Richard Metzler

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We identify a process of global pattern formation that causes regions to differentiate by culture. Violence arises at boundaries between regions that are not sufficiently well defined. We model cultural differentiation as a separation of groups whose members prefer similar neighbors, with a characteristic group size at which violence occurs. Application of(More)
Several scenarios of interacting neural networks which are trained either in an identical or in a competitive way are solved analytically. In the case of identical training each perceptron receives the output of its neighbor. The symmetry of the stationary state as well as the sensitivity to the used training algorithm are investigated. Two competitive(More)
Complex bit sequences generated by a perceptron that learns the opposite of its own prediction are studied, and the success of a student perceptron trained on this sequence is calculated. A system of interacting perceptrons with a directed flow of information is solved analytically. A symmetry breaking phase transition is found with increasing learning(More)
We reconsider the persistence of information under the dynamics of the logistic map in order to discuss communication through a nonlinear channel where the sender can set the initial state of the system with finite resolution, and the recipient measures it with the same accuracy. We separate out the contributions of global phase-space shrinkage and(More)
The generalization of the problem of adaptive competition, known as the minority game, to the case of K possible choices for each player, is addressed, and applied to a system of interacting perceptrons with input and output units of a type of K-state Potts spins. An optimal solution of this minority game, as well as the dynamic evolution of the adaptive(More)
A perceptron that "learns" the opposite of its own output is used to generate a time series. We analyze properties of the weight vector and the generated sequence, such as the cycle length and the probability distribution of generated sequences. A remarkable suppression of the autocorrelation function is explained, and connections to the Bernasconi model(More)
We apply a recently developed measure of multiscale complexity to the Gaussian model consisting of continuous spins with bilinear interactions for a variety of interaction matrix structures. We find two universal behaviors of the complexity profile. For systems with variables that are not frustrated, an exponential decay of multiscale complexity in the(More)