Nikola Mirkov | Searcharxiv

arXiv2026

Percolation and Threshold-like Behavior in Multiple Sclerosis Progression

In this study we investigate the Percolation Hypothesis for Multiple Sclerosis Progression. The methodology relies on cross-reference analysis centered around a question: What is the evidence for a Percolation/phase-transition hypothesis in Multiple Sclerosis (MS), especially the idea that the RRMS dynamic balance can abruptly break akin to crossing a percolation threshold into SPMS? We identify theoretical models invoking percolation/critical thresholds, network/connectome studies assessing percolation robustness or threshold-like behavior, clinical markers showing thresholds or early-warning signals, and counter-evidence arguing for gradual/continuum transitions.

cond-mat.dis-nn↗

arXiv2012

A Bernstein Polynomial Collocation Method for the Solution of Elliptic Boundary Value Problems

In this article, a formulation of a point-collocation method in which the unknown function is approximated using global expansion in tensor product Bernstein polynomial basis is presented. Bernstein polynomials used in this study are defined over general interval [a,b]. Method incorporates several ideas that enable higher numerical efficiency compared to Bernstein polynomial methods that have been previously presented. The approach is illustrated by a solution of Poisson, Helmholtz and Biharmonic equations with Dirichlet and Neumann type boundary conditions. Comparisons with analytical solutions are given to demonstrate the accuracy and convergence properties of the current procedure. The method is implemented in an open-source code, and a library for manipulation of Bernstein polynomials bernstein-poly, developed by the authors.

math.NA↗