arXiv research

Unified approach to experimental design using interlacing polynomials.

Characterizes 2-sphere unions from immersed circles, akin to Rosenstiehl's plane curve codes.

Study eigenvector overlaps in large Gaussian matrices, simplifying for GOE.

A knot diagram has an associated looped interlacement graph, obtained from the intersection graph of the Gauss diagram by attaching loops to the vertices that correspond to negative crossings. This construction suggests an extension of the Kauffman bracket to an invariant of looped graphs, and an extension of Reidemeis…

Loops in surfaces and chord diagrams are studied with graph factorizations and grammars.

Uncountably many contractible 3-manifolds with double 3-space property and those without are identified.

New concept of regular separation for ODEs leads to improved Hardy field results.

In earlier work we introduced the graph bracket polynomial of graphs with marked vertices, motivated by the fact that the Kauffman bracket of a link diagram D is determined by a looped, marked version of the interlacement graph associated to a directed Euler system of the universe graph of D. Here we extend the graph b…

New risk-dependent centrality measures assess node importance in financial networks.

New method combines personal and reference genomes for better machine learning in DNA sequencing.

New framework estimates eigenvalues of kernel matrices without full matrix construction.

In this paper, we study distribution of the zeros of the Alexander polynomials of knots and links in S^3. We call a knot or link "real stable" (resp. "circular stable") if all the zeros of its Alexander polynomial are real (resp. unit complex). We give a general construction of real stable and circular stable knots and…

Study surfaces with constant ratio of principal curvatures in Euclidean and isotropic geometries.

We propose a model in which a spliced vector bundle (with an arbitrary number of gauge structures in the splice) possesses a geometry which do not split. The model employs connection 1-forms with values in a space-product of Lie algebras, and therefore interlaces the various gauge structures in a non-trivial manner. Sp…

The present paper is a review of the current state of Graph-Link Theory (graph-links are also closely related to homotopy classes of looped interlacement graphs), dealing with a generalisation of knots obtained by translating the Reidemeister moves for links into the language of intersection graphs of chord diagrams. I…

Weaved helices form mechanically stable 3D structures.

Paper classifies SU(n) Toda systems related to hypergeometric equations.

Equation discovery method reconstructs model structure and parameters from data.

The paper examines circle graphs of Gauss diagrams and finds counterexamples to previous descriptions.

Solves Gursky-Streets equations for $σ_k$ Yamabe problem in dimensions $n \geq 2k$.

Let $D$ be an oriented classical or virtual link diagram with directed universe $\vec{U}$. Let $C$ denote a set of directed Euler circuits, one in each connected component of $U$. There is then an associated looped interlacement graph $L(D,C)$ whose construction involves very little geometric information about the way …

Paper proposes a robust framework for detecting multiple periodic components in time series.

This work explains how tempering improves Bayesian neural networks by reducing the impact of data augmentation.

This paper synthesizes mp-MRI data for prostate cancer detection.

The geometric approach [1312.1262] to iterated variations of local functionals -- e.g., of the (master-)action functional -- resulted in an extension of the deformation quantisation technique to the set-up of Poisson models of field theory [IHES/M/15/13]. It also allowed of a rigorous proof ([1312.1262],[1210.0726]) fo…

Study of WKB asymptotics of Stokes matrices and spectral curves, proving rhombus inequalities.

Study on Sturm-Liouville problems with zero potential and Neumann boundary conditions.

New insights into spectral statistics of sample covariance matrix for stable linear systems.