Proceedings of the Fifth Mexican School on Statistical Physics, EMFE 5, Oaxtepec, Mexico, 1989

Proceedings of the Fifth Mexican School on Statistical Physics, EMFE 5, Oaxtepec, Mexico, 1989
Author: Francisco Ramos-Gómez
Publisher: World Scientific Publishing Company Incorporated
Total Pages: 145
Release: 1991-01-01
Genre: Science
ISBN: 9789810205843

Four lectures delivered to graduate students and researchers new to statistical physics at Oaxtepec, Mexico, August 1989, review the field and describe recent advances. The topics are coherent fields in disordered systems; the thermodyanmic behavior of two-dimensional vesicles; randomness, information, and complexity; and the aerodynamics of Leonardo da Vinci. Mostly double-spaced. No index. Acidic paper. Annotation copyrighted by Book News, Inc., Portland, OR

Chaos

Chaos
Author: Angelo Vulpiani
Publisher: World Scientific
Total Pages: 482
Release: 2010
Genre: Mathematics
ISBN: 9814277665

Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.

Cognitive Science

Cognitive Science
Author: Harald Maurer
Publisher: CRC Press
Total Pages: 415
Release: 2021-07-08
Genre: Medical
ISBN: 1351043501

The Mind and Brain are usually considered as one and the same nonlinear, complex dynamical system, in which information processing can be described with vector and tensor transformations and with attractors in multidimensional state spaces. Thus, an internal neurocognitive representation concept consists of a dynamical process which filters out statistical prototypes from the sensorial information in terms of coherent and adaptive n-dimensional vector fields. These prototypes serve as a basis for dynamic, probabilistic predictions or probabilistic hypotheses on prospective new data (see the recently introduced approach of "predictive coding" in neurophilosophy). Furthermore, the phenomenon of sensory and language cognition would thus be based on a multitude of self-regulatory complex dynamics of synchronous self-organization mechanisms, in other words, an emergent "flux equilibrium process" ("steady state") of the total collective and coherent neural activity resulting from the oscillatory actions of neuronal assemblies. In perception it is shown how sensory object informations, like the object color or the object form, can be dynamically related together or can be integrated to a neurally based representation of this perceptual object by means of a synchronization mechanism ("feature binding"). In language processing it is shown how semantic concepts and syntactic roles can be dynamically related together or can be integrated to neurally based systematic and compositional connectionist representations by means of a synchronization mechanism ("variable binding") solving the Fodor-Pylyshyn-Challenge. Since the systemtheoretical connectionism has succeeded in modeling the sensory objects in perception as well as systematic and compositional representations in language processing with this vector- and oscillation-based representation format, a new, convincing theory of neurocognition has been developed, which bridges the neuronal and the cognitive analysis level. The book describes how elementary neuronal information is combined in perception and language, so it becomes clear how the brain processes this information to enable basic cognitive performance of the humans.