The applied-mathematics tag has no wiki summary.

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**1**answer

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### 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 ...

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**5**answers

881 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 ...

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vote

**1**answer

201 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**

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**0**answers

67 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 ...

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**2**answers

108 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 ...

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**0**answers

19 views

### Connectedness of conincidence set [duplicate]

Is there any criterion for connectedness of coincidence set, for obstacle question
$min{Δu, u-ϕ}=0$ and with prescribed boundary value $\lim_{|x|\rightarrow\infty}u(x)=0$?
Or any other kinds of ...

**2**

votes

**2**answers

100 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 ...

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**8**answers

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 ...

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**0**answers

45 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

**1**answer

235 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 ...

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**0**answers

102 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 ...

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**4**answers

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 ...

**8**

votes

**1**answer

224 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

210 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

**1**answer

48 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 ...

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votes

**1**answer

98 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 ...

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votes

**1**answer

93 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 ...

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**5**answers

894 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

**1**answer

424 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

**1**answer

66 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 ...

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**17**answers

7k 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 ...

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**0**answers

36 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

**2**answers

267 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 ...

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**0**answers

728 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

**2**answers

257 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 ...

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votes

**1**answer

151 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 $A, \beta, r, d,$ ...

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votes

**2**answers

294 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 ...

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**5**answers

2k 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 ...

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**2**answers

1k 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 ...

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**0**answers

140 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 ...

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**3**answers

592 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 ...

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**1**answer

338 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 ...

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vote

**1**answer

197 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 ...

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votes

**3**answers

297 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 ...

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**0**answers

285 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 ...

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vote

**1**answer

154 views

### Approximating $\prod_{i=1}^{n-1} (1-ai)$ for large $n$

I have a function of the form:
$f(n) = \prod_{i=1}^{n-1} (1-ai)$
Here, $a \geq 0$ and $(a*i) < 1$. For $n > 10^5$ or $10^6$, what is the best possible analytic approximation for $f(n)$ that ...

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votes

**1**answer

162 views

### Regular Perturbation Series soln to eqn

I want to find the a 3 term perturbation soln of
(i) $(1+x)^3 = ex$ where $e\ll1$
Direct substitution of the regular perturbation series $x = x_0 + ex_1 + e^2x_2$
into (i) does not work
I ...

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votes

**12**answers

3k views

### Mathematics and cancer research?

What are applications of mathematics in cancer research?
My answer.
Unfortunately I heard quite small about math, but I heard something about
applications of physics. And let me put this story here, ...

**12**

votes

**1**answer

623 views

### 2/3 power law in the plane

I've recently come across a particular problem whose solution turns out to be a probability distribution given by $f(x) = \alpha \|x\|^{-2/3}$ in the unit disk in $\mathbb{R}^2$ and zero elsewhere (I ...

**2**

votes

**0**answers

161 views

### Number of breakpoints in parametric maximum flow problems

The parametric maximum flow problem can be formulated as
$$f(\lambda) = \min_{x\in\{0,1\}^n} \left( \sum_{i}(a_i + b_i\lambda)x_i + \sum_{i,j}c_{ij}x_ix_j \right),
$$
where all $c_{ij}<0$ (so that ...

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votes

**14**answers

3k views

### Interesting mathematical topics arising from Biology

I've heard that there's a relatively new field of science called Mathematical Biology.
It will certainly apply well known and less known mathematical techniques to the understanding of some ...

**2**

votes

**1**answer

577 views

### name for $\underset{x}{\operatorname{argmin}} \displaystyle\sum\limits_{i=1}^n |x_i - x|$

Given a real-valued data set $ x_1, \dots, x_n $, what do you call the quantity
$$\underset{x}{\operatorname{argmin}} \displaystyle\sum\limits_{i=1}^n |x_i - x|$$
This seems like a pretty basic ...

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votes

**6**answers

2k views

### 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 ...

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votes

**28**answers

7k views

### Examples of theorems misapplied to non-mathematical contexts

For something I'm writing -- I'm interested in examples of bad arguments which involve the application of mathematical theorems in non-mathematical contexts. E.G. folks who make theological arguments ...

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votes

**1**answer

1k views

### On the non-rigorous calculations of the trajectories in the moon landings

In a paragraph written by a person emphasizing that rigour is not everything in mathematics (I wish I had written down the details), it was stated that the moon landings would have been impossible ...

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**1**answer

2k views

### Is fuzzy mathematics useful in pure mathematics ?

Fuzzy sets and logic seem to be mostly used for applying to real-world situations, control-theory, game-theory, economics, statistics, data management, artificial intelligence, automated reasoning etc
...

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votes

**2**answers

1k views

### Rotationally-Invariant 2D Discrete Transforms

Hello all,
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 ...

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votes

**4**answers

2k views

### Applied linear algebra textbook? [closed]

I have a copy of Linear Algebra Done Right, which I worked through years ago in college. I have been using that book to refresh my knowledge, but it does not have an applied or computational aspect ...

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votes

**4**answers

900 views

### Reasonable “Random” matrices to test numerical algorithms

Hello,
in numerical analysis, it is common to compare the behavior of different algorithms, and of different implementation of algorithms. This occurs not only on the theoretical level, but also on ...

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**5**answers

2k views

### Matlab book recommendation

Which book or books do you recommend that cover advanced engineering topics and problem solving using matlab?
I already finished a very good introductory book and i want something more advanced.
Do ...