Fractal and Trans scale Nature of Entropy

Fractal and Trans scale Nature of Entropy
Author: Diogo Queiros Conde,Michel Feidt
Publsiher: Elsevier
Total Pages: 252
Release: 2018-11-16
Genre: Science
ISBN: 9780081017906

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Fractal and Trans-scale Nature of Entropy: Towards a Geometrization of Thermodynamics develops a new vision for entropy in thermodynamics by proposing a new method to geometrize. It investigates how this approach can accommodate a large number of very different physical systems, going from combustion and turbulence towards cosmology. As an example, a simple interpretation of the Hawking entropy in black-hole physics is provided. In the life sciences, entropy appears as the driving element for the organization of systems. This book demonstrates this fact using simple pedagogical tools, thus showing that entropy cannot be interpreted as a basic measure of disorder. Develop a new vision of entropy in thermodynamics Study the concept of entropy Propose a simple interpretation the entropy of Hawking Demonstrate entropy as a measure of energy dispersal

12th Chaotic Modeling and Simulation International Conference

12th Chaotic Modeling and Simulation International Conference
Author: Christos H. Skiadas,Yiannis Dimotikalis
Publsiher: Springer Nature
Total Pages: 306
Release: 2020-02-07
Genre: Science
ISBN: 9783030395155

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Gathering the proceedings of the 12th CHAOS2019 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the Engineering Sciences. The respective chapters address key methods, empirical data and computer techniques, as well as major theoretical advances in the applied nonlinear field. Beyond showcasing the state of the art, the book will help academic and industrial researchers alike apply chaotic theory in their studies.

Machine Learning and Intelligent Communications

Machine Learning and Intelligent Communications
Author: Xiaolin Jiang
Publsiher: Springer Nature
Total Pages: 352
Release: 2022-05-17
Genre: Computers
ISBN: 9783031044090

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This volume constitutes the refereed post-conference proceedings of the 6th International Conference on Machine Learning and Intelligent Communications, MLICOM 2021, held in November 2021. Due to COVID-19 pandemic the conference was held virtually. The 28 revised full papers were carefully selected from 58 submissions. The papers are organized thematically in tracks as follows: internet of vehicle communication system; applications of neural network and deep learning; intelligent massive MIMO communications; intelligent positioning and navigation systems; intelligent space and terrestrial integrated networks; machine learning algorithms and intelligent networks; image information processing.

Fractal Dimensions of Networks

Fractal Dimensions of Networks
Author: Eric Rosenberg
Publsiher: Springer Nature
Total Pages: 524
Release: 2020-07-07
Genre: Computers
ISBN: 9783030431693

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Current interest in fractal dimensions of networks is the result of more than a century of previous research on dimensions. Fractal Dimensions of Networks ties the theory and methods for computing fractal dimensions of networks to the “classic” theory of dimensions of geometric objects. The goal of the book is to provide a unified treatment of fractal dimensions of sets and networks. Since almost all of the major concepts in fractal dimensions originated in the study of sets, the book achieves this goal by first clearly presenting, with an abundance of examples and illustrations, the theory and algorithms for sets, and then showing how the theory and algorithms have been applied to networks. Thus, the book presents the classical theory and algorithms for the box counting dimension for sets, and then presents the box counting dimension for networks. All the major fractal dimensions are studied, e.g., the correlation dimension, the information dimension, the Hausdorff dimension, the multifractal spectrum, as well as many lesser known dimensions. Algorithm descriptions are accompanied by worked examples, many applications of the methods are presented, and many exercises, ranging in difficulty from easy to research level, are included.

Beyond the Second Law

Beyond the Second Law
Author: Roderick C. Dewar,Charles H. Lineweaver,Robert K. Niven,Klaus Regenauer-Lieb
Publsiher: Springer
Total Pages: 434
Release: 2013-12-02
Genre: Technology & Engineering
ISBN: 9783642401541

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The Second Law, a cornerstone of thermodynamics, governs the average direction of dissipative, non-equilibrium processes. But it says nothing about their actual rates or the probability of fluctuations about the average. This interdisciplinary book, written and peer-reviewed by international experts, presents recent advances in the search for new non-equilibrium principles beyond the Second Law, and their applications to a wide range of systems across physics, chemistry and biology. Beyond The Second Law brings together traditionally isolated areas of non-equilibrium research and highlights potentially fruitful connections between them, with entropy production playing the unifying role. Key theoretical concepts include the Maximum Entropy Production principle, the Fluctuation Theorem, and the Maximum Entropy method of statistical inference. Applications of these principles are illustrated in such diverse fields as climatology, cosmology, crystal growth morphology, Earth system science, environmental physics, evolutionary biology and technology, fluid turbulence, microbial biogeochemistry, plasma physics, and radiative transport, using a wide variety of analytical and experimental techniques. Beyond The Second Law will appeal to students and researchers wishing to gain an understanding of entropy production and its central place in the science of non-equilibrium systems – both in detail and in terms of the bigger picture.

Recent Trends in the Condition Monitoring of Transformers

Recent Trends in the Condition Monitoring of Transformers
Author: Sivaji Chakravorti,Debangshu Dey,Biswendu Chatterjee
Publsiher: Springer Science & Business Media
Total Pages: 280
Release: 2013-10-21
Genre: Business & Economics
ISBN: 9781447155508

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Recent Trends in the Condition Monitoring of Transformers reflects the current interest in replacing traditional techniques used in power transformer condition monitoring with non-invasive measures such as polarization/depolarization current measurement, recovery voltage measurement, frequency domain spectroscopy and frequency response analysis. The book stresses the importance of scrutinizing the condition of transformer insulation which may fail under present day conditions of intensive use with the resulting degradation of dielectric properties causing functional failure of the transformer. The text shows the reader how to overcome the key challenges facing today’s maintenance policies, namely: The selection of appropriate techniques for dealing with each type of failure process accounting for the needs of plant owners, plant users and wider society; and Cost-efficiency and durability of effect. Many of the failure-management methods presented rely on the fact that most failures give warning when they are imminent. These potential failures give rise to identifiable physical conditions and the novel approaches described detect them so that action can be taken to avoid degeneration into full-blown functional failure. This “on-condition” maintenance means that equipment can be left in service as long as a specified set of performance standards continue to be met, avoiding the costly downtime imposed by routine and perhaps unnecessary maintenance but without risking equally expensive failure. Recent Trends in the Condition Monitoring of Transformers will be of considerable interest to both academic researchers in power systems and to engineers working in the power generation and distribution industry showing how new and more efficient methods of fault diagnosis and condition management can increase transformer efficiency and cut costs.

Fractal Geometry and Stochastics

Fractal Geometry and Stochastics
Author: Christoph Bandt,Siegfried Graf,Martina Zähle
Publsiher: Birkhäuser
Total Pages: 248
Release: 2013-11-27
Genre: Mathematics
ISBN: 9783034877558

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Fractal geometry is a new and promising field for researchers from different disciplines such as mathematics, physics, chemistry, biology and medicine. It is used to model complicated natural and technical phenomena. The most convincing models contain an element of randomness so that the combination of fractal geometry and stochastics arises in between these two fields. It contains contributions by outstanding mathematicians and is meant to highlight the principal directions of research in the area. The contributors were the main speakers attending the conference "Fractal Geometry and Stochastics" held at Finsterbergen, Germany, in June 1994. This was the first international conference ever to be held on the topic. The book is addressed to mathematicians and other scientists who are interested in the mathematical theory concerning: • Fractal sets and measures • Iterated function systems • Random fractals • Fractals and dynamical systems, and • Harmonic analysis on fractals. The reader will be introduced to the most recent results in these subjects. Researchers and graduate students alike will benefit from the clear expositions.

Nonlinear Analysis in Neuroscience and Behavioral Research

Nonlinear Analysis in Neuroscience and Behavioral Research
Author: Tobias A. Mattei
Publsiher: Frontiers Media SA
Total Pages: 135
Release: 2016-10-31
Genre: Electronic Book
ISBN: 9782889199969

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Although nonlinear dynamics have been mastered by physicists and mathematicians for a long time (as most physical systems are inherently nonlinear in nature), the recent successful application of nonlinear methods to modeling and predicting several evolutionary, ecological, physiological, and biochemical processes has generated great interest and enthusiasm among researchers in computational neuroscience and cognitive psychology. Additionally, in the last years it has been demonstrated that nonlinear analysis can be successfully used to model not only basic cellular and molecular data but also complex cognitive processes and behavioral interactions. The theoretical features of nonlinear systems (such unstable periodic orbits, period-doubling bifurcations and phase space dynamics) have already been successfully applied by several research groups to analyze the behavior of a variety of neuronal and cognitive processes. Additionally the concept of strange attractors has lead to a new understanding of information processing which considers higher cognitive functions (such as language, attention, memory and decision making) as complex systems emerging from the dynamic interaction between parallel streams of information flowing between highly interconnected neuronal clusters organized in a widely distributed circuit and modulated by key central nodes. Furthermore, the paradigm of self-organization derived from the nonlinear dynamics theory has offered an interesting account of the phenomenon of emergence of new complex cognitive structures from random and non-deterministic patterns, similarly to what has been previously observed in nonlinear studies of fluid dynamics. Finally, the challenges of coupling massive amount of data related to brain function generated from new research fields in experimental neuroscience (such as magnetoencephalography, optogenetics and single-cell intra-operative recordings of neuronal activity) have generated the necessity of new research strategies which incorporate complex pattern analysis as an important feature of their algorithms. Up to now nonlinear dynamics has already been successfully employed to model both basic single and multiple neurons activity (such as single-cell firing patterns, neural networks synchronization, autonomic activity, electroencephalographic measurements, and noise modulation in the cerebellum), as well as higher cognitive functions and complex psychiatric disorders. Similarly, previous experimental studies have suggested that several cognitive functions can be successfully modeled with basis on the transient activity of large-scale brain networks in the presence of noise. Such studies have demonstrated that it is possible to represent typical decision-making paradigms of neuroeconomics by dynamic models governed by ordinary differential equations with a finite number of possibilities at the decision points and basic heuristic rules which incorporate variable degrees of uncertainty. This e-book has include frontline research in computational neuroscience and cognitive psychology involving applications of nonlinear analysis, especially regarding the representation and modeling of complex neural and cognitive systems. Several experts teams around the world have provided frontline theoretical and experimental contributions (as well as reviews, perspectives and commentaries) in the fields of nonlinear modeling of cognitive systems, chaotic dynamics in computational neuroscience, fractal analysis of biological brain data, nonlinear dynamics in neural networks research, nonlinear and fuzzy logics in complex neural systems, nonlinear analysis of psychiatric disorders and dynamic modeling of sensorimotor coordination. Rather than a comprehensive compilation of the possible topics in neuroscience and cognitive research to which non-linear may be used, this e-book intends to provide some illustrative examples of the broad range of

Fractal and Multifractal Facets in the Structure and Dynamics of Physiological Systems and Applications to Homeostatic Control Disease Diagnosis and Integrated Cyber Physical Platforms

Fractal and Multifractal Facets in the Structure and Dynamics of Physiological Systems and Applications to Homeostatic Control  Disease Diagnosis and Integrated Cyber Physical Platforms
Author: Paul Bogdan,Plamen Ch. Ivanov,Andras Eke
Publsiher: Frontiers Media SA
Total Pages: 135
Release: 2020-06-25
Genre: Electronic Book
ISBN: 9782889635313

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Widespread chronic diseases (e.g., heart diseases, diabetes and its complications, stroke, cancer, brain diseases) constitute a significant cause of rising healthcare costs and pose a significant burden on quality-of-life for many individuals. Despite the increased need for smart healthcare sensing systems that monitor / measure patients’ body balance, there is no coherent theory that facilitates the modeling of human physiological processes and the design and optimization of future healthcare cyber-physical systems (HCPS). The HCPS are expected to mine the patient’s physiological state based on available continuous sensing, quantify risk indices corresponding to the onset of abnormality, signal the need for critical medical intervention in real-time by communicating patient’s medical information via a network from individual to hospital, and most importantly control (actuate) vital health signals (e.g., cardiac pacing, insulin level, blood pressure) within personalized homeostasis. To prevent health complications, maintain good health and/or avoid fatal conditions calls for a cross-disciplinary approach to HCPS design where recent statistical-physics inspired discoveries done by collaborations between physicists and physicians are shared and enriched by applied mathematicians, control theorists and bioengineers. This critical and urgent multi-disciplinary approach has to unify the current state of knowledge and address the following fundamental challenges: One fundamental challenge is represented by the need to mine and understand the complexity of the structure and dynamics of the physiological systems in healthy homeostasis and associated with a disease (such as diabetes). Along the same lines, we need rigorous mathematical techniques for identifying the interactions between integrated physiologic systems and understanding their role within the overall networking architecture of healthy dynamics. Another fundamental challenge calls for a deeper understanding of stochastic feedback and variability in biological systems and physiological processes, in particular, and for deciphering their implications not only on how to mathematically characterize homeostasis, but also on defining new control strategies that are accounting for intra- and inter-patient specificity – a truly mathematical approach to personalized medicine. Numerous recent studies have demonstrated that heart rate variability, blood glucose, neural signals and other interdependent physiological processes demonstrate fractal and non-stationary characteristics. Exploiting statistical physics concepts, numerous recent research studies demonstrated that healthy human physiological processes exhibit complex critical phenomena with deep implications for how homeostasis should be defined and how control strategies should be developed when prolonged abnormal deviations are observed. In addition, several efforts have tried to connect these fractal characteristics with new optimal control strategies that implemented in medical devices such as pacemakers and artificial pancreas could improve the efficiency of medical therapies and the quality-of-life of patients but neglecting the overall networking architecture of human physiology. Consequently, rigorously analyzing the complexity and dynamics of physiological processes (e.g., blood glucose and its associated implications and interdependencies with other physiological processes) represents a fundamental step towards providing a quantifiable (mathematical) definition of homeostasis in the context of critical phenomena, understanding the onset of chronic diseases, predicting deviations from healthy homeostasis and developing new more efficient medical therapies that carefully account for the physiological complexity, intra- and inter-patient variability, rather than ignoring it. This Research Topic aims to open a synergetic and timely effort between physicians, physicists, applied mathematicians, signal processing, bioengineering and biomedical experts to organize the state of knowledge in mining the complexity of physiological systems and their implications for constructing more accurate mathematical models and designing QoL-aware control strategies implemented in the new generation of HCPS devices. By bringing together multi-disciplinary researchers seeking to understand the many aspects of human physiology and its complexity, we aim at enabling a paradigm shift in designing future medical devices that translates mathematical characteristics in predictable mathematical models quantifying not only the degree of homeostasis, but also providing fundamentally new control strategies within the personalized medicine era.

Synthetic Microstructures in Biological Research

Synthetic Microstructures in Biological Research
Author: M. Peckerar,J.M. Schnur
Publsiher: Springer Science & Business Media
Total Pages: 249
Release: 2013-11-11
Genre: Science
ISBN: 9781489916303

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The Third International Conference on Synthetic Microstructures in Biological Research (SMIBR) was held in Williamsburg, Virginia, September 9-12, 1991. This book represents the compilation of many of the papers and posters presented at the meeting. Publications resulting from previous SMIBR meetings held at Airlie House, Airlie, Virginia (March 24-26, 1986 and March 20-23, 1988) can be obtained from the Institute of Electrical and Electronic Engineers, Inc. (IEEE) Service Center (908 562-5418). The purpose of these conferences is to provide an interface between the engineering community and those at the cutting edge of biological and related material science. The overriding motive for assembling representatives from these diverse disciplines is clear. Engineers, even in 1986, could manipulate materials over dimensional scales on the order of those critical to biological systems. The devices that emerge from these manipulations could then be tailored to monitor system function more directly with significantly more localization than ever before. Thus, one important goal of the meetings is to provide the detailed specifications required for effective interfacing of devices with biological systems under investiga tion.

Fractal Analyses Statistical And Methodological Innovations And Best Practices

Fractal Analyses  Statistical And Methodological Innovations And Best Practices
Author: John G. Holden
Publsiher: Frontiers E-books
Total Pages: 135
Release: 2022
Genre: Electronic Book
ISBN: 9782889191383

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Fractals and Multifractals in Ecology and Aquatic Science

Fractals and Multifractals in Ecology and Aquatic Science
Author: Laurent Seuront
Publsiher: CRC Press
Total Pages: 360
Release: 2009-10-12
Genre: Nature
ISBN: 1420004247

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Ecologists sometimes have a less-than-rigorous background in quantitative methods, yet research within this broad field is becoming increasingly mathematical. Written in a step-by-step fashion, Fractals and Multifractals in Ecology and Aquatic Science provides scientists with a basic understanding of fractals and multifractals and the techniques for utilizing them when analyzing ecological phenomenon. With illustrations, tables, and graphs on virtually every page – several in color – this book is a comprehensive source of state-of-the-art ecological scaling and multiscaling methods at temporal and spatial scales, respectfully ranging from seconds to months and from millimeters to thousands of kilometers. It illustrates most of the data analysis techniques with real case studies often based on original findings. It also incorporates descriptions of current and new numerical techniques to analyze and deepen understanding of ecological situations and their solutions. Includes a Wealth of Applications and Examples This book also includes nonlinear analysis techniques and the application of concepts from chaos theory to problems of spatial and temporal patterns in ecological systems. Unlike other books on the subject, Fractals and Multifractals in Ecology and Aquatic Science is readily accessible to researchers in a variety of fields, such as microbiology, biology, ecology, hydrology, geology, oceanography, social sciences, and finance, regardless of their mathematical backgrounds. This volume demystifies the mathematical methods, many of which are often regarded as too complex, and allows the reader to access new and promising concepts, procedures, and related results.

Multi Chaos Fractal and Multi Fractional Artificial Intelligence of Different Complex Systems

Multi Chaos  Fractal and Multi Fractional Artificial Intelligence of Different Complex Systems
Author: Yeliz Karaca,Dumitru Baleanu,Yu-Dong Zhang,Osvaldo Gervasi,Majaz Moonis
Publsiher: Academic Press
Total Pages: 350
Release: 2022-07-01
Genre: Science
ISBN: 9780323886161

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Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, case studies as well as applications including theoretical aspects of complexity. Foregrounding Multi-chaos, Fractal and Multi-fractional in the era of Artificial Intelligence (AI), the edited book deals with multi- chaos, fractal, multifractional, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications, artificial intelligence, mathematics-informed and data driven processes aside from the means of modelling, and simulations for the solution of multifaceted problems characterized by nonlinearity, non-regularity and self-similarity, frequently encountered in different complex systems. The fundamental interacting components underlying complexity, complexity thinking, processes and theory along with computational processes and technologies, with machine learning as the core component of AI demonstrate the enabling of complex data to augment some critical human skills. Appealing to an interdisciplinary network of scientists and researchers to disseminate the theory and application in medicine, neurology, mathematics, physics, biology, chemistry, information theory, engineering, computer science, social sciences and other far-reaching domains, the overarching aim is to empower out-of-the-box thinking through multifarious methods, directed towards paradoxical situations, uncertain processes, chaotic, transient and nonlinear dynamics of complex systems. Constructs and presents a multifarious approach for critical decision-making processes embodying paradoxes and uncertainty. Includes a combination of theory and applications with regard to multi-chaos, fractal and multi-fractional as well as AI of different complex systems and many-body systems. Provides readers with a bridge between application of advanced computational mathematical methods and AI based on comprehensive analyses and broad theories.

The New Frontier of Network Physiology From Temporal Dynamics to the Synchronization and Principles of Integration in Networks of Physiological Systems

The New Frontier of Network Physiology  From Temporal Dynamics to the Synchronization and Principles of Integration in Networks of Physiological Systems
Author: Plamen Ch. Ivanov,Andras Eke,Olga Sosnovtseva
Publsiher: Frontiers Media SA
Total Pages: 135
Release: 2022-02-17
Genre: Science
ISBN: 9782889714353

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Nature s Patterns and the Fractional Calculus

Nature   s Patterns and the Fractional Calculus
Author: Bruce J. West
Publsiher: Walter de Gruyter GmbH & Co KG
Total Pages: 213
Release: 2017-09-11
Genre: Mathematics
ISBN: 9783110535136

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Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a system‘s information gradient. Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations. The resulting lowest order moments in system size and functionality gives rise to the empirical allometry relations. Taking examples from various topics in nature, the book is of interest to researchers in applied mathematics, as well as, investigators in the natural, social, physical and life sciences. Contents Complexity Empirical allometry Statistics, scaling and simulation Allometry theories Strange kinetics Fractional probability calculus