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Athalye V: Quantum Modelling of Economic
and Financial Systems

Quantum Modelling of Economic and Financial Systems

Selected Topics

Lectures On Quantum State Estimation

A Realist’s Guide to the Economy and How We Can Fix it

Why We’re Getting Poorer

This book is the first one that shows how to accurately and efficiently solve time-varying problems in real-time or online using continuous- or discrete-time zeroing dynamics. The authors provide a comprehensive treatment of the theory of both static and dynamic neural networks. They develop, analyze, model, simulate, and compare zeroing dynamics models for the online solution of numerous time-varying problems, such as root finding, nonlinear equation solving, matrix inversion, matrix square root finding, quadratic optimization, and inequality solving.

Neural networks and neural dynamics are powerful approaches for the online solution of mathematical problems arising in many areas of science, engineering, and business. Compared with conventional gradient neural networks that only deal with static problems of constant coefficient matrices and vectors, the authors’ new method called zeroing dynamics solves time-varying problems. Zeroing Dynamics, Gradient Dynamics, and Newton Iterations is the first book that shows how to accurately and efficiently solve time-varying problems in real-time or online using continuous- or discrete-time zeroing dynamics. The book brings together research in the developing fields of neural networks, neural dynamics, computer mathematics, numerical algorithms, time-varying computation and optimization, simulation and modeling, analog and digital hardware, and fractals.The authors provide a comprehensive treatment of the theory of both static and dynamic neural networks. Readers will discover how novel theoretical results have been successfully applied to many practical problems. The authors develop, analyze, model, simulate, and compare zeroing dynamics models for the online solution of numerous time-varying problems, such as root finding, nonlinear equation solving, matrix inversion, matrix square root finding, quadratic optimization, and inequality solving.

Zeroing Dynamics, Gradient Dynamics, and Newton Iterations

Manchester Physics

Cosmology

Radon Series on Computational and Applied Mathematics

Hilbert Space Methods for the Theory of Electromagnetism

Maxwell’s Equations

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

World Scientific Book Series In Quantum Information, Science And Technology

This unique compendium gives an overview of the current research activities and developments within the areas of quantum hardware, quantum computing, quantum software, quantum communication and quantum sensing in Denmark. Renowned contributing authors are part of the Danish research community and work in research institutions or companies dealing with and related to quantum technologies.The useful reference text allows readers to identify the research groups within Denmark working on specific topics as well as learning about topics which might be unfamiliar to them. The intention of each chapter is to give a good introduction to the scientific theory and the current state of the art.

Quantum Hardware And Algorithms For Engineering And Life Sciences Applications: A Review Of The Danish Quantum Research Community

Origami Engineering: Combining Science, Art, And Industry

Series in Materials Science and Engineering

This book provides an introduction to the geometrical and topological methods that have become essential tools for soft condensed matter physicists. The emphasis is on providing mathematical tools in clear but precise language, focusing on fundamental concepts using real examples to illustrate for readers in vivid, three-dimensional fashion. The motivation is clearly provided using problems from soft condensed matter, from the packing of colloids to liquid crystals and thermal fluctuations of lipid membranes.

This book provides an introduction to the geometrical and topological methods that have become essential tools for soft condensed matter physicists. The emphasis is on providing mathematical tools in clear but precise language, focusing on fundamental concepts using real examples to illustrate for readers in vivid, three-dimensional fashion. The motivation is clearly provided using problems from soft condensed matter, from the packing of colloids to liquid crystals and thermal fluctuations of lipid membranes.

Geometry and Topology of Soft Materials

Manchester Physics Series

Properties and Applications of Advanced Materials

This text focuses on the parts of stochastic theory that are particularly relevant to applications. It begins with a description of Brownian motion and the associated stochastic calculus, including the relationship to partial differential equations. It then solves stochastic differential equations by a variety of methods. The author also studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions as well as weak convergence of Markov chains to diffusions.

This text focuses on the parts of stochastic theory that are particularly relevant to applications. It begins with a description of Brownian motion and the associated stochastic calculus, including the relationship to partial differential equations. It then solves stochastic differential equations by a variety of methods. The author also studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions as well as weak convergence of Markov chains to diffusions.

An Elementary Introduction Emphasizing Applications

Stochastic Calculus

Quantum Modelling of Economic and Financial Systems

Bibliografische Angaben

Schlagworte

Bibliografische Angaben

Schlagworte

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