Nondeterministic graph property testing

A property of finite graphs is called nondeterministically testable if it has a "certificate" such that once the certificate is specified, its correctness can be verified by random local testing. In this paper we study certificates that consist of one or more unary and/or binary relations on the nodes, in the case of dense graphs. Using the theory of graph limits, we prove that nondeterministically testable properties are also deterministically testable.Comment: Version 2: 11 pages; we allow orientation in the certificate, describe new application

Effective Monte Carlo simulation on System-V massively parallel associative string processing architecture

We show that the latest version of massively parallel processing associative string processing architecture (System-V) is applicable for fast Monte Carlo simulation if an effective on-processor random number generator is implemented. Our lagged Fibonacci generator can produce $10^8$ random numbers on a processor string of 12K PE-s. The time dependent Monte Carlo algorithm of the one-dimensional non-equilibrium kinetic Ising model performs 80 faster than the corresponding serial algorithm on a 300 MHz UltraSparc.Comment: 8 pages, 9 color ps figures embedde

The two largest distances in finite planar sets

AbstractWe determine all homogenous linear inequalities satisfied by the numbers of occurrences of the two largest distances among n points in the plane

New results and perspectives on R_{AA} measurements below 20 GeV CM-energy at fixed target machines

Transverse momentum spectra of pi^{+/-} at midrapidity are measured at high p_T in p+p and p+Pb collisions at 158 GeV/nucleon beam energy by the NA49 experiment. This study is complementary to our previous results on the same spectra from Pb+Pb collisions. The nuclear modification factors R_{A+A/p+p}, R_{p+A/p+p} and R_{A+A/p+A} as a function of p_T are extracted and compared to RHIC measurements, thus providing insight into the energy dependence of nuclear modification. The modification factor R_{A+A/p+A} proved to be consistent with our previous results on the central to peripheral modification factor R_{CP}. The limitation of our current p_T range is discussed and planned future upgrades are outlined. Some aspects of the FAIR-CBM experiment are also presented as a natural future continuation of the measurements at very high p_T.Comment: Proceedings of Quark Matter 200

On the distribution of distances in finite sets in the plane

AbstractLet nk denote the number of times the kth largest distance occurs among a set S of n points. We show that if S is the set of vertices of a convex polygone in the euclidean plane, then n1+2n2⩽3n and n2⩽n+n1. Together with the well-known inequality n1⩽n and the trivial inequalities n1⩾0 and n2⩾0, all linear inequalities which are valid for n, n1 and n2 are consequences of these. Similar results are obtained for the hyperbolic plane

Convergent Sequences of Dense Graphs I: Subgraph Frequencies, Metric Properties and Testing

We consider sequences of graphs and define various notions of convergence related to these sequences: ``left convergence'' defined in terms of the densities of homomorphisms from small graphs into the graphs of the sequence, and ``right convergence'' defined in terms of the densities of homomorphisms from the graphs of the sequence into small graphs; and convergence in a suitably defined metric. In Part I of this series, we show that left convergence is equivalent to convergence in metric, both for simple graphs, and for graphs with nodeweights and edgeweights. One of the main steps here is the introduction of a cut-distance comparing graphs, not necessarily of the same size. We also show how these notions of convergence provide natural formulations of Szemeredi partitions, sampling and testing of large graphs.Comment: 57 pages. See also http://research.microsoft.com/~borgs/. This version differs from an earlier version from May 2006 in the organization of the sections, but is otherwise almost identica

A model for Intelligent Random Access Memory architecture (IRAM): cellular automata algorithms on the Associative String Processing machine (ASTRA)

In the near future, the computer performance will be completely determined by how long it takes to access memory. There are bottle-necks in memory latency and memory-to processor interface bandwidth. The IRAM initiative could be the answer by putting Processor-In-Memory (PIM). Starting from the massively parallel processing concept, one reached a similar conclusion. The MPPC (Massively Parallel Processing Collaboration) project and the 8K processor ASTRA machine (Associative String Test bench for Research \& Applications) developed at CERN \cite{kuala} can be regarded as a forerunner of the IRAM concept. The computing power of the ASTRA machine, regarded as an IRAM with 64 one-bit processors on a 64$\times$64 bit-matrix memory chip machine, has been demonstrated by running statistical physics algorithms: one-dimensional stochastic cellular automata, as a simple model for dynamical phase transitions. As a relevant result for physics, the damage spreading of this model has been investigated