The applied-mathematics tag has no usage guidance.

**14**

votes

**1**answer

769 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

**2**answers

779 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

**3**answers

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

**0**answers

224 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

**3**answers

440 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 ...

**0**

votes

**0**answers

59 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

**9**answers

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?

**15**

votes

**0**answers

475 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

**0**answers

221 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**

votes

**4**answers

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

**1**answer

352 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

**0**answers

211 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**

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**0**answers

51 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

**3**answers

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

**1**answer

103 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

**1**answer

163 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

**2**answers

270 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 ...

**7**

votes

**2**answers

794 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

**0**answers

182 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 ...

**-1**

votes

**3**answers

2k 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

**2**answers

328 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

**2**answers

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

**1**answer

641 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**

votes

**2**answers

541 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**

votes

**0**answers

279 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

**1**answer

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

**1**answer

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

**3**answers

256 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

**1**answer

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

**4**answers

522 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.
...

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votes

**1**answer

630 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**

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**1**answer

273 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

**1**answer

664 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

**1**answer

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 ...

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votes

**8**answers

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

**2**answers

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

**1**answer

355 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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**3**answers

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

**2**answers

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 ...

**55**

votes

**9**answers

7k 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

**1**answer

923 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

**0**answers

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

**2**answers

652 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

**2**answers

284 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**

votes

**9**answers

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

**0**answers

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

**0**answers

636 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 ...

**15**

votes

**4**answers

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 ...

**11**

votes

**2**answers

479 views

### Orthogonal polynomial under linear transformation

Let $M_n(x) = x^n$ be the standard monomials. The binomial formula allows one to expand $M_n(ax+b)$ as a linear combination of $M_k(x)$, for $k \leq n$, giving
$$
M_n(ax+b) = (ax+b)^n = \sum_{k=0}^n \...

**5**

votes

**1**answer

355 views

### Book about the history of mathematics for weather prediction

Can someone recommend a book about the history of mathematics being used for weather prediction, preferable one which covers recent developments?