29,713 research outputs found
Complex Objects in the Polytopes of the Linear State-Space Process
A simple object (one point in -dimensional space) is the resultant of the
evolving matrix polynomial of walks in the irreducible aperiodic network
structure of the first order DeGroot (weighted averaging) state-space process.
This paper draws on a second order generalization the DeGroot model that allows
complex object resultants, i.e, multiple points with distinct coordinates, in
the convex hull of the initial state-space. It is shown that, holding network
structure constant, a unique solution exists for the particular initial space
that is a sufficient condition for the convergence of the process to a
specified complex object. In addition, it is shown that, holding network
structure constant, a solution exists for dampening values sufficient for the
convergence of the process to a specified complex object. These dampening
values, which modify the values of the walks in the network, control the
system's outcomes, and any strongly connected typology is a sufficient
condition of such control
An inflationary differential evolution algorithm for space trajectory optimization
In this paper we define a discrete dynamical system that governs the
evolution of a population of agents. From the dynamical system, a variant of
Differential Evolution is derived. It is then demonstrated that, under some
assumptions on the differential mutation strategy and on the local structure of
the objective function, the proposed dynamical system has fixed points towards
which it converges with probability one for an infinite number of generations.
This property is used to derive an algorithm that performs better than standard
Differential Evolution on some space trajectory optimization problems. The
novel algorithm is then extended with a guided restart procedure that further
increases the performance, reducing the probability of stagnation in deceptive
local minima.Comment: IEEE Transactions on Evolutionary Computation 2011. ISSN 1089-778
Dense periodic packings of tori
Dense packings of nonoverlapping bodies in three-dimensional Euclidean space
are useful models of the structure of a variety of many-particle systems that
arise in the physical and biological sciences. Here we investigate the packing
behavior of congruent ring tori, which are multiply connected nonconvex bodies
of genus 1, as well as horn and spindle tori. We analytically construct a
family of dense periodic packings of unlinked tori guided by the organizing
principles originally devised for simply connected solid bodies [Torquato and
Jiao, PRE 86, 011102 (2012)]. We find that the horn tori as well as certain
spindle and ring tori can achieve a packing density higher than the densest
known packing of both sphere and ellipsoids. In addition, we study dense
packings of cluster of pair-linked ring tori (i.e., Hopf links).Comment: 15 pages, 7 figure
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