Recently, Laplacian matrices of graphs are studied as density matrices in quantum mechanics. We continue this study and give conditions for separability of generalized Laplacian matrices of weighted graphs with unit trace. In particular, we show that the Peres-Horodecki positive partial transpose separability condition is necessary and sufficient for separability in C2 ⊗ C. In addition, we pres...

Yuliy V. Bludov,1,* Daria A. Smirnova,2 Yuri S. Kivshar,2 N. M. R. Peres,1 and Mikhail I. Vasilevskiy1 1Centro de Fı́sica and Departamento de Fı́sica, Universidade do Minho, Campus de Gualtar, Braga 4710-057, Portugal 2Nonlinear Physics Center, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia (Received 5 August 2013; revised manuscript recei...

Polarizing Mexico: The Impact of Liberalization Strategy by Enrique DUSSELPETERS, Boulder, Colorado: Lynne Rienner Publishers, 2000, 249 pp., ISBN 1-55587-861-X (bound). Growth, Employment and Equity: The Impact of the Economic Reforms in Latin America and the Caribbean by Barbara STALLINGS and Wilson PERES, Washington, D.C.: Brookings Institution Press and United Nations Economic Commission fo...

Preface These notes provide an elementary and self-contained introduction to branching random walks. Chapter 1 gives a brief overview of Galton–Watson trees, whereas Chapter 2 presents the classical law of large numbers for branching random walks. These two short chapters are not exactly indispensable, but they introduce the idea of using size-biased trees, thus giving motivations and an avant-...

Human modification of ecosystems is threatening biodiversity on a global scale (Whitmore 1997; W. F.Laurance 1999; Nepstad et aL 1999b; Chapman and Peres 2001). This is illustrated by the fact that an estimated 65.1 million hectares of forest were destroyed between 1990 and 1995 (FAa 1999). Many other areas are affected by forest degradation that involves logging, fire, and hunting; as a result...

Shi-Jian Gu, N. M. R. Peres, J. M. P. Carmelo Department of Physics and Institute of Theoretical Physics, The Chinese University of Hong Kong, Hong Kong, China Zhejiang Institute of Modern Phys, Zhejiang University, Hangzhou, 310027, China Center of Physics and Physics Department of the University of Minho, School of Sciences, Campus of Gualtar, P-4710-057 Braga, Portugal 4 GCEP-Center of Physi...

The x log x condition is a fundamental criterion for the rate of growth of a general branching process, being equivalent to non-degeneracy of the limiting random variable. In this paper we adopt the ideas from Lyons, Pemantle and Peres (1995) to present a new proof of this well-known theorem. The idea is to compare the ordinary branching measure on the space of population trees with another mea...

We prove a comparison theorem for the spatial mass of the solutions of two exterior parabolic problems, one of them having symmetrized geometry, using approximation of the Schwarz symmetrization by polarizations, as it was introduced inBrock andSolynin (TransAmMathSoc 352(4):1759–1796, 2000). This comparison provides an alternative proof, based on PDEs, of the isoperimetric inequality for the W...