Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators [Risorsa elettronica] / by Ivan Veselic

• Record Nr.: UNINA990009254460403321
• Autore: Veselic, Ivan
• Pubbl/distr/stampa: Berlin ; Heidelberg : Springer, 2008
• ISBN: 9783540726913
• Collana: Lecture Notes in Mathematics , 0075-8434 ; 1917
• Lingua di pubblicazione: Inglese
• Formato: Risorsa elettronica
• Livello bibliografico: Monografia

Fractal physiology and chaos in medicine [[electronic resource] /] / Bruce J. West

• Record Nr.: UNINA9910465413703321
• Autore: West Bruce J
• Pubbl/distr/stampa: Singapore ; ; London, : World Scientific, 2013
• ISBN: 1-299-28117-6; 981-4417-80-7
• Edizione: [2nd ed.]
• Descrizione fisica: 1 online resource (345 p.)
• Collana: Studies of nonlinear phenomena in life sciences ; ; v. 16
• Disciplina: 610.151539; 612.0154; 612/.0154
• Soggetti: Chaotic behavior in systems; Fractals; Medicine - Mathematical models; Physiology - Mathematical models; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Contents; Preface; 1 Introduction; 1.1 What is Linearity?; 1.2 Why Uncertainty?; 1.3 How Does Nonlinearity Change Our View?; 1.4 Complex Networks; 1.5 Summary and a Look Forward; 2 Physiology in Fractal Dimensions; 2.1 Complexity and the Lung; 2.2 The Principle of Similitude; 2.2.1 Fractals, Self-similarity and Renormalization; 2.2.2 Fractal Lungs; 2.2.3 Why fractal transport?; 2.3 Allometry Relations; 2.3.1 Empirical Allometry; 2.3.2 WBE model; 2.3.3 WW model; 2.4 Fractal Signals; 2.4.1 Spectral decomposition; 2.5 Summary; 3 Dynamics in Fractal Dimensions; 3.1 Nonlinear Bio-oscillators; 3.1.1 Super Central Pattern Generator (SCPG) model of gait3.1.2 The cardiac oscillator; 3.1.3 Strange attractors (deterministic randomness); 3.2 Nonlinear Bio-mapping; 3.2.1 One-dimensional maps; 3.2.2 Two-dimensional maps; 3.2.3 The Lyapunov exponent; 3.3 Measures of Strange Attractors; 3.3.1 Correlational dimension; 3.3.2 Attractor reconstruction from data; 3.3.3 Chaotic attractors and false alarms; 3.4 Summary and perspective; 4 Statistics in Fractal Dimensions; 4.1 Complexity and Unpredictability; 4.1.1 Scaling Measures; 4.2 Fractal Stochastic Dynamics; 4.2.1 Simple Random Walks; 4.2.2 Fractional random walks and scaling4.2.3 Physical/physiological models; 4.3 Physiologic Time Series; 4.3.1 Heart Rate Variability (HRV); 4.3.2 Breath rate variability (BRV); 4.3.3 Stride rate variability (SRV); 4.4 Summary and Viewpoint; 5 Applications of Chaotic Attractors; 5.1 The Dynamics of Epidemics; 5.2 Chaotic Neurons; 5.3 Chemical Chaos; 5.4 Cardiac Chaos; 5.5 EEG Data and Brain Dynamics; 5.5.1 Normal activity; 5.5.2 Epilepsy: reducing the dimension; 5.5.3 Task-related scaling; 5.6 Retrospective; 6 Physiological Networks: The Final Chapter?; 6.1 Introduction to Complex Networks; 6.1.1 A little history6.1.2 Inverse power laws; 6.2 The Decision Making Model (DMM); 6.2.1 Topological Complexity; 6.2.2 Temporal Complexity; 6.3 Criticality; 6.3.1 Neuronal Avalanches; 6.3.2 Multiple Organ Dysfunction Syndrome (MODS); 6.4 Finale; References; Index
• Sommario/riassunto: This exceptional book is concerned with the application of fractals and chaos, as well as other concepts from nonlinear dynamics to biomedical phenomena. Herein we seek to communicate the excitement being experienced by scientists upon making application of these concepts within the life sciences. Mathematical concepts are introduced using biomedical data sets and the phenomena being explained take precedence over the mathematics.In this new edition what has withstood the test of time has been updated and modernized; speculations that were not borne out have been expunged and the breakthroughs