Santa Clara University

Mathematics and Computer Science department

Colloquium Series

Fall 2011

Unless 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 106bern-75

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 106pratt-75

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 106vancott-75

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 106tan-75

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
interactions of diverse systems across many disciplines, no one system or knowledge base can incorporate all models or data related to health. Consider obesity: models of transportation, eating habits, shopping choices for food, exercise, and metabolism need to be combined with geographic, store location, and population data to play "what if," asking, for instance, how community obesity measures would change if a healthy but inexpensive store opens near an obesity "hot spot." Splash?Smarter Planet Platform for Analysis and Simulation of Health? is a framework for combining heterogeneous simulation models and data. By enabling interoperability and reuse of models and data, Splash enables experts from different disciplines to collaborate to exploit their combined knowledge. The resulting composite simulation models can be used for deep predictive analytics, enabling "what if" analyses that cut across disciplines and supporting complex health decisions when expertise from a single domain does not suffice.

Tuesday, November 15, O'Connor 106ibarra-75

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,
please call/email Nicholas Tran 408-554-4465/ntran at scu dot edu (or
use 1-800-735-2929 TTY—California Relay).

Abstracts of previous talks are available here.
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