Investigating the role of the visual system in solving the traveling salespersonproblem

This article used an empirical experiment and a computationalmodel to test the hypothesis that humans rely on the visualsystem to solve the traveling salesperson problem (TSP). Wetested two consequences of this hypothesis: (1) humans shouldperform better on Euclidean TSP than not–Euclidean TSP; (2)a model of the visual system should account for performance inEuclidean TSP. Participants were asked to solve Euclidean ornot–Euclidean TSP, and a pyramid model of the visual systemwas used to solve the same tours as the humans. The resultsshow that deviations from the optimal tour were smaller in Eu-clidean problems than in not–Euclidean problems, and the fitof the pyramid model to human performance was worse onnot–Euclidean problems then on Euclidean problems. Theseresults suggest that participants solve Euclidean problems withthe visual system, but that other mechanisms are needed to suc-cesfully solve non–visual problems

Viscosity solutions of systems of PDEs with interconnected obstacles and Multi modes switching problems

This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is connected with the valuation of a power plant in the energy market. The main tool is the notion of systems of reflected BSDEs with oblique reflection.Comment: 36 page

Fluctuation spectrum of fluid membranes coupled to an elastic meshwork: jump of the effective surface tension at the mesh size

We identify a class of composite membranes: fluid bilayers coupled to an elastic meshwork, that are such that the meshwork's energy is a function $F_\mathrm{el}[A_\xi]$ \textit{not} of the real microscopic membrane area $A$, but of a \textit{smoothed} membrane's area $A_\xi$, which corresponds to the area of the membrane coarse-grained at the mesh size $\xi$. We show that the meshwork modifies the membrane tension $\sigma$ both below and above the scale $\xi$, inducing a tension-jump $\Delta\sigma=dF_\mathrm{el}/dA_\xi$. The predictions of our model account for the fluctuation spectrum of red blood cells membranes coupled to their cytoskeleton. Our results indicate that the cytoskeleton might be under extensional stress, which would provide a means to regulate available membrane area. We also predict an observable tension jump for membranes decorated with polymer "brushes"

Is There A String Theory Landscape

We examine recent claims of a large set of flux compactification solutions of string theory. We conclude that the arguments for AdS solutions are plausible. The analysis of meta-stable dS solutions inevitably leads to situations where long distance effective field theory breaks down. We then examine whether these solutions are likely to lead to a description of the real world. We conclude that one must invoke a strong version of the anthropic principle. We explain why it is likely that this leads to a prediction of low energy supersymmetry breaking, but that many features of anthropically selected flux compactifications are likely to disagree with experiment.Comment: 39 pages, Latex, ``Terminology surrounding the anthropic principle revised to conform with accepted usage. More history of the anthropic principle included. Various references added.

Tube Research and Development

Contains reports on two research projects

Communication Research

Contains reports on seven research projects.Carnegie Foundatio