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Sweep coverage of discrete time multi-robot networks with general topologies

Chao Zhai (2014)

Kybernetika

This paper addresses a sweep coverage problem of multi-robot networks with general topologies. To deal with environmental uncertainties, we present discrete time sweep coverage algorithms to guarantee the complete coverage of the given region by sweeping in parallel with workload partition. Moreover, the error between actual coverage time and the optimal time is estimated with the aid of continuous time results. Finally, numerical simulation is conducted to verify the theoretical results.

Symbol Declarations in Mathematical Writing

Wolska, Magdalena, Grigore, Mihai (2010)

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

We present three corpus-based studies on symbol declaration in mathematical writing. We focus on simple object denoting symbols which may be part of larger expressions. We look into whether the symbols are explicitly introduced into the discourse and whether the information on once interpreted symbols can be used to interpret structurally related symbols. Our goal is to support fine-grained semantic interpretation of simple and complex mathematical expressions. The results of our analysis empirically...

Symbolic discrepancy and self-similar dynamics

Boris Adamczewski (2004)

Annales de l'Institut Fourier

We consider subshifts arising from primitive substitutions, which are known to be uniquely ergodic dynamical systems. In order to precise this point, we introduce a symbolic notion of discrepancy. We show how the distribution of such a subshift is in part ruled by the spectrum of the incidence matrices associated with the underlying substitution. We also give some applications of these results in connection with the spectral study of substitutive dynamical systems.

Symmetric flows and broadcasting in hypercubes

Jean-Claude Bermond, A. Bonnecaze, T. Kodate, Stéphane Pérennes, Patrick Solé (1999)

Annales de l'institut Fourier

In this paper, we propose a method which enables to construct almost optimal broadcast schemes on an n -dimensional hypercube in the circuit switched, Δ -port model. In this model, an initiator must inform all the nodes of the network in a sequence of rounds. During a round, vertices communicate along arc-disjoint dipaths. Our construction is based on particular sequences of nested binary codes having the property that each code can inform the next one in a single round. This last property is insured...

Synthesis of finite state machines for CPLDs

Robert Czerwiński, Dariusz Kania (2009)

International Journal of Applied Mathematics and Computer Science

The paper presents a new two-step approach to FSM synthesis for PAL-based CPLDs that strives to find an optimum fit of an FSM to the structure of the CPLD. The first step, the original state assignment method, includes techniques of twolevel minimization and aims at area minimization. The second step, PAL-oriented multi-level optimization, is a search for implicants that can be shared by several functions. It is based on the graph of outputs. Results of experiments prove that the presented approach...

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