darklight03/StackMIAsub huggingface dataset:
I am a computer science student that is struggling with a problem of mathematical nature. Thus far I have only studied calculus, discrete mathematics and linear algebra, but cannot figure out how to approach this problem. I tried Stack Exchange, but due to the mathematical nature they suggested me to ask here, so here goes: I am trying to create shopping lists from a collection of products, where the returned shopping list should be optimized for cost as well as to meet another condition. For example, let's say that I want to create shopping lists based on the energy content of the products. When the user enters a total sum, the returned shopping list should try to max out the kcal content while keeping the total sum at or around the sum specified by the user. I've gotten so far as to create the collection of products, and all products are stored as objects with fields holding nutritional values and price etc. The kcal-value is also stored as a member variable in each product's object. At first I considered looping through all combinations of products, sort out those that are way out of the price interval, and then return the one with the highest kcal content. But as the numbers of products available increases this soon becomes a non-viable option I think. I now wonder if there is any algorithm to solve this problem, if not, is there any way to easily implement this? I've understood that this is a problem of linear type, (discrete?, diophantine?), but that's about all.
As far as I understand it, quantum mechanics requires that a particle's position to be not specifically determined in space, but rather be 'spread' out through space, in the sense that we can only know the probability a particle is at a particular location. This can be visualised through the wavefunction. When we then try to measure the particle's position, (say by firing a high energy photon at it), the particle will turn out to be at some particular location, which corresponds to the wave function collapsing (I'm not too sure if this is the right use of the term). The particle could however be found in a large range of positions. Consider an air particle, which has an initial wavefunction (in black), which we then fire a photon at to determine the position of. The air particle could then be found at position A or found at position B, with roughly equal probability. The two circumstances however cause a slight disturbance, which 'propagates' through space. What I mean by this is this air particle's position and momentum will affect the air particles near it, which will affect the air particles near those, and so on and so forth. Through chaos theory, a small change in initial conditions will result in a very different outcome, so this single misplaced air molecule has the potential to change everything about Earth. In the above diagram, air particles are depicted by dashes, with their velocities depicted by the length of the dash. As can be seen, the two situations A and B lead to a 'propagation of disturbance' (the area in which the air particles are different between situation A and situation B) which is depicted by the black circle. What I'm interested in is how quickly the circle grown in size. At first, I thought that it should propagate at the speed of light. Imagine that our air particle is situated at the North Pole. An air particle situated at the south pole will have a wavefunction that is VERY NEARLY zero at the north pole, but it will still be finite(I think). For this reason, a small disturbance of the air particle at the north pole will result in a disturbance at the South Pole directly, at the speed of light. Another voice in my head however said that this was rather silly. The disturbance should propagate rather slowly, and should only propagate through the collision of air particles. Through the atmosphere it would travel at roughly the average speed of air particles in the atmosphere, and through the solid ground it would travel very slowly. Which of the two, if either, is correct?
I am by no means an expert in the realm of physics. I do from time to time, try to understand the concepts of modern physics and their applications. I came across this video that I am currently watching, and in the beginning it explains what would happen to someone if they crossed over the event horizon of a black hole. From my understanding, the time dilation is so great near a black hole, that if you were to cross over the event horizon someone viewing you from further away would never actually see you cross and you would appear frozen forever at the edge of the event horizon due to this time dilation near great mass. If this is true, in the sense that the entire existence of the universe outside the black hole would unfold while you were stuck at the edge of the event horizon due to time dilation (Please fact check me here, I would love to know if time does actually stop for you if you cross the event horizon of a black hole), wouldn't it be true that you would actually spend no time at all inside the black hole due to hawking radiation and it's effect on the evaporation of black holes? What I mean by this is that, apparently from what I've read, a black hole will evaporate and cease to exist at the end of some finite period of time in the universe due to it giving off hawking radiation. If this is true, and if the fact that you appear to be forever frozen at the event horizon due to time dilation is also true, wouldn't it seem from the perspective of the person crossing the event horizon that the black hole ceases to exist? I am very intrigued by this possible paradox that I was questioning and I would love to know more about it's ramifications, if there are any, from many of you whom are more advanced that I. Thank you in advance.
What determines whether something is a "noun adjunct" or just a garden-variety adjective? Does it matter in any meaningful way? Here is my hypothesis, but I can't find any authoritative source to back it up. I'm hoping someone here can weigh in more definitively. Classification of noun adjuncts is based subjectively on whether the word is in "common usage" as a noun. "Book" and "chicken" are commonly nouns and would be considered noun adjuncts in "book collector" and "chicken soup"; "yellow", not so much. Noun adjuncts may share some common qualities that differentiate them from other adjectives (like not being able to be inflected into superlative forms... one can't be a "book-est collector"). But they are still fundamentally adjectives and may even appear in the dictionary as such if the adjectival usage is common enough. What I've found so far... Wikipedia defines a "noun adjunct" as: an optional noun that modifies another noun; it is a noun functioning as an adjective. But English words are not decreed to be nouns or adjectives by some higher authority. So it seems strange that one can prescriptively conclude that something "is a noun" in the first place, let alone extrapolate that it "is a noun functioning as an adjective". The wiki article cites "chicken soup" as an example of a noun adjunct, but at least one dictionary gives a definition for "chicken" as: adj. (of food) containing, made from, or having the flavor of chicken So it seems that there are some differing points of view on how to categorize these words. This question was spawned from some discussion in this question, this question and this other question.
The past few months I have been studying astronomy and Integral Field Spectroscopy (IFS). What I want to do is to fit a galaxy kinematic model to data (ie: estimate the model parameters that give the best fit result). At the moment I extract the velocity and velocity dispersion maps from an IFS datacube but I am not sure how to deal with the Point Spread Function (PSF). What is more correct: Deconvolve the data with the PSF and then fit the model to the deconvolved data? Or convolve the model with the PSF and then fit the PSF-convolved model to the data? The first approach sounds computationally faster to me because only one deconvolution is involved, but at the same time it won't give the best result because deconvolution is ill-posed even if the PSF is known. Is that right? The second solution sounds computationally slower because I will have to convolve the PSF with the model for every single model evaluation, but it will give better results because the convolution result/solution is well defined. Is that right? The data sources I use for my experiments are products of some data reduction pipeline. Why the deconvolution of the PSF is not part of the data-reduction step? Is it because of what I mentioned above? ie: The deconvolution is an ill-posed procedure and it may affect (in a bad way) the data. I am not very familiar with the deconvolution procedure but so far I have found that the Richardson-Lucy technique is a method for deconvolving with a known PSF. Are there other better techniques that are proven to give better results?
Before getting into the question, here are some remarks: Given a single point charge, the value of electric field at the position of the charge is singular/undefined, which makes sense, since a particle cannot interact with itself. Given a discrete charge distribution, the value of the field at an empty point(i.e. no particles reside at that point), is the field contribution from all the charges. However, if the point of interest contains a point-charge, then the value of the field is the field contribution from all the charges except the charge that resides at that point. Now here's my inquiry: In the case of discrete charge distribution, it makes sense to speak of the value of the electric field at a given point, whether that point contains a point-charge or not. What about continuous distributions? My intuition says yes, we can; since one can think of continuous distributions as an extension of discrete ones, with the difference being that the former contains uncountably infinite charges. Therefore, to calculate the field value at any given point on the continuous charge distribution, one has to consider the field contributions from all the charges except the one residing at that point. Example: The value of the electric field at any point on an infinite sheet (plane) of charges should be zero. Since at any given point on the sheet, one can think of that point as being surrounded by infinite concentric rings, where the field contribution from each ring (by symmetry) is zero. So does it make sense to speak of the value of electric field on continuous charge distribution? Or is it not defined?
A rather simple question for liquids specialists I guess but I have hard time finding information about this. Here is my problem. I understand the ideal gas theory and the Maxwell's speed distribution. I see an ideal gas as small balls (mostly surrounded by void) moving around very fast and colliding elasticly with each others. If you want to be more precise, you use an interatomic potential such as the Lennard Jones potential that takes into account Van der Waals attractive interactions as well as the repulsive ones. You can define a kinetic (positive) pressure, kinetic temperature and molecular (negative) pressure with such a simple model. I think I understand that pretty well for now. On the other side, I think I understand cristals fine as well. I see them as atoms bounded together by springs in which waves can flow and each atom oscillates around an minimal potential energy position. I have seen how you can calculate cristal's thermal capacity using Debye's model. So for now I think I have an idea of how a solid behaves at the molecular scale. But what about liquids? I have read very interesting posts here about molecules velocity in liquids and I would be glad to have a more general view of what a liquid is from a molecular perspective. As I understood it, molecules in liquids also oscillate around a minimal potential energy position but they can also swap positions with each other. Is that correct? Are there any tabulated values of molecules swapping speed in liquids ? Concerning pressure. Should I represent pressure in liquids as a sum of a (positive) kinetic pressure due to molecules collision and a (negative) molecular pressure due to attractive interactions between molecules? Is this a good way of representing myself a liquid at a molecular scale? Is there a model explaining the relation between viscosity and molecules attractive interactions ? -----------EDIT--------- I got the answer about swapping molecules. Now this brings me to my question about pressure in liquids from a molecular perspective. Concerning ideal gases, pressure is due to molecules collisions. Does this still stand for liquids or is it more a question of "weight" exerted by molecules on each others? Does any one know a molecular pressure model for liquids? Thank you
We can speak of "microbes" or "micro-organisms," and I used to think that these terms clearly included viruses. And they are used this way by at least some other people; here's a website that refers to viruses as a category of microbe. However, I recently discovered that these terms are usually defined as referring to microscopic "life," and the definition of "life" with regards to viruses is a contentious topic. When dealing with disease-causing agents, we can use the word "pathogen." However, not all bacteria and viruses are pathogenic. All viruses must infect living cells to reproduce, so it is appropriate to refer to all viruses as "infectious agents" (this is what the Wikipedia article on viruses uses in its introduction). However, not all bacteria are necessarily infectious. The informal terms "bug" and "germ" do exist. While these don't seem strictly limited to pathogens, that seems to be their most typical use. But for a technical audience, does any term exist for which there is a consensus that it refers to both all bacteria and all viruses? If no single word exists, a short two-word phrase along the lines of "biological entity" would also be OK. (This phrase also comes from the "virus" Wikipedia article, and seems to be the best fit I've found so far. I can also think of a few others along these lines, like "microbial entity" which could be seen as a shorter equivalent to "microscopic biological entity.") Here are the most important criteria I'll consider when deciding whether to accept an answer: technical correctness: The term must be acceptable regardless of whether one considers viruses to be living or non-living, organisms or not organisms. "Micro-organism" does not meet this criterion because some people do not consider viruses to be organisms. positive scope: It must include all viruses and all bacteria. "Pathogen" does not meet this criterion because not all viruses or bacteria are pathogenic. negative scope: It should not include inorganic objects, whether microscopic or macroscopic. E.g. rock particles. It's OK if it includes protists or multi-cellular organisms, or prions and other "pro-life," or some combination of any of these. Other important criteria for me: established terminology: I'd prefer a term that is already in use to a neologism. If a neologism seems to be necessary, I'd like it to be linguistically well-formed and etymologically transparent. length: all else equal, I'd prefer a shorter term. grammatical number: I'd prefer a term that can be used in the singular to refer to a single species of viruses or bacteria, as opposed to an always-plural word or a singular mass noun.
I recently had an argument with a friend around the question "have you ever thought about something?" The question was asked in the context of exploring some life possibilities, such as buying a sports car or moving to a different country. The disagreement was around whether an affirmative answer to the question bears the hidden meaning that the something being considered is something that the person answering actively wants. To give an example: when asked "have you ever thought about moving to Sweden?", if a person answers in the affirmative, which of the following two meanings best describes their answer? They consider moving to Sweden a practical possibility, and they actually want to do so in the future. The thought has crossed their mind, but nothing can be inferred about whether they want or plan to move to Sweden in the future. Assume the subject is not currently living in Sweden :) Question update: Some of you answered that the meaning depends on other factors, such as tone of voice, body language, context, etc. As I said in a comment, to the purposes of this question, ignore such secondary conversational artifacts. They can always extend the range of meaning of any sentence or word, from the "proper" sense, to the complete opposite, such as when being sarcastic (e.g. "Would you like to go to Sweden?" "Yeah, right...") Consequently, the disclaimer "it depends on the tone of voice" can probably be applied to most answers on this site. To put it another way: assume you read the text, with minimal context. What's the meaning then?
Ok so I'm a programmer, I'm not a mathematician, I've got a minor in math but I didn't even do particularly well at it so please bear with some possibly really stupid thoughts. Just please try to explain to me why what I'm asking is stupid so that I don't keep making a fool of myself. I recently found myself thinking along the following lines: If you take the stand that it's solipsism to talk about anything that cannot be put to use in predicting an outcome then cannot you apply the same axiom to basic mathematical operations? For example does addition really have any meaning outside of the context of placing two objects in a box and predicting how many are inside? Yeah, I realize that's a dangerous question to ask a board full of mathematicians but I imagine you can ask this question about any axiom. The problem is that in reality if you put one thing and then another into a box it does not mean that there will be two things in the box. There will likely be two things of course but if the objects are point particles like electrons there's a chance there will be one or three, or a million electrons there. Heck, the same is even possible with apples, just incredibly unlikely. I don't have the mathematical wherewithal to think through what this would mean but intuitively it would seem that this might not have many implications for addition, but might for subtraction (unless you could somehow have negative amounts of particles which I won't rule out), and certainly for things like integration and derivation. I would assume that someone's done work along these lines before? Has anyone actually created a system around it? Was it useful? Are there any accessible books or articles about it? Just interested
This question was actually asked by Alan Munn in a comment to How do I create a LCM tree diagram?. I repeat (and self-answer) it here because the answer is too long to fit the margin :-) qtree is a well-known and heavily used package for drawing trees using the so-called bracket notation. (The bracket notation is especially familiar to linguists.) forest is my own, recent package for the same job. Due to the awesome power of pgf/tikz (in particular, the pgfkeys utility), which it is based on, forest is an extremely flexible package. ---From the feedback I got so far, including feedback from this site, I don't seem to be the only one who believes so. Which makes me happy. :-) Although both qtree and forest encode trees using the bracket notation, the exact syntax is somewhat different. While forest requires that each node (including its children) be enclosed in square brackets (like this: [node [child node] ... [child node]]), qtree relaxes this requirement in the case of terminal nodes (leaves): they can be separated simply by whitespace, like this: [.node leaf ... leaf ]. Furthermore, the packages differ in the encoding of node labels: as showh above, in qtree a bracketed (usually non-terminal) node's label must be preceded by a dot (.). (forest uses the same syntax as synttree; another package that uses (and extends) qtree's syntax is (obviously) tikz-qtree. As I mentioned in a comment in the above-mentioned question, I have decided for synttree-like syntax purely out of personal taste. I guess I found it more consistent.) As Alan pointed out, the difference in the syntax makes the potential transition from qtree to forest harder: nobody wants to throw away tons of trees (s)he has painstakingly drawn. Thus Alan's question: would it be possible for forest to support both syntactic dialects?
My good friend is from Pittsburgh and frequently uses the word whenever to mean the word when. I am aware this is a regional dialect and really wish to respect that, but it is causing numerous problems in our spoken communication. (I am also a native English speaker but am not accustomed to this usage of "when" and "whenever".) I have expressed my concerns to him and asked him to use a neutral dialect to improve communication, but he argues it is valid English, he doesn't understand the difference between the two anyway, he "doesn't have problems with anyone else understanding [him]", and that my misunderstandings are because I "have Asperger's and understand [his] speech literally". (I would guess if no one else has an issue with his speech, it's because he speaks English primarily with people who have the same regional dialect and non-native English-speakers and uses French and German for work. That said, perhaps everyone else does understand what he means without any confusion. When I ask for clarification, he gets irritated.) What should I do? Examples of such misunderstandings are below: Example: Whenever my aunt was about to die, she called me into the room and told me she loved me. I understood this as his aunt periodically became ill to the point where she was close to dying and called him into the room to say she loved him. (My background in healthcare makes this seem like a very plausible situation.) I responded to him in a way that reflected my understanding of the habitual nature of this. He was annoyed and said it was obvious that the aunt was about to die one time and that, as such, this calling-into-the-room was a one-time occurrence. Example: Whenever my sister was born, my dad fainted. It is obvious to me that his sister was born one time. In this instance, although I believe the better word choice is when, I can understand that his father fainted when his sister was born. Example: Whenever I moved to Germany, I lived in Berlin. I knew he had moved to Germany once for a (temporary, location-based) job. However, his statement surprised me, and I thought maybe I was wrong (and as a friend I wanted to learn more if he had actually moved numerous times), so I asked how many times he'd moved to/lived in Germany. He was equally surprised by my question, responded he'd moved to Germany once, and could not understand how there could be any confusion in the statement.