arXiv research

Unified approach to experimental design using interlacing polynomials.

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

We characterize those unions of embedded disjoint circles in the 2-sphere which can be the multiple point set of a generic immersion of the 2-sphere into 3-dimensional space in terms of the interlacement of the given circles. Our result is the one higher dimensional analogue of Rosenstiehl's characterization of words b…

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…

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.

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

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…

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.

This paper establishes certain existence and classification results for solutions to $SU(n)$ Toda systems with three singular sources at 0, 1, and $\infty$. First, we determine the necessary conditions for such an $SU(n)$ Toda system to be related to an $n$th order hypergeometric equation. Then, we construct solutions …

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

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…

Weaved helices form mechanically stable 3D structures.

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

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

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

Equation discovery method reconstructs model structure and parameters from data.

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

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

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…

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 paper synthesizes mp-MRI data for prostate cancer detection.

Discrete Morse-Bott theory on CW complexes generalizes Forman's theory.

The paper connects function theory, dynamics, and ergodic theory via Thurston's theory.

Survey of Floer theories and their connections.

New classes from 4D gauge theories.

Lectures on topological field theories and differential cohomology.

New theory couples Chern-Simons to matter, topological.

The paper defines strong emergence in field theories and proves it exists between certain theories.

Topological string theory derived from string geometry for non-perturbative effects.

New cohomology theory for Lie 2-algebras extends classical theory.

Researchers solve M-theory's gauge enhancement problem using advanced homotopy theory.

Unified Higgs bundle vacua from M-theory on Spin(7) spaces.

This is the first paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory, Gromov-Witten Theory and Symplectic Field Theory.

Researchers find new $G_2$-conifolds in $M$-theory with potential field theory duals.

We survey three different ways in which K-theory in all its forms enters quantum field theory. In Part 1 we give a general argument which relates topological field theory in codimension two with twisted K-theory, and we illustrate with some finite models. Part 2 is a review of pfaffians of Dirac operators, anomalies, a…

New theory captures framing anomaly in gauge theory.

Researchers compute K-theory for cohomogeneity-one actions.

Distributivity in algebraic structures appeared in many contexts such as in quasigroup theory, semigroup theory and algebraic knot theory. In this paper we give a survey of distributivity in quasigroup theory and in quandle theory.

Survey on algebraic K- and L-theory conjecture.

Study pin manifolds using Clifford linear Dirac operator and KO-theory.

Main mathematical applications of Frobenius manifolds are in the theory of Gromov - Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and of their extensions, in the hamiltonian theory of integrable hierarchies. The theory of Frobenius manifolds establishes rema…