Colloquium SeriesFall 2011Unless otherwise noted, talks will be at 3:50 PM in O'Connor 106. Also, there will be refreshments before each talk in O'Connor 31 at 3:40 PM. Tuesday October 4, O'Connor 106 Speaker: Marshall Bern, Palo Alto Research Center Title: The mathematics of origami Abstract: Origami, the ancient art of paper folding, connects to many branches of mathematics, from elementary to advanced. I will survey a number of origami mathematics questions, including flat folding, curved folding, and shrinking, flattening, and inflating polyhedra. Tuesday, October 11, O'Connor 106 Speaker: Vaughan Pratt, Stanford University Title: Linear process algebra as an expressive denotational model of concurrency Abstract: Concurrent processes can be modeled inter alia as higher dimensional automata representing n concurrently ongoing events as an n-dimensional cell, and as Chu spaces representing relationships between events and states. Linear process algebra unifies these two models by defining a process (A,X) as a set X of state vectors indexed by a set A of events serving as coordinates. At each coordinate an event may be in one of three event states or scalars, *ready*, *ongoing*, or *terminated*. These permit the expression of run time, mutual exclusion, and event independence. A fourth scalar, *cancelled*, permits the expression of process termination, sequential composition, and a notion of branching time. The operations are those of linear logic together with sequential composition and choice. We give an alternative formulation of the model that replaces its set theoretic foundations with a category theoretic one by representing processes as primitive objects, events and states as process transformations, and the four scalars as all and only those transformations that are both events and states. Tuesday, November 1, O'Connor 106 Speaker: Cornelia Van Cott, University of San Francisco Title: Chicken nuggets and the Frobenius number Abstract: Suppose chicken nuggets are sold in packages of size 6, 9, and 20. With these package sizes, if you wanted to order, say, 25 chicken nuggets, you would be out of luck. After some investigation, one will discover many different sizes which also cannot be ordered; the largest such size is 43. You cannot order 43 nuggets, but you can order N chicken nuggets for all N>43, given the package sizes of 6, 9, and 20. This problem, the so-called Chicken Nugget Problem, is a special case of a classical question first investigated by Frobenius and Sylvester in the nineteenth century. The more general question goes as follows: given a finite set A of positive integers, what is the largest number which cannot be written as a nonnegative integral linear combination of elements in A? This number, denoted g(A), is called the Frobenius number of A. We will discuss the special case where A contains only two integers. We will also consider related results, including Sylvester's Theorem which counts the integers that cannot be represented as combinations of integers in A.
Tuesday, November 8, O'Connor 106 Speaker: Wang-Chiew Tan, UC Santa Cruz/IBM Title: Splash: A Platform for Analysis and Simulation of Health Abstract: Health decision support systems typically assist doctors and patients making treatment decisions based on knowledge gleaned from research studies, pharmaceutical data, disease models, epidemiological simulations, and more. But health also depends on decisions made by law-makers, community leaders, and people in advertising, transportation, agriculture, education, sanitation, and government. Because health decisions frequently require understanding complex Tuesday, November 15, O'Connor 106 Speaker: Oscar Ibarra, UC Santa Barbara Title: Natural Computing: Membrane Systems Abstract: We give a brief overview of the basic ideas, results, and applications of membrane computing, a branch of natural computing inspired by the structure and the functioning of biological cells, cell tissues, or colonies of cells. Membrane computing has given rise to an unconventional computing model, namely a P system, which abstracts from the way living cells process chemical compounds in their compartmental structure. They are a class of distributed and maximally parallel computing devices which process multisets of objects in compartments defined by membranes. We describe various classes of P systems, give examples, and recall some results, especially those that concern computational issues such as Turing completeness, determinism versus nondeterminism, membrane and object-size hierarchies, various notions of parallelism, and computational complexity. We also look at neural-like systems which incorporate the idea of spiking neurons in membrane computing and discuss various classes and characterize their computing power. If you have a disability and require a reasonable accommodation, |
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Abstracts of previous talks are available here. |
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