Questions tagged [applied-mathematics]

the branch of mathematics that deals with the mathematical aspects of problems from science and engineering: applied analysis, numerical mathematics, applied statistics etc. (For applications of mathematics in general, cf. also the [applications] tag.)

Filter by
Sorted by
Tagged with
2 votes
0 answers
18 views

How to construct lattice points in bounded symmetric domain?

Consider the Hermitian bounded symmetric domain for $k \leq m$: $$ C_{k, m} = \{ Z \in \mathbb{C}^{m\times k} \,|\, Z^*Z < I_k \} $$ where $I_k$ is the $k\times k$ unit matrix. If I am not mistaken,...
user avatar
  • 7,804
16 votes
4 answers
6k views

Mathematicians learning from applications to other fields

Once upon a time a speaker at the weekly Applied Mathematics Colloquium at MIT (one of two weekly colloquia in the math department (but the other one is not called "pure")) said researchers ...
2 votes
1 answer
84 views

What are partial differential equations with fast reaction terms?

I know $u_t(t,x)=\Delta u^m(t,x),\;\; (t,x)\in (0,\infty)\times \mathbb{R}$ is the fast-diffusion equation when $m\in (0,1).$ But how are PDEs with fast reaction terms defined in general? I also wish ...
user avatar
2 votes
1 answer
108 views

Is it possible to obtain orthogonal (but not normalized) vectors after QR factorization?

After QR decomposition of a matrix, $M$, the columns of Q are orthonormal. Is it possible after obtaining Q, we recover unnormalized column vectors from $Q$? For example, the matrix M has the ...
user avatar
  • 677
16 votes
2 answers
735 views

What tools should I use for this problem?

Suppose we have $d$ cylindrical metal bars, with radius $l$, attached orthogonal to a support in random places: Now we have to attach bars with radius $k$ EVENLY SPACED, with distance $p$ between ...
user avatar
1 vote
1 answer
110 views

General strategy of error bound of matrix exponential

I want to ask General strategy of the error bound of the matrix exponential. For example, suppose, $A, B$ are finite dimension $n \times n$ matrices with complex coefficients. Using Baker–Campbell–...
user avatar
35 votes
17 answers
4k views

Listing applications of the SVD

The SVD (singular value decomposition) is taught in many linear algebra courses. It's taken for granted that it's important. I have helped teach a linear algebra course before, and I feel like I need ...
25 votes
2 answers
2k views

Importance of integral equations

Differential equations are at the heart of applied mathematics - they are used to great success in fields from physics to economics. Certainly, they are very useful in modelling a wide range of ...
user avatar
  • 3,462
2 votes
1 answer
110 views

Reference request: probabilistic models on climate (change)

I am looking for probabilistic models to address climate change. Are they known in the existing literature? I have found the post Math behind climate modeling. concerning PDE models. Many thanks for ...
user avatar
8 votes
3 answers
594 views

Explain seemingly non-random figures which arise from random Poisson points with normalization

Context Working with some biological datasets it was puzzling to see the patterns like Figure 2 (right) below. The first feeling was, that it corresponds to some biological effects like correlations ...
user avatar
0 votes
0 answers
174 views

How to measure perceived note similarity in music / simplicity of ratios?

I have discovered a method to measure the similarity of two successive musical notes which I wanted to share with a question: It is known in music theory that two successive pitches $a,b$ which sound “...
user avatar
0 votes
0 answers
203 views

A new method for processing music scores?

I have developed a method and python script: https://github.com/githubuser1983/algorithmic_python_music which allows the user to input a midi file and then chose a few numbers as parameters, and the ...
user avatar
0 votes
1 answer
151 views

Applied Topology/Topological Data Analysis conferences and journals

Can someone point out links to Applied Topology/Topological Data Analysis conferences and journals? Thank you!
user avatar
  • 3
3 votes
0 answers
60 views

What is known about discrete versions of the spatially homogenous Boltzmann equation with finitely many (but arbitrarily many) velocities?

Consider a discrete version of spatially homogenous Boltzmann equation with finitely many (but arbitrarily many) velocities $v_i \in \mathbb R^n$ with $i \in I$. Equivalently, consider a system of ...
user avatar
  • 101
2 votes
1 answer
110 views

Ramp and Cliff Solutions to the Viscous Burgers Equation: Explicit Formula?

I read an article in which the authors describe an observed phenomenon as being related to the "classical ramp and cliff Burgers solutions''. Those are described as Burgers solutions that behave ...
user avatar
3 votes
0 answers
90 views

Linearized NLS/GP around a soliton and the spectrum of the evolution operator

I apologize if this has been asked before but so far I haven't found it anywhere. Consider the Nonlinear Schrödinger equation with a potential (i.e. Gross- Pitaevskii) in $\mathbb{R}^{d}$ $$i\Psi_{t} =...
user avatar
3 votes
0 answers
462 views

Another question from Villani's monograph "Hypocoercivity"

I think there is an (possible) error in Villani's monograph titled "Hypocoercivity". To be specific, in page 62 (the first snapshot), he defined a new inner product $((\cdot,\cdot))$ as in (...
user avatar
  • 410
1 vote
0 answers
75 views

Recursive formula for integral of Chebyshev-type integral

Define $$ I_{m,n}(x,y,r) = \int_a^b T_m(x + r \sin(\gamma)) T_n(y-r \cos(\gamma)) d\gamma $$ where $T_m(x)$ are the Chebyshev polynomials of the first kind, and $a$ and $b$ are constants. Assume that ...
user avatar
  • 11
1 vote
0 answers
814 views

Is Steven J. Miller's "research" on election fraud sound? And was he paid for it? [closed]

I recently encountered the following piece regarding alleged massive voter fraud in Pennsylvania: https://justthenews.com/sites/default/files/2020-11/...
user avatar
11 votes
5 answers
475 views

What are efficient pooling designs for RT-PCR tests?

I realize this is long, but hopefully I think it may be worth the reading for people interested in combinatorics and it might prove important to Covid-19 testing. Slightly reduced in edit. The ...
user avatar
3 votes
0 answers
119 views

Notions of "completeness" and "sufficiency" of a mathematical model

I'm modelling a real-world problem as having instances $i$ in a set $P$. As a very simple artificial example, consider the problem of choosing a meeting room given a certain number of people. Then $i =...
user avatar
5 votes
2 answers
238 views

Examples of applications of hyperbolic conservation laws

I am giving a talk in front of my applied PDE research group on hyperbolic conservation laws, the most basic form of which is the PDE $$ u_t + f(u)_x = 0 $$ where $u$ is the conserved quantity and $f$ ...
user avatar
  • 590
27 votes
1 answer
2k views

Recent uses of applied mathematics in pure mathematics

In this answer Yves de Cornulier mentioned a talk about the possible uses of persistent homology in geometric topology and group theory. Persistent homology is a tool from the area of topological data ...
2 votes
0 answers
57 views

SIR model constraint [closed]

During these past months, I've heard a lot about some pandemic modelling techniques, specially the so-called SIR model. Before I begin, I'd like to stress that my interest and question are just a ...
user avatar
  • 2,707
5 votes
1 answer
247 views

Renormalization group strategies

Before introducing block spin transformations in chapter four of Random Walks, Critical Phenomena and Triviality in Quantum Field Theory, the authors state the following: "In this chapter we sketch ...
user avatar
  • 2,707
1 vote
0 answers
70 views

Gradient descent in $U(n)^r$

I have a function $f:U(n)^r\rightarrow \mathbb{R}$ which I would like to minimize. Here, $U(n)$ is the set of unitary matrices, and $r$ should be considered to be much bigger than $n$. For instance, $...
user avatar
1 vote
0 answers
101 views

Spins in classical statistical mechanics

I'm reading Kupiainen's notes on the renormalization group and also caught my attention. Actually, this is something that often causes my some confusion. On page 43, in the section about Ginzburg-...
user avatar
  • 2,707
3 votes
0 answers
50 views

Multiexponential analysis of infection counts with errors

In the past, I have seen some decompositions of sums of exponential decays into components by the Padé-Laplace method: Apply the Laplace transform $${\frak L}(\sum_{i=1}^n a_i e^{k_i t}) = \sum_{i=1}^...
user avatar
  • 27.1k
2 votes
1 answer
263 views

How many persons pass your 1.5 meter neighbourhood during 1 week ? If the distribution is power law what is the exponent?

Consider a graph with vertices being people (in some region), and make an edge if one person pass another closer than say 1.5 meter during say one week. (Such a graph might be thought a kind of ...
user avatar
16 votes
7 answers
3k views

Relevant mathematics to the recent coronavirus outbreak

I would like to ask about (old* and new) reliable mathematical literature relevant to various mathematical aspects of the recent coronavirus outbreak: In particular, standard statistical/mathematical ...
2 votes
1 answer
112 views

Persistent homology stability results (query about Lipschitz functions)

One of the beneficial properties of persistent homology is its stability results (so called robustness to noise). Usually the referenced paper is this paper titled "Lipschitz functions have $L_p$-...
user avatar
  • 1,119
14 votes
2 answers
1k views

Physical interpretation of the Manifold Hypothesis

Motivation: Most dimensionality reduction algorithms assume that the input data are sampled from a manifold $\mathcal{M}$ whose intrinsic dimension $d$ is much smaller than the ambient dimension $D$. ...
user avatar
  • 3,203
0 votes
0 answers
155 views

Help to understand a limit $\varepsilon\rightarrow 0$ computation on a fluid mechanic paper

In Córdoba and Gancedo - Contour dynamics of incompressible 3-D fluids in a porous medium with different densities (page 4) I read that if $$ v (x_1,x_2,x_3,t)=-\frac{\rho_2-\rho_1}{4\pi} \...
user avatar
1 vote
0 answers
66 views

Physical applications based on mathematical model of non-instantaneous impulsive evolution equations

In this paperhttps://www.researchgate.net/publication/269404928_Periodic_solutions_for_nonlinear_evolution_equations_with_non-instantaneous_impulses authors prove the existence and stability of the ...
user avatar
  • 59
2 votes
2 answers
241 views

A question involving directional derivatives and differential inequalities

This is a follow-up question to A question about copulas and directional derivatives. Since no answer was given, I am going to precise the definition of copula. I am interested in proving (or ...
user avatar
30 votes
7 answers
5k 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 ...
2 votes
0 answers
133 views

The topological complexity of polytopes

Polytopes arise naturally when modelling fundamental structures in Biology such as RNA and proteins [1,2]. Recently, it occurred to me that a complexity measure on the topology of polytopes might be ...
user avatar
  • 3,203
5 votes
1 answer
430 views

Fast Bourgain embedding (or similar embeddings)?

Currently I am working on applications of Bourgain Embedding (or similar embeddings of finite metric spaces to $l_2$) to automatic feature engineering for machine learning/data science ( http://www....
user avatar
16 votes
4 answers
1k views

Differential geometry applied to biology

This was originally a question posted here on MathSE. But I'll ask again here to see if I can get some different answers. I'm looking for current areas of research which apply techniques from ...
user avatar
  • 161
2 votes
1 answer
76 views

Probability distributions with irregular behaviour

Might there be a probability distribution $\mathcal{D}$ such that if we sample $a_i \sim \mathcal{D}([-N,N])$ where $[-N,N] \subset \mathbb{Z}$ then if we define the asymptotic estimate $f$: \begin{...
user avatar
  • 3,203
1 vote
0 answers
207 views

Research-level blogs on complex networks:

I'm an applied mathematician that has a research interest in complex networks for modelling biological systems and I wondered whether the MathOverflow community might know of research-level blogs that ...
1 vote
0 answers
84 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 ...
user avatar
  • 12.8k
3 votes
0 answers
62 views

Second order non-instantaneous impulsive evolution equations

The first order linear non-instantaneous impulsive evolution equations is given as; $$u'(t)=Au(t)~~ t\in[s_i,t_{i+1}],\,i\in\mathbb{N_0}:=\{0,1,2,...\}$$ $$u(t_i^+)=(E+B_i)u(t_i^-),\,\,i\in\mathbb{...
user avatar
  • 59
58 votes
22 answers
11k views

Which high-degree derivatives play an essential role?

Q. Which high-degree derivatives play an essential role in applications, or in theorems? Of course the 1st derivative of distance w.r.t. time (velocity), the 2nd derivative (acceleration), and the ...
24 votes
5 answers
5k views

Is the field of q-series 'dead'? [closed]

I had a discussion with my advisor about what am I interested as my future research direction and I said it is special functions and q-series. He laughed and said that the topic is essentially dead ...
0 votes
0 answers
724 views

The collected works of John von Neumann

Might there be an online collection of John von Neumann's collected works in pdf format? I'm particularly interested in his approach to applied mathematics(ex. shockwaves, hydrodynamics). Note: I ...
user avatar
  • 3,203
1 vote
0 answers
144 views

Doubts related Shifting from Pure to Applied math [closed]

I am a second year (Pure) Math and (Theoretical) Physics undergraduate in India. I want to do a masters in Applied/Computational Science or Math, for which I have apply after next 7 months. I have ...
user avatar
  • 127
5 votes
1 answer
125 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 ...
user avatar
3 votes
1 answer
142 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 \...
user avatar
  • 31
6 votes
1 answer
294 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 ...
user avatar
  • 9,976