Symmetry breaking dynamics of human multilimb coordination.

The dynamics of pattern formation and change are studied in a complex multicomponent system, specifically the arms and legs of human Ss. Among the novel features observed are differential stability of coordinative modes produced by limbs moving in the same vs different directions (Exp 1); transitions between coordinative modes preceded by a slow drift in relative phase (Exps 1 and 2); bifurcations or phase transitions from one 4-limb pattern to another (Exp 2); and spontaneous emergence of non-1:1-frequency- and phase-locked patterns, in addition to periods of relative coordination (Exp 3). All observed relative phasing patterns and their dynamics (stability, loss of stability, intermittency) are shown to arise from the same underlying nonlinear dynamical structure, an important feature of which is broken symmetry. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Symmetry breaking and training from incomplete data with Radial Basis Boltzmann Machines

A Radial Basis Boltzmann Machine (RBBM) is a specialized Boltzmann Machine architecture that combines feed-forward mapping with probability estimation in the input space, and for which very efficient learning rules exist. The hidden representation of the network displays symmetry breaking as a function of the noise in the dynamics. Thus, generalization can be studied as a function of the noise in the neuron dynamics instead of as a function of the number of hidden units. We show that the RBBM can be seen as an elegant alternative of k-nearest neighbor, leading to comparable performance without the need to store all data. We show that the RBBM has good classification performance compared to the MLP. The main advantage of the RBBM is that simultaneously with the input-output mapping, a model of the input space is obtained which can be used for learning with missing values. We derive learning rules for the case of incomplete data, and show that they perform better on incomplete data than the traditional learning rules on a 'repaired' data set.