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Geometry, Mechanics, and Dynamics
This book illustrates the broad range of Jerry Marsden’s mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy. The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well.
Secrecy and Deceit
Comprehensive history of crypto-Jewish beliefs and social customs.
Analysis and Geometry in Control Theory and its Applications
Since the 1950s control theory has established itself as a major mathematical discipline, particularly suitable for application in a number of research fields, including advanced engineering design, economics and the medical sciences. However, since its emergence, there has been a need to rethink and extend fields such as calculus of variations, differential geometry and nonsmooth analysis, which are closely tied to research on applications. Today control theory is a rich source of basic abstract problems arising from applications, and provides an important frame of reference for investigating purely mathematical issues. In many fields of mathematics, the huge and growing scope of activity h...
Blockchain
De la mano del dinero virtual, en los últimos años blockchain ha acaparado el foco de interés de la actualidad tecnológica. Blockchain ofrece un mecanismo descentralizado de recolección de trazas inmutables y permite, por ejemplo, la construcción de sistemas financieros alternativos, sin bancos centrales, o de organizaciones autónomas basadas en contratos inteligentes. Y como ejemplo, Bitcoin y Ethereum, con sus monedas virtuales, el bitcoin y el ether. Esta obra explica los fundamentos de los componentes tecnológicos y criptográficos de blockchain, analiza sus limitaciones en la gestión de la identidad y privacidad, y discute críticamente su papel protagonista en la configuración de la web 3.0.
Geometric Structures of Statistical Physics, Information Geometry, and Learning
Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract repres...
Discrete Mechanics, Geometric Integration and Lie–Butcher Series
This volume resulted from presentations given at the international “Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie–Butcher Series”, that took place at the Instituto de Ciencias Matemáticas (ICMAT) in Madrid, Spain. It combines overview and research articles on recent and ongoing developments, as well as new research directions. Why geometric numerical integration? In their article of the same title Arieh Iserles and Reinout Quispel, two renowned experts in numerical analysis of differential equations, provide a compelling answer to this question. After this introductory chapter a collection of high-quality research articles aim at explo...
Mathematical Reviews
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Challenges in Cybersecurity and Privacy - the European Research Landscape
Cybersecurity and Privacy issues are becoming an important barrier for a trusted and dependable global digital society development. Cyber-criminals are continuously shifting their cyber-attacks specially against cyber-physical systems and IoT, since they present additional vulnerabilities due to their constrained capabilities, their unattended nature and the usage of potential untrustworthiness components. Likewise, identity-theft, fraud, personal data leakages, and other related cyber-crimes are continuously evolving, causing important damages and privacy problems for European citizens in both virtual and physical scenarios. In this context, new holistic approaches, methodologies, technique...
Journal of Physics A
Focuses on fundamental mathematical and computational methods underpinning physics. Relevant to statistical physics, chaotic and complex systems, classical and quantum mechanics, classical and quantum integrable systems and classical and quantum field theory.
