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Regulatory Competition in the Digital Economy: Artificial Intelligence, Data, and Platforms (Advanced Studies in Diginomics and Digitalization)
by Lars Hornuf Michael DengaThe digital economy is reinvigorating regulatory competition, yet little is known about which rules and jurisdictions can effectively bind companies nor what competitive motivations underlie certain rules. In addition to purely economic motives, legislators are now also driving the pursuit of digital sovereignty and the enforcement of social values in digital spaces. It also remains unclear what regulatory weight the self-regulation of private companies has in multi-level governance systems. This book examines regulatory competition in the three main pillars of digital markets: artificial intelligence, data, and platforms. It brings together legal scholars, economists and information systems experts, providing relevant examples and structured analysis of the aims and outcomes of regulatory competition in the digital economy. “A timely exploration of the balancing acts regulators must perform to manage private power in a globalized digital economy. Essential for understanding the intersection of law, economics, and technology in the contemporary digital ecosystem.” Jens Frankenreiter, Associate Professor of Law, Washington University “The book by Denga and Hornuf provides a comprehensive and timely exploration of the intricate regulatory challenges posed by big data, artificial intelligence, and platforms in the Digital Single Market. If offers critical insights for policymakers, scholars, and businesses navigating this evolving landscape.” Philipp Hacker, Professor for Law and Ethics of the Digital Society, European University Viadrin “Artificial Intelligence is fundamentally disrupting how we enable economic growth and how we regulate fair competition. Luckily, Denga and Hornuf provide a detailed and comprehensive overview of the thorniest and most complex regulatory issues while at the same time offering thoughtful and feasible solutions. "Regulatory Competition in the Digital Economy" is a treasure trove for anyone interested in market regulation, fair competition, consumer protection, and geopolitical questions.” Sandra Wachter, Professor of Technology and Regulation, Oxford Internet Institute
Regulierung von Künstlicher Intelligenz in der EU: Praxisbezogene Lösungsansätze für die Sicherheit von KI-Anwendungen (Vertrauenswürdige KI)
by Rainer Bernnat Jordan PötschDieses Buch bietet eine praxisorientierte Einführung in die Regulierung von Künstlicher Intelligenz (KI) in der EU. Es vereint theoretisches Wissen mit konkreten Handlungsempfehlungen zur Umsetzung von KI-Standards und Gesetzen, insbesondere im Rahmen des EU AI Acts. Durch eine speziell entwickelte Systematik werden KI-relevante Gesetze und Standards systematisch erfasst und bewertet. Führungskräfte, CISOs und Cybersecurity-Experten erhalten wertvolle Einblicke, wie sie die Vertrauenswürdigkeit von KI-Systemen in ihren Organisationen gewährleisten können. Ein besonderer Schwerpunkt liegt auf der Integration von KI in bestehende Sicherheitsstrukturen sowie der Nutzung bewährter Frameworks.
Rehabilitation in Practice: Ethnographic Perspectives
by Paul M. W. Hackett Christopher M. Hayre Dave J. MullerThis book focuses on developing the use of ethnographic research for rehabilitation practitioners by recognizing its value methodologically and empirically in the field of rehabilitation. The very nature of ethnographic research offers an array of opportunities for researchers to understand the social world around them. The book identifies the multifaceted use of ethnographic methods in the rehabilitation setting. It touches on how acute and chronic conditions can affect the nature of ethnographic work in attempts to offer originality in a range of rehabilitation settings. Readers will find this collection of examples useful for informing their own research, and it aims to enlighten new discussion and arguments regarding both methodological and empirical use of ethnographic work internationally.
Reimagining Rural Transformation: Market Dynamics and Social Inequalities in North India
by Prashant K TrivediThis book examines the effects of the pattern of growing integration between the rural and urban economies in India. Drawing on in-depth surveys conducted in villages in north India, it examines the rural agricultural economy's transformation, productivity, technology deployment, and social relations over a period of seven years. The book focuses on the socially embedded nature of the dynamics of transformation, weaving analysis around the axis of land, caste, and gender. It also identifies policy gaps and recommends steps for a sustainable and inclusive rural transformation in the Global South.An important contribution to the study of India’s economic and social landscape, this book will be useful for scholars of agriculture, sociology, economics, political science, development studies, and South Asian studies. It will also be of interest to policymakers and journalists interested in rural development, migration, employment, agriculture, and demography.
Reinforcement Learning Methods in Speech and Language Technology (Signals and Communication Technology)
by Baihan LinThis book offers a comprehensive guide to reinforcement learning (RL) and bandits methods, specifically tailored for advancements in speech and language technology. Starting with a foundational overview of RL and bandit methods, the book dives into their practical applications across a wide array of speech and language tasks. Readers will gain insights into how these methods shape solutions in automatic speech recognition (ASR), speaker recognition, diarization, spoken and natural language understanding (SLU/NLU), text-to-speech (TTS) synthesis, natural language generation (NLG), and conversational recommendation systems (CRS). Further, the book delves into cutting-edge developments in large language models (LLMs) and discusses the latest strategies in RL, highlighting the emerging fields of multi-agent systems and transfer learning. Emphasizing real-world applications, the book provides clear, step-by-step guidance on employing RL and bandit methods to address challenges in speech and language technology. It includes case studies and practical tips that equip readers to apply these methods to their own projects. As a timely and crucial resource, this book is ideal for speech and language researchers, engineers, students, and practitioners eager to enhance the performance of speech and language systems and to innovate with new interactive learning paradigms from an interface design perspective.
Reinforcement Learning for Optimal Feedback Control: A Lyapunov-based Approach (Communications and Control Engineering)
by Patrick Walters Joel Rosenfeld Rushikesh Kamalapurkar Warren DixonReinforcement Learning for Optimal Feedback Control develops model-based and data-driven reinforcement learning methods for solving optimal control problems in nonlinear deterministic dynamical systems. In order to achieve learning under uncertainty, data-driven methods for identifying system models in real-time are also developed. The book illustrates the advantages gained from the use of a model and the use of previous experience in the form of recorded data through simulations and experiments. The book’s focus on deterministic systems allows for an in-depth Lyapunov-based analysis of the performance of the methods described during the learning phase and during execution. To yield an approximate optimal controller, the authors focus on theories and methods that fall under the umbrella of actor–critic methods for machine learning. They concentrate on establishing stability during the learning phase and the execution phase, and adaptive model-based and data-driven reinforcement learning, to assist readers in the learning process, which typically relies on instantaneous input-output measurements. This monograph provides academic researchers with backgrounds in diverse disciplines from aerospace engineering to computer science, who are interested in optimal reinforcement learning functional analysis and functional approximation theory, with a good introduction to the use of model-based methods. The thorough treatment of an advanced treatment to control will also interest practitioners working in the chemical-process and power-supply industry.
Reinforcement Learning for Reconfigurable Intelligent Surfaces: Assisted Wireless Communication Systems (SpringerBriefs in Computer Science)
by Octavia A. Dobre Alice Faisal Ibrahim Al-Nahhal Telex M. NgatchedThis book presents the intersection of two dynamic fields: Reinforcement Learning (RL) and RIS- Assisted Wireless Communications. With an emphasis on both discrete and continuous problems, it introduces a comprehensive overview of RL techniques and their applications in the evolving world of RIS-assisted wireless communications. Chapter 1 introduces the fundamentals of RL and deep RL (DRL), providing a solid foundation for understanding subsequent chapters. It also presents the Q-learning, deep Q-learning, and deep deterministic policy gradient algorithms. Chapter 2 provides a holistic overview of RIS-assisted systems and details several use cases in wireless communications. Then, Chapters 3 and 4 present various applications of the discrete and continuous DRL to RIS-assisted wireless communications. From maximizing the sum-rate to minimizing, the system resources and maximizing the energy efficiency. These chapters showcase the versatility of the DRL algorithms in tackling arange of challenges. This book concludes with Chapter 5, which introduces the challenges and future directions in this field. It explores the particulars of hyperparameter tuning, problem design, and complexity analysis, while also highlighting the potential of hybrid DRL, multi-agent DRL, and transfer learning techniques for advancing wireless communication systems. Optimizing RIS-Assisted Wireless Systems requires powerful algorithms to cope with the dynamic propagation environment. DRL is envisioned as one of the key enabling techniques to exploit the full potential of RIS-Assisted Wireless Communication Systems. It empowers these systems to intelligently adapt to dynamic wireless environments, maximize performance metrics, and adjusts their configurations to accommodate diverse use cases efficiently. This book serves as a valuable resource, shedding light on the potential of DRL to optimize RIS-Assisted Wireless Communication, enabling researchers, engineers, advanced level students in computer science and electrical engineering and enthusiasts to grasp the intricacies of this topic. It offers a comprehensive understanding of the principles, applications, and challenges, making it a reference to recognize the full potential of the RIS technology in modern wireless communication systems.
Reinforcement Learning in the Ridesharing Marketplace (Synthesis Lectures on Learning, Networks, and Algorithms)
by Hongtu Zhu Jieping Ye Zhiwei (Tony) Qin Xiaocheng Tang Qingyang LiThis book provides a comprehensive overview of reinforcement learning for ridesharing applications. The authors first lay out the fundamentals of the ridesharing system architectures and review the basics of reinforcement learning, including the major applicable algorithms. The book describes the research problems associated with the various aspects of a ridesharing system and discusses the existing reinforcement learning approaches for solving them. The authors survey the existing research on each problem, and then examine specific case studies. The book also includes a review of two of methods closely related to reinforcement learning: approximate dynamic programming and model-predictive control.
Reinforcement Learning: Aktuelle Ansätze verstehen – mit Beispielen in Java und Greenfoot
by Uwe LorenzIn uralten Spielen wie Schach oder Go können sich die brillantesten Spieler verbessern, indem sie die von einer Maschine produzierten Strategien studieren. Robotische Systeme üben ihre Bewegungen selbst. In Arcade Games erreichen lernfähige Agenten innerhalb weniger Stunden übermenschliches Niveau. Wie funktionieren diese spektakulären Algorithmen des bestärkenden Lernens? Mit gut verständlichen Erklärungen und übersichtlichen Beispielen in Java und Greenfoot können Sie sich die Prinzipien des bestärkenden Lernens aneignen und in eigenen intelligenten Agenten anwenden. Greenfoot (M.Kölling, King’s College London) und das Hamster-Modell (D.Bohles, Universität Oldenburg) sind einfache, aber auch mächtige didaktische Werkzeuge, die entwickelt wurden, um Grundkonzepte der Programmierung zu vermitteln. Wir werden Figuren wie den Java-Hamster zu lernfähigen Agenten machen, die eigenständig ihre Umgebung erkunden. Die zweite Auflage enthält neue Themen wie "Genetische Algorithmen" und "Künstliche Neugier" sowie Korrekturen und Überarbeitungen.
Reinsurance: Actuarial and Statistical Aspects
by Hansjöerg Albrecher Jan Beirlant Jozef L. TeugelsReinsurance: Actuarial and Statistical Aspects provides a survey of both the academic literature in the field as well as challenges appearing in reinsurance practice and puts the two in perspective. The book is written for researchers with an interest in reinsurance problems, for graduate students with a basic knowledge of probability and statistics as well as for reinsurance practitioners. The focus of the book is on modelling together with the statistical challenges that go along with it. The discussed statistical approaches are illustrated alongside six case studies of insurance loss data sets, ranging from MTPL over fire to storm and flood loss data. Some of the presented material also contains new results that have not yet been published in the research literature. An extensive bibliography provides readers with links for further study.
Reinventing Mountain and Rural Villages: Strategies for Regeneration in the Perspective of a Circular Economy (SpringerBriefs in Applied Sciences and Technology)
by Angela Colucci Manuela Grecchi Laura Elisabetta Malighetti Fernanda SpecialeThis book explores problems generated by the abandonment of mountain villages, which also represented strategic sites for guarding against environmental hazards, and proposes a process of regeneration and upgrade of the built environment, with a view to a circular economy and social and economic development. It provides principles, methods, and tools supporting the design and management of the regeneration of abandoned mountain/rural villages and presents the transferable results of multidisciplinary applied research involving several local contexts and compares methodological and technical design solutions developed in successful practices. The book consists of six chapters that address specific issues in the regeneration process of depopulated mountain villages.
Reinventing STEM in Early Childhood Education: A Constructivist Approach
by Eugene GeistTeaching STEM to young children is about more than helping them learn their numbers and facts. It is an important and complex process that, to be effective, should honor the way children’s brains are developing. This book outlines how early childhood educators can best support young children’s STEM journeys as children naturally take in information about their environment, synthesize it, and grow in the process. This comprehensive text details different theories of learning; research on how young brains develop; practical information on preparing your environment and yourself for teaching STEM to children; guidance for supporting diverse populations of students; and developmental guidelines, sample standards, resources, and lesson plans. Organized chronologically, the book connects relevant STEM topics with each developmental age range and outlines common school standards for each grade. Reinventing STEM in Early Childhood Education is meant to be a core text for preservice teachers in math and science methods courses and is also important reading for teacher educators and professional development programs.
Rekenek 101: Pushing Mathematical Understanding
by Amy HowDesigned and developed by a mathematic curriculum researcher at the Freudenthal Institute at Utrecht University, the rekenrek is an exciting and innovative classroom tool that enhances and supports the natural development of number sense in children. It encourages learning across a range of mathematical skills and concepts, from simple addition and subitization to commutativity, distributive property and fractions. However, despite the potential and versatility of this manipulative, there has been surprisingly little written about either its application or its benefits - until now.When the stacks of rekenreks first arrived at Amy How's school, she was tasked with discovering and explaining their function to the rest of the staff - despite the scarcity of current research or other information. Over the six years since, she has developed her own set of tasks and strategies, which she regularly presents to teachers around the world. These techniques – effective, straightforward and very popular – are the basis of this book. Rekenrek 101 is written in a format that makes for a useful teacher resource: not too long; clear, concise and inspiring enough for readers to try the new ideas the next day in class. It is easy to follow and easy to navigate while demonstrating a simple change in practice that stays up with current trends. This is not a book on theory, but it is based on what the latest research is telling us.
Rekenrek 101: Pushing Mathematical Understanding
by Amy HowDesigned and developed by a mathematic curriculum researcher at the Freudenthal Institute at Utrecht University, the rekenrek is an exciting and innovative classroom tool that enhances and supports the natural development of number sense in children. It encourages learning across a range of mathematical skills and concepts, from simple addition and subitization to commutativity, distributive property and fractions. However, despite the potential and versatility of this manipulative, there has been surprisingly little written about either its application or its benefits - until now.When the stacks of rekenreks first arrived at Amy How's school, she was tasked with discovering and explaining their function to the rest of the staff - despite the scarcity of current research or other information. Over the six years since, she has developed her own set of tasks and strategies, which she regularly presents to teachers around the world. These techniques – effective, straightforward and very popular – are the basis of this book. Rekenrek 101 is written in a format that makes for a useful teacher resource: not too long; clear, concise and inspiring enough for readers to try the new ideas the next day in class. It is easy to follow and easy to navigate while demonstrating a simple change in practice that stays up with current trends. This is not a book on theory, but it is based on what the latest research is telling us.
Relational Calculus for Actionable Knowledge (Information Fusion and Data Science)
by Éloi Bossé Michel BarèsThis book focuses on one of the major challenges of the newly created scientific domain known as data science: turning data into actionable knowledge in order to exploit increasing data volumes and deal with their inherent complexity. Actionable knowledge has been qualitatively and intensively studied in management, business, and the social sciences but in computer science and engineering, its connection has only recently been established to data mining and its evolution, ‘Knowledge Discovery and Data Mining’ (KDD). Data mining seeks to extract interesting patterns from data, but, until now, the patterns discovered from data have not always been ‘actionable’ for decision-makers in Socio-Technical Organizations (STO). With the evolution of the Internet and connectivity, STOs have evolved into Cyber-Physical and Social Systems (CPSS) that are known to describe our world today. In such complex and dynamic environments, the conventional KDD process is insufficient, and additional processes are required to transform complex data into actionable knowledge. Readers are presented with advanced knowledge concepts and the analytics and information fusion (AIF) processes aimed at delivering actionable knowledge. The authors provide an understanding of the concept of ‘relation’ and its exploitation, relational calculus, as well as the formalization of specific dimensions of knowledge that achieve a semantic growth along the AIF processes. This book serves as an important technical presentation of relational calculus and its application to processing chains in order to generate actionable knowledge. It is ideal for graduate students, researchers, or industry professionals interested in decision science and knowledge engineering.
Relational Data Clustering: Models, Algorithms, and Applications
by Philip S. Yu Zhongfei Zhang Bo LongA culmination of the authors' years of extensive research on this topic, Relational Data Clustering: Models, Algorithms, and Applications addresses the fundamentals and applications of relational data clustering. It describes theoretic models and algorithms and, through examples, shows how to apply these models and algorithms to solve real-world problems.After defining the field, the book introduces different types of model formulations for relational data clustering, presents various algorithms for the corresponding models, and demonstrates applications of the models and algorithms through extensive experimental results. The authors cover six topics of relational data clustering:Clustering on bi-type heterogeneous relational dataMulti-type heterogeneous relational data Homogeneous relational data clusteringClustering on the most general case of relational dataIndividual relational clustering frameworkRecent research on evolutionary clusteringThis book focuses on both practical algorithm derivation and theoretical framework construction for relational data clustering. It provides a complete, self-contained introduction to advances in the field.
Relational Topology (Lecture Notes in Mathematics #2208)
by Michael Winter Gunther SchmidtThis book introduces and develops new algebraic methods to work with relations, often conceived as Boolean matrices, and applies them to topology. Although these objects mirror the matrices that appear throughout mathematics, numerics, statistics, engineering, and elsewhere, the methods used to work with them are much less well known. In addition to their purely topological applications, the volume also details how the techniques may be successfully applied to spatial reasoning and to logics of computer science. Topologists will find several familiar concepts presented in a concise and algebraically manipulable form which is far more condensed than usual, but visualized via represented relations and thus readily graspable. This approach also offers the possibility of handling topological problems using proof assistants.
Relational and Algebraic Methods in Computer Science
by Peter Höfner Damien Pous Georg StruthThis volume contains the proceedings of the 7th International Seminar on - lational Methods in Computer Science (RelMiCS 7) and the 2nd International Workshop onApplications ofKleeneAlgebra. Thecommonmeetingtookplacein Bad Malente (near Kiel), Germany, from May May 12-17,2003. Its purpose was to bring together researchers from various subdisciplines of Computer Science, Mathematics and related ?elds who use the calculi of relations and/or Kleene algebra as methodological and conceptual tools in their work. This meeting is the joint continuation of two di'erent series of meetings. Previous RelMiCS seminars were held in Schloss Dagstuhl (Germany) in J- uary 1994, Parati (Brazil) in July 1995, Hammamet (Tunisia) in January 1997, Warsaw (Poland) in September 1998, Quebec (Canada) in January 2000, and Oisterwijk (The Netherlands) in October 2001. The ?rst workshop on appli- tions of Kleene algebra was also held in Schloss Dagstuhl in February 2001. To join these two events in a common meeting was mainly motivated by the s- stantialcommoninterestsandoverlapofthetwocommunities. Wehopethatthis leads to fruitful interactions and opens new and interesting research directions.
Relational and Algebraic Methods in Computer Science: 17th International Conference, RAMiCS 2018, Groningen, The Netherlands, October 29 – November 1, 2018, Proceedings (Lecture Notes in Computer Science #11194)
by Jules Desharnais Walter Guttmann Stef JoostenThis book constitutes the proceedings of the 17th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2018, held in Groningen, The Netherlands, in October/November 2018. The 21 full papers and 1 invited paper presented together with 2 invited abstracts and 1 abstract of a tutorial were carefully selected from 31 submissions. The papers are organized in the following topics: Theoretical foundations; reasoning about computations and programs; and applications and tools.
Relational and Algebraic Methods in Computer Science: 18th International Conference, RAMiCS 2020, Palaiseau, France, October 26–29, 2020, Proceedings (Lecture Notes in Computer Science #12062)
by Michael Winter Peter Jipsen Uli FahrenbergThis book constitutes the proceedings of the 18th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2020, which was due to be held in Palaiseau, France, in April 2020. The conference was cancelled due to the COVID-19 pandemic. The 20 full papers presented together with 3 invited abstracts were carefully selected from 29 submissions. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond.
Relational and Algebraic Methods in Computer Science: 21st International Conference, RAMiCS 2024, Prague, Czech Republic, August 19–22, 2024, Proceedings (Lecture Notes in Computer Science #14787)
by Uli Fahrenberg Roland Glück Wesley FussnerThis book constitutes the refereed proceedings of the 21st International Conference, RAMiCS 2024, held in Prague, Czech Republic, during August 19–22, 2024. The 15 full papers presented in this book were carefully reviewed and selected from 21 submissions. They focus on mathematical foundations to applications as conceptual and methodological tools in computer science and beyond.
Relationale Datenbanken: Von den theoretischen Grundlagen zu Anwendungen mit PostgreSQL (Examen. Press Ser.)
by Thomas StuderDieses Buch erläutert Theorie und Praxis zu relationalen Datenbanken Was sind relationale Datenbanken? Die Antwort darauf geben die theoretischen Grundlagen und Praxisbeispiele in diesem Buch. Zunächst erläutert Thomas Studer die mathematisch präzise Darstellung des relationalen Modells und die relationale Algebra. Daneben widmet er sich der Datenbanksprache SQL und schafft damit den Praxisbezug. Die zahlreichen Beispiele auf Basis der open-source Datenbank PostgreSQL erleichtern die Anwendung. Dieses Buch erklärt die grundlegenden Prinzipien des Schemaentwurfs und Normalformen fundiert und praxisnah und verbindet die relationale Datenbanktheorie mit Datenbankdesign. Studer hat aktuelle Entwicklungen im Blick Die vorliegende Auflage ist umfassend aktualisiert und dem aktuellen Kenntnisstand angepasst. Studer widmet sich in diesem Buch den folgenden Teilaspekten relationaler Datenbanken: Logische und physische Query-Optimierung Isolation von serializable Snapshots Zerlegung der dritten Normalform in die Boyce-Codd Normalform Rollen und Berechtigungen SQL als Sprache zur Datendefinition und Datenmanipulation Sicherheitsrichtlinien auf Zeilenebene Durch die nachhaltige Verbindung von Theorie und Praxis eignet sich das Buch „Relationale Datenbanken“ für: Studierende aus den Bereichen (Wirtschafts-)Informatik Praktiker wie Softwareentwickler, Systemadministratoren oder Fachinformatiker Besuchen Sie uns online und entdecken Sie die zahlreichen Begleitmaterialien zu diesem Buch, die alle frei zugänglich sind.
Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms: CIRM Jean-Morlet Chair, Spring 2016 (Lecture Notes in Mathematics #2221)
by Volker Heiermann Dipendra PrasadThis volume presents a panorama of the diverse activities organized by V. Heiermann and D. Prasad in Marseille at the CIRM for the Chaire Morlet event during the first semester of 2016. It assembles together expository articles on topics which previously could only be found in research papers. Starting with a very detailed article by P. Baumann and S. Riche on the geometric Satake correspondence, the book continues with three introductory articles on distinguished representations due to P. Broussous, F. Murnaghan, and O. Offen; an expository article of I. Badulescu on the Jacquet–Langlands correspondence; a paper of J. Arthur on functoriality and the trace formula in the context of "Beyond Endoscopy", taken from the Simons Proceedings; an article of W-W. Li attempting to generalize Godement–Jacquet theory; and a research paper of C. Moeglin and D. Renard, applying the trace formula to the local Langlands classification for classical groups. The book should be of interest to students as well as professional researchers working in the broad area of number theory and representation theory.
Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems (Communications and Control Engineering)
by Xi-Ren CaoThis monograph applies the relative optimization approach to time nonhomogeneous continuous-time and continuous-state dynamic systems. The approach is intuitively clear and does not require deep knowledge of the mathematics of partial differential equations. The topics covered have the following distinguishing features: long-run average with no under-selectivity, non-smooth value functions with no viscosity solutions, diffusion processes with degenerate points, multi-class optimization with state classification, and optimization with no dynamic programming.The book begins with an introduction to relative optimization, including a comparison with the traditional approach of dynamic programming. The text then studies the Markov process, focusing on infinite-horizon optimization problems, and moves on to discuss optimal control of diffusion processes with semi-smooth value functions and degenerate points, and optimization of multi-dimensional diffusion processes. The book concludes with a brief overview of performance derivative-based optimization.Among the more important novel considerations presented are:the extension of the Hamilton–Jacobi–Bellman optimality condition from smooth to semi-smooth value functions by derivation of explicit optimality conditions at semi-smooth points and application of this result to degenerate and reflected processes;proof of semi-smoothness of the value function at degenerate points;attention to the under-selectivity issue for the long-run average and bias optimality; discussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; anddevelopment of the multi-dimensional Tanaka formula for semi-smooth functions and application of this formula to stochastic control of multi-dimensional systems with degenerate points.The book will be of interest to researchers and students in the field of stochastic control and performance optimization alike.
Relative Trace Formulas (Simons Symposia)
by Werner Müller Sug Woo Shin Nicolas TemplierA series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume. The present volume is the third and final in this series and focuses on relative trace formulas in relation to special values of L-functions, integral representations, arithmetic cycles, theta correspondence and branching laws. The first volume focused on Arthur’s trace formula, and the second volume focused on methods from algebraic geometry and representation theory. The three proceedings volumes have provided a snapshot of some of the current research, in the hope of stimulating further research on these topics. The collegial format of the symposia allowed a homogeneous set of experts to isolate key difficulties going forward and to collectively assess the feasibility of diverse approaches.