arXiv research

We reduce variance in monetization metrics for ranking experiments.

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

We reveal a model rank that predicts successful recovery of target functions at overparameterization.

Stratifies representation varieties of twisted Hopf links.

Clarifies the structure of quantum states using algebraic methods.

This paper studies geodesics between covariance matrices of different ranks using the Bures-Wasserstein metric.

For an equivariant Morse stratification which contains a unique open stratum, we introduce the notion of equivariant antiperfection, which means the difference of the equivariant Morse series and the equivariant Poincare series achieves the maximal possible value (instead of the minimal possible value 0 in the equivari…

Global stability bounds for matrix frames in phase retrieval problems.

In the paper we discuss certain classes of vector distributions in the tangent bundles to manifolds, obtained by series of applications of the so-called generalized Cartan prolongations (gCp). The classical Cartan prolongations deal with rank-2 distributions and are responsible for the appearance of the Goursat distrib…

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 space of matrices of positive determinant GL^+_n inherits an extrinsic metric space structure from R^{n^2}. On the other hand, taking the infimum of the lengths of all paths connecting two points in GL^+_n gives an intrinsic metric. We prove bilipschitz equivalence for intrinsic and extrinsic metrics on GL^+_n, exp…

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

A clinician desires to use a risk-stratification method that achieves confident risk-stratification - the risk estimates of the different patients reflect the true risks with a high probability. This allows him/her to use these risks to make accurate predictions about prognosis and decisions about screening, treatments…

We show that the number of conjugacy classes of maximal finite subgroups of a lattice in a semisimple Lie group is linearly bounded by the covolume of the lattice. Moreover, for higher rank groups, we show that this number grows sublinearly with covolume. We obtain similar results for isotropy subgroups in lattices. Ge…

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

By proving precisely which singularity index lists arise from the pair of invariant foliations for a pseudo-Anosov surface homeomorphism, Masur and Smillie determined a Teichmueller flow invariant stratification of the space of quadratic differentials. In this paper we determine an analog to the theorem for $Out(F_3)$.…

Paper confirms MCS spaces are equivalent to CS sets.

Alexandrov spaces have a special stratification that maps to spheres.

Investigates properties of moment maps and stratifications on Lie groups.

Let X be the moduli space of SL(n,C), SU(n), GL(n,C), or U(n)-valued representations of a rank r free group. We classify the algebraic singular stratification of X. This comes down to showing that the singular locus corresponds exactly to reducible representations if there exist singularities at all. Then by relating a…

Optimizes biharmonic map regularity using stratification methods.

New stratification reveals intrinsic singularity types of orbit spaces.

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…

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 …

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 invariant $c_{sm}$ simplifies computing geometric invariants of recursive group orbits.

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…