相关论文: Surgery and Stratified Spaces

The current status of asteroseismic studies is here reviewed and the adequate techniques of analysis available today for the study of the oscillation frequencies are presented. Comments on prospects for future investigations through the…

Pathology images of histopathology can be acquired from camera-mounted microscopes or whole slide scanners. Utilizing similarity calculations to match patients based on these images holds significant potential in research and clinical…

Spatial transcriptomics (ST) has advanced significantly in the last few years. Such advancement comes with the urgent need for novel computational methods to handle the unique challenges of ST data analysis. Many artificial intelligence…

The $S$ topology on the Skorokhod space was introduced by the author in 1997 and since then it proved to be a useful tool in several areas of the theory of stochastic processes. The paper brings complementary information on the $S$…

Objective: The aim of this paper is to survey the recent work in medical documents summarization. Background: During the last decade, documents summarization got increasing attention by the AI research community. More recently it also…

Several coupled maps models are sketched and reviewed in this short communication. First, a discrete logistic type model that was proposed for the symbiotic interaction of two species. Second, a model of many of these symbiotic species…

This paper studies a two-stage model of experimentation, where the researcher first samples representative units from an eligible pool, then assigns each sampled unit to treatment or control. To implement balanced sampling and assignment,…

Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…

The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…

We introduce stratified toposes, which are toposes that are stratified by a suitable hierarchy of universes. The term `stratified topos' recalls the notion of stratified pseudotopos of Moerdijk and Palmgren (2002). However, the details of…

This historical introduction is in two parts. The first is reprinted with permission from ``A century of mathematics in America, Part II,'' Hist. Math., 2, Amer. Math. Soc., 1989, pp.543-585. Virtually no change has been made to the…

We give an explicit simple construction for classifying spaces of maps obtained as hyperplane projections of immersions. We prove structure theorems for these classifying spaces.

This is an expository article/encyclopedia entry explaining the history, techniques, and central results in the field of smooth ergodic theory.

This note reports the results of an undergraduate research project from the year 2013-14, concerning the convergence of iterated Steiner symmetrizations in the plane. The directions of symmetrization are chosen according to the Van der…

This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification. While there has been substantial progress across all areas of control, the theory…

In this paper, we build the foundation for a theory of controlled rough paths on manifolds. A number of natural candidates for the definition of manifold valued controlled rough paths are developed and shown to be equivalent. The theory of…

This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision…

Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…

A topological field theory is used to study the cohomology of mapping space. The cohomology is identified with the BRST cohomology realizing the physical Hilbert space and the coboundary operator given by the calculations of tunneling…