37,556 research outputs found
Tensor product of filtered -algebras
We define the tensor product of filtered -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 -algebras our definition recovers the one given by Markl
and Shnider. We also give a criterion that implies that a given
-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
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
Floer cohomology of torus fibers and real lagrangians in Fano toric manifolds
In this article, we consider the Floer cohomology (with 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
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