arXiv research

Study clarifies variance of stratification estimators for causal effects.

Investigates properties of moment maps and stratifications on Lie groups.

Study fractional Allen-Cahn equation and nonlocal minimal surfaces, improving energy and perimeter estimates.

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

A/B testing improves marketing decisions by selecting effective stratification variables.

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

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…

New method evaluates personalized treatment in critical care, robust to death.

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…

Stratifies representation varieties of twisted Hopf links.

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

Paper confirms MCS spaces are equivalent to CS sets.

Classifies knots by lattice size, finding unknot ratios and crossing numbers.

Alexandrov spaces have a special stratification that maps to spheres.

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.

Given a solution $u$ to a linear homogeneous second order elliptic equation with Lipschitz coefficients, we introduce techniques for giving improved estimates of the critical set $\Cr(u)\equiv \{x:|\nabla u|(x)=0\}$. The results are new even for harmonic functions on $\dR^n$. Given such a $u$, the standard {\it first o…

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

In this paper, we study the singular sets of $F$-subharmonic functions $u: B_{2}(0^{n})\rightarrow\mathbf{R}$, where $F$ is a subequation. The singular set $\mathcal{S}(u)\subset B_{2}(0^{n})$ has a stratification $\mathcal{S}^{0}(u)\subset\mathcal{S}^{1}(u)\subset\cdots\subset\mathcal{S}^{k}(u)\subset\cdots\subset\mat…

We consider Type I Ricci flows and obtain integral estimates for the curvature tensor valid up to, and including, the singular time. Our estimates partially extend to higher dimensions a curvature estimate recently shown to hold in dimension three by Kleiner and Lott. To do this we adapt the technique of quantitative s…

Let $\cM$ be a Brakke flow of $n$-dimensional surfaces in $R^N$. The singular set $\cS\subset\cM$ has a stratification $\cS^0\subset\cS^1\subset...\cS$, where $X\in \cS^j$ if no tangent flow at $X$ has more than $j$ symmetries. Here, we define quantitative singular strata $\cS^j_{η,r}$ satisfying $\cup_{η>0}\cap_{0<r} …

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 …

A new cross-validation method reduces redundancy and improves model performance.

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

The main theorem of this paper is a result of estimated transversality with respect to stratifications of jet spaces in the approximately holomorphic category over an almost-complex manifold. The notion of asymptotic ampleness of complex vector bundles over an almost-complex manifold is also discussed, as well as appli…

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.

In this paper, we prove estimates and quantitative regularity results for the harmonic map flow. First, we consider H^1_loc-maps u defined on a parabolic ball P\subset M\times R and with target manifold N, that have bounded Dirichlet-energy and Struwe-energy. We define a quantitative stratification, which groups togeth…

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

Let $A$ be a connection of a principal bundle $P$ over a Riemannian manifold $M$, such that its curvature $F_A\in L_{\text{loc}}^2(M)$ satisfies the stationarity equation. It is a consequence of the stationarity that $θ_A(x,r)=e^{cr^2}r^{4-n}\int_{B_r(x)}|F_A|^2$ is monotonically increasing in $r$, for some $c$ dependi…

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…

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…