“…In this paper, starting from the recently introduced kinetic multi-agent model with competence by the first two authors, we propose to derive reduced-order models through the notion of social closure in the mean-field approximation that has its roots in the classical hydrodynamic closure of kinetic theory. …”
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“…In this respect, the reliability of the presented method mainly depends on the quality of the force field used in the MD simulations and on the ability to discriminate in a physically coherent way between semi-classical and quantum degrees of freedom. …”
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“…We show that the collective excitations can be described in terms of classical fields, and develop for these a Hamiltonian formalism. …”
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“…The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. …”
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“…An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. …”
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“…High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. …”
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“…Upon publication, Science called it “a pedagogic masterpiece,” and it has since become a classic, considered essential reading for every serious student and researcher in the field of relativity. …”
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“…It explores up-and-coming theories, techniques, and tools for the application of rever…”
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“…The first edition, published in 1973, has become a classic reference in the field. Now with the second edition, readers will find information on key new topics such as neural networks and statistical pattern recognition, the theory of machine learning, and the theory of invariances. …”
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“…Many approaches have been proposed to deal with this data structure, but none of them in the field of pathway analysis. Pathway analyses have acquired great relevance for helping the interpretation of gene expression data. …”
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“…We also show that the survival of genetically similar individuals can be linked to life-long differences in behaviour according to classical life-history theory predictions.…”
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“…In this paper, we focus on the structure and characteristics of convolutional neural networks through the study of deep learning theory, discuss three classical convolutional neural network models, such as AlexNet, VGG, and GoogLeNet, and propose a convolutional neural network model applicable to cross-media teaching in college English classroom and carry out experimental validation, and the results show that the proposed neural network model is based on output-driven hypothesis. …”
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“…Konrad Schöbel aims to lay the foundations for a consequent algebraic geometric treatment of variable separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modern moduli space theory, Stasheff polytopes and operads. …”
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“…Satzer, The Mathematical Association of America, March, 2009) “The second edition of this text infuses new mathematical substance and relevance into an already modern classic … and is sure to excite future generations of readers. … This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. … it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” …”
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“…Grammatical inference is a field that lies at the intersection of multiple disciplines, with contributions from computational linguistics, pattern recognition, machine learning, computational biology, formal learning theory and many others. …”
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“…Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields. Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. …”
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“…It probes the relation between cohomology of arithmetic groups and automorphic forms and their L-functions, and spans the range from classical Bianchi groups to the theory of Shimura varieties. …”
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“…From the reviews of the first edition: "...Masterful blending of observation and theory; lucid exposition... (D. E. Hogg, CHOICE, Vol. 44 (10), June, 2007)" "Through the richness of the color illustrations and through the deep insight of the content, the book will most certainly lead the reader to the forefront of astronomical research in this very interesting and fascinating domain of astronomy. … will not only be highly appreciated by undergraduate students in astronomy but also by graduate students and researchers involved in the field who will certainly appreciate its comprehensive coverage. …”
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