These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograp
This book brings together into a general setting various techniques in the study of the topological properties of spaces of continuous functions. The two major classes of function space topologies stu
Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book
?Random Matrices are one of the major research areas in modern probability theory, due to their prominence in many different fields such as nuclear physics, statistics, telecommunication, free probabi
The book is based on the PhD thesis “Descriptive Set Theoretic Methods in Automata Theory,” awarded the E.W. Beth Prize in 2015 for outstanding dissertations in the fields of logic, language, and info
The topic of this book is the following optimisation problem: given a set of discrete variables and a set of functions, each depending on a subset of the variables, minimise the sum of the functions o
In four volumes, the "Principles" develop the theory of random functions, the main tool in statistical radiophysics and a variety of other branches of physics and engineering. The course addresses stu
Principles of Statistical Radiophysics is a four-volume series that introduces the newcomer to the theory of random functions. It aims at providing the background necessary to understand papers and mo
Principles of Statistical Radiophysics is a four-volume series that introduces the newcomer to the theory of random functions. It aims at providing the background necessary to understand papers and mo
This is an English translation of Bourbaki’s Fonctions d'une Variable Reelle. Coverage includes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a f
The two internationally renowned authors elucidate the structure of "fast" parallel computation. Its complexity is emphasised through a variety of techniques ranging from finite combinatorics, probabi
Integrates traditional statistical data analysis with new computational experimentation capabilities and concepts of algorithmic complexity and chaotic behavior in nonlinear dynamic systems, offering
With parallel treatment of smooth and non-smooth problems, this text on non-linear boundary value problems and related analysis has new material on Neumann problems involving non-homogeneous different
Random walks, Markov chains and electrical networks serve as an introduction to the study of real-valued functions on finite or infinite graphs, with appropriate interpretations using probability theo
This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the
Featuring experimental approaches that shed light on the complexity of Ras GTPase biological functions, Ras Signaling: Methods and Protocols contains general overviews and detailed applications of bot
This book presents the basics of stochastic, risk and uncertainty analysis and random sampling techniques using practical examples, solved step by step. Includes appropriate Excel functions as an alte
The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori different
The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori different
Hepatocytes account for approximately 80% of the liver mass and play a significant role in various aspects of liver physiopathology, exhibiting unrivaled complexity and diversity of functions. In Hep
Being interfaces between living organisms and an environment, biological surfaces serve variety of functions. Because of the structural and chemical complexity of biological surfaces, exact working me
The origins of the word problem are in group theory, decidability and complexity. But through the vision of M. Gromov and the language of filling functions, the topic now impacts the world of large-sc
Also called Ito calculus, the theory of stochastic integration has applications in virtually every scientific area involving random functions. This introductory textbook provides a concise introductio
This introductory text develops the geometry of n-dimensional oriented surfaces in Rn+1. By viewing such surfaces as level sets of smooth functions, the author is able to introduce global ideas early
