Related papers: Ernest Michael and theory of continuous selections
In 1963 Edward Lorenz revealed deterministic predictability to be an illusion and gave birth to a field that still thrives. This Feature Article discusses Lorenz's discovery and developments that followed from it.
Despite having advanced a reaction-diffusion model of ODE's in his 1952 paper on morphogenesis, reflecting his interest in mathematical biology, Alan Turing has never been considered to have approached a definition of Cellular Automata.…
Considerable thought has been devoted to an adequate definition of the class of infinite, random binary sequences (the sort of sequence that almost certainly arises from flipping a fair coin indefinitely). The first mathematical exploration…
The expectation-maximization (EM) algorithm introduced by Dempster et al in 1977 is a very general method to solve maximum likelihood estimation problems. In this informal report, we review the theory behind EM as well as a number of EM…
Shape theory was founded by K.~Borsuk 50 years ago. In essence, this is spectral homotopy theory; it occupies an important place in geometric topology. The article presents the basic concepts and the most important, in our opinion, results…
This article recounts the interaction of topology and singularity theory (mainly singularities of complex algebraic varieties) which started in the early part of this century and bloomed in the 1960's with the work of Hirzebruch, Brieskorn,…
Proponents of category theory long hoped to escape the limits of set theory by founding mathematics on an unlimited category theory in which large categories, such as the category Grp of all groups, the category Top of all topological…
Ren{\'e} Thom discovered several refined topological notions in the writings of Aristotle, especially the biological. More generally, he considered that some of the assertions of the Greek philosophers have a definite topological content,…
Selection, the tendency of some traits to become more frequent than others in a population under the influence of some (natural or artificial) agency, is a key component of Darwinian evolution and countless other natural and social…
We use tools from applied topology for feature selection on time series data. We develop a method for scoring the variables in a multivariate time series that reflects their contributions to the topological features of the corresponding…
In this work, a variant of the birth and death chain with constant intensities, originally introduced by Bruno de Finetti way back in 1957, is revisited. This fact is also underlined by the choice of the title, which is clearly a literal…
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas of computer science. Their development was also inextricably…
Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…
Anomaly detection in multivariate signals is a task of paramount importance in many disciplines (epidemiology, finance, cognitive sciences and neurosciences, oncology, etc.). In this perspective, Topological Data Analysis (TDA) offers a…
April 25, 2003, marked the 100th anniversary of the birth of Andrei Nikolaevich Kolmogorov, the twentieth century's foremost contributor to the mathematical and philosophical foundations of probability. The year 2003 was also the 70th…
Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered…
We study some closure-type properties of function spaces endowed with the new topology of strong uniform convergence on a bornology introduced by Beer and Levy in 2009. The study of these function spaces was initiated in [2] and [3]. The…
An intriguing heuristic model of development, decline, and change conceived by Bernard J.F. Lonergan (BL) in the late 1940's was laid out in a manner now recognizable as representing an early model of complexity. This report is a first…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
We review some selected recent results concerning selection principles in topology and their relations with several topological constructions.