darklight03/StackMIAsub huggingface dataset:
I'm interested in writing a document following not only the Chicago Manual of Style in principle but also very literally the style used by the University of Chicago Press in their publishing. In other words, I'm not just trying to follow the style guidelines outlined in the manual, but also directly emulating the full style used in their publications. Here is a sample page: Obviously their style has a large number of rules (many more than used on that particular page) and I may not need to use all of them, but even a small subset would be painful to implement manually. So what I'm wondering is, is there an existing (la)tex template that has already implemented most or all of their style? When I search, I only find results for templates for their bibliography style, and that's more about following their guidelines rather than directly reproducing their formatting.
Suppose we have an arbitrarily well-isolated empty region which we initialize with a cold, diffuse, homogenous photon gas, such that the only energy density gradients are random thermodynamic fluctuations and the only massive particles are those that are created after initialization. Thor pokes a tiny hole in the arbitrarily isolating boundary, puts his magic omni-detector on the hole, and measures an interaction event every time a particle - typically a photon, but sometimes perhaps a massive particle or antiparticle - reaches the omni-detector. Magic omni-detectors always interact with every kind of particle. However, Loki has secretly tampered with Thor's omni-detector so that it records everything as if time was proceeding many times faster - not just the time stamp on each measurement, but also the values measured, as if the SI Second had been re-defined to be some multiple of its current value with all the downstream consequences on other units and constants. Is there any way Thor can tell, by looking at a subset of his data (i.e. not just comparing the total run time of his experiment to a clock that hasn't been tampered with), that he was looking at a large, diffuse, cold region, and not a small, dense, hot region?
I have been revising some maths and in particular I have been focusing on vector calculus. Today I have just finished looking at surface integrals. I do understand how we parametrize a surface integral starting from a region R, but I am having troubles actually understanding how these integrals are put in context when having a scalar function or a vector function. For instance, a popular example is that you have a surface (for instance a metal sheet) and then you have a function which gives the density of each point of this metal sheet (if I were to plot this function, would it have the same shape of the surface?) Further, I dont understand why calculating the surface integral of the density function gives me the mass (isn't the definition of density mass/volume and hence I would need some kind of volume?) Thank you for whoever can explain this in simple terms
Something got messed up in my lyx settings and now the editor window previews the text in a very ugly and informal looking font. The pdf output is still the regular latex font. How can I reset the editor window font? This would probably be fixed by a complete uninstall and reinstall of lyx, but I can't figure out how to do that either. Here are some screenshots of what the editor window and pdf output look like For context, this happened after I tried to add a lyx -> markdown converter (https://wiki.lyx.org/Tips/ConvertMarkdown). I couldn't get it to work, and quickly gave up. But not my lyx font is hideous! Things I've tried: Uninstalling and reinstalling, but all my previous settings are maintained, including this font issue. I tried looking for any saved files in the indicated directory here, but don't see any files. How can I completely uninstall lyx? Tweaking the screen fonts options, but not exhaustively Running "tools/reconfigure", which produces an error
My question is both naive and subtle. Naive because I don't know much more than the layman about physics and in particular quantum physics. Subtle because physics is an attempt to model the world, and as a computer scientist, with a strong interest in machine learning but also formal logic and models, a model is just that, a model. Not necessarily reality. It is not because a model fits reality that the model is the truth about reality. From my understanding, we know that: the quantum physics model has not been contradicted on the notion of superposition that it introduces there are experiments that can be explained using the quantum model where the classical model fails Am I correct to say that this only proves that the classical model, is just that, a model, and therefore incomplete? And that for those cases quantum mechanics has a better predictability power. Now the question: Has it been somehow proven that a physical entity can a some point in time and space have a dual state (independently of the model)? Or is it only that quantum mechanics is the only known model that allows us to explain things we otherwise couldn't? I would like to know if objects of our world can be in two states at the same time or that it is just more practical for predictability purposes to model things this way.
I live in an arabic speaking country, and while I was sitting in a food court today, I noticed that the sound of the crowd was the same as the one I see in the stereotypical sound of the crowd. I have seen many threads discussing this on different forms, eg: Quora , reddit, Metafilter, and on this site, there is this tangentially related question. The problem with all of these is that, none of them is concrete, in sense of not having any calculative evidence. Going down the reddit rabbithole and reading the metafilter thread gives me some idea on how a calculation should look like, but I don't feel so confident in my abilities to do it, could someone provide a fermi type calculation of this? Else, link to a source which does?
Recently I was on an airplane on a sunny day. The sun was shining on the other side of the plane and noticed a bright patch on the ground following beside us. Eventually I noticed a dark centre to this bright patch, the plane's shadow, which became more distant as the plane descended. When the plane flew over a city road signs in this bright patch lit up brightly because of their retro-reflective paint. My question is, what was acting as a retro-reflector to produce this bright patch when it wasn't passing over a road sign? When flying over water the bright patch disappeared, or was very faint. I could see it over forests, more clearly over cut grain fields and, at least faintly over a wide range of terrain.
For a general linear map, there are infinitely many matrix representations. You choose a basis of the vector space, and this gives you a certain matrix for the linear map. You choose a different basis, and this gives you another matrix different from the first. For a linear map that does nothing however, we only get the identity matrix no matter what basis we choose. It isn't hard to see that the identity matrix will always do what we want from this linear map mechanically. But I feel there is some deeper intuition for why the matrix for this linear map shouldn't change with the basis, without thinking mechanically about the matrix. On a side note, is there any other linear map where the choice of basis doesn't change the matrix representation or is this the only one?
In quantum mechanics, unbound states will tend to spread out in space over time according to the Shrodinger equation. So it seems to me there is a degree of freedom for "wild" particles (i.e. those have not been prepared in the lab) as to how much they are spread in space and momentum. So my question is: do we have any knowledge of how disperse "wild" particles (i.e. those which have travelled a long way such as photons from the Sun or cosmic rays) are? Is there any way to tell, or are we completely unable to extract this knowledge? Fundamentally we can't for an individual particle, but I mean statistically. I know that the spread must satisfy the Heisenberg uncertainty---my question is what do we know beyond that?
Why can't we see light from beyond the observable universe? I've done a lot of research on this and all I've found is unsatisfactory answers and straight up nonsense. Some claim that the universe "expands faster than the speed of light" beyond the observable universe. Such a claim doesn't even make sense because the units of speed are m/s and for expansion are Hz. That's like saying "the area of this square is larger than the volume of this cube". All that the expansion can do to light (as far as I know) is redshift it. And light doesn't have a minimum possible frequency or energy value. So even if the expansion of the universe is very rapid, why does the light of distant objects "never reach us". Surely it still would, just extremely redshifted. In this case it does still reach us, and yet the claim is that it cannot. We often detect redshifted light, and that light has not been slowed down. When we detect it, it still goes at c, even though (in fact a better word than "even though" here is "because") it is redshifted. Light is always propagating at c no matter the reference frame. More precisely: does the light really never reach us, or can we just not detect it? If it never reaches us - why? If we cannot detect it although it does reach us - why?
Let's suppose the earth is perfect sphere and let's ignore its rotation and movement. What would happen if i would be in the center of the earth? Would the gravity be zero in any direction so i wouldn't feel any gravity force? Or would there be 'pulling' forces (of half of the gravity force on the surface) that would attract me in every direction. Or in other words - If i would be in the center of the sun, would i be in a weightlessness state or would i be torn to a pieces (except of having a serios sunburn of course)? I know there are similar questions here: Effect of gravity at center of Earth Would you be weightless at the center of the Earth? but they are ot answering whether there would be no force or there would be forces to all direction. Some answers implies that the forces would be the same but in every direction so they would 'cancel' each other. But i'm not sure what does it mean. If I'm dragging a paper to different directions the forces are not zeroed, the paper is torn apart.
If I'm trying to advertise that you can scroll through this webpage to find additions that go in/on your home, would it be... "Find new additions for your home." "Find new additions to your home." Does "find for your home" technically mean that your home itself is literally looking for new additions and you're looking on its behalf? And therefore "to" is correct? The problem is, what if it were something like advertising gift-giving, and said... "Find shoes for your friend." In that case, it could be read as finding shoes on behalf of your friend, but also finding shoes that suit your friend. Certainly, "find shoes to your friend" is absurd. So, why does it work in the home example (assuming "to" is correct in the home one)? Thank you :)
I was once asked the question: What French word is commonly used in English for which an English word is commonly used in French? The answer was respectively rendezvous and date, which I found very unsatisfying. So, does such a situation exist, in which a French loanword is used in English to mean something for which an English loanword is used in French? Criteria: Both loanwords should be fairly common in the language that borrow them. By that, I mean that it is expected of the general population to know this word. A more precise definition of this criterion would be the absence of the "specialised" tag in the Cambridge dictionary. Both words should ideally be actual loanwords, meaning that their spelling hasn't changed, except for any punctuation. ("Gastronomy" or "beef" wouldn't count.) Research done: I've looked at various lists of French words used in English and did not find a match, as well as this related question. ChatGPT was no help.
I am working with optically active nanomaterials (quantum dots, perovskites), that have pretty large exciton binding energies and can form multiexcitonic complexes, e.g. biexcitons, relatively easily. It has been well established that they also exhibit biexcitonic lasing/ASE under above threshold excitation, so here I have a question. To have lasing behavior/ASE, stimulated emission process should occur which requires population inversion between upper (biexciton) and lower (exciton) states. However, in the current literature when this effect is reported for any new material, population inversion requirement is barely ever mentioned and I wonder why. Is it for some reason biexcitonic recombination is a "special" transition, and therefore this requirement is lifted, or population inversion indeed takes place? If any of these options is correct, could you, please, elaborate why that happens? What is the mechanism lasing or inversion build-up? Thank you!
Massive compact halo objects ("MACHOs") include a wide variety of hardly detectable bodies such as brown / white / black dwarfs and black holes, to name a few. If we take into account the inevitable end of all stars into either a white dwarf, a neutron star or a black hole and we compare the average lifespan of a star with the time star formation has been active since the Universe started, then we can tell galaxies already contain many dead stars which still have mass and can therefore interact gravitationally with the rest of the bodies in said galaxy. Furthermore, stars tend to accumulate in the galaxy's bulk (primarily) and in the galactic disc as well, so if dark matter happened to be MACHOs, which are distributed in said proportions, then this would account for the fact that models such as the dark matter halo need to have a density such that it decreases the further away we get from the centre of the galaxy. Finally, MACHOs are bodies we know to exist for a fact, whilst particle dark matter (e.g. WIMPs) has not been found. Is there a reason for which MACHOs are not the most likely candidate for dark matter?
I have recently watched a couple of lectures in order to revise some of the notions that I will have to tackle in the coming months, and as I did so I have stumbled over something which baffled me a tad. Now, within these lectures the lecturer described a relation as being a function solely if it maps one element from the domain to one sole, unique element from the codomain (or range assuming it is a surjective function we are dealing with); I found this a tad confusing since, ever since I can remember we considered functions to map a value from the domain to one sole value from the codomain/range, and if no value from the domain is mapped multiple times to the same value within the codomain/range then it is injective, hence abiding to the lecture's definition of a function. Have I been missing something, do people automatically discard non-bijective, or at least non-injective functions for whatever reason?
According to Archimedes' principle, the buoyancy force on a submerged object is given by the product of the mass of the displace fluid and the gravitational acceleration. Effectively, it is determined by the net pressure difference of the fluid between the bottom and the top of the object, or in other words the weight difference of the corresponding columns of fluid. However, if we have a weight placed on a scale for instance, this weight will change if we accelerate the scale upwards or downwards. As scale in freefall for instance will register zero weight. Now as the buoyancy force will accelerate an object initially at rest, should it not be reduced as a result of this (the buoyant object can be considered the scale here and the fluid column the weight being measured)?
I want to start learning some optimization theory (mainly to get into ML in the future but I'm also just very interested in mathematics that intersects heavily with engineering) and I would like to get some recommendations to start tackling the subject. I found two books: Bierlaire's Optimization book and Convex Optimization by Boyd and Vandenberghe but the former seems to lack convex optimization which I've heard is quite foundational and the latter seems to target more practitioners of optimization algorithm where I want to get into theory to understand exactly why the algorithms work and both mention that they target engineers in their preface and I'm not sure if that's a good or a bad thing. So are there any other introductory references to the subject that target mathematicians which I'm missing?
Very roughly, dark energy tends to cause space to expand and mass tends to cause space to contract. If nothing gets in the way, the math on that contraction breaks down when it forms a black hole singularity. So the question is, can enough energy halt the contraction before it forms a singularity, but after it forms a black hole (i.e. an event horizon)? Are there any theories that have tried to use this to avoid the the math breaking down? Edit: after some digging, I have found that the Penrose-Hawking singularity theorems gives conditions where a singularity must form, but I've yet to find a description of what happens (or could happen) if those conditions are not met. Namely, it seems like "interesting" thing might happen if negative energy became part of the conditions inside a black hole.
For each segment of a piecewise Lyapunov function that exhibits asymptotic stability, we can utilize the LaSalle-Yoshizawa theorem and solve it using a differential inclusion. This allows us to merge all the piecewise Lyapunov functions and demonstrate that the entire system is asymptotically stable. Now, if each segment of my piecewise Lyapunov function achieves finite-time convergence, specifically in the form of square root, how can I utilize the differential inclusion? Can you explain whether the overall system is finite-time stable? Upon searching through some resources, I found that these studies generally assume each segment to be asymptotically stable and then prove that when the function obtained through the differential inclusion exhibits square root convergence, the overall system is finite-time stable. However, if my current equations do not exhibit asymptotic stability for each segment but instead demonstrate finite-time stability, how can I prove it?
I'm not a physicist in any way, but I'm curious enough to watch and attend some pop-science lectures. Let's imagine the following situation - there is a free-standing unbound electron. It has its wave-function describes probabilities to find it in particular position. Also there is incoming photon with a proper wave-length to be absorbed. How the electron "decides" to absorb it, from what distance? If it's probabilistic too then electrons can absorb photons from centimeters away? And we shoud be able to verify it statistically by observations of many photons and electrons. Since the photons are stretched out by cosmological expansion, then I assume that they have the length in physical space. Is the absorption instant or does it take time to absorb the "whole" photon? If the absorption is not instant then it's possible to make a trick: make the electron annihilate with positron - after it started to absorb photon, but right before it finished. What will happen to "unabsorbed part" of photon? What is a correct theoretical answer to my questions?
Was all the energy that is the universe today, present at that femtosecond theory has pushed back to or was there an influx of energy for a period of time? My question was: is the big bang like a pin prick in an infinite balloon of water? Initially, you have very high pressure, then as the hole expands the pressure drops but the flow doesn't stop. In the case of the universe is the big bang still pouring gluons and muons in everywhere at about the same rate as it always has, it's just that over this much larger volume it is less dramatic than the first few centuries. Does our universe create a back pressure at its various stages that would explain the changes in rate of expansion over time? It is equally likely I am fundamentally misunderstanding what it means to be in an expanding universe. I suspect it's fairly obvious to those that might answer that I've watched more science documentaries than is healthy but fail to comprehend most of the wikipedia pages describing the physics and maths that support them. I expect you see lots of these stupid questions and I suspect this has been asked before, but I couldn't find it.
I was interested in electromagnetic induction in loops, since ground loops and such tend to be a problem in electronic system engineering. To me, it seems like induction in loops may tend to cancel out. For example, if the plane of a simple wire loop (that is just a ring of wire and nothing else) is perpendicular to an electromagnetic wave, using the normal rules for induction in wires, the E-field of the electromagnetic wave would be parallel to the top and bottom of the loop, and induce a current in the same direction in both the top and bottom. The sides, would be perpendicular to the E-field, and have no electromotive force on them. I asked about this on Quora, and was told that a "counterclockwise circulation" would be induced per Lenz's law. I know inserting a north pole into a wire loop does that, but, that was not what I asked. I found this question here on Physics Stack Exchange, EM waves from AC current in a loop?, and it seems to suggest cancellation of forces for a radiating wire loop. A receiving wire loop seems like it might have similar behaviour. So my question is, what current is induced in a wire loop whose plane is perpendicular to an electromagnetic wave, when the electromagnetic wave passes over it.
We, as humans, given our height and size, view the world from the same general perspective. An ant, on the other hand, will understand the same world in a completely different way, given how limited their knowledge and experiences can be. When we spend a couple seconds taking a step out onto our front yard, it might have taken a microbe years to travel that same distance (assuming it can survive and all that). To the ants living in your front yard, your back yard might just be the "edge of the Universe" for them, let alone the other side of the city or continent. For an organism smaller than even Planck's length, assuming such thing exists, then Planck's length might just be the limit of their world, and who knows what's going on down there. Let's reverse that thinking and apply it to something that's bigger than us. Now, we are playing as the "ants" or the "organisms smaller than Planck's length". A bear, for example, can travel farther than a human given the same amount of time, and what we view as "further apart" might seem "closer" to the bear. To something as big as a planet, the Earth might be its "front yard" and the moon its "back yard". For something much much bigger, the size of a galaxy, lets say, what would be its "other side of the city"? By "taking a step", that thing would travel a distance worth of many light years in just a few seconds, right?
I am very poor at English, so I used ChatGPT to translate my question. My question is here (Is my idea right?): Is it possible to conceive concepts like a coordinate system in a completely empty space? I believe that without some reference, even establishing an origin becomes impossible. In a space where there is just one object (please consider the object is very small), it is possible to consider an origin. You can regard the location of that object as the origin. However, I think it's not possible to conceive axes in this context. In a space with exactly two objects (please consider the objects are very small), it is possible to establish an origin and one axis. You can choose a location of one object as the origin and define an axis with a positive direction towards the other object's location. Nevertheless, I believe it's not possible to conceive the other two axes. It is only when there are three objects (please consider the objects are very small) in a space that one can begin to consider a coordinate system.