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This book contains various works presented at the Dynamics Days Latin America and the Caribbean (DDays LAC) 2018. Since its beginnings, a key goal of the DDays LAC has been to promote cross-fertilization of ideas from different areas within nonlinear dynamics. On this occasion, the contributions range from experimental to theoretical research, including (but not limited to) chaos, control theory, synchronization, statistical physics, stochastic processes, complex systems and networks, nonlinear time-series analysis, computational methods, fluid dynamics, nonlinear waves, pattern formation, population dynamics, ecological modeling, neural dynamics, and systems biology. The interested reader will find this book to be a useful reference in identifying ground-breaking problems in Physics, Mathematics, Engineering, and Interdisciplinary Sciences, with innovative models and methods that provide insightful solutions. This book is a must-read for anyone looking for new developments of Applied Mathematics and Physics in connection with complex systems, synchronization, neural dynamics, fluid dynamics, ecological networks, and epidemics.

self-organization --- temporal aliasing effect --- point scatterer --- recurrence time --- calcium signals --- theta neuron --- synchrony --- neural network --- reaction fronts --- cyclic dynamics --- annular billiard --- convection --- local field potential --- complex systems --- Dicke model --- coupled oscillators --- diffusive instabilities --- Slater’s theorem --- stochastic processes --- nonlinear dynamics --- computational methods --- waves --- ecological methods --- sampling rates --- out of equilibrium system --- predator–prey system --- IP3Rs dsitribution --- birthday problem --- mean field models --- population dynamics --- puffs --- delay bifurcation --- epidemic models --- suppression of synchronization --- population biology --- Lyapunov exponent --- Markov processes --- synchronization

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This book presents a collection of seven technical papers on fractional-order complex systems, especially chaotic systems with hidden attractors and symmetries, in the research front of the field, which will be beneficial for scientific researchers, graduate students, and technical professionals to study and apply. It is also suitable for teaching lectures and for seminars to use as a reference on related topics.

History of engineering & technology --- Puu system of fractional order --- Caputo-like delta difference --- impulsive control --- chaos suppression --- Fractional dynamics --- Power law behavior --- Complex systems --- Soccer --- fraction-order memristor --- device property --- serial and parallel --- Dynamical analysis --- wind speed forecasting --- fractional Levy stable motion --- long-range dependence --- Lyapunov exponent --- discrete fractional systems --- chaotic systems --- closed curve fixed points --- symmetry --- 0–1 test --- bifurcation diagram --- Lyapunov exponents --- chaos --- coexisting attractors --- hidden attractors --- caputo fractional derivative --- bessel functions --- collocation method --- multi-order fractional differential equations

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William Thurston (1946–2012) was one of the great mathematicians of the twentieth century. He was a visionary whose extraordinary ideas revolutionized a broad range of mathematical fields, from foliations, contact structures, and Teichmüller theory to automorphisms of surfaces, hyperbolic geometry, geometrization of 3-manifolds, geometric group theory, and rational maps. In addition, he discovered connections between disciplines that led to astonishing breakthroughs in mathematical understanding as well as the creation of entirely new fields. His far-reaching questions and conjectures led to enormous progress by other researchers. What's Next? brings together many of today's leading mathematicians to describe recent advances and future directions inspired by Thurston's transformative ideas.Including valuable insights from his colleagues and former students, What's Next? discusses Thurston's fundamental contributions to topology, geometry, and dynamical systems and includes many deep and original contributions to the field. This incisive and wide-ranging book also explores how he introduced new ways of thinking about and doing mathematics, innovations that have had a profound and lasting impact on the mathematical community as a whole.

Dynamics. --- Geometry. --- Topology. --- MATHEMATICS / General. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Mathematics --- Euclid's Elements --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Thurston, William P., --- Thurston, W. P. --- Arbitrarily large. --- Asymptotic expansion. --- Automorphism. --- Big O notation. --- Braid group. --- Branch point. --- Central series. --- Character variety. --- Characterization (mathematics). --- Cohomology operation. --- Cohomology. --- Commutative property. --- Conjecture. --- Conjugacy class. --- Convex hull. --- Covering space. --- Coxeter group. --- Curvature. --- Dehn's lemma. --- Diagram (category theory). --- Disjoint union. --- Eigenfunction. --- Endomorphism. --- Epimorphism. --- Equivalence class. --- Equivalence relation. --- Euclidean space. --- Extreme point. --- Faithful representation. --- Fiber bundle. --- Free group. --- Free product. --- Fundamental group. --- Geometrization conjecture. --- HNN extension. --- Haar measure. --- Homeomorphism. --- Homotopy. --- Hyperbolic 3-manifold. --- Hyperbolic geometry. --- Hyperbolic manifold. --- Hyperbolic space. --- Hypercube. --- I0. --- Inclusion map. --- Incompressible surface. --- JSJ decomposition. --- Jordan curve theorem. --- Julia set. --- Klein bottle. --- Kleinian group. --- Lebesgue measure. --- Leech lattice. --- Limit point. --- Lyapunov exponent. --- Mahler measure. --- Manifold decomposition. --- Mapping cylinder. --- Marriage theorem. --- Maxima and minima. --- Moduli space. --- Möbius strip. --- Möbius transformation. --- Natural topology. --- Non-Euclidean geometry. --- Non-positive curvature. --- Normal subgroup. --- Open set. --- Orientability. --- Pair of pants (mathematics). --- Perfect group. --- Pleated surface. --- Polynomial. --- Preorder. --- Probability measure. --- Pullback (category theory). --- Pullback (differential geometry). --- Quadric. --- Quasi-isometry. --- Quasiconvex function. --- Rectangle. --- Riemann surface. --- Riemannian manifold. --- Saddle point. --- Sectional curvature. --- Sign (mathematics). --- Simple algebra. --- Simply connected space. --- Special case. --- Subgroup. --- Subset. --- Symplectic geometry. --- Theorem. --- Total order. --- Unit disk. --- Unit sphere. --- Upper and lower bounds. --- Vector bundle.

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Complexity is a ubiquitous phenomenon in physiology that allows living systems to adapt to external perturbations. Fractal structures, self-organization, nonlinearity, interactions at different scales, and interconnections among systems through anatomical and functional networks, may originate complexity. Biomedical signals from physiological systems may carry information about the system complexity useful to identify physiological states, monitor health, and predict pathological events. Therefore, complexity analysis of biomedical signals is a rapidly evolving field aimed at extracting information on the physiological systems. This book consists of 16 contributions from authors with a strong scientific background in biomedical signals analysis. It includes reviews on the state-of-the-art of complexity studies in specific medical applications, new methods to improve complexity quantifiers, and novel complexity analyses in physiological or clinical scenarios. It presents a wide spectrum of methods investigating the entropic properties, multifractal structure, self-organized criticality, and information dynamics of biomedical signals touching upon three physiological areas: the cardiovascular system, the central nervous system, the heart-brain interactions. The book is aimed at experienced researchers in signal analysis and presents the latest trends in the complexity methods in physiology and medicine with the hope of inspiring future works advancing this fascinating area of research.

autonomic nervous function --- heart rate variability (HRV) --- baroreflex sensitivity (BRS) --- photo-plethysmo-graphy (PPG) --- digital volume pulse (DVP) --- percussion entropy index (PEI) --- heart rate variability --- posture --- entropy --- complexity --- cognitive task --- sample entropy --- brain functional networks --- dynamic functional connectivity --- static functional connectivity --- K-means clustering algorithm --- fragmentation --- aging in human population --- factor analysis --- support vector machines classification --- Sampen --- cross-entropy --- autonomic nervous system --- heart rate --- blood pressure --- hypobaric hypoxia --- rehabilitation medicine --- labor --- fetal heart rate --- data compression --- complexity analysis --- nonlinear analysis --- preterm --- Alzheimer’s disease --- brain signals --- single-channel analysis --- biomarker --- refined composite multiscale entropy --- central autonomic network --- interconnectivity --- ECG --- ectopic beat --- baroreflex --- self-organized criticality --- vasovagal syncope --- Zipf’s law --- multifractality --- multiscale complexity --- detrended fluctuation analysis --- self-similarity --- sEMG --- approximate entropy --- fuzzy entropy --- fractal dimension --- recurrence quantification analysis --- correlation dimension --- largest Lyapunov exponent --- time series analysis --- relative consistency --- event-related de/synchronization --- motor imagery --- vector quantization --- information dynamics --- partial information decomposition --- conditional transfer entropy --- network physiology --- multivariate time series analysis --- State–space models --- vector autoregressive model --- penalized regression techniques --- linear prediction --- fNIRS --- brain dynamics --- mental arithmetics --- multiscale --- cardiovascular system --- brain --- information flow