whilst you are right in that it may broadcast it if using DHCP to communicate with the ISP network this isn't a requirement for DHCP to work.

Does your ISP know your router's name?


Does Asperger's syndrome exist in other animal species?

Question: I once spent some time working on a dairy farm and it seems that one commonality between the cows is that they all have, let's say, quirks. but there was this one cow in particular who exhibited behavior of routinely remaining in precisely the same position every time she was going in to get milked. None of the other cows did this, and at one point the notion of autism struck me; I think it's something about the idea of repetitive behavior and the potential for a connection there. I'd like to know what you think and to be as expansive on this as possible.
Comment: There have been some talk about monkeys with autism and the possibility of creating it through genetic engineering. See articles: [(link 1)](https://www.spectrumnews.org/news/monkey-mutation-top-autism-gene-shows-social-problems/) and [(link 2)](https://www.scientificamerican.com/article/possible-autism-biomarker-found-in-monkeys/).

I haven't studied it enough to feel confident in saying that this research is sound. Whether there is any validity to it or not, I can't say.
Comment: That's really interesting, thanks. It's less surprising that it'd be present in animals as intelligent as monkeys but if it were present in cows then I think the implication would be that it's probably present in most species of mammal, that'd be incredible I think. Cheers for those links.
Comment: There is a saying that "All cats have aspergers"
Answer: It is difficult to identify autism definitively in other species, especially since autism encompasses a very diverse group of people who have different experiences.
However, because there is so much interest in studying autism, researchers have developed models for autism in model organisms, specifically in mice, which share some of the diagnostic features of autism.
Therefore, it is at least plausible that any social animal could have some individuals that share traits associated with autism, although it is going to be a matter of opinion whether these traits are autism or just something similar (at least until the mechanisms are better understood). Likely a repetitive behavior alone is not sufficient as a diagnostic criteria, but it could be one out of several.

Silverman, J. L., Yang, M., Lord, C., & Crawley, J. N. (2010). Behavioural phenotyping assays for mouse models of autism. Nature Reviews Neuroscience, 11(7), 490.
Comment: Thank you Bryan, it was just an idea really but having spent a lot of time with this particular animal and observing her behavior (and I know cows aren't especially social animals to begin with) I felt as though an interpretation of autism might be applicable given her particular lack of socialization (compared with the others) and her repetitive behavior. Thanks for your answer.


Exterior lead paint headache

Question: My recently purchased circa 1900 Victorian house sheds paint flakes when it rains. To try to remedy this I had it repainted, and although the painting crew put in a decent effort into cleaning up after themselves there are now even more paint chips laying around than before.
Being as old as this house is, is I am sure there is lead in that paint. I did make sure to tell them it was probably lead paint and they hand-scraped rather than using power tools. I have scoured the Internet for cleanup procedures but almost everything is on preventing lead paint from getting everywhere (it's too late for that) and on interior cleanup, except for one section on this Minnesota DoH website. Do you have any additional advice on cleanup?
Comment: It would be rare for 100-year old siding to be intact enough to get repainted, so we can't assume based on the age of the house that the exterior paint is lead-based. I wouldn't grow veggies next to the house, but other than that, there's not really anything you need to do, lead is not radioactive or anything, you just shouldn't eat it. I would also be weary of getting formal test results that create a mandatory disclosure upon selling as that could turn off a potential buyer. Use a self-test swab if you need to know; you might be pleasantly surprised.
Comment: The danger is to young children eating lead paint. It should sink into the ground over time and be covered up.  Unless you are running a daycare where expensive ground remediation(dig up and remove) will be required, adding some mulch and/or dirt on top should reduce your worries.
Answer: EPA gives good guidance on this here: https://www.epa.gov/sites/default/files/2020-10/documents/lead-in-soil-aug2020.pdf. Note: the soil specific lead level is determined by the cumulative paint work done around the house over its century long tenure.
Main points are:

Get soil tested. 100-200 ppm is deemed acceptable for fruit and veg gardening and kids' playing areas.
If the soil level is higher than that, you can excavate the first six or so inches of soil. You have to find out if it needs to be discarded at a hazardous waste facility - other facilities might accept soil with higher lead contamination levels (the solution to pollution is dilution).
Build up the soil with a new layer of compost and mulch, and try no-till gardening to prevent dredging up old layers of dirt.
Comment: Add: no chickens around the house and then eating the eggs. Lead accumulates in animal tissues.

Exterior lead paint headache


Use the Downloads folder as shared folder between two Macs with Dropbox

Question: I would like to have the Downloads folder of my Mac shared between two Macs using Dropbox. The idea is to have the same archives in both Download folders.
How can I accomplish this?
Answer: I would probably be simpler in the long run - if a little tedious depending on how many apps might use that Downloads folder - to set your Dropbox folder to be your download destination, rather than trying to persuade Dropbox to use another folder.
For Safari, set it in Prefs > General. Click download location, select other & navigate to your Dropbox folder.

You would have to do the same for any other apps that would use your standard downloads folder - but I'm certain it would be easier than trying to persuade Dropbox to use your original Downloads folder as its shared location.
I'm sure the alternative would be to make a symlink from Dropbox to Downloads, but I'm just not convinced it would be simpler to maintain.
Answer: Since many processes write to downloads (AirDrop, Safari, others) and Dropbox doesn't have a feature to pull an arbitrary folder into the sync domain, I would get a tool like Hazel to make folder actions to move anything that enters your actual ~/Downloads folder and moves the files to your Dropbox nominated Downloads folder.
You can automate this using the Automator app for free, but Hazel is so cool, I like to recommend it since once you start automating things like this, the options to be more efficient are much higher with Hazel and the integrations it makes easier than Automator does.

http://macosxautomation.com/automator/
https://gigaom.com/2010/07/08/how-to-combining-hazel-and-dropbox-to-automate-file-management/
Comment: I'm going to have to have a look at this - not because I need it right now, but a) I might in future & b) it sounds pretty cool ;)
Comment: Folder actions are cool, Hazel is a swiss army knife of "getting it done" when it comes to file management.
Answer: Use a symlink or a hardlink to the downloads folder from within the dropbox. You can use the Terminal or if you are less technically saavy or uncomfortable there are tools to do this. http://www.dropboxwiki.com/tips-and-tricks/sync-other-folders


How to say my bike is running out of air and needs to be filled with air

Question: I'd appreciate if you tell me what is the right way to say my bike/motorbike/car's tire is running out of air and needs to be filled with air again in English.
Comment: It might be said to be "going flat".
Comment: "It's going flat and I need to get it pumped up" *or* "...and I need to pump it up."
Comment: Simply saying "need air" and pointing at the vehicle would get the point across in most cases.
Comment: @AndrewLeach And how would you say it needs to be refilled?
Answer: In the UK, it's common to say a tyre (note the spelling!) is going flat.
If it needs to be refilled, a common expression might be "It's going flat and I need to get it pumped up" or "...and I need to pump it up".
We don't normally mention "air" explicitly, because it's a given that tyres are supposed to be full of air under pressure. And we use pump because — despite the ubiquity of garage air lines — the mental image is of one of these:

Screwfix
Comment: *Going flat* is pretty common in AmE also, in my experience. I also hear *pump it up* but I think *fill it up* might be more common. A garage air line is just as much a pump as the item in the image. It is just powered by electricity rather than muscles.
Answer: We say the tire pressure is low. Also, if the tire is punctured, we say it is a "flat" or is "deflated."
To get the air into the tire we say that we need to put air into it, pump air into it, inflate or fill it.
Comment: @Mori (while bicycling) "We have to stop at that service station; I need some air."
Comment: And how would you say it needs to be refilled?
Answer: You can say it's flat, deflated, in need of inflating or inflation, low, low on air, needs to be pumped up, needs a pump, needs filling, or the pressure/tire pressure is low.


How fourier transform of a tempered distribution could be a function (Homogeneous Sobolev space)?

Question: I met the following definition of homogeneous Sobolev space:
$\dot{H^s}(\mathbb{R}^n) = \left\{ f \in \mathcal{S}': \hat{f} \in L_{loc}^1(\mathbb{R}^n) \,\,\, \text{and} \,\,\, || f||_{\dot{H^s}} < \infty \right\}$,  where $s \geq 0$ (does not have to be an integar),  $\hat{f}$ is the fourier transform of $f$,  $|| f||_{\dot{H^s}} =\left(\displaystyle\int_{\mathbb{R}^n}^{} |\xi|^{2s} |\hat{f}(\xi)|^2 \, d\xi \right)^\frac{1}{2}$ and  $\mathcal{S}'$ is the space of linear and continuous functionals from Schwarz Space $\mathcal{S}$ to $\mathbb{C}$ (called space of tempered distribiutions). If $F \in \mathcal{S}'$ and $f \in \mathcal{S}$, then the fourier transform on it can be defined as $\hat{F}(f) = F(\hat{f}).$  And my question is: if $g \in \dot{H^s}(\mathbb{R}^n)$ then how $\hat{g} \in L_{loc}^1(\mathbb{R}^n)$, I mean how $\hat{g}$ can be a function if $g$ is a functional?  Similarly what does mean the integral defined in $||.||_{\dot{H^s}}$ provided that i do not know if $\hat{g}$ is a function?
Answer: For simplicity let me assume that $s$ is a positive integer.
You should interpret $\int_{\mathbb{R}^n}^{} |\xi|^{2s} |\hat{f}(\xi)|^2 \, d\xi<\infty$ as meaning that $f$ is a tempered distribution with Fourier transform $\hat{f}$ so that $(\sum_{j=1}^n \xi_j^2)^s \hat{f}$ is a tempered distribution which is represented by a function $g\in L^2(\Bbb{R}^n)$, that is $\langle \hat{f},\phi \rangle= \int_{\Bbb{R}^n} g(\xi)\phi(\xi)d\xi$ for all $\phi \in S(\Bbb{R}^n)$.
So it is allowed to say that $|\xi|^{2s} \hat{f} \in L^2(\Bbb{R^n})\subset
 L^1_{loc}(\Bbb{R^n})$.
It doesn't have to be that $\hat{f}$ is $L^1_{loc}$.
What you can say is that taking $\psi\in C^\infty_c(\Bbb{R}^n), \psi=1$ on $|\xi|<1$ then $T(\phi)=|\xi|^{-2s}(\phi-\psi \sum_{|\alpha|<2s} \frac{\xi^\alpha}{\alpha!}\partial^\alpha \phi(0))$ defines a continuous map $\phi \to T(\phi), S(\Bbb{R}^n)\to S(\Bbb{R}^n)$, and the tempered distribution $$\langle h,\phi \rangle = \langle \hat{f},\phi \rangle - \langle g,T(\phi) \rangle$$
is of order $\le 2s$ and supported at $0$. So that $$ h = \sum_{|\alpha|\le 2m} c_\alpha \partial^\alpha \delta$$ and $$\langle \hat{f},\phi \rangle = \sum_{|\alpha|\le 2m} c_\alpha \partial^\alpha \phi(0) + \int_{\Bbb{R}^n} g(\xi) |\xi|^{-2s}(\phi(\xi)-\psi(\xi) \sum_{|\alpha|<2s} \frac{\xi^\alpha}{\alpha!}\partial^\alpha \phi(0)) d\xi$$
Comment: So, if I understand properly, the condition $\hat{f} \in L_{loc}^1$ means $\hat{f}$ is represented by some $g \in L_{loc}^1?$ There is also a theorem saying that for a very specific s and p $\dot{H^s}(\mathbb{R}^n) \subset L^p(\mathbb{R}^n)$. Does it just say that $h \in \dot{H^s}$ has a representative in $L^p$?
Comment: I also wonder if expressions like for example $\displaystyle\int_{A} e^{2 \pi i x \xi}\hat{f}(\xi)\ d\xi$ could be somehow sensible  for $f \in \dot{H^s}$ and some sensible set $A$, because in some works I saw people writing similar things and i am still not sure what "$\hat{f}(\xi)$" means.


Can't call existing Solidity function with Brownie due AttributeError

Question: I have deployed a simple contract on the BSC testnet which has a simple function that executes a swap on Pancakeswap.
This is how I call the function with Brownie:
def main():
    tx = contract1.buyToken(0.01,10000,'0x094616F0BdFB0b526bD735Bf66Eca0Ad254ca81F','0xC880a918eDB02E9cf006369927a68c5e7F778B4B')
    return True

And I get this error:
Running '\python_projects\docs3\coin_observer\brownie\scripts\testz.py::main'...
  File "c:\users\home\appdata\roaming\python\python38\lib\site-packages\brownie\_cli\run.py", line 50, in main
    return_value, frame = run(
  File "c:\users\home\appdata\roaming\python\python38\lib\site-packages\brownie\project\scripts.py", line 103, in run
    return_value = f_locals[method_name](*args, **kwargs)
  File "\python_projects\docs3\coin_observer\brownie\scripts\testz.py", line 7, in main
    tx = contract1.buyToken(0.01,10000,'0x094616F0BdFB0b526bD735Bf66Eca0Ad254ca81F','0xC880a918eDB02E9cf006369927a68c5e7F778B4B')
AttributeError: 'ContractContainer' object has no attribute 'buyToken'

And here is the Solidity part:
function buyToken(uint amountToSpend, uint amountToBuy, address tokenToSpendAddress, address tokenToBuyAddress) public returns (uint[] memory amounts)  {
    require(address(this).balance > amountToSpend);
    uint256[] memory receivedTokens;
    address[] memory path = new address[](2);
    path[0] = tokenToSpendAddress;
    path[1] = tokenToBuyAddress;
    receivedTokens = _pancakeRouter.swapExactETHForTokens{value: amountToSpend}(amountToBuy,path,address(this),block.timestamp + 30);
    return receivedTokens;
}

So my problem is why I get the object has no attribute 'buyToken' error? The buyToken exists in the contract and it compiled correctly.
UPDATE
I compiled and deployed the contract again and printed the ABI that seems fine, it contains the function, but the error still exists. I assume something with the ContractContainer is wrong.
Comment: Why are you passing 0.01 as parameter? Solidity doesn't support floating point.
Answer: In your brownie script you need to specify the value you want to send with that transaction.
so
def main():
    tx = contract1.buyToken(0.01,10000,'0x094616F0BdFB0b526bD735Bf66Eca0Ad254ca81F','0xC880a918eDB02E9cf006369927a68c5e7F778B4B', {"from": account, "value": 10})
    return True

The value should match the amount you pass to the contract. Hope this helps.
Answer: I had a same error. The problem was in variable. I accidently write MainContract insted of main_contract. MainContract was a storage of compiled contracts and main_contract is deployed contract


Deducting related educational trading expenses from LLC?

Question: From what I understand, you need to trade full-time in order to deduct educational related trading expenses such as magazines, courses, or newsletter subscriptions.  If I'm not a full-time trader but create an LLC that has its own bank account and trading account under the LLC, can the above type of educational expenses then be deducted?
Comment: A comment/observation. An LLC is a pass thru entity. I'm not aware of it providing changes to taxation as you're seeking. But someone more knowledgeable might have a better real answer for you.
Answer: A single member llc is a tax nothing, a disregarded entity that does not affect tax filing unless you elect to pay entity/corporate tax.  It will not alter your status or increase your reach.
The rules to deduct expenses stem from IRC §212 and Reg §1.212-1, and are partially explained in Pub 550 and Pub 535.  The llc will get these deductions if you check the box with Form 8832, but it will then be paying corporate tax.  You may also hit certain tax rules for investment companies or Personal Holding Companies.
Note that an LLC will not be taxed at a beneficial capital gains rate.
Comment: @NL7 - excellent. I have an LLC, and my purpose was to limit my personal liability as the acronym implies. Nice answer, keep them coming.
Comment: What do you mean by "beneficial capital gains rate"?
Comment: @JoeTaxpayer: As it seems I can't deduct educational related expenses, personal liability was the other deciding factor for putting together the LLC.  It's enough alone to form the LLC.
Comment: @4thSpace - Income is generally grouped into "ordinary income" and "capital gains."  For individuals in the US, the normal long-term [capital gains tax rate](http://www.law.cornell.edu/uscode/text/26/1#h) tops out at 20% (previously 15%).  There are multiple different CG rates, such as short-term, collectibles, QSBS, etc.  Corporate taxpayers still have capital gains, which track separately from their ordinary income, but they do not receive a preferential rate.  They pay the [corporate rate](http://www.law.cornell.edu/uscode/text/26/11) on both OI and CG.
Comment: @4thSpace - I wouldn't say that investor education is necessarily not deductible.  You should dive into it and then consult a CPA or tax lawyer.  I saw some stuff suggesting that travel, publications, and maybe education could be investment expenses, but I did not look at the details.  There are probably Revenue Rulings or court cases on point.  IRC §212 is the relevant code section.


Self-organized criticality and the butterfly effect

Question: We know that in a critical system and for self-organized criticality we have long range interactions due to power-law decay of correlation. Is this fact equivalent to the butterfly effect?
Answer: No, or at least not in the sense the phrase "butterfly effect" is normally used. Well, possibly, but only if the critical system is chaotic.
The phrase is normally applied to systems that show chaotic behaviour. In such systems the trajectory of the system is very sensitive to the starting point i.e. if you take two points very close together in phase space the trajectories from those points will diverge exponentially fast. Hence the claim that a very small change to the system, such as a butterfly flapping its wings, will cause a big change in the future evolution of the system.
Critical systems may well show chaotic behaviour, and if so then I suppose the phrase "butterfly effect" does apply to them. However if this is the case the phrase would be used because they are chaotic not because they're critical.
Comment: no --> no in the sense that --> possibly....
 -Physics at work
Answer: No.
There are similarities, but chaos and criticality are not equivalent.
Loosely speaking, chaotic behavior implies a fast loss of information, i.e., a shorter range correlation in time.
In simpler terms, John Rennie's answer gives a definition of chaos and thus shows it's not equivalent to long range correlations.
On the other hand, if we consider the concrete example of a magnetic material, at criticality ($T\to T_c$: Curie temperature) the susceptibility diverges, which means its magnetization can vary wildly in response to small perturbations such as changes in the external field or thermal fluctuations. In this sense it's indeed reminiscent of chaos, but the dynamical systems concept truly related to it is bifurcation theory.


Transit visa in Paris

Question: I'm going from Morocco to USA via Paris and I will have to change terminals and pick up and check in my luggage between flights. Do I need a transit visa in Paris even if I have a valid US visa?
Comment: Are you Moroccan?
Answer: You will enter France, and having a US visa doesn't exempt you from needing a Schengen visa.
So assuming you're Moroccan: yes, you need a short-stay (type C) visa from the French embassy. If the application form asks for the purpose of the trip, select transit.

Transit visa in Paris


Why are there infinitely many proofs for any tautology in Natural Deduction?

Question: I've recently come across the claim that there are infinitely many derivations in Natural Deduction for any given tautology. Intuitively, this seems odd, because there is, say, a perfectly straightforward way of proving 'P or not-P' (assume P, use disjunction introduction to get 'P or not-P', etc). How would I go about making an argument to the effect that there are infinitely many other ways of proving, say, 'P or not-P' in Natural Deduction? I'm a bit stuck here!
Answer: Because nothing prevents you from additionally talking irrelevant nonsense during your proof.
Answer: Comment
The following :
1) $P$ --- assumed [a]
2) $P \lor \lnot P$ --- from 1) by $\lor$-intro
is not a derivation of $P \lor \lnot P$, because the assumption [a] has not been discharged; it is a proof of :

$P \vdash P \lor \lnot P$.

Now for the real question.
Here is a proof :
1) $\lnot (P \lor \lnot P)$ --- ssumed [a]
2) $P$ --- assumed [b]
3) $P \lor \lnot P$ --- from 2) by $\lor$-intro
4) $\bot$ --- from 1) and 3)
5) $\lnot P$ --- from 2) and 4), discharging [b]
6) $P \lor \lnot P$ --- from 5) by $\lor$-intro
7) $\bot$ --- from 1) and 6)

8) $P \lor \lnot P$ --- from 1) and 7), by Double Negation, discharging [a].

After step 6) we can insert a detour : use $\lor$-elimination to derive $P \lor \lnot P$ from 6) (i.e. from : $P \lor \lnot P$) and then go on with 7).
The new derivation is formally correct and thus is a new ("longer") derivation of $P \lor \lnot P$.
Comment: That's great, thanks! One question though: how does one generalise this result? My original question was why the statement that there are infinitely proofs for any tautology holds true, and P or not-P is only one instance of this. And of course not all proofs in ND need to use the disjunction rule, so what works in the case of 'P or not P' won't work in all cases (say for 'not (P and not-P).


How long does it take to receive feedback for Junior Professorship (W1) in Germany after interview?

Question: I was invited for an interview in a German university in Ruhr area, for a Junior Professorship position.
In total three people (including me) were interviewed, so I guess it should not take so much for the committee to decide!
Does any one have any idea how long it will take for them to conclude the recruiting process? I have an offer for a postdoc and need to let them know if I would take the offer for the postdoc.
Thanks.
Comment: In principle, the hiring process for a W1 position is exactly the same as for a W2 or W3 position. http://academia.stackexchange.com/a/24457 mentions six months (assuming you're the first person on the list), which is reasonable (note that reference letters are usually requested *after* the interviews in Germany). The only major difference affecting timing is that for a W1, there is usually not much room to negotiate (as always, depending on the field), so going down the list if the first person declines the offer will be a bit faster. (For W2/3, I'd estimate another 6 months per offer.)
Comment: Also, it's entirely possible that you will *never* get (official) feedback if you're not offered the position.
Comment: Formally we do indeed have to inform those who did not get the position, but we don't do that until someone (place 1, 2, or 3) has assumed the position. That might take years :)
Comment: Thanks a lot Christian, so you mean provided that I'm (hopefuly) the first choice, the first feedback (official or informal) would be provided to me in six month after interview?!
Comment: Actually I read the link you shared here before poseing my question, but I was not certain the "first feedback" was infact the "offer letter".
Comment: Usually, the *only* official feedback you get is an offer letter (although sometimes you are also notified if you have made the ranked short list, and even on which place -- but this very much depends on the university, the department, and even the individual committees). Unsuccessful candidates are usually not notified, for fear of legal action. It's certainly possible to contact the head of the committee and politely ask; often you'll get unofficial feedback. But I wouldn't expect them to even have a list before late October.
Comment: Thanks a lot Christian. I highly appreciate your feedback.
Answer: Christian Clason's comment is basically correct. The hiring process for W1 is the same as W2 and W3 and reports are collected after the interviews. So the time from interview to notification is not short. However, it don't need to be six month.
What usually happens after
the interviews is that the committee solicites reports and the referees get about six to ten weeks for their reports. Then the committee meets again and forms its recommendation. This is the first point at which you may be told your suggested listing, but this is unofficial and at some places even against the rules. The next steps are that a number of committees have to approve the list (can be something between two and four) and only after the head of the university has approved the list, the first place may be informed officially. This whole process may well take six months, but it can be less, but do not expect less than six weeks between interviews and unofficial notification and not less then three months between interview and official offer.
Comment: Beat me to it :) A few additional remark: 1) If they are really in a hurry, they might bypass the external reports by having more external members in the committee itself (some universities have regulations that allow this). In this case, it's possible that the hiring committee made their list right after the last talk -- rare, but possible (a starting date of October for the position would be an indicator for this). 2) You will never get any unofficial notification in writing, even by email. If you need to know, you should call a member of the committee or try to talk to them at a conference.
Comment: I thank you very much for so much detail. Highly appreciated.
Comment: I see, they might be in a hurry as the starting date for the position was 1st of September (which is past). There were 2 external members in the Advisory Appointment Board, 1 representative for the researchers of the university, 1 representative for the students of the university and 5 other internal members.
Comment: @cristianclason Sorry, I thought that you did not plan to write an answer after a longer comment...
Comment: Update: After 2 years still I am not made aware of the search committee's decision. I even wrote an email once and got no answer. I checked their page and figured they have hired a German candidate.


Best angle to pull an object

Question: I'm fairly new to physics (high school) but really enjoy. I recently came across a problem of my own that I tried to solve: what is the best angle to pull an object at? I derived $F=F\cos \theta-\mu mg-F\sin\theta$ after deciding mass would be a constant and canceling out all the masses leaving me with just accelerations in stead of forces. But I came across a very peculiar graph that showed acceleration shooting off to infinity at $2\tan^{-1}(u)$, but if this was true it would that mean it would take no force to accelerate something at that angle. This obviously can't be right so I was looking for some explanation.
Comment: A little diagram would replace a 1000 words here.
Answer: Drawing a free body diagram, the following equations can be found:
$F_y = F_\text{pull}\sin(\theta) + F_\text N - mg$
$F_x = F_\text{pull}\cos(\theta) - F_\text R$
Stipulations on variables:

$F_\text N$ (normal force) must be positive; the ground cannot exert an attractive force.
$F_\text R$ (frictional force) must be less than or equal to $\mu$ (coefficient of kinetic/static friction depending on what you're examining) times the normal force.
$F_y$ should probably be zero; otherwise you'd be lifting up the object or crushing it into the ground!
If you're looking for constant velocity, $F_x$ is also zero.

Solve the equations... and you'll get something.
Now, this only holds true when $F_\text N$, $F_\text R$ match the above equations. So you may be looking at a case where there is negative normal force, or higher than possible frictional force. Verify that your solution obeys constraints that aren't applied through the equations alone.
Answer: You arrived at almost correct answer. I get net horizontal accelerating force as:
$$
F_x(\theta) = F_{pull}(\cos\theta+\mu\sin\theta) - \mu m g
$$
You are just missing the $\mu$ before the sin and it also has a different sign. Double check your diagram, especially the orientation of forces. But nevertheless you still seem to arrive at almost correct outcome.
Let's just say we want find $\theta$, so that $F_x$ is maximised (because maximal horizontal force will yield maximal horizontal acceleration, which is what we want to achieve). So then let's take a derivative with respect to theta:
$$
\frac{dF_x}{d\theta} = F_{pull}(-\sin\theta+\mu\cos\theta)
$$
Placing this derivative equal to zero gives:
$$
\mu\cos\theta = \sin\theta \\
\\
\theta = \arctan\mu
$$
Which actually makes perfect sense!
For $\mu = 0$ you get $\theta = 0$, so with frictionless surface the obvious best direction of pull would be parallel to the surface. With increasing $\mu$ the optimal angle increases somewhat, because it's suddenly optimal to sacrifice some of the x component of pulling force, to lift the thing a little and thus reduce drag. But if you look at properties of arctan function, optimal theta will never exceed $90^o$, and that also makes perfect sense. You will be pulling more and more upwards, but you will always retain some horizontal/forward component.
Of course, this solution is only valid when the vertical component of the pulling force is smaller than the gravitational force on the object. Otherwise you will lift it from the surface completely.
Comment: This makes sense since tan($)=u

Best angle to pull an object


Difference between inproc and outproc

Question: I am trying to find difference between inproc and outproc in c#. If I have a dll running on the server and my question is will it run in both inproc and outproc? Performance-wise which process is better?
Comment: Wow, this is a very broad topic, with a lot of "it depends". An important difference is that code that runs in-proc can call each others methods in the same address space. If it is out-proc there needs to be marshalling of parameters and the crossing of process space boundaries, which cost time and cpu.
Answer: An inproc server runs in the same process as the calling application.  It's close to a normal function call on a dll.  Calling an outproc server, data needs to be marshalled across the process boundry which is an expensive operation.  An inproc server is fast but it can bring down your application.
Comment: What do you mean by "bring down your application" ? Can you be more specific? Are we talking session, or logging? I don't see where the OP specified. If logging, then I'm assuming what you mean is that if the log operation fails, then it can crash the entire app, but how is that any different than out proc?
Comment: I think he means something similar to if the outproc server runs out of memory, it will crash but the program itself will stay alive and can restart it. Eg std::vector is fast but uses the stack/heap of the container process, and if it runs out of memory, the whole program crashes, but if you wrap it in an outproc server, the container program stays alive.
Answer: From MSDN
ASP.NET session state supports several different storage options for session data. Each option is identified by a value in the SessionStateMode enumeration. The following list describes the available session state modes:
InProc mode, which stores session state in memory on the Web server. This is the default.
StateServer mode/OutProc, which stores session state in a separate process called the ASP.NET state service. This ensures that session state is preserved if the Web application is restarted and also makes session state available to multiple Web servers in a Web farm.
SQLServer mode stores session state in a SQL Server database. This ensures that session state is preserved if the Web application is restarted and also makes session state available to multiple Web servers in a Web farm.
Custom mode, which enables you to specify a custom storage provider.
Off mode, which disables session state.
Comment: I *think* he's talking about COM, not ASP.Net session state.

Difference between inproc and outproc


Numerics for Bose-Hubbard model

Question: For the Bose-Hubbard model, we know that there are the Mott insulator phase with $\langle a_i \rangle = 0$ and the superfluid phase with $\langle a_i \rangle \neq 0$. However, when we are trying to solve the Bose-Hubbard model numerically, we often assume a fixed site number and a fixed total particle number. But if $\langle a_i \rangle \neq 0$, the total particle number is not conserved. Does that mean we cannot really get the true superfluid phase numerically, thus we don't really have a phase transition if we solve the Bose-Hubbard model numerically?
Comment: To distinguish these phases, the single-particle momentum density is often calculated. That is flat in the Mott regime, and sharply peaked in the superfluid case.
Comment: Experiments also (typically) have a fixed particle number, yet they see the superfluid phase without a problem.
Answer: The numerical calculations are usually always carried out in the grand canonical ensemble, so you assume your system of $N$ particles is connected to a large particle reservoir. The chemical potential is fixed, which ensures $\langle N \rangle$ is fixed.
This is of course not physical, but in the thermodynamic limit everything tends to the same anyway.
But what really happens is that the total number of particles (system + reservoir) is conserved because of baryon number conservation. So the fluctuations in atom number for the superfluid phase would be balanced by equal and opposite fluctuations in atom number in the reservoir. They have actually proven this experimentally for partially and fully condensed Bose-Einstein condensates.

Numerics for Bose-Hubbard model


How to join Clips in iMovie 10?

Question: I know there was a function in the context menu to join video clips together, but I can't find it in the newer version of iMovie 10. Is it still available?
Answer: There is still the Join Clips function here:
Answer: The joining clips function in iMovie 10 is located under the "Modify" menu.
YouTube video tutorial I made about how to join clips in iMovie 10: http://www.youtube.com/watch?v=-56DJblknE8

How to join Clips in iMovie 10?


another way to connect with WSO2 IS

Question:
A few days ago, I started to work with WSO2 Identity Server in my project as an authorization server in my architecture, I found that it can be interfaced with an external data source like LDAP, then I can use the enterprise LDAP instead re-create all users and roles in WSO2 IS.
My question is about authentication on WSO2 IS, when the user authenticates on WSO2 IS and approves access normally this is done by HTTPS protocol.
I don't know if it's possible to use another authentication protocol like Kerberos or Radius to connect to WSO2 IS?
Answer: by default the WSO2 IS on the frontend supports OAuth 2.0, SAML 2.0, OpenID and WS-Trust STS protocol. They are indeed all based on the HTTPS. Next to that you may use Kerberos KDC.
For Kerberos configuration you may check this article. http://wso2.com/library/articles/2012/07/kerberos-authentication-using-wso2-products/
g.
Comment: Can you please give an answer to this question on :
http://stackoverflow.com/questions/31306243/wso2-is-login-with-radius-kerberos ?
Answer: WSO2IS has the kerberos support [1]. But it doesn't support RADIUS yet.
[1] https://docs.wso2.com/display/IS500/Kerberos+Security
Comment: We implemented RADIUS support by custom Authenticator implementation with TinyRadius library

another way to connect with WSO2 IS


Calculate the mean for all the attributes of a zipcode?

Question: I have a spreadsheet with two columns: Zipcode and Housing Price. Is it possible to calculate the average Housing Price per zipcode without manually using Excel commands per zip code?
Comment: e.g. python, R, name any scripting language as well as a couple of methods in excel itself I guess. I know zip codes are tempting to be thought of as spatial, but in this case, it seems to be a 'simple' table analysis, not strictly related to spatial data and therefor would be better suited for an other board...
Comment: An excel pivot table will do it. https://www.myexcelonline.com/blog/show-averages-with-an-excel-pivot-table/
Answer: In ArcGIS you could do a resume statistics so you can calculate the mean of an attribute for each case of zip code. Just an idea.
Answer: The easiest way is with an excel pivot table. Here's a link to a blog.
If you want to do it do it in ArcGIS use Summary Statistics. Use your housing price field as the input field and choose MEAN as your statistics type. Use your zip code field as your case field.


Terminology: types of inflection and features

Question: Happy New Year, everyone!
I am reading an article by G.Corbett on canonical morphosyntactic features. He mentiones two kinds of inflection: inherent and contextual. These notions look to me somewhat alike the distinction between interpretable and uninterpretable features in the generative framework. I question whether the things are realy so, are the both dichotomies parallel and concerning the same phenomena? Thank you.
Comment: Are you (ultimately) asking about Booij 1996 "Inherent versus contextual inflection and the split morphology hypothesis"?
Comment: @user6726 probably; at least it seems so.
Answer: Geert Booij defines inherent inflection as "inflection of a word that is not required by its syntactic context" whereas by contextual inflection he understands "inflection that is required by the syntactic context in which a word occurs" (Booij 2007). He gives some examples, e.g. he argues that case markings on nouns are contextual but the present tense on the verb is inherent inflection.
It seems that inherent inflection is indeed equivalent to interpretable features in MP (understood as those features that have an effect on semantic interpretation, e.g. Adger 2003), whereas contextual inflection is equivalent to uninterpretable features.


Will Shimano 105 FC-R7000 replace R565

Question: I have a 2013 Trek Madone 4.5 with 10-speed Ultegra groupset, current crankset is a Shimano R565 50/36 compact. I want to replace the worn out crankset with a new lighter and up to date crankset. Will the new Shimano 105 FC-R7000 11 speed crankset work on this bike?
Comment: what do you mean wear and tear on the crankset? if you want to replace the whole crankset, you should, but it seems unlikely you actually need to. the aluminum arms won't actually wear out. the anodizing may have worn off from shoe rub, but the structure is pretty hard to actually damage in normal riding.
Comment: Normally, the only part of the crankset that wears out is the chainrings. Have you considered just replacing those?
Comment: Yes, very good option although this has already been done. The wear and tear on the crankset makes me want to place whole thing rather than repair chainrings again. Thanks.
Comment: An FC-R5800 can probably be found cheaper.  Heck, you wouldn't notice the difference if you used an FC-4600 Tiagra crankset.
Answer: Should be a drop-in replacement.
Presumably you have a Hollowtech external bearing bottom bracket in a 68mm shell. Latest generation Shimano cranks all have 25mm axles that fit in Hollowtech BBs.
11 speed crank will work with a 10 speed chain.
Comment: Thanks, will look into this.
Answer: According to the latest Shimano Compatibility page the FC-565 and the FC-R7000 share compatibility with the same Hollowtech 2 road bottom brackets. So, as far as fit, you could drop in the FC-R7000.  Be aware that the spacing of the 11 speed, 105, crankset will vary slightly from the R565's 10 speed spacing, and you may encounter some shifting hiccups from a wider 10 speed chain in use.  The Ultegra front shifter and derailleur, designed for 10 speed systems but used on 11s design, may have a slightly different actuation ratio which may effect the smoothness of shifting in front.  Shimano will not say these two crankset are replaceable with each other. Nor the ten speed Ultegra shifter and front derailleur with the 11 speed 105 crankset.
However, my experience as well as others' (with lots of documentation online) has been that with the front drive systems, moving up to the next generation chainwheel and/or derailleur will not cause significant problems. Things work just fine if set up properly.  I currently run 10 speed chainsets on my mountain bikes, which have nine speed rear drivetrains. The hardtail has a 10 speed front derailleur (Deore FD-6xx) that is shifted by a 3x9 front shifter.  Initially it moved the chain perfectly on a triple Deore (FC-M510) chainset marketed as 9 speed. I recently got a 10 speed Hollowtech 2 crankset (FC-M610) and using same shifter and a 9s chain, things are very smooth.  My FSR Stumpjumper, still equipped with the 9s Deore components didn't miss a beat when I updated the crankset to a 10s triple (FC-M622--or something like that). Again, I continued using a 9s chain, new, as I also replaced the 9s cassette with the 9s XT model.  Point is, up front, there's more flexibility to mix things up successfully.
With the rear drivetrain, especially in the higher speeds, 9 and up, there are a good many caveats to address before successful hybridization can occur and is seldom worth the trouble.
In your case, it's likely to work out just right, though I'd think about some of the suggestions in the comments.  Especially note the 10s 5800 model 105 is a great value with very similar appearance to the 7000 105.

Will Shimano 105 FC-R7000 replace R565


How do I find files that are checked out?

Question: We are moving data from sharepoint to Google Drive and many files are checked out and can't be moved over. We need to find all the checked out files. How do we do this?
Comment: Where are you moving from? A single library, a single site collection or a complex multiple web application / site collections design? Are you allowed to use PowerShell?
Comment: Moving from several libraries. Do not have PowerShell. Just need to find the checked out files.
Answer: This question is quite common and one of the universal solutions is to run some PowerShell locally and retrieve a list of all such files. The problem you are facing is SharePoint hierarchical structure (Site Collection > Subsites > Document Libraries > Folders) and you would have to crawl up to the last level in order to make sure you got all the files.
You can find such a script here, but as Mike points out in his comment in all depends what exactly you are moving out of SharePoint. In any case, it is a good start but will require some work.
Commercial tools like SPDocKit can also retrieve such reports. (Disclaimer: I am affiliated with this company)


Online/offline tool for collection of coordinates for simulation purposes

Question: Is there any good free online tool to collect coordinate positions given, say a trajectory; or a polygon. For example, retrieve all coordinates between two points, every 500 meters.
Comment: Could you clarify a bit? Two points is a line, so do you want to find all points that intersect a line? Or do you want to generate a line with vertices every 500 meters? As far as the Polygon, do you want to find all the points inside the polygon? Do you want a library?
Comment: Agree that further information is required with this one.
Comment: Right, I am working on a prototype application and trying to put together a test deck to run simulations. the collection of coordinates is taking a while and I was wondering if  there is a smarter way to do this. In other words, given a trajectory find points that belong to such trajectory ( or area) and applying some filters to this set would be nice as well. Libraries are fine as far as are well documented and easy to integrate. Thank you.
Answer: You might try using the ArcGIS REST Geometry Service, which gets installed by default with ArcGIS Server.
The Densify method would allow you to create points along a great circle path based on some spacing.  You would provide the first an last points, or at least 3 points in the case of a polygon.
For example this url returns points every 200 km. between Longitude 98E, Latitude 24N and Longitude 20E Latitude 55N (degrees).  This url makes the same request but asks for an html formatted response instead.


Arduino Prototype to Finished Product

Question: I have seen this question asked before but it was over 8 years ago and I assume things must have changed since then. Basically, I am working on a personal project that I would like to see if I can sell, I made a wearable prototype using an Arduino Nano 33 BLE , all it does is send accelerometer/gyroscope data over bluetooth to an iOS Application I made. I can't use the Arduino in a commercial project and I need something more compact to fit in a wearable enclosure. My question is, is my next step to replace the Arduino with a custom made PCB or are there other options out there now such as pre built boards that can satisfy my BLE, Accel/Gyro , and Small Size requirements? I couldn't find much information besides building a PCB. I would like to keep the overhead as low as possible so if custom PCB is the route then I would be designing the PCB myself (I have never done this before but I can learn) and sending the files to get manufactured. Any insight on the route I should take going forward would be greatly appreciated. Thank You.
Comment: Wide open question. But I gather this is a cost sensitive application as well as being space and likely energy sensitive, too. So in general strokes, I'd say you will be designing your system, doing layout, worrying about sources and supplies, etc. First thing along that path is who you know who can help you. Their experience and knowledge will have a lot to do with the specific choices you will make. Then settle down and go for it.
Answer: The route to go will probably be to design a custom pcb, it is almost certainly the most cost effective option. If you go down this route you will very likely need someone with experience in hardware design because there is very many things to consider here if you want to do it properly, especially since it is probably going to be a low power application?
Bare in mind also that true professional embedded programming (like stm32wb, nrf52, BGM or other Bluetooth MCUs) is nothing like programming an Arduino, so even this will be a project of its own with which you will probably have your hands full for months.
Good luck!
Comment: Sounds like custom PCB Is the route to go. I understand it will be a lot of work but I do have a background with embedded systems programming so I'm aware of how much programming goes into a board unlike an Arduino. Thank you for the inputs!

Arduino Prototype to Finished Product


Organic reactions reactions memorising

Question: What is the best possible way to learn organic chemistry reactions rather than memorising blindly?
Comment: undersanding reaction mechanisms will surely help you....but before that you need to have a thorough knowledge(not mandatory but useful) of acid-base theory,chemical kinetics,nature and type of reactants etc.
Answer:
Recognize functional groups.
Be aware what nucleophiles and electrophiles are.
Apply 2 on 1.

Yes, there's more to it, and you still have to memorize name reactions, but the upper will definitely make your life a lot easier.

Organic reactions reactions memorising


Hide custom list definition?

Question: I have a custom list definition, created in visual studio.  We no longer want users to create lists from it.  We have existing lists created from it, therefore deactivating the solution is not an option.  Is there a way to hide the list definition so users can no longer create lists with it?
Comment: Could you please paste the CAML for your list defintions that you created in VS2010?
Answer: As Per my understanding, you can do it by Editing Elements.xml like Hidden="True"
and then deploy once again.
Also, you can do directly by editing
C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\14\TEMPLATE\FEATURES\ YourSolutionName \Elements.xml
Jinesh

Hide custom list definition?


How "Principia Mathematica" builds foundations

Question: I understand that "Principia Mathematica" tries to build foundations of mathematics. For comparison ZFC achieves same task. From what I understand ZFC are axioms formalized in First Order Logic. Question is what is Principia based on and why it took so many pages to prove 2=1+1. I suspect that this is less tedious task in ZFC.
Comment: I also have to say that I'm not sure what your question is. Yes, proving $1+1=2$ in $\sf ZFC$ is quite easy if you agree on how to interpret integers as sets, and how to define their addition; and if you already have all the rules of logic behind you. If you don't then you will find this to be equally tedious.
Comment: It might interest you to know that Russell once said roughly "there are only 6 people in the world who've read through all the volumes of Principia Mathematica; 3 Poles and 3 Texans."  I can guess who the Poles were, but who were the Texans????
Answer: If you're really interested in this, it would be worth your while to take a look at the actual Principia and see what it does and how it does it. There are a few reasons why it takes so long to prove $1+1=2$.
One reason  is that the Principia starts with considerably less than the ZF axioms; it starts with only five logical axioms along the lines of $p\lor p \implies p$.  It does not start with any axioms about sets or relations or numbers.
Another reason is that the foundational machinery was not fully developed in 1911.  In 2013, we would define an ordered pair as a certain sort of set (typically, $\langle x, y\rangle {\buildrel \text{def}\over \equiv } \{\{x\}, \{x,y\}\} $) and then define a relation as a set of ordered pairs.  This approach hadn't been invented yet at the time Whitehead and Russell were writing.  So there are several chapters of Principia Mathematica that develop properties of sets, and then several more chapters that develop properties of relations which, from a 21st-century point of view, are completely redundant. Similarly there is a chapter on propositional functions of one variable, and then a very similar chapter about functions of two variables.
But the biggest reason for the length is that the Principia proves everything in extremely small steps.  For example, an important precursor to the $1+1=2$ theorem is $$∗54\cdot 43.⊢((α,β∈1)⊃((α∩β=Λ)≡(α∪β∈2)))$$ which says that if $\alpha$ and $\beta$ are sets that each have one element, then they are disjoint if and only if their union has exactly two elements.  The steps in the proof are tiny.  They start with the previously-proved $\ast 54\cdot 26$, which states that $\{x\}\cup\{y\}$ has two elements if and only if $x\ne y$.  To get from there to $\ast 54\cdot 43$ takes about twelve steps.
The hypotheses at one point of the proof include that $\alpha$ and $\beta$ are sets with one element each.  They invoke a theorem to conclude that $\alpha = \{x\}$ and $\beta=\{y\}$ for some $x$ and $y$.  Most treatments would gloss over this point.  Then they prove, via a previous theorem $\ast51\cdot231$, that $\{x\}\cap\{y\}$ is empty.  Most treatments at this point would take as proved that $\alpha\cap \beta$ is empty, but in Principia Mathematica this is a separate, explicit deduction, justified by theorem $\ast13\cdot12$, which states that if $x=y$, then a predicate $\psi$ is true of $x$ if and only if it is true of $y$.
All these tiny steps quickly add up to a lot of paper.
Finally, Principia Mathematica does not take 300 pages to only prove $1+1=2$.  There is a great deal of explanation and discussion, and a great deal more is proved besides.
I wrote a blog article about this a few years back that provides more details.
Comment: So if I understand correctly main difference is that PM starts with fewer axioms than ZFC?
Comment: Yes, but that is not relevant.  What is relevant is that they much weaker axioms.
Comment: So why this approach is discontinued? Did it proved to be to too tedious? Another question is what the power of such system comparing to ZFC is.
Answer: Perhaps the first point to grasp is that Principia is a type theory rather than a set theory -- indeed the authors officially do not believe in sets, thinking that talk purportedly of such things needs to translated away.
Now, the obvious places one might first look at for an account of Russell and Whitehead's type theory and the overall project of Principia are unfortunately both rather unhelpful (I mean Wikipedia and the Stanford Encyclopedia of Philosophy, whose respective entries -- here and here -- are not up to the best standards). But they may help a bit, though here are two more serious suggestions:

For a philosophical discussion of the project, see Ch.5 of Michael Potter's fine book Reason's Nearest Kin (OUP, 2000)
For an excellent paper on the early history of type theories by Fairouz Kamareddine, Twan Laan, and Rob Nederpelt which puts things in perspective, see here.

But neither of those is exactly easy. I too would be interested to know if, somewhere out there on the web, someone has posted a decently reliable ten-page exposition of what's going on in Principia that you can point students to.
Comment: about *PM*, I think that two recent books are useful : Gregory Landini, *Russell's Hidden Substitutional Theory* (1998) and Bernard Linsky, *The Evolution of Principia Mathematica: Bertrand Russell's Manuscripts and Notes for the Second Edition* (2011). The first one contains a lot of material and reflections about the philosophical background of logicism, but is hard to follow (for me). The second one is more historical, and more readable, but gives a lot of informations about the process of transformation of math log from *PM* to the "modern" one. 1/2
Comment: Regarding shorter papers, I may suggest some of the papers collected into Peter Hylton, *Propositions Functions and Analysis Selected Essays on Russell's Philosophy* (2005), mainly chapter 3 : Logic in Russell's Logicism, and some of the chapters of Nicholas Griffin (editor), *The Cambridge Companion to Bertrand Russell* (2003), mainly : Russell and Frege (Ch.4, by M.Beaney), Mathematics in and behind Russell's Logicism" (Ch.1, by I.Grattan-Guinness), Bertrand Russell's Logicism (Ch.5, by M.Godwyn & A.D.Irvine) and The Theory of Types (Ch.8, by A.Urquhart). 2/2
Answer: You are referring to the Russell--Whitehead "Principia" (rather than Newton's); see here.  Russell's was a logicist program aimed at placing symbolic logic at the foundation of mathematics.  ZFC is a competing program that placed set theory at the foundation, instead.  The logicist approach was initiated by Frege and was much more popular at the beginning of the 20th century than it is today.  Perhaps one of the reasons is the number of pages it took to prove 2=1+1 :-)
Comment: So this distinction between logic approach and set theoretic approach is exactly what I wanted to ask about. I do not get what is the difference because ZFC is formulated in FOL, which is logic after all. Is the difference in lesser number of axioms or is it something very different?
Comment: First order logic serves as a tool to formulate ZFC, but the fundamental object is the concept of a set in this approach, as well as the fundamental relation $\in$.  Meanwhile, in the logicist approach, the fundamental entities are in the realm of symbolic logic.
Comment: I would venture the following comment which may or may not reflect accurately your views but here it goes.  Due to the success of ZFC, many mathematicians view "sets" as being built into the structure of reality itself.  They are conditioned by their professional training to such an extent that it is very hard to imagine the world before Cantor & Co.  This is what makes it difficult even to understand what it could possibly mean that the logicist program was not based on sets.


Skyrim HearthFire

Question: When I load up Skyrim on my Xbox 360, it pops up with select storage device I select the one with my save and DLC. Moments later it pops on the text onto the screen 'Loading Add-ons' this Is where the problem starts I tried using toothpaste on the disc I checked all solutions non worked right now am looking on my screen and it says the same 'loading Add-ons' this has been on for 2 hours. anybody with solutions? Thanks (However I don't think/know if it is the dlc itself doing the glitch) this has been going on for 2 weeks :/
Comment: First off, back up your save :P  Can you try deleting the DLC in the storage menu and then try loading the game again?  If that works, try re-downloading the DLC.
Comment: Okay I am now downloading the dlc back on. And it worked thanks bro.
Comment: No problem!  I made an answer, if you click the green check mark it will mark this question as solved, in case someone else has a similar issue in the future.
Answer: In the comments, I suggested deleting and re-downloading the DLC.  This seems to have worked!

Skyrim HearthFire


Why are pointers of structs not printed like pointers of variables?

Question: Consider the following code:
package main

import "fmt"

type Vertex struct {
    X, Y int
}

var (
    i = 10
    p = &i
    v = Vertex{1,2}
    q = &v
)

func main() {
    fmt.Println(p) // Outputs the memory location of the pointer
    fmt.Println(q) // Outputs the string &{1 2}
}

Why isn't the memory location of pointer q printed, like it is with p?
Answer: This is because go allows you to use type pointers the same way you would use a regular var. So if you pass a pointer to a type the receiving function will operate on the original copy. If you pass a copy of the data than the modifications do not get applied back to the original var.
If the function explicitly asks for a pointer than you have to pass a pointer.
Here is a modification of your example that might clarify how go works.
package main

import "fmt"

type Vertex struct {
    X, Y int
}

var (
    i = 10
    p = &i
    v = Vertex{1, 2}
    q = &v
    t = &v.X
)

func main() {
    fmt.Println(p) // Outputs the memory location of the pointer
    fmt.Println(q) // Outputs the string &{1 2}
    fmt.Println(t)
    fmt.Println(&q)
}

This section from Effective GO

Pointers vs. Values
As we saw with ByteSize, methods can be defined for any named type (except
a pointer or an interface); the receiver does not have to be a
struct.

In the discussion of slices above, we wrote an Append function. We can
define it as a method on slices instead. To do this, we first
declare a named type to which we can bind the method, and then make
the receiver for the method a value of that type.

    type ByteSlice []byte

    func (slice ByteSlice) Append(data []byte) []byte {
    // Body exactly the same as the Append function defined above.
    }
This still requires the method to return the updated slice. We can
eliminate that clumsiness by redefining the method to take a pointer
to a ByteSlice as its receiver, so the method can overwrite the
caller's slice.

    func (p *ByteSlice) Append(data []byte) {
        slice := *p
        // Body as above, without the return.
        *p = slice
    }
In fact, we can do even better. If we modify our function so it looks like
a standard Write method, like this,

    func (p *ByteSlice) Write(data []byte) (n int, err error) {
        slice := *p
        // Again as above.
        *p = slice
        return len(data), nil
    }
then the type *ByteSlice satisfies the standard interface io.Writer, which
is handy. For instance, we can print into one.

    var b ByteSlice
    fmt.Fprintf(&b, "This hour has %d days\n", 7)
We pass the address of a ByteSlice because only *ByteSlice satisfies
io.Writer. The rule about pointers vs. values for receivers
is that value methods can be invoked on pointers and values, but
pointer methods can only be invoked on pointers.

This rule arises because pointer methods can modify the receiver; invoking
them on a value would cause the method to receive a copy of
the value, so any modifications would be discarded. The language
therefore disallows this mistake. There is a handy exception, though.
When the value is addressable, the language takes care of the common
case of invoking a pointer method on a value by inserting the address
operator automatically. In our example, the variable b is addressable,
so we can call its Write method with just b.Write. The compiler will
rewrite that to (&b).Write for us.

By the way, the idea of using Write on a slice of bytes is central to the
implementation of bytes.Buffer.


express $\sum_{i,j\in\{0,1,2\}\atop i\neq j} x_ix_j^2$ by means of the elementary symmetric functions.

Question: $\mathbf{Corrected\ Question}$: How to express
$$
\sum_{i,j\in\{0,1,2\}\atop i\neq j} x_ix_j^2
$$
by means of the elementary symmetric functions
$$
\begin{array}{}
e_1=x_0+x_1+x_2\\
e_2=x_0x_1+x_1x_2+x_0x_2\\
e_3=x_0x_1x_2
\end{array}
$$
and
$$
\begin{array}{l}
p_2=x_0^2+x_1^2+x_2^2\\
p_3=x_0^3+x_1^3+x_2^3\ ?
\end{array}
$$
Thanks!
Comment: Uhm... Last two edits were not symmetric. I suspect it was a problem. And I suspect this one is not symmetric either.
Comment: Thanks. Do you mean that the given function is not symmetric?
Comment: For instance, if you switch $x_0$ and $x_2$, you get $$ x_2x_1^2+x_1x_0^2+x_0x_2^2\ne x_0x_1^2+x_1x_2^2+x_2x_0^2$$

The monomial $x_0x_1^2$ has six "symmetric friends", not three. You need all of them.
Comment: Thanks @G.Saggetelli. I corrected the question.
Answer: $$a b^2+a c^2+b a^2+b c^2+ c a^2+ c b^2=-3 a b c + (a+b+c)(a b + b c + c a)$$
Answer: The five given polynomial are redundant, so there can be many ways to do it: for instance, since $$(x_0+x_1+x_2)^3=\\=x_0^3+x_1^3+x_2^3+6x_1x_2x_3+3x_0x_1^2+3x_1x_2^3+3x_1x_2^2+3x_2x_0^2+3x_2x_1^2+3x_1x_0^2$$
Your polynomial is $$\frac13 (x_0+x_1+x_2)^3-2x_0x_1x_2-\frac13 (x_0^3+x_1^3+x_2^3)$$
The polynomials $e_1,e_2,e_3$ are a tight choice, and Lozenges' answer covered them.
I'll illustrate an approach (with some trick that might turn useful in general) to find the polynomial in terms of $e_1,p_2,p_3$.
For an expression in terms of $e_1,p_2,p_3$, notice that, the polynomial being homogeneous of degree $3$, you want to find it as linear combination of $e_1^3$, $e_1p_2$, and $p_3$.
$$ae^3_1+be_1p_2+cp_3=\text{your polynomial}$$
This is ultimately an exercise of linear algebra (finding the the coordinates of a vector with respect to the basis of a subspace that contains it). It could be written explicitly in matricial form using the standard coordinates of $\Bbb C_{3}^{\hom}[x_0,x_1,x_2]$, but let's cut through the details with tricks and exercises for the reader.
By confronting coefficients of $x_0^3+x_1^3+x_2^3$, you see that you want $a+b+c=0$
Since terms in the form $x_0x_1x_2$ come only from $e_1^3$, you want $a=0$.
You should be able to go on.


Rails.Vim :RInvert

Question: How reliable is this plugin for writing down migrations. Some people in the rails community I have spoken with have told me they swear by it and others are telling me to just stay away. Any and all thoughts will be appreciated.
Answer: It is phenomenal, but I have had it not work quite right before. However, I would highly recommend doing a rake db:migrate:redo after running a migration for the first time anyways to make sure that the up and the down both work. Even if it only writes 90% of the down migration for you, I don't know why you would stay away.
Answer: From Rails 3.1 onwards, for most cases, you don't need to write a down method. The migrations will have one change method and Rails automatically does the down migration in case of rollbacks.
Refer: http://edgeguides.rubyonrails.org/migrations.html#writing-your-change-method
Answer: If you're just generating DDL changes (adding columns, etc), it has always been rock solid for me. However, if you're removing columns or generating DML statements such as copying data from one field to another, translating data, etc... :RInvert will not handle those.  But there's still no reason I can think of to not use what they do generate as a starting point. If you don't like the generated down migration by :RInvert, just delete it and you're no worse off than before you ran it.

Rails.Vim :RInvert


Error while selecting a field in Process Builder

Question: I am using process builder for my opportunity record. I wish to add a criteria in process builder to define the criteria for the action group. In set conditions sections I select a field from the opportunity object and click choose. I get an error as show in the attached screen shot. I am unable to add any of the fields to the set condition section.
Please provide your insights.
Answer: This happens often.  Process Builder is nice and buggy. Keep trying and it should work.  Sometimes you have to close out of the page.  I usually see it going away after 3 or so attempts.  If you continue having issues check the FLS of the field just for safe measures, though it shouldn't have an affect (had it error a Flow from being saved once).
Comment: Ok I will try this and comment back


Tiling Simplex Noise?

Question: I've been interested (as a hobbyist) in pseudo-random noise generation, specifically the Perlin and Simplex algorithms. The advantage to Simplex is speed (especially at higher dimensions), but Perlin can be tiled relatively easily. I was wondering if anyone was aware of a tiling simplex algorithm? Fixed-dimension is fine, generic is better; pseudocode is fine, c/c++ is better.
Comment: [This question was also answered here](http://gamedev.stackexchange.com/questions/23625/how-do-you-generate-tileable-perlin-noise), though the answers here are also interesting
Comment: I have wasted several days working on tiling Simplex Noise, only to find out that it is PATENTED (US Patent #6867776)! Total waste of my time. Don't waste yours, use the "Classic Noise" instead.
Comment: And Perlin Noise isn't patented? http://www.wikipatents.com/US-Patent-6867776/standard-for-perlin-noise and just in case if you didn't know, Kenneth Perlin created Simplex noise to replace his old Perlin noise, since it's faster and has less artifacts.
Comment: I had the same question in mind some time back. This link may help you a bit. http://www.gamedev.net/community/forums/topic.asp?topic_id=409855
Comment: Thanks for the link; unfortunately the end of the thread concludes that the implementations only have tiling Perlin noise, not Simplex noise.
Answer: Just tile your noise the same way you would in Perlin only do it after the skew. You can do this by modifying the part that gets the permutaions to do the mod 256 (or & 255, whatever you are using) after (instead of before) you add to offsets to the get the other corners from the base corner. This is the modified bit of code in HLSL:
uint3 iIdx0 = p0SI % 256;
uint3 iIdx1 = (p0SI + pI1) % 256;
uint3 iIdx2 = (p0SI + pI2) % 256;
uint3 iIdx3 = (p0SI + 1.0f) % 256;
uint iGI0 = gPerm[ iIdx0.x + gPerm[ iIdx0.y + gPerm[ iIdx0.z ] ] ] % 12;
uint iGI1 = gPerm[ iIdx1.x + gPerm[ iIdx1.y + gPerm[ iIdx1.z ] ] ] % 12;
uint iGI2 = gPerm[ iIdx2.x + gPerm[ iIdx2.y + gPerm[ iIdx2.z ] ] ] % 12;
uint iGI3 = gPerm[ iIdx3.x + gPerm[ iIdx3.y + gPerm[ iIdx3.z ] ] ] % 12;

p0SI is the corner 0 point and pI2 and PI2 are vectors to corner one and corner 2 calculated in the usual way. Note that in HLSL scalars promote to vectors automatically in mixed operatons so for instance 1.0f is actually (1.0,1.0,1.0). I just figured this tiling stuf out but apprently it works. If you need to shade a large planet or some shit but only have single precision on your card there are a few more steps. Hit me up.
Edit: you know after thinking about it some more I don't think you have to change anything. I think it tiles autmatically at 256 units as implemented.
Answer: It would seem this question has been reasonably solved here, with a detailed description of the idea behind the working solution here. A fantastic answer to a long-standing problem!
Comment: Higher-dimensional noise doesn't have the same properties, though. https://computergraphics.stackexchange.com/q/4212/15908
Answer: Even if few years passed, this question is still among best results on Google.
In simplex noise, x and y from a straight (ortonormal) grid get skewed to find the simplex the point is in (a triangle in 2D), so with common tiling techniques (%255 or whatever), it DOES tile, but tiles on skewed coordinates, that is it tiles "diagonally", which is quite useless.
A simple solution I've found is to "un-skew" the result, so that original X and Y are first skewed "to the left", then the algorithm will skew them "to the right", and the final result will be re-aligned to a non skewed grid.
If, for example, your simplex implementation is similar to SimplexNoise.java you can find everywhere on the net, it skews the grid using :
var F2 = 0.5*(Math.sqrt(3.0)-1.0);
var s = (xin+yin)*F2; // Hairy factor for 2D
var i = Math.floor(xin+s);
var j = Math.floor(yin+s);

You can simply "pre-skew" it in the opposite direction at the entry point of the method:
var G2 = (3.0-Math.sqrt(3.0))/6.0;
var t = (xin+yin)*G2;
xin-=t;
yin-=t;

Unfortunately, it produces a somehow strange-looking effect (that is, it looks a bit skewed :D ), which is not usually a problem, but depends on what you need that noise for.
Since it was a problem for me, I tried applying this "inverse-skewing" only to a couple of octaves, those that weight more in the final output, and instead used interpolation for "lighter" octaves. This solution gave me satisfactory tiling based on simplex Perlin noise, cause interpolation on all octaves would produce too much attenuation on tile borders, and when more octaves are added without artificial skewing the strage-looking effect gets buried under the additional noise.
Comment: This is the best answer I've found to this anywhere.  I've just stuck to using perlin noise since tiling it is much easier, but the key is skew transforms.  I believe appropriately skewing is possible, but I've not found anyone whose managed to do that yet.
Answer: I recently needed tiling simplex noise and came across this question.
For tiling noise using any noise function, you can linearly interpolate additional tile samples:
Ftileable(x, y) = (
       F(x, y) * (w - x) * (h - y) +
       F(x - w, y) * (x) * (h - y) +
       F(x - w, y - h) * (x) * (y) +
       F(x, y - h) * (w - x) * (y)
) / (wh)

where F() is your noise function. Note that x, y must be coordinates within an individual tile: x in [0, w), y in [0, h). You could use something like tileX = x - Math.Floor(x / w) * w or fmod().
If performance is critical or for higher dimensions, this may not be the way to go because it requires 2^D lookups for dimension D. It also produced lower values toward the centers of tiles for me.
Taken from:
http://webstaff.itn.liu.se/~stegu/TNM022-2005/perlinnoiselinks/perlin-noise-math-faq.html
Comment: That's tiling Perlin noise, however, not Simplex noise.
Comment: The link discusses Perlin noise, but doesn't explicitly state that the method is for it only. I have a working 2D implementation tiling simplex noise, but chose an alternative because the amplitude is decreased toward the tile centers. Gabor noise seems to produce good results and tiles without having to resort to this method (http://graphics.cs.kuleuven.be/publications/LLDD09PNSGC/).

Tiling Simplex Noise?


SharePoint 2010 Visual Web Part development @_parser.AddParsedSubObject LiteralControl WebPartPageUserException

Question: I am using SharePoint 2010 Foundation on a vmware virtual machine.  I am using Visual Studio 2012 update 3.
I am working on a visual web part project.  I have so far in this project only used asp.net controls in the markup.  I have had no html tags.
I tried to add an html tag  to the .ascx markup file.
When I build and deploy/ran the project the debugger catches an exception in the .ascx.g.cs file in the @_BuildControlTree function.  The following line is where the exception occurs.
@__parser.AddParsedSubObject(new System.Web.UI.LiteralControl("\r\n\r\n
\r\n\r\n    "));

The exception is WebPartPageUserException.  I tried to find out more about what is going on.  I found this msdn article: http://msdn.microsoft.com/en-us/library/microsoft.sharepoint.webpartpages.webpartzone.addparsedsubobject.aspx.  It gives 1 sentance about what the AddParsedSubObject method does.  It has a second sentance in the article that describes conditions for a WebPartPageUserException to be thrown.  It says the exception will be thrown if the object is not a LiteralControl or its Text Property is not empty.  Could that sentance be wrong?  Should the or be an and?
The AddParsedSubObject is called for every control.  The LiteralControls are generated for every html tag I have.  I only have one which is a div tag.  At the line where that LiteralControl with a non empty text of div tag is called that exception gets thrown.
Can visual webparts have html tags?  Does something special have to be done when they do?  I can't think of any other reasons why this exception would be thrown.
Answer: Just put runat="server" to your div!


Network Manager icon is missing on Ubuntu 14.04 LTS

Question: A while after I installed Ubuntu 14.04 LTS, the network manager icon disappeared from the panel, although the WiFi is working. Also the Bluetooth icon disappeared too. How can I fix this issue?
Answer: Bluetooth can be re-added by going into the Bluetooth menu in System Settings and checking the box at the bottom that says

Show Bluetooth status in the menu bar

Unfortunately the Network menu has no such button. I have not yet found a way to restore it on my machine, as reinstalling 'network-manager-gnome' did not help at all.


Counting the number of tree when the set of the subtrees is given

Question: There are a set $A$ of trees. There is another set $B$ of trees that is the collection of all possible subtrees of the trees in $A$. I don't have $A$ but only have $B$, and I need to figure out the size of $A$. A brute-force way is making a graph of the trees. For each root node in $B$, find a tree that contains the node, if there exists such a tree, then make a link from the root node's tree to the containing tree. Finally I can obtain the number of trees in $A$ by counting the number of connected components in the graph. However, this may not be so efficient. How can I do it efficiently?
Answer: You can't do it at all, let alone do it efficiently. Consider a tree $T$ and let its set of subtrees be $S$. If you're told $B=S$, the cardinality could be anything between $1$ and $|S|$, inclusive, because $A$ could be any subset of $S$ that contains $T$.
Comment: Maybe he meant that B is a multiset?
Answer: In addition to David's answer I wanna say that, if B was a multiset (meaning you can store several trees that are the same in that set) then you could do it by taking the biggest size tree in B and generating all it's subtrees and removing them from B, then taking the next biggest subtree in B (out of what's left) and doing the same thing until your multiset is empty.
All that can be efficiently achieved with a priority queue.
It's similar to this problem: codeforces.com/problemset/problem/582/A?locale=en .


Are there legal cases related to trademark infringement for using names inside a work?

Question: Are there any legal cases regarding trademark infringement when a name is used inside a work? E.g a video game containing a location named using a trademarked name.
Answer: You cannot copyright or trademark a name.   Trademarks typically are more than just a name, but include stylizations including font, coloring, logos, or other icons and symbols.  For example, The Golden Arches of McDonalds or the Nike Swish logo.   In writing, these two symbols are difficult to reproduce so saying "He laced up his Nikes and went to grab a burger from McDonald's" is not a copyright or trademark violation.   Hell, naming a character Clark Kent is not a violation of Copyright, so long as it's clear that he is not the more famous Clark Kent in even the slightest way.
Comment: You can have a word mark that is trademarked, so long as it is not merely descriptive. A trade name and a trade mark are not the same, but trade marks are routinely used nominatively. The greater limiting principle is "nominative use", i.e. that a trademark violation generally involve using the trademark in commerce in a way that implies an affiliation with the trademark owner.