Matematisk datateori

This book is the first to present a comprehensive investigation of the technical features of the metainferential logics developed in the last years, with their most relevant results and applications. It provides some new paths to define and investigate metainferential logics and offers a thorough study of the semantics and the proof-theories of this new and exciting variety of families of logics.This volume examines the hierarchies of metainferential logics and gives a general and systematic theory of them, and of the truth theories based on these logics. This book puts forward the prospects for truth-theories based on the metainferential logics of the TS/ST hierarchy and argues for its promise noting that each of these logics can be safely expanded with a transparent truth predicate. It also goes onto to explore new developments in three fields related to logics ¿ namely metainferential logics built by means of the Weak Kleene schema and combining them with logics defined through the Strong Kleene schema, proof-theoretic presentations, and those with a with a global or an absolutely global validity standard, instead of a local one. This book is of interest to scholars in formal logic.

This book provides a comprehensive introduction to the foundations and frontiers of graph neural networks. In addition, the book introduces the basic concepts and definitions in graph representation learning and discusses the development of advanced graph representation learning methods with a focus on graph neural networks. The book providers researchers and practitioners with an understanding of the fundamental issues as well as a launch point for discussing the latest trends in the science. The authors emphasize several frontier aspects of graph neural networks and utilize graph data to describe pairwise relations for real-world data from many different domains, including social science, chemistry, and biology. Several frontiers of graph neural networks are introduced, which enable readers to acquire the needed techniques of advances in graph neural networks via theoretical models and real-world applications. 

This book comprehensively introduces readers to Digital Twins, from the basic concepts, core technologies and technical architecture, to application scenarios and other aspects. Readers will gain a profound understanding of the emerging discipline of Digital Twins. Covering the latest and cutting-edge application technologies of Digital Twins in various fields, the book offers practitioners concrete problem-solving strategies. At the same time, it helps those working in Digital Twins-related fields to deepen their understanding of the industry and enhance their professional knowledge and skills. Given its scope, the book can also be used as teaching material or a reference book for teachers and students of product design, industrial design, design management, design marketing and related disciplines at colleges and universities. Covering a variety of groundbreaking Digital Twins technologies, it can also provide new directions for researchers.

This book presents a methodology for the real-time scheduling problems of real-time systems (RTS) from the viewpoint of control theory. Generally, any system can be viewed as an RTS if it performs real-time application functions and behaves correctly depending on given logical activities and satisfying specified deadlines for the activities. This monograph provides broad views and detailed introductions to supervisory control theory (SCT) and its application in real-time scheduling and reconfiguration. Based on three popular SCT modelling frameworks, discrete-event system (DES), timed DES (TDES), and state-tree structures (STS), the authors provide RTS modelling frameworks; thereafter, SCT is used to find their safe execution sequences.As the main contribution, we use (untimed) DES events to represent the execution and preemption of each individual RTS task. This modelling formalism brings the possibilities to model the preemptions of tasks¿ executions. Furthermore, in somecases, priorities cannot be assigned to real-time tasks. In order to solve this problem, a matrix-based priority-free conditional-preemption (PFCP) relation is provided, which generalizes fixed-priority (FP) RTS scheduling. As a natural extension, a generalized modular modelling framework is presented to model the task parameters instead of the global real-time task. The modular models are taken to be generic entities, which also considers the exact execution time of real-time tasks. STS are undoubtedly recognized as a computationally efficient SCT framework which manages the state explosion problem significantly. Hence, building on the (untimed) modular RTS models, a novel STS-based RTS modeling framework is formulated, by assigning dynamic priorities as specified optimality criteria, which can be utilized to model sporadic RTS processing both sporadic and (multi-period) periodic tasks, providing a small set of the safe execution sequences which rank at the top.

Die Kryptographie, wie sie in diesem Jahrhundert betrieben wird, ist stark mathematisch geprägt. Aber sie hat auch ihre Wurzeln in dem, was rechnerisch machbar ist.In diesem einzigartigen Lehrbuch werden die Theoreme der Mathematik gegen die Machbarkeit von Berechnungen abgewogen. Kryptografie ist etwas, das man tatsächlich "macht", kein mathematisches Spiel, über das man Theoreme beweist. Es gibt tiefgründige Mathematik; es gibt einige Theoreme, die bewiesen werden müssen; und es besteht die Notwendigkeit, die brillante Arbeit derjenigen anzuerkennen, die sich auf die Theorie konzentrieren. Auf der Ebene eines Grundstudiums sollte der Schwerpunkt jedoch zunächst darauf liegen, die Algorithmen zu kennen und zu verstehen und zu wissen, wie sie zu implementieren sind, und sich auch bewusst zu machen, dass die Algorithmen sorgfältig implementiert werden müssen, um die "einfachen" Wege zum Brechen der Kryptografie zu vermeiden. Dieser Text deckt die algorithmischen Grundlagen ab und wird durch Kernmathematik und Arithmetik ergänzt.

Welcome to "Machine Learning and Algorithms: A Comprehensive Guide." In an age where data is generated at an unprecedented pace and technology continually reshapes the landscape, understanding the fundamental concepts of machine learning and algorithms has become essential.This book is designed to be your companion on a journey through the captivating realm of machine learning and algorithms. Whether you're a student taking your first steps into this exciting field, a professional looking to enhance your skills, or simply curious about the inner workings of the technologies shaping our world, this comprehensive guide aims to provide you with a solid foundation and a clear path forward.

This open access book gives a systematic introduction into the spectral theory of differential operators on metric graphs. Main focus is on the fundamental relations between the spectrum and the geometry of the underlying graph.The book has two central themes: the trace formula and inverse problems.The trace formula is relating the spectrum to the set of periodic orbits and is comparable to the celebrated Selberg and Chazarain-Duistermaat-Guillemin-Melrose trace formulas. Unexpectedly this formula allows one to construct non-trivial crystalline measures and Fourier quasicrystals solving one of the long-standing problems in Fourier analysis. The remarkable story of this mathematical odyssey is presented in the first part of the book.To solve the inverse problem for Schrödinger operators on metric graphs the magnetic boundary control method is introduced. Spectral data depending on the magnetic flux allow one to solve the inverse problem in full generality, this means to reconstruct not only the potential on a given graph, but also the underlying graph itself and the vertex conditions.The book provides an excellent example of recent studies where the interplay between different fields like operator theory, algebraic geometry and number theory, leads to unexpected and sound mathematical results. The book is thought as a graduate course book where every chapter is suitable for a separate lecture and includes problems for home studies. Numerous illuminating examples make it easier to understand new concepts and develop the necessary intuition for further studies.

This book, fully updated for Python version 3.6+, covers the key ideas that link probability, statistics, and machine learning illustrated using Python modules in these areas.  All the figures and numerical results are reproducible using the Python codes provided. The author develops key intuitions in machine learning by working meaningful examples using multiple analytical methods and Python codes, thereby connecting theoretical concepts to concrete implementations. Detailed proofs for certain important results are also provided. Modern Python modules like Pandas, Sympy, Scikit-learn, Tensorflow, and Keras are applied to simulate and visualize important machine learning concepts like the bias/variance trade-off, cross-validation, and regularization. Many abstract mathematical ideas, such as convergence in probability theory, are developed and illustrated with numerical examples. This updated edition now includes the Fisher Exact Test and the Mann-Whitney-Wilcoxon Test. A new section on survival analysis has been included as well as substantial development of Generalized Linear Models. The new deep learning section for image processing includes an in-depth discussion of gradient descent methods that underpin all deep learning algorithms.   As with the prior edition, there are new and updated *Programming Tips* that the illustrate effective Python modules and methods for scientific programming and machine learning. There are 445 run-able code blocks with corresponding outputs that have been tested for accuracy.  Over 158 graphical visualizations (almost all generated using Python) illustrate the concepts that are developed both in code and in mathematics. We also discuss and use key Python modules such as Numpy, Scikit-learn, Sympy,  Scipy, Lifelines, CvxPy, Theano, Matplotlib, Pandas, Tensorflow, Statsmodels,  and Keras.This book is suitable for anyone with an undergraduate-level exposure to probability, statistics, or machine learning and with rudimentary knowledge of Python programming.

This volume includes six lectures given at the ICTAC (International Colloquium on Theoretical Aspects of Computing) School on Formal Methods for an Informal World, held on September 1-7, 2021, originally scheduled to take place in Astana but held in virtual mode due to the pandemic.The school addressed the use of formal methods at various levels of rigour in different application domains: human-computer interaction, cognitive science, business process management, robotics, and healthcare. The emphasis of the school was on practical applications in which formal methods provide unambiguous descriptions of the real world that facilitate understanding and formal and informal analysis. The target audience consists of graduate students, young researchers and industrial practitioners, from both computer science and other fields that make use of computational methods.

One of the main benefits of this book is that it presents a comprehensive and innovative eHealth framework that leverages deep learning and IoT wearable devices for the evaluation of Parkinson's disease patients. This framework offers a new way to assess and monitor patients' motor deficits in a personalized and automated way, improving the efficiency and accuracy of diagnosis and treatment.Compared to other books on eHealth and Parkinson's disease, this book offers a unique perspective and solution to the challenges facing patients and healthcare providers. It combines state-of-the-art technology, such as wearable devices and deep learning algorithms, with clinical expertise to develop a personalized and efficient evaluation framework for Parkinson's disease patients.This book provides a roadmap for the integration of cutting-edge technology into clinical practice, paving the way for more effective and patient-centered healthcare. To understand this book, readers should have a basic knowledge of eHealth, IoT, deep learning, and Parkinson's disease. However, the book provides clear explanations and examples to make the content accessible to a wider audience, including researchers, practitioners, and students interested in the intersection of technology and healthcare.

This book constitutes the refereed proceedings of the 21st Asian Symposium on Programming Languages and Systems, APLAS 2023, held in Taipei, Taiwan, during November 26¿29, 2023.The 15 full papers included in this book are carefully reviewed and selected from 32 submissions. They were organized in topical sections as follows: semantics, logics, and foundational theory; design of languages, type systems, and foundational calculi; domain-specific languages; compilers, interpreters, and abstract machines; program derivation, synthesis, and transformation; program analysis, verification, and model-checking; logic, constraint, probabilistic, and quantum programming; software security; concurrency and parallelism; tools and environments for programming and implementation; and applications of SAT/SMT to programming and implementation.

This book constitutes the refereed proceedings of the XXIInd International Conference on AIxIA 2023 ¿ Advances in Artificial Intelligence, AIxIA 2023, held in Rome, Italy, during November 6¿10, 2023.The 33 full papers included in this book were carefully reviewed and selected from 53 submissions. They were organized in topical sections as follows: Argumentation and Logic Programming, Natural Language Processing, Machine Learning, Hybrid AI and Applications of AI.

This book explores music with respect to quantum computing, a nascent technology that is advancing rapidly. There is a long history of research into using computers for music since the 1950s.Nowadays, computers are essential for the music economy. Therefore, it is very likely that quantum computers will impact the music industry in the time to come.  Consequently, a new area of research and development is emerging: Quantum Computer Music.This unprecedented book presents the new field of Quantum Computer Music. It introduces the fundamentals of quantum computing for musicians and the latest developments by pioneering practitioners.

This monograph introduces a novel multiset-based conceptual, mathematical and knowledge engineering paradigm, called multigrammatical framework (MGF), used for planning and scheduling in resource-consuming, resource-producing (industrial) and resource-distributing (economical) sociotechnological systems (STS). This framework is meant to enable smart operation not only in a "e;business-as-usual"e; mode, but also in extraordinary, highly volatile or hazardous environments. It is the result of convergence and deep integration into a unified, flexible and effectively implemented formalism operating on multisets of several well-known paradigms from classical operations research and modern knowledge engineering, such as: mathematical programming, game theory, optimal scheduling, logic programming and constraint programming. The mathematical background needed for MGF, its algorithmics, applications, implementation issues, as well as its nexus with known models from operations research and theoretical computer science areas are considered. The resilience and recovery issues of an STS are studied by applying the MGF toolkit and on paying special attention to the multigrammatical assessment of resilience of energy infrastructures. MGF-represented resource-based games are introduced, and directions for further development are discussed. The author presents multiple applications to business intelligence, critical infrastructure, ecology, economy and industry. This book is addressed to scholars working in the areas of theoretical and applied computer science, artificial intelligence, systems analysis, operations research, mathematical economy and critical infrastructure protection, to engineers developing software-intensive solutions for implementation of the knowledge-based digital economy and Industry 4.0, as well as to students, aspirants and university staff. Foundational knowledge of set theory, mathematical logic and routine operations on data bases is needed to read this book. The content of the monograph is gradually presented, from simple to complex, in a well-understandable step-by-step manner. Multiple examples and accompanying figures are included in order to support the explanation of the various notions, expressions and algorithms.

This book constitutes the refereed proceedings of the 11th International Conference on Code-Based Cryptography, CBCrypto 2023, held in Lyon, France, during April 22¿23, 2023. The 8 full papers included in this book were carefully reviewed and selected from 28 submissions. The conference offers a wide range of many important aspects of code-based cryptography such as cryptanalysis of existing schemes, the proposal of new cryptographic systems and protocols as well as improved decoding algorithms.

These two volumes constitute the proceedings of the 10th International Symposium on Integrated Uncertainty in Knowledge Modelling and Decision Making, IUKM 2023, held in Kanazawa, Japan, during November 2-4, 2023. The 58 full papers presented were carefully reviewed and selected from 107 submissions. The papers deal with all aspects of research results, ideas, and experiences of application among researchers and practitioners involved with all aspects of uncertainty modelling and management.

These two volumes constitute the proceedings of the 10th International Symposium on Integrated Uncertainty in Knowledge Modelling and Decision Making, IUKM 2023, held in Kanazawa, Japan, during November 2-4, 2023.The 58 full papers presented were carefully reviewed and selected from 107 submissions. The papers deal with all aspects of research results, ideas, and experiences of application among researchers and practitioners involved with all aspects of uncertainty modelling and management.

This book constitutes the proceedings of the First International Conference on Complex Computational Ecosystems, CCE 2023, held in Baku, Azerbaijan, during April 25¿27, 2023. The 16 full papers and the 4 keynote abstracts included in this volume were carefully reviewed and selected from 46 submissions. They explore trans-disciplinary challenges that crossed theoretical questions with empirical observations of multi-level and multi-modal computational ecosystems.

This volume LNCS 14213 constitutes the refereed proceedings of the 19th International Conference, LENLS 2019, held in November 2022, in Tokyo, Japan.The 13 full papers presented were carefully reviewed and selected from 34 submissions. The conference focuses on theoretical and computational linguistics covering topics ranging from syntax, semantics, and pragmatics to the philosophy of language and natural language processing.

This book constitutes the refereed proceedings of the 30th International Symposium on Static Analysis, SAS 2023, held in Lisbon, Portugal, in October 2023. The 20 full papers included in this book were carefully reviewed and selected from 40 submissions. Static analysis is widely recognized as a fundamental tool for program verification, bug detection, compiler optimization, program understanding, and software maintenance. The papers deal with theoretical, practical and application advances in the area.Chapter 21 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Bei klassischer Vorgehensweise werden die Identität des Erstellers und die Echtheit eines Dokuments durch manuelle Unterschrift auf Papier bezeugt. Dieses Vorgehen ist bei digitalen Texten und Nachrichten so nicht mehr möglich. Will man digitalisierte Daten unterschreiben und somit deren Echtheit und die eigene Identität bezeugen, so spricht man von einer digitalen Signatur. Dieses Buch beschreibt die drei wichtigsten Verfahren, nämlich die RSA-Signatur, die DSA-Signatur und die ECDSA-Signatur. Hierfür werden die jeweiligen algebraischen Grundlagen bereitgestellt.

This book constitutes the post-conference proceedings of the satellite events held at the 20th Extended Semantic Web Conference, ESWC 2023, held in Hersonissos, Greece, during May 28¿June 1, 2023.The 50 full papers included in this book were carefully reviewed and selected from 109 submissions. They were organized in sections as follows: Posters and Demos, Industry, and PhD Symposium.