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About forty years after its discovery, it is still common to read in the literature that quasicrystals (QCs) occupy an intermediate position between amorphous materials and periodic crystals. However, QCs exhibit high-quality diffraction patterns containing a collection of discrete Bragg reflections at variance with amorphous phases. Accordingly, these materials must be properly regarded as long-range ordered materials with a symmetry incompatible with translation invariance. This misleading conceptual status can probably arise from the use of notions borrowed from the amorphous solids framework (such us tunneling states, weak interference effects, variable range hopping, or spin glass) in order to explain certain physical properties observed in QCs. On the other hand, the absence of a general, full-fledged theory of quasiperiodic systems certainly makes it difficult to clearly distinguish the features related to short-range order atomic arrangements from those stemming from long-range order correlations. The contributions collected in this book aim at gaining a deeper understanding on the relationship between the underlying structural order and the resulting physical properties in several illustrative aperiodic systems, including the border line between QCs and related complex metallic alloys, hierarchical superlattices, electrical transmission lines, nucleic acid sequences, photonic quasicrystals, and optical devices based on aperiodic order designs.

nucleic acids --- aperiodic --- quasiperiodic --- fractal --- order --- disorder --- energy structure --- charge transport --- Mg-Zn-Gd alloys --- symmetrical rod phase --- quasicrystal --- morphologies and properties --- quasiperiodic order --- self-similarity --- quasiperiodic photonic micro/nanostructures --- fractal-like photonic micro/nanostructures --- quasiperiodic or fractal-like plasmonic structures --- non-periodic systems --- localization properties --- electrical transmission lines --- quasiperiodicity --- localization --- tight-binding model --- Kubo formula --- low-dimensional systems --- n/a

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This book provides a short, hands-on introduction to the science of complexity using simple computational models of natural complex systems-with models and exercises drawn from physics, chemistry, geology, and biology. By working through the models and engaging in additional computational explorations suggested at the end of each chapter, readers very quickly develop an understanding of how complex structures and behaviors can emerge in natural phenomena as diverse as avalanches, forest fires, earthquakes, chemical reactions, animal flocks, and epidemic diseases.Natural Complexity provides the necessary topical background, complete source codes in Python, and detailed explanations for all computational models. Ideal for undergraduates, beginning graduate students, and researchers in the physical and natural sciences, this unique handbook requires no advanced mathematical knowledge or programming skills and is suitable for self-learners with a working knowledge of precalculus and high-school physics.Self-contained and accessible, Natural Complexity enables readers to identify and quantify common underlying structural and dynamical patterns shared by the various systems and phenomena it examines, so that they can form their own answers to the questions of what natural complexity is and how it arises.

Complexity (Philosophy) --- Physics --- Computational complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Philosophy --- Emergence (Philosophy) --- Methodology. --- Burridge-Knopoff stick-slip model. --- Gutenberg-Richter law. --- Johannes Kepler. --- Olami-Feder-Christensen model. --- Python code. --- accretion. --- active flockers. --- agents. --- automobile traffic. --- avalanches. --- cells. --- cellular automata. --- chaos. --- clusters. --- complex behavior. --- complex structure. --- complex system. --- complexity. --- computational model. --- computer program. --- contagious diseases. --- criticality. --- diffusion-limited aggregation. --- earthquake forecasting. --- earthquakes. --- emergence. --- emergent behavior. --- emergent structure. --- epidemic spread. --- epidemic surges. --- excitable system. --- flocking. --- forest fires. --- fractal clusters. --- fractal geometry. --- growth. --- hodgepodge machine. --- infection rate. --- iterated growth. --- lattice. --- lichens. --- natural complex system. --- natural complexity. --- natural order. --- natural phenomena. --- nature. --- open dissipative system. --- panic. --- passive flockers. --- pattern formation. --- percolation threshold. --- percolation. --- phase transition. --- planetary motion. --- power-law. --- random walk. --- randomness. --- repulsion. --- rule-based growth. --- sandpile. --- scale invariance. --- segregation. --- self-organization. --- self-organized criticality. --- self-propulsion. --- self-similarity. --- simple rules. --- small-world network. --- solar flares. --- spaghetti. --- spatiotemporal pattern. --- spiral. --- tagging algorithm. --- traffic jams. --- waves. --- wildfire management.

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The modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications. After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration. Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications. Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity.

Self-similar processes. --- Distribution (Probability theory) --- Processus autosimilaires --- Distribution (Théorie des probabilités) --- 519.218 --- Self-similar processes --- 519.24 --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Selfsimilar processes --- Stochastic processes --- Special stochastic processes --- 519.218 Special stochastic processes --- Distribution (Théorie des probabilités) --- Almost surely. --- Approximation. --- Asymptotic analysis. --- Autocorrelation. --- Autoregressive conditional heteroskedasticity. --- Autoregressive–moving-average model. --- Availability. --- Benoit Mandelbrot. --- Brownian motion. --- Central limit theorem. --- Change of variables. --- Computational problem. --- Confidence interval. --- Correlogram. --- Covariance matrix. --- Data analysis. --- Data set. --- Determination. --- Fixed point (mathematics). --- Foreign exchange market. --- Fractional Brownian motion. --- Function (mathematics). --- Gaussian process. --- Heavy-tailed distribution. --- Heuristic method. --- High frequency. --- Inference. --- Infimum and supremum. --- Instance (computer science). --- Internet traffic. --- Joint probability distribution. --- Likelihood function. --- Limit (mathematics). --- Linear regression. --- Log–log plot. --- Marginal distribution. --- Mathematica. --- Mathematical finance. --- Mathematics. --- Methodology. --- Mixture model. --- Model selection. --- Normal distribution. --- Parametric model. --- Power law. --- Probability theory. --- Publication. --- Random variable. --- Regime. --- Renormalization. --- Result. --- Riemann sum. --- Self-similar process. --- Self-similarity. --- Simulation. --- Smoothness. --- Spectral density. --- Square root. --- Stable distribution. --- Stable process. --- Stationary process. --- Stationary sequence. --- Statistical inference. --- Statistical physics. --- Statistics. --- Stochastic calculus. --- Stochastic process. --- Technology. --- Telecommunication. --- Textbook. --- Theorem. --- Time series. --- Variance. --- Wavelet. --- Website.

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This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development.Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws-PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs-mixed type, free boundaries, and corner singularities-that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.

Shock waves --- Von Neumann algebras. --- MATHEMATICS / Differential Equations / Partial. --- Algebras, Von Neumann --- Algebras, W --- Neumann algebras --- Rings of operators --- W*-algebras --- C*-algebras --- Hilbert space --- Shock (Mechanics) --- Waves --- Diffraction --- Diffraction. --- Mathematics. --- A priori estimate. --- Accuracy and precision. --- Algorithm. --- Andrew Majda. --- Attractor. --- Banach space. --- Bernhard Riemann. --- Big O notation. --- Boundary value problem. --- Bounded set (topological vector space). --- C0. --- Calculation. --- Cauchy problem. --- Coefficient. --- Computation. --- Computational fluid dynamics. --- Conjecture. --- Conservation law. --- Continuum mechanics. --- Convex function. --- Degeneracy (mathematics). --- Demetrios Christodoulou. --- Derivative. --- Dimension. --- Directional derivative. --- Dirichlet boundary condition. --- Dirichlet problem. --- Dissipation. --- Ellipse. --- Elliptic curve. --- Elliptic partial differential equation. --- Embedding problem. --- Equation solving. --- Equation. --- Estimation. --- Euler equations (fluid dynamics). --- Existential quantification. --- Fixed point (mathematics). --- Flow network. --- Fluid dynamics. --- Fluid mechanics. --- Free boundary problem. --- Function (mathematics). --- Function space. --- Fundamental class. --- Fundamental solution. --- Fundamental theorem. --- Hyperbolic partial differential equation. --- Initial value problem. --- Iteration. --- Laplace's equation. --- Linear equation. --- Linear programming. --- Linear space (geometry). --- Mach reflection. --- Mathematical analysis. --- Mathematical optimization. --- Mathematical physics. --- Mathematical problem. --- Mathematical proof. --- Mathematical theory. --- Mathematician. --- Melting. --- Monotonic function. --- Neumann boundary condition. --- Nonlinear system. --- Numerical analysis. --- Parameter space. --- Parameter. --- Partial derivative. --- Partial differential equation. --- Phase boundary. --- Phase transition. --- Potential flow. --- Pressure gradient. --- Quadratic function. --- Regularity theorem. --- Riemann problem. --- Scientific notation. --- Self-similarity. --- Special case. --- Specular reflection. --- Stefan problem. --- Structural stability. --- Subspace topology. --- Symmetrization. --- Theorem. --- Theory. --- Truncation error (numerical integration). --- Two-dimensional space. --- Unification (computer science). --- Variable (mathematics). --- Velocity potential. --- Vortex sheet. --- Vorticity. --- Wave equation. --- Weak convergence (Hilbert space). --- Weak solution.

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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.

Research & information: general --- Mathematics & science --- 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