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Chatterjee P: Nonlinear Partial
Differential Equations: Techniques And

Nonlinear Partial Differential Equations: Techniques And Recent Developments

Gibbs Measures In Machine Learning

Origami Engineering: Combining Science, Art, And Industry

De Gruyter Studies in Mathematical Physics

Mirror symmetry is one of the most exciting ideas in mathematics to emerge in the last two decades. It was introduced in physics as a duality between superconformal field theories. This book discusses this rapidly developing aspect of string theory.

Laurent Polynomials in Mirror Symmetry

Interdisciplinarity In The Sciences: Nonlinear Dynamics, Chaos And Complexity

Quantum Communication and Cryptography introduces readers to the theory of quantum cryptography, with a focus will on quantum key distribution (QKD) and more advanced quantum cryptographic protocols beyond QKD. It contains a brief introduction to the field of modern cryptography that is needed to fully appreciate and understand how quantum cryptographic systems are proven secure, and how they can be safely used in combination with current day classical systems. Readers are then introduced to quantum key distribution (QKD) - perhaps the most celebrated, and currently the most practical, of quantum cryptographic techniques. Basic protocols are described, and security proofs are given, providing readers with the knowledge needed to understand how QKD protocols are proven secure using modern, state- of-the-art definitions of security. Following this, more advanced QKD protocols are discussed, along with alternative quantum and classical methods to improve QKD performance. Finally, alternative quantum cryptographic protocols are covered, along with a discussion on some of the practical considerations of quantum secure communication technology. Throughout, protocols are described in a clear and consistent manner that still provides comprehensive, theoretical proofs and methods.

Quantum Communication and Cryptography

Lectures On Quantum State Estimation

Scaling (zooming in or out) is taking a close or distant view of an object. Infinite scaling (the scaling parameter tends to zero or infinity) may lead to a limit which is self-similar and much simpler than the original object. For instance, the classical Donsker's theorem says that all weakly dependent stationary processes with finite variance scale to Brownian motion at large scales. In the case of a random field indexed by two-dimensional parameter, both types of scaling can be anisotropic, meaning that the horizontal and vertical axes are scaled at different rate determined by the ratio γ&gt;0 of the scaling exponents along the axes. The natural questions under such scaling are whether the scaling limits exist for any γ&gt;0, and what are these limits are. The book tries to answer these questions. It introduces the concept of scaling transition and discusses its existence for a natural class of planar random fields including Gaussian, linear and some nonlinear ones. The scaling limits are identified and exhibit a surprising trichitomy at a critical point γ0, with 'unbalanced' limits having unusual path properties and dependence structure along one of the coordinate axes. Scaling transition occurs in applied sciences (telecommunications and econometrics) when aggregating independent processes with long-range dependence in which case 'unbalanced' limits are classical Gaussian or stable random fields.

Anisotropic Scaling Of Random Fields With Long-range Dependence: Scaling Limits Of Random Fields With Applications

Advances in Computers

Post-Quantum Cryptography Algorithms and Approaches for IoT and Blockchain Security: Volume 138

Radon Series on Computational and Applied Mathematics

Hilbert Space Methods for the Theory of Electromagnetism

Maxwell’s Equations

Series in Computational Biophysics

Multiscale methods are ideally suited to simulate the processes at work in many biomolecular systems, which often span a large range of time and length scales. Multiscale Methods in Molecular Biophysics highlights the advantages of these methods for integrating different levels of detail in a single simulation setting. It covers the practical methodology and successful applications in areas such as enzyme catalysis, protein folding, and ligand binding. The book is divided into three main sections: combination quantum and classical (atomistic) descriptions, approaches that combine atomistic and coarse-grained level of details, and multiscale methods where the resolution coupling is between global collective coordinates and local details.

Multiscale methods are ideally suited to simulate the processes at work in many biomolecular systems, which often span a large range of time and length scales. Multiscale Methods in Molecular Biophysics highlights the advantages of these methods for integrating different levels of detail in a single simulation setting. It covers the practical methodology and successful applications in areas such as enzyme catalysis, protein folding, and ligand binding. The book is divided into three main sections: combination quantum and classical (atomistic) descriptions, approaches that combine atomistic and coarse-grained level of details, and multiscale methods where the resolution coupling is between global collective coordinates and local details.

Multiscale Methods in Molecular Biophysics

Geometric Morphometrics for Biologists: A Primer, Third Edition explores how these geometric methods allow for the study of biological shape by incorporating the geometry of organisms throughout data analyses. Novel content on phylogenetic comparative methods, evolutionary morphology, analyses of disparity, genetics of shape, and simulating shape data is included. This edition delivers step-by-step guidance on how to effectively utilize updated analytical software while also providing guidance on important methodologies that remain relevant to the field to ensure clear and effective instruction to audiences new to this branch of data analysis. It succeeds the second edition as the primary resource for teaching modern geometric methods of shape analysis to students, researchers, and practicing scientists in the field of organismal biology. Users will find it to be an immensely valuable introduction for students and practicing biologists interested in learning applications of multivariate statistics and matrix algebra to organismal biology.

A Primer

Geometric Morphometrics for Biologists

An Introduction to the Finite Element Method with the Variational Approach offers a comprehensive solution to the gaps often found in introductory texts on the Finite Element Method (FEM). The book provides a thorough introduction to the fundamental principles of linear and time-independent FEM within the variational framework. It meticulously covers the derivation of 1-D FEM equations based on variational functionals, encompassing both linear and higher-order elements, and shape functions driven by convergence criteria. Furthermore, it explores 1-D numerical integration, outlines coding procedures, and provides insights into handling material nonlinearity and time-dependent scenarios. Expanding into 2-D problems, the book offers derivations of 2-D FEM equations tailored to diverse engineering disciplines, including Steady-State Heat Conduction, Solid Mechanics (covering torsion, plane strain/axisymmetric cases, and the bending, stability, and vibrations of thin plates), as well as Fluid Mechanics (addressing incompressible inviscid and viscous fluids). It includes detailed discussions on element continuity, numerical integration techniques, and even includes 2-D codes for selected problems. The book concludes by delving into recent advancements in FEM, with a specific focus on applications in machine learning and isogeometric analysis.

An Introduction to the Finite Element Method with the Variational Approach

Nonlinear Partial Differential Equations: Techniques And Recent ...

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