Mathematics and Cognition  Seminar

Fall 2004

Tuesdays 12:00  GWC 604

Seminar Schedule:<http://math.la.asu.edu/~tom/cognition/math+cogsched.html>On Tuesday, October 5, at 12:00 Noon in GWC 604,
the Mathematics and Cognition Seminar will
present brief discussion with Root Gorelick
of the School of Life Sciences and SIRG
on the topic of 

"Quantifying Social Interactions"

Abstract

 The ratio of mutual to marginal entropy (which asymptotically has an F-distribution) provides a measure of social interactions and social structure.  This statistic can be used to measure the ensemble of all pair-wise interactions within a social group (where rows and columns of the data matrix are individuals and where the matrix components are the time each pair spends interacting) division of labor within a social group (where rows of the data matrix are individuals and columns are tasks and the matrix components are the time each individual spends on each task).  By broadening the concept of what constitutes a social group, we can apply this methodology to many non-obvious applications.  With the social group consisting of species in an ecosystem, normalized mutual entropy can be used to quantify levels of predator-prey interactions or levels of specialization of pollinating animals and the plants they pollinate.  With rows of the data matrix being females, columns being males, and entries in the matrix being number of matings, we can quantify the continuum amongst monogamy, polygyny, and polyandry, or the intensity of sexual selection.  With the social group consisting of all trinucleotides and tasks consisting of all amino acids, we can estimate the change in specialization over the evolution of the modern genetic code.  The one limitation on this methodology is the data structure, a matrix.  Otherwise there is a myriad of biological applications for normalized mutual entropy.  The use of normalized mutual entropy broadens our concept of social groups (and division of labor) to any biological systems that can be represented by a matrix of behaviors, interactions, or relationships.