Biomedical subjects

W Garrett Mitchener

Publications and source records attributed to W Garrett Mitchener.

4 recordsLinked to original sources

PubMed2005

Force distributions in a triangular lattice of rigid bars.

We study the uniformly weighted ensemble of force balanced configurations on a triangular network of nontensile contact forces. For periodic boundary conditions corresponding to isotropic compressive stress, we find that the probability distribution for single-contact forces decays faster than exponentially. This superexponential decay persists in lattices diluted to the rigidity percolation threshold. On the other hand, for anisotropic imposed stresses, a broader tail emerges in the force distribution, becoming a pure exponential in the limit of infinite lattice size and infinitely strong anisotropy.

Journal Article↗

PubMed2004

Chaos and language.

Human language is a complex communication system with unlimited expressibility. Children spontaneously develop a native language by exposure to linguistic data from their speech community. Over historical time, languages change dramatically and unpredictably by accumulation of small changes and by interaction with other languages. We have previously developed a mathematical model for the acquisition and evolution of language in heterogeneous populations of speakers. This model is based on game dynamical equations with learning. Here, we show that simple examples of such equations can display complex limit cycles and chaos. Hence, language dynamical equations mimic complicated and unpredictable changes of languages over time. In terms of evolutionary game theory, we note that imperfect learning can induce chaotic switching among strict Nash equilibria.

Biological Evolution↗

PubMed2003

Competitive exclusion and coexistence of universal grammars.

Universal grammar (UG) is a list of innate constraints that specify the set of grammars that can be learned by the child during primary language acquisition. UG of the human brain has been shaped by evolution. Evolution requires variation. Hence, we have to postulate and study variation of UG. We investigate evolutionary dynamics and language acquisition in the context of multiple UGs. We provide examples for competitive exclusion and stable coexistence of different UGs. More specific UGs admit fewer candidate grammars, and less specific UGs admit more candidate grammars. We will analyze conditions for more specific UGs to outcompete less specific UGs and vice versa. An interesting finding is that less specific UGs can resist invasion by more specific UGs if learning is more accurate. In other words, accurate learning stabilizes UGs that admit large numbers of candidate grammars.

Biological Evolution↗

PubMed2003

Bifurcation analysis of the fully symmetric language dynamical equation.

In this paper, I study a continuous dynamical system that describes language acquisition and communication in a group of individuals. Children inherit from their parents a mechanism to learn their language. This mechanism is constrained by a universal grammar which specifies a restricted set of candidate languages. Language acquisition is not error-free. Children may or may not succeed in acquiring exactly the language of their parents. Individuals talk to each other, and successful communication contributes to biological (or cultural) fitness. I provide a full bifurcation analysis of the case where the parameters are chosen to yield a highly symmetric dynamical system. Populations approach either an incoherent steady state, where many different candidate languages are represented in the population, or a coherent steady state, where the majority of the population speaks a single language. The main result of the paper is a description of how learning reliability affects the stability of these two kinds of equilibria. I rigorously find all fixed points, determine their stabilities, and prove that all populations tend to some fixed point. I also demonstrate that the fixed point representing an incoherent steady state becomes unstable in an S (n)-symmetric transcritical bifurcation as learning becomes more reliable.

Child↗