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Scott A. Ч Neuroscience: a mathematical primer
Scott A. Ч Neuroscience: a mathematical primer

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Ќазвание: Neuroscience: a mathematical primer

јвтор: Scott A.

јннотаци€:

This is an introductory text of mathematical neuroscience intended for anyone who wants to appreciate the role that mathematics and mathematical modeling and analysis can do to aid an understanding of how the brain works and the nature of the mind. In particular, the book will be of interest to established neuroscientists and neuroscience students who wish to know what roles mathematical formulations can play in attempting to comprehend the dynamics of a human brain. It is expected that this text will be interesting for mathematics faculty teaching in neuroscience programs. It also aims to serve as a general introduction to neuromathematics in neuroscience programs at both undergraduate and graduate levels. Physical scientists and bioengineers who plan to extend their research activities into the realms of cognitive science will find this an ideal guide, as will philosophers and social scientists who wish to understand the degree to which dynamics of a brain can be reduced to mathematical formulations. Mathematical formulations in neuroscience are of five sorts: (i) Exact descriptions of well understood dynamic processes, like the Hodgkin Ч Huxley theory of the nerve impulse. (ii) Metaphorical descriptions of more complex phenomena, like the stationary states of a Hopfield model. (iii) Information theory for dealing with the storage and transmission of data. (iv) Logical calculus (Boolean algebra) for the analysis of information processing systems. (v) Number theory for counting large numbers of possibilities. (vi) Statistical tools for organizing and evaluating data.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2002

 оличество страниц: 352

ƒобавлена в каталог: 10.12.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abbott, L.F.      221
Absolute refractory zone      88 89
Action integral      316
Action potential      4 84 118 131 212
Action potential, space-clamped      74Ч77
Active medium      2
Active nodes      7 74 139 153
Active nodes, measurements of      148Ч153 157 158
Active nodes, model of      140Ч143
ADALINE      237
Adelman, W.J.      87 219
Adenosine-triphosphate (ATP)      64
Adjoint operator      322 332
Admittance and impedance      197
Adrian, Edgar Douglas      3 5 86
Alignment parameter      179 180 181
All-or-nothing response      287
All-or-nothing response dendrites      188 195 206
All-or-nothing response nerve impulse      3 5 6 10
All-or-nothing response neurons      41 235
All-or-nothing response of cell assemblies      268 306
Altenberger, R.      202 223
Amit, Daniel J.      307
AND, OR, and NOT gates      235 237
Anderson, Philip      297
Arbib, Michael      187
Arctic fish      158 159
Arimoto, S.      123
Aristotle      11
AristotleТs final cause      299 310
AristotleТs final cause types of causality      298Ч299
Arnold, John M.      68
Arrow of time      33 34 45 129
Arvanitaki, A.      166
Associative cortex      264
Attention      17 18 259 308
Attractor      15 287
Attractor for cell assembly      268 307
Attractor for cell assembly, nerve impulse      84
Attractor in weak downward causation      302
Attractor neural networks      244Ч248 276 307
Attractor neural networks, basin of attraction      244 247
Attractor neural networks, interconnection matrix      245 247
Attractor neural networks, limit cycles      244
Attractor neural networks, memory patterns      247
Attractor neural networks, storage in      147Ч248
Attractor neural networks, transients in      244
Attractor, basin of      91 244 246
Autoassociative memories      277 278
Automatic frequency control      302
Axonal computation      187
Axonal computation impulses, stability of      323Ч330
Axonal computation processes      9 10 26Ч27 33
Axonal information processing      8 217Ч220
Axonal information processing ephaptic coupling      219Ч220
Axonal information processing impulse steering      219 220 224
Axonal information processing myelinated fibers      219
Axonal information processing potassium build up      219
Axonal information processing synapses on active nodes      219
Axonal information processing Уhot spotsФ      219
Axoplasmic resistivity      see Cytoplasmic resistivity
Baas, Nils A.      309
Baker, R.F.      90
Barenblatt, G.I.      108 324
Batteries, ionic      73 76 80 86 127
Bazhenov, M.      284
Behaviorism      12 234 258 265 293
Belgium, population of      15 16 271
Benedict, Ruth      309
Bernstein, Julius      3
Beurle, R.L.      248
Bimolecular soap film      51
Binczak, Stephane      180
Binding problem      249
Biological hierarchy      293Ч294 306 310
Biological reductionism      294Ч296
Biological reductionism, objections to      296Ч305
Biological reductionism, objections to causality      298
Biological reductionism, objections to closed causal loops      303Ч305
Biological reductionism, objections to constructivism      297
Biological reductionism, objections to emergence      304
Biological reductionism, objections to immense numbers of possibilities      297Ч298
Biological reductionism, objections to nature of time      301
Biological reductionism, objections to open systems      303
Biomolecular cell membrane      51Ч52
Bipolar transistor      59
Block at abrupt widening      201Ч202
Block at abrupt widening, M-C analysis      202
Block at abrupt widening, MornevТs analysis      202Ч204
Block at branchings      204Ч205 223
Block at branchings, H-H model      202 204
Block at branchings, leading-edge models      205
Block at branchings, M-C model      205
Bodegard, A.      307
Bogoslovskaya, L.S.      199
Boltzmann constant      59
Boolean algebra      235
Boolean algebra functions      211 213 235Ч237 240 243
Boolean algebra networks, general      241Ч243
Boolean algebra numbers      245
Boolean algebra, arithmetic      236
Bottom-up vs. top-down approaches to brain studies      273
Bound charge      53 55
Boundary layers for F-N      132
Bower, J.M.      207
Boyd, L.A.      157
Branching exponents      213
Branching exponents, natural systems      206
Branching exponents, regions of nerve fibers      43
Broca, Paul      11
Brown, Robert      58
Brownian motion      58 59
Buratti, R.J.      199Ч200 324
Buss, L.W.      309
Cable equation      91 110 115
Cable equation, derivation of      77Ч78
Cable equation, parameters for      77
Calcium ions      37 38 62Ч63 77
Calcium ions spikes      216
Candle flame      2 16 18 31 33 34 115 303
Capacitance of membrane      53Ч55
Capacitive current      60 68
Casten, R.G.      331 333
Cat sciatic nerves      149 150 151
Cataracts      259
Causality      34 37 43 296
Causality downward      301Ч303 309
Causality downward medium      302 306
Causality downward strong      302 306
Causality downward weak      302 306
Causality joint      299 300
Causality, four types of      298Ч300
Causality, nonlinear      43 300Ч301
Cause and effect      34 321
Cell assemblies      17Ч18 19
Cell assemblies primary learning      265
Cell assemblies vs. associative networks      277Ч278
Cell assemblies, A/S ratio      265
Cell assemblies, ambiguous perceptions      262 287
Cell assemblies, animal learning environments      264
Cell assemblies, birth of theory      258Ч261
Cell assemblies, early evidence for      261Ч265
Cell assemblies, elementary dynamics of      266Ч270
Cell assemblies, emergence of      268
Cell assemblies, firing rate      267Ч268 271
Cell assemblies, ignition of      260 266 270 279Ч280
Cell assemblies, information in      310
Cell assemblies, language learning      261Ч262
Cell assemblies, latent vs. strong contacts      275
Cell assemblies, number of      274Ч278
Cell assemblies, organization of      307Ч308
Cell assemblies, realistic models of      278Ч282
Cell assemblies, realistic models of after activity      279 288
Cell assemblies, realistic models of competition      280
Cell assemblies, realistic models of neural models      278Ч279
Cell assemblies, realistic models of noise suppression      280
Cell assemblies, realistic models of pattern completion      279Ч280
Cell assemblies, realistic models of reaction times      279
Cell assemblies, realistic models of slow firing rates      280Ч281
Cell assemblies, realistic models of time delays      280 308
Cell assemblies, recent evidence for      282Ч287
Cell assemblies, robustness      261
Cell assemblies, role of inhibition      287
Cell assemblies, role of inhibition in cell assemblies      270Ч274 280Ч281
Cell assemblies, role of inhibition in cortical waves      250
Cell assemblies, role of inhibition in NOT elements      213
Cell assemblies, sensory deprivation      264Ч265 287
Cell assemblies, stabilized image experiments      262Ч264 287
Cell assemblies, subassemblies      263 274 275 276
Cell assemblies, УMark IIФ theory      270 272
Cell membrane      28
Cerebellum      11 207
Characteristic admittance and conductance      196Ч197 206
Chemical synapses      35Ч38 44 45 215Ч217
Chemical synapses active      39 216
Chemical synapses passive      38 216
Chimpanzees      258
Chizmadzhev, Y.A.      105 115Ч122 136
Christensen, Tom      285
Christmas lectures of Faraday      2Ч3
Closed causal loops      234 294 304 305
Closed causal loops in brain models      11 12 244 287
Closed causal loops in brain models morphogenesis      252
Closed causal loops in brain models nerve impulses      2 7 79 122
Closed causal loops in brain models nonlinear hierarchies      306Ч307
Closed causal loops in brain models origins of life      14Ч15
Closed systems      34 316Ч318
Cluster sensitivity      215Ч217 221
Cochlear (auditory) neurons      201
Cognitive hierarchy      293 299 305Ч309
Cognitive hierarchy, cell assemblies in      305Ч306
Cognitive hierarchy, interaction with biological hierarchy      309
Cognitive hierarchy, internal levels of      305Ч306 310
Cognitive reductionism      306
Cohen, H.      331
Cohen, L.B.      284
Coherent states      2 119 234 304 306
Cole, Kenneth      3Ч4 68 69 70 73 90 103 115 142 159
Color bands      51
Compartmental models      215
Compartmental models, NEURON and GENESIS      221 222
Compartmental models, possible errors in      222Ч223
Computational anatomy      222
Computational power of a neuron      10 187 213 219Ч220
Computational power of a neuron, McCulloch Ч Pitts neuron      42^3
Computational power of a neuron, multiplex neuron      43 222
Computational power of a neuron, real neurons      44Ч45 187
Condouris, G.A.      86
Conduction current      28 56Ч57 61 62
Connection theory      258
Conservation laws      193 315Ч316
Conservation laws, approximate      110
Conservation of energy      2 30 31 34 45 128Ч129
Conservative systems      316Ч318
Conserved quantities      315 316
Conserved quantities, density of      315
Conserved quantities, flow of      315
Constantine Ч Paton, Martha      251
Constructivism vs. reductionism      297 301
Cooley, J.W.      85 86
Coordinate transformation(s)      108 323Ч324
Coppin, C.M.L.      157
Corpus callosum      177 182
Correlation      18 282Ч284 287 288
Cortical field theories      234 248Ч252
Cortical field theories УstripesФ      251
Cowan, Jack      249
Crayfish (Orconectes virilis) axon, branching GR for      218
Critical point for F-N      125
Critical point for F-N for impulse propagation      85
Critical wavelength      126
Critical wavelength widening ratio      202
Cubic polynomial model      4 99 100
Cubic polynomial model for cell assemblies      269
Cubic polynomial model for cell assemblies cortical waves      249
Cubic polynomial model for cell assemblies FitzHugh Ч Nagumo model      123
Cubic polynomial model for cell assemblies leading-edge      102Ч103 104 105 170 203
Cubic polynomial model for cell assemblies myelinated nerves      142
Curtis, H.J.      103
Cybernetics      13 14 299
Cytoplasmic resistivity      40 77 83 197
De Schutter, E.      207
Deadwyler, S.A.      286
Decoherence times      34
Decremental conduction      6 86Ч87 194Ч195
Decremental conduction, critical point for      85Ч86 125 223
Decremental conduction, effect(s) of temperature      87
Decremental conduction, effect(s) of temperature, leakage conductance      87
Decremental conduction, effect(s) of temperature, potassium ion concentration      87
Degradation of impulse      84Ч87
Dendritic models      34 187 225
Dendritic models branchings      196 208 209
Dendritic models calcium channels      210
Dendritic models cat motoneurons      192
Dendritic models spines      35 36 199
Dendritic models trees      8 9 26Ч27 189 208
Dendritic models, AND bifurcations      209Ч210 211 215 217
Dendritic models, Boolean logic in      33 207Ч213
Dendritic models, diffusion constants      191
Dendritic models, electrotonic length      192 197 198
Dendritic models, linear      188Ч199
Dendritic models, multiplicative nonlinearities      213Ч217
Dendritic models, OR bifurcations      208Ч209 211
Dendritic models, RailТs equivalent cylinder      195Ч199 224
Dendritic models, reasons for lower safety factor      210
Dendritic models, reflections in      196
Dendritic models, thermal analog of      193
Dendrodendritic interactions      44Ч45
Density of conserved quantity      315
Depolarization      37
Descartes, Rene      11
Detailed balance      58
Dev, P.      44 45
Diffusion (Nernst) potential      37 62 97 142 143 144
Diffusion (Nernst) potential constant(s)      3 32 57 249
Diffusion (Nernst) potential current      28 40 57 61 62 65
Diffusion (Nernst) potential equation, linear      32 189 192 318
Diffusion (Nernst) potential equation, nonlinear      see Nonlinear diffusion
Dirac delta function      32 191 192
Discreteness parameter      144 179
Displacement current      28 53Ч55 68
Dissipative systems      316
DNA and RNA      300 301 304
Dodge, F.A.      85 86
Double impulse experiments      87Ч90 224
Double impulse experiments blocking observations      211 212
Double impulse experiments KhodorovТs calculations      211 224
Double impulse experiments refractory zones      88 89
Drift current      40 56
Drift current velocity      56
Drift current-diffusion equation      200
Du BoisЧReymond, Emil      2
Dualism, substance vs. property      295
Dynamite fuse      2
Earthworm (Lumbricus terrestris), enhancement zone for      90
Edelman, Gerald      18
Efficient causes      299 300 301
Eigen, Manfred      309
Eigenfunctions      134 325
Eigenvalues, continuous      134 325Ч326
1 2 3 4
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