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New Lower Bound for the Optimal Ball Packing Density in Hyperbolic 4-spaceJan 23 2014Aug 22 2014In this paper we consider ball packings in $4$-dimensional hyperbolic space. We show that it is possible to exceed the conjectured $4$-dimensional realizable packing density upper bound due to L. Fejes T\'oth (Regular Figures, 1964). We give seven examples ... More

Horoball Packing Density Lower Bounds in Higher Dimensional Hyperbolic $n$-space for $6 \leq n \leq 9$Jul 01 2019Koszul type Coxeter Simplex tilings exist in hyperbolic space $\mathbb{H}^n$ for $2 \leq n \leq 9$, and their horoball packings have the highest known regular ball packing densities for $3 \leq n \leq 5$. In this paper we determine the optimal horoball ... More

New Horoball Packing Density Lower Bound in Hyperbolic 5-spaceSep 13 2018We describe the optimal horoball packings of asymptotic Koszul type Coxeter simplex tilings of $5$-dimensional hyperbolic space where the symmetries of the packings are generated by Coxeter groups. We find that the optimal horoball packing density of ... More

On removing one point from a compact spaceApr 15 2005If B is a compact space and B\{pt} is Lindelof then B^k\{pt} is star-Linedlof for every cardinality k. If B\{pt} is compact then B^k\{pt} is discretely star-Lindelof. In particular, this gives new examples of Tychonoff discretely star-Lindelof spaces ... More

Structure and Visualization of Optimal Horoball Packings in $3$-dimensional Hyperbolic SpaceJan 14 2016Four packings of hyperbolic 3-space are known to yield the optimal packing density of $0.85328\dots$. They are realized in the regular tetrahedral and cubic Coxeter honeycombs with Schl\"afli symbols $\{3,3,6 \}$ and $\{4,3,6\}$. These honeycombs are ... More

Optimally Dense Packings for Fully Asymptotic Coxeter Tilings by Horoballs of Different TypesJul 05 2010Jul 12 2012The goal of this paper to determine the optimal horoball packing arrangements and their densities for all four fully asymptotic Coxeter tilings (Coxeter honeycombs) in hyperbolic 3-space $\mathbb{H}^3$. Centers of horoballs are required to lie at vertices ... More

Central limit theorem for random walks in divergence-free random drift field: "H-minus-one" sufficesNov 15 2014We prove central limit theorem under diffusive scaling for the displacement of a random walk on ${\mathbb Z}^d$ in stationary divergence-free random drift field, under the ${\mathcal H}_{-1}$-condition imposed on the drift field. The condition is equivalent ... More

Exponential Riesz bases, discrepancy of irrational rotations and BMOSep 11 2010Mar 13 2011We study the basis property of systems of exponentials with frequencies belonging to 'simple quasicrystals'. We show that a diophantine condition is necessary and sufficient for such a system to be a Riesz basis in L^2 on a finite union of intervals. ... More

A note about critical percolation on finite graphsSep 24 2009Nov 16 2009In this note we study the geometry of the largest component C_1 of critical percolation on a finite graph G which satisfies the finite triangle condition, defined by Borgs et al. There it is shown that this component is of size n^{2/3}, and here we show ... More

Central Limit Theorem for Random Walks in Doubly Stochastic Random Environment: $\mathcal{H}_{-1}$ SufficesFeb 22 2017We prove a central limit theorem under diffusive scaling for the displacement of a random walk on ${\mathbb Z}^d$ in stationary and ergodic doubly stochastic random environment, under the $\mathcal{H}_{-1}$-condition imposed on the drift field. The condition ... More

Groups with minimal harmonic functions as small as you like (With an appendix by Nicolas Matte Bon)May 24 2016Feb 05 2017For any order of growth $f(n)=o(\log n)$ we construct a finitely-generated group $G$ and a set of generators $S$ such that the Cayley graph of $G$ with respect to $S$ supports a harmonic function with growth $f$ but does not support any harmonic function ... More

Thermodynamic Model of Criticality in the Cortex Based On EEG/ECOG DataJun 06 2012Criticality in the cortex emerges from the seemingly random interaction of microscopic components and produces higher cognitive functions at mesoscopic and macroscopic scales. Random graphs and percolation theory provide natural means to de- scribe critical ... More

A modified bootstrap percolation on a random graph coupled with a latticeJul 29 2015Dec 14 2018In this paper a random graph model $G_{\mathbb{Z}^2_N,p_d}$ is introduced, which is a combination of fixed torus grid edges in $(\mathbb{Z}/N \mathbb{Z})^2$ and some additional random ones. The random edges are called long, and the probability of having ... More

STDP Learning of Image Patches with Convolutional Spiking Neural NetworksAug 24 2018Spiking neural networks are motivated from principles of neural systems and may possess unexplored advantages in the context of machine learning. A class of \textit{convolutional spiking neural networks} is introduced, trained to detect image features ... More

Bootstrap percolation on a random graph coupled with a latticeJul 29 2015Nov 12 2015In this paper a random graph model $G_{\mathbb{Z}^2_N,p_d}$ is introduced, which is a combination of fixed torus grid edges in $(\mathbb{Z}/N \mathbb{Z})^2$ and some additional random ones. The random edges are called long, and the probability of having ... More

Complete stability analysis of a heuristic ADP control designAug 15 2013Jul 28 2015This paper provides new stability results for Action-Dependent Heuristic Dynamic Programming (ADHDP), using a control algorithm that iteratively improves an internal model of the external world in the autonomous system based on its continuous interaction ... More

Localization for Linearly Edge Reinforced Random WalksMar 19 2012We prove that the linearly edge reinforced random walk (LRRW) on any graph with bounded degrees is recurrent for sufficiently small initial weights. In contrast, we show that for non-amenable graphs the LRRW is transient for sufficiently large initial ... More

Unsupervised Learning with Self-Organizing Spiking Neural NetworksJul 24 2018We present a system comprising a hybridization of self-organized map (SOM) properties with spiking neural networks (SNNs) that retain many of the features of SOMs. Networks are trained in an unsupervised manner to learn a self-organized lattice of filters ... More

Improved robustness of reinforcement learning policies upon conversion to spiking neuronal network platforms applied to ATARI gamesMar 26 2019Various implementations of Deep Reinforcement Learning (RL) demonstrated excellent performance on tasks that can be solved by trained policy, but they are not without drawbacks. Deep RL suffers from high sensitivity to noisy and missing input and adversarial ... More

Faster and simpler algorithms for finding large patterns in permutationsFeb 23 2019Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this area is deciding ... More

Minimum Average Distance TriangulationsDec 08 2011Jun 20 2012We study the problem of finding a triangulation T of a planar point set S such as to minimize the expected distance between two points x and y chosen uniformly at random from S. By distance we mean the length of the shortest path between x and y along ... More

Percolation, Perimetry, PlanaritySep 10 2005Apr 11 2006Let G be a planar graph with polynomial growth and isoperimetric dimension bigger than 1. Then the critical p for Bernoulli percolation on G satisfies p<1.

Random homeomorphisms and Fourier expansions - the pointwise behaviorNov 02 2005Let phi be a Dubins-Freedman random homeomorphism on [0,1] derived from the base measure uniform on the vertical line x=1/2, and let f be a periodic function satisfying that |f(x)-f(0)| = o(1/log log log 1/x). Then the Fourier expansion of f composed ... More

Bessel Functions in Mass Action. Modeling of Memories and RemembrancesJun 14 2015Data from experimental observations of a class of neurological processes (Freeman K-sets) present functional distribution reproducing Bessel function behavior. We model such processes with couples of damped/amplified oscillators which provide time dependent ... More

Lattice Map Spiking Neural Networks (LM-SNNs) for Clustering and Classifying Image DataJun 04 2019Spiking neural networks (SNNs) with a lattice architecture are introduced in this work, combining several desirable properties of SNNs and self-organized maps (SOMs). Networks are trained with biologically motivated, unsupervised learning rules to obtain ... More

BindsNET: A machine learning-oriented spiking neural networks library in PythonJun 04 2018Dec 10 2018The development of spiking neural network simulation software is a critical component enabling the modeling of neural systems and the development of biologically inspired algorithms. Existing software frameworks support a wide range of neural functionality, ... More

Faster and simpler algorithms for finding large patterns in permutationsFeb 23 2019Apr 16 2019Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this area is deciding ... More

Reinforced random walkAug 01 2012A survey of reinforced random walk, with emphasis on the linear case.

Locally Connected Spiking Neural Networks for Unsupervised Feature LearningApr 12 2019In recent years, Spiking Neural Networks (SNNs) have demonstrated great successes in completing various Machine Learning tasks. We introduce a method for learning image features by \textit{locally connected layers} in SNNs using spike-timing-dependent ... More

Improved robustness of reinforcement learning policies upon conversion to spiking neuronal network platforms applied to ATARI gamesMar 26 2019May 02 2019Various implementations of Deep Reinforcement Learning (RL) demonstrated excellent performance on tasks that can be solved by trained policy, but they are not without drawbacks. Deep RL suffers from high sensitivity to noisy and missing input and adversarial ... More

Modeling supernova emission at late timesMar 26 1999We compare model calculations with observations of supernovae at late times to infer the time evolution of temperature, ionization and line emission. Here we mainly report on our results from our modeling of SN 1987A. We discuss the oxygen mass from the ... More

Continuous vs discrete spins in the hyperbolic planeSep 28 2016Oct 17 2016We study the $O(n)$ model on planar hyperbolic cocompact lattices, with free boundary conditions. We observe that the pair correlations decay exponentially with distance, for all temperatures, if and only if $n>1$.

A null series with small anti-analytic partOct 19 2005We show that it is possible for a square integrable function on the circle, which is a sum of an almost everywhere convergent series of exponentials with positive frequencies, to not belong to the Hardy space. A consequence in the uniqueness theory is ... More

Is PLA large?Oct 06 2005Oct 18 2005We examine the class of functions representable by an analytic sum (by which we mean a trigonometric sum involving only positive frequencies) converging almost everywhere. We show that it is dense but that it is first category and has zero Wiener measure. ... More

Combining Riesz bases in $R^d$Jan 21 2015We prove that every finite union of rectangles in $R^d$ admits a Riesz basis of exponentials.

Lower bound for the escape probability in the Lorentz Mirror Model on the latticeNov 28 2013We show that in the Lorentz mirror model, at any density of mirrors, the probability of a particle starting at the origin to reach distance n is at least 1/(2n+1).

One cannot hear the winding numberDec 07 2006We construct an example of two continuous maps f and g of the circle to itself with the same absolute value of the Fourier transform but with different winding numbers, answering a question of Brezis.

Streaming Algorithms for Partitioning Integer SequencesApr 07 2014Jul 07 2014We study the problem of partitioning integer sequences in the one-pass data streaming model. Given is an input stream of integers $X \in \{0, 1, \dots, m \}^n$ of length $n$ with maximum element $m$, and a parameter $p$. The goal is to output the positions ... More

Maximum Scatter TSP in Doubling MetricsDec 09 2015Jun 28 2016We study the problem of finding a tour of $n$ points in which every edge is long. More precisely, we wish to find a tour that visits every point exactly once, maximizing the length of the shortest edge in the tour. The problem is known as Maximum Scatter ... More

Maximal smoothness of the anti-analytic part of a trigonometric null seriesOct 19 2005We proved recently math.CA/0510403 that the anti-analytic part of a trigonometric series, converging to zero almost everywhere, may be square integrable on the circle. Here we prove that it can even be infinitely differentiable, and we characterize precisely ... More

Representation of non periodic functions by trigonometric series with almost integer frequenciesDec 02 2005Inspired by Menshov's representation theorem, we prove that there exists a sequence of frequecies such that any measurable (complex valued) function on R can be represented as a sum of almost everywhere convergent trigonometric series with these frequencies. ... More

Loop-erased random walk on a torus in dimensions 4 and aboveAug 31 2003Sharp estimates for the length of loop erased random walk between two vertices on the [n]^d -torus, d > 4, are established. The mean length is order n^{d/2} . In dimension 4 we have only an upper bound.

Nonamenable Liouville GraphsOct 16 2010Add to each level of binary tree edges to make the induced graph on the level a uniform expander. It is shown that such a graph admits no non-constant bounded harmonic functions.

On common roots of random Bernoulli polynomialsSep 11 2011We prove that with high probability, d+1 random Bernoulli polynomials in d variables of degree n (n goes to infinity) do not possess a common root.

Divisibility and Laws in Finite Simple GroupsMar 10 2014May 20 2014We provide new bounds for the divisibility function of the free group F_2 and construct short laws for the symmetric groups Sym(n). The construction is random and relies on the classification of the finite simple groups. We also give bounds on the length ... More

Groups with minimal harmonic functions as small as you likeMay 24 2016For any order of growth $f(n)=o(\log n)$ we construct a finitely-generated group $G$ and a set of generators $S$ such that the Cayley graph of $G$ with respect to $S$ supports a harmonic function with growth $f$ but does not support any harmonic function ... More

Late Spectral Evolution of SN 1987A: II. Line EmissionDec 17 1997Using the temperature and ionization calculated in our previous paper, we model the spectral evolution of SN 1987A. The IR-catastrophe is seen in the metal lines as a transition from thermal to non-thermal excitation, most clearly in the [O I] 6300, 6364 ... More

Uniqueness of percolation on products with ZMay 13 2011Jul 28 2012We show that there exists a connected graph G with subexponential volume growth such that critical percolation on the product of G with the line has infinitely many infinite clusters. We also give some conditions under which this cannot occur.

Binary search trees and rectangulationsMar 26 2016We revisit the classical problem of searching in a binary search tree (BST) using rotations, and present novel connections of this problem to a number of geometric and combinatorial structures. In particular, we show that the execution trace of a BST ... More

Analytic representation of functions and a new quasi-analyticity thresholdJun 14 2004Apr 27 2007We characterize precisely the possible rate of decay of the anti-analytic half of a trigonometric series converging to zero almost everywhere.

Singular distributions and symmetry of the spectrumJan 12 2013This is a survey of the "Fourier symmetry" of measures and distributions on the circle in relation with the size of their support. Mostly it is based on our paper arxiv:1004.3631 and a talk given by the second author in the 2012 Abel symposium.

Singular distributions, dimension of support, and symmetry of Fourier transformApr 21 2010Jan 25 2011We study the "Fourier symmetry" of measures and distributions on the circle, in relation with the size of their supports. The main results of this paper are: (1) A one-side extension of Frostman's theorem, which connects the rate of decay of Fourier transform ... More

Combining Riesz basesOct 23 2012Apr 15 2014We show that any finite union of intervals supports a Riesz basis of exponentials

Consensus formation on coevolving networks: groups' formation and structureJan 31 2008We study the effect of adaptivity on a social model of opinion dynamics and consensus formation. We analyze how the adaptivity of the network of contacts between agents to the underlying social dynamics affects the size and topological properties of groups ... More

The mean-field quantum Heisenberg ferromagnet via representation theoryNov 26 2018We use representation theory to write a formula for the magnetisation of the quantum Heisenberg ferromagnet. The core new result is a spectral decomposition of the function $\alpha_k 2^{\alpha_1+\dotsb+\alpha_n}$ where $\alpha_k$ is the number of cycles ... More

Random Menshov spectraOct 20 2005We show that a spectrum of frequencies obtained by a random perturbation of the integers allows one to represent any measurable function on R by an almost everywhere converging sum of harmonics almost surely.

Menshov representation spectraOct 28 2005A Menshov spectrum is a subset of the integers that is sufficient for representing every measurable function as an almost-everywhere converging trigonometric (non-Fourier) sum. In this language the celebrated "Menshov representation theorem" states that ... More

Every exponential group supports a positive harmonic functionOct 31 2017May 20 2018We prove that all groups of exponential growth support non-constant positive harmonic functions. In fact, out results hold in the more general case of strongly connected, finitely supported Markov chains invariant under some transitive group of automorphisms ... More

Counting batsApr 10 2013We demonstrate an algorithm that reconstructs the number of walkers in an unknown graph from observations of their returns to a fixed point.

A Resistance Bound via an Isoperimetric InequalityDec 23 2002Jun 09 2012An isoperimetric upper bound on the resistance is given. As a corollary we resolve two problems, regarding mean commute time on finite graphs and resistance on percolation clusters. Further conjectures are presented.

Cycle structure of the interchange process and representation theoryMay 21 2012Consider the process of random transpositions on the complete graph. We use representation theory to give an exact, simple formula for the expected number of cycles of size k at time t, in terms of an incomplete Beta function. Using this we show that ... More

Consensus formation on adaptive networksJul 30 2007The structure of a network can significantly influence the properties of the dynamical processes which take place on them. While many studies have been devoted to this influence, much less attention has been devoted to the interplay and feedback mechanisms ... More

Comparing with octopiNov 26 2018Operator inequalities with a geometric flavour have been successful in studying mixing of random walks and quantum mechanics. We suggest a new way to extract such inequalities using the octopus inequality of Caputo, Liggett and Richthammer.

Ordering the representations of S_n using the interchange processMar 08 2010Jul 21 2011Inspired by Aldous' conjecture for the spectral gap of the interchange process and its recent resolution by Caputo, Liggett and Richthammer, we define an associated order on the irreducible representations of S_n. Aldous' conjecture is equivalent to certain ... More

On the gaps between zeros of trigonometric polynomialsJan 02 2006We show that for every finite symetric set S of integer vectors, every real trigonometric polynomial on the d dimensional torus with spectrum in S has a zero in every closed ball of diameter D, where D is the sum over S of 1 over 4 times the L2 norm of ... More

An "Analytic" Version of Menshov's Representation TheoremDec 01 2005Every measurable function f on the circle can be represented as a sum of harmonics with positive spectrum, converging in measure. For convergence almost everywhere this is not true. We discuss several other subsets of Z for which one might get a Menshov ... More

Perturbing PLAFeb 24 2012We proved earlier that every measurable function on the circle, after a uniformly small perturbation, can be written as a power series (i.e. a series of exponentials with positive frequencies), which converges almost everywhere. Here we show that this ... More

Stochastic Growth in a Small WorldMay 01 2003We considered the Edwards-Wilkinson model on a small-world network. We studied the finite-size behavior of the surface width by performing exact numerical diagonalization for the underlying coupling matrix. We found that the spectrum exhibits a gap or ... More

Arm exponents in high dimensional percolationNov 04 2009We study the probability that the origin is connected to the sphere of radius r (an arm event) in critical percolation in high dimensions, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We prove that ... More

The Alexander-Orbach conjecture holds in high dimensionsJun 09 2008Nov 16 2009We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random ... More

I knew I should have taken that left turn at AlbuquerqueAug 25 2010May 02 2011We study the Laplacian-infinity path as an extreme case of the Laplacian-alpha random walk. Although, in the finite alpha case, there is reason to believe that the process converges to SLE, we show that this is not the case when alpha is infinite. In ... More

Radioactivities and nucleosynthesis in SN 1987ADec 17 2001The nucleosynthesis and production of radioactive elements in SN 1987A are reviewed. Different methods for estimating the masses of 56Ni, 57Ni, and 44Ti are discussed, and we conclude that broad band photometry in combination with time-dependent models ... More

Late Spectral Evolution of SN 1987A: I. Temperature and IonizationDec 17 1997The temperature and ionization of SN 1987A is modeled between 200 and 2000 days in its nebular phase, using a time-dependent model. We include all important elements, as well as the primary composition zones in the supernova. The energy input is provided ... More

The probability of long cycles in interchange processesSep 20 2010May 25 2012We examine the number of cycles of length k in a permutation, as a function on the symmetric group. We write it explicitly as a combination of characters of irreducible representations. This allows to study formation of long cycles in the interchange ... More

Shattering, Graph Orientations, and ConnectivityNov 06 2012We present a connection between two seemingly disparate fields: VC-theory and graph theory. This connection yields natural correspondences between fundamental concepts in VC-theory, such as shattering and VC-dimension, and well-studied concepts of graph ... More

Smooth heaps and a dual view of self-adjusting data structuresFeb 15 2018Dec 29 2018We present a new connection between self-adjusting binary search trees (BSTs) and heaps, two fundamental, extensively studied, and practically relevant families of data structures. Roughly speaking, we map an arbitrary heap algorithm within a natural ... More

Finsler connection for general Lagrangian systemsAug 11 2014Feb 24 2016We give a Finsler non-linear connection by a new simplified definition for not only regular case but also singular case. In regular case, it corresponds to non-linear connection part of Berwald's connection, but our connection is expressed not in line ... More

Is a bivariate polynomial with plus minus 1 coefficients irreducible? Very likely!Feb 21 2016Apr 19 2016We prove that a random bivariate polynomial with plus minus 1 coefficients is irreducible with high probability.

On non-positive curvature properties of the Hilbert metricMar 02 2018In this paper, we consider different types of non-positive curvature properties of the Hilbert metric of a convex domain in R^n. First, we survey the relationships among the concepts and prove that in the case of Hilbert metric some of them are equivalent. ... More

Irreducible polynomials of bounded heightOct 14 2017The goal of this paper is to prove that a random polynomial with i.i.d. random coefficients taking values uniformly in $\{1,\ldots, 210\}$ is irreducible with probability tending to $1$ as the degree tends to infinity. Moreover, we prove that the Galois ... More

On the hyperplane conjecture for random convex setsDec 18 2006Let N > n, and denote by K the convex hull of N independent standard gaussian random vectors in an n-dimensional Euclidean space. We prove that with high probability, the isotropic constant of K is bounded by a universal constant. Thus we verify the hyperplane ... More

The Toom Interface Via CouplingJan 20 2015Sep 19 2016We consider a one dimensional interacting particle system which describes the effective interface dynamics of the two dimensional Toom model at low temperature and noise. We prove a number of basic properties of this model. First we consider the dynamics ... More

Random walks with $k$-wise independent incrementsMay 31 2004We construct examples of a random walk with pairwise-independent steps which is almost-surely bounded, and for any $m$ and $k$ a random walk with $k$-wise independent steps which has no stationary distribution modulo $m$.

A balanced excited random walkSep 03 2010The following random process on $\Z^4$ is studied. At first visit to a site, the two first coordinates perform a (2-dimensional) simple random walk step. At further visits, it is the last two coordinates which perform a simple random walk step. We prove ... More

Supercritical self-avoiding walks are space-fillingOct 13 2011Sep 25 2012We consider random self-avoiding walks between two points on the boundary of a finite subdomain of Z^d (the probability of a self-avoiding trajectory gamma is proportional to mu^{-length(gamma)}). We show that the random trajectory becomes space-filling ... More

Why did Supernova 1054 shine at late times?Dec 15 2000The Crab nebula is the remnant of supernova 1054 (SN 1054). The progenitor of this supernova has, based on nucleosynthesis arguments, been modeled as an 8-10 solar mass star. Here we point out that the observations of the late light curve of SN 1054, ... More

On the connectivity of the Poisson process on fractalsApr 11 2006For a measure mu supported on a compact connected subset of a Euclidean space which satisfies a uniform d-dimensional decay of the volume of balls we show that the maximal edge in the minimum spanning tree of n indepndent samples from mu is, with high ... More

The late-time light curve of the Type Ia supernova 2000cxSep 14 2004We have conducted a systematic and comprehensive monitoring programme of the Type Ia supernova 2000cx at late phases using the VLT and HST. The VLT observations cover phases 360 to 480 days past maximum brightness and include photometry in the BVRIJH ... More

Hubble Space Telescope and Ground-Based Observations of SN 1993J and SN 1998S: CNO Processing in the ProgenitorsSep 17 2004Ground-based and Hubble Space Telescope observations are presented for SN 1993J and SN 1998S. SN 1998S shows strong, relatively narrow circumstellar emission lines of N III-V and C III-IV, as well as broad lines from the ejecta. Both the broad ultraviolet ... More

The minimal spanning tree and the upper box dimensionNov 26 2003Nov 30 2003We show that the alpha-weight of an MST over n points in a metric space with upper box dimension d has a bound independent of n if alpha is smaller than d and does not have one if alpha is larger than d.

The 44Ti-powered spectrum of SN 1987AMar 18 2011May 25 2011SN 1987A provides a unique opportunity to study the evolution of a supernova from explosion into very late phases. Due to the rich chemical structure, the multitude of physical process involved, and extensive radiative transfer effects, detailed modeling ... More

Testing the Collective Properties of Small-World Networks through Roughness ScalingSep 08 2003Motivated by a fundamental synchronization problem in scalable parallel computing and by a recent criterion for ``mean-field'' synchronizability in interacting systems, we study the Edwards-Wilkinson model on two variations of a small-worldnetwork. In ... More

Diffusion Processes on Small-World Networks with Distance-Dependent Random-LinksApr 19 2007Jun 15 2007We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in task-completion networks, ... More

Diffusion Processes on Power-Law Small-World NetworksJan 20 2005May 20 2005We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying exponents. The ... More

Who's talking first? Consensus or lack thereof in coevolving opinion formation modelsNov 08 2007We investigate different opinion formation models on adaptive network topologies. Depending on the dynamical process, rewiring can either (i) lead to the elimination of interactions between agents in different states, and accelerate the convergence to ... More

X-ray emission from radiative shocks in Type II supernovaeOct 28 2005The X-ray emission from the circumstellar interaction in Type II supernovae with a dense circumstellar medium is calculated. In Type IIL and Type IIn supernovae mass loss rates are generally high enough for the region behind the reverse shock to be radiative, ... More

The Toom Interface Via CouplingJan 20 2015Jan 13 2018We consider a one dimensional interacting particle system which describes the effective interface dynamics of the two dimensional Toom model at low temperature and noise. We prove a number of basic properties of this model. First we consider the dynamics ... More

Upper bounds on the percolation correlation lengthFeb 08 2019We study the size of the near-critical window for Bernoulli percolation on $\mathbb Z^d$. More precisely, we use a quantitative Grimmett-Marstrand theorem to prove that the correlation length, both below and above criticality, is bounded from above by ... More

Excited random walk against a wallSep 21 2005Oct 27 2006We analyze random walk in the upper half of a three dimensional lattice which goes down whenever it encounters a new vertex, a.k.a. excited random walk. We show that it is recurrent with an expected number of returns of square-root log n.

The late UVOIR light curve of SN 2000cxNov 04 2003We present preliminary data and modeling of the late time light curve of the Type Ia supernova SN 2000cx. Optical and near-infrared data obtained with the VLT at 360 to 480 days past maximum light show the increasing importance of the near-infrared regime. ... More