We define the harmonic evolution of states of a graph by iterative application of the harmonic operator (Laplacian over Z2). This provides graphs with a new geometric context and leads to a new tool to analyze them. The digraphs of evolutions are analyzed and classified. This construction can also be viewed as a certain topological generalization of cellular automata. MSC: 05C50, 15A33, 05C75, ...

Given a reduced local algebra T over a suitable ring or field k we study the question of whether there are nontrivial algebra surjections R → T which induce isomorphisms Ω R/k ⊗ T → Ω T /k. Such maps, called evolutions, arise naturally in the study of Hecke algebras, as they implicitly do in the recent work of Wiles, Taylor-Wiles, and Flach. We show that the existence of non-trivial evolutions ...

In this paper a experiment is presented in which two simulated robots evolved a form of communication to allow one of the robots to complete the task of finding a light placed in the world. The robots are constrained so that one has inputs about the world, seeing robot, and the other, blind robot, has no sensors besides an input from the seeing robot. The evolved communication allowed the seein...

It is known that evolution may lead to a new species while adaptation may lead to a new variety. In this manuscript, we present an analysis of the number of evolutions (defined by improvement of the score associated with an objective function of a genetic algorithm) in an experiment supervised by a genetic algorithm, experiment conducted on octan-1-ol/H20 partition coefficient of polychlorinate...

To be able to statistically compare evolutions of image timeseries data requires a method to express these evolutions in a common coordinate system. This requires a mechanism to transport evolutions between coordinate systems: e.g., parallel transport has been used for largedisplacement diffeomorphic metric mapping (LDDMM) approaches. A common purpose to study evolutions is to assess local tiss...