A predicative variant of a realizability tripos for the Minimalist Foundation.

open2noHere we present a predicative variant of a realizability tripos validating the intensional level of the Minimalist Foundation extended with Formal Church thesis.the file attached contains the whole number of the journal including the mentioned pubblicationopenMaietti, Maria Emilia; Maschio, SamueleMaietti, MARIA EMILIA; Maschio, Samuel

Rethinking the notion of oracle: A link between synthetic descriptive set theory and effective topos theory

We present three different perspectives of oracle. First, an oracle is a blackbox; second, an oracle is an endofunctor on the category of represented spaces; and third, an oracle is an operation on the object of truth-values. These three perspectives create a link between the three fields, computability theory, synthetic descriptive set theory, and effective topos theory

The extensional ordering of the sequential functionals

AbstractWe investigate the extensional ordering of the sequential functionals of finite types, with a focus on when the sequential functionals of a given type form a directed complete partial ordering, and on when a finite sequential functional will be the nontrivial least upper bound of an infinite chain of sequential functionals. We offer a full characterization for finite functionals of pure types

An Agent Based Model of Disease Diffusion in the Context of Heterogeneous Sexual Motivation

Thesis (PhD) - Indiana University, School of Health, Physical Education and Recreation, 2006This project focused on building and analyzing an agent-based model of disease diffusion in order to explore the hypothesis that the relative risk associated with an individual's "sexual motivation profile" (SMP) is influenced by the distribution of strategies represented in the population - that is, that sexual motivation functions as a frequency dependent trait. Sexual motivation is hypothesized to be composed of a sexual inhibition system (SIS) and a sexual excitation system (SES), following the Dual Control Model of Sexual Response. Results of the model show that the relative risk of a SMP does vary depending on the relative representation within a population, but that that variance is constrained by agents' absolute values of SIS and SES. The model produced several parallels with empirical data on humans, suggesting that the model accurately reproduced some aspects of human sexual behavior. For example, agents' SES was a better predictor than SIS of total number of partners, while SIS was a better predictor than SES of Age at Infection. Also, the more accurately the agent population matched the human population, the more the model produced human-like results. Future work should focus on increasing the verisimilitude of agents and their environments, in order to make models more practical for designing and testing intervention and policy strategies

Generalized Domination.

This thesis develops the theory of the everywhere domination relation between functions from one infinite cardinal to another. When the domain of the functions is the cardinal of the continuum and the range is the set of natural numbers, we may restrict our attention to nicely definable functions from R to N. When we consider a class of such functions which contains all Baire class one functions, it becomes possible to encode information into these functions which can be decoded from any dominator. Specifically, we show that there is a generalized Galois-Tukey connection from the appropriate domination relation to a classical ordering studied in recursion theory. The proof techniques are developed to prove new implications regarding the distributivity of complete Boolean algebras. Next, we investigate a more technical relation relevant to the study of Borel equivalence relations on R with countable equivalence classes. We show than an analogous generalized Galois-Tukey connection exists between this relation and another ordering studied in recursion theory.PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113539/1/danhath_1.pd