Partial differential equations (PDEs) are the main tool to describe spatially and temporally extended systems in nature. PDEs usually come with parameters, and the study of the parameter dependence of their solutions is an important task. Letting one parameter vary typically yields a branch of solutions, and at special parameter values, new branches may bifurcate. Numerical Continuation and Bifurcation in Nonlinear PDEs: Presents hands-on approach to numerical continuation and bifurcation for nonlinear PDEs, in 1D, 2D and 3D. ,Provides a concise but sound review of analytical background and numerical methods. Explains the use of the free MATLAB package pde2path via a large variety of examples with ready to use code. Contains demo codes that can be easily adapted to the reader's given problem. This book will be of interest to applied mathematicians and scientists from physics, chemistry, biology, and economics interested in the numerical solution of nonlinear PDEs, particularly the parameter dependence of solutions. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.

Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical.

This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.

This book focuses on a development for assessing mental changes using eye pupil reactions, namely extracting emotional change from the response to evaluate the viewer's interest in visual information. The pupil of the eye reacts to both brightness and emotional state, including interest, enjoyment, and mental workload. Because pupillary change is a biological signal, various artifacts influence measurements of eye images. Technical procedures are required to extract mental activities from pupillary changes, and they are summarized here step by step, although some procedures contain earlier techniques such as analog video processing. This study examines the possibility of estimating the viewer's interest and enjoyment of viewing movies by measuring the dynamic pupillary changes, blinking, and subjective interest responses. In evaluation of pupil size, there was a significant difference in pupil size between the higher and the lower shot for the degree of subject interest response in each kind of movies. The first part of the book shows a pupil reaction model for brightness changes to extract mental activities. Pupil reactions were observed for various visual stimuli in brightness changes. With regard to the characteristics of pupillary changes, a model with a three-layer neural network was developed and the performance was evaluated. Characteristics of pupil reactions during model development are summarized here. The second part examines the possibility of estimating the viewer's interest and enjoyment of television programs by measuring dynamic pupillary changes, blinking, and subjective interest responses. The final part describes a development of estimation model of pupil size for blink artifact. The model development was able to estimate pupillary changes and pupil size while the viewer was blinking and was applied to pupillary changes in viewing television programs.

Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.

This book introduces the engineering application of the discrete element method (DEM), especially the simulation analysis of the typical equipment (scraper conveyor, coal silos, subsoiler) in the coal and agricultural machinery. In this book, the DEM is applied to build rigid and loose coupling model, and the kinematic effect of the bulk materials, the mechanical effect of the interaction between the bulk materials, and the mechanical equipment in the operation process of the relevant equipment are studied. On this basis, the optimization design strategy of the relevant structure is proposed. This book effectively promotes the application of DEM in engineering, analyzes the operation state, failure mechanism, and operation effect of related equipment in operation, and provides theoretical basis for the optimal design of equipment. The book is intended for undergraduate and graduate students who are interested in mechanical engineering, researchers investigating coal and agricultural machinery, and engineers working on designing related equipments.

This volume is part of collection of contributions devoted to analytical and experimental techniques of dynamical systems, presented at the 15th International Conference "Dynamical Systems: Theory and Applications", held in Lodz, Poland on December 2-5, 2019. The wide selection of material has been divided into three volumes, each focusing on a different field of applications of dynamical systems. The broadly outlined focus of both the conference and these books includes bifurcations and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, optimization problems in applied sciences, stability of dynamical systems, experimental and industrial studies, vibrations of lumped and continuous systems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.

Actuaries must pass exams, but more than that: they must put knowledge into practice. This coherent book supports the Society of Actuaries' short-term actuarial mathematics syllabus while emphasizing the concepts and practical application of nonlife actuarial models. A class-tested textbook for undergraduate courses in actuarial science, it is also ideal for those approaching their professional exams. Key topics covered include loss modelling, risk and ruin theory, credibility theory and applications, and empirical implementation of loss models. Revised and updated to reflect curriculum changes, this second edition includes two brand new chapters on loss reserving and ratemaking. R replaces Excel as the computation tool used throughout - the featured R code is available on the book's webpage, as are lecture slides. Numerous examples and exercises are provided, with many questions adapted from past Society of Actuaries exams.

This book includes selected contributions on applied mathematics, numerical analysis, numerical simulation and scientific computing related to fluid mechanics problems, presented at the FEF-"Finite Element for Flows" conference, held in Rome in spring 2017. Written by leading international experts and covering state-of-the-art topics in numerical simulation for flows, it provides fascinating insights into and perspectives on current and future methodological and numerical developments in computational science. As such, the book is a valuable resource for researchers, as well as Masters and Ph.D students.

The unification of symbolist and connectionist models is a major trend in AI. The key is to keep the symbolic semantics unchanged. Unfortunately, present embedding approaches cannot. The approach in this book makes the unification possible. It is indeed a new and promising approach in AI. -Bo Zhang, Director of AI Institute, Tsinghua It is indeed wonderful to see the reviving of the important theme Nural Symbolic Model. Given the popularity and prevalence of deep learning, symbolic processing is often neglected or downplayed. This book confronts this old issue head on, with a historical look, incorporating recent advances and new perspectives, thus leading to promising new methods and approaches. -Ron Sun (RPI), on Governing Board of Cognitive Science Society Both for language and humor, approaches like those described in this book are the way to snickerdoodle wombats. -Christian F. Hempelmann (Texas A&M-Commerce) on Executive Board of International Society for Humor Studies

This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

This volume brings together a group of philosophically oriented logicians and logic-minded philosophers, mainly from Asia, to address a variety of logical and philosophical topics, such as modal logic and related directions (e.g. temporal logic, epistemic logic, deontic logic, logic of conditionals, and modal proof theory), theory of truth, paradoxes, intentionality, and social networks. New approaches are also proposed, such as extended modal logic with planarity of graphs, extended branching time temporal logic with conditional operators, and a relational treatment of language and logical systems, to name but a few.Given the variety of topics and issues discussed here, the book will appeal to readers from a broad range of disciplines, from mathematical/philosophical logic, computing science, cognitive science and artificial intelligence, to linguistics, game theory and beyond.

This book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2019. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe's leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance. The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.

This book illustrates how modern mathematical wavelet transform techniques offer fresh insights into the complex behavior of neural systems at different levels: from the microscopic dynamics of individual cells to the macroscopic behavior of large neural networks. It also demonstrates how and where wavelet-based mathematical tools can provide an advantage over classical approaches used in neuroscience. The authors well describe single neuron and populational neural recordings. This 2nd edition discusses novel areas and significant advances resulting from experimental techniques and computational approaches developed since 2015, and includes three new topics: * Detection of fEPSPs in multielectrode LFPs recordings. * Analysis of Visual Sensory Processing in the Brain and BCI for Human Attention Control; * Analysis and Real-time Classification of Motor-related EEG Patterns; The book is a valuable resource for neurophysiologists and physicists familiar with nonlinear dynamical systems and data processing, as well as for graduate students specializing in these and related areas.

Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.

This self-contained textbook covers the fundamentals of two basic topics of linear functional analysis: locally convex spaces and harmonic analysis. Readers will find detailed introductions to topological vector spaces, distribution theory, weak topologies, Fourier transform, Hilbert transform, and Calderon-Zygmund singular integrals. An ideal introduction to more advanced texts, the book complements Ciarlet's Linear and Nonlinear Functional Analysis with Applications (SIAM), where the titular topics were not treated. Pedagogical features such as detailed theorems and 93 problems make the book ideal for a one-semester first-year graduate course or for self-study. The book is intended for advanced undergraduates and first-year graduate students and researchers. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory

Statistical inference carries great significance in model building from both the theoretical and the applications points of view. Its applications to engineering and economic systems, financial economics, and the biological and medical sciences have made statistical inference for stochastic processes a well-recognized and important branch of statistics and probability.
The class of semimartingales includes a large class of stochastic processes, including diffusion type processes, point processes, and diffusion type processes with jumps, widely used for stochastic modeling. Until now, however, researchers have had no single reference that collected the research conducted on the asymptotic theory for semimartingales.

Semimartingales and their Statistical Inference, fills this need by presenting a comprehensive discussion of the asymptotic theory of semimartingales at a level needed for researchers working in the area of statistical inference for stochastic processes. The author brings together into one volume the state-of-the-art in the inferential aspect for such processes. The topics discussed include:

· Asymptotic likelihood theory
· Quasi-likelihood
· Likelihood and efficiency
· Inference for counting processes
· Inference for semimartingale regression models

The author addresses a number of stochastic modeling applications from engineering, economic systems, financial economics, and medical sciences. He also includes some of the new and challenging statistical and probabilistic problems facing today's active researchers working in the area of inference for stochastic processes.

This book concerns issues related to biomathematics, medicine, or cybernetics as practiced by engineers. Considered population dynamics models are still in the interest of researchers, and even this interest is increasing, especially now in the time of SARS-CoV-2 coronavirus pandemic, when models are intensively studied in order to help predict its behaviour within human population. The structures of population dynamics models and practical methods of finding their solutions are discussed. Finally, the hypothesis of the existence of non-trivial ergodic properties of the model of erythropoietic response dynamics formulated by A. Lasota in the form of delay differential equation with unimodal feedback is analysed. The research can be compared with actual medical data, as well as shows that the structures of population models can reflect the dynamic structures of reality.

This book gathers the proceedings of the 4th conference on Recent Advances in Engineering Math. & Physics (RAEMP 2019), which took place in Cairo, Egypt in December 2019. This international and interdisciplinary conference highlights essential research and developments in the field of Engineering Mathematics and Physics and related technologies and applications. The proceedings is organized to follow the main tracks of the conference: Advanced computational techniques in engineering and sciences; computational intelligence; photonics; physical measurements and big data analytics; physics and nano-technologies; and optimization and mathematical analysis.

This book discusses significant research and study topics related to mathematical modelling and analysis of infectious diseases. It includes several models and modelling approaches with different aims, such as identifying and analysing causes of occurrence and re-occurrence, causes of spreading, treatments and control strategies. A valuable resource for researchers, students, educators, scientists, professionals and practitioners interested in gaining insights into various aspects of infectious diseases using mathematical modelling and mathematical analysis, the book will also appeal to general readers wanting to understand the dynamics of various diseases and related issues. Key Features Mathematical models that describe population prevalence or incidence of infectious diseases Mathematical tools and techniques to analyse data on the incidence of infectious diseases Early detection and risk estimate models of infectious diseases Mathematical models that describe the transmission of infectious diseases and analyse data Dynamical analysis and control strategies for infectious diseases Studies comparing the utility of particular models in describing infected diseases-related issues such as social, health and economic

This collection of selected papers presented at the 12th International Conference on Scientific Computing in Electrical Engineering, SCEE 2018, held in Taormina, Sicily, Italy, in September 2018, showcases the state of the art in SCEE. The aim of the SCEE 2018 conference was to bring together scientists from academia and industry, mathematicians, electrical engineers, computer scientists, and physicists, and to promote intensive discussions on industrially relevant mathematical problems, with an emphasis on the modeling and numerical simulation of electronic circuits and of electromagnetic fields. This extensive reference work is divided into five parts: Computational Electromagnetics, Device Modeling and Simulation, Circuit Simulation, Mathematical and Computational Methods, Model Order Reduction. Each part starts with a general introduction, followed by the respective contributions. The book will appeal to mathematicians and electrical engineers. Further, it introduces algorithm and program developers to recent advances in the other fields, while industry experts will be introduced to new programming tools and mathematical methods.

Practical Handbook of Genetic Algorithms, Volume 3: Complex Coding Systems contains computer-code examples for the development of genetic algorithm systems - compiling them from an array of practitioners in the field.
Each contribution of this singular resource includes:
unique code segments
documentation
description of the operations performed
rationale for the chosen approach
problems the code overcomes or addresses
Practical Handbook of Genetic Algorithms, Volume 3: Complex Coding Systems complements the first two volumes in the series by offering examples of computer code. The first two volumes dealt with new research and an overview of the types of applications that could be taken with GAs. This volume differs from its predecessors by specifically concentrating on specific functions in genetic algorithms, serving as the only compilation of useful and usable computer code in the field.

This book features a selection of revised and extended research articles written by prominent researchers who participated in the 26th World Congress on Engineering and Computer Science (WCECS 2018), held in San Francisco, USA, on October 23-25, 2018. Topics covered include engineering mathematics, electrical engineering, communications systems, computer science, chemical engineering, systems engineering, manufacturing engineering and industrial applications. With contributions carefully chosen to represent the most cutting-edge research presented at the conference and highlighting the state of the art in engineering technologies and the physical sciences and their applications, the book is a valuable reference resource for graduate students and researchers working in these fields.

Modelling and Mechanics of Carbon-based Nanostructured Materials sets out the principles of applied mathematical modeling in the topical area of nanotechnology. It is purposely designed to be self-contained, giving readers all the necessary modeling principles required for working with nanostructures. The unique physical properties observed at the nanoscale are often counterintuitive, sometimes astounding researchers and thus driving numerous investigations into their special properties and potential applications. Typically, existing research has been conducted through experimental studies and molecular dynamics simulations. This book goes beyond that to provide new avenues for study and review.

Quantum systems with many degrees of freedom are inherently difficult to describe and simulate quantitatively. The space of possible states is, in general, exponentially large in the number of degrees of freedom such as the number of particles it contains. Standard digital high-performance computing is generally too weak to capture all the necessary details, such that alternative quantum simulation devices have been proposed as a solution. Artificial neural networks, with their high non-local connectivity between the neuron degrees of freedom, may soon gain importance in simulating static and dynamical behavior of quantum systems. Particularly promising candidates are neuromorphic realizations based on analog electronic circuits which are being developed to capture, e.g., the functioning of biologically relevant networks. In turn, such neuromorphic systems may be used to measure and control real quantum many-body systems online. This thesis lays an important foundation for the realization of quantum simulations by means of neuromorphic hardware, for using quantum physics as an input to classical neural nets and, in turn, for using network results to be fed back to quantum systems. The necessary foundations on both sides, quantum physics and artificial neural networks, are described, providing a valuable reference for researchers from these different communities who need to understand the foundations of both.

This second edition of the outstanding monograph on coherent states by Combescure and Robert published in 2012 is enriched with figures, historical information and numerical simulations and enlarged with five new chapters presenting important rigorous results obtained in the recent years. The new chapters include various applications such as to the time dependent Schroedinger equation and the Ehrenfest time, to the growth of norms and energy exchanges, to chaotic systems and classical systems with quantum ergodic behavior, and to open quantum systems, and to adiabatic decoupling for multicomponent systems Overall, this book presents the various types of coherent states introduced and studied in the physics and mathematics literature and describes their properties together with application to quantum physics problems. It is intended to serve as a compendium on coherent states and their applications for physicists and mathematicians, stretching from the basic mathematical structures of generalized coherent states in the sense of Perelomov via the semiclassical evolution of coherent states to various specific examples of coherent states (hydrogen atom, quantum oscillator, etc.). It goes beyond existing books on coherent states in terms of a rigorous mathematical framework