A differential calculus for multifunctions

Mathematical analysis of multifunction

Equilibria Resistant to Mutation

The paper requires that equilibrium behavior for two person symmetric games be resistant to genetic evolution. In particular the paper assumes that the evolution of genotypes selecting a behavioral rule can be described according to some generalization of the replicator model. This paper defines an equilibrium concept, 'evolutionary equilibrium', which is defined as the limit of stationary points of the evolutionary process as the proportion of the population that mutates goes to zero. Then the set of evolutionary equilibria, as defined in the paper, is a nonempty subset of the set of perfect equilibria (and thus of the set of Nash equilibria) and a superset of the set of regular equilibria and the set of ESS

Equilibria Resistant to Mutation

The paper requires that equilibrium behavior for two person symmetric games be resistant to genetic evolution. In particular the paper assumes that the evolution of genotypes selecting a behavioral rule can be described according to some generalization of the replicator model. This paper defines an equilibrium concept, 'evolutionary equilibrium', which is defined as the limit of stationary points of the evolutionary process as the proportion of the population that mutates goes to zero. Then the set of evolutionary equilibria, as defined in the paper, is a nonempty subset of the set of perfect equilibria (and thus of the set of Nash equilibria) and a superset of the set of regular equilibria and the set of ESS

Aggregation of variables and system decomposition: Applications to fitness landscape analysis

In this paper we present general results on aggregation of variables, specifically as it applies to decomposable (partitionable) dynamical systems. We show that a particular class of transition matrices, namely, those satisfying an equitable partitioning property, are aggregable under appropriate decomposition operators. It is also shown that equitable partitions have a natural application to the description of mutation-selection matrices (fitness landscapes) when their fitness functions have certain symmetries concordant with the neighborhood relationships in the underlying configuration space. We propose that the aggregate variable descriptions of mutation-selection systems offer a potential formal definition of units of selection and evolution

Rational Information Choice in Financial Market Equilibrium

Adding a stage of signal acquisition to the expected utility model shows that Bayesian updating results in a well defined law of demand for financial information when asset return distributions are conjugate priors to signals such as in the gamma-Poisson case. Signals have a positive marginal utility value that falls in their number if and only if investors are risk averse, asset markets large, and variance-mean ratios of asset returns high in fully revealing rational expectations equilibrium. Expected asset price increases in the number of signals so that expected excess return drops. The diminishing excess return prevents Bayesian investors from unbounded information demand even if signals are costless, unless the riskfree asset is removed. Signals mutually benefit homogeneous investors because revealing asset price permits updating so that a Pareto criterion judges competitive equilibrium as not sufficiently informative. However, asset price responses make incentives for signal acquisition dependent on portfolios so that welfare and distributional consequences become intricately linked when investors are heterogeneous.

On output statistics of nonlinear devices : 1) third and higher order information, 2) quadriphase carrier reconstruction, 3) analysis of point processes

This thesis deals with the output statistics of nonlinear devices. It develops the classical output autocorrelation function in two dimensions and extends the theory to three and four dimensions. Closed form solutions for the output correlation function in two and three dimensions are given for the full- and half-wave rectifier families while a series solution with numerical results is presented in the case of the smooth limiter in four dimensions. A nonlinear device used to provide a coherent reference signal in a digital phase modulation system is analyzed and results presented in terms of average error rate performance degradation. Finally, the problem of determining the average number of times per unit of time that a process consisting of a sinusoidal signal plus Gaussian noise transgresses a fixed level or has summits above or below a fixed level is investigated

Imagism in Locke, Berkeley and Hume

Thesis (Ph.D.)--Boston UniversityLocke, Berkeley, and Hume--referred to as "the classical British empiricists"--are examined for the extent to which a doctrine, called 'imagism' by Price, played a formative role in their philosophies. Imagism as defined has two main varieties, the polemical version and the constructive version. According to the former, images are the primary symbols in thinking and all other symbols are secondary and derivative. According to the latter, thought is the manipulation of mental images. It is this latter doctrine which is demonstrated as applicable to the classical British empiricists; so far as the former doctrine appears at all, it is an aberrant doctrine.[TRUNCATED