Series Foreword |
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xi | |
Preface |
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xiii | |
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1 | (24) |
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1 | (2) |
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1.2 A Motivational Example |
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3 | (7) |
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10 | (4) |
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1.4 Expectation and Covariance |
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14 | (3) |
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1.5 Recursive Least Squares |
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17 | (2) |
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1.6 It's a Bayesian World |
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19 | (6) |
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25 | (16) |
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2.1 Linear Kalman Filtering |
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25 | (4) |
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2.2 Nonlinear Kalman Filtering |
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29 | (8) |
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2.3 Why Not Neuroscience? |
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37 | (4) |
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3 The Hodgkin-Huxley Equations |
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41 | (38) |
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3.1 Pre-Hodgkin and Huxley |
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41 | (2) |
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3.2 Hodgkin and Huxley and Colleagues |
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43 | (6) |
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49 | (30) |
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4 Simplified Neuronal Models |
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79 | (18) |
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4.1 The Van der Pol Equations |
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79 | (3) |
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4.2 Frequency Demultiplication |
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82 | (1) |
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4.3 Bonhoeffer and the Passivation of Iron |
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82 | (4) |
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4.4 Fitzhugh and Neural Dynamics |
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86 | (5) |
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4.5 Nagumo's Electrical Circuit |
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91 | (1) |
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91 | (3) |
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4.7 Simplified Models and Control |
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94 | (3) |
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5 Bridging from Kalman to Neuron |
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97 | (18) |
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97 | (2) |
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5.2 Variables and Parameters |
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99 | (2) |
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5.3 Tracking the Lorenz System |
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101 | (3) |
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104 | (2) |
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5.5 The Fitzhugh-Nagumo Equations |
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106 | (9) |
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6 Spatiotemporal Cortical Dynamics---The Wilson Cowan Equations |
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115 | (38) |
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6.1 Before Wilson and Cowan |
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115 | (1) |
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6.2 Wilson and Cowan before 1973 |
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116 | (10) |
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6.3 Wilson and Cowan during 1973 |
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126 | (5) |
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6.4 Wilson and Cowan after 1973 |
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131 | (2) |
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6.5 Spirals, Rings, and Chaotic Waves in Brain |
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133 | (6) |
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6.6 Wilson-Cowan in a Control Framework |
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139 | (14) |
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153 | (30) |
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153 | (3) |
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7.2 The Second Rehnquist Court |
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156 | (5) |
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7.3 The Geometry of Singular Value Decomposition |
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161 | (3) |
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7.4 Static Image Decomposition |
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164 | (2) |
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7.5 Dynamic Spatiotemporal Image Analysis |
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166 | (2) |
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7.6 Spatiotemporal Brain Dynamics |
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168 | (15) |
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183 | (32) |
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183 | (2) |
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8.2 The Philosophy of Model Inadequacy |
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185 | (1) |
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8.3 The Mapping Paradigm---Initial Conditions |
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186 | (4) |
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8.4 The Transformation Paradigm |
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190 | (5) |
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8.5 Generalized Synchrony |
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195 | (4) |
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8.6 Data Assimilation as Synchronization of Truth and Model |
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199 | (9) |
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208 | (7) |
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9 Brain-Machine Interfaces |
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215 | (22) |
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215 | (1) |
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215 | (1) |
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216 | (3) |
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219 | (5) |
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9.5 Beyond Bins---Moving from Rates to Points in Time |
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224 | (3) |
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227 | (5) |
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9.7 When Bad Models Happen to Good Monkeys |
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232 | (2) |
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234 | (3) |
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237 | (36) |
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237 | (2) |
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10.2 The Networks of Parkinson's Disease |
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239 | (1) |
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10.3 The Thalamus---It's Not a Simple Relay Anymore |
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240 | (1) |
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10.4 The Contribution of China White |
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241 | (1) |
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10.5 Dynamics of Parkinson's Networks |
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242 | (4) |
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10.6 The Deep Brain Stimulation Paradox |
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246 | (2) |
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10.7 Reductionist Cracking the Deep Brain Stimulation Paradox |
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248 | (8) |
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10.8 A Cost Function for Deep Brain Stimulation |
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256 | (3) |
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10.9 Fusing Experimental GPi Recordings with DBS Models |
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259 | (1) |
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10.10 Toward a Control Framework for Parkinson's Disease |
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259 | (10) |
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269 | (4) |
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11 Control Systems with Electrical Fields |
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273 | (28) |
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273 | (1) |
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11.2 A Brief History of the Science of Electrical Fields and Neurons |
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273 | (4) |
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11.3 Applications of Electrical Fields in Vitro |
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277 | (2) |
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11.4 A Brief Affair with Chaos |
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279 | (4) |
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11.5 And a Fling with Ice Ages |
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283 | (1) |
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11.6 Feedback Control with Electrical Fields |
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284 | (3) |
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11.7 Controlling Propagation---Speed Bumps for the Brain |
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287 | (2) |
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11.8 Neurons in the Resistive Brain |
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289 | (1) |
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11.9 How Small an Electrical Field Will Modulate Neuronal Activity? |
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290 | (3) |
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11.10 Transcranial Low-Frequency Fields |
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293 | (1) |
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11.11 Electrical Fields for Control Within the Intact Brain |
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293 | (4) |
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11.12 To Sleep Perchance to Dream |
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297 | (1) |
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11.13 Toward an Implantable Field Controller |
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298 | (3) |
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301 | (26) |
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301 | (1) |
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12.2 Hodgkin-Huxley Revisited |
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302 | (4) |
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12.3 The Dynamics of Potassium |
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306 | (10) |
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12.4 Control of Single Cells with Hodgkin-Huxley and Potassium Dynamics |
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316 | (3) |
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12.5 Assimilating Seizures |
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319 | (1) |
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12.6 Assimilation in the Intact Brain |
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320 | (3) |
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323 | (4) |
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327 | (10) |
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13.1 We Are All State Estimation Machines |
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327 | (1) |
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327 | (1) |
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13.3 Robot Beliefs versus Cogito Ergo MRI |
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328 | (2) |
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13.4 Black versus Gray Swans |
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330 | (2) |
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13.5 Mirror, Mirror, within My Mind |
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332 | (1) |
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13.6 Carl Jung's Synchronicity |
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333 | (4) |
Bibliography |
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337 | (20) |
Index |
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357 | |