Matematik til informatikfag

This book constitutes the refereed proceedings of the 18th International Symposium on Algorithms and Data Structures, WADS 2023, held during July 31-August 2, 2023. The 47 regular papers, presented in this book, were carefully reviewed and selected from a total of 92 submissions. They present original research on the theory, design and application of algorithms and data structures.

Reverse mathematics studies the complexity of proving mathematical theorems and solving mathematical problems. Typical questions include: Can we prove this result without first proving that one? Can a computer solve this problem? A highly active part of mathematical logic and computability theory, the subject offers beautiful results as well as significant foundational insights.This text provides a modern treatment of reverse mathematics that combines computability theoretic reductions and proofs in formal arithmetic to measure the complexity of theorems and problems from all areas of mathematics. It includes detailed introductions to techniques from computable mathematics, Weihrauch style analysis, and other parts of computability that have become integral to research in the field. Topics and features:Provides a complete introduction to reverse mathematics, including necessary background from computability theory, second order arithmetic, forcing, induction, and model constructionOffers a comprehensive treatment of the reverse mathematics of combinatorics, including Ramsey's theorem, Hindman's theorem, and many other resultsProvides central results and methods from the past two decades, appearing in book form for the first time and including preservation techniques and applications of probabilistic argumentsIncludes a large number of exercises of varying levels of difficulty, supplementing each chapterThe text will be accessible to students with a standard first year course in mathematical logic. It will also be a useful reference for researchers in reverse mathematics, computability theory, proof theory, and related areas.Damir D. Dzhafarov is an Associate Professor of Mathematics at the University of Connecticut, CT, USA. Carl Mummert is a Professor of Computer and Information Technology at Marshall University, WV, USA.

This book teaches the fundamentals and mathematical formulas of reversible transformations (or transforms) that are used in many source coding and signal processing systems. These mathematical transforms are often necessary or crucial toward reduction of data storage and transmission rate requirements. The author emphasizes the wavelet transform as it is the preferred transform for practical application in many coding and signal processing systems. The book also covers the tap (coefficient) values for some of those filters that satisfy the perfect reconstruction property. Examples of the use of filter-based and matrix-based transforms are also provided. This self-contained work contains insight gained through research and practice, which makes it a valuable reference and tutorial for readers interested in the subject of mathematical transforms.This book:Teaches the fundamentals and mathematical formulas of reversible transformations, as well as theirapplicationsHighlights the wavelet transformation, which is the preferred transform for many practical applicationsContains insight gained through research and practice, making it a valuable resource those interested in the topic

Lattice rules are a powerful and popular form of quasi-Monte Carlo rules based on multidimensional integration lattices. This book provides a comprehensive treatment of the subject with detailed explanations of the basic concepts and the current methods used in research. This comprises, for example, error analysis in reproducing kernel Hilbert spaces, fast component-by-component constructions, the curse of dimensionality and tractability, weighted integration and approximation problems, and applications of lattice rules.

The first edition of this textbook was published in 2021. Over the past two years, we have invested in enhancing all aspects of deep learning methods to ensure the book is comprehensive and impeccable. Taking into account feedback from our readers and audience, the author has diligently updated this book. The second edition of this textbook presents control theory, transformer models, and graph neural networks (GNN) in deep learning. We have incorporated the latest algorithmic advances and large-scale deep learning models, such as GPTs, to align with the current research trends. Through the second edition, this book showcases how computational methods in deep learning serve as a dynamic driving force in this era of artificial intelligence (AI). This book is intended for research students, engineers, as well as computer scientists with interest in computational methods in deep learning. Furthermore, it is also well-suited for researchers exploring topics such as machine intelligence, robotic control, and related areas.

This book constitutes the refereed proceedings of the 16th International Conference on Graph Transformation, ICGT 2023, held as Part of STAF 2023 in Leicester, UK, in July 2023. The 14 full papers and 2 short papers presented in this book were carefully reviewed and selected from 29 submissions. The conference focuses on describing new unpublished contributions in the theory and applications of graph transformation as well as tool presentation papers that demonstrate main new features and functionalities of graph-based tools.

This book constitutes the refereed proceedings of the 20th Annual RECOMB Satellite Workshop on Comparative Genomics, RECOMB-CG 2023 which took place in Istanbul, Turkey, in April 2023. The 15 full papers included in this book were carefully reviewed and selected from 25 submissions. The papers present cutting edge research in comparative genomics, with an emphasis on computational approaches and novel experimental results.Chapters "Inferring Clusters of Orthologous and Paralogous Transcripts" and "Gene Order Phylogeny via Ancestral Genome Reconstruction under Dollo" are published Open Access under Creative Commons Attribution license (CC BY 4.0).

This book includes the refereed Selected Papers of the 20th International Conference on Computer-Aided Architectural Design. INTERCONNECTIONS: Co-computing Beyond Boundaries, CAAD Futures 2023, held in Delft, The Netherlands, in July 5¿7, 2023. The 43 full papers included in this book were carefully reviewed and selected from 144 submissions. They were organized in topical sections as follows: ¿algorithmic architectural design; AI-powered architectural ideation; performance-based design, urban models and analysis; urban design; digital design, materials and fabrication; spatial information, data and semantics; building data analysis, visualisation, interaction; and building massing and layouts.

The theory developed for  4-additive codes is the starting point for much generalization about codes over mixed alphabets. They have opened a new, emergent area of research.  The techniques used for  4-linear codes are being generalized and applied to more general codes.  By example, these codes have contributed to the classification of many nonlinear codes. Moreover, they can be considered as the starting point of many different generalizations given over mixed alphabets, thereby representing a useful area of research.  Since 2010, more than 30 papers have been published about the codes considered in the book, which includes important classes of binary codes (1-perfect, Hadamard, etc.) that are not linear in general. For example, much recent research has shown the application of the techniques described for the family of cyclic  4-linear codes.   Topics and Features:Examines everything from the basic definitions to very advanced results                             Provides numerous examples, succinctly and comprehensively gathering and using the relevant information                                                                                                         Includes examples using commands from a new Magma package, developed mostly by the same authors                                                                                                          Proposes algorithms, for instance to describe coding and decoding strategiesThis unique volume will be eminently suitable for researchers working on coding theory over rings, especially over mixed alphabets. Experts will find commands and algorithms that will be useful in the generalization to codes over mixed alphabets. Additionally, by outlining the basic theory of codes over mixed alphabets and providing numerous examples, the book will be useful to researchers wanting to be introduced to the topic.The authors are all affiliated with the Dept. of Information and Communications Engineering at the Universitat Autonoma de Barcelona, Spain. Joaquim Borges and Cristina Fernandez-Cordoba are Associate Professors, Jaume Pujol is a now retired Associate Professor, Josep Rifa is Professor Emeritus, and Merce Villanueva is Associate Professor.

This book constitutes the proceedings of the 17th International Conference on Formal Concept Analysis, ICFCA 2023, which took place in Kassel, Germany, in July 2023.The 13 full papers presented in this volume were carefully reviewed and selected from 19 submissions. The International Conference on Formal Concept Analysis serves as a platform for researchers from FCA and related disciplines to showcase and exchange their research findings. The papers are organized in two topical sections, first "Theory" and second "Applications and Visualization".

This book constitutes refereed proceedings of the Third International Conference on Computer and Communication Engineering, CCCE 2023, held in Stockholm, Sweden, in March 2023.The 18 full papers presented were carefully reviewed and selected from 36 submissions. The papers are organized in the following topical sections: image analysis and method; network model and function analysis of mobile network; system security estimation and analysis of data network; and AI-based system model and algorithm.

This book constitutes the refereed proceedings of the 31st Annual International Cryptology Conference, CRYPTO 2011, held in Santa Barbara, CA, USA in August 2011. The 42 revised full papers presented were carefully reviewed and selected from 230 submissions. The volume also contains the abstract of one invited talk. The papers are organized in topical sections on randomness and its use; computer-assisted cryptographic proofs; outsourcing and delegatin computation; symmetric cryptanalysis and constructions; secure computation: leakage and side channels; quantum cryptography; lattices and knapsacks; public-key encryption; symmetric schemes; signatures; obilvious transfer and secret sharing; and multivariate and coding-based schemes.

This book constitutes the proceedings of the 28th International Conference on Information Processing in Medical Imaging, IPMI 2023, which took place in San Carlos de Bariloche, Argentina, in June 2023.The 63 full papers presented in this volume were carefully reviewed and selected from 169 submissions. They were organized in topical sections as follows: biomarkers; brain connectomics; computer-aided diagnosis/surgery; domain adaptation; geometric deep learning; groupwise atlasing; harmonization; federated learning; image synthesis; image enhancement; multimodal learning; registration; segmentation; self supervised learning; surface analysis and segmentation.

This book constitutes the refereed proceedings of the 34th International Workshop on Combinatorial Algorithms, IWOCA 2023, held in Tainan, Taiwan, during June 7¿10, 2023. The 33 full papers included in this book were carefully reviewed and selected from 86 submissions. They were organized in topical sections as follows: algorithms and data structures; algorithmic and combinatorical aspects of cryptography and information security; algorithmic game theory and complexity of games; approximation algorithms; complexity theory; combinatorics and graph theory; combinatorial generation, enumeration and counting; combinatorial optimization; combinatorics of words; computational biology; computational geometry; decompositions and combinatorial designs; distributed and network algorithms; experimental combinatorics; fine-grained complexity; graph algorithms and modelling with graphs; graph drawing and graph labelling; network theoryand temporal graphs; quantum computing and algorithms for quantum computers; online algorithms; parameterized and exact algorithms; probabilistic and randomized algorithms; and streaming algorithms.

This book discusses Artificial Neural Networks (ANN) and their ability to predict outcomes using deep and shallow learning principles. The author first describes ANN implementation, consisting of at least three layers that must be established together with cells, one of which is input, the other is output, and the third is a hidden (intermediate) layer. For this, the author states, it is necessary to develop an architecture that will not model mathematical rules but only the action and response variables that control the event and the reactions that may occur within it. The book explains the reasons and necessity of each ANN model, considering the similarity to the previous methods and the philosophical - logical rules.

Professor Stephen A. Cook is a pioneer of the theory of computational complexity. His work on NP-completeness and the P vs. NP problem remains a central focus of this field. Cook won the 1982 Turing Award for "his advancement of our understanding of the complexity of computation in a significant and profound way." This volume includes a selection of seminal papers embodying the work that led to this award, exemplifying Cook's synthesis of ideas and techniques from logic and the theory of computation including NP-completeness, proof complexity, bounded arithmetic, and parallel and space-bounded computation. These papers are accompanied by contributed articles by leading researchers in these areas, which convey to a general reader the importance of Cook's ideas and their enduring impact on the research community. The book also contains biographical material, Cook's Turing Award lecture, and an interview. Together these provide a portrait of Cook as a recognized leader and innovator in mathematics and computer science, as well as a gentle mentor and colleague.

This volume constitutes the proceedings of the 9th International Conference on Variable Neighborhood Search, ICVNS 2023, held in Abu Dhabi, United Arab Emirates, in October 2022.The 11 full papers presented in this volume were carefully reviewed and selected from 29 submissions. The papers describe recent advances in methods and applications of variable neighborhood search.

Im Studienalltag ist oft die Mathematik von den Inhalten der Informatik durch separate Vorlesungen abgegrenzt. Dadurch wird es schwierig einzusehen, warum im Informatik-Studium so viel Mathematik unterrichtet wird. In diesem Buch werden daher Fragestellungen der Informatik in den Mittelpunkt gestellt, für die dann die benötigte Mathematik entwickelt wird.Da das Buch als Einführung geschrieben ist, genügen elementare Schulkenntnisse in Mathematik. Bruchrechnung oder das Umstellen von Gleichungen setzen wir aber als bekannt voraus. Sie sollten auch schon ein wenig programmiert haben, um die (einfachen) Programmbeispiele unmittelbar zu verstehen. Da viele Querbezüge zur Informatik dargestellt werden, eignet sich das Buch insbesondere auch zum Auffrischen der Mathematikkenntnisse - z. B. nach einer Pause zwischen Bachelor- und Master-Studium.Bei der Stoffauswahl haben wir uns an den Kernfächern der Informatik orientiert: Logik und Rechnen mit Bits, Relationen und endlicheAutomaten, Graphen und Graphenalgorithmen, Zahlen und ihre Darstellung im Computer, Primzahlen und Verschlüsselung, Differenzial- und Integralrechnung in Verbindung mit Aufwandsabschätzungen, Lineare Algebra und Codes.Wir möchten mit dem Buch auch die Grundlage dafür legen, dass Sie sich weitere Themen der Mathematik aneignen können, wenn Sie diese bei der Anwendung der Informatik für andere Disziplinen benötigen.Die zweite Auflage ist um Lösungen der Aufgaben ergänzt und enthält weitere Inhalte wie Nullstellenberechnung und beschreibende Statistik mit Beispielen aus der Informatik.

This book constitutes the proceedings of the 44th International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETS 2023, which took place in Lisbon, Portugal, in June 2023. The 21 full papers included in this book were carefully reviewed and selected from 47 submissions. They were organized in topical sections as follows: Process mining; semantics; tools; verification; timed models; model transformation. The book also includes two invited talks in full paper length.

This book constitutes the proceedings of the 20th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research, CPAIOR 2022, held in Nice, France, during May 29¿June 1, 2023. The 26 full papers and the 6 short papers presented in this book were carefully reviewed and selected from a total of 71 submissions. The content of the papers present new techniques or new applications, and provide an opportunity for researchers in one area to learn about techniques in the others. Besides they give researchers the opportunity to show how the integration of techniques from different fields can lead to interesting results on large and complex problems.

This book constitutes the refereed proceedings of the 24th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2023, held in Madison, WI, USA, during June 21¿23, 2023.The 33 full papers presented were carefully reviewed and selected from 119 submissions. IPCO is under the auspices of the Mathematical Optimization Society, and it is an important forum for presenting present recent developments in theory, computation, and applications. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.