darklight03/StackMIAsub huggingface dataset:
I am rather puzzled and confused, I have been trying to get a clear understanding of how would spectral clustering work for an undirected weighted graph, I have used the normalized Laplacian, but I always get complex not strictly positive eigenvalues, all the resources I am finding build on the results that the Laplacian is real symmetric positive semi-definite matrix, hence real non-negative eigenvalues. Any guidance is greatly appreciated, specially in the answer to the question if I take the norm of the normalized Laplacian would spectral clustering algorithms be still valid with same results.
Is there any "second-countable" theorem ? With this i mean if there is any result like Nagata-Smirnov Theorem (that states necessary and sufficient condition for a space be metrizable), but for second-countable spaces. Also, with Urysohn Metrization Theorem it's straightforward to prove that if a space is compact and Hausdorff, then is secound countable iff is metrizable. Is there any result like this but with the hypothesis that the space is only Hausdorff (i mean, something like : Let X be a Hausdorff space. Then X is second-countable iff [something]) ? Thanks a lot !
As an external observer at infinity, I observe a star collapsing. But because the surface of the star will be infinitely redshifted, I will never see the formation of the black hole. For me, there will be always some matter outside, it never crosses the event horizon. So, can I observe the Hawking radiation if I never observe the formation of the black hole ?
A finite presentation is a presentation where the set of generators and the set of relators are finite (Source) I'm studying for an exam where one of the "exam topics" is: The example of the infinite presentation. But what is an infinite presentation? From the finite presentation my first thought was a presentation where the set of generators and the set of relators are both infinite. But since I can't find any example on this in my notes, I suspect that the definition only requires that the set of relators is infinite.
So basically, you have three different types of 'things' (for lack of a better term): You have that which is necessary, that which is contingent (you have a choice), and that which is necessary but only because it must be so after a contingent choice has been made. So it's necessary, but not to begin with, and is necessary in a very different way. I guess you could call that which was necessary to begin with, necessarily necessary, and that which is necessary by choice, not necessarily necessary. But of course, am sure there's a better word, or at least term, to describe this phenomenon.
I took matrix computations course, our course book is Numerical Linear Algebra and Optimization. As a computer science student, sometimes I get the impression that I lack some fundamental background knowledge about it. It'd be great if you could introduce some useful but not very long elementary linear algebra sources (not very long, since I should get back to my course book ASAP). Please note that I've Googled the subject and got some cookbooks but I am looking for some sources which are specifically related to the above mentioned book and covers those topics.
I have see a lot of people said it is not possible to draw a circle by Bezier Curve. However, I want to know why? I did see somebody explain, but I am not quite sure what they mean. Like, Bezier curve is parabola, so it is impossible to draw a circle by it. But how can I proof it? proof that Bezier curve is only parabola and never be circle?
I know that demonstrating the Mandelbrot Set is connected requires a non-trivial proof, and that Mandelbrot himself was fooled at first. But can it be demonstrated visually that the set is connected? If the Set were known to be path-connected, I might hope for a computer program that would let me select two points in the set and demonstrate the path between them. Showing connectedness visually seems harder to me. Is there an intuitive way to do it? Perhaps allow the user to draw a region R and then identify at least one point on the boundary of R is in the Mandelbrot Set? Unfortunately that seems less satisfying than demonstrating a path.
I'm currently studying electricity on my own, and as I read in a metal electrons are moving across the metal freely (depending on the attraction of the nucleus). As we close the circuit, an electromagnetic waves spreads into the metal moving the electron from the minus pole to the plus pole. Can someone explain to me why is there an electromagnetic wave created when we close the circuit and why it forces the electrons to move like this? Thanks a lot
Which one should it be? One of the guys' One of the guy's EDIT: Never mind, I think I answered my own question. I realized it would probably be related to the object being possessed. E.g.: "One of the guys' swords" means "There are multiple guys. They own multiple swords. I am referring to one of those swords." "One of the guy's swords" means "There are multiple guys. One of them owns multiple swords. I am referring to one of those swords."
Can anyone please explain exactly how formulas like Tupper's self referential formula can be constructed? I'll like to see the reasoning behind the derivation of such formulas and the steps required to create a new one. NOTE: I know Tupper's self referential formula is not as 'self referential' as it is claimed but some form of 'universal' formula capable of producing any bitmap of a given size, given the value of N.
Imagine a structure that is held above the water by pylons that are grounded on the ocean floor. In between these pylons is a pontoon that, when tides are rising holds and lifts a heavy weight. When the tide is falling the weight is supported by the structure, which can gradually let the weight down, and in doing so create electricity. Would this be a practical or even viable way to create electricity? Why or why not?
I have a image in a beamer and I want to overlay a table on that image. How can I achieve that ? I have a figure that I created in powerpoint which is as follows: In the above figure, the statistical parameters such as RMSE and NSE are added later. Is it possible to add similar thing in latex beamer ? I want to show the text first on the upper panel and then on the bottom panel. Thanks.
I wonder what could be a good book to start learning in depth all aspects of the Fourier transform up to the FFT algorithm, and beyond. I am going to dedicate quite some time on the subject, so I expect something with a lot of exercises (calculus, demonstrations) and solutions, from the basics up to the most complex topics. Could be nice to also have some exercises (with solutions) with practical applications in Matlab or Python/Numpy. Any pointers? Tutorials, books, chapters, websites? thanks! :)
I was trying to measure the noise of a device with metal probes. I was not sure whether I should trust the results because I was told contact noise might contribute to some degree. I am a little confused about the notion of "contact noise". Is it because of the contact resistance (every resistor is a noise source)? Or is it something related to other factors such as probing materials or surface? Could anyone make a brief explanation? I am eager to know the origin of this "contact noise", and how I can evaluate such noise.
Usually, I think "have to" indicates obligation, which is pretty similar to "must". But today I found this sentence and its usage of "have to" confused me: (it is from NYTimes.com) Long-term forecasts seem to me rather like time capsules, designed more to provide retrospective amusement for those who eventually have to read them, than to be taken seriously as they are first uttered. It would be uncomfortable to interpret have to as must since we are not "compelled to read them". Can anybody explain this for me?
For Hausdorff spaces the following are equivalent: Every point admits a compact local base. Every point admits a compact neighborhood. Every point admits a precompact neighborhood. Every point admits a precompact open neighborhood. (Among these the local compactness is the usually applied one.) For non-Hausdorff spaces: What are examples where neither of them are equivalent? What situations make the latter two become important? (I'm just wondering as these are almost always taken as definition.)
In German, there's a term "Reizblase" which describes the bladder of someone who has to hit the bathroom every ten minutes. The dictionaries suggested "irritable bladder" as a translation which - seeing how other "Reiz-" organs are also called "irritable" - makes sense. The thing is, the German word holds up nicely in a highly colloquial sentence. I'll try to emulate that in English. Dude, again? WTF? You really got yourself one irritable bladder right there. I am not a native speaker but I feel like "irritable bladder" doesn't fit in with the rest of this sentence because it is a different register. Is there a more colloquial term? If not, would people say a sentence like the one in the example?
Basically a friend of mine and I have had this hot debate for a little too long, I contend that these two tools are not only logically unconnected but they require different assumptions (I believe one requires a continuously differentiable function and another requires it to simply be continuous). We've even gone through the proofs and disagree on how the assumptions are used. I don't see the connection... Maybe I'm wrong, maybe they are equivalent (you have one as a tool if and only if you have the other). Anyway, any fresh perspective would be welcomed and any deeper discussion on either appreciated, thanks.
There are many books, in which Yang-Mills theory is introduced "just like that". But I didn't find some book with set of historical arguments, which had led people to using it in quantum field theory. Can you tell me about this? Maybe, my question leads to the next question: how did people guess that they need to expand the group of local gauge invariance for describing, for example, quarks?
When saying a sentence like: Nikola Tesla __ famous because he was a genius. Should the blank be replaced by is or was? Or is it dependent on when the person is/was famous? If so, what exactly are the rules? I searched on Google and English.SE but didn't find an answer, even after using quotes to counter the amount of stop words in the question...
When I look in old mathematical textbooks from the seventies and before, mathematics is always upright. Their use of italic letters in other contexts, however, shows that this is not because of technical limits. On the other hand, all textbooks I have seen with italic math look very TeX-like. So I was wondering if this is a coincidence? could italic math be an invention by Knuth introduced in TeX? Does someone know the history of italic math?
In compton scattering, a photon may deliver only some of its energy to an electron. But when dealing with photon electron interaction in an atom, it's all or nothing. Why the difference? Also, within compton scattering, given the initial wavelength of the photon, we get a relationship between scattering angle, and wavelength of the scattered photon. But we can't know the scattering angle without knowing the wavelength of the scattered photon. So there's a free variable. What determines the wavelength of the scattered photon? Is it some type of random process? Thanks in advance.
Possible Duplicate: Is the word 'whose' referring to an inanimate object correct in this sentence? Is there a more appropriate word? Basically I'm wondering if a sentence like this is grammatically correct: "Meaning is thwarted by its delivery, whose poetry is relative to taste." I cannot avoid it with, "Meaning is thwarted by its delivery; its poetry is relative to taste" because 'its' seems to refer to 'meaning.' There needs to be a word like 'whichs' or something. Or is there? Please clarify my question if you know the proper grammatical labels for what I'm talking about; I know them not.
I was going to post a comment on my own theory about Mars and Jupiter colliding, but I just read the rules and it breaks it...badly. I was looking for informal peer review. So my question is, has there been any mainstream published work about the possibility of planets colliding or interacting greatly? (Velikovsky doesn't count obviously, I'm thinking an actual scientist) (besides the Earth-Moon of course) I can't seem to find any.
Question: Find a conformal map from the exterior of the closed unit disk to the unit disk. Also, prove that it is indeed a conformal map (bijective and holomorphic along with its inverse). I missed that the two days we covered conformal mapping due to chaos in my life. I have been trying to find worked out examples and have been reading up to get some insight, but I am lost since I can't find something that details a complete worked out problem. p.s. If anyone knows a great resource that would help me out to further my grasp of conformal maps in complex analysis it'd be much appreciated if you could disclose this.
Consider the following situation. You are standing in a room that is perfectly circular with mirrors for walls. You shine a light, a single ray of light, in a random direction. Will the light ever return to its original position (the single point where the light originated from)? If so, will it return to its position an infinite amount of times or a definite amount of times? Will it ever return to its original position in the original direction? I thought of this little teaser when reading about a problem concerning rays in a circle and wondered about this question. As for my attempts, this is well beyond my skill.
An proverbial anecdote I've heard for a problem solving deadlock is something along the lines of: A farmer needs to fix a bucket, which requires this, that then requires that and so on and so forth until it requires a bucket to fix the bucket. However I haven't been able to find this particular proverbial anecdote for a problem solving deadlock, so I'm wondering: What is the most common (folksy?) proverbial anecdote for describing a problem solving deadlock?
What does this phrase from The adventures of Tom Sawyer sentence mean: "True, the knife would not cut anything, but it was a "sure-enough" Barlow, and there was inconceivable grandeur in that -- though where the Western boys ever got the idea that such a weapon could possibly be counterfeited to its injury is an imposing mystery and will always remain so, perhaps." Thank you!
Given a Matroid (E,I), I is a set of independent subsets of E, right? And independent subsets means that no two of these subsets must have an element in common, right? Now according to the hereditary property of Matroids, if A is a subset of B which is a subset of E and if B belongs to I, then A also belongs to I. If A is a subset of B, then all the elements in A are in B, then how are these two independent? All the sets that are supposed to belong to I (i.e. A and B in this case) must be independent (i.e. must not have any common element) right?
I am currently reading about the subject given in the title of this thread. The definition they give for equivalence classes in my textbook is a rather ostentatious in its wording, so I just want to make certain that I am understanding it properly. They say to let R be an equivalence relation on a set A, meaning that this this particular relation is reflexive, symmetric, and transitive, right? Essentially the rest of it seems to say that you can partition off the elements that make the relation reflexive, thereby creating a subset of the relation R. Does that seem right? I could really use some help, thank you!
I am studying various crystals and the two-dimensional materials that could be potentially obtained by cleaving them (isolating a region bounded by two parallel planes). In elucidating the properties of these materials, it would be good to know what symmetries could the cleaved material possess given the symmetry of the original crystal. What is the best way to approach this problem? My question can be alternatively interpreted as follows: how to find all the layer subgroups of all the space groups? ("Look them up" is a legitimate answer for my purposes, if you can tell me where to look!)
Are there any resources online for astronomy experiments that I can perform myself? I am looking if anyone knows any measurements to take while looking for various objects during the evening particularly using a telescope/binoculars. A couple of examples would be determining the orbits of the moons of Jupiter through an evenings observations or trying to measure a stars parallax from measurements throughout the year. I can think of a handful of other ones but was wondering if there were any other resources to provide some more ideas.
So, I've noticed over time that I see both "afterward" and "afterwards" at different times. Having a pet peeve (though I'm not certain it's actually a well-founded prejudice, lexicographically speaking) against hearing "anyways", I've started to wonder recently about "afterwards". With a quick bit of web searching, I turned up this analysis, which I find to be somewhat helpful, I'm just wondering if there's more that people could say to help me get an intuitive understanding of when to use which, or otherwise why to use one versus the other. I suppose (as mentioned in the linked article) this question could also apply to forward, backward, toward, etc. Which shall I use? When? Why? Does the 's' indicate some sort of plural meaning, or something else?
I am an undergraduate in Mathematics writing his dissertation on General Relativity this year. The next couple of months will be dedicated to learning the math (geometry) and the physics, and to this end I am looking for must-read/must-watch material on the topic. General book recommendations are welcome, but keep in mind I can use Google! I am mainly looking for really good introductory content that I would have a hard time finding myself, whether it be videos, course notes, books or blog posts. My apologies if this is a duplicate!
I am trying to determine if the plane on which two triangles lie intersects for a collision-detection implementation. Unfortunately, I'm stuck at step one, which is finding the plane on which a triangle lies. I tried looking around on Google and what I can find seems to imply that I need to find the normal to the plane instead of the plane, and the direction of the normal. Can anyone explain why I just need to find those two?
You often hear that black holes are so strong in their gravitational pull that matter, even light cannot escape. But this seems to contradict the laws of conservation of energy. Is it possible that perhaps light (photons) are not themselves elementary particles, and within the immense gravity of black holes decompose into some other sub-particle or dark matter that we cannot yet measure/see? I know there is no way, yet, to measure or determine this, but it seems like there is a more simple explanation than matter just "disappearing". Thoughts?
If A is a closed set,then what can we say about closure of A^C ? It is a closed set.But my doubt is whether A and closure of A^C is disjoint or not? what i had tried is: if A is closed, A = closure of A. A and A^C is disjoint, so closure of A AND A^C is disjoint.Can anyone help me to understand whether they are disjoint or not..
In terms of dollars per watt, using theoretical efficiency limits, what technology holds the most promise to become the primary solar energy capture technology? My hunch is carbon-based modules, since materials are abundant and relatively easy to manufacture; however their efficiency currently is nowhere near silicon-based semiconductors. In the future, assuming that scientists will push very close to the theoretical limits, what will provide the most power for the lowest cost? If this is relevant at all, I am trying to decide where to focus my graduate studies in physics, and I want to contribute in getting the most promising technology to its limit. If you can at least point me in the right direction to figure out the answer myself, I would greatly appreciate it.
Possible Duplicate: How does gravity escape a black hole? How can gravity get out of a black hole? If a black hole is so powerful that even light does not travel fast enough to get out, and gravity, or rather, gravitational waves, travel at the speed of light, how does gravity get out? And please don't say that the black hole creates a "well" in space that other masses "slide" down. Such a well would be unstable and, if two black holes pass near each other, neither would be able to "slide" down the other since both are infinitely deep. These wells would make gravity selective.
If I have a cup of water filled with air at the bottom of a pool, then when the cup is "upside down" the air doesn't leave because the water pressure is pushing it up against the top of the container. But then when I flip the cup, such that it is no longer upside down, the air rushes upwards. But why on earth does this happen? I mean the water's pressure is pushing this air downwards against the bottom of the container. If I were to draw an FBD which force is causing this air bubble to rush upwards? Thanks
Many years ago I heard a radio broadcast featuring a beeping sound that always seemed to come from behind me. The announcer said that the sound would have this quality and it did, even when I turned around. It was a plain beep, and the radio only had one loudspeaker. It was a complete mystery to me then and it still is, so can anyone explain the effect? (Previously posted at https://www.newscientist.com/topic/lastword/its-behind-you/.)
I wrote a technical article in which I used (probably overused) constructions of the form "The main point is that...", "The problem is that...". As I am a native Italian speaker, these sentences have the natural form that I would use in my language. One of the reviewers suggested that a better way to formulate these sentences in English is "As the main point,...", "As the problem,...". I feel these sentences carry "less power" than my original ones since the main word is not the subject anymore. Any thoughts? Is the construction I used incorrect, inelegant, or good English? Thank you
What do echo and reverbation have in common? They are the reflection of sound waves, they are formed when sound waves meet a hard surface, they cause a repetition of the sound. The waves keep having the same frequency (the source doesn't change); They have the same speed and length as they had before the reflection, because the environment doesn't change. Is there anything else?
I am working (writing and typesetting) on a book for children. I have used the memoir class. The book looks good for an adult audience. But I had ideas of making it more interesting for the children. More specifically, how about adding little thumbnails to the table of contents page? These will be tiny images placed randomly and rotated randomly. Or a different pattern border around each page? Like bright colored zigzag pattern for one page and may be, colored crayon strips on another? With my limited experience and expertise in latex, I could not crack this one. Any ideas/ suggestions/ solutions?
"Working for the man". Does "Working" act as a noun, verb or something else in this case and why? If I said, "I am working for the man." Then clearly working is a verb. However, I'm confused by the colloquial phrase "working for the man." It seems to have a "poetic" tone if you will. Because the subject does not exist I wonder if "Working" is a state of being in this case? As "Peter Shor" pointed out Maybe the answer is that because this is not a complete sentence then we don't know what role "working" plays in the sentence. FWIW, I'm imaginging how I can translate the phrase into Japanese. Which word I use for "Working" depends on whether it is a noun or a verb.