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10
votes
0answers
316 views

Which limit to take as a key applied math decision

The Borel-Kolmogorov paradox refers to situations where non-uniqueness in the notion of conditioning on a set of measure zero leads to apparent contradictions. As a formal matter, one requires ...
7
votes
0answers
190 views

Coherence between different ranking methods of a graph's vertices

Given a (connected) graph $G$ it is natural to want to rank its vertices, with the more "central" vertices ranked higher. Two natural ways of doing it are: By the degrees. By the entries in a ...
3
votes
0answers
96 views

The Damworld model of Hamilton and Henderson

I've been reading some of the literature around Lovelock and Watson's famous Daisyworld earth-system model. It is a simple non-linear system of ODEs that illustrates various interesting principles in ...
2
votes
0answers
110 views

Optimization over Spectral Laplacian in cycles and trees

Is there any idea on how one can deal with an optimization problem of sum of k largest eigenvalues(min) of Laplacian matrix of a simple cycle or tree? I would like to use semidefinite programming for ...
1
vote
0answers
52 views

Are there any known bounds on the value of solutions of linear integer programming?

Given a linear objective function and a system of linear constraints; are there any known bounds on the values of (positive) integral solutions in terms of the coefficient matrix of the constraints? ...
1
vote
0answers
86 views

Influence of parameter variations on the solution of an ODE system

Hello community, suppose we are given a system of ODEs \begin{align} x'(t) &=f(x(t),p) \newline x(0) &= x_0 \end{align} where $f\in C^1(U,\mathbb{R}^n)$, $U\subseteq \mathbb{R}_{+}^n\times ...
0
votes
0answers
24 views

convection/transport with different velocities

What is the prototypical model for convective transport of a quantity whose constituents move with constant but varying velocities? In order to illustrate what a mean: Suppose that a large number of ...
0
votes
0answers
24 views

The use of wavelets in time series modelling

I have been working on modelling a time series using wavelets for a long time. I am quite familiar with the wavelet theory and all...However, I have a big understanding issue and really appreciate it ...
0
votes
0answers
312 views

Covariance matrix/kriging interpolation

I have a covariance matrix that I am trying to interpolate using kriging interpolation. The point of the kriging is to statistically predict any unknown point in-between know points. For example if I ...
0
votes
0answers
263 views

Orthogonal Projections in Lie Theory

I have been studying a finite element method where rigid & elastic spatial motions are separated using an orthogonal projection (actually two: one for translations/stretches, the other for ...
0
votes
0answers
211 views

Use Lie Sub-Groups of GL(3, R) for elastic deformation ?

I'm interested in representing elastic deformations (e.g. stretching) using Lie groups. There are a few references to using $GL(3,\mathbf{R})$ but I'm wondering if possible to use subgroups of ...