darklight03/StackMIAsub huggingface dataset:
"Weed" (the annoying plant you don't want in your garden) and "weed" (the psychoactive drug) are treated differently grammatically. Just some example sentences "There are weeds in my garden" vs "There is weed in my garden" "There is a weed growing in this pot" vs "There is weed growing in this pot" "How many weeds are growing there" vs "How much weed is growing there" "I'm going to get rid of twice the weeds" vs "I'm going to get rid of twice the weed" "Here are two types of weeds" vs "Here are two types of weed" Basically, the two words are treated completely different grammatically. I was wondering how in particular the two words are categorized that links to their different treatment. (e.g. maybe one is a proper noun, and the other is not [I know that's not the case, but it's just an example of the kind of answer I'm looking for]). Or is this just some weird slang thing that only applies to the drug "weed"? P.S.: I swear I'm not high while asking this question >.<. The impetus was actually because an anime brought up "happa", which could either mean "leaf" or "weed" in Japanese, and I wasn't sure which they were referring to. And then I got down this line of thinking >.<.
I just thought of this question, and a quick wiki search did not turn up anything. So, here is the question: Rel is the category whose objects are sets, and whose morphisms are binary relations. Is there a way to differentiate between morphisms that are functions and morphisms that aren't using purely category theoretical means (that is, not using the set structure whatsoever). Followup question: If the answer turns out to be yes, let's call a generic morphism that follows the definition an f-morphism (for function). What are the f-morphisms in other, more commonly used categories, like Set, Top, Grp, Ring, etc.? What are the co-f-morphisms (i.e. morphisms defined dually to f-morphisms)? Note that I have not yet given the question serious thought, so it may be extremely difficult or extremely easy to answer.
I'm currently working on a variant of a non-convex low-rank matrix completion algorithm, whereby we take a uniform sample of entries in a (symmetric) matrix and look to complete said matrix. For various reasons, we're interested in trying to reduce the bandwidth of our matrix initialization for our algorithm, and our first idea was using the reverse Cuthill-McKee algorithm to do this (mostly just because it's pre-built in matlab). However, the output structure of the Cuthill-McKee algorithm provides a poor initialization for our algorithm. I'm mostly just curious if there are other bandwidth reducing algorithms that people use regularly. I did a brief literature search and found some papers using neural networks to try and learn permutations to decrease the bandwidth, which looks interesting but is more work than I think is worth for this particular problem.
In some linguistics papers that I have been reading, it has been argued that a false sentence has the same semantic status as a noun phrase that fails to refer. A classic example of an English noun phrase that fails to refer would be the present King of France, if uttered today. This is because, of course, France has no monarchy any more. However, one of the examples discussed by several papers is the highest prime number. Now, intuitively it seems to me, even as a lay non-mathematician, that there are obviously an infinitely large number of prime numbers. But that's just my intuition. My intuition as a schookid would have been that it would be easy to predict which numbers were going to be prime and which weren't. So much for intuition then. Do we know that there are an infinitely large number of prime numbers? Is it possible to explain how we know (or don't) to a non-mathematician like me?
It's commonly stated in the literature that the free distance of a convolutional code is the minimum Hamming distance between the all-zero path and any other (non-all-zero) path in the trellis originating in the zero state and ending in the zero state. (The free distance of a code is defined as the minimum Hamming distance between any two distinct codewords.) My question: Is this true in general? Or is it true only conditionally (e.g. when we assume that the code is terminated in the zero state)? If it's the latter, what's the condition for it to be true? It appears to me that a sufficient condition is that the convolutional code is a linear block code. This includes the finite length "zero-tail" codes and "direct truncation" codes. The former refers to codes which include all paths that end in the zero state; the latter means the codes allow the paths to terminate in all possible states. Am I mistaken?
I have a setup consisting of two lidar sensors with a known extrinsic calibration. Both lidars have messages with the same timestamps (no timedelay between them). My goal is to estimate odometry using the data from these lidars. To achieve this, I have performed a scan-matching algorithm (ICP) and obtained transformation matrices between the consecutive pointclouds. However, I'm facing difficulties in transferring the translation and rotation frames from one lidar to another to put into some filter. The lidars are mounted on a level arm and do not have the same translation due to the Euler rigid body equation. I would greatly appreciate your assistance in understanding how to appropriately transfer the translation and rotation frames between the lidars. Any insights, suggestions, or code examples would be highly valuable. Thank you in advance for your help!
I'd like track my LaTeX projects using git, especially when collaborating with other authors. I'd also like to track my texmf directory in a separate git repository. My desire is to add my texmf repository as a git submodule to each LaTeX project. However, I can't figure out how to tell latexmk (really, pdflatex) to see my project-local texmf. Ultimately, I want my LaTeX projects to be standalone, i.e. they depend on nothing other a TeX Live install and the files in the project directory so they can seamlessly be compiled on different machines or in a CI pipeline. How can this be done? Note: I have tried the solutions presented in similar questions, e.g. here (the TEXMFHOME environment variable seems to be ignored) and here (requires updating system texmf.cnf), to no success so far.
I have a relatively strong background in the theory of numerical analysis of partial differential equations (PDEs) and functional analysis, particularly applied to the numerical analysis of PDEs using the finite element method. I'm also very interested in graph theory. I was wondering if there are any theories or research areas that unify these fields and that I could explore given my background. Are there any connections between graph theory, functional analysis, and numerical analysis of PDEs that I should be aware of? I am aware that there is another question about this, but I am interested in it being in the context of PDEs and numerical methods. Also I am looking for open questions to initiate a research project, so I am seeking topics where the intersection is significant and there are open problems. Thank you in advance for your assistance.
In Borevich & Shafarevich's Number Theory, the authors define integral equivalence of quadratic forms as follows: Two forms of the same degree with rational coefficients are called integrally equivalent if each can be obtained from the other by a linear change of variables with rational integer coefficients. They further state a second definition In the case of forms which depend on the same number of variables, this is equivalent to saying that one of the forms can be transformed into the other by a linear change of variables with unimodular matrix. But I cannot see how to prove the equivalence of the two definitions. Specifically, it seems to me that to show the first definition implies the second, one has to prove that the two linear changes in the first definition are inverse of each other, or that both changes are nonsingular. Can anyone help? edit: Mr. Stucky's example in the comments has shown that the two changes occurred in the first definition need not be invertible. But still, I think to prove that the first definition implies the second, one has to show the existence of two nonsingular changes, as is pointed out by Stucky.
Here is the sentence in dispute: In humans, the femoral angle shows no correlation with femoral length. The question: why would 'femoral angle' receive a definite article, but not 'femoral length'? I feel like it does, but my co-author says no. I can't really justify it, but I feel like 'angle' somehow needs the article whereas 'length' does not. Thoughts? Thanks for all the answers. Yes, I am aware the anatomy may be esoteric, and apologies for that. In this case, the angle is measured in degrees, or fractions (in decimal) of degrees. The length is similarly measured in centimeters or fractions (in decimals) of centimeters. (And there really is only one of each on a person's leg.) So while I felt like angle requires a definite article because of the way I have always seen it used, in this case I can't logically defend the difference between angle and length.
In Reed-Solomon codes, the symbols of a code word contains multiple bits. Since the error correction and detection happens at the symbol level, it doesn't matter how many errors there are within the same symbol, it only counts as a single symbol error. Because of this, Reed Solomon codes are considered to be a great candidate for transmissions that are subject to burst errors. On the other hand, BCH codes are always considered to be a good candidate for random errors. But is that also true in an apples to apples comparison where you compare total number of message and parity bits (not symbols!) are the same for a Reed-Solomon code and a BCH code? Would there be any way in which the BCH would lose against the RS code in terms of error correcting capability?
I'm a graduate aerospace engineering who's really interested in the topic of numerical methods and in particular for structure preserving schemes. Hopefully at September I will start a phd in this subject, as a consequence of my work of thesis. However, I do feel my mathematical background is kinda poor, coming from an aerospace engineering master degree. Indeed, I'm already excited to follow some of the courses I will in my phd courses about advanced linear algebra and functional analysis. During the summer I have some spare time, and I would love to study some of the books I encountered during my work of thesis. In particular "Geometric Numerical Integration" by Hairer et al. As soon as I started reading this book I encountered some mathematical topics that I never encountered during my degree courses: Lie algebra, Lie groups (groups in general) and manifold. I would like to know what are the books you suggest to get into these topics. I saw that "Lie Groups, Lie Algebras, and Representations" by Brian C. Hall is a really good book as a starting point for this topic, but I know there's a more general introduction to lie groups which is related to manifolds. So which books do you suggest to introduce me to these topics ? Also, I would like to refresh some knowledge about the algebra courses I did in the past, but I don't really know which book I should refer to. Thank you so much for your help.
I was going through the derivation of a mathematical equation for the upthrust exerted on a body which is given in my book. It says that the downward pressure exerted on the upper surface is less than the upward pressure on the lower surface. Thus, there is a net pressure acting in the upward direction and therefore, a net upward force. The lateral pressure gets counterbalanced. I am able to understand that the pressure in the downward direction is due to gravity and the lateral pressure is due to the fluid's tendency to flow. However, I am not able to understand how the fluid exerts pressure in upward direction. I have worked on the problem and arrived at two different explanation:- The pressure inside a fluid is due to the collision of the particles. Since, collision is random, pressure can be considered to be equal in all directions at the same horizontal level. The fluid exerts a pressure and thus, a force on the bottom of the container and the reaction of this force exerts upward pressure. Question:- How does a static fluid exert pressure in the upward direction? Which explanation of mine is correct?
While I was reading the book "In Search of Schrodinger's Cat" I found an interesting excerpt on how Max Planck used Boltzmann's statistical equations to solve the Blackbody radiation problem. The book mentions that there will be very few electric oscillators at very high energy end and at the lower end, electric oscillators would not have that much energy to add up to any significance. So most will be on the middle range. But my question is why and how this distribution of electric oscillators comes into picture. I mean why can't be the this distribution skewed, so that we may have electric oscillators concentrated at high ends. More specifically how this probability distribution was derived by Boltzmann? ( I am a layman interested in Physics so please be simple in your explanation)
I was reading a Mathematics books and it gave the axiomatic definition of a function as being a mapping from a set called "The domaine of the function" to another set called "The codomaine of the function", and at first I thought the codomaine is the image of the domaine by the function (i.e. the set that contains and only contains the images of every element of the domaine). Turns out that's the range or image of the domaine which is only a subset of the codomaine and is equal to the codomaine only if the function is surjective. My question is : Why not define a function as a mapping from a domaine (the set A) to the set B (defined as the set containing and only containing the image of every element of the domaine)? Why the need for the Codomaine set with extra elements? Isn't the complement of the range in the Codomaine irrelevant to the function? In other words, aren't all functions surjective in the end? Sometimes they say that the codomaine is the set of possible outcomes of a function, but I don't understand what they mean by "possible" in this context.
I have a hard time understanding GR. I understand a lot (from a math point) about (pseudo)Riemannian manifolds, and I also learned about Einstein's elevator thought experiment. So let me elaborate: From a physics point of view, you can take the elevator and derive that light has to bend, also that there has to be gravitational time delay. So far so good. Then almost all the literature I saw, turns to the next chapters, and assumes from the previous discussion that it is clear the (pseudo)Riemannian metric is all what matters now. For me, there is a bit gap, a 'how'/'why'/'what' in between. I do not see how the metric tensor relates to accelerated reference frames. I feel like I am missing something very obvious, but what is it? Can somebody elaborate?
I'm trying to create a transition effect in a situation when a character suddenly finds himself falling, and his last word, which ends in '-y', is transitioning into an unintelligible scream. However, English is not my native language, and when I've tried to write it as 'Maryeeee!!' it was criticized as awkward and weird. At the same time, the counter-suggestion of simply extending the '-y' at the end and writing 'Maryyyyy!' doesn't feel right to me. It may be grammatically correct, but my goal was to create an impression of a word seamlessly transitioning into a scream, preferably making it clear that it is an unintelligible scream and not just the character's speech trailing off, and if the resulting word would be a horrible mess, it was fine for as long as I achieved the desired effect. So the question is, how should I go about it?
I'm working on a problem where I need to convert an undirected and unweighted graph with cycles into a tree while preserving the edge information (all the edges from the graph are preserved in the resulting tree). For the resulting tree, the height and nodes duplication should be minimized. Nodes duplication can happen because in order to preserve the edge information from the graph, we will need to break the cycles by removing the edge(s) and then make a copy of the node(s) then connect it in the tree, or in other scenarios that I haven't thought of. I don't think minimum spanning tree algorithms will work because the algorithms will lose the edge information. So far my heuristic is: For choosing the root node of the tree, pick the vertex with the highest betweenness centrality in the graph. Because that vertex likely serves as a bridge which many shortest paths flow. When breaking the cycles, remove the edge whose nodes have the least total sum of degrees. This works for some examples I crafted.example My question is, how can I verify the heuristic is indeed optimal and provide a formal proof? Or is there a better strategy? Any insights, references, or alternative approaches would be greatly appreciated!
I am beginning to learn chemistry/physics, and I have recently read about JJ Thompson's experiment which led to the discovery of the electron. In every source that I've read, the writers note that Thompson used an anode and a cathode to conduct electricity. In addition, the magnet supposedly had N/S ends. I did not know what a charge was, so I looked it up. But, frustratingly, I always get answers that refer to electrons and protons. That is, things that are negative have more electrons than protons, and vice versa. This gives me no idea as to how Thompson inferred that electrons are negatively charged from his experiment. My question is, can you define charge without talking about electrons and protons? Thompson didn't know electrons existed, so it seems to me that he must've had some other working definition of charge in order to determine that electrons were negatively charged. What makes an object a cathode or an anode, without referring to protons and electrons? If that question doesn't make sense, is it possible to adapt it just for the sake of understanding the experiment?
My understanding of a simple k-vector is that it is the wedge product of k vectors. Also, two simple k-vectors are the same, when their magnitude, attitude and orientation match. Now my question is, could I just define a simple k-vector in this way? Meaning "a simple k-vector is an equivalence class of ordered k-tuple of vectors. Two tuples are equivalent if their attitudes and orientation match, and if the parallelograms they span attain the same magnitude." Especially a reference where this is stated would be greatly appreciated! I feel like I have read something like this somewhere, but I cannot find it anymore. I am only using k-vectors for something I am writing for university and having to explain the wedge product would deviate from my topic a little. That's why I am trying to avoid this definition.
So I am writing a program that works with regular polygons, and in part of that I need to represent circles that are inscribed and/or circumscribed upon the polygon. As this is programming, I need to refer to the relationship between the polygon and these circles. I have searched all around, but all of the places I have found that educate on calculating these circles never refer to this relational quality. As I said, I need a way to refer to this relationship and I cannot seem to find a word that represents whether a circle has the quality of being circumscribed or inscribed upon a polygon. Does any such word even exist? This pseudocode example might help clarify what I am trying to find: var myPolygon = new Hexagon(); var myCircle = CreateCircleOnPolygon(myPolygon, CircleType.Inscribed); ^^^^^^^^^^ ............ if (myCircle.CircleType == CircleType.Inscribed) { ... } ^^^^^^^^^^ ^^^^^^^^^^ The name emphasized in the above example is what I am currently using; however, considering that there are lots of different possible parts of my code that could need a different "type" of circle, the usage of the name CircleType is a little too broad in this context. I suppose the word "quality" is what I am going for, but I thought I would reach out to the language experts to see if there is a term I am unaware of that is more appropriate.
I can imagine a relatively simple experimental setup whose resulting data could easily be compared with theoretical predictions: Send two identical atomic clocks into orbit and settle them at rest relative to each other. Then synchronize them. Then use thrusters attached to one clock to oscillate it, causing it to experience a series of counterbalanced accelerations (not changing it's average distance from the non-accelerated clock). Then collect data from both clocks to measure their desynchronization over time. My preliminary calculations suggest that the energies involved to reach relative velocities between the clocks that should produce measurable desynchronization in a matter of days or weeks are feasible, since atomic clocks are so accurate. I know the twin paradox isn't really a 'paradox' and that the predictions in general relativity are completely coherent. I've read a bunch of responses to related questions, explaining exactly what is predicted. But I can't find any experiments that confirm those predictions directly.
As I understand, for elevation mapping using InSAR, one typically requires an out-of-plane baseline to create the required phase difference between images to detect objects at height. This usually requires either multiple satellites flying in formation or waiting for a repeat pass of a single satellite. This paper, A New Single-Pass SAR Interferometry Technique with a Single-Antenna for Terrain Height Measurements, suggests that one could achieve this in a single pass (along-track interferometry), if we are able to image at a high squint angle. The idea is that a grazing-angle difference is still present in the along-track case when squint angle is high. This is not the case for broadside imaging. However apart from this paper, I was not able to find any other sources to cross-reference the viability of this approach, nor does it seem that anyone else has reproduced the results. The mathematical principle behind seem sound to me. If it works, why is this concept not being used more often, and if it doesn't actually work, where is the error in the logic?
I would like to ask your opinion on the point that looks simple. Consider the group of orthogonal matrices of order n over the field R of reals, equipped with the topology induced by the Euclidean norm of matrices. Let g be one of such matrix and denote by X the topological closure of the cyclic group generated by g. My question: May I find a matrix g with the property that: if the identity matrix I is the accumulation point in X of some sequence of powers of g, then the sequence is definitely trivial, that is, all the elements (except finitely many) equal I? In other words, can I exclude that, for a suitable g, the identity I is obtained as the accumulation point of a non trivial sequence in X? I don't think such g exists but I'm not be able to exclude it with a direct argument. Thank you very much for help.
Perhaps another way to put it is, what exactly does it mean to quantize the EM field and why is it necessary? What mathematical properties does the quantized version of the field have that the classical version doesn't and vice versa? For context, I was reading a thread about where specifically classical E&M fails and we hence need QED to get accurate predictions, and stuff like the ultraviolet catastrophe and the photoelectric effect were mentioned. I get why those things necessitated the introduction of quantum mechanics and especially modeling photons as wavefunctions. What I don't get is why we can't just use "regular" relativistic QM with Maxwell's equations and the same mathematical E and B fields (which together form the EM field) from classical E&M. What goes wrong if we try to do this and how exactly does QED fix it? Or, to put it another way, what properties does a field modeling photons as wavefunctions need to have that the classical EM field doesn't have?