Mathematics Commons^™

The Intersection Between Science And Computer Science Is Almost Empty, Dick Hamlet

Systems Science Friday Noon Seminar Series

Traditionally, a science such as physics overlaps with mathematics and engineering in a way that has been astonishingly productive. The math provides precise expression for the science, which in turn supplies the engineering with the information it needs to exploit physical phenomena. Computer science naturally wishes to put itself in the center of the traditional picture as a science. Unfortunately, it won't wash. The `science' of programming is pure and simple mathematics, not science. The distinction is more than linguistic, since science and mathematics have quite distinct goals and methods. By making the wrong choice, computer science research has been …

Integer Optimization And Computational Algebraic Topology, Bala Krishnamoorthy

Systems Science Friday Noon Seminar Series

We present recently discovered connections between integer optimization, or integer programming (IP), and homology. Under reasonable assumptions, these results lead to efficient solutions of several otherwise hard-to-solve problems from computational topology and geometric analysis. The main result equates the total unimodularity of the boundary matrix of a simplicial complex to an algebraic topological condition on the complex (absence of relative torsion), which is often satisfied in real-life applications . When the boundary matrix is totally unimodular, the problem of finding the shortest chain homologous under Z (ring of integers) to a given chain, which is inherently an integer program, can …

Modal Logic And Its Applications, Explained Using Puzzles And Examples, Marek Perkowski

Systems Science Friday Noon Seminar Series

The talk introduces Modal Logic as an extension of classical propositional and First Order Logics. We discuss motivations of Lewis to create modal logic system, axioms and rules of proof. Several examples illustrate deriving theorems from axioms. "Muddy Children" puzzle is used to explain the principles of dealing with uncertainty problems where a temporal lack of response is used as additional information. Other examples include "Narrow Bridge" problem/game which relates to the problem of necessary evil in the world, robot planning and law and robot morality problems, especially related to military robots and use of force by police. Kripke semantics …

Reconstructability Analysis Of Elementary Cellular Automata, Martin Zwick, Hui Shi

Systems Science Friday Noon Seminar Series

Reconstructability analysis is a method to determine whether a multivariate relation, defined set- or information-theoretically, is decomposable with or without loss (reduction in constraint) into lower ordinality relations. Set-theoretic reconstructability analysis (SRA) is used to characterize the mappings of elementary cellular automata. The degree of lossless decomposition possible for each mapping is more effective than the λ parameter (Walker & Ashby, Langton) as a predictor of chaotic dynamics.

Complete SRA yields not only the simplest lossless structure but also a vector of losses of all decomposed structures, indexed by parameter, τ. This vector subsumes λ, Wuensche’s Z parameter, and Walker …