{"product_id":"nonlinear-dynamic-modeling-of-physiological-systems-9780471469605","title":"Nonlinear Dynamic Modeling of Physiological Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA considerable body of knowledge has grown in the search for effective ways to obtain nonlinear dynamic models from stimulus-response data in a practical context. This book summarizes some 30 years of research progress in that arena, and details the most recent methodologies that offer practical solutions to this daunting problem.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"...a perfect research tool, as reference book, and even as a textbook. I highly recommend it to everyone interested in nonlinear dynamics.\" (\u003ci\u003eJournal of Intelligent \u0026amp; Fuzzy Systems\u003c\/i\u003e, Vol. 16, No. 2, 2005)  \u003cp\u003e\"...a well-written methodology book...a useful addition to [researchers, engineers and graduate students']...personal libraries.\" (\u003ci\u003eE-STREAMS\u003c\/i\u003e, September 2005)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePrologue xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Purpose of this Book 1\u003c\/p\u003e \u003cp\u003e1.2 Advocated Approach 4\u003c\/p\u003e \u003cp\u003e1.3 The Problem of System Modeling in Physiology 6\u003c\/p\u003e \u003cp\u003e1.3.1 Model Specification and Estimation 10\u003c\/p\u003e \u003cp\u003e1.3.2 Nonlinearity and Nonstationarity 12\u003c\/p\u003e \u003cp\u003e1.3.3 Definition of the Modeling Problem 13\u003c\/p\u003e \u003cp\u003e1.4 Types of Nonlinear Models of Physiological Systems 13\u003c\/p\u003e \u003cp\u003eExample 1.1. Vertebrate Retina 15\u003c\/p\u003e \u003cp\u003eExample 1.2. Invertebrate Photoreceptor 18\u003c\/p\u003e \u003cp\u003eExample 1.3. Volterra analysis of Riccati Equation 19\u003c\/p\u003e \u003cp\u003eExample 1.4. Glucose-Insulin Minimal Model 21\u003c\/p\u003e \u003cp\u003eExample 1.5. Cerebral Autoregulation 22\u003c\/p\u003e \u003cp\u003e1.5 Deductive and Inductive Modeling 24\u003c\/p\u003e \u003cp\u003eHistorical Note #1: Hippocratic and Galenic Views of 26\u003c\/p\u003e \u003cp\u003eIntegrative Physiology\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Nonparametric Modeling 29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Volterra Models 31\u003c\/p\u003e \u003cp\u003e2.1.1 Examples of Volterra Models 37\u003c\/p\u003e \u003cp\u003eExample 2.1. Static Nonlinear System 37\u003c\/p\u003e \u003cp\u003eExample 2.2. L–N Cascade System 38\u003c\/p\u003e \u003cp\u003eExample 2.3. L–N–M “Sandwich” System 39\u003c\/p\u003e \u003cp\u003eExample 2.4. Riccati System 40\u003c\/p\u003e \u003cp\u003e2.1.2 Operational Meaning of the Volterra Kernels 41\u003c\/p\u003e \u003cp\u003eImpulsive Inputs 42\u003c\/p\u003e \u003cp\u003eSinusoidal Inputs 43\u003c\/p\u003e \u003cp\u003eRemarks on the Meaning of Volterra Kernels 45\u003c\/p\u003e \u003cp\u003e2.1.3 Frequency-Domain Representation of the Volterra Models 45\u003c\/p\u003e \u003cp\u003e2.1.4 Discrete-Time Volterra Models 47\u003c\/p\u003e \u003cp\u003e2.1.5 Estimation of Volterra Kernels 49\u003c\/p\u003e \u003cp\u003eSpecialized Test Inputs 50\u003c\/p\u003e \u003cp\u003eArbitrary Inputs 52\u003c\/p\u003e \u003cp\u003eFast Exact Orthogonalization and Parallel-Cascade Methods 55\u003c\/p\u003e \u003cp\u003eIterative Cost-Minimization Methods for Non-Gaussian 55\u003c\/p\u003e \u003cp\u003eResiduals\u003c\/p\u003e \u003cp\u003e2.2 Wiener Models 57\u003c\/p\u003e \u003cp\u003e2.2.1 Relation between Volterra and Wiener Models 60\u003c\/p\u003e \u003cp\u003eThe Wiener Class of Systems 62\u003c\/p\u003e \u003cp\u003eExamples of Wiener Models 63\u003c\/p\u003e \u003cp\u003eComparison of Volterra\/Wiener Model Predictions 64\u003c\/p\u003e \u003cp\u003e2.2.2 Wiener Approach to Kernel Estimation 67\u003c\/p\u003e \u003cp\u003e2.2.3 The Cross-Correlation Technique for Wiener Kernel Estimation 72\u003c\/p\u003e \u003cp\u003eEstimation of \u003ci\u003eh\u003c\/i\u003e\u003csub\u003e0\u003c\/sub\u003e 73\u003c\/p\u003e \u003cp\u003eEstimation of \u003ci\u003eh\u003c\/i\u003e\u003csub\u003e1\u003c\/sub\u003e (\u003ci\u003e𝜏\u003c\/i\u003e) 73\u003c\/p\u003e \u003cp\u003eEstimation of \u003ci\u003eh\u003c\/i\u003e\u003csub\u003e2\u003c\/sub\u003e (\u003ci\u003e𝜏\u003c\/i\u003e\u003csub\u003e1\u003c\/sub\u003e, \u003ci\u003e𝜏\u003c\/i\u003e\u003csub\u003e2\u003c\/sub\u003e) 74\u003c\/p\u003e \u003cp\u003eEstimation of \u003ci\u003eh\u003c\/i\u003e\u003csub\u003e3\u003c\/sub\u003e (\u003ci\u003e𝜏\u003c\/i\u003e\u003csub\u003e1\u003c\/sub\u003e, \u003ci\u003e𝜏\u003c\/i\u003e\u003csub\u003e2\u003c\/sub\u003e, \u003ci\u003e𝜏\u003c\/i\u003e\u003csub\u003e3\u003c\/sub\u003e) 75\u003c\/p\u003e \u003cp\u003eSome Practical Considerations 77\u003c\/p\u003e \u003cp\u003eIllustrative Example 78\u003c\/p\u003e \u003cp\u003eFrequency-Domain Estimation of Wiener Kernels 78\u003c\/p\u003e \u003cp\u003e2.2.4 Quasiwhite Test Inputs 80\u003c\/p\u003e \u003cp\u003eCSRS and Volterra Kernels 84\u003c\/p\u003e \u003cp\u003eThe Diagonal Estimability Problem 85\u003c\/p\u003e \u003cp\u003eAn Analytical Example 86\u003c\/p\u003e \u003cp\u003eComparison of Model Prediction Errors 88\u003c\/p\u003e \u003cp\u003eDiscrete-Time Representation of the CSRS Functional Series 89\u003c\/p\u003e \u003cp\u003ePseudorandom Signals Based on m-Sequences 89\u003c\/p\u003e \u003cp\u003eComparative Use of GWN, PRS, and CSRS 92\u003c\/p\u003e \u003cp\u003e2.2.5 Apparent Transfer Function and Coherence Measurements 93\u003c\/p\u003e \u003cp\u003eExample 2.5. L–N Cascade System 96\u003c\/p\u003e \u003cp\u003eExample 2.6. Quadratic Volterra System 97\u003c\/p\u003e \u003cp\u003eExample 2.7. Nonwhite Gaussian Inputs 98\u003c\/p\u003e \u003cp\u003eExample 2.8. Duffing System 98\u003c\/p\u003e \u003cp\u003eConcluding Remarks 99\u003c\/p\u003e \u003cp\u003e2.3 Efficient Volterra Kernel Estimation 100\u003c\/p\u003e \u003cp\u003e2.3.1 Volterra Kernel Expansions 101\u003c\/p\u003e \u003cp\u003eModel Order Determination 104\u003c\/p\u003e \u003cp\u003e2.3.2 The Laguerre Expansion Technique 107\u003c\/p\u003e \u003cp\u003eIllustrative Examples 112\u003c\/p\u003e \u003cp\u003e2.3.3 High-Order Volterra Modeling with Equivalent Networks 122\u003c\/p\u003e \u003cp\u003e2.4 Analysis of Estimation Errors 125\u003c\/p\u003e \u003cp\u003e2.4.1 Sources of Estimation Errors 125\u003c\/p\u003e \u003cp\u003e2.4.2 Estimation Errors Associated with the Cross-Correlation 127\u003c\/p\u003e \u003cp\u003eTechnique Estimation Bias 128\u003c\/p\u003e \u003cp\u003eEstimation Variance 130\u003c\/p\u003e \u003cp\u003eOptimization of Input Parameters 131\u003c\/p\u003e \u003cp\u003eNoise Effects 134\u003c\/p\u003e \u003cp\u003eErroneous Scaling of Kernel Estimates 136\u003c\/p\u003e \u003cp\u003e2.4.3 Estimation Errors Associated with Direct Inversion Methods 137\u003c\/p\u003e \u003cp\u003e2.4.4 Estimation Errors Associated with Iterative 139\u003c\/p\u003e \u003cp\u003eCost-Minimization Methods Historical Note #2: Vito Volterra and Norbert Wiener 140\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Parametric Modeling 145\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Basic Parametric Model Forms and Estimation Procedures 146\u003c\/p\u003e \u003cp\u003e3.1.1 The Nonlinear Case 150\u003c\/p\u003e \u003cp\u003e3.1.2 The Nonstationary Case 152\u003c\/p\u003e \u003cp\u003e3.2 Volterra Kernels of Nonlinear Differential Equations 153\u003c\/p\u003e \u003cp\u003eExample 3.1. The Riccati Equation 157\u003c\/p\u003e \u003cp\u003e3.2.1 Apparent Transfer Functions of Linearized Models 158\u003c\/p\u003e \u003cp\u003eExample 3.2. Illustrative Example 160\u003c\/p\u003e \u003cp\u003e3.2.2 Nonlinear Parametric Models with Intermodulation 161\u003c\/p\u003e \u003cp\u003e3.3 Discrete-Time Volterra Kernels of NARMAX Models 164\u003c\/p\u003e \u003cp\u003e3.4 From Volterra Kernel Measurements to Parametric Models 167\u003c\/p\u003e \u003cp\u003eExample 3.3. Illustrative Example 169\u003c\/p\u003e \u003cp\u003e3.5 Equivalence Between Continuous and Discrete Parametric Models 171\u003c\/p\u003e \u003cp\u003eExample 3.4. Illustrative Example 175\u003c\/p\u003e \u003cp\u003e3.5.1 Modular Representation 177\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Modular and Connectionist Modeling 179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Modular Form of Nonparametric Models 179\u003c\/p\u003e \u003cp\u003e4.1.1 Principal Dynamic Modes 180\u003c\/p\u003e \u003cp\u003eIllustrative Examples 186\u003c\/p\u003e \u003cp\u003e4.1.2 Volterra Models of System Cascades 191\u003c\/p\u003e \u003cp\u003eThe \u003ci\u003eL–N–M, L–N, \u003c\/i\u003eand \u003ci\u003eN–M\u003c\/i\u003e Cascades 194\u003c\/p\u003e \u003cp\u003e4.1.3 Volterra Models of Systems with Lateral Branches 198\u003c\/p\u003e \u003cp\u003e4.1.4 Volterra Models of Systems with Feedback Branches 200\u003c\/p\u003e \u003cp\u003e4.1.5 Nonlinear Feedback Described by Differential Equations 202\u003c\/p\u003e \u003cp\u003eExample 1. Cubic Feedback Systems 204\u003c\/p\u003e \u003cp\u003eExample 2. Sigmoid Feedback Systems 209\u003c\/p\u003e \u003cp\u003eExample 3. Positive Nonlinear Feedback 213\u003c\/p\u003e \u003cp\u003eExample 4. Second-Order Kernels of Nonlinear 215\u003c\/p\u003e \u003cp\u003eFeedback Systems Nonlinear Feedback in Sensory Systems 216\u003c\/p\u003e \u003cp\u003eConcluding Remarks on Nonlinear Feedback 220\u003c\/p\u003e \u003cp\u003e4.2 Connectionist Models 223\u003c\/p\u003e \u003cp\u003e4.2.1 Equivalence between Connectionist and Volterra Models 223\u003c\/p\u003e \u003cp\u003eRelation with PDM Modeling 230\u003c\/p\u003e \u003cp\u003eIllustrative Examples 232\u003c\/p\u003e \u003cp\u003e4.2.2 Volterra-Equivalent Network Architectures for Nonlinear 235\u003c\/p\u003e \u003cp\u003eSystem Modeling Equivalence with Volterra Kernels\/Models 238\u003c\/p\u003e \u003cp\u003eSelection of the Structural Parameters of the VEN Model 238\u003c\/p\u003e \u003cp\u003eConvergence and Accuracy of the Training Procedure 240\u003c\/p\u003e \u003cp\u003eThe Pseudomode-Peeling Method 244\u003c\/p\u003e \u003cp\u003eNonlinear Autoregressive Modeling (Open-Loop) 246\u003c\/p\u003e \u003cp\u003e4.3 The Laguerre-Volterra Network 246\u003c\/p\u003e \u003cp\u003eIllustrative Example of LVN Modeling 249\u003c\/p\u003e \u003cp\u003eModeling Systems with Fast and Slow Dynamic (LVN-2) 251\u003c\/p\u003e \u003cp\u003eIllustrative Examples of LVN-2 Modeling 255\u003c\/p\u003e \u003cp\u003e4.4 The VWM Model 260\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 A Practitioner’s Guide 265\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Practical Considerations and Experimental Requirements 265\u003c\/p\u003e \u003cp\u003e5.1.1 System Characteristics 266\u003c\/p\u003e \u003cp\u003eSystem Bandwidth 266\u003c\/p\u003e \u003cp\u003eSystem Memory 267\u003c\/p\u003e \u003cp\u003eSystem Dynamic Range 267\u003c\/p\u003e \u003cp\u003eSystem Linearity 268\u003c\/p\u003e \u003cp\u003eSystem Stationarity 268\u003c\/p\u003e \u003cp\u003eSystem Ergodicity 268\u003c\/p\u003e \u003cp\u003e5.1.2 Input Characteristics 269\u003c\/p\u003e \u003cp\u003e5.1.3 Experimental Characteristics 270\u003c\/p\u003e \u003cp\u003e5.2 Preliminary Tests and Data Preparation 272\u003c\/p\u003e \u003cp\u003e5.2.1 Test for System Bandwidth 272\u003c\/p\u003e \u003cp\u003e5.2.2 Test for System Memory 272\u003c\/p\u003e \u003cp\u003e5.2.3 Test for System Stationarity and Ergodicity 273\u003c\/p\u003e \u003cp\u003e5.2.4 Test for System Linearity 274\u003c\/p\u003e \u003cp\u003e5.2.5 Data Preparation 275\u003c\/p\u003e \u003cp\u003e5.3 Model Specification and Estimation 276\u003c\/p\u003e \u003cp\u003e5.3.1 The MDV Modeling Methodology 277\u003c\/p\u003e \u003cp\u003e5.3.2 The VEN\/VWM Modeling Methodology 278\u003c\/p\u003e \u003cp\u003e5.4 Model Validation and Interpretation 279\u003c\/p\u003e \u003cp\u003e5.4.1 Model Validation 279\u003c\/p\u003e \u003cp\u003e5.4.2 Model Interpretation 281\u003c\/p\u003e \u003cp\u003eInterpretation of Volterra Kernels 281\u003c\/p\u003e \u003cp\u003eInterpretation of the PDM Model 282\u003c\/p\u003e \u003cp\u003e5.5 Outline of Step-by-Step Procedure 283\u003c\/p\u003e \u003cp\u003e5.5.1 Elaboration of the Key Step # 5 284\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Selected Applications 285\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Neurosensory Systems 286\u003c\/p\u003e \u003cp\u003e6.1.1 Vertebrate Retina 287\u003c\/p\u003e \u003cp\u003e6.1.2 Invertebrate Retina 396\u003c\/p\u003e \u003cp\u003e6.1.3 Auditory Nerve Fibers 302\u003c\/p\u003e \u003cp\u003e6.1.4 Spider Mechanoreceptor 307\u003c\/p\u003e \u003cp\u003e6.2 Cardiovascular System 320\u003c\/p\u003e \u003cp\u003e6.3 Renal System 333\u003c\/p\u003e \u003cp\u003e6.4 Metabolic-Endocrine System 342\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Modeling of Multiinput\/Multioutput Systems 359\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 The Two-Input Case 360\u003c\/p\u003e \u003cp\u003e7.1.1 The Two-Input Cross-Correlation Technique 362\u003c\/p\u003e \u003cp\u003e7.1.2 The Two-Input Kernel-Expansion Technique 362\u003c\/p\u003e \u003cp\u003e7.1.3 Volterra-Equivalent Network Models with Two Inputs 364\u003c\/p\u003e \u003cp\u003eIllustrative Example 366\u003c\/p\u003e \u003cp\u003e7.2 Applications of Two-Input Modeling to Physiological Systems 369\u003c\/p\u003e \u003cp\u003e7.2.1 Motion Detection in the Invertebrate Retina 369\u003c\/p\u003e \u003cp\u003e7.2.2 Receptive Field Organization in the Vertebrate Retina 370\u003c\/p\u003e \u003cp\u003e7.2.3 Metabolic Autoregulation in Dogs 378\u003c\/p\u003e \u003cp\u003e7.2.4 Cerebral Autoregulation in Humans 380\u003c\/p\u003e \u003cp\u003e7.3 The Multiinput Case 389\u003c\/p\u003e \u003cp\u003e7.3.1 Cross-Correlation-Based Method for Multiinput Modeling 390\u003c\/p\u003e \u003cp\u003e7.3.2 The Kernel-Expansion Method for Multiinput Modeling 393\u003c\/p\u003e \u003cp\u003e7.3.3 Network-Based Multiinput Modeling 393\u003c\/p\u003e \u003cp\u003e7.4 Spatiotemporal and Spectrotemporal Modeling 395\u003c\/p\u003e \u003cp\u003e7.4.1 Spatiotemporal Modeling of Retinal Cells 398\u003c\/p\u003e \u003cp\u003e7.4.2 Spatiotemporal Modeling of Cortical Cells 401\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Modeling of Neuronal Systems 407\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 A General Model of Membrane and Synaptic Dynamics 408\u003c\/p\u003e \u003cp\u003e8.2 Functional Integration in the Single Neuron 414\u003c\/p\u003e \u003cp\u003e8.2.1 Neuronal Modes and Trigger Regions 417\u003c\/p\u003e \u003cp\u003eIllustrative Examples 427\u003c\/p\u003e \u003cp\u003e8.2.2 Minimum-Order Modeling of Spike-Output Systems 432\u003c\/p\u003e \u003cp\u003eThe Reverse-Correlation Technique 432\u003c\/p\u003e \u003cp\u003eMinimum-Order Wiener Models 435\u003c\/p\u003e \u003cp\u003eIllustrative Example 439\u003c\/p\u003e \u003cp\u003e8.3 Neuronal Systems with Point-Process Inputs 439\u003c\/p\u003e \u003cp\u003e8.3.1 The Lag-Delta Representation of \u003ci\u003eP–V\u003c\/i\u003e or \u003ci\u003eP–W\u003c\/i\u003e Kernels 445\u003c\/p\u003e \u003cp\u003e8.3.2 The Reduced \u003ci\u003eP–V\u003c\/i\u003e or \u003ci\u003eP–W\u003c\/i\u003e Kernels 446\u003c\/p\u003e \u003cp\u003e8.3.3 Examples from the Hippocampal Formation 450\u003c\/p\u003e \u003cp\u003eSingle-Input Stimulation in Vivo and Cross-Correlation  450\u003c\/p\u003e \u003cp\u003eTechnique\u003c\/p\u003e \u003cp\u003eSingle-Input Stimulation in Vitro and Laguerre-Expansion 455\u003c\/p\u003e \u003cp\u003eTechnique\u003c\/p\u003e \u003cp\u003e Dual-Input Stimulation in the Hippocampal Slice 457\u003c\/p\u003e \u003cp\u003eNonlinear Modeling of Synaptic Dynamics 461\u003c\/p\u003e \u003cp\u003e8.4 Modeling of Neuronal Ensembles 463\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Modeling of Nonstationary Systems 467\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Quasistationary and Recursive Tracking Methods 468\u003c\/p\u003e \u003cp\u003e9.2 Kernel Expansion Method 469\u003c\/p\u003e \u003cp\u003e9.2.1 Illustrative Example 474\u003c\/p\u003e \u003cp\u003e9.2.2 A Test of Nonstationarity 475\u003c\/p\u003e \u003cp\u003e9.2.3 Linear Time-Varying Systems with Arbitrary Inputs 479\u003c\/p\u003e \u003cp\u003e9.3 Network-Based Methods 480\u003c\/p\u003e \u003cp\u003e9.3.1 Illustrative Examples 481\u003c\/p\u003e \u003cp\u003e9.4 Applications to Nonstationary Physiological Systems 484\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Modeling of Closed-Loop Systems 489\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Autoregressive Form of Closed-Loop Model 490\u003c\/p\u003e \u003cp\u003e10.2 Network Model Form of Closed-Loop Systems 491\u003c\/p\u003e \u003cp\u003eAppendix I Function Expansions 495\u003c\/p\u003e \u003cp\u003eAppendix II Gaussian White Noise 499\u003c\/p\u003e \u003cp\u003eAppendix III Construction of the Wiener Series 503\u003c\/p\u003e \u003cp\u003eAppendix IV Stationarity, Ergodicity, and Autocorrelation Functions of Random Processes 505\u003c\/p\u003e \u003cp\u003e References 507\u003c\/p\u003e \u003cp\u003eIndex 535\u003c\/p\u003e","brand":"Wiley-Blackwell","offers":[{"title":"Default Title","offer_id":53515428036951,"sku":"9780471469605","price":147.56,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/nonlinear-dynamic-modeling-of-physiological-systems-9780471469605","provider":"Book Curl","version":"1.0","type":"link"}