LEADER 05433nam 2200685Ia 450 001 9910828029503321 005 20230721033232.0 010 $a1-281-92446-6 010 $a9786611924461 010 $a981-277-279-0 035 $a(CKB)1000000000552355 035 $a(EBL)1209932 035 $a(SSID)ssj0000304524 035 $a(PQKBManifestationID)12113041 035 $a(PQKBTitleCode)TC0000304524 035 $a(PQKBWorkID)10285184 035 $a(PQKB)10439732 035 $a(MiAaPQ)EBC1209932 035 $a(WSP)00006240 035 $a(Au-PeEL)EBL1209932 035 $a(CaPaEBR)ebr10698844 035 $a(CaONFJC)MIL192446 035 $a(OCoLC)854972286 035 $a(EXLCZ)991000000000552355 100 $a20070321d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNonlinear dynamics in physiology$b[electronic resource] $ea state-space approach /$fMark Shelhamer 210 $aSingapore ;$aHackensack, NJ $cWorld Scientific$dc2007 215 $a1 online resource (367 p.) 300 $aDescription based upon print version of record. 311 $a981-270-029-3 320 $aIncludes bibliographical references and index. 327 $aPreface; Contents; 1. The mathematical analysis of physiological systems: goals and approaches; 1.1 The goals of mathematical analysis in physiology; 1.2 Outline of dynamic systems; 1.3 Types of dynamic systems - random, deterministic, linear, nonlinear; 1.4 Types of dynamic behaviors - random, fixed point, periodic, quasi-periodic, chaotic; 1.5 Follow the ""noise""; 1.6 Chaos and physiology; General Bibliography; References for Chapter 1; 2. Fundamental signal processing and analysis concepts and measures; 2.1 Sampled data and continuous distributions; 2.2 Basic statistics 327 $a2.3 Correlation coefficient2.4 Linear regression, least-squares, squared-error; 2.5 Random processes, white noise, correlated noise; 2.6 Autocorrelation; 2.7 Concluding remarks; References for Chapter 2; 3. Analysis approaches based on linear systems; 3.1 Definition and properties of linear systems; 3.2 Autocorrelation, cross-correlation, stationarity; 3.3 Fourier transforms and spectral analysis; 3.4 Examples of autocorrelations and frequency spectra; 3.5 Transfer functions of linear systems, Gaussian statistics; References for Chapter 3; 4. State-space reconstruction 327 $a4.1 State variables, state space4.2 Time-delay reconstruction; 4.3 A digression on topology; 4.4 How to do the reconstruction correctly; 4.5 Example: detection of fast-phase eye movements; 4.6 Historical notes, examples from the literature; 4.7 Points for further consideration; References for Chapter 4; 5. Dimensions; 5.1 Euclidean dimension and topological dimension; 5.2 Dimension as a scaling process - coastline length, Mandelbrot, fractals, Cantor, Koch; 5.3 Box-counting dimension and correlation dimension; 5.4 Correlation dimension - how to measure it correctly 327 $a5.5 Error bars on dimension estimates5.6 Interpretation of the dimension; 5.7 Tracking dimension overtime; 5.8 Examples; 5.9 Points for further consideration; References for Chapter 5; 6. Surrogate data; 6.1 The need for surrogates; 6.2 Statistical hypothesis testing; 6.3 Statistical randomization and its implementation; 6.4 Random surrogates; 6.5 Phase-randomization surrogate; 6.6 AAFT surrogate; 6.7 Pseudo-periodic surrogate; 6.8 First differences and surrogates; 6.9 Multivariate surrogates; 6.10 Surrogates tailored to specific physiological hypotheses; 6.11 Examples of different surrogates 327 $a6.12 Physiological examplesReferences for Chapter 6; 7. Nonlinear forecasting; 7.1 Predictability of prototypical systems; 7.2 Methodology; 7.3 Variations; 7.4 Surrogates, global linear forecasting; 7.5 Time-reversal and amplitude-reversal for detection of nonlinearity; 7.6 Chaos versus colored noise; 7.7 Forecasting of neural spike trains and other discrete events; 7.8 Examples; References for Chapter 7; 8. Recurrence analysis; 8.1 Concept and methodology; 8.2 Recurrence plots of simple systems; 8.3 Recurrence quantification analysis (RQA); 8.4 Extensions; 8.5 Examples 327 $aReferences for Chapter 8 330 $aThis book provides a compilation of mathematical-computational tools that are used to analyze experimental data. The techniques presented are those that have been most widely and successfully applied to the analysis of physiological systems, and address issues such as randomness, determinism, dimension, and nonlinearity. In addition to bringing together the most useful methods, sufficient mathematical background is provided to enable non-specialists to understand and apply the computational techniques. Thus, the material will be useful to life-science investigators on several levels, from phys 606 $aPhysiology$xMathematical models 606 $aNonlinear systems 606 $aState-space methods 615 0$aPhysiology$xMathematical models. 615 0$aNonlinear systems. 615 0$aState-space methods. 676 $a515.252 676 $a571.01/5118 676 $a571.015118 700 $aShelhamer$b Mark$0511746 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910828029503321 996 $aNonlinear Dynamics in Physiology$9764149 997 $aUNINA