Author: Si Si
Publisher: World Scientific
ISBN: 9812836888
Category : Mathematics
Languages : en
Pages : 268

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Book Description
This book provides the mathematical definition of white noise and gives its significance. White noise is in fact a typical class of idealized elemental (infinitesimal) random variables. Thus, we are naturally led to have functionals of such elemental random variables that is white noise. This book analyzes those functionals of white noise, particularly the generalized ones called Hida distributions, and highlights some interesting future directions. The main part of the book involves infinite dimensional differential and integral calculus based on the variable which is white noise.The present book can be used as a supplementary book to Lectures on White Noise Functionals published in 2008, with detailed background provided.

Author: Luigi Accardi
Publisher: World Scientific
ISBN: 9814447536
Category : Mathematics
Languages : en
Pages : 280

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Book Description
This volume contains the current research in quantum probability, infinite dimensional analysis and related topics. Contributions by experts in these fields highlight the latest developments and interdisciplinary connections with classical probability, stochastic analysis, white noise analysis, functional analysis and quantum information theory. This diversity shows how research in quantum probability and infinite dimensional analysis is very active and strongly involved in the modern mathematical developments and applications. Tools and techniques presented here will be of great value to researchers.

Author: Rolando Rebolledo
Publisher: World Scientific
ISBN: 9814338737
Category : Mathematics
Languages : en
Pages : 339

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Book Description
This volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.

Author: Habib Ouerdiane
Publisher: World Scientific
ISBN: 9814295434
Category : Mathematics
Languages : en
Pages : 314

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Book Description
On the central extensions of the Heisenberg algebra / L. Accardi & A. Boukas -- Representations of the Lévy-Meixner oscillator algebra and the overcompleteness of the associated sequences of coherent states / A. Barhoumi, H. Ouerdiane & A. Riahi -- Some systems of dualities in white noise analysis / T. Hida -- Quantum white noise derivatives and associated differential equations for white noise operators / U.C. Ji & N. Obata -- The Gibbs conditioning principle for white noise distributions : interacting and non-interacting cases / F. Cipriano, S. Gheryani & H. Ouerdiane -- Markov triplets on CAR algebras / J. Pitrik -- Quantum Fokker-Planck models : limiting case in the Lindblad condition / F. Fagnola & L. Neumann -- Generalized Euler heat equation / A. Barhoumi, H. Ouerdiane & H. Rguigui -- On quantum De Finetti's theorems / V. Crismale & Y.G. Lu -- Kolmogorovian model for EPR-experiment / D. Avis [und weitere] -- Free white noise stochastic equation / L. Accardi, W. Ayed & H. Ouerdiane -- Lévy models robustness and sensitivity / F.E. Benth, G. Di Nunno & A. Khedher -- Quantum heat equation with quantum K-Gross Laplacian : solutions and integral representation / S. Horrigue & H. Ouerdiane -- On Marginal Markov processes of quantum quadratic stochastic processes / F. Mukhamedov -- On the applicability of multiplicative renormalization method for certain power functions / I. Kubo, H.-H. Kuo & S. Namli -- Convolution equation : solution and probabilistic representation / J.L. Da Silva, M. Erraoui & H. Ouerdiane -- From classical to quantum entropy production / F. Fagnola & R. Rebolledo -- Extending the set of quadratic exponential vectors / L. Accardi, A. Dhahri & M. Skeide -- On operator-parameter transforms based on nuclear algebra of entire functions and applications / A. Barhoumi [und weitere] -- Dissipative quantum annealing / D. de Falco, E. Pertoso & D. Tamascelli

Author: Habib Ouerdiane
Publisher: World Scientific
ISBN: 9814465631
Category : Mathematics
Languages : en
Pages : 314

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Book Description
This is the proceedings of the 29th Conference on Quantum Probability and Infinite Dimensional Analysis, which was held in Hammamet, Tunisia.

Author: Andrew Barbour
Publisher: Springer Science & Business Media
ISBN: 1461419654
Category : Mathematics
Languages : en
Pages : 166

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Book Description
In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen. Chen made the first of several seminal contributions to the theory and application of Stein’s method. One of his most important contributions has been to turn Stein’s concentration inequality idea into an effective tool for providing error bounds for the normal approximation in many settings, and in particular for sums of random variables exhibiting only local dependence. This conference attracted a large audience that came to pay homage to Chen and to hear presentations by colleagues who have worked with him in special ways over the past 40+ years. The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.

Author: Gianfausto Dell'Antonio
Publisher: Springer
ISBN: 9462391157
Category : Science
Languages : en
Pages : 389

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Book Description
The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.

Author: Francesca Biagini
Publisher: Springer Science & Business Media
ISBN: 1846287979
Category : Mathematics
Languages : en
Pages : 331

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Book Description
The purpose of this book is to present a comprehensive account of the different definitions of stochastic integration for fBm, and to give applications of the resulting theory. Particular emphasis is placed on studying the relations between the different approaches. Readers are assumed to be familiar with probability theory and stochastic analysis, although the mathematical techniques used in the book are thoroughly exposed and some of the necessary prerequisites, such as classical white noise theory and fractional calculus, are recalled in the appendices. This book will be a valuable reference for graduate students and researchers in mathematics, biology, meteorology, physics, engineering and finance.

Author: Luigi Accardi
Publisher: World Scientific
ISBN: 9814304069
Category : Science
Languages : en
Pages : 512

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Book Description
Classical and quantum conditioning : mathematical and information theoretical aspects / L. Accardi -- Dynamics and potentials / F. Araki -- Kossakowski-Ohya teleportation scheme and its applications / M. Asano, M. Ohya and Y. Tanaka -- Utility and value of information in cognitive science, biology and quantum theory / R.V. Belavkin -- Spectral properties of entanglement witnesses and positive maps / D. Chruściński -- Quantum entanglement and multipartite symmetric states / D. Chruściński -- On a quantum model of brain activities / K.-H. Fichtner [und weitere] -- Some of the recent topics in white noise theory / T. Hida -- Note on generalized white noise functionals / T. Hida -- On estimation of the position distribution of the ideal Bose gas / K.-H. Fichtner, K. Inoue and M. Ohya -- On generalization of quantum mutual entropy by using liftings / S. Iriyama and M. Ohya -- A new approach to stroboscopic tomography of open systems / A. Jamiolkowski -- An introduction to frames and their applications to quantum optics / A. Jamiolkowski -- Memory in a nonlocally damped oscillator / D. Chruściński and J. Jurkowski -- An introduction to quantization of dissipative systems. The damped harmonic oscillator case / J. Jurkowski -- Classical and quantum probability for biologists - introduction / A. Khrennikov -- 2-adic degeneration of the genetic code and energy of binding of codons / A. Yu. Khrennikov and S.V. Kozyrev -- On positive maps; PPT states and entanglement / W.A. Majewski -- Detecting entanglement in spin lattice models / M. Michalski -- How to detect entanglement in quantum systems / M. Michalskii -- Tunneling study on high-T[symbol] superconductors / M. Minematsu, S. Kawashima and N. Miyakawa -- Quantum dynamics of superconducting qubit readout with a driven nonlinear Josephson oscillator / H. Nakano -- Roles of asymptotic condition and S-matrix as micro-macro duality in QFT / I. Ojima -- Gaussian Markov triplets / D. Petz and J. Pitrik -- pre-mRNA introns as a model for cryptographic algorithm : theory and experiments / M. Regoli -- Duality arising from multiple Markov Gaussian processes / Si Si and W.W. Htay -- Novel computational approaches to drug discovery / J. Skolnick and M. Brylinski -- Feynman type formulae for quantum evolution and diffusion on manifolds and graphs / O.G. Smolyanov -- Poisson noise and the dynamics of infinite particle systems / L. Streit -- Replica-exchange molecular dynamics simulations of Amyloid precursor protein dimer in membrane / N. Miyashita and Y. Sugita -- Comparison of square contingency tables using measure of departure from marginal homogeneity / K. Tahata [und weitere] -- On the statics for micro-array data analysis / T. Urushibara [und weitere] -- Functional mechanics and time irreversibility problem / I.V. Volovich -- Regulatory networks : inferring functional relationships through co-expression / D. Wanke [und weitere] -- On entropies of quantum dynamical systems / N. Watanabe -- Significant improvement of sequence alignment can be done by considering transition probability between two consecutive pairs of residues / T. Ham, K. Sato and M. Ohya -- A computational approach to explore protein translocation through Type III secretion apparatus / T. Rathinavelan and W. Im -- Carbon nanotubes for building blocks of quantum computing devices / K. Ishibashi [und weitere] -- In silico analysis for the study of botulinum toxin structure / T. Suzuki and S. Miyazaki -- Gene discovery methods from large-scale gene expression data / A. Shimizu and K. Yano

Author: Luigi Accardi
Publisher: World Scientific
ISBN: 9814460605
Category : Science
Languages : en
Pages : 503

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Book Description
The purpose of this proceedings volume is to return to the starting point of bio-informatics and quantum information, fields that are growing rapidly at present, and to seriously attempt mutual interaction between the two, with a view to enumerating and solving the many fundamental problems they entail. For such a purpose, we look for interdisciplinary bridges in mathematics, physics, information and life sciences, in particular, research for new paradigm for information science and life science on the basis of quantum theory.