“…The validity of our approach is tested on a conductance based neuronal model showing WLC and through the extraction of Lévy flights inducing fractals from recordings of rat hippocampus during open field foraging. …”
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“…This extraordinary work takes the reader on a long and fascinating journey--from the dual invention of numbers and language, through the major realms of arithmetic, algebra, geometry, trigonometry, and calculus, to the final destination of differential equations, with excursions into mathematical logic, set theory, topology, fractals, probability, and assorted other mathematical byways. …”
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“…Topics covered include the following: stochastic analysis on configuration spaces, specifically a mathematically rigorous approach to the stochastic dynamics of Gibbs measures and infinite interacting particle systems; subelliptic PDE, homogenization, and fractals; geometric aspects of Dirichlet forms on metric spaces and function theory on such spaces; generalized harmonic maps as nonlinear analogues of Dirichlet forms, with an emphasis on non-locally compact situations; and a stochastic approach based on Brownian motion to harmonic maps and their regularity. …”
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“…In a series of 10 independent samples with a total of 255 participants, we show for the first time that using this non-reinforced method we can enhance preferences for faces, fractals and affective images, as well as snack foods, using auditory, visual and even aversive cues. …”
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“…We can quantify complexity using measures derived from the concept of fractals that describe patterns of behavior across different scales in space or time. …”
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“…We investigate the shape and properties of the potential appearing in this equation in simulated small-world and scale-free network ensembles, using measures of fractality. Besides, we employ the proposed framework to compare real-world networks with the Erdős-Rényi, Watts-Strogatz and Barabási-Albert benchmark models. …”
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“…Its solution would be tremendously important for a unified analysis of a wide range of the nature’s [Formula: see text]-hard problems, including problems in the physics of many-body systems, critical phenomena, quantum computing, quantum field theory, theory of chaos, fractals, theory of graphs, number theory, combinatorics, cryptography, etc.…”
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“…Processes as varied as regular diffusion, anomalous diffusion, and diffusion in disordered media and fractals, fall into the same universality classes.…”
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“…The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. …”
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“…The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and fractals for graduate and postgraduate students. The volume will also serve as a valuable reference guide for specialists working in applied mathematics, physics, geophysics and the engineering sciences.…”
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“…But there are many others, for example Fourier analysis and fractals. In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. …”
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“…The results show strong evidence of asymmetric multifractality that increases as the fractality scale increases. Moreover, multifractality is especially higher in the downside (upside) trend for Brent oil (gold), and this excess asymmetry has been more accentuated during the COVID-19 outbreak. …”
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“…Time-series generated by complex systems (CS) are often characterized by phenomena such as chaoticity, fractality and memory effects, which pose difficulties in their analysis. …”
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“…In this way, we can observe how, the behavior of many variables usually transgress the conventional plane and moves towards non-linearity and fractality, making a complex tissue that will maintain its structure while thermodynamically viable. …”
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“…Utilization of the concepts of chaos and sensitive dependence on initial conditions, and the concepts of self-organization, stigmergy, and fractals may help us to understand some of the puzzles that have not been solved by conventional linear models. …”
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“…The second part covers a broad range of applications in physics and applied mathematics, including negative and complex bases, the double pendulum, fractals, the logistic map, the quantum harmonic oscillator, the quantum square potential, the Van der Pol oscillator, the Duffing oscillator, multilane bidirectional pedestrian traffic, public-key encryption, tautochrone curves, Iterated function systems, motion of a bead on a rotating circle, Mersenne and perfect numbers, Lindenmayer systems, skydiving, Lorenz equations, the Foucault's pendulum, and Julia and Mandelbrot sets.…”
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“…Included are discussions of geometry, proportional systems, linear algebra, periodic and aperiodic tilings, fractals, perspective, computer science and mechanics. …”
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“…This book addresses the issue step-by-step, from phenomenological analogies between complex systems and statistical physics to more complex aspects, such as correlations, fluctuation-dissipation theorem, susceptibility, the concept of free energy, renormalization group approach and scaling. Fractals and multifractals, the Ising model, percolation, damage phenomena, critical and spinodal phase transitions, crossover effects and finite-size effects are some of the topics covered in Statistical Physics of Non-Thermal Phase Transitions.…”
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