On the non-ergodicity of the Swendsen-Wang-Kotecky algorithm on the kagome lattice

We study the properties of the Wang-Swendsen-Kotecky cluster Monte Carlo algorithm for simulating the 3-state kagome-lattice Potts antiferromagnet at zero temperature. We prove that this algorithm is not ergodic for symmetric subsets of the kagome lattice with fully periodic boundary conditions: given an initial configuration, not all configurations are accessible via Monte Carlo steps. The same conclusion holds for single-site dynamics.Comment: Latex2e. 22 pages. Contains 11 figures using pstricks package. Uses iopart.sty. Final version accepted in journa

A-type K(+) channels impede supralinear summation of clustered glutamatergic inputs in layer 3 neocortical pyramidal neurons

A-type K+ channels restrain the spread of incoming signals in tufted and apical dendrites of pyramidal neurons resulting in strong compartmentalization. However, the exact subunit composition and functional significance of K+ channels expressed in small diameter proximal dendrites remain poorly understood. We focus on A-type K+ channels expressed in basal and oblique dendrites of cortical layer 3 pyramidal neurons, in ex vivo brain slices from young adult mice. Blocking putative Kv4 subunits with phrixotoxin-2 enhances depolarizing potentials elicited by uncaging RuBi-glutamate at single dendritic spines. A concentration of 4-aminopyridine reported to block Kv1 has no effect on such responses. 4-aminopyridine and phrixotoxin-2 increase supralinear summation of glutamatergic potentials evoked by synchronous activation of clustered spines. The effect of 4-aminopyridine on glutamate responses is simulated in a computational model where the dendritic A-type conductance is distributed homogeneously or in a linear density gradient. Thus, putative Kv4-containing channels depress excitatory inputs at single synapses. The additional recruitment of Kv1 subunits might require the synchronous activation of multiple inputs to regulate the gain of signal integration

Metastates in mean-field models with random external fields generated by Markov chains

We extend the construction by Kuelske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that, for a degenerate non-reversible chain this CLT approximation is not enough and the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.Comment: 20 pages, 2 figure

Networks become navigable as nodes move and forget

We propose a dynamical process for network evolution, aiming at explaining the emergence of the small world phenomenon, i.e., the statistical observation that any pair of individuals are linked by a short chain of acquaintances computable by a simple decentralized routing algorithm, known as greedy routing. Previously proposed dynamical processes enabled to demonstrate experimentally (by simulations) that the small world phenomenon can emerge from local dynamics. However, the analysis of greedy routing using the probability distributions arising from these dynamics is quite complex because of mutual dependencies. In contrast, our process enables complete formal analysis. It is based on the combination of two simple processes: a random walk process, and an harmonic forgetting process. Both processes reflect natural behaviors of the individuals, viewed as nodes in the network of inter-individual acquaintances. We prove that, in k-dimensional lattices, the combination of these two processes generates long-range links mutually independently distributed as a k-harmonic distribution. We analyze the performances of greedy routing at the stationary regime of our process, and prove that the expected number of steps for routing from any source to any target in any multidimensional lattice is a polylogarithmic function of the distance between the two nodes in the lattice. Up to our knowledge, these results are the first formal proof that navigability in small worlds can emerge from a dynamical process for network evolution. Our dynamical process can find practical applications to the design of spatial gossip and resource location protocols.Comment: 21 pages, 1 figur

Stochastic analysis of exit fluid temperature records from the active TAG hydrothermal mound (Mid-Atlantic Ridge, 26°N) : 2. Hidden Markov models of flow episodes

Author Posting. © American Geophysical Union, 2007. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 112 (2007): B09102, doi:10.1029/2007JB004961.I develop a stochastic signal model for episodic modes of variability in hydrothermal flow records using probabilistic functions of Markov processes (i.e., hidden Markov models, HMMs) and fit the model to exit fluid temperature time series data from diffuse flow sites on the active TAG hydrothermal mound. The flow states are modeled using Gamma densities to provide flexibility for application to a range of signal types. Between three and five flow states are needed to fit the diffuse flow temperature records from TAG, which correspond to models with between 10 and 28 degrees of freedom. The number of flow states required to fit a given record is related to the signal variance, with more variable records requiring a larger state space. HMMs thus provide an efficient signal model for episodic variability in hydrothermal flow records, suggesting that Markov processes may provide a means to generate stochastic subsurface flow models for deep-sea hydrothermal fields if the spatial flow correlations can be incorporated into a statistical framework. I also use the Viterbi algorithm to “decode” the time series data into best fitting state sequences, which can be used to classify the records into discrete flow episodes. This may provide an objective means to identify discrete events in a flow record if misclassification issues arising from nonepisodic variability (e.g., tidal forcing) can be addressed.This work was supported by the National Science Foundation (OCE-0137329)

Non-Equilibrium Statistical Physics of Currents in Queuing Networks

We consider a stable open queuing network as a steady non-equilibrium system of interacting particles. The network is completely specified by its underlying graphical structure, type of interaction at each node, and the Markovian transition rates between nodes. For such systems, we ask the question ``What is the most likely way for large currents to accumulate over time in a network ?'', where time is large compared to the system correlation time scale. We identify two interesting regimes. In the first regime, in which the accumulation of currents over time exceeds the expected value by a small to moderate amount (moderate large deviation), we find that the large-deviation distribution of currents is universal (independent of the interaction details), and there is no long-time and averaged over time accumulation of particles (condensation) at any nodes. In the second regime, in which the accumulation of currents over time exceeds the expected value by a large amount (severe large deviation), we find that the large-deviation current distribution is sensitive to interaction details, and there is a long-time accumulation of particles (condensation) at some nodes. The transition between the two regimes can be described as a dynamical second order phase transition. We illustrate these ideas using the simple, yet non-trivial, example of a single node with feedback.Comment: 26 pages, 5 figure