arXiv research

The paper defines a stratification for Lie groupoids in a tame topology context.

New stratification reveals intrinsic singularity types of orbit spaces.

We present some features of the smooth structure, and of the canonical stratification on the orbit space of a proper Lie groupoid. One of the main features is that of Morita invariance of these structures - it allows us to talk about the canonical structure of differentiable stratified space on the orbispace (an object…

We construct the moduli space of r-jets at a point of Riemannian metrics on a smooth manifold. The construction is closely related to the problem of classification of jet metrics via differential invariants. The moduli space is proved to be a differentiable space which admits a finite canonical stratification into smoo…

Develops Poisson and Dirac manifolds of compact types with applications.

The paper calculates the motive of a specific knot's character variety.

Let $G$ be a torus and $M$ a compact Hamiltonian $G$-manifold with finite fixed point set $M^G$. If $T$ is a circle subgroup of $G$ with $M^G=M^T$, the $T$-moment map is a Morse function. We will show that the associated Morse stratification of $M$ by unstable manifolds gives one a canonical basis of $K_G(M)$. A key in…

We prove the existence of Verdier stratifications for sets definable in any o-minimal structure on (R, +, .). It is also shown that the Verdier condition (w) implies the Whitney condition (b) in o-minimal structures on (R, +, .). As a consequence the Whitney Stratification Theorem holds. The existence of (wf)-stratific…

The paper studies HKKN stratifications for non-compact spaces and proves convexity properties.

Stratifies representation varieties of twisted Hopf links.

Paper confirms MCS spaces are equivalent to CS sets.

Alexandrov spaces have a special stratification that maps to spheres.

Abstract: Generalizes stability theories over toric varieties and Novikov type rings.

Investigates properties of moment maps and stratifications on Lie groups.

A $k$-differential on a Riemann surface is a section of the $k$-th power of the canonical line bundle. Loci of $k$-differentials with prescribed number and multiplicities of zeros and poles form a natural stratification of the moduli space of $k$-differentials. In this paper we give a complete description for the compa…

Optimizes biharmonic map regularity using stratification methods.

The aim of this paper is to compare stratifications of moduli spaces given by group actions in the case of similarity of matrices introduced by Arnold and the author's stratification by projective orbifolds, and its relation to deformations o elements in the moduli space.

Combines k-means and hill climbing for stratification and allocation.

Social media enhances or diminishes scientific status, depending on usage.

We give a geometric proof of existence of Whitney stratifications of definable sets in o-minimal structures.

Study clarifies variance of stratification estimators for causal effects.

This paper provides a stratification of semi-algebraic sets in the plane with finitely many geodesic segments.

The Bialynicki-Birula decomposition of the space of lambda-connections restricts to the Morse stratification on the moduli space of Higgs bundles and to the partial oper stratification on the de Rham moduli space of holomorphic connections. For both the Morse and partial oper stratifications, every stratum is a holomor…

We study the topology of the inertia space of a smooth $G$-manifold $M$ where $G$ is a compact Lie group. We construct an explicit Whitney stratification of the inertia space, demonstrating that the inertia space is a triangulable differentiable stratified space. In addition, we demonstrate a de Rham theorem for differ…

Machine learning models for medical image analysis often suffer from poor performance on important subsets of a population that are not identified during training or testing. For example, overall performance of a cancer detection model may be high, but the model still consistently misses a rare but aggressive cancer su…

Paper proves Whitney stratified spaces can be given a conically smooth structure.

The paper studies harmonic map flows and proves rectifiability of singular sets.

The paper describes a stratification of a compactified Hurwitz space using combinatorial trees.

The complement of a complex hyperplane arrangement is known to be homotopic to a minimal CW complex. There are several approaches to the minimality. In this paper, we restrict our attention to real two dimensional cases, and introduce the "dual" objects so called minimal stratifications. The strata are explicitly descr…

Let $G$ be a Lie group, and let $(M,ω)$ be a symplectic manifold. If $G$ admits a Hamiltonian action on $(M,ω)$ with momentum map $μ$, then $M$, the zero-level set of $μ$, the orbit space, and the corresponding symplectic quotient all have induced stratifications. We push this setting into the language of differential …

For curved projective manifolds we introduce a notion of a normal tractor frame field, based around any point. This leads to canonical systems of (redundant) coordinates that generalise the usual homogeneous coordinates on projective space. These give preferred local maps to the model projective space that encode geome…

The paper offers simple, near-optimal algorithms for multi-group learning.

The monster tower is a tower of spaces over a specified base; each space in the tower is a parameter space for curvilinear data up to a specified order. We describe and analyze a natural stratification of these spaces.

Decomposes smooth manifolds into algebraic submanifolds.

We introduce a natural stratification of the space of projective classes of measured laminations on a complete hyperbolic surface of finite area. We prove a rigidity result, namely, the group of self-homeomorphisms of the space of projective measured laminations that preserve such a stratification is in general identif…

Study chaotic dynamics in social stratification models leading to thermalization and turbulence.

Study almost rigidity of super Ricci flow with non-negative Muller quantity.

Study identifies and estimates treatment effect heterogeneity within principal stratification subpopulations.

We consider a Morse function $f$ and a Morse-Smale gradient-like vector field $X$ on a compact connected oriented 3-manifold $M$ such that $f$ has only one critical point of index 3. Based on Laudenbach's ideas, we will show that the flow of $X$ can be isotoped into one so that the trajectory spaces of the new flow pro…

New method improves compatibility of risk stratification models without sacrificing accuracy.

Study cohomology of abelian differentials, find new stratifications.

A homology stratification is a filtered space with local homology groups constant on strata. Despite being used by Goresky and MacPherson [Intersection homology theory: II, Inventiones Mathematicae, 71 (1983) 77-129] in their proof of topological invariance of intersection homology, homology stratifications do not appe…

Survey on hyperplane arrangements and their topology.

Deep learning model creates patient representations for scalable EHR-based stratification.

The analysis of the USA 2001 income distribution shows that it can be described by at least two main components, which obey the generalized Tsallis statistics with different values of the q parameter. Theoretical calculations using the gas kinetics model with a distributed saving propensity factor and two ensembles rep…

We reduce variance in monetization metrics for ranking experiments.

Clarifies the structure of quantum states using algebraic methods.

Within its traditional range of perversity parameters, intersection cohomology is a topological invariant of pseudomanifolds. This is no longer true once one allows superperversities, in which case intersection cohomology may depend on the choice of the stratification by which it is defined. Topological invariance also…