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Time Dependent Phase Space Filters by Avy Soffer,Chris Stucchio,Minh-Binh Tran Pdf
This book introduces an interesting and alternative way to design absorbing boundary conditions (ABCs) for quantum wave equations, basically the nonlinear Schrödinger equation. The focus of this book is the application of the phase space filter approach to derive accurate radiation conditions for Schrödinger equations. Researchers who are interested in partial differential equations and mathematical physics might find this book appealing.
Frontiers of Applied and Computational Mathematics by Denis L. Blackmore,Amithaba Bose,Peter G. Petropoulos Pdf
This volume contains a selection of papers presented at the 2008 Conference on Frontiers of Applied and Computational Mathematics (FACM'08), held at the New Jersey Institute of Technology (NJIT), May 19?21, 2008. The papers reflect the conference themes of mathematical biology, mathematical fluid dynamics, applied statistics and biostatistics, and waves and electromagnetics. Some of the world's most distinguished experts in the conference focus areas provide a unique and timely perspective on leading-edge research, research trends, and important open problems in several fields, making it a ?must read? for active mathematical scientists. Included are major new contributions by a distinguished trio of plenary speakers: Frank Hoppensteadt contributes a thought-provoking paper on the evolving relationship between applied mathematics and the computer; Pranab Sen explores exciting new trends in computational biology and informatics; and Jean-Marc Vanden-Broeck describes his recent research on 3D free surface flows. There are also many innovative contributions by a prestigious group of invited mini-symposium speakers, making this an indispensable collection for professionals and graduate students in the mathematical sciences and related fields.Finally, the 75th birthday dedication to Daljit S Ahluwalia ? for his many contributions to building a world-class mathematical sciences department at NJIT ? adds to making this a one-of-a-kind volume.
Applications of State Space Models in Finance by Sascha Mergner Pdf
State space models play a key role in the estimation of time-varying sensitivities in financial markets. The objective of this book is to analyze the relative merits of modern time series techniques, such as Markov regime switching and the Kalman filter, to model structural changes in the context of widely used concepts in finance. The presented material will be useful for financial economists and practitioners who are interested in taking time-variation in the relationship between financial assets and key economic factors explicitly into account. The empirical part illustrates the application of the various methods under consideration. As a distinctive feature, it includes a comprehensive analysis of the ability of time-varying coefficient models to estimate and predict the conditional nature of systematic risks for European industry portfolios.
Inverse Problems in Atmospheric Constituent Transport by I. G. Enting Pdf
This book describes mathematical techniques for interpreting measurements of greenhouse gases in order to learn about their sources and sinks. It is aimed at researchers and graduate students embarking upon studies in this area. Established researchers will also find its extensive referencing invaluable.
Modeling Phase Transitions in the Brain by D. Alistair Steyn-Ross,Moira Steyn-Ross Pdf
Foreword by Walter J. Freeman. The induction of unconsciousness using anesthetic agents demonstrates that the cerebral cortex can operate in two very different behavioral modes: alert and responsive vs. unaware and quiescent. But the states of wakefulness and sleep are not single-neuron properties---they emerge as bulk properties of cooperating populations of neurons, with the switchover between states being similar to the physical change of phase observed when water freezes or ice melts. Some brain-state transitions, such as sleep cycling, anesthetic induction, epileptic seizure, are obvious and detected readily with a few EEG electrodes; others, such as the emergence of gamma rhythms during cognition, or the ultra-slow BOLD rhythms of relaxed free-association, are much more subtle. The unifying theme of this book is the notion that all of these bulk changes in brain behavior can be treated as phase transitions between distinct brain states. Modeling Phase Transitions in the Brain contains chapter contributions from leading researchers who apply state-space methods, network models, and biophysically-motivated continuum approaches to investigate a range of neuroscientifically relevant problems that include analysis of nonstationary EEG time-series; network topologies that limit epileptic spreading; saddle--node bifurcations for anesthesia, sleep-cycling, and the wake--sleep switch; prediction of dynamical and noise-induced spatiotemporal instabilities underlying BOLD, alpha-, and gamma-band Hopf oscillations, gap-junction-moderated Turing structures, and Hopf-Turing interactions leading to cortical waves.
Neural Networks and the Financial Markets by Jimmy Shadbolt Pdf
This volume looks at financial prediction from a broad range of perspectives. It covers: - the economic arguments - the practicalities of the markets - how predictions are used - how predictions are made - how predictions are turned into something usable (asset locations) It combines a discussion of standard theory with state-of-the-art material on a wide range of information processing techniques as applied to cutting-edge financial problems. All the techniques are demonstrated with real examples using actual market data, and show that it is possible to extract information from very noisy, sparse data sets. Aimed primarily at researchers in financial prediction, time series analysis and information processing, this book will also be of interest to quantitative fund managers and other professionals involved in financial prediction.
Data Modeling for the Sciences by Steve Pressé,Ioannis Sgouralis Pdf
With the increasing prevalence of big data and sparse data, and rapidly growing data-centric approaches to scientific research, students must develop effective data analysis skills at an early stage of their academic careers. This detailed guide to data modeling in the sciences is ideal for students and researchers keen to develop their understanding of probabilistic data modeling beyond the basics of p-values and fitting residuals. The textbook begins with basic probabilistic concepts, models of dynamical systems and likelihoods are then presented to build the foundation for Bayesian inference, Monte Carlo samplers and filtering. Modeling paradigms are then seamlessly developed, including mixture models, regression models, hidden Markov models, state-space models and Kalman filtering, continuous time processes and uniformization. The text is self-contained and includes practical examples and numerous exercises. This would be an excellent resource for courses on data analysis within the natural sciences, or as a reference text for self-study.
Bayesian Inference of State Space Models by Kostas Triantafyllopoulos Pdf
Bayesian Inference of State Space Models: Kalman Filtering and Beyond offers a comprehensive introduction to Bayesian estimation and forecasting for state space models. The celebrated Kalman filter, with its numerous extensions, takes centre stage in the book. Univariate and multivariate models, linear Gaussian, non-linear and non-Gaussian models are discussed with applications to signal processing, environmetrics, economics and systems engineering. Over the past years there has been a growing literature on Bayesian inference of state space models, focusing on multivariate models as well as on non-linear and non-Gaussian models. The availability of time series data in many fields of science and industry on the one hand, and the development of low-cost computational capabilities on the other, have resulted in a wealth of statistical methods aimed at parameter estimation and forecasting. This book brings together many of these methods, presenting an accessible and comprehensive introduction to state space models. A number of data sets from different disciplines are used to illustrate the methods and show how they are applied in practice. The R package BTSA, created for the book, includes many of the algorithms and examples presented. The book is essentially self-contained and includes a chapter summarising the prerequisites in undergraduate linear algebra, probability and statistics. An up-to-date and complete account of state space methods, illustrated by real-life data sets and R code, this textbook will appeal to a wide range of students and scientists, notably in the disciplines of statistics, systems engineering, signal processing, data science, finance and econometrics. With numerous exercises in each chapter, and prerequisite knowledge conveniently recalled, it is suitable for upper undergraduate and graduate courses.
System Identification (SYSID '03) by Paul Van Den Hof,Bo Wahlberg,Siep Weiland Pdf
The scope of the symposium covers all major aspects of system identification, experimental modelling, signal processing and adaptive control, ranging from theoretical, methodological and scientific developments to a large variety of (engineering) application areas. It is the intention of the organizers to promote SYSID 2003 as a meeting place where scientists and engineers from several research communities can meet to discuss issues related to these areas. Relevant topics for the symposium program include: Identification of linear and multivariable systems, identification of nonlinear systems, including neural networks, identification of hybrid and distributed systems, Identification for control, experimental modelling in process control, vibration and modal analysis, model validation, monitoring and fault detection, signal processing and communication, parameter estimation and inverse modelling, statistical analysis and uncertainty bounding, adaptive control and data-based controller tuning, learning, data mining and Bayesian approaches, sequential Monte Carlo methods, including particle filtering, applications in process control systems, motion control systems, robotics, aerospace systems, bioengineering and medical systems, physical measurement systems, automotive systems, econometrics, transportation and communication systems *Provides the latest research on System Identification *Contains contributions written by experts in the field *Part of the IFAC Proceedings Series which provides a comprehensive overview of the major topics in control engineering.
Progress in Advanced Computing and Intelligent Engineering by Chhabi Rani Panigrahi,Arun K. Pujari,Sudip Misra,Bibudhendu Pati,Kuan-Ching Li Pdf
This book features high-quality research papers presented at the International Conference on Advanced Computing and Intelligent Engineering (ICACIE 2017). It includes sections describing technical advances in the fields of advanced computing and intelligent engineering, which are based on the presented articles. Intended for postgraduate students and researchers working in the discipline of computer science and engineering, the proceedings also appeal to researchers in the domain of electronics as it covers hardware technologies and future communication technologies.
Handbook of Developmental Research Methods by Brett Laursen,Todd D. Little,Noel A. Card Pdf
Appropriate for use in developmental research methods or analysis of change courses, this is the first methods handbook specifically designed to meet the needs of those studying development. Leading developmental methodologists present cutting-edge analytic tools and describe how and when to use them, in accessible, nontechnical language. They also provide valuable guidance for strengthening developmental research with designs that anticipate potential sources of bias. Throughout the chapters, research examples demonstrate the procedures in action and give readers a better understanding of how to match research questions to developmental methods. The companion website (www.guilford.com/laursen-materials) supplies data and program syntax files for many of the chapter examples.
Mathematical Modeling of Random and Deterministic Phenomena by Solym Mawaki Manou-Abi,Sophie Dabo-Niang,Jean-Jacques Salone Pdf
This book highlights mathematical research interests that appear in real life, such as the study and modeling of random and deterministic phenomena. As such, it provides current research in mathematics, with applications in biological and environmental sciences, ecology, epidemiology and social perspectives. The chapters can be read independently of each other, with dedicated references specific to each chapter. The book is organized in two main parts. The first is devoted to some advanced mathematical problems regarding epidemic models; predictions of biomass; space-time modeling of extreme rainfall; modeling with the piecewise deterministic Markov process; optimal control problems; evolution equations in a periodic environment; and the analysis of the heat equation. The second is devoted to a modelization with interdisciplinarity in ecological, socio-economic, epistemological, demographic and social problems. Mathematical Modeling of Random and Deterministic Phenomena is aimed at expert readers, young researchers, plus graduate and advanced undergraduate students who are interested in probability, statistics, modeling and mathematical analysis.
Quantum Electrodynamics and Quantum Optics by A. O. Barut Pdf
The borderline of quantum electrodynamics and quantum optics offer spectacular results and problems concerning the foundations of radiation theory. Perhaps the major new viewpoint that has emerged from recent investigations is that one can now work inside a time-dependent quantum process, whereas up to now all elementary quantum processes were either stationary, or one worked with asymptotic in-and out-states, i.e. an S-matrix approach. In the-rirst part of this volume, the Quantum Electrodynamics, the present status of the main approaches to this most accurate of all physical theories are discussed: the Hamiltonian approach, the Green's function approach with particular emphasis to bound state problems, and the newer, nonperturbative approach. The latest numerical results on radiative corrections, Lamb shifts and anomalous magnetic moments are reviewed with new results for high Z atoms. Also discussed are different theoretical interpretations of the radiative phenomena as due to quantized field vacuum fluctuations or due to self energy. A small group of contributions are devoted to the physics and mathematical description of decaying or unstable states in quantum theory. This remarkable phenomenon of quantum theory still needs complete clarification, it is a time-dependent phenomenon, which can be described also by asymptotic S-matrix methods, but with complex energies.
Gabor Analysis and Algorithms by Hans G. Feichtinger,Thomas Strohmer Pdf
In his paper Theory of Communication [Gab46], D. Gabor proposed the use of a family of functions obtained from one Gaussian by time-and frequency shifts. Each of these is well concentrated in time and frequency; together they are meant to constitute a complete collection of building blocks into which more complicated time-depending functions can be decomposed. The application to communication proposed by Gabor was to send the coeffi cients of the decomposition into this family of a signal, rather than the signal itself. This remained a proposal-as far as I know there were no seri ous attempts to implement it for communication purposes in practice, and in fact, at the critical time-frequency density proposed originally, there is a mathematical obstruction; as was understood later, the family of shifted and modulated Gaussians spans the space of square integrable functions [BBGK71, Per71] (it even has one function to spare [BGZ75] . . . ) but it does not constitute what we now call a frame, leading to numerical insta bilities. The Balian-Low theorem (about which the reader can find more in some of the contributions in this book) and its extensions showed that a similar mishap occurs if the Gaussian is replaced by any other function that is "reasonably" smooth and localized. One is thus led naturally to considering a higher time-frequency density.