Questions tagged [applications]
Applications of mathematics to any field inside or outside mathematics
156
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Applications of moduli of curves theory
Are there some applications of moduli of curves theory? I was wondering if moduli of curves theory is used (or could be used) for doing research in applied mathematics.
I am doing my PhD in algebraic ...
5
votes
1
answer
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Distances on generalizations of the symmetric group
I'm a computer vision student, and I'm looking for some symmetric group literature guidance. I'm going to provide some context, and finally ask two questions.
The Cayley distance and other distances ...
0
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1
answer
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Frequency calculation using fourier transform [closed]
How to calculate the frequency of an audio file using Fourier Transform
30
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4
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Elementary applications of Krein-Milman
This is a cross-post from MSE: Elementary applications of Krein-Milman. I'm starting to suspect that the question just doesn't really have a great answer, it's worth a try.
Recall that the Krein-...
2
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2
answers
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Application of Catalan number [closed]
Hi guys just a quick questions
What are the real life application of catalan numbers?
Thanks a lot!
6
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2
answers
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Non-trivial consequences of Löb's theorem
Informally, Löb's theorem (Wikipedia, PlanetMath) shows that:
a mathematical system cannot assert its own soundness without becoming inconsistent [Yudkowsky]
In symbols:
if $PA\vdash$ $Bew$(#P) $\...
9
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2
answers
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Applications of algebraic geometry/commutative algebra to biology/pharmacology
Are there applications of algebraic geometry/commutative algebra to biology/pharmacology?
It might be that some Gröbner basis technique is used somewhere? I know there are some applications to ...
10
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3
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Applications of knot theory to biology/pharmacology
What are the applications of knot theory to biology/pharmacology?
I guess there should be some, since proteins are quite long and some of their properties are probably related to whether they are ...
1
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3
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"Graphical models" and "gene finding and diagnosis of diseases" ?
Quote Wikipedia: Applications of graphical models include ... gene finding and diagnosis of diseases...
Unfortunately there is no comment what are these applications...
Can one comment on this ?
...
25
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Applications of group theory to mathematical biology (pharmacology)
Are there applications of group theory — broadly, say, representation theory, Lie algebras, $q$-groups, etc — to mathematical biology?
In particular, I am interested in applications to pharmacology — ...
10
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Any applications integrable systems (pde,ode, q-,...) to math. biology (pharmakinetics, pharmadynamics)?
Question Are there any relations/applications of integrable system theory (take it as broadly as one can: ODE, PDE, quantum, box-ball,...) to mathematical biology (in particular pharmacokinetics, ...
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Stochastic process with Bessel function autocorrelation. (Rayleigh (Jakes) fading for radiowave propagation)
Have the following stochastic process $f(t)$ been studied in mathematics ?
It is stationary, Gaussian, $f(t)-$complex independent Gaussians $N(0,1)$.
The autocorrelation is given by the
zero-order ...
25
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5
answers
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Sperner Lemma Applications
I was always fascinated with this result. Sperner's lemma is a combinatorial result which can prove some pretty strong facts, as Brouwer fixed point theorem. I know at least another application of ...
14
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1
answer
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Application for Morse-Smale systems
All my life I do topological classification of Morse-Smale systems (flows and cascades). Today, fundamental science is not in fashion, to receive grants require an application. Can you please tell ...
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Mathematics and cancer research
What are applications of mathematics in cancer research?
Unfortunately, I heard quite little about applications of mathematics, but I heard something about applications of physics, and let me put this ...
0
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L1-regularized Least Squares on a matrix with Toeplitz Blocks (not block-Toeplitz)
I am trying to speed up a sparse signal recovery algorithms.
My sensing matrix is a set of Toeplitz Blocks, M = [T1,T2,T3,...,Tk]
The objective is min ||Mx - b||_2^2 + ||x||1
What I'm actually ...
4
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1
answer
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Applications of Chevalley groups theory for dummies
As an algebraist i frequently receive questions from my friends-mathematicians and non-mathematicians about applications of my topic "in real life". I study algebraic groups in the stream of ...
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Applications of Hilbert's metric
Among the fascinating constructions in mathematics is the Hilbert metric on a bounded convex subset of ${\mathbb R}^n$.
Where, within mathematics, is it used ? I know at least a proof of the Perron--...
9
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1
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Any nice examples of small cancellation theory appearing in applied mathematics?
Are there any nice discussions of applications of small cancellation theory, or other cases of the word problem, in applied mathematics or algorithms for seemingly non-group theoretic problems?
I ...
2
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2
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Diffusion processes in probabilistic modelling
I'm working on a PhD project that involves parameter estimation for diffusion processes. I'm based in a machine learning research group, and the emphasis here is strongly on "practical" research.
I'...
18
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3
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Applications of and motivation for von Neumann's mean ergodic theorem
I stated von Neumann's mean ergodic theorem (VNMET) in a talk recently and someone in the audience asked what it was good for. The only application I knew of VNMET was to prove Birkhoff's ergodic ...
3
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0
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Concrete questions that turn into math problems [closed]
I'm writing an article about the way we teach math, trying to find out why so many people are discouraged from learning, and have no interest for math and logic.
At some point, I want to show that ...
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Recent Applications of Mathematics
What are the recent and new applications of Mathematics in other Sciences ?
Let me try to be more precise about the question:
By "recent" I mean the last 15 years.
By "new" I want to exclude the ...
13
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6
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Applications of commutative algebra
Hi. I'm preparing a thesis in commutative algebra, and when I say this to my friends they always ask me what are the applications to "real-world", and I don't know what to answer. This let me think ...
142
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Occurrences of (co)homology in other disciplines and/or nature
I am curious if the setup for (co)homology theory appears outside the realm of pure mathematics. The idea of a family of groups linked by a series of arrows such that the composition of consecutive ...
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Applications of mathematics
All of us have probably been exposed to questions such as: "What are the applications of group theory...".
This is not the subject of this MO question.
Here is a little newspaper article that I found ...
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Nice applications of the spectral theorem?
Most books and courses on linear algebra or functional analysis present at least one version of the spectral theorem (either in finite or infinite dimension) and emphasize its importance to many ...
0
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1
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Helpful services based on mathoverflow API [closed]
My area of research is math information retrieval. In particular, I come up with several basic ideas how to make use of a promising discussion platform offered by mathoverflow.net (MO). That's why I'd ...
4
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Rotationally-Invariant 2D Discrete Transforms
I'm interested in 2D discrete transforms (such as discrete wavelet transforms, Curvelets, Ridgelets, Beamlets etc.) that operate on a discrete unit disk and:
Are invariant to rotations only
Output a ...
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Applications of finite continued fractions
I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For Applications of periodic continued fractions I have made a special topic.)
1) (Trivial) ...
10
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Robust black box function minimization with extremely expensive cost function
There is an enormous amount of information about the common applied math problem of minimizing a function.. software packages, hundreds of books, research, etc.
But I still have not found a good ...
9
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Applications of Math: Theory vs. Practice
I have a problem: I learned about a lot of the applications of mathematics from academics. Neither they nor I have had much contact with the "real world" to go and see for ourselves how mathematics ...
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Given a function $f(t): \mathbb{R}\to\mathbb{R}^n$, can 2D, or $n$D discrete Fourier transforms be used on $f(t)$ to perform frequency analysis?
$\DeclareMathOperator{\R}{\mathbb{R}}$Frequency analysis is often performed on wave forms (1D DFT = discrete Fourier transform), and images (2D DFT), where the function in question often takes the ...
35
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Interesting applications (in pure mathematics) of first-year calculus
What interesting applications are there for theorems or other results studied in first-year calculus courses?
A good example for such an application would be using a calculus theorem to prove a ...
9
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3
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Why are divisible abelian groups important?
I just quote wikipedia:
"Divisible groups are important in understanding the structure of abelian groups, especially because they are the injective abelian groups."
I am asking for detail ...
11
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0
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How connected are you? [closed]
I apologize if this question seems frivolous, but the motivation for it is quite serious.
When I encounter the endless topic of the 'relevance' of mathematics, I am rather
fond of referring to a ...
22
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3
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Applications of topological and diferentiable stacks
What are some examples of theorems about topology or differential geometry that have been proven using topological/differentiable stacks, or, some examples of proofs made easier by them? I'm well ...
20
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Algebraic geometry used "externally" (in problems without obvious algebraic structure).
This is a request for a list of examples of problems (or other mathematical situations) that are not initially of algebro-geometric nature, but can be solved or understood by using algebraic geometry. ...
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14
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Applications of compactness [closed]
Similar to this question: Applications of connectedness I want to collect applications of compactness.
E.g.: compact + discrete => finite, which can be used to prove the finiteness of the ...
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Does the Axiom of Choice (or any other "optional" set theory axiom) have real-world consequences? [closed]
Or another way to put it: Could the axiom of choice, or any other set-theoretic axiom/formulation which we normally think of as undecidable, be somehow empirically testable? If you have a particular ...
36
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8
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Practical applications of algebraic number theory?
I'm interested in learning about any applications, the more worldly the better*.
Pointing to a nice reference on the number field sieve, for example, would be fine.
However, let me mention one ...
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Where have you used computer programming in your career as an (applied/pure) mathematician?
For background: I'm working on a book to help mathematicians learn how to program. However, I need to see some examples from people in the field that have done different kinds of things than I have.
...
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Can I relate the L1 norm of a function to its Fourier expansion?
I would like to express the integral of the absolute value of a real-valued function $f$ (over a finite interval) in terms of the Fourier coefficients of $f$. Failing that, I would like to know of any ...
106
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Most striking applications of category theory?
What are the most striking applications of category theory? I'm trying to motivate deeper study of category theory and I have only come across the following significant examples:
Joyal's ...
31
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Applications of Brouwer's fixed point theorem
I'm presenting Brouwer's fixed point theorem to an audience that knows some point-set topology. Does anyone have any zippy / enlightening / cool applications or consequences of it? So far, I have:
...
4
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Rectifying texture from image
I have a camera matrix $P$ which defines a projective transformation $\mathbb{P}^3 \rightarrow \mathbb{P}^2$. In the former space there is a plane $[ x|\pi^Tx=0 ]$. The image of the plane under $P$ ...
8
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Defining "average rank" when not every ranking covers the whole set
Here's a mathematical modeling problem I came across while working on a hobby project.
I have a website that presents each visitor with a list of movie titles. The user has to rank them from most to ...
44
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15
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What are the applications of hypergraphs?
Hypergraphs are like simple graphs, except that instead of having edges that only connect 2 vertices, their edges are sets of any number of vertices. This happens to mean that all graphs are just a ...
21
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Applications of infinite Ramsey's Theorem (on N)?
Finite Ramsey's theorem is a very important combinatorial tool that is often used in mathematics. The infinite version of Ramsey's theorem (Ramsey's theorem for colorings of tuples of natural numbers) ...
13
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2
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Archaeogenetics
This question is meant to be applied to recover historic information from genetic data.
The following model, is (probably) the simplest possible which takes recombinations into account.
First, let ...