Jaime San Martín – författare
Dynamics and Randomness
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High Performance Computing
11th Latin American High Performance Computing Conference, CARLA 2024, Santiago de Chile, Chile, September 30 – October 4, 2024, Revised Selected Papers
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This book constitutes the refereed revised selected papers of the 11th Latin American Conference on High Performance Computing, CARLA 2024, held in Santiago de Chile, Chile, during September 30–October 4, 2024.The 21 full papers included in this book were carefully reviewed and selected from 42 submissions. They were organized in topical sections as follows: High Performance Computing Track; Artificial Intelligence at HPC Scale Track; High Performance Computing Applications Track.
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From Classical to Modern Probability
CIMPA Summer School 2001
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Inverse M-Matrices and Ultrametric Matrices
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The study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains. The main focus of this monograph is the so-called inverse M-matrix problem, which asks for a characterization of nonnegative matrices whose inverses are M-matrices. We present an answer in terms of discrete potential theory based on the Choquet-Deny Theorem. A distinguished subclass of inverse M-matrices is ultrametric matrices, which are important in applications such as taxonomy. Ultrametricity is revealed to be a relevant concept in linear algebra and discrete potential theory because of its relation with trees in graph theory and mean expected value matrices in probability theory. Remarkable properties of Hadamard functions and products for the class of inverse M-matrices are developed and probabilistic insights are provided throughout the monograph.
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Main concepts of quasi-stationary distributions (QSDs) for killed processes are the focus of the present volume. For diffusions, the killing is at the boundary and for dynamical systems there is a trap. The authors present the QSDs as the ones that allow describing the long-term behavior conditioned to not being killed. Studies in this research area started with Kolmogorov and Yaglom and in the last few decades have received a great deal of attention. The authors provide the exponential distribution property of the killing time for QSDs, present the more general result on their existence and study the process of trajectories that survive forever. For birth-and-death chains and diffusions, the existence of a single or a continuum of QSDs is described. They study the convergence to the extremal QSD and give the classification of the survival process. In this monograph, the authors discuss Gibbs QSDs for symbolic systems and absolutely continuous QSDs for repellers.
The findingsdescribed are relevant to researchers in the fields of Markov chains, diffusions, potential theory, dynamical systems, and in areas where extinction is a central concept. The theory is illustrated with numerous examples. The volume uniquely presents the distribution behavior of individuals who survive in a decaying population for a very long time. It also provides the background for applications in mathematical ecology, statistical physics, computer sciences, and economics.
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From Classical to Modern Probability
CIMPA Summer School 2001
549 kr
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549 kr
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1 367 kr
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1 091 kr
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