## About

25

Publications

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## Publications

Publications (25)

We present a simple approach to high-accuracy calculations of critical properties for the three-dimensional Ising model, without prior knowledge of the critical temperature. The iterative method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group trajectory. We found exp...

We present a simple approach to high-accuracy calculations of critical properties for the three-dimensional Ising model, without prior knowledge of the critical temperature. The iterative method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group trajectory. We found exp...

We present a surprisingly simple approach to high-accuracy calculations of the critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group. The block-spin parameter must be tuned differently for different expon...

We present a surprisingly simple approach to high-accuracy calculations of critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in Monte Carlo renormalization group. The block-spin parameter must be tuned differently for different exponents to...

The Bitcoin scheme is the most popular and talked about alternative payment scheme. One of the most active parts of the Bitcoin ecosystem was the Silk Road marketplace, in which highly illegal substances and services were traded. It was run by a person who called himself Dread Pirate Roberts (DPR), whose bitcoin holdings are estimated to be worth h...

The Bitcoin scheme is a rare example of a large scale global payment system in which all the transactions are publicly accessible (but in an anonymous way). We downloaded the full history of this scheme, and analyzed many statistical properties of its associated transaction graph. In this paper we answer for the first time a variety of interest-ing...

In this paper we generalize and improve the multiscale organization of graphs by introducing a new measure that quantifies the "closeness" between two nodes. The calculation of the measure is linear in the number of edges in the graph and involves just a small number of relaxation sweeps. A similar notion of distance is then calculated and used at...

International audience
In the hidden clique problem, one needs to find the maximum clique in an $n$-vertex graph that has a clique of size $k$ but is otherwise random. An algorithm of Alon, Krivelevich and Sudakov that is based on spectral techniques is known to solve this problem (with high probability over the random choice of input graph) when $...

Linear ordering problems are combinatorial optimization problems which deal with the minimization of different functionals in which the graph vertices are mapped onto (1, 2,…, n). These problems are widely used and studied in many practical and theoretical applications. In this review we summarize a variety of linear-time algorithms for these probl...

The two-dimensional layout optimization problem reinforced by the efficient space utilization demand has a wide spectrum of practical applications. Formulating the problem as a nonlinear minimization problem under planar equality and/or inequality density constraints, we present a linear time multigrid algorithm for solving correction to this probl...

Linear ordering problems are combinatorial optimization problems which deal with the minimization of dierent functionals in which the graph vertices are mapped onto (1,2,...,n). These problems are widely used and studied in many practical and theoretical applications. In this paper we present a variety of linear-time algorithms for these problems i...

Linear ordering problems are combinatorial optimization problems which deal with the minimization of different functionals in which the graph vertices are mapped onto (1, 2, ..., n). These problems are widely used and studied in many practical and theoret-ical applications. In this review we summarize a variety of linear-time algorithms for these p...

Fast multi-level techniques are developed for large-scale problems whose variables may assume only discrete values (such as
spins with only “up” and “down” states), and/or where the relations between variables is probabilistic. Motivation and examples
are taken from statistical mechanics and field theory. Detailed procedures are developed for the f...

The minimum linear arrangement problem is widely used and studied in many practical and theoretical applications. In this paper we present a linear-time algorithm for the problem inspired by the algebraic multigrid approach which is based on weighted edge contraction rather than simple contraction. Our results turned out to be better than every kno...

In this paper we introduce a direct motivation for solving the minimum 2-sum problem, for which we present a linear-time algorithm inspired by the Algebraic Multigrid approach which is based on weighted edge contraction. Our results turned out to be better than previous results, while the short running time of the algorithm enabled experiments with...

Following Brandt and Ron's suggestion of inverting the renormalization group transformation used in Monte Carlo renormalization, it is shown that efficient computer simulations of the fixed point of the transformation can be carried out on very large systems without critical slowing down. We illustrate the new method with calculations of critical e...

The Graph partitioning problem is widely used and studied in many practical and theoretical applications. The problem concerns the partitioning of the nodes of a graph into a given number of disjoint subsets, while minimizing the number of inter-edges, edges that connect one set to the other. Furthermore, the sets must be of roughly equal size. In...

We introduce a computationally stable inverse Monte Carlo renormalization group transformation method that provides a number of advantages for the calculation of critical properties. We are able to simulate the fixed point of a renormalization group for arbitrarily large lattices without critical slowing down. The log-log scaling plots obtained wit...

An optimization problem is the task of minimizing (or maximizing — for definiteness we discuss minimization) a certain real-valued “objective functional” (or “cost” , or “energy” , or “performance index”, etc.) E(x), possibly under a set of equality and/or inequality constraints, where x = (x
1, …, x
n
) is a vector (often the discretization of one...

We introduce a Monte Carlo approach to the calculation of more distant renormalized interactions with higher accuracy than is possible with previous methods. We have applied our method to study the effects of multispin interactions, which turn out to be far more important than commonly assumed. Even though the individual multispin interactions usua...

We develop a method for calculating renormalized Hamiltonians based on the Brandt-Ron representation of renormalization-group transformations. Our approach allows us to make a stable calculation for larger sets of renormalized coupling constants than either the Swendsen or the Gupta-Cordery methods, thus reducing the effects of truncation in renorm...

New renormalization-group algorithms are developed with adaptive representations of the renormalized system which automatically express only significant interactions. As the amount of statistics grows, more interactions enter, thereby systematically reducing the truncation error. This allows statistically optimal calculation of thermodynamic limits...

Beyond eliminating the critical slowing down, multigrid algorithms can also eliminate the need to produce many independent fine-grid configurations for averaging out their statistical deviations, by averaging over the many samples produced in coarse grids during the multigrid cycle. Thermodynamic limits can be calculated to accuracy in justO(-2) co...

We have developed a novel simulation method that combines a multigrid technique with a stochastic blocking procedure. Our algorithm eliminates critical slowing down completely, as demonstrated by simulations of the two-dimensional Ising model at criticality.

A design for a hardware interface that implements CSP-like communication primitives is presented. The design is based on a bus scheme that allows processes to eavesdrop on messages not directly addressed to them. A temporal logic specification is given for the network and an outline of a verification proof is sketched.

## Projects

Projects (3)

Fast and scalable multilevel algorithms for combinatorial optimization on graphs and hypergraphs that are inspired by multiscale and multigrid methods.