Related papers: Predicting Euler Characteristics and Constructing …
The statistical analysis of marked point processes requires disentangling complex spatial arrangements from attribute-dependent interactions. While classical summary statistics are effective for second-order dependencies, they frequently…
In this short note we present a generating function computing the compactly supported Euler characteristic $\chi_c(F(X, n), K^{\boxtimes n})$ of the configuration spaces on a topologically stratified space $X$, with $K$ a constructible…
The physics of phase transitions in low-dimensional systems has long been a subject of significant research interest. Long-range magnetic order in the strict two-dimensional limit, whose discovery circumvented the Mermin-Wagner theorem, has…
Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…
We study the stable pair theory on toric surfaces and determine the virtual tangent space over the fixed point loci. Further, we present a program to compute the virtual Euler characteristic, illustrated by the case of the projective plane.…
Hierarchical networks are attracting a renewal interest for modelling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the…
The index theorem of Euler-Poincar\'e characteristic of manifold with boundary is given by making use of the general decomposition theory of spin connection. We shows the sum of the total index of a vector field $\phi $ and half the total…
For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most basic intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
This publication serves as an overview of clique topology -- a novel matrix analysis technique used to extract structural features from neural activity data that contains hidden nonlinearities. We highlight work done by Gusti et al. which…
In this paper, we present a novel method for analysis and segmentation of laminar structure of the cortex based on tissue characteristics whose change across the gray matter underlies distinctive between cortical layers. We develop and…
We investigate the self-organization of strongly interacting particles confined in 1D and 2D. We consider hardcore bosons in spinless Hubbard lattice models with short-range interactions. We show that many-body states with topological…
In order to study the spin configurations of the classical one-dimensional Heisenberg model, we map the normalized unit vector, representing the spin, to a space curve. We show that the total chirality of the configuration is a conserved…
The skyrmion, which is characterised by a topological integer, is a structure that is topologically stable against local disturbances. The huge potential of skyrmions for use in magnetic storage systems has drawn considerable research…
Magnetic skyrmions are localized swirls of magnetization with a non-trivial topological winding number. This winding increases their robustness to superparamagnetism and gives rise to a myriad of novel dynamical properties, making them…
We deal with magnetic structures that attain integer and half-integer skyrmion numbers. We model and solve the problem analytically, and show how the solutions appear in materials that engender distinct, very specific physical properties,…
Brain morphology is shaped by genetic and mechanical factors and is linked to biological development and diseases. Its fractal-like features, regional anisotropy, and complex curvature distributions hinder quantitative insights in medical…
We discuss an algorithm computing the push-forward to projective space of several classes associated to a (possibly singular, reducible, nonreduced) projective scheme. For example, the algorithm yields the topological Euler characteristic…
We propose a general framework to extract microscopic interactions from raw configurations with deep neural networks. The approach replaces the modeling Hamiltonian by the neural networks, in which the interaction is encoded. It can be…
Previous work on predicting or generating 3D human pose sequences regresses either joint rotations or joint positions. The former strategy is prone to error accumulation along the kinematic chain, as well as discontinuities when using Euler…