Questions tagged [applications]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
3
votes
1answer
161 views

Abstract mathematical concepts/tools appeared in machine learning research

I am interested in knowing about abstract mathematical concepts, tools or methods that have come up in theoretical machine learning. By "abstract" I mean something that is not immediately related to ...
4
votes
1answer
374 views

Schemes over (locally) ringed spaces: working over complex-analytic spaces, rigid-analytic spaces, formal schemes, etc

Monique Hakim developed in her doctoral thesis [1] the theory of relative schemes. These comprise, as a special case, the theory of schemes over (locally) ringed spaces. What makes the study of these ...
2
votes
0answers
151 views

Applications of linear algebra in the design of aircraft [closed]

David Lay mentioned one application of linear algebra in the design of aircraft in the introductory part of chapter 2 of his book: [...] A computer creates a model of the surface by first ...
5
votes
0answers
371 views

Status of the Salmon Conjecture

The set-theoretic version of the Salmon Conjecture (that is, finding the equations that cut out the fourth secant variety of the Segre embedding of $\mathbb P^3 \times \mathbb P^3 \times \mathbb P^3$ ...
0
votes
0answers
29 views

How to get stationary process from a self-similar process in practical scenario?

I know, theoretically, if $X(t)$ is an H-self-similar process, then we can make a time deformation of $X(t)$ to get a stationary process $Y(t) = e^{-tH}X(e^t)$. My question is, in real-life, if I ...
25
votes
6answers
3k views

Applications of mathematics in clinical setting

What are some examples of successful mathematical attempts in clinical setting, specifically at the patient-disease-drug level? To clarify, by patient-disease-drug level, I mean the mathematical work ...
9
votes
2answers
435 views

Character theory and Quantum Chemistry

Who (presumably a chemist) realized first the efficiency of character theory in calculations of orbitals of atoms? In which year?
3
votes
2answers
156 views

Reference request on a bijection on trees related to Narayana numbers

The following bijection on rooted plane trees arises in the following context : the counting sequence of (rooted plane) trees with $n$ edges ($n+1$ vertices) and $k$ leaves is given by: $$\frac{1}{n} ...
1
vote
0answers
80 views

Plethora of variant neural networks?

Since a decade ago when new life was breathed in to neural networks in the form of deep learning a plethora of different architectures have come about. Is there a reference that gives compendium of ...
2
votes
0answers
338 views

Is there such a field as applied $\infty$-category theory?

It seems that applied category theory has exploded in popularity in recent years. My question is simple: had there been any work using $\infty$-category theory in applications? Edit: By ...
20
votes
0answers
722 views

Caramello's theory: applications

In this text, the author says (well, he says it in French, but I am too lazy to fix all the accents, so here is a Google translation): In any case, contemporary mathematics provides an example of ...
8
votes
1answer
320 views

Constants of motion for Droop equation

There is an important ODE system in biochemistry, Droop's equations: $$s'=1-s-\frac{sx}{a_1+s}$$ $$x'=a_2\big(1-\frac{1}{q}\big)x-x$$ $$q'=\frac{a_3s}{a_1+s}-a_2(q-1)$$ Relatively easy one finds a ...
3
votes
2answers
307 views

Applications of flat submanifolds to other fields of mathematics

Developable surfaces in $\mathbb{R}^{3}$ have lots of applications outside geometry (e.g., cartography, architecture, manufacturing). I am a curious about potential or actual applications to other ...
4
votes
1answer
234 views

Applications of De-Bruijn Sequences in “Pure Mathematics”

I know of a few applications of De-Bruijn Sequences and De Bruijn Graphs in combinatorics, applied mathematics, Engineering and computer science. But I have only found one application of De Bruijn ...
3
votes
2answers
83 views

Maximizing minimal distance between consecutive brushstrokes when painting a checkerboard torus

Suppose you have a 2-torus and you want to paint an $m\times n$ checkerboard pattern on it. Every brushstroke could paint a single square. How does one maximize the minimal distance between ...
11
votes
2answers
537 views

Reference Request: Theoretical Mixing Times Research in Machine Learning / Artificial Intelligence (AI)

I'm doing a PhD in probability theory, focusing mostly on mixing times. It's a pure maths PhD, considering precise models and showing rigorous mixing results. I'm also interested in stuff like machine ...
20
votes
5answers
2k views

Research in applied algebraic geometry that essentially needs a background of modern algebraic geometry at Hartshorne's level

By applied algebraic geometry, I don't mean applications of algebraic geometry to pure mathematics or super-pure theoretical physics. Not number theory, representation theory, algebraic topology,...
1
vote
0answers
236 views

Industrial research projects on “mathematical modeling and PDEs” [closed]

Apparently there are several companies in a great variety of fields (medical, biological, engineering, etc.) that need "consulting on mathematical modeling and PDEs" from applied mathematicians. I'...
4
votes
3answers
543 views

Application of simple Lie algebras over finite fields

I am now interested in simple Lie algebras over finite fields. In Lie algebras over the complex numbers, there are several applications and some related topics. Is there any potential application for ...
8
votes
1answer
405 views

Persistent homology over the integers

Is it likely that in the future, there will be interest in computing persistent homology over the integers (or other PIDs)? Currently, persistent homology is usually done over a field (like $\mathbb{...
3
votes
0answers
185 views

Applications of logic in theoretical and practical Computer Science [closed]

Can anyone suggest theoretical and/or practical applications of logic (modal, dynamic, Lukasiewici etc.) in Computer Science (like Markov Chains for linear algebra), as well as some open-source books ...
2
votes
0answers
117 views

References on computational PDE (in fluid dynamics, solid mechanics, etc) that emphasize both rigorous analysis and coding

I'm interested in learning about computational aspects of PDE and integro partial differential equations. In particular, I'd like to know some reference monographs that cover PDE and IPDE from in ...
6
votes
5answers
2k views

Applications of Perfect Matching

I'm exploring some applications of perfect matching and I would like some input. I have found many applications in chemistry (storing information, estimating bond lengths, estimating resonance energy, ...
39
votes
4answers
4k views

Is algebraic geometry constructive?

Notes: 1) I know next to nothing about algebraic geometry, although I am greatly interested in the field. 2) I realize that "constructive" might be a technical term, here I am using it only in an ...
1
vote
0answers
35 views

Envelope of a parametrized family of convolutions

For a certain application I need to compute a pointwise supremum of this family of gaussian convolutions: $$\sup_s f(x)\otimes e^{-\frac{x^2}{s^2}}$$ where $f(x),x\in \mathbb{R}^2$ is known and $\...
3
votes
1answer
278 views

Using High Level Probability Theory (eg Markov Chain Mixing) in Cryptography/Cryptanalysis

I'm currently doing a PhD in probability theory, specifically (discrete space) Markov chains and their mixing properties. As well as my current main project, I'm looking to have a side project, eg to ...
11
votes
3answers
703 views

What are some applications of Sperner style theorems?

I'm currently working through "Combinatorics of Finite Sets" by Ian Anderson, mostly to improve at a style of mathematics that I've historically been quite bad at, and I find myself wondering why this ...
19
votes
4answers
891 views

Applications of linear programming duality in combinatorics

So, I know that one can apply the strong LP duality theorem to specific instances of maximum flow problems to recover some nontrivial theorems in combinatorics, such as Hall's theorem, Koenig's ...
3
votes
2answers
1k views

Application for Differential Equation of higher order [closed]

We found some interesting insights in differential equations of the form $y^{(n)}(x)+F_\lambda(y(x),y'(x),...,y^{(n-1)}(x))=0$, i.e. for ordinary differential equations of $n$-th order with $n\geq2$....
7
votes
1answer
896 views

Easy Applications of Model Theory

I've also posted this question on MathSE. I'm posting it here in hopes of a more comprehensive answer. The question is inspired by the following: Model theoretic applications to algebra and number ...
6
votes
2answers
706 views

Applications of Topological Complexity of configuration space

I'm starting to work on topological complexity of configuration spaces. Articles say that this field has applications in robotic and control theory. One of the important articles belongs to Michael ...
1
vote
0answers
33 views

Formalization of adaptive sampling [closed]

The notion on adaptive sampling or adaptive plotting is fairly popular, but I have not found a formal definition. I have developed an algorithm for plotting implicit algebraic curves in the plane. ...
14
votes
5answers
2k views

Applications of space filling curves

I am seeking articles where a space filling curve has been used as a theoretical application, such as in the study of general orthogonal polynomials.
1
vote
0answers
58 views

Applications of systems with multiple time

A dynamical system with multiple time is an action of a group $\mathbb{Z}^d$ or $\mathbb{R}^d$ on a metric space. I am interested in informative examples and applications of such systems. I know ...
2
votes
2answers
328 views

Non-Formal Applications: Higman and Kruskal

After looking through many papers, I noticed that most of the discussions and proofs for Higman's Lemma and Kruskal's Tree Theorem only have formal applications in set theory, logic, and type theory. ...
7
votes
1answer
157 views

Least-squares solution of systems of Sylvester equations

The Sylvester equation $AX+XB=C$ has been studied quite a lot and there are known algorithms for solving it. But has the situation where (an over-determined) system of equations $A_{i}X+XB_{i}=C_{i}$ ...
6
votes
4answers
346 views

Application and usage of representation of integers as sum of powers?

We know that there are many articles and manuscripts from the ancient to date talking about representation of integers as sum of squares, cubes etc. I would like to know what is it the usage and ...
28
votes
8answers
8k views

How is differential geometry used in immediate industrial applications and what are some sources to learn about it?

Intuitively it might be clear that differential geometry is a very applicable subject in engineering and industry. I'd like to know how some industries/companies use differential geometry. I'd guess ...
13
votes
1answer
1k views

Which journals publish applied mathematics with mostly pure mathematics content?

In the spirit of Which journals publish expository work? please advise: What consistently high quality journals (1) today publish results that would otherwise go to a pure mathematics journal were ...
4
votes
1answer
442 views

Information theory from negative probability

Szekely provides a convincing argument of negative probability here: http://www.wilmott.com/pdfs/100609_gjs.pdf What does a reformulation of classical information theory built from negative ...
69
votes
11answers
9k views

Deep Learning / Deep neural nets for mathematician

I am interested in finding out the math ideas behind the technologies that are under the umbrella of "Deep Learning" or "Deep neural nets". Most of the papers/books that are often quoted in papers/...
4
votes
4answers
653 views

Applications of Szemeredi's Theorem

Szemeredi's Theorem is a famous theorem in Additive Combinatorics, Ergodic Theory and maybe some other parts of Mathemtatics: (Szemeredi's Theorem) Let $\Lambda \in \mathbb{Z}$ be a subset of ...
7
votes
1answer
3k views

Prime labelling of graphs

A prime labeling of a graph is an injective function $f: V(G) \to \{1, 2, ..., |V(G)|\}$ such that for every pair of adjacent vertices $u$ and $v$, $\text{gcd}(f(u), f(v)) = 1$ (labels of any two ...
15
votes
4answers
3k views

Robotics, Cryptography, and Genetics applications of Grothendieck's work? [closed]

I was reading about the passing of Alexander Grothendieck, and something caught my interest: Mr. Grothendieck was able to answer concrete questions about these relationships by finding universal ...
0
votes
2answers
319 views

Can a monotone exponentially decreasing function be uniformely approximated bt Gaussians?

This question originates an engineering application. There is a certain process that is presumed to be a sequence of diffusions and is usually modelled as a sum of Gaussians: $$\Sigma_n w_ne^{-\...
16
votes
5answers
1k views

Examples of research on how people perceive mathematical objects

What examples are there on research related to human perception and mathematical objects? For example, the shape of a beer glass influences drinking habits, since people are bad at integrating. ...
2
votes
0answers
42 views

Where to read about this kind of “measure of irredundancy” of a set from a family of sets?

Studying a very practical problem from psychometrics, I encountered the following construction. Let $(X,\mu)$ be a measure space; if preferred, you can presume $\mu$ is a probability measure. In any ...
1
vote
2answers
287 views

What is known about $\displaystyle \sum_k{a^{b^k}}$?

What is known about $\displaystyle \sum_k{a^{b^k}}$? I am very interested in the possible applications of this series. I have asked about this on Mathematics Stack Exchange here. I'm wondering if ...
3
votes
2answers
412 views

Physical and real life interpretation of the concept of regularity used in differential equations?

I guess the title kind of speaks for my questions: I'm curious to know what could be the physical interpretation or real life application of the concept of regularity that arises in PDE: take for ...
23
votes
3answers
2k views

Algebra and Cancer Research

Let me start by acknowledging the existence of this thread: Mathematics and cancer research? It is well-known that mathematical modeling and computational biology are effective tools in cancer ...