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Symmetry and complexity are the focus of a selection of outstanding papers, ranging from pure Mathematics and Physics to Computer Science and Engineering applications. This collection is based around fundamental problems arising from different fields, but all of them have the same task, i.e. breaking the complexity by the symmetry. In particular, in this Issue, there is an interesting paper dealing with circular multilevel systems in the frequency domain, where the analysis in the frequency domain gives a simple view of the system. Searching for symmetry in fractional oscillators or the analysis of symmetrical nanotubes are also some important contributions to this Special Issue. More papers, dealing with intelligent prognostics of degradation trajectories for rotating machinery in engineering applications or the analysis of Laplacian spectra for categorical product networks, show how this subject is interdisciplinary, i.e. ranging from theory to applications. In particular, the papers by Lee, based on the dynamics of trapped solitary waves for special differential equations, demonstrate how theory can help us to handle a practical problem. In this collection of papers, although encompassing various different fields, particular attention has been paid to the common task wherein the complexity is being broken by the search for symmetry.

History of engineering & technology --- fractional differential equations --- fractional oscillations (vibrations) --- fractional dynamical systems --- nonlinear dynamical systems --- harmonic wavelet --- filtering --- multilevel system --- forced Korteweg-de Vries equation --- trapped solitary wave solutions --- numerical stability --- two bumps or holes --- finite difference method --- Laplacian spectra --- categorical product --- Kirchhoff index --- global mean-first passage time --- spanning tree --- degradation trajectories prognostic --- asymmetric penalty sparse decomposition (APSD) --- rolling bearings --- wavelet neural network (WNN) --- recursive least squares (RLS) --- health indicators --- first multiple Zagreb index --- second multiple Zagreb index, hyper-Zagreb index --- Zagreb polynomials --- Nanotubes

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The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects now returns with a brand-new compilation of fascinating problems and solutions in recreational mathematics.This latest volume gathers together the top experts in recreational math and presents a compelling look at board games, card games, dice, toys, computer games, and much more. The book is divided into five parts: puzzles and brainteasers, geometry and topology, graph theory, games of chance, and computational complexity. Readers will discover what origami, roulette wheels, and even the game of Trouble can teach about math. Essays contain new results, and the contributors include short expositions on their topic's background, providing a framework for understanding the relationship between serious mathematics and recreational games. Mathematical areas explored include combinatorics, logic, graph theory, linear algebra, geometry, topology, computer science, operations research, probability, game theory, and music theory.Investigating an eclectic mix of games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.

Mathematical recreations --- Mathematical puzzles --- Number games --- Recreational mathematics --- Recreations, Mathematical --- Puzzles --- Scientific recreations --- Games in mathematics education --- Magic squares --- Magic tricks in mathematics education --- Research. --- Bernard Frenicle de Bessy. --- Central Circle. --- Clickomania. --- Euclidean geometry. --- Hasbro. --- Le Professeur N. Claus. --- Leonhard Euler. --- Lewis Carroll. --- Matrix Tree Theorem. --- Multinational War. --- Penney's Game. --- Percy MacMahon. --- Pop-O-Matic Trouble. --- Raymond Smullyan. --- Tangle. --- Tower of Hanoi. --- algebraic graph theory. --- board games. --- children's card games. --- classical logic. --- coin-flipping. --- coloring. --- combinatorics. --- computer games. --- computer science. --- counting problems. --- counting trees. --- crossing numbers. --- cubes. --- distributed processing. --- dragons. --- duels. --- game theory. --- geometry. --- graph theory. --- graphs. --- gruels. --- integer programming. --- iterative duels. --- kasha. --- linear algebra. --- logic puzzles. --- logic. --- magic constant. --- magic squares. --- math. --- mathematical puzzles. --- music. --- musical arrangement. --- nine-point circle. --- nonclassical logics. --- orthocenter. --- paper folding. --- prisoners. --- probability. --- recreational mathematics. --- representation theory. --- roulette wheel. --- spanning tree. --- topology. --- triangles. --- truels. --- twenty-sided dice. --- Éduard Lucas.

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Graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, and each chapter contains math exercises for readers to savor. An eye-opening journey into the world of graphs, The Fascinating World of Graph Theory offers exciting problem-solving possibilities for mathematics and beyond.

Graph theory. --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Extremal problems --- 1-Factorization Conjecture. --- 1-factorable graph. --- 2-factorable graph. --- Alfred Bray Kempe. --- Alspach's Conjecture. --- Around the World Problem. --- Art Gallery Problem. --- Arthur Cayley. --- Brick-Factory Problem. --- Cayley's Tree Formula. --- Chinese Postman Problem. --- Christian Goldbach. --- Erdős number. --- Euler Identity. --- Euler Polyhedron Formula. --- Eulerian graph. --- First Theorem of Graph Theory. --- Five Color Theorem. --- Five Queens Problem. --- Four Color Conjecture. --- Four Color Problem. --- Gottfried Leibniz. --- Graceful Tree Conjecture. --- Hall's Theorem. --- Hamiltonian graph. --- Herbert Ellis Robbins. --- Icosian Game. --- Instant Insanity. --- Internet. --- Job-Hunters Problem. --- King Chicken Theorem. --- Kirkman's Schoolgirl Problem. --- Knight's Tour Puzzle. --- Kruskal's Algorithm. --- Kuratowski's Theorem. --- Königsberg Bridge Problem. --- Leonhard Euler. --- Lights Out Puzzle. --- Marriage Theorem. --- Minimum Spanning Tree Problem. --- Paul Erdős. --- Peter Guthrie Tait. --- Petersen graph. --- Petersen's Theorem. --- Pierre Fermat. --- Polyhedron Problem. --- Problem of the Five Princes. --- Prüfer code. --- Ramsey number. --- Reconstruction Problem. --- Road Coloring Theorem. --- Robbins's Theorem. --- Sir William Rowan Hamilton. --- Steiner triple system. --- Thomas Penyngton Kirkman. --- Three Friends or Three Strangers Problem. --- Three Houses and Three Utilities Problem. --- Traveling Salesman Problem. --- Traveller's Dodecahedron. --- Tutte's Theorem. --- Vizing's Theorem. --- Voyage Round the World. --- Wagner's Conjecture. --- What Is Mathematics?. --- William Tutte. --- bipartite graph. --- bridge. --- chromatic index. --- coloring. --- complete graph. --- complex numbers. --- connected graph. --- crossing number. --- cyclic decomposition. --- decision tree. --- distance. --- dominating set. --- edge coloring. --- geometry of position. --- graceful graph. --- graph theory. --- graph. --- icosian calculus. --- irregular graph. --- irregular multigraph. --- isomorphic graph. --- leaf. --- mathematicians. --- mathematics. --- orientation. --- oriented graph. --- planar graph. --- problem solving. --- regular graph. --- round robin tournament. --- subgraph. --- theorem. --- tree. --- vertex coloring. --- voting. --- weighted graph.

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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.

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

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Our Special Issue we publish at a turning point, which we have not dealt with since World War II. The interconnected long-term global shocks such as the coronavirus pandemic, the war in Ukraine, and catastrophic climate change have imposed significant humanitary, socio-economic, political, and environmental restrictions on the globalization process and all aspects of economic and social life including the existence of individual people. The planet is trapped—the current situation seems to be the prelude to an apocalypse whose long-term effects we will have for decades. Therefore, it urgently requires a concept of the planet's survival to be built—only on this basis can the conditions for its development be created. The Special Issue gives evidence of the state of econophysics before the current situation. Therefore, it can provide excellent econophysics or an inter-and cross-disciplinary starting point of a rational approach to a new era.

energy --- economic growth --- output elasticities --- entropy production --- emissions --- optimization --- speculative attacks --- currency crisis --- neural networks --- deep learning --- Quantum-Inspired Neural Network --- traveling salesman problem --- simulated annealing technique --- kinetic exchange model --- Gini index --- Kolkata index --- minority game --- Kolkata Paise Restaurant problem --- time series analysis --- cross-correlations --- power law classification scheme --- network analysis --- globalisation --- entropy --- portfolio optimization --- regularization --- renormalization --- econophysics --- highway freight transportation --- radiation model --- transportation network --- network diversity --- power law --- economic development --- decision-making --- bounded rationality --- complexity economics --- information-theory --- maximum entropy principle --- quantal response statistical equilibrium --- correlation coefficient --- detrended cross-correlation analysis --- COVID-19 --- mobility indices --- random geometry --- risk measurement --- disordered systems --- replica theory --- return distributions --- power-law tails --- stretched exponentials --- q-Gaussians --- financial markets --- financial complexity --- collective intelligence --- emergent property --- stock correlation --- lexical evolution of econophysics --- text as data --- correspondence analysis --- long-range memory --- 1/f noise --- absolute value estimator --- anomalous diffusion --- ARFIMA --- first-passage times --- fractional Lèvy stable motion --- Higuchi’s method --- mean squared displacement --- multiplicative point process --- correlation filtering --- minimal spanning tree --- planar maximally filtered graph --- topological data analysis --- SGX --- TAIEX --- complex systems --- ecological economics --- urban–regional economics --- income distribution --- financial market dynamics --- income tax --- tax deduction --- income redistribution --- government transfer --- government dependency --- poverty line --- basic income guarantee --- effective tax rate --- balanced budget --- elastic tax --- Cantor set --- fractals --- homeomorphism --- detrended fluctuation analysis --- Hurst exponent --- continuous time random walk --- intertrade times --- volatility clustering --- local transfer entropy --- long-short-term-memory --- Bitcoin --- cryptocurrencies --- multiscale analysis --- detrended cross-correlations --- covariance matrices --- copulas --- high-frequency trading --- market stability --- agent-based models --- structural entropy --- Economic Freedom of the World index --- Index of Economic Freedom --- rank-size law technique --- power law behaviour --- exponential behaviour --- multiscale partition function --- multifractal analysis --- company market --- export readiness --- internationalization --- options pricing --- mortality --- companies --- start-up --- FTSE100 --- Gompertz --- MinMax --- survival probability distribution --- high-frequency trader --- multivariate Hawkes process --- forex market --- wealth distribution --- kinetic models --- wealth inequalities --- compartmental epidemic modelling --- vaccination campaign --- flash crash --- systemic risk --- financial networks --- high frequency trading --- market microstructure --- phase transition --- criticality --- dynamics of complex networks --- cascading failure --- network science --- economic complexity --- relatedness --- products and services --- planar graph --- partial correlation --- discounting --- bond pricing --- real interest rates --- calendar anomalies --- day-of-the-week effect --- market indices --- multifractal detrended fluctuation analysis --- n/a --- fractional Lèvy stable motion --- Higuchi's method --- urban-regional economics