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Michael F Shlesinger: Why Not Nonlinear
Algebra: Math, Science, Applications And

Why Not Nonlinear Algebra: Math, Science, Applications And Funding

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

While the field of Deep Learning has been advancing at frightening speeds during the last ten years, we do not have a plausible theoretical explanation of its success yet. One can safely say that Deep Learning works, but nobody really understands why. Nevertheless, starting around five years before now, a decent number of theoretical papers specifically concerning neural nets started to emerge at top machine learning venues. This makes us think that the core of Deep Learning theory has already started to crystallize.The goal of the present book is to present these core concepts of Deep Learning theory to readers so that they could directly dive into recent papers of this area. For this purpose, each chapter elaborates a simple model or a classical result in details first and then discusses possible generalizations and more recent developments of the same idea.We have to warn the reader that the present book is not a mathematical manuscript. Not all results here are stated as formal theorems and not all theorems are provided with complete and rigorous proofs. Many of the theorems of the book are proven up to some technical lemmas, while for some there is only a proof sketch. This conforms with the main idea of the book: present and illustrate concepts rather than reproduce all the results.The book, in its present form, covers the following topics: uniform generalization bounds, PAC-bayesian generalization bounds, double descent phenomena, infinitely-wide networks, implicit bias of gradient descent, loss landscape, gradient descent convergence guarantees, and initialization strategies.

Elements Of Deep Learning Theory

The aim of this textbook is to improve students' ability to formulate economic problems and provide essential mathematical tools for analysis across various contexts. This book presents the author's current understanding of mathematics, shaped by several years of teaching this subject as well as enriched through interactions with his students. To aid students in their learning, the book is written in a manner that better highlights key concepts and provides additional clarity when possible. In this way, it is hoped that students will feel more guided in their study of mathematics and its applications in microeconomics.

Essential Mathematics For Microeconomics: A Student's Guide To Key Mathematical Techniques

Agent-Based Models with MATLAB introduces Agent-Based Modeling (ABM), one of the most important methodologies for complex systems modeling. The book explores computational implementations and accompanying MATLAB software code as a means of inspiring readers to apply agent-based models to solve a diverse range of problems. It comes with a large amount of software code that accompanies the main text, and the modeling systems described in the book are implemented using MATLAB as the programming language. Despite the heavy mathematical components of Agent-Based Models and complex systems, it is possible to utilize these models without in-depth understanding of their mathematical fundamentals. This book enables computer scientists, mathematicians, researchers, and engineers to apply ABM in a wide range of research and engineering applications. It gradually advances from basic to more advanced methods while reinforcing complex systems through practical, hands-on applications of various computational models.

Agent-Based Models with MATLAB

This monograph is devoted to the recently developed thermostatted kinetic theory and its application to the modeling of complex systems in a variety of fields. In the first part, the frameworks of the theory, which are obtained by coupling the kinetic theory for active particles with the thermostats coming from non-equilibrium statistical mechanics (Gaussian isokinetic thermostat), are presented. Among the theoretical results discussed are existence and uniqueness of the solution of the different mathematical frameworks, existence and uniqueness of the nonequilibrium stationary state, convergence to the nonequilibrium stationary state, derivation of macroscopic equations by asymptotic limits, and the construction of solutions to inverse problems based on the thermostatted kinetic theory. The second part deals with the derivation of mathematical models for nonequilibrium complex systems. Among those described within this new framework are immune systems and competition with tumors, keloid formation and therapy, dynamics of train crowds, modeling of a smart grid composed by different energy sources, and financial markets.

Thermostatted Kinectic Theory Approach, The: Theory, Inverse Problems, And Models

De Gruyter Studies in Mathematics

Orthogonal Polynomials

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 in Molecular Biophysics

Models and Applications of Tourists’ Travel Behavior offers an exhaustive overview of various approaches to modeling tourists’ travel behavior, aiding readers in selecting the most suitable theoretical approach based on the available data. The book bridges traditional travel behavior theories and tourist studies, introducing specific tourist contexts in travel demand modeling. It transcends theoretical understanding, providing practical insights for choosing the right model and data source. It covers theoretical, descriptive, and statistical approaches to modeling, discussing choice models based on both Stated Preference Data and Revealed Preference Data. The book starts by exploring the role of transport in tourist travel behavior and employs a comprehensive literature review to establish a foundational understanding. The concluding chapters delve into machine learning methods, emphasizing the modeling of transport in tourism, including mode choice, waiting time, and delay modeling. This resource is beneficial for educators, students, and researchers alike, providing a solid foundation for future model development.

Models and Applications of Tourists’ Travel Behavior

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

Lectures On Quantum State Estimation

Computation and Analysis of Turbulent Flows

Numerical Modeling of Turbulent Combustion provides readers with a comprehensive understanding of the specificities involved in numerical simulation of gaseous turbulent reactive flows and flames, including their most current applications. This title is intended for individuals with a background in fluid mechanics who are seeking to delve into the fundamentals of turbulent combustion modeling. It offers methodologies to simulate flames while taking into account their multi-physics character. Moreover, the text addresses emerging numerical technologies within this field and highlights the relevance of new sustainable fuels. The structure of the book is carefully organised to cover various aspects. It begins with an exploration of the fundamentals of aerothermochemistry, presenting key quantities and their corresponding balance equations that require numerical solutions. The book then delves into the essential concepts and tools necessary to handle the strongly non-linear nature of turbulent flames, with a specific focus on the interplay between turbulence and chemistry. Furthermore, readers will gain insights into the numerical modeling of flames within the context of sustainable combustion. This includes the introduction of novel fuels, such as hydrogen and solid metals, which have become increasingly relevant in recent times. The book also takes into account cutting-edge techniques, like the systematic integration of machine learning in numerical simulations of complex systems and the lattice Boltzmann approach. These innovations open new possibilities for tackling challenges in numerical turbulent combustion research. Both the fundamental methods and modeling tools are presented in detail, along with best practice guidelines for their practical application in simulations. This ensures that readers not only grasp the underlying theories but also gain valuable insights into how to implement these techniques effectively. Overall, Numerical Turbulent Combustion serves as a valuable resource for researchers and practitioners alike, offering a comprehensive and up-to-date understanding of numerical simulations in the field of turbulent combustion.

Numerical Modeling of Turbulent Combustion

Advances in Quantum Chemistry

Recent developments of molecular electronic structure theory: Volume 91

Why Not Nonlinear Algebra: Math, Science, Applications And Funding

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