Sheaf models for choice sequences

Sheaf models for choice sequences

Leray in Oflag XVIIA: The origins of sheaf theory, sheaf cohomology, and spectral sequences

Jean Leray (November 7, 1906–November 10, 1998) was confined to an officers’ prison camp (“Oflag”) in Austria for the whole of World War II. There he took up algebraic topology, and the result was a spectacular flowering of highly original ideas, ideas which have, through the usual metamorphism of history, shaped the course of mathematics in the sixty years since then. Today we would divide his...

Sheaf and Trace Models of Concurrency

Optimal Stopping Policy for Multivariate Sequences a Generalized Best Choice Problem

  In the classical versions of “Best Choice Problem”, the sequence of offers is a random sample from a single known distribution. We present an extension of this problem in which the sequential offers are random variables but from multiple independent distributions. Each distribution function represents a class of investment or offers. Offers appear without any specified order. The objective is...

Applications of Sheaf Cohomology and Exact Sequences on Network Codings

Sheaf cohomology is a mathematical tool for collating local algebraic data into global structures. The purpose of this paper is to apply sheaf theory into network coding problems. After the definition of sheaves, we define so called network coding sheaves for a general multi source network coding scenario, and consider various forms of sheaf cohomologies. The main theorem states that 0-th netwo...