Towards gravitationally assisted negative refraction of light by vacuum

Propagation of electromagnetic plane waves in some directions in gravitationally affected vacuum over limited ranges of spacetime can be such that the phase velocity vector casts a negative projection on the time-averaged Poynting vector. This conclusion suggests, inter alia, gravitationally assisted negative refraction by vacuum.Comment: 6 page

Local control of Hamiltonian chaos

We review a method of control for Hamiltonian systems which is able to create smooth invariant tori. This method of control is based on an apt modification of the perturbation which is small and localized in phase space

Quantum affine Toda solitons

We review some of the progress in affine Toda field theories in recent years, explain why known dualities cannot easily be extended, and make some suggestions for what should be sought instead.Comment: 16pp, LaTeX. Minor revision

Routine data linkage to identify and monitor diabetes in clozapine-treated patients with schizophrenia

No abstract available

Generalizing with perceptrons in case of structured phase- and pattern-spaces

We investigate the influence of different kinds of structure on the learning behaviour of a perceptron performing a classification task defined by a teacher rule. The underlying pattern distribution is permitted to have spatial correlations. The prior distribution for the teacher coupling vectors itself is assumed to be nonuniform. Thus classification tasks of quite different difficulty are included. As learning algorithms we discuss Hebbian learning, Gibbs learning, and Bayesian learning with different priors, using methods from statistics and the replica formalism. We find that the Hebb rule is quite sensitive to the structure of the actual learning problem, failing asymptotically in most cases. Contrarily, the behaviour of the more sophisticated methods of Gibbs and Bayes learning is influenced by the spatial correlations only in an intermediate regime of $\alpha$, where $\alpha$ specifies the size of the training set. Concerning the Bayesian case we show, how enhanced prior knowledge improves the performance.Comment: LaTeX, 32 pages with eps-figs, accepted by J Phys

Breathers in the weakly coupled topological discrete sine-Gordon system

Existence of breather (spatially localized, time periodic, oscillatory) solutions of the topological discrete sine-Gordon (TDSG) system, in the regime of weak coupling, is proved. The novelty of this result is that, unlike the systems previously considered in studies of discrete breathers, the TDSG system does not decouple into independent oscillator units in the weak coupling limit. The results of a systematic numerical study of these breathers are presented, including breather initial profiles and a portrait of their domain of existence in the frequency-coupling parameter space. It is found that the breathers are uniformly qualitatively different from those found in conventional spatially discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely rewritte

Community Detection as an Inference Problem

We express community detection as an inference problem of determining the most likely arrangement of communities. We then apply belief propagation and mean-field theory to this problem, and show that this leads to fast, accurate algorithms for community detection.Comment: 4 pages, 2 figure

Belief propagation algorithm for computing correlation functions in finite-temperature quantum many-body systems on loopy graphs

Belief propagation -- a powerful heuristic method to solve inference problems involving a large number of random variables -- was recently generalized to quantum theory. Like its classical counterpart, this algorithm is exact on trees when the appropriate independence conditions are met and is expected to provide reliable approximations when operated on loopy graphs. In this paper, we benchmark the performances of loopy quantum belief propagation (QBP) in the context of finite-tempereture quantum many-body physics. Our results indicate that QBP provides reliable estimates of the high-temperature correlation function when the typical loop size in the graph is large. As such, it is suitable e.g. for the study of quantum spin glasses on Bethe lattices and the decoding of sparse quantum error correction codes.Comment: 5 pages, 4 figure

Clustering of solutions in the random satisfiability problem

Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in agreement with previous predictions of the cavity method and give a rigorous confirmation to one of its main building blocks. It can be generalized to other systems of both physical and computational interest.Comment: 4 pages, 1 figur

Warren McCulloch and the British cyberneticians

Warren McCulloch was a significant influence on a number of British cyberneticians, as some British pioneers in this area were on him. He interacted regularly with most of the main figures on the British cybernetics scene, forming close friendships and collaborations with several, as well as mentoring others. Many of these interactions stemmed from a 1949 visit to London during which he gave the opening talk at the inaugural meeting of the Ratio Club, a gathering of brilliant, mainly young, British scientists working in areas related to cybernetics. This paper traces some of these relationships and interaction