Dual Monte Carlo and Cluster Algorithms

We discuss the development of cluster algorithms from the viewpoint of probability theory and not from the usual viewpoint of a particular model. By using the perspective of probability theory, we detail the nature of a cluster algorithm, make explicit the assumptions embodied in all clusters of which we are aware, and define the construction of free cluster algorithms. We also illustrate these procedures by rederiving the Swendsen-Wang algorithm, presenting the details of the loop algorithm for a worldline simulation of a quantum $S=$ 1/2 model, and proposing a free cluster version of the Swendsen-Wang replica method for the random Ising model. How the principle of maximum entropy might be used to aid the construction of cluster algorithms is also discussed.Comment: 25 pages, 4 figures, to appear in Phys.Rev.

Current-Induced Step Bending Instability on Vicinal Surfaces

We model an apparent instability seen in recent experiments on current induced step bunching on Si(111) surfaces using a generalized 2D BCF model, where adatoms have a diffusion bias parallel to the step edges and there is an attachment barrier at the step edge. We find a new linear instability with novel step patterns. Monte Carlo simulations on a solid-on-solid model are used to study the instability beyond the linear regime.Comment: 4 pages, 4 figure

Cluster update and recognition

We present a fast and robust cluster update algorithm that is especially efficient in implementing the task of image segmentation using the method of superparamagnetic clustering. We apply it to a Potts model with spin interactions that are are defined by gray-scale differences within the image. Motivated by biological systems, we introduce the concept of neural inhibition to the Potts model realization of the segmentation problem. Including the inhibition term in the Hamiltonian results in enhanced contrast and thereby significantly improves segmentation quality. As a second benefit we can - after equilibration - directly identify the image segments as the clusters formed by the clustering algorithm. To construct a new spin configuration the algorithm performs the standard steps of (1) forming clusters and of (2) updating the spins in a cluster simultaneously. As opposed to standard algorithms, however, we share the interaction energy between the two steps. Thus the update probabilities are not independent of the interaction energies. As a consequence, we observe an acceleration of the relaxation by a factor of 10 compared to the Swendson and Wang procedure.Comment: 4 pages, 2 figure

The Persistence of Long-Term Memory A Molecular Approach to Self-Sustaining Changes in Learning-Induced Synaptic Growth

AbstractRecent cellular and molecular studies of both implicit and explicit memory storage suggest that experience-dependent modulation of synaptic strength and structure is a fundamental mechanism by which these diverse forms of memory are encoded and stored. For both forms of memory storage, some type of synaptic growth is thought to represent the stable cellular change that maintains the long-term process. In this review, we discuss recent findings on the molecular events that underlie learning-related synaptic growth in Aplysia and discuss the possibility that an active, prion-based mechanism is important for the maintenance of the structural change and for the persistence of long-term memory

Time-dependent correlation functions in a one-dimensional asymmetric exclusion process

We study a one-dimensional anisotropic exclusion process describing particles injected at the origin, moving to the right on a chain of $L$ sites and being removed at the (right) boundary. We construct the steady state and compute the density profile, exact expressions for all equal-time n-point density correlation functions and the time-dependent two-point function in the steady state as functions of the injection and absorption rates. We determine the phase diagram of the model and compare our results with predictions from dynamical scaling and discuss some conjectures for other exclusion models.Comment: LATEX-file, 32 pages, Weizmann preprint WIS/93/01/Jan-P

Cluster Algorithm for a Solid-On-Solid Model with Constraints

We adapt the VMR (valleys-to-mountains reflections) algorithm, originally devised by us for simulations of SOS models, to the BCSOS model. It is the first time that a cluster algorithm is used for a model with constraints. The performance of this new algorithm is studied in detail in both phases of the model, including a finite size scaling analysis of the autocorrelations.Comment: 10 pages, 3 figures appended as ps-file

Transcriptional regulation of long-term memory in the marine snail Aplysia

Whereas the induction of short-term memory involves only covalent modifications of constitutively expressed preexisting proteins, the formation of long-term memory requires gene expression, new RNA, and new protein synthesis. On the cellular level, transcriptional regulation is thought to be the starting point for a series of molecular steps necessary for both the initiation and maintenance of long-term synaptic facilitation (LTF). The core molecular features of transcriptional regulation involved in the long-term process are evolutionally conserved in Aplysia, Drosophila, and mouse, and indicate that gene regulation by the cyclic AMP response element binding protein (CREB) acting in conjunction with different combinations of transcriptional factors is critical for the expression of many forms of long-term memory. In the marine snail Aplysia, the molecular mechanisms that underlie the storage of long-term memory have been extensively studied in the monosynaptic connections between identified sensory neuron and motor neurons of the gill-withdrawal reflex. One tail shock or one pulse of serotonin (5-HT), a modulatory transmitter released by tail shocks, produces a transient facilitation mediated by the cAMP-dependent protein kinase leading to covalent modifications in the sensory neurons that results in an enhancement of transmitter release and a strengthening of synaptic connections lasting minutes. By contrast, repeated pulses of 5-hydroxytryptamine (5-HT) induce a transcription- and translation-dependent long-term facilitation (LTF) lasting more than 24 h and trigger the activation of a family of transcription factors in the presynaptic sensory neurons including ApCREB1, ApCREB2 and ApC/EBP. In addition, we have recently identified novel transcription factors that modulate the expression of ApC/EBP and also are critically involved in LTF. In this review, we examine the roles of these transcription factors during consolidation of LTF induced by different stimulation paradigms

Cluster Dynamics for Randomly Frustrated Systems with Finite Connectivity

In simulations of some infinite range spin glass systems with finite connectivity, it is found that for any resonable computational time, the saturatedenergy per spin that is achieved by a cluster algorithm is lowered in comparison to that achieved by Metropolis dynamics.The gap between the average energies obtained from these two dynamics is robust with respect to variations of the annealing schedule. For some probability distribution of the interactions the ground state energy is calculated analytically within the replica symmetry assumptionand is found to be saturated by a cluster algorithm.Comment: Revtex, 4 pages with 3 figure

Magic Islands and Barriers to Attachment: A Si/Si(111)7x7 Growth Model

Surface reconstructions can drastically modify growth kinetics during initial stages of epitaxial growth as well as during the process of surface equilibration after termination of growth. We investigate the effect of activation barriers hindering attachment of material to existing islands on the density and size distribution of islands in a model of homoepitaxial growth on Si(111)7x7 reconstructed surface. An unusual distribution of island sizes peaked around "magic" sizes and a steep dependence of the island density on the growth rate are observed. "Magic" islands (of a different shape as compared to those obtained during growth) are observed also during surface equilibration.Comment: 4 pages including 5 figures, REVTeX, submitted to Physical Review