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This book commemorates Solomon Marcus’s fifth death anniversary with a selection of articles in mathematics, theoretical computer science, and physics written by authors who work in Marcus’s research fields, some of whom have been influenced by his results and/or have collaborated with him.

automata theory --- formal language theory --- bio-informatics --- recursive function theory --- evolutionary processor --- network of evolutionary processors --- network topology --- theory of computation --- computational models --- intrinsic perception --- Hausdorff dimension --- fractal --- computational complexity --- Turing machine --- oracle Turing machine --- shortest computations --- quasiperiod --- formal language --- asymptotic growth --- polynomial --- membrane computing --- computational complexity theory --- P vs. NP problem --- evolutional communication --- symport/antiport --- Kolmogorov complexity --- random strings --- extractors --- finite languages --- deterministic finite cover automata --- multiple entry automata --- automata with “do not care” symbols --- similarity relations --- process calculus --- communication patterns --- control structures --- hypergraph model --- P systems --- cP systems --- NP-complete --- NP-hard --- SAT --- logarithmic time complexity

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Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled ‘Advances and Novel Approaches in Discrete Optimization’. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms.

Research & information: general --- Mathematics & science --- forgotten index --- balaban index --- reclassified the zagreb indices --- ABC4 index --- GA5 index --- HDN3(m) --- THDN3(m) --- RHDN3(m) --- degree of vertex --- extended adjacency index --- scheduling with rejection --- machine non-availability --- operator non-availability --- dynamic programming --- FPTAS --- Transportation --- batching scheduling --- total weighted completion time --- unary NP-hard --- approximation algorithm --- bi-criteria scheduling --- online algorithm --- makespan --- maximum machine cost --- competitive ratio --- network optimization --- dynamic flow --- evacuation planning --- contraflow configuration --- partial lane reversals, algorithms and complexity --- logistic supports --- scheduling algorithm --- release-time --- due-date --- divisible numbers --- lateness --- bin packing --- time complexity --- batch scheduling --- linear deterioration --- job families --- Max-cut problem --- combinatorial optimization --- deep learning --- pointer network --- supervised learning --- reinforcement learning --- capacitated lot sizing --- mixed integer formulation --- retail --- inventory --- shortages --- graph --- join product --- crossing number --- cyclic permutation --- arithmetic mean --- combinatorial generation --- method --- algorithm --- AND/OR tree --- Euler-Catalan's triangle --- labeled Dyck path --- ranking algorithm --- unranking algorithm --- Harris hawks optimizer --- load frequency control --- sensitivity analysis --- smart grid --- particle swarm optimization --- genetic algorithm --- meta-heuristics --- packing --- irregular 3D objects --- quasi-phi-function s --- nonlinear optimization --- single-machine scheduling --- minimization of maximum penalty --- dual problem --- inverse problem --- branch and bound --- LNS --- numerical conversion --- RISC --- FPGA --- embedded systems --- scheduling --- job-shop --- makespan criterion --- uncertain processing times --- forgotten index --- balaban index --- reclassified the zagreb indices --- ABC4 index --- GA5 index --- HDN3(m) --- THDN3(m) --- RHDN3(m) --- degree of vertex --- extended adjacency index --- scheduling with rejection --- machine non-availability --- operator non-availability --- dynamic programming --- FPTAS --- Transportation --- batching scheduling --- total weighted completion time --- unary NP-hard --- approximation algorithm --- bi-criteria scheduling --- online algorithm --- makespan --- maximum machine cost --- competitive ratio --- network optimization --- dynamic flow --- evacuation planning --- contraflow configuration --- partial lane reversals, algorithms and complexity --- logistic supports --- scheduling algorithm --- release-time --- due-date --- divisible numbers --- lateness --- bin packing --- time complexity --- batch scheduling --- linear deterioration --- job families --- Max-cut problem --- combinatorial optimization --- deep learning --- pointer network --- supervised learning --- reinforcement learning --- capacitated lot sizing --- mixed integer formulation --- retail --- inventory --- shortages --- graph --- join product --- crossing number --- cyclic permutation --- arithmetic mean --- combinatorial generation --- method --- algorithm --- AND/OR tree --- Euler-Catalan's triangle --- labeled Dyck path --- ranking algorithm --- unranking algorithm --- Harris hawks optimizer --- load frequency control --- sensitivity analysis --- smart grid --- particle swarm optimization --- genetic algorithm --- meta-heuristics --- packing --- irregular 3D objects --- quasi-phi-function s --- nonlinear optimization --- single-machine scheduling --- minimization of maximum penalty --- dual problem --- inverse problem --- branch and bound --- LNS --- numerical conversion --- RISC --- FPGA --- embedded systems --- scheduling --- job-shop --- makespan criterion --- uncertain processing times

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This self-contained introduction to the distributed control of robotic networks offers a distinctive blend of computer science and control theory. The book presents a broad set of tools for understanding coordination algorithms, determining their correctness, and assessing their complexity; and it analyzes various cooperative strategies for tasks such as consensus, rendezvous, connectivity maintenance, deployment, and boundary estimation. The unifying theme is a formal model for robotic networks that explicitly incorporates their communication, sensing, control, and processing capabilities--a model that in turn leads to a common formal language to describe and analyze coordination algorithms. Written for first- and second-year graduate students in control and robotics, the book will also be useful to researchers in control theory, robotics, distributed algorithms, and automata theory. The book provides explanations of the basic concepts and main results, as well as numerous examples and exercises. Self-contained exposition of graph-theoretic concepts, distributed algorithms, and complexity measures for processor networks with fixed interconnection topology and for robotic networks with position-dependent interconnection topology Detailed treatment of averaging and consensus algorithms interpreted as linear iterations on synchronous networks Introduction of geometric notions such as partitions, proximity graphs, and multicenter functions Detailed treatment of motion coordination algorithms for deployment, rendezvous, connectivity maintenance, and boundary estimation

Robotics. --- Computer algorithms. --- Robots --- Automation --- Machine theory --- Robot control --- Robotics --- Algorithms --- Control systems. --- Computer algorithms --- Control systems --- 1-center problem. --- Adjacency matrix. --- Aggregate function. --- Algebraic connectivity. --- Algebraic topology (object). --- Algorithm. --- Analysis of algorithms. --- Approximation algorithm. --- Asynchronous system. --- Bellman–Ford algorithm. --- Bifurcation theory. --- Bounded set (topological vector space). --- Calculation. --- Cartesian product. --- Centroid. --- Chebyshev center. --- Circulant matrix. --- Circumscribed circle. --- Cluster analysis. --- Combinatorial optimization. --- Combinatorics. --- Communication complexity. --- Computation. --- Computational complexity theory. --- Computational geometry. --- Computational model. --- Computer simulation. --- Computer vision. --- Connected component (graph theory). --- Connectivity (graph theory). --- Consensus (computer science). --- Control function (econometrics). --- Differentiable function. --- Dijkstra's algorithm. --- Dimensional analysis. --- Directed acyclic graph. --- Directed graph. --- Discrete time and continuous time. --- Disk (mathematics). --- Distributed algorithm. --- Doubly stochastic matrix. --- Dynamical system. --- Eigenvalues and eigenvectors. --- Estimation. --- Euclidean space. --- Function composition. --- Hybrid system. --- Information theory. --- Initial condition. --- Instance (computer science). --- Invariance principle (linguistics). --- Invertible matrix. --- Iteration. --- Iterative method. --- Kinematics. --- Laplacian matrix. --- Leader election. --- Linear dynamical system. --- Linear interpolation. --- Linear programming. --- Lipschitz continuity. --- Lyapunov function. --- Markov chain. --- Mathematical induction. --- Mathematical optimization. --- Mobile robot. --- Motion planning. --- Multi-agent system. --- Network model. --- Network topology. --- Norm (mathematics). --- Numerical integration. --- Optimal control. --- Optimization problem. --- Parameter (computer programming). --- Partition of a set. --- Percolation theory. --- Permutation matrix. --- Polytope. --- Proportionality (mathematics). --- Quantifier (logic). --- Quantization (signal processing). --- Robustness (computer science). --- Scientific notation. --- Sensor. --- Set (mathematics). --- Simply connected space. --- Simulation. --- Simultaneous equations. --- State space. --- State variable. --- Stochastic matrix. --- Stochastic. --- Strongly connected component. --- Synchronous network. --- Theorem. --- Time complexity. --- Topology. --- Variable (mathematics). --- Vector field.

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Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics-but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits.From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics.Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.

Mathematics --- Math --- Science --- Study and teaching (Higher) --- Abstract algebra. --- Addition. --- Algebra. --- Algebraic equation. --- Algebraic number. --- Algorithm. --- Arbitrarily large. --- Arithmetic. --- Axiom. --- Binomial coefficient. --- Bolzano–Weierstrass theorem. --- Calculation. --- Cantor's diagonal argument. --- Church–Turing thesis. --- Closure (mathematics). --- Coefficient. --- Combination. --- Combinatorics. --- Commutative property. --- Complex number. --- Computable number. --- Computation. --- Constructible number. --- Continuous function (set theory). --- Continuous function. --- Continuum hypothesis. --- Dedekind cut. --- Dirichlet's approximation theorem. --- Divisibility rule. --- Elementary function. --- Elementary mathematics. --- Equation. --- Euclidean division. --- Euclidean geometry. --- Exponentiation. --- Extended Euclidean algorithm. --- Factorization. --- Fibonacci number. --- Floor and ceiling functions. --- Fundamental theorem of algebra. --- Fundamental theorem. --- Gaussian integer. --- Geometric series. --- Geometry. --- Gödel's incompleteness theorems. --- Halting problem. --- Infimum and supremum. --- Integer factorization. --- Integer. --- Least-upper-bound property. --- Line segment. --- Linear algebra. --- Logic. --- Mathematical induction. --- Mathematician. --- Mathematics. --- Method of exhaustion. --- Modular arithmetic. --- Natural number. --- Non-Euclidean geometry. --- Number theory. --- Pascal's triangle. --- Peano axioms. --- Pigeonhole principle. --- Polynomial. --- Predicate logic. --- Prime factor. --- Prime number. --- Probability theory. --- Probability. --- Projective line. --- Pure mathematics. --- Pythagorean theorem. --- Ramsey theory. --- Ramsey's theorem. --- Rational number. --- Real number. --- Real projective line. --- Rectangle. --- Reverse mathematics. --- Robinson arithmetic. --- Scientific notation. --- Series (mathematics). --- Set theory. --- Sign (mathematics). --- Significant figures. --- Special case. --- Sperner's lemma. --- Subset. --- Successor function. --- Summation. --- Symbolic computation. --- Theorem. --- Time complexity. --- Turing machine. --- Variable (mathematics). --- Vector space. --- Word problem (mathematics). --- Word problem for groups. --- Zermelo–Fraenkel set theory.

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"A few short decades ago, we were informed by the smooth signals of analog television and radio; we communicated using our analog telephones; and we even computed with analog computers. Today our world is digital, built with zeros and ones. Why did this revolution occur? The Discrete Charm of the Machine explains, in an engaging and accessible manner, the varied physical and logical reasons behind this radical transformation. The spark of individual genius shines through this story of innovation: the stored program of Jacquard’s loom; Charles Babbage’s logical branching; Alan Turing’s brilliant abstraction of the discrete machine; Harry Nyquist’s foundation for digital signal processing; Claude Shannon’s breakthrough insights into the meaning of information and bandwidth; and Richard Feynman’s prescient proposals for nanotechnology and quantum computing. Ken Steiglitz follows the progression of these ideas in the building of our digital world, from the internet and artificial intelligence to the edge of the unknown. Are questions like the famous traveling salesman problem truly beyond the reach of ordinary digital computers? Can quantum computers transcend these barriers? Does a mysterious magical power reside in the analog mechanisms of the brain? Steiglitz concludes by confronting the moral and aesthetic questions raised by the development of artificial intelligence and autonomous robots. The Discrete Charm of the Machine examines why our information technology, the lifeblood of our civilization, became digital, and challenges us to think about where its future trajectory may lead." -- Publisher's description.

Digital communications. --- Technological innovations. --- Breakthroughs, Technological --- Innovations, Industrial --- Innovations, Technological --- Technical innovations --- Technological breakthroughs --- Technological change --- Creative ability in technology --- Inventions --- Domestication of technology --- Innovation relay centers --- Research, Industrial --- Technology transfer --- Communications, Digital --- Digital transmission --- Pulse communication --- Digital electronics --- Pulse techniques (Electronics) --- Telecommunication --- Digital media --- Signal processing --- Digital techniques --- Digital communications --- Technological innovations --- AND gate. --- Alan Turing. --- Algorithm. --- Analog computer. --- Analog device. --- Analog signal. --- Analog-to-digital converter. --- Artificial neural network. --- Autonomous robot. --- Bell's theorem. --- Calculation. --- Charles Babbage. --- Church–Turing thesis. --- Classical physics. --- Claude Shannon. --- Compact disc. --- Computation. --- Computer music. --- Computer program. --- Computer science. --- Computer scientist. --- Computer. --- Computing. --- Data transmission. --- Detection. --- Difference engine. --- Differential equation. --- Digital data. --- Digital electronics. --- Digital signal processing. --- Digital signal. --- Diode. --- Electrical network. --- Electricity. --- Electromagnetic radiation. --- Electronics. --- Exponential growth. --- Field-effect transistor. --- Fourier analysis. --- High frequency. --- Information theory. --- Instance (computer science). --- Instruction set. --- Integrated circuit. --- Integrator. --- Isaac Asimov. --- Johnson–Nyquist noise. --- Laptop. --- Laughter. --- Logarithm. --- Low frequency. --- Mathematician. --- Mathematics. --- Measurement. --- Microphone. --- Microphotograph. --- Microscope. --- Molecule. --- Moore's law. --- NP-completeness. --- Optical fiber. --- P versus NP problem. --- Patch panel. --- Photograph. --- Photon. --- Physicist. --- Probability. --- Processing (programming language). --- Proportionality (mathematics). --- Punched card. --- Quantity. --- Quantum computing. --- Quantum mechanics. --- Radio wave. --- Resistor. --- Result. --- Retransmission (data networks). --- Richard Feynman. --- Scientist. --- Semiconductor. --- Shot noise. --- Silicon. --- Simulation. --- Solid-state electronics. --- Sound recording and reproduction. --- Standardization. --- Technology. --- Television. --- Theorem. --- Theoretical computer science. --- Time complexity. --- Transistor. --- Turing machine. --- Uncertainty. --- Vacuum tube. --- Vacuum. --- Video. --- Wafer (electronics). --- Wave–particle duality. --- Your Computer (British magazine).