Efficient numerical integrators for stochastic models

The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It follows that, in the stochastic case, some care is required in splitting the stochastic generator. We test the Trotter integrators on an energy-conserving Brownian model and derive a new numerical scheme for dissipative particle dynamics. We find that the stochastic Trotter scheme provides a mathematically correct and easy-to-use method which should find wide applicability.Comment: v

AGI and the Knight-Darwin Law: why idealized AGI reproduction requires collaboration

Can an AGI create a more intelligent AGI? Under idealized assumptions, for a certain theoretical type of intelligence, our answer is: “Not without outside help”. This is a paper on the mathematical structure of AGI populations when parent AGIs create child AGIs. We argue that such populations satisfy a certain biological law. Motivated by observations of sexual reproduction in seemingly-asexual species, the Knight-Darwin Law states that it is impossible for one organism to asexually produce another, which asexually produces another, and so on forever: that any sequence of organisms (each one a child of the previous) must contain occasional multi-parent organisms, or must terminate. By proving that a certain measure (arguably an intelligence measure) decreases when an idealized parent AGI single-handedly creates a child AGI, we argue that a similar Law holds for AGIs

Towards Better Integrators for Dissipative Particle Dynamics Simulations

Coarse-grained models that preserve hydrodynamics provide a natural approach to study collective properties of soft-matter systems. Here, we demonstrate that commonly used integration schemes in dissipative particle dynamics give rise to pronounced artifacts in physical quantities such as the compressibility and the diffusion coefficient. We assess the quality of these integration schemes, including variants based on a recently suggested self-consistent approach, and examine their relative performance. Implications of integrator-induced effects are discussed.Comment: 4 pages, 3 figures, 2 tables, accepted for publication in Phys. Rev. E (Rapid Communication), tentative publication issue: 01 Dec 200

Global Optimization by Energy Landscape Paving

We introduce a novel heuristic global optimization method, energy landscape paving (ELP), which combines core ideas from energy surface deformation and tabu search. In appropriate limits, ELP reduces to existing techniques. The approach is very general and flexible and is illustrated here on two protein folding problems. For these examples, the technique gives faster convergence to the global minimum than previous approaches.Comment: to appear in Phys. Rev. Lett. (2002

Entropy-based analysis of the number partitioning problem

In this paper we apply the multicanonical method of statistical physics on the number-partitioning problem (NPP). This problem is a basic NP-hard problem from computer science, and can be formulated as a spin-glass problem. We compute the spectral degeneracy, which gives us information about the number of solutions for a given cost $E$ and cardinality $m$. We also study an extension of this problem for $Q$ partitions. We show that a fundamental difference on the spectral degeneracy of the generalized ($Q>2$) NPP exists, which could explain why it is so difficult to find good solutions for this case. The information obtained with the multicanonical method can be very useful on the construction of new algorithms.Comment: 6 pages, 4 figure

Aging at Criticality in Model C Dynamics

We study the off-equilibrium two-point critical response and correlation functions for the relaxational dynamics with a coupling to a conserved density (Model C) of the O(N) vector model. They are determined in an \epsilon=4-d expansion for vanishing momentum. We briefly discuss their scaling behaviors and the associated scaling forms are determined up to first order in epsilon. The corresponding fluctuation-dissipation ratio has a non trivial large time limit in the aging regime and, up to one-loop order, it is the same as that of the Model A for the physically relevant case N=1. The comparison with predictions of local scale invariance is also discussed.Comment: 13 pages, 1 figur

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, that corresponds to the limit $N\to 0$ of an $N$-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions concerning the critical crossover functions, finding a good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal lscrossover behavior of our data for any finite range.Comment: 43 pages, revte

Theory blending: extended algorithmic aspects and examples

In Cognitive Science, conceptual blending has been proposed as an important cognitive mechanism that facilitates the creation of new concepts and ideas by constrained combination of available knowledge. It thereby provides a possible theoretical foundation for modeling high-level cognitive faculties such as the ability to understand, learn, and create new concepts and theories. Quite often the development of new mathematical theories and results is based on the combination of previously independent concepts, potentially even originating from distinct subareas of mathematics. Conceptual blending promises to offer a framework for modeling and re-creating this form of mathematical concept invention with computational means. This paper describes a logic-based framework which allows a formal treatment of theory blending (a subform of the general notion of conceptual blending with high relevance for applications in mathematics), discusses an interactive algorithm for blending within the framework, and provides several illustrating worked examples from mathematics