Martin Grotschel is one of the most influential mathematicians of our time. He has received numerous honors and holds a number of key positions in the international mathematical community. He celebrated his 65th birthday on September 10, 2013. Martin Grotschel s doctoral descendant tree 1983 2012, i.e., the first 30 years, features 39 children, 74 grandchildren, 24 great-grandchildren and 2 great-great-grandchildren, a total of 139 doctoral descendants.

This book starts with a personal tribute to Martin Grotschel by the editors (Part I), a contribution by his very special predecessor Manfred Padberg on Facets and Rank of Integer Polyhedra (Part II), and the doctoral descendant tree 1983 2012 (Part III). The core of this book (Part IV) contains 16 contributions, each of which is coauthored by at least one doctoral descendant.

The sequence of the articles starts with contributions to the theory of mathematical optimization, including polyhedral combinatorics, extended formulations, mixed-integer convex optimization, super classes of perfect graphs, efficient algorithms for subtree-telecenters, junctions in acyclic graphs and preemptive restricted strip covering, as well as efficient approximation of non-preemptive restricted strip covering.

Combinations of new theoretical insights with algorithms and experiments deal with network design problems, combinatorial optimization problems with submodular objective functions and more general mixed-integer nonlinear optimization problems. Applications include VLSI layout design, systems biology, wireless network design, mean-risk optimization and gas network optimization.

Computational studies include a semidefinite branch and cut approach for the max k-cut problem, mixed-integer nonlinear optimal control, and mixed-integer linear optimization for scheduling and routing of fly-in safari planes.

The two closing articles are devoted to computational advances in general mixed integer linear optimization, the first by scientists working in industry, the second by scientists working in academia.

These articles reflect the scientific facets of Martin Grotschel who has set standards in theory, computation and applications.

This book provides state-of-the-art results and theories in homogeneous turbulence, including anisotropy and compressibility effects with extension to quantum turbulence, magneto-hydodynamic turbulence and turbulence in non-newtonian fluids. Each chapter is devoted to a given type of interaction (strain, rotation, shear, etc.), and presents and compares experimental data, numerical results, analysis of the Reynolds stress budget equations and advanced multipoint spectral theories. The role of both linear and non-linear mechanisms is emphasized. The link between the statistical properties and the dynamics of coherent structures is also addressed. Despite its restriction to homogeneous turbulence, the book is of interest to all people working in turbulence, since the basic physical mechanisms which are present in all turbulent flows are explained. The reader will find a unified presentation of the results and a clear presentation of existing controversies. Special attention is given to bridge the results obtained in different research communities. Mathematical tools and advanced physical models are detailed in dedicated chapters.

A unique, integrated treatment of computer modeling and simulation "The future of science belongs to those willing to make the shift to simulation-based modeling," predicts Rice Professor James Thompson, a leading modeler and computational statistician widely known for his original ideas and engaging style. He discusses methods, available to anyone with a fast desktop computer, for integrating simulation into the modeling process in order to create meaningful models of real phenomena. Drawing from a wealth of experience, he gives examples from trading markets, oncology, epidemiology, statistical process control, physics, public policy, combat, real-world optimization, Bayesian analyses, and population dynamics. Dr. Thompson believes that, so far from liberating us from the necessity of modeling, the fast computer enables us to engage in realistic models of processes in , for example, economics, which have not been possible earlier because simple stochastic models in the forward temporal direction generally become quite unmanageably complex when one is looking for such things as likelihoods. Thompson shows how simulation may be used to bypass the necessity of obtaining likelihood functions or moment-generating functions as a precursor to parameter estimation. Simulation: A Modeler’s Approach is a provocative and practical guide for professionals in applied statistics as well as engineers, scientists, computer scientists, financial analysts, and anyone with an interest in the synergy between data, models, and the digital computer.

This book is offers a comprehensive overview of information theory and error control coding, using a different approach then in existed literature. The chapters are organized according to the Shannon system model, where one block affects the others. A relatively brief theoretical introduction is provided at the beginning of every chapter, including a few additional examples and explanations, but without any proofs. And a short overview of some aspects of abstract algebra is given at the end of the corresponding chapters. The characteristic complex examples with a lot of illustrations and tables are chosen to provide detailed insights into the nature of the problem. Some limiting cases are presented to illustrate the connections with the theoretical bounds. The numerical values are carefully selected to provide in-depth explanations of the described algorithms. Although the examples in the different chapters can be considered separately, they are mutually connected and the conclusions for one considered problem relate to the others in the book.

This book discusses control units represented by the model of a finite state machine (FSM). It contains various original methods and takes into account the peculiarities of field-programmable gate arrays (FPGA) chips and a FSM model. It shows that one of the peculiarities of FPGA chips is the existence of embedded memory blocks (EMB). The book is devoted to the solution of problems of logic synthesis and reduction of hardware amount in control units. The book will be interesting and useful for researchers and PhD students in the area of Electrical Engineering and Computer Science, as well as for designers of modern digital systems.

The aim of this book is to describe the methods leading to mechanical and numerical modelling of the linear vibrations of elastic structures coupled with internal fluids (sloshing, hydroelasticity and structural acoustics). It is characteristic of the problems under consideration that they are multidisciplinary involving structural and fluid representation and related numerical aspects. The problems are solved by direct resolution of the coupled systems by finite element methods and modal reduction procedures using the eigenmodes of ?elementary subsystems?. The numerical methods described in this book have applications in various engineering disciplines such as the automotive and aerospace industries, civil engineering, nuclear engineering and bioengineering.

This book focuses on unhealthy cyber-physical systems. Consisting of 14 chapters, it discusses recognizing the beginning of the fault, diagnosing the appearance of the fault, and stopping the system or switching to a special control mode known as fault-tolerant control. Each chapter includes the background, motivation, quantitative development (equations), and case studies/illustration/tutorial (simulations, experiences, curves, tables, etc.). Readers can easily tailor the techniques presented to accommodate their ad hoc applications.

The focus of this thesis is the interplay of synchrony and adaptivity in complex networks. Synchronization is a ubiquitous phenomenon observed in different contexts in physics, chemistry, biology, neuroscience, medicine, socioeconomic systems, and engineering. Most prominently, synchronization takes place in the brain, where it is associated with cognitive capacities like learning and memory, but is also a characteristic of neurological diseases like Parkinson and epilepsy. Adaptivity is common in many networks in nature and technology, where the connectivity changes in time, i.e., the strength of the coupling is continuously adjusted depending upon the dynamic state of the system, for instance synaptic neuronal plasticity in the brain. This research contributes to a fundamental understanding of various synchronization patterns, including hierarchical multifrequency clusters, chimeras and other partial synchronization states. After a concise survey of the fundamentals of adaptive and complex dynamical networks and synaptic plasticity, in the first part of the thesis the existence and stability of cluster synchronization in globally coupled adaptive networks is discussed for simple paradigmatic phase oscillators as well as for a more realistic neuronal oscillator model with spike-timing dependent plasticity. In the second part of the thesis the interplay of adaptivity and connectivity is investigated for more complex network structures like nonlocally coupled rings, random networks, and multilayer systems. Besides presenting a plethora of novel, sometimes intriguing patterns of synchrony, the thesis makes a number of pioneering methodological advances, where rigorous mathematical proofs are given in the Appendices. These results are of interest not only from a fundamental point of view, but also with respect to challenging applications in neuroscience and technological systems.

This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications. Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method.

This book illustrates how to use description logic-based formalisms to their full potential in the creation, indexing, and reuse of multimedia semantics. To do so, it introduces researchers to multimedia semantics by providing an in-depth review of state-of-the-art standards, technologies, ontologies, and software tools. It draws attention to the importance of formal grounding in the knowledge representation of multimedia objects, the potential of multimedia reasoning in intelligent multimedia applications, and presents both theoretical discussions and best practices in multimedia ontology engineering. Readers already familiar with mathematical logic, Internet, and multimedia fundamentals will learn to develop formally grounded multimedia ontologies, and map concept definitions to high-level descriptors. The core reasoning tasks, reasoning algorithms, and industry-leading reasoners are presented, while scene interpretation via reasoning is also demonstrated. Overall, this book offers readers an essential introduction to the formal grounding of web ontologies, as well as a comprehensive collection and review of description logics (DLs) from the perspectives of expressivity and reasoning complexity. It covers best practices for developing multimedia ontologies with formal grounding to guarantee decidability and obtain the desired level of expressivity while maximizing the reasoning potential. The capabilities of such multimedia ontologies are demonstrated by DL implementations with an emphasis on multimedia reasoning applications.

This monograph deals with the mechanics and thermodynamics of materials with memory, including properties of the dynamical equations that describe their evolution in time under varying loads. A work in four parts, the first is an introduction to continuum mechanics, including classical fluid mechanics, linear and non-linear elasticity. The second part considers continuum thermodynamics and its use to derive constitutive equations of materials with memory, including viscoelastic solids, fluids, heat conductors and some examples of non-simple materials. In the third part, free energies for materials with linear memory constitutive relations are discussed. The concept of a minimal state is introduced. Explicit formulae are presented for the minimum and related free energies. The final part deals with existence, uniqueness, and stability results for the integrodifferential equations describing the dynamical evolution of viscoelastic materials, including a new approach based on minimal states rather than histories. There are also chapters on the controllability of thermoelastic systems with memory, the Saint-Venant problem for viscoelastic materials and on the theory of inverse problems. The second edition includes a new chapter on thermoelectromagnetism as well as recent findings on minimal states and free energies. It considers the case of minimum free energies for non-simple materials and dielectrics, together with an introduction to fractional derivative models.

Introduction to Traveling Waves is an invitation to research focused on traveling waves for undergraduate and masters level students. Traveling waves are not typically covered in the undergraduate curriculum, and topics related to traveling waves are usually only covered in research papers, except for a few texts designed for students. This book includes techniques that are not covered in those texts. Through their experience involving undergraduate and graduate students in a research topic related to traveling waves, the authors found that the main difficulty is to provide reading materials that contain the background information sufficient to start a research project without an expectation of an extensive list of prerequisites beyond regular undergraduate coursework. This book meets that need and serves as an entry point into research topics about the existence and stability of traveling waves. Features Self-contained, step-by-step introduction to nonlinear waves written assuming minimal prerequisites, such as an undergraduate course on linear algebra and differential equations. Suitable as a textbook for a special topics course, or as supplementary reading for courses on modeling. Contains numerous examples to support the theoretical material. Supplementary MATLAB codes available via GitHub.

This book involves the topics on the frontier of the tissue engineering and regenerative medicine. It transits new ideas, new scientific results, and discusses on the design of the self-organized tissues. This book will have a broader readership, because it provides scientific information for diverse disciplinary fields (biology, material science, engineering, medicine, and life science). More scientists, professors, graduates, undergraduates and researchers would be inspired.This book will provide some 3D structure images that would impress the readers with intuitional and abundant information which includes experimental and simulative results.

State-space models as an important mathematical tool has been widely used in many different fields. This edited collection explores recent theoretical developments of the models and their applications in economics and finance. The book includes nonlinear andnon-Gaussian time series models, regime-switching and hidden Markov models, continuous- or discrete-time state processes, and models of equally-spaced or irregularly-spaced (discrete or continuous) observations.The contributed chapters are divided into four parts. The first part is on Particle Filtering and Parameter Learning in Nonlinear State-Space Models.The second part focuseson the application of Linear State-Space Models in Macroeconomics and Finance.The third part deals with Hidden Markov Models, Regime Switching and Mathematical Finance and the fourth part is on Nonlinear State-Space Models for High Frequency Financial Data. The book will appeal to graduate students and researchers studying state-space modeling in economics, statistics, and mathematics, as well as to finance professionals."

for one year from the date of release.

This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations. The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.

This book, first published in 1981, offers a critical review of the techniques of mathematical modelling and their appropriate application to military operations research - the analysis of data (historical data, exercise and test results, and intelligence) in preparation for war. The virtues of sophistication via simplicity, and the beauty of the artful finesse, emerge as the signature of successful modelling.

This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and cover both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.

Since the parameters in dynamical systems of biological interest are inherently positive and bounded, bounded noises are a natural way to model the realistic stochastic fluctuations of a biological system that are caused by its interaction with the external world. Bounded Noises in Physics, Biology, and Engineering is the first contributed volume devoted to the modeling of bounded noises in theoretical and applied statistical mechanics, quantitative biology, and mathematical physics. It gives an overview of the current state-of-the-art and is intended to stimulate further research. The volume is organized in four parts. The first part presents the main kinds of bounded noises and their applications in theoretical physics. The theory of bounded stochastic processes is intimately linked to its applications to mathematical and statistical physics, and it would be difficult and unnatural to separate the theory from its physical applications. The second is devoted to framing bounded noises in the theory of random dynamical systems and random bifurcations, while the third is devoted to applications of bounded stochastic processes in biology, one of the major areas of potential applications of this subject. The final part concerns the application of bounded stochastic processes in mechanical and structural engineering, the area where the renewed interest for non-Gaussian bounded noises started. Pure mathematicians working on stochastic calculus will find here a rich source of problems that are challenging from the point of view of contemporary nonlinear analysis. Bounded Noises in Physics, Biology, and Engineering is intended for scientists working on stochastic processes with an interest in both fundamental issues and applications. It will appeal to a broad range of applied mathematicians, mathematical biologists, physicists, engineers, and researchers in other fields interested in complexity theory. It is accessible to anyone with a working knowledge of stochastic modeling, from advanced undergraduates to senior researchers.

This book describes Python3 programming resources for implementing decision aiding algorithms in the context of a bipolar-valued outranking approach. These computing resources, made available under the name Digraph3, are useful in the field of Algorithmic Decision Theory and more specifically in outranking-based Multiple-Criteria Decision Aiding (MCDA). The first part of the book presents a set of tutorials introducing the Digraph3 collection of Python3 modules and its main objects, such as bipolar-valued digraphs and outranking digraphs. In eight methodological chapters, the second part illustrates multiple-criteria evaluation models and decision algorithms. These chapters are largely problem-oriented and demonstrate how to edit a new multiple-criteria performance tableau, how to build a best choice recommendation, how to compute the winner of an election and how to make rankings or ratings using incommensurable criteria. The book's third part presents three real-world decision case studies, while the fourth part addresses more advanced topics, such as computing ordinal correlations between bipolar-valued outranking digraphs, computing kernels in bipolar-valued digraphs, testing for confidence or stability of outranking statements when facing uncertain or solely ordinal criteria significance weights, and tempering plurality tyranny effects in social choice problems. The fifth and last part is more specifically focused on working with undirected graphs, tree graphs and forests. The closing chapter explores comparability, split, interval and permutation graphs. The book is primarily intended for graduate students in management sciences, computational statistics and operations research. The chapters presenting algorithms for ranking multicriteria performance records will be of computational interest for designers of web recommender systems. Similarly, the relative and absolute quantile-rating algorithms, discussed and illustrated in several chapters, will be of practical interest to public and private performance auditors.

This book addresses the challenging topic of modeling adaptive networks, which often manifest inherently complex behavior. Networks by themselves can usually be modeled using a neat, declarative, and conceptually transparent Network-Oriented Modeling approach. In contrast, adaptive networks are networks that change their structure; for example, connections in Mental Networks usually change due to learning, while connections in Social Networks change due to various social dynamics. For adaptive networks, separate procedural specifications are often added for the adaptation process. Accordingly, modelers have to deal with a less transparent, hybrid specification, part of which is often more at a programming level than at a modeling level. This book presents an overall Network-Oriented Modeling approach that makes designing adaptive network models much easier, because the adaptation process, too, is modeled in a neat, declarative, and conceptually transparent Network-Oriented Modeling manner, like the network itself. Thanks to this approach, no procedural, algorithmic, or programming skills are needed to design complex adaptive network models. A dedicated software environment is available to run these adaptive network models from their high-level specifications. Moreover, because adaptive networks are described in a network format as well, the approach can simply be applied iteratively, so that higher-order adaptive networks in which network adaptation itself is adaptive (second-order adaptation), too can be modeled just as easily. For example, this can be applied to model metaplasticity in cognitive neuroscience, or second-order adaptation in biological and social contexts. The book illustrates the usefulness of this approach via numerous examples of complex (higher-order) adaptive network models for a wide variety of biological, mental, and social processes. The book is suitable for multidisciplinary Master's and Ph.D. students without assuming much prior knowledge, although also some elementary mathematical analysis is involved. Given the detailed information provided, it can be used as an introduction to Network-Oriented Modeling for adaptive networks. The material is ideally suited for teaching undergraduate and graduate students with multidisciplinary backgrounds or interests. Lecturers will find additional material such as slides, assignments, and software.

This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth manifolds in modeling spaces other than Euclidean space, particularly the concepts of smooth atlas and tangent space, which are crucial to understanding the topic. Two of the most important concepts, namely the tangent bundle and the Lie derivative, are subsequently worked out.

A Mezze of Mathematical Methods is Volume 1 of Science by Simulation. It is a recipe book of mathematical models that can be enlivened by the transmutation of equations into computer code. In this volume, the examples chosen are an eclectic mix of systems and stories rooted in common experience, rather than those normally associated with constrained courses on Physics, Chemistry or Biology which are taught in isolation and susceptible to going out of date in a few years. Rather than a 'what' of Science, this book is aimed at the 'how', readily applied to projects by students and professionals. Written in a friendly style based upon the author's expertise in teaching and pedagogy, this mathematically rigorous book is designed for readers to follow arguments step-by-step with stand-alone chapters which can be read independently. This approach will provide a tangible and readily accessible context for the development of a wide range of interconnected mathematical ideas and computing methods that underpin the practice of Science.

"The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics. The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.