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The issue "Mathematical Logic and Its Applications 2020" contains articles related to the following three directions: Descriptive Set Theory (3 articles). Solutions for long-standing problems, including those of A. Tarski and H. Friedman, are presented. Exact combinatorial optimization algorithms, in which the complexity relative to the source data is characterized by a low, or even first degree, polynomial (1 article). III. Applications of mathematical logic and the theory of algorithms (2 articles). The first article deals with the Jacobian and M. Kontsevich’s conjectures, and algorithmic undecidability; for these purposes, non-standard analysis is used. The second article provides a quantitative description of the balance and adaptive resource of a human. Submissions are invited for the next issue "Mathematical Logic and Its Applications 2021"

Research & information: general --- Mathematics & science --- definability --- nonconstructible reals --- projective hierarchy --- generic models --- almost disjoint forcing --- Harvey Friedman’s problem --- almost-disjoint forcing --- universal algebraic geometry --- affine algebraic geometry --- elementary equivalence --- isotypic algebras --- first order rigidity --- Ind-group --- affine spaces --- automorphisms --- free associative algebras --- Weyl algebra automorphisms --- polynomial symplectomorphisms --- deformation quantization --- infinite prime number --- semi-inner automorphism --- embeddability of varieties --- undecidability --- noncommutative Gröbner-Shirshov basis --- finitely presented algebraic systems --- algorithmic unsolvability --- turing machine --- discrete optimization --- exact algorithm --- additively exact algorithm --- graph transformation --- graph of degree 2 --- chain-cycle graph --- operation cost --- minimization of total cost --- definability of definable --- tarski problem --- type theoretic hierarchy --- adaptive resource --- resilience --- resistance --- tipping point --- theory of catastrophes

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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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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 --- n/a