The magnetic reversal in dot arrays recognized by the self-organized adaptive neural network

The remagnetization dynamics of monolayer dot array superlattice XY 2-D spin model with dipole-dipole interactions is simulated. Within the proposed model of array, the square dots are described by the spatially modulated exchange-couplings. The dipole-dipole interactions are approximated by the hierarchical sums and spin dynamics is considered in regime of the Landau-Lifshitz equation. The simulation of reversal for $40 000$ spins exhibits formation of nonuniform intra-dot configurations with nonlinear wave/anti-wave pairs developed at intra-dot and inter-dot scales. Several geometric and parametric dependences are calculated and compared with oversimplified four-spin model of reversal. The role of initial conditions and the occurrence of coherent rotation mode is also investigated. The emphasis is on the classification of intra-dot or inter-dot (interfacial) magnetic configurations done by adaptive neural network with varying number of neurons.Comment: 16 figure

Elastic Lattice Polymers

We study a model of "elastic" lattice polymer in which a fixed number of monomers $m$ is hosted by a self-avoiding walk with fluctuating length $l$. We show that the stored length density $\rho_m = 1 - /m$ scales asymptotically for large $m$ as $\rho_m=\rho_\infty(1-\theta/m + ...)$, where $\theta$ is the polymer entropic exponent, so that $\theta$ can be determined from the analysis of $\rho_m$. We perform simulations for elastic lattice polymer loops with various sizes and knots, in which we measure $\rho_m$. The resulting estimates support the hypothesis that the exponent $\theta$ is determined only by the number of prime knots and not by their type. However, if knots are present, we observe strong corrections to scaling, which help to understand how an entropic competition between knots is affected by the finite length of the chain.Comment: 10 page

A new algorithm for recognizing the unknot

The topological underpinnings are presented for a new algorithm which answers the question: `Is a given knot the unknot?' The algorithm uses the braid foliation technology of Bennequin and of Birman and Menasco. The approach is to consider the knot as a closed braid, and to use the fact that a knot is unknotted if and only if it is the boundary of a disc with a combinatorial foliation. The main problems which are solved in this paper are: how to systematically enumerate combinatorial braid foliations of a disc; how to verify whether a combinatorial foliation can be realized by an embedded disc; how to find a word in the the braid group whose conjugacy class represents the boundary of the embedded disc; how to check whether the given knot is isotopic to one of the enumerated examples; and finally, how to know when we can stop checking and be sure that our example is not the unknot.Comment: 46 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper9.abs.htm

Understanding Hydrogen-Bond Patterns in Proteins using a Novel Statistical Model

Proteins are built from basic structural elements and their systematic characterization is of interest. Searching for recurring patterns in protein contact maps, we found several network motifs, patterns that occur more frequently in experimentally determined protein contact maps than in randomized contact maps with the same properties. Some of these network motifs correspond to sub-structures of alpha helices, including topologies not previously recognized in this context. Other motifs characterize beta-sheets, again some of which appear to be novel. This topological characterization of patterns serves as a tool to characterize proteins, and to reveal a high detailed differences map for comparing protein structures solved by X-ray crystallography, NMR and molecular dynamics (MD) simulations. Both NMR and MD show small but consistent differences from the crystal structures of the same proteins, possibly due to the pair-wise energy functions used. Network motifs analysis can serve as a base for many-body energy statistical energy potential, and suggests a dictionary of basic elements of which protein secondary structure is made

Termination Detection of Local Computations

Contrary to the sequential world, the processes involved in a distributed system do not necessarily know when a computation is globally finished. This paper investigates the problem of the detection of the termination of local computations. We define four types of termination detection: no detection, detection of the local termination, detection by a distributed observer, detection of the global termination. We give a complete characterisation (except in the local termination detection case where a partial one is given) for each of this termination detection and show that they define a strict hierarchy. These results emphasise the difference between computability of a distributed task and termination detection. Furthermore, these characterisations encompass all standard criteria that are usually formulated : topological restriction (tree, rings, or triangu- lated networks ...), topological knowledge (size, diameter ...), and local knowledge to distinguish nodes (identities, sense of direction). These results are now presented as corollaries of generalising theorems. As a very special and important case, the techniques are also applied to the election problem. Though given in the model of local computations, these results can give qualitative insight for similar results in other standard models. The necessary conditions involve graphs covering and quasi-covering; the sufficient conditions (constructive local computations) are based upon an enumeration algorithm of Mazurkiewicz and a stable properties detection algorithm of Szymanski, Shi and Prywes

Growth Algorithms for Lattice Heteropolymers at Low Temperatures

Two improved versions of the pruned-enriched-Rosenbluth method (PERM) are proposed and tested on simple models of lattice heteropolymers. Both are found to outperform not only the previous version of PERM, but also all other stochastic algorithms which have been employed on this problem, except for the core directed chain growth method (CG) of Beutler & Dill. In nearly all test cases they are faster in finding low-energy states, and in many cases they found new lowest energy states missed in previous papers. The CG method is superior to our method in some cases, but less efficient in others. On the other hand, the CG method uses heavily heuristics based on presumptions about the hydrophobic core and does not give thermodynamic properties, while the present method is a fully blind general purpose algorithm giving correct Boltzmann-Gibbs weights, and can be applied in principle to any stochastic sampling problem.Comment: 9 pages, 9 figures. J. Chem. Phys., in pres