A continuous model of ant foraging with pheromones and trail formation

We propose and numerically analyze a PDE model of ant foraging behavior. Ant foraging is a prime example of individuals following simple behavioral rules based on local information producing complex, organized and ``intelligent'' strategies at the population level. One of its main aspects is the widespread use of pheromones, which are chemical compounds laid by the ants used to attract other ants to a food source. In this work, we consider a continuous description of a population of ants and simulate numerically the foraging behavior using a system of PDEs of chemotaxis type. We show that, numerically, this system accurately reproduces observed foraging behavior, such as trail formation and efficient removal of food sources.Comment: Conference proceeding

Tensor product of filtered A∞A_\infty-algebras

We define the tensor product of filtered $A_\infty$-algebras. establish some of its properties and give a partial description of the space of bounding cochains in the tensor product. Furthermore we show that in the case of classical $A_\infty$-algebras our definition recovers the one given by Markl and Shnider. We also give a criterion that implies that a given $A_\infty$-algebra is quasi-isomorphic to the tensor product of two subalgebras. This will be used in a sequel to prove a K\"unneth Theorem for the Fukaya algebra of a product of Lagrangian submanifolds.Comment: v2: Longer version of the paper to appear in Journal of Pure and Applied Algebr

Floer cohomology of torus fibers and real lagrangians in Fano toric manifolds

In this article, we consider the Floer cohomology (with $\Z_2$ coefficients) between torus fibers and the real Lagrangian in Fano toric manifolds. We first investigate the conditions under which the Floer cohomology is defined, and then develop a combinatorial description of the Floer complex based on the polytope of the toric manifold. We show that if the Floer cohomology is defined, and the Floer cohomology of the torus fiber is non-zero, then the Floer cohomology of the pair is non-zero. We use this result to develop some applications to non-displaceability and the minimum number of intersection points under Hamiltonian isotopy.Comment: v2: Modified exposition and new corollary adde

Decoding the urban grid: or why cities are neither trees nor perfect grids

In a previous paper (Figueiredo and Amorim, 2005), we introduced the continuity lines, a compressed description that encapsulates topological and geometrical properties of urban grids. In this paper, we applied this technique to a large database of maps that included cities of 22 countries. We explore how this representation encodes into networks universal features of urban grids and, at the same time, retrieves differences that reflect classes of cities. Then, we propose an emergent taxonomy for urban grids