Department of Mathematics and Statistics Talks for the week January 26-30, 2009 (previous week)

Time Scales Seminar: "Discrete densities and Fisher information"   Date Wednesday, January 28, 2009 Time 4:00 pm – 4:50 pm CST Where Room G-4, Rolla Building Event Type Lectures & Seminars Presenter Thomas Matthews Sponsored by Department of Mathematics and Statistics Contact Martin Bohner More http://web.mst.edu/~bohner/seminar/ts.html Topology/Algebra Seminar: "Intro to Contact Algebras (Continued)"   Date Thursday, January 29, 2009 Time 4:00 pm – 5:00 pm CST Where Room G-5, Rolla Building Event Type Lectures & Seminars Presenter Dr Matt Insall Sponsored by Mathematics and Statistics Contact Robert Roe Description In [1], Dimiter Vakarelov describes the concept of a contact algebra, which was introduced by Dimov and Vakarelov in [2] to help formalize a notion, championed by Whitehead in [3], of "contact" between regions in space. Formally, a contact algebra is a pair A=(B, C), where B=(B,0,1,^,v,~) is a Boolean algebra, and C is a binary relation on the set B, such that the following hold: (C1) xCy implies x>0; (C2) xC(yvz) if either xCy or xCz; (C3) xCy implies yCx; (C4) x^y>0 implies xCy. Examples of contact algebras include the algebra of regular closed subsets of a topological space, and the algebra of regular open subsets of a topological space. This kind of "pointless" topology, or "pointless" geometry, has applications in artificial intelligence and knowledge representation, via qualitative spatial reasoning, and represents a fertile area of interaction between classical Boolean algebra, topology and logic. [1] D. Vakarelov, Region-Basel Theory of Space: Algebras of Regions, Represent at ion Theory, and Logics, In: Mathematical Problems from Applied Logic. Logics for the XX-Ist Century. II. Edited by Dov M. Gabbay et. al. Int'l Mathematical Series, 5, Springer, 2007. [2] G. Dimov and D. Vakarelov, Contact algebras and region-based theory of space. A proximity approach. I, Fundam. Inform. (2006) [3] A. N. Whitehead, Process and Reality. New York, MacMillan, 1929.