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Networks, communications, and computing have become ubiquitous and inseparable parts of everyday life. This book is based on a Special Issue of the Algorithms journal, and it is devoted to the exploration of the many-faceted relationship of networks, communications, and computing. The included papers explore the current state-of-the-art research in these areas, with a particular interest in the interactions among the fields.

Information technology industries --- communication traffic prediction --- intelligent traffic management --- deformable convolution --- attention mechanism --- the next generation of telecommunication (5G) --- deep learning --- reinforcement learning --- systematic review --- cellular networks --- underwater wireless sensor networks --- ant colony optimization algorithms --- clustering routing algorithms --- energy efficiency --- network lifetime --- unmanned aerial vehicles --- UAV placement --- metaheuristics --- routing --- NP-complete --- NP-hard --- approximation --- polynomial time algorithm --- disjoint connecting paths --- unsplittable flow --- network design --- communication traffic prediction --- intelligent traffic management --- deformable convolution --- attention mechanism --- the next generation of telecommunication (5G) --- deep learning --- reinforcement learning --- systematic review --- cellular networks --- underwater wireless sensor networks --- ant colony optimization algorithms --- clustering routing algorithms --- energy efficiency --- network lifetime --- unmanned aerial vehicles --- UAV placement --- metaheuristics --- routing --- NP-complete --- NP-hard --- approximation --- polynomial time algorithm --- disjoint connecting paths --- unsplittable flow --- network design

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Complex networks are one of the most challenging research focuses of disciplines, including physics, mathematics, biology, medicine, engineering, and computer science, among others. The interest in complex networks is increasingly growing, due to their ability to model several daily life systems, such as technology networks, the Internet, and communication, chemical, neural, social, political and financial networks. The Special Issue “Computation in Complex Networks" of Entropy offers a multidisciplinary view on how some complex systems behave, providing a collection of original and high-quality papers within the research fields of: • Community detection • Complex network modelling • Complex network analysis • Node classification • Information spreading and control • Network robustness • Social networks • Network medicine

Technology: general issues --- city interaction network --- evolution model --- preferential attachment --- WeChat --- maximum likelihood --- chimera states --- coupled map lattice --- nilpotent matrix --- community detection --- membrane algorithm --- self-organizing map network --- complex networks --- optimization --- structural balance --- minimum memory based sign adjustment --- social networks --- NW network --- convergence --- complex system simulation --- cloud computing architecture --- service-oriented modeling --- semantic search framework --- QoS-based service selection --- cascading failures --- network topology --- null models --- SciSci --- knowledge evolution --- machine learning --- bridging centrality --- disjoint nodes --- disjunct nodes --- node similarity --- overlapping nodes --- Bayesian networks --- entropy --- socio-ecological system --- complex network --- chaotic time series --- Gaussian mixture model --- maximum mean discrepancy --- angiogenesis --- network properties --- variational inference --- graph neural network --- variational autoencoder --- network embedding --- online social networks --- social media --- information spreading --- information diffusion --- cross-entropy --- cross-domain recommendation --- sentiment analysis --- latent sentiment review feature --- non-linear mapping --- dissimilarity spaces --- support vector machines --- kernel methods --- computational biology --- systems biology --- protein contact networks --- data mining --- overlapping communities --- modularity --- literary works --- genre classification --- stylistic attributes --- lemmatization --- renormalisation process --- network growth --- inverse preferential attachment --- language networks --- language development --- multilayer complex networks --- stability --- spreading control --- graph neural networks --- node classification --- active learning --- graph representation learning --- city interaction network --- evolution model --- preferential attachment --- WeChat --- maximum likelihood --- chimera states --- coupled map lattice --- nilpotent matrix --- community detection --- membrane algorithm --- self-organizing map network --- complex networks --- optimization --- structural balance --- minimum memory based sign adjustment --- social networks --- NW network --- convergence --- complex system simulation --- cloud computing architecture --- service-oriented modeling --- semantic search framework --- QoS-based service selection --- cascading failures --- network topology --- null models --- SciSci --- knowledge evolution --- machine learning --- bridging centrality --- disjoint nodes --- disjunct nodes --- node similarity --- overlapping nodes --- Bayesian networks --- entropy --- socio-ecological system --- complex network --- chaotic time series --- Gaussian mixture model --- maximum mean discrepancy --- angiogenesis --- network properties --- variational inference --- graph neural network --- variational autoencoder --- network embedding --- online social networks --- social media --- information spreading --- information diffusion --- cross-entropy --- cross-domain recommendation --- sentiment analysis --- latent sentiment review feature --- non-linear mapping --- dissimilarity spaces --- support vector machines --- kernel methods --- computational biology --- systems biology --- protein contact networks --- data mining --- overlapping communities --- modularity --- literary works --- genre classification --- stylistic attributes --- lemmatization --- renormalisation process --- network growth --- inverse preferential attachment --- language networks --- language development --- multilayer complex networks --- stability --- spreading control --- graph neural networks --- node classification --- active learning --- graph representation learning

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Study 79 contains a collection of papers presented at the Conference on Discontinuous Groups and Ricmann Surfaces at the University of Maryland, May 21-25, 1973. The papers, by leading authorities, deal mainly with Fuchsian and Kleinian groups, Teichmüller spaces, Jacobian varieties, and quasiconformal mappings. These topics are intertwined, representing a common meeting of algebra, geometry, and analysis.

Group theory --- Complex analysis --- Number theory --- RIEMANN SURFACES --- Discontinuous groups --- congresses --- Congresses --- Riemann surfaces --- Congresses. --- Groupes discontinus --- Combinatorial topology --- Functions of complex variables --- Surfaces, Riemann --- Functions --- Abelian variety. --- Adjunction (field theory). --- Affine space. --- Algebraic curve. --- Algebraic structure. --- Analytic function. --- Arithmetic genus. --- Automorphism. --- Bernhard Riemann. --- Boundary (topology). --- Cauchy sequence. --- Cauchy–Schwarz inequality. --- Cayley–Hamilton theorem. --- Closed geodesic. --- Combination. --- Commutative diagram. --- Commutator subgroup. --- Compact Riemann surface. --- Complex dimension. --- Complex manifold. --- Complex multiplication. --- Complex space. --- Complex torus. --- Congruence subgroup. --- Conjugacy class. --- Convex set. --- Cyclic group. --- Degeneracy (mathematics). --- Diagram (category theory). --- Diffeomorphism. --- Differential form. --- Dimension (vector space). --- Disjoint sets. --- E7 (mathematics). --- Endomorphism. --- Equation. --- Equivalence class. --- Euclidean space. --- Existence theorem. --- Existential quantification. --- Finite group. --- Finitely generated group. --- Fuchsian group. --- Fundamental domain. --- Fundamental lemma (Langlands program). --- Fundamental polygon. --- Galois extension. --- Holomorphic function. --- Homeomorphism. --- Homology (mathematics). --- Homomorphism. --- Hurwitz's theorem (number theory). --- Inclusion map. --- Inequality (mathematics). --- Inner automorphism. --- Intersection (set theory). --- Irreducibility (mathematics). --- Isomorphism class. --- Isomorphism theorem. --- Jacobian variety. --- Jordan curve theorem. --- Kleinian group. --- Limit point. --- Mapping class group. --- Metric space. --- Monodromy. --- Monomorphism. --- Möbius transformation. --- Non-Euclidean geometry. --- Orthogonal trajectory. --- Permutation. --- Polynomial. --- Power series. --- Projective variety. --- Quadratic differential. --- Quadric. --- Quasi-projective variety. --- Quasiconformal mapping. --- Quotient space (topology). --- Rectangle. --- Riemann mapping theorem. --- Riemann surface. --- Schwarzian derivative. --- Simply connected space. --- Simultaneous equations. --- Special case. --- Subgroup. --- Subsequence. --- Surjective function. --- Symmetric space. --- Tangent space. --- Teichmüller space. --- Theorem. --- Topological space. --- Topology. --- Uniqueness theorem. --- Unit disk. --- Variable (mathematics). --- Winding number. --- Word problem (mathematics). --- RIEMANN SURFACES - congresses --- Discontinuous groups - Congresses --- Geometrie algebrique --- Fonctions d'une variable complexe --- Surfaces de riemann

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Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area.The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.

Differential geometry. Global analysis --- Manifolds (Mathematics) --- Piecewise linear topology --- Triangulating manifolds --- Variétés (Mathématiques) --- Topologie linéaire par morceaux --- 515.16 --- Manifolds, Triangulating --- PL topology --- Topology --- Geometry, Differential --- Topology of manifolds --- Piecewise linear topology. --- Triangulating manifolds. --- Manifolds (Mathematics). --- 515.16 Topology of manifolds --- Variétés (Mathématiques) --- Topologie linéaire par morceaux --- Triangulation. --- Triangulation --- Affine space. --- Algebraic topology (object). --- Approximation. --- Associative property. --- Automorphism. --- Big O notation. --- CW complex. --- Calculation. --- Cap product. --- Cartesian product. --- Category of sets. --- Chain complex. --- Classification theorem. --- Classifying space. --- Cobordism. --- Codimension. --- Cofibration. --- Cohomology. --- Connected space. --- Continuous function (set theory). --- Continuous function. --- Counterexample. --- Diffeomorphism. --- Differentiable manifold. --- Differential structure. --- Differential topology. --- Dimension (vector space). --- Direct proof. --- Disjoint union. --- Elementary proof. --- Embedding. --- Euclidean space. --- Existence theorem. --- Existential quantification. --- Fiber bundle. --- Fibration. --- General position. --- Geometry. --- Group homomorphism. --- H-cobordism. --- H-space. --- Handle decomposition. --- Handlebody. --- Hauptvermutung. --- Hausdorff space. --- Hilbert cube. --- Homeomorphism group. --- Homeomorphism. --- Homomorphism. --- Homotopy group. --- Homotopy. --- Inclusion map. --- Injective function. --- Invertible matrix. --- K-cell (mathematics). --- Kan extension. --- Linear subspace. --- Linear topology. --- Manifold. --- Mapping cylinder. --- Mathematical induction. --- Mathematician. --- Metric space. --- Morse theory. --- Neighbourhood (mathematics). --- Open set. --- Partition of unity. --- Piecewise linear manifold. --- Piecewise linear. --- Poincaré conjecture. --- Polyhedron. --- Principal bundle. --- Product metric. --- Pushout (category theory). --- Regular homotopy. --- Retract. --- Sheaf (mathematics). --- Simplicial complex. --- Smoothing. --- Spin structure. --- Stability theory. --- Stable manifold. --- Standard map. --- Submanifold. --- Submersion (mathematics). --- Subset. --- Surgery exact sequence. --- Surjective function. --- Theorem. --- Topological group. --- Topological manifold. --- Topological space. --- Topology. --- Transversal (geometry). --- Transversality (mathematics). --- Transversality theorem. --- Union (set theory). --- Uniqueness theorem. --- Vector bundle. --- Zorn's lemma. --- Variétés topologiques

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On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial.Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials.

Knot theory --- Knots (Topology) --- Low-dimensional topology --- Knot theory. --- Algebraic topology --- 3-sphere. --- Addition theorem. --- Addition. --- Alexander polynomial. --- Algebraic variety. --- Algorithm. --- Ambient isotopy. --- Arf invariant. --- Basepoint. --- Bijection. --- Bilinear form. --- Borromean rings. --- Bracket polynomial. --- Braid group. --- Branched covering. --- Chiral knot. --- Chromatic polynomial. --- Cobordism. --- Codimension. --- Combination. --- Combinatorics. --- Complex analysis. --- Concentric. --- Conjecture. --- Connected sum. --- Conway polynomial (finite fields). --- Counting. --- Covering space. --- Cyclic group. --- Dense set. --- Determinant. --- Diagram (category theory). --- Diffeomorphism. --- Dimension. --- Disjoint union. --- Disk (mathematics). --- Dual graph. --- Elementary algebra. --- Embedding. --- Enumeration. --- Existential quantification. --- Exotic sphere. --- Fibration. --- Formal power series. --- Fundamental group. --- Geometric topology. --- Geometry and topology. --- Geometry. --- Group action. --- Homotopy. --- Integer. --- Intersection form (4-manifold). --- Isolated singularity. --- Jones polynomial. --- Knot complement. --- Knot group. --- Laws of Form. --- Lens space. --- Linking number. --- Manifold. --- Module (mathematics). --- Morwen Thistlethwaite. --- Normal bundle. --- Notation. --- Obstruction theory. --- Operator algebra. --- Pairing. --- Parity (mathematics). --- Partition function (mathematics). --- Planar graph. --- Point at infinity. --- Polynomial ring. --- Polynomial. --- Quantity. --- Rectangle. --- Reidemeister move. --- Remainder. --- Root of unity. --- Saddle point. --- Seifert surface. --- Singularity theory. --- Slice knot. --- Special case. --- Statistical mechanics. --- Substructure. --- Summation. --- Symmetry. --- Theorem. --- Three-dimensional space (mathematics). --- Topological space. --- Torus knot. --- Trefoil knot. --- Tubular neighborhood. --- Underpinning. --- Unknot. --- Variable (mathematics). --- Whitehead link. --- Wild knot. --- Writhe. --- Variétés topologiques --- Topologie combinatoire --- Theorie des noeuds