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Questions tagged [applied-mathematics]

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4
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1answer
57 views

Numerical instability of the axis-angle representation of rotations in 3D

Suppose that I have $1000$ pair of points where each pair consists of a point in $\mathbb{R}^3$ and its image after a rotation in $\mathrm{SO}(3)$ with some noise. I have used RANSAC to find the ...
2
votes
1answer
76 views

Variation of steepest descent/Laplace methods for non-exponential integrands

I was wondering if versions of the Laplace/steepest descent methods exists for integrals of the type $$\int_C f(z) M(\lambda g(z)) dz$$ for $\lambda >>0$ functions $f(z), g(z): \mathbb C \...
6
votes
1answer
85 views

Further Developments of Lieb-Schultz-Mattis theorem in Mathematics

The Lieb-Schultz-Mattis theorem [1] and its higher-dimensional generalizations [2] says that a translation-invariant lattice model of spin-1/2's cannot allow a non-degenerate ground state preserving ...
14
votes
1answer
876 views

Is there any paper which summarizes the mathematical foundation of deep learning?

Is there any paper which summarizes the mathematical foundation of deep learning? Now, I am studying about the mathematical background of deep learning. However, unfortunately I cannot know to what ...
3
votes
2answers
789 views

On Mathematical Foundations of Football

Football (soccer) is arguably one of the most unpredictable sports. Countless variables play a role in determining the outcome of a certain football match. Due to the high complexity of the entire set ...
33
votes
3answers
2k views

On Mathematical Analysis of MathSciNet & MathOverflow

This question has two original motivations: mathematical and social. The mathematical motivation is mainly based on what I have seen about Zipf's law here and there. The Zipf's law simply states ...
2
votes
0answers
229 views

How to promote a blog?

Math behind might be interesting. Quite recent bloggingg activity might have interesting math model. The point is that bloggers compete for subscribers and at the same time cooperate gaining ...
9
votes
3answers
441 views

Are there any books/articles that apply abstract coordinate free differential geometry to basic thermodynamics?

The mathematical structure of thermodynamics by Peter Salamon (pdf) would be an example, but i would like a more abstract natural formulation of application of differential geometry or even geometric ...
1
vote
0answers
62 views

Questions about generalized Polynomial Chaos, book by Dongbin Xiu

I have some questions about Chapter 5 from the book Numerical Methods for Stochastic Computations, by Dongbin Xiu. Theorem 5.7: Let $Y$ be a random variable and $\mathbb{E}[Y^2]<\infty$. Let $Z$ ...
65
votes
9answers
7k views

Mathematical conjectures on which applications depend

What are some examples of mathematical conjectures that applied mathematicians assume to be true in applications, despite it being unknown whether or not they are true?
16
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0answers
535 views

Why is Persistent Cohomology so much faster than Persistent Homology

I refer to this paper: http://www.mrzv.org/publications/dualities-persistence/manuscript/ According to the results in the paper, especially the experiments in page 15 it shows that persistent ...
1
vote
0answers
222 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'...
47
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4answers
4k views

Is there a mathematical explanation for this cube packing phenomenon?

I saw this unintuitive result on dice packing: A jumble of thousands of cubic dice, agitated by an oscillating rotation, can rapidly become completely ordered, a result that is hard to produce ...
7
votes
1answer
356 views

A game-theoretical question in a political economy model

My research question in a dynamic model of political competition boils down to the following conjecture. I am confident that it holds (all simulations work), but I have not been able to prove it yet. ...
6
votes
0answers
212 views

Quantum Optimization as approximating $\mathbb{CP}^{2^n -1}$ with the orbits of a subgroup of SU($2^n$)

For example given a great circle within the sphere, we can think about computing the average distance of a point on the sphere from the great circle. Slightly more generally, given a subgroup $H \...
1
vote
0answers
57 views

Hedges' estimator of $\tau$ in the random effects model ( meta analysis)

In the random effects model we observe the $y_i$ with the standard errors $s_i^2$ where it is assumed that $y_i = \psi + a_i + e_i$ where $a_i$ is normally distributed with mean $0$ and standard ...
32
votes
3answers
2k views

Do bubbles between plates approximate Voronoi diagrams?

For example, soap bubbles:                   Image from UPenn: "A 2-dimensional foam of wet soap bubbles squashed between glass plates, after 10 hours ...
1
vote
1answer
105 views

Infinitesimal generators and conserved quantities (Schrodinger type evolution)

First, I'm no expert in symmetry analysis of evolution equations and so I apologize if this post is a bit of a cobble. The question I have is about the evolution of $\psi: \mathbb{R}^{1+1}\to \mathbb{...
5
votes
1answer
168 views

Boundary of the image of a compact manifold in the complex plane

The Question Consider the trace of an $n \times n$ unitary matrix with determinant 1 \begin{align} f: SU(n) &\rightarrow \mathbb{C}\\ U \mapsto \text{tr}\, U &= \sum\limits_{i=1}^{n-1} z_i + ...
5
votes
2answers
283 views

Mathematical physics applications in present-day image processing

During the past few years several important areas of image processing and image classification or generation became dominated by convolutional neural networks. I'm interested if there are any methods ...
8
votes
2answers
838 views

Is it fine to inquire about a paper that's been under review for around 9 months?

I have submitted a paper on applied probability in one of SIAM journals. The paper is under review for 9 months. I asked the editor 1 month ago about it, I was told that one review report has come and ...
4
votes
0answers
183 views

Game theory of writing multiple choice tests

Here is a model which seems pretty close to my experience of writing multiple choice tests. Let's view the answer $t$ to each question as a binary string in $S:=\{ 0,1 \}^k$, all equally likely. The ...
0
votes
3answers
3k views

How can I combine my interests for pure mathematics and computer science in college? [closed]

I’m a high school senior who's gone through quite the self-introspection the past few months while applying for college, and I have a bit of a dilemma. All my life, I've loved & excelled at ...
5
votes
2answers
333 views

Human brains considered as directed graphs

I assume that human brains can be considered as directed graphs with neurons as nodes and synapses as edges. I explicitly don't want to consider the weights, the dynamics of neural activity (based on ...
6
votes
2answers
1k views

What are the top journals in applied mathematics and what are the differences between them? [closed]

This question is essentially an applied mathematics version of Which are the best mathematics journals, and what are the differences between them? Unfortunately, unlike the above question I was not ...
0
votes
1answer
667 views

What are the differences between The Princeton Companion to Applied Mathematics and Mathematics for Physics by Michael Stone and Paul Goldbart?

Both of them are applied mathematics books. What are the main differences between them? Which is more mathematical i.e. mathematically advanced, mathematically rigorous?
6
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2answers
545 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 ...
8
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0answers
303 views

The function space defined by deep neural nets

Given a deep net graph and the activation functions on the hidden vertices do we have a description of the function space spanned by it? (even if for some specific architectures and activation ...
0
votes
1answer
79 views

Finding a vector representation for a data where we only know the inner products

I am an engineer working on speech signal processing and I have a problem that I have encountered while trying to model speech signals. The mathematical formulation is not entirely pure and I try to ...
4
votes
1answer
71 views

Separate a special poset by function

Assume $A = \prod_{i=1}^n\{0,1\}$, i.e. element $(a_1,\cdots,a_n)=a\in A$ is n-tuples like $(1,0,1,\cdots)$. There is an obvious partial order on the $A$: say $a < b$ for $a,b\in A$ if and only ...
4
votes
3answers
259 views

Relation between diametral path and regularity of a graph

Let $G(V,E)$ be a graph. A path whose length is equal to the diameter of a graph is called a diametral path. In a cycle graph every vertex has $2$ diametral paths. Now I need to prove that this: If ...
4
votes
1answer
2k views

Kalman filters and stock price prediction

Could someone be so kind as to direct me to a good source that would explain time series (more specifically) stock price prediction using Kalman filters, Extended kalman filters or particle filters. ...
10
votes
4answers
540 views

Moduli spaces in applied mathematics and condensed matter physics?

In this MO question it is stated that there is a relation between some aspects of condensed matter physics (namely the fractional quantum Hall effect) and the algebraic geometry of Hilbert schemes. ...
7
votes
1answer
647 views

How is Ricci flow related to computer graphics?

I recently came across the book Ricci Flow for Shape Analysis and Surface Registration: Theories, Algorithms and Applications by Wei Zeng and Xianfeng David Gu. Because, I just saw the book on the ...
3
votes
1answer
282 views

stability of the Monge-Ampère equation

Is there any hope to prove this conjecture (or a similar one)? Conjecture Let $\Omega_k$ be a family of convex (smooth) domains, and let $u_k$ be convex Alexandrov solution of $$ \begin{cases} ...
10
votes
1answer
685 views

positions of a methane molecule with carbon atom at the origin

Let $\text{CH}_4$ be the molecule of Methane: The four hydrogen atoms form vertices of a regular tetrahedron with the carbon atom in the center of the regular tetrahedron. Here we regard all atoms to ...
0
votes
1answer
92 views

Fit a system of linear ODEs from several experiments

Assume we are given several initial vectors $x^{(1)},\ldots,x^{(r)} \in \mathbb{R}^n$, where the dimension $n=6$ (in any event a number below 10) , and the number of initial vectors $r$ is in the ...
26
votes
8answers
6k 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 ...
24
votes
2answers
1k views

Persistence barcodes and spectral sequences

Persistent homology is a well-developed tool which allows topological analysis of large data sets. From a topological perspective, the input is a filtered complex, and the output is a sequence of ...
2
votes
1answer
357 views

What kind of role has Functional Analysis played in Signal Processing? [closed]

Does it serve mainly as a narration or is there any substantive consequence which might not be derived without tools of functional analysis?
12
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3answers
1k views

Models for graphs representing real-life networks

I am interested in basic models of graphs (stochastic or deterministic) that are offered for real-life networks (like social networks, the Internet, neuron networks). I will be thankful for answers ...
8
votes
2answers
1k views

random category theory

This question is in some sense dual to the one asked in Is there an introduction to probability theory from a structuralist/categorical perspective? since contrary to the OP who asks for references ...
63
votes
11answers
8k 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/...
3
votes
1answer
954 views

Is there a way to define a Lie derivative of a connection?

I've been reading a little bit about the definition of symmetries on General Relativity, and they are related with the concept of Killing vector, i.e., vectors along which the Lie derivative of the ...
2
votes
0answers
76 views

How analyze the following fully nonlinear equation

Now I want to consider the following pde $u_t(x,t)=\sigma(x,t)(1+|D_xu(x)|^2)^{1/2}$, with initial condition $u(x,0)=g(x)$ which is analytic, and on domain $D\times \mathbf{R}^{+}$, $D\subset \mathbf{...
1
vote
2answers
671 views

Curves similarity metric [closed]

I am working on an optical character recognition algorithm that takes vector data (i.e. polylines) as input rather than raster picture. E.g., we have N polyline samples, and when certain polyline is ...
3
votes
2answers
287 views

What is the sum capacity of a scalar gaussian broadcast channel?

"On the Achievable Throughput of a Multiantenna Gaussian Broadcast Channel" by Giuseppe Carie and Shlomo Shamai talks, in part, about the following type of link (paraphrasing): A transmitter with $...
32
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9answers
5k views

What “real life” problems can be solved using billiards?

Recently I gave an interview to local media where I explained some basic open problems in billiard dynamics. After a 45 min interview the reported asked me what "real life" problems can be solved ...
1
vote
0answers
64 views

connectedness of coincidence set

Consider the following obstacle problem in the whole domain $\mathbb{R}^n$ min{$\Delta u$, $u$-$\phi$}=0 with prescribed boundary value $\lim_{|x|\rightarrow\infty}u(x)=0$ and $\phi$ (can be assumed ...
2
votes
0answers
663 views

Is the stationary distribution of this Markov chain uniform?

First, a little bit of background: Since 2012, Canada has decided to phase out the penny for its coinage system. Product prices may still use arbitrary cents, especially since prices do not typically ...