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0
votes
1answer
71 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
66 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
185 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: ...
0
votes
0answers
24 views

Adaptive refinement of integral domain

In electromagnetics we need to calculate the radiated power which is defined as something like $P_r=\int_0^{2\pi}\int_0^{\pi}R(\theta,\phi)\sin{\theta}d{\theta}d\phi$ We already have $R(\theta,\phi)...
4
votes
1answer
299 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. ...
9
votes
4answers
335 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. ...
8
votes
1answer
440 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
212 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} ...
3
votes
0answers
413 views

Examples of beautiful theories without applications [closed]

What are examples of beautiful theories, which have no known applications?
10
votes
1answer
490 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 ...
0
votes
1answer
87 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 ...
0
votes
0answers
191 views

Best measure for curve similarity

I would like to measure similarity between two curves represented by two arrays of points. The similarity measure should not depend on the size of these shapes. Two similar shapes but have different ...
12
votes
4answers
2k views

How is differential geometry used in immediate industrial applications and what are some source to know 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 ...
18
votes
2answers
616 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
231 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
votes
3answers
683 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
811 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 ...
37
votes
7answers
4k 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/...
1
vote
1answer
377 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
73 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
262 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
162 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 $...
26
votes
8answers
4k 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
53 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 ...
-3
votes
1answer
328 views

Hilbert space vector representation for data in a metric space. Where am i wrong in this experiment?

Consider the function space $M$ such that all its elements are of bounded variation, square integrable and of unit norm. An equivalence class is defined over this set as, $f \sim g$ iff for some $\...
1
vote
0answers
240 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 ...
12
votes
4answers
2k 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
2answers
435 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
1answer
289 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?
2
votes
1answer
58 views

IVP accuracy - scheme accuracy Vs. derivative accuracy?

General Question: If I have an IVP with periodic and continuous initial condition, which rules the accuracy of the scheme - the manner in which we approximate spatial derivative or the acuuracy of the ...
4
votes
1answer
119 views

Continuity of the stationary distribution of $M/G/1$ queue w.r.t. the input rate

Let $(\lambda_n)_{n\geq0}$ be a sequence of positive numbers such that $\lambda_n\rightarrow \lambda$ as $n\rightarrow +\infty$. These $\lambda_n$ are the parameters of a sequence of Poisson Processes ...
0
votes
1answer
100 views

Comparing ideals in posets

Consider a partially ordered set $P$, and two upper sets $U_1$, $U_2$ in this poset. What are some natural ways to measure how equal these two upper sets are? This question arise naturally in the ...
15
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
1answer
455 views

Computer Science applications of Roth's Theorem [closed]

I have been reading about Additive Combinatorics and in particular Roth's theorem which states any positive upper density set has infinitely many 3-step arithmetic progressions. Let $A \subset \...
1
vote
1answer
80 views

Explicitly relating two functions containing exponential terms [closed]

This is an extremely basic question for a forum like this, but I am unable to think of any workable approaches myself. I have two functions related to the distribution of administered drugs in the ...
105
votes
18answers
10k views

How does one justify funding for mathematics research?

G. H. Hardy's A Mathematician's Apology provides an answer as to why one would do mathematics, but I'm unable to find an answer as to why mathematics deserves public funding. Mathematics can be ...
2
votes
0answers
41 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 ...
3
votes
2answers
360 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 ...
12
votes
0answers
756 views

Malaysia Airlines Flight 370? [closed]

News reports about Flight 370's disappearance have given a sketchy idea of how hourly pings to a satellite have helped build up a picture of where it went. From a naive intuitive point of view, if ...
5
votes
2answers
313 views

Average number of distinguished leaves in a binary tree

By a binary tree, I mean in this question a full rooted binary tree in which left and right child are labeled. A leaf of such a tree is a vertex of degree at most 1 (most references would probably ...
-2
votes
1answer
172 views

Solving a difficult equation for a variable?

I'm trying to obtain the maximum likelihood estimate of the parameters for a model I'm building. I have constants $\sigma$, $\mu$, and $q_0$; a boolean matrix $\alpha$; and vectors $A, \beta, r, d,$ ...
3
votes
2answers
320 views

Is there a source linking Robinson's work in wing theory with his theory of infinitesimals?

Abraham Robinson worked in applied mathematics for several decades. MathSciNet lists 12 articles by Robinson in wing theory. His production included the book Robinson, A.; Laurmann, J. A. Wing theory....
30
votes
5answers
4k views

Differentiable functions with discontinuous derivatives

For years I've taught my honors calculus students about functions like (the continuous extension of) $x^2 \sin 1/x$, and for just as many years I've told them that they won't encounter functions like ...
10
votes
2answers
2k views

How difficult will it be for me to switch fields (details below) after my Ph.D. in pure mathematics?

I'm a first year postdoctoral researcher, working in pure areas of Riemann surfaces and differential geometry, after just finishing my Ph.D. in 2013. Recently I've also started taking interest in ...
0
votes
0answers
193 views

Job sites for applied/interdisciplinary Mathematics?

I was wondering whether there're job sites that post jobs in applied/interdisciplinary mathematics, more specially, say postdocs or higher positions in mathematics and medical imaging, mathematics and ...
5
votes
3answers
916 views

New trends in Applied Graph Theory [closed]

What are current trends in Applied Graph Theory? I am interested mainly in non-algorithmical problems. Maybe even in applications of graphs to other mathematical disciplines. For example, abstract ...
3
votes
1answer
424 views

A particular contour integral

Mathoverflow, I'd like to carry out the following integral, $$f(t) = \int_{- \infty}^{\infty}\frac{-i\Omega e^{i \Omega t}}{1-\sqrt{-i\Omega}\coth(\sqrt{-i\Omega})} d\Omega.$$ Here's what I've ...
1
vote
1answer
206 views

Request for some references exploring the connections of Riemann surfaces with medical imaging

I'd like to know some references for a beginner who has basic background in Riemann surfaces and differential geometry, and would like to start learning/working on more applied areas, medical imaging/...
5
votes
3answers
301 views

Visualizing a graph

I have a finite but huge metric graph with say 1000 vertices. It comes say as 10000x10000 symmetric matrix filled by $0,1,\dots$ and $\infty$; 0's on the diagonal and $\infty$ is for pairs of vertices ...
1
vote
0answers
346 views

Distribution of random vectors

Two positive numbers $\alpha$ and $\beta$ are given. We are going to describe a process of choosing a random vector on the unit sphere $S$ in $\mathbb R^3$ (given by $x^2+y^2+z^2=1$). A vector $u\in ...