Time Evolution of Non-Lethal Infectious Diseases: A Semi-Continuous Approach

A model describing the dynamics related to the spreading of non-lethal infectious diseases in a fixed-size population is proposed. The model consists of a non-linear delay-differential equation describing the time evolution of the increment in the number of infectious individuals and depends upon a limited number of parameters. Predictions are in good qualitative agreement with data on influenza.Comment: 21 page

Finite times to equipartition in the thermodynamic limit

We study the time scale T to equipartition in a 1D lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam beta model). We take the initial energy to be either in a single mode gamma or in a package of low frequency modes centered at gamma and of width delta-gamma, with both gamma and delta-gamma proportional to N. These initial conditions both give, for finite energy densities E/N, a scaling in the thermodynamic limit (large N), of a finite time to equipartition which is inversely proportional to the central mode frequency times a power of the energy density E/N. A theory of the scaling with E/N is presented and compared to the numerical results in the range 0.03 <= E/N <= 0.8.Comment: Plain TeX, 5 `eps' figures, submitted to Phys. Rev.

A Bayesian framework for optimal motion planning with uncertainty

Modeling robot motion planning with uncertainty in a Bayesian framework leads to a computationally intractable stochastic control problem. We seek hypotheses that can justify a separate implementation of control, localization and planning. In the end, we reduce the stochastic control problem to path- planning in the extended space of poses x covariances; the transitions between states are modeled through the use of the Fisher information matrix. In this framework, we consider two problems: minimizing the execution time, and minimizing the final covariance, with an upper bound on the execution time. Two correct and complete algorithms are presented. The first is the direct extension of classical graph-search algorithms in the extended space. The second one is a back-projection algorithm: uncertainty constraints are propagated backward from the goal towards the start state

The Gysin map is compatible with mixed Hodge structures

We prove that the Gysin map is compatible with mixed Hodge Structures.Comment: Published in CRM Proceedings and Lecture Series, vol. 38, 200

High surface area, emulsion-templated carbon foams by activation of polyHIPEs derived from Pickering emulsions.

Carbon foams displaying hierarchical porosity and excellent surface areas of >1400 m2/g can be produced by the activation of macroporous poly(divinylbenzene). Poly(divinylbenzene) was synthesized from the polymerization of the continuous, but minority, phase of a simple high internal phase Pickering emulsion. By the addition of KOH, chemical activation of the materials is induced during carbonization, producing Pickering-emulsion templated carbon foams, or carboHIPEs, with tailorable macropore diameters and surface areas almost triple that of those previously reported. The retention of the customizable, macroporous open-cell structure of the poly(divinylbenzene) precursor and the production of a large degree of microporosity during activation leads to tailorable carboHIPEs with excellent surface areas