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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

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There is no term that better describes the essential features of human society than complexity. On various levels, from the decision-making processes of individuals, through to the interactions between individuals leading to the spontaneous formation of groups and social hierarchies, up to the collective, herding processes that reshape whole societies, all these features share the property of irreducibility, i.e., they require a holistic, multi-level approach formed by researchers from different disciplines. This Special Issue aims to collect research studies that, by exploiting the latest advances in physics, economics, complex networks, and data science, make a step towards understanding these economic and social systems. The majority of submissions are devoted to financial market analysis and modeling, including the stock and cryptocurrency markets in the COVID-19 pandemic, systemic risk quantification and control, wealth condensation, the innovation-related performance of companies, and more. Looking more at societies, there are papers that deal with regional development, land speculation, and the-fake news-fighting strategies, the issues which are of central interest in contemporary society. On top of this, one of the contributions proposes a new, improved complexity measure.

Information technology industries --- volatility clustering --- Baidu Index --- information demand --- generalized autoregressive conditional heteroscedasticity model (GARCH) --- mixture of distribution hypothesis --- speculation --- land acquisition --- motivation --- real estate --- development --- Ethiopia --- systemic risk --- macroprudential policy --- agent-based modelling --- inequality --- central-banking --- information transfer --- transfer entropy --- stock markets --- econophysics --- complexity science --- information theory --- economic complexity --- evolutionary dynamics --- network theory --- leveraged trading --- stock price crash risk --- threshold effect --- complexity in stock market --- entropy economics --- non-extensive cross-entropy econometrics --- non-ergodic ill-behaved inverse problems --- general system theory --- non-linear dynamics --- complex adaptive systems --- homo oeconomicus --- edge of chaos --- complexity economics --- pricing constraint --- IPO timing --- dynamic game model --- real option --- complexity of IPOs --- financial institution --- complex network --- jump volatility --- entropy weight TOPSIS --- structural entropy --- stock market --- EMD --- cluster-entropy --- Shannon-entropy --- financial markets --- time series --- dynamics --- Tsallis entropy --- copula functions --- cross-shareholding network --- finance --- cryptocurrencies --- multivariate transfer entropy --- complex networks --- liquidity proxy --- liquidity benchmark --- volatility estimate --- correlation coefficient --- partial determination --- mutual information --- forecasting market risk --- value at risk --- extreme returns --- peaks over threshold --- self-exciting point process --- discrete-time models --- generalized Pareto distribution --- dynamical complexity --- universal complexity measure --- irreversible processes --- entropies --- entropic susceptibilities --- complex systems --- multifractal analysis --- detrended cross-correlations --- minimal spanning tree --- wealth condensation --- agent-based computational economics --- bargaining --- gain function --- macroeconomics --- innovative activity --- manufacturing industry --- conjunctural movements --- cybernetics --- feedback loops --- correspondence analysis --- Polish Green Island effect --- Red Queen effect --- Kondratieff waves --- power law --- Zipf law --- gender productivity gap --- fake news --- rumor spreading --- Nash equilibrium --- evolutionarily stable strategies --- evolutionary information search dynamics --- nonlinear dynamics --- chaos --- time series analysis --- stock exchange market --- Lyapunov --- recurrence plots --- BDS --- correlation dimension --- GARCH model --- measure of economic development --- websites --- public administration sector --- municipality --- four-colour theorem --- prosumption --- platforms for participation --- location quotient --- dual graph --- Euler characteristic --- n/a

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

There is no term that better describes the essential features of human society than complexity. On various levels, from the decision-making processes of individuals, through to the interactions between individuals leading to the spontaneous formation of groups and social hierarchies, up to the collective, herding processes that reshape whole societies, all these features share the property of irreducibility, i.e., they require a holistic, multi-level approach formed by researchers from different disciplines. This Special Issue aims to collect research studies that, by exploiting the latest advances in physics, economics, complex networks, and data science, make a step towards understanding these economic and social systems. The majority of submissions are devoted to financial market analysis and modeling, including the stock and cryptocurrency markets in the COVID-19 pandemic, systemic risk quantification and control, wealth condensation, the innovation-related performance of companies, and more. Looking more at societies, there are papers that deal with regional development, land speculation, and the-fake news-fighting strategies, the issues which are of central interest in contemporary society. On top of this, one of the contributions proposes a new, improved complexity measure.

volatility clustering --- Baidu Index --- information demand --- generalized autoregressive conditional heteroscedasticity model (GARCH) --- mixture of distribution hypothesis --- speculation --- land acquisition --- motivation --- real estate --- development --- Ethiopia --- systemic risk --- macroprudential policy --- agent-based modelling --- inequality --- central-banking --- information transfer --- transfer entropy --- stock markets --- econophysics --- complexity science --- information theory --- economic complexity --- evolutionary dynamics --- network theory --- leveraged trading --- stock price crash risk --- threshold effect --- complexity in stock market --- entropy economics --- non-extensive cross-entropy econometrics --- non-ergodic ill-behaved inverse problems --- general system theory --- non-linear dynamics --- complex adaptive systems --- homo oeconomicus --- edge of chaos --- complexity economics --- pricing constraint --- IPO timing --- dynamic game model --- real option --- complexity of IPOs --- financial institution --- complex network --- jump volatility --- entropy weight TOPSIS --- structural entropy --- stock market --- EMD --- cluster-entropy --- Shannon-entropy --- financial markets --- time series --- dynamics --- Tsallis entropy --- copula functions --- cross-shareholding network --- finance --- cryptocurrencies --- multivariate transfer entropy --- complex networks --- liquidity proxy --- liquidity benchmark --- volatility estimate --- correlation coefficient --- partial determination --- mutual information --- forecasting market risk --- value at risk --- extreme returns --- peaks over threshold --- self-exciting point process --- discrete-time models --- generalized Pareto distribution --- dynamical complexity --- universal complexity measure --- irreversible processes --- entropies --- entropic susceptibilities --- complex systems --- multifractal analysis --- detrended cross-correlations --- minimal spanning tree --- wealth condensation --- agent-based computational economics --- bargaining --- gain function --- macroeconomics --- innovative activity --- manufacturing industry --- conjunctural movements --- cybernetics --- feedback loops --- correspondence analysis --- Polish Green Island effect --- Red Queen effect --- Kondratieff waves --- power law --- Zipf law --- gender productivity gap --- fake news --- rumor spreading --- Nash equilibrium --- evolutionarily stable strategies --- evolutionary information search dynamics --- nonlinear dynamics --- chaos --- time series analysis --- stock exchange market --- Lyapunov --- recurrence plots --- BDS --- correlation dimension --- GARCH model --- measure of economic development --- websites --- public administration sector --- municipality --- four-colour theorem --- prosumption --- platforms for participation --- location quotient --- dual graph --- Euler characteristic --- n/a