A Hybrid Linear Logic for Constrained Transition Systems

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus

A Hybrid Linear Logic for Constrained Transition Systems

International audienceLinear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus

A Hybrid Linear Logic for Constrained Transition Systems with Applications to Molecular Biology

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus. We also present some preliminary experiments of direct encoding of biological systems in the logic

T-folds, doubled geometry, and the SU(2) WZW model

The SU(2) WZW model at large level N can be interpreted semiclassically as string theory on S^3 with N units of Neveu-Schwarz H-flux. While globally geometric, the model nevertheless exhibits an interesting doubled geometry possessing features in common with nongeometric string theory compactifications, for example, nonzero Q-flux. Therefore, it can serve as a fertile testing ground through which to improve our understanding of more exotic compactifications, in a context in which we have a firm understanding of the background from standard techniques. Three frameworks have been used to systematize the study of nongeometric backgrounds: the T-fold construction, Hitchin's generalized geometry, and fully doubled geometry. All of these double the standard description in some way, in order to geometrize the combined metric and Neveu Schwarz B-field data. We present the T-fold and fully doubled descriptions of WZW models, first for SU(2) and then for general group. Applying the formalism of Hull and Reid-Edwards, we indeed recover the physical metric and H-flux of the WZW model from the doubled description. As additional checks, we reproduce the abelian T-duality group and known semiclassical spectrum of D-branes.Comment: 69 pages; uses amslatex; v4 minor revision

Modeling Human Mobility Entropy as a Function of Spatial and Temporal Quantizations

The knowledge of human mobility is an integral component of several different branches of research and planning, including delay tolerant network routing, cellular network planning, disease prevention, and urban planning. The uncertainty associated with a person's movement plays a central role in movement predictability studies. The uncertainty can be quantified in a succinct manner using entropy rate, which is based on the information theoretic entropy. The entropy rate is usually calculated from past mobility traces. While the uncertainty, and therefore, the entropy rate depend on the human behavior, the entropy rate is not invariant to spatial resolution and sampling interval employed to collect mobility traces. The entropy rate of a person is a manifestation of the observable features in the person's mobility traces. Like entropy rate, these features are also dependent on spatio-temporal quantization. Different mobility studies are carried out using different spatio-temporal quantization, which can obscure the behavioral differences of the study populations. But these behavioral differences are important for population-specific planning. The goal of dissertation is to develop a theoretical model that will address this shortcoming of mobility studies by separating parameters pertaining to human behavior from the spatial and temporal parameters