Author : Boyan Sirakov
Publisher : World Scientific
Page : 5393 pages
File Size : 39,53 MB
Release : 2019-02-27
Category : Mathematics
ISBN : 9813272899
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Author : R. Tyrrell Rockafellar
Publisher : Springer Science & Business Media
Page : 747 pages
File Size : 49,22 MB
Release : 2009-07-17
Category : Mathematics
ISBN : 3540627723
From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Author : Andreas Holzinger
Publisher : Springer Nature
Page : 397 pages
File Size : 33,86 MB
Release : 2022
Category : Artificial intelligence
ISBN : 303104083X
This is an open access book. Statistical machine learning (ML) has triggered a renaissance of artificial intelligence (AI). While the most successful ML models, including Deep Neural Networks (DNN), have developed better predictivity, they have become increasingly complex, at the expense of human interpretability (correlation vs. causality). The field of explainable AI (xAI) has emerged with the goal of creating tools and models that are both predictive and interpretable and understandable for humans. Explainable AI is receiving huge interest in the machine learning and AI research communities, across academia, industry, and government, and there is now an excellent opportunity to push towards successful explainable AI applications. This volume will help the research community to accelerate this process, to promote a more systematic use of explainable AI to improve models in diverse applications, and ultimately to better understand how current explainable AI methods need to be improved and what kind of theory of explainable AI is needed. After overviews of current methods and challenges, the editors include chapters that describe new developments in explainable AI. The contributions are from leading researchers in the field, drawn from both academia and industry, and many of the chapters take a clear interdisciplinary approach to problem-solving. The concepts discussed include explainability, causability, and AI interfaces with humans, and the applications include image processing, natural language, law, fairness, and climate science.
Author : Olga Kosheleva
Publisher : Springer Nature
Page : 638 pages
File Size : 18,65 MB
Release : 2020-02-28
Category : Computers
ISBN : 3030310418
Data processing has become essential to modern civilization. The original data for this processing comes from measurements or from experts, and both sources are subject to uncertainty. Traditionally, probabilistic methods have been used to process uncertainty. However, in many practical situations, we do not know the corresponding probabilities: in measurements, we often only know the upper bound on the measurement errors; this is known as interval uncertainty. In turn, expert estimates often include imprecise (fuzzy) words from natural language such as "small"; this is known as fuzzy uncertainty. In this book, leading specialists on interval, fuzzy, probabilistic uncertainty and their combination describe state-of-the-art developments in their research areas. Accordingly, the book offers a valuable guide for researchers and practitioners interested in data processing under uncertainty, and an introduction to the latest trends and techniques in this area, suitable for graduate students.
Author : Samir Alamad
Publisher : Springer Nature
Page : 395 pages
File Size : 28,1 MB
Release :
Category :
ISBN : 3031497481
Author : Tim Roughgarden
Publisher : Cambridge University Press
Page : 705 pages
File Size : 18,21 MB
Release : 2021-01-14
Category : Computers
ISBN : 1108786170
There are no silver bullets in algorithm design, and no single algorithmic idea is powerful and flexible enough to solve every computational problem. Nor are there silver bullets in algorithm analysis, as the most enlightening method for analyzing an algorithm often depends on the problem and the application. However, typical algorithms courses rely almost entirely on a single analysis framework, that of worst-case analysis, wherein an algorithm is assessed by its worst performance on any input of a given size. The purpose of this book is to popularize several alternatives to worst-case analysis and their most notable algorithmic applications, from clustering to linear programming to neural network training. Forty leading researchers have contributed introductions to different facets of this field, emphasizing the most important models and results, many of which can be taught in lectures to beginning graduate students in theoretical computer science and machine learning.
Author : Mehiddin Al-Baali
Publisher : Springer Nature
Page : 307 pages
File Size : 47,60 MB
Release : 2021-12-01
Category : Mathematics
ISBN : 3030720403
This book gathers selected, peer-reviewed contributions presented at the Fifth International Conference on Numerical Analysis and Optimization (NAO-V), which was held at Sultan Qaboos University, Oman, on January 6-9, 2020. Each chapter reports on developments in key fields, such as numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, derivative-free optimization methods, programming models, and challenging applications that frequently arise in statistics, econometrics, finance, physics, medicine, biology, engineering and industry. Many real-world, complex problems can be formulated as optimization tasks, and can be characterized further as large scale, unconstrained, constrained, non-convex, nondifferentiable or discontinuous, and therefore require adequate computational methods, algorithms and software tools. These same tools are often employed by researchers working in current IT hot topics, such as big data, optimization and other complex numerical algorithms in the cloud, devising special techniques for supercomputing systems. This interdisciplinary view permeates the work included in this volume. The NAO conference series is held every three years at Sultan Qaboos University, with the aim of bringing together a group of international experts and presenting novel and advanced applications to facilitate interdisciplinary studies among pure scientific and applied knowledge. It is a venue where prominent scientists gather to share innovative ideas and know-how relating to new scientific methodologies, to promote scientific exchange, to discuss possible future cooperations, and to promote the mobility of local and young researchers.
Author : Indrasen Singh
Publisher : CRC Press
Page : 246 pages
File Size : 22,10 MB
Release : 2024-02-26
Category : Computers
ISBN : 1003836003
5G and Beyond Wireless Networks: Technology, Network Deployments, and Materials for Antenna Design offers a comprehensive overview of 5G and beyond 5G wireless networks along with emerging technologies that support the design and development of wireless networks. It also includes discussions on various materials used for practical antenna design which are suitable for 5G, beyond 5G applications, and cell-free massive MIMO systems. The book discusses the latest techniques used in 5G and beyond 5G (B5G) communication, such as non-orthogonal multiple access (NOMA), device-to-device (D2D) communication, 6G ultra-dense O-RAN, rate-splitting multiple access (RSMA), simultaneous wireless information and power transfer (SWIPT), massive multiple input multiple output (mMIMO), and cell-free massive MIMO systems, which are explained in detail for 5G and beyond cellular networks. The description of NOMA and their benefit for 5G and beyond networks is also addressed along with D2D communication for next generation cellular networks. RSMA technique is also explained for 6G communication. Detailed descriptions for the design and development of 5G and beyond networks over various techniques are included. The materials specification to design antenna for 5G application are also given. The role of metalens in designing effective antennas and material specifications for 5G applications is explained in this book. Apart from the above emerging topics, this book also gives ideas about intelligent communication, Internet of Multimedia Things (IOMT), millimeter-wave MIMO-UFMC, and fog computing cloud networks. The last chapter gives details about the legal frameworks for 5G technology for responsible and sustainable deployment. Overall, this book may benefit network design engineers and researchers working in the area of next generation cellular networks. The contents of this book will be helpful for young researchers and master students, and network design engineers who are working in the area of next generation cellular networks.
Author : Matthias A. Müller
Publisher : Logos Verlag Berlin GmbH
Page : 154 pages
File Size : 42,76 MB
Release : 2014
Category : Mathematics
ISBN : 3832538216
In this thesis, we study model predictive control (MPC) schemes for control tasks which go beyond the classical objective of setpoint stabilization. In particular, we consider two classes of such control problems, namely distributed MPC for cooperative control in networks of multiple interconnected systems, and economic MPC, where the main focus is on the optimization of some general performance criterion which is possibly related to the economics of a system. The contributions of this thesis are to analyze various systems theoretic properties occurring in these type of control problems, and to develop distributed and economic MPC schemes with certain desired (closed-loop) guarantees. To be more precise, in the field of distributed MPC we propose different algorithms which are suitable for general cooperative control tasks in networks of interacting systems. We show that the developed distributed MPC frameworks are such that the desired cooperative goal is achieved, while coupling constraints between the systems are satisfied. Furthermore, we discuss implementation and scalability issues for the derived algorithms, as well as the necessary communication requirements between the systems. In the field of economic MPC, the contributions of this thesis are threefold. Firstly, we analyze a crucial dissipativity condition, in particular its necessity for optimal steady-state operation of a system and its robustness with respect to parameter changes. Secondly, we develop economic MPC schemes which also take average constraints into account. Thirdly, we propose an economic MPC framework with self-tuning terminal cost and a generalized terminal constraint, and we show how self-tuning update rules for the terminal weight can be derived such that desirable closed-loop performance bounds can be established.
Author : Coralia Cartis
Publisher : SIAM
Page : 549 pages
File Size : 12,86 MB
Release : 2022-07-06
Category : Mathematics
ISBN : 1611976995
A popular way to assess the “effort” needed to solve a problem is to count how many evaluations of the problem functions (and their derivatives) are required. In many cases, this is often the dominating computational cost. Given an optimization problem satisfying reasonable assumptions—and given access to problem-function values and derivatives of various degrees—how many evaluations might be required to approximately solve the problem? Evaluation Complexity of Algorithms for Nonconvex Optimization: Theory, Computation, and Perspectives addresses this question for nonconvex optimization problems, those that may have local minimizers and appear most often in practice. This is the first book on complexity to cover topics such as composite and constrained optimization, derivative-free optimization, subproblem solution, and optimal (lower and sharpness) bounds for nonconvex problems. It is also the first to address the disadvantages of traditional optimality measures and propose useful surrogates leading to algorithms that compute approximate high-order critical points, and to compare traditional and new methods, highlighting the advantages of the latter from a complexity point of view. This is the go-to book for those interested in solving nonconvex optimization problems. It is suitable for advanced undergraduate and graduate students in courses on advanced numerical analysis, data science, numerical optimization, and approximation theory.
