Presenting topics that have not previously been contained in a single volume, this book offers an up-to-date review of computational methods in electromagnetism, with a focus on recent results in the numerical simulation of real-life electromagnetic problems and on theoretical results that are useful in devising and analyzing approximation algorithms. Based on four courses delivered in Cetraro …
This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greate…
The physics of condensed matter, in contrast to quantum physics or cosmology, is not traditionally associated with deep philosophical questions. However, as science - largely thanks to more powerful computers - becomes capable of analysing and modelling ever more complex many-body systems, basic questions of philosophical relevance arise. Questions about the emergence of structure, the nature o…
This book reviews the mechanisms, patterns, and processes that regulate prokaryotic diversity through different habitats in the context of evolutionary and ecological hypotheses, principles, and theories. Despite the tremendous role of prokaryotic diversity in the function of the global ecosystem, it remains understudied in comparison to the rest of biological diversity. In this book, the autho…
This book presents the latest advances in ultrafast science, including both ultrafast optical technology and the study of ultrafast phenomena. It covers picosecond, femtosecond, and attosecond processes relevant to applications in physics, chemistry, biology, and engineering. Ultrafast technology has a profound impact in a wide range of applications, amongst them biomedical imaging, chemical dy…
This book covers the major problems of turbulence and turbulent processes, including physical phenomena, their modeling and their simulation. After a general introduction in Chapter 1 illustrating many aspects dealing with turbulent flows, averaged equations and kinetic energy budgets are provided in Chapter 2. The concept of turbulent viscosity as a closure of the Reynolds stress is also i…
This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957. The theory extends the theory of matrix factorizations of …
In this introductory text, physics concepts are introduced as a means of understanding experimental observations, not as a sequential list of facts to be memorized. The book is structured around the key scientific discoveries that led to much of our current understanding of the universe. Numerous exercises are provided that utilize Mathematica software to help students explore how the language …
This book introduces formal semantics techniques for a natural language processing audience. Methods discussed involve: (i) the denotational techniques used in model-theoretic semantics, which make it possible to determine whether a linguistic expression is true or false with respect to some model of the way things happen to be; and (ii) stages of interpretation, i.e., ways to arrive at meaning…
This book describes current problems in data science and Big Data. Key topics are data classification, Graph Cut, the Laplacian Matrix, Google Page Rank, efficient algorithms, hardness of problems, different types of big data, geometric data structures, topological data processing, and various learning methods. For unsolved problems such as incomplete data relation and reconstruction, the book…