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



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Íàçâàíèå: Neuroscience: a mathematical primer

Àâòîð: Scott A.

Àííîòàöèÿ:

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 — 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.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 2002

Êîëè÷åñòâî ñòðàíèö: 352

Äîáàâëåíà â êàòàëîã: 10.12.2005

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
McCulloch, Warren      9 11 233 235 237 252
McLeod, J.B.      135
McMullen, T.      279
Meaningful information      9 310
Mel, Bartlett      213 215 217 220 243
Membrane(s)      3 49—65
Membrane(s) batteries      37 38 60—63 73 80 127
Membrane(s) capacitance      31 53—55
Membrane(s) energetics      49 50—52
Membrane(s) model      60—62
Membrane(s) patches      10 219
Membrane(s) permeability      4 37 61—63
Membrane(s) permeability in H-H model      70—73
Membrane(s) pores (channels)      61 76—77
Membrane(s) proteins, intrinsic      28 45 61
Membrane(s) time constant      190 191 199
Memory      8 279—280
Memory in associative neural nets      247—248
Memory in associative neural nets cell assembly theory      261—262 279—280 307—308
Microprobe arrays      see Multiple electrode recordings
Milner, Peter      270 272
Mobility, ionic      56
Molecular Dynamics      28—30 34
Molecular dynamics, structure      50
Molecular dynamics, vibrations      33
Mollusk (Aplysia)      284
Momentum density      317
Monkeys, experiments on      284
Moore, John W.      140 141 147 167
Mornev, Oleg      202
Morphogenesis      49
Moth (Manduca sexto)      285
Moving coordinate system      134 323—324
Mueller, Paul      52
Multiple electrode recordings      18 19 285 287
Multiplex neuron      43 44 46 222
Myelinated nerve(s)      6 7 8 27 74 139—159
Myelinated nerve(s) continuum limit      145—146 147 159
Myelinated nerve(s) energy expended in      7 139 140
Myelinated nerve(s) evolutionary design temperature (EDT)      155
Myelinated nerve(s) evolutionary design temperature perspective      153—158 159
Myelinated nerve(s) failure      146 159
Myelinated nerve(s) impulse speed      144—146
Myelinated nerve(s) integrate and fire model      154 156
Myelinated nerve(s) internode conduction time      150
Myelinated nerve(s) internode conduction time predicted for artic fish      158
Myelinated nerve(s) internode conduction time vertebrates      152
Myelinated nerve(s) internode conduction time, general expression for      154
Myelinated nerve(s) internode distance      151 152 157
Myelinated nerve(s) numerical studies      147—148
Myelinated nerve(s) optimal design of      149 153—159
Myelinated nerve(s) saltatory limit      146—147 159
Myelinated nerve(s) statistical properties of      149 150 157—158
Myelinated nerve(s) various vertebrates      152
Myelinated nerve(s) warm- vs. cold-blooded animals      153 155 157 158 159
Myelinated nerve(s), electrical model of      140—144
Na/K—ATPase      64
Nagumo, Jin-ichi      5 123 136
Narcotization of nerve      85—86 126
Navier—Stokes equations      295
Necker cube      262 272—273 280
Negative feedback      13—14 68 304
Neocortical structure      265 307—308
Nernst potential      see Diffusion potential
Nernst, Walther      3 59
Nerve cell      see Neuron
Nerve impulse(s)      27 31—33 34
Nerve impulse(s), FitzHugh — Nagumo model of      130—132
Nerve impulse(s), Hodgkin—Huxley model of      9 82—84
Nerve impulse(s), leading-edge model of      95—106
Nerve impulse(s), Markin — Chizmadzhev model of      115—122
Nerve impulse(s)on myelinated nerves      7 139—159
Nerve impulse(s)on myelinated nerves squid giant axon      4 84 212
Nets with circles      11 12 18 233 234 241—248
Nets without circles      11 12 233 234—241
Neural models      8—11 19 41—43 187—225
Neural models general structure      25—28
Neural network theory      9 43 233—252
Neuristor(s)      5 104 123 140 199—200
Neuron, generic      25—28 45
Neurotransmitters      35 36 37 44
Newton, Isaac      29 50 294
Newtonian dynamics      28—31 45 58 129 293 295
Newtonian dynamics vs. nonlinear diffusion      33—36
Newtonian dynamics, nature of time in      34 301
Nicolelis, M.A.      282 285
Nicolis, J.S.      309
Noble, D.      199
Nonlinear diffusion      2 5 34 199—206
Nonlinear diffusion discrete      144
Nonlinear diffusion in cortical field theories      248—250
Nonlinear diffusion, equation for      31—33 78 318 324
Nonlinear dynamic hierarchies      28 45 293
Nonlinear dynamic hierarchies biological      293—294
Nonlinear dynamic hierarchies cognitive      305—306
Nonlinear dynamic hierarchies neural      41
Nonlinearity, definition of      300—301
Nonlocal phenomenon      119
Null space      322 332
Numerical models of neurons      220—221
Numerical models of neurons compartmental codes      215 221 222—223
Numerical models of neurons Fourier and Laplace transforms      221
Numerical models of neurons Green functions      221
Numerical models of neurons statistical models      18 222 225
Numerical models of neurons statistically equivalent neurons      220—221
Occipital (optic) lobe      11 307
Offner, F.      103
Ohm’s Law      39 40 77 141
Open systems      34 316
Open systems vs. closed systems      303
Owl, auditory map of      217
Paintel, A.S.      153
Palm, Gunther      276 278
Panizza, Bartolomeo      11
Parietal lobes      307
Parnas, I.      219
Pastushenko, V.F.      105 202
Patch clamp      76
Patterns in context      12
Perceptron      12 233 237—241
Perceptron augmented pattern vector      239
Perceptron learning algorithm      233 237
Perceptron linear discriminant plane      238
Perceptron training period      233
Perceptron training period theorem      240
Perceptron weight vector      238 300
Periaxonal space      87 219
Period of latent addition      235
Perpetual isolation experiments      264—265
Perspiration      13
Perturbation theory for nerve impulses      331—333
Phase plane analysis      99—102
Phase sequence      17 260 264 286 305 308
Phase space      30 32—33 302 303 307
Phase space analysis of F-N equation      5 124—127
Phase space analysis of H-H system      80—82
Phase space equations, autonomous      81
Phase space singular points in      81
Phase space trajectories, heteroclinic vs. homoclinic      81—82 91
Phase space traveling-wave analysis      80—82 91
Phase waves      251
Physicalism      295 306
Piecewise FitzHugh — Nagumo model      123 126
Piecewise linear model      103—104 105
Pitts, Walter      9 11 233 235 237 252
Place cells      287
Planck, Max      59
Planetary motion      30—31 33 129 295
Poggio, T.      221
Poirazi, P.      243
Polling error      40
Positive feedback      14—17 302—303 304 311
Positive feedback in biological hierarchy      294
Positive feedback in biological hierarchy brain models      234 244
Positive feedback in biological hierarchy cell assemblies      268
Positive feedback in biological hierarchy morphogenesis      252
Positive feedback in biological hierarchy nerve impulse      2 7 79
Postsynaptic membrane      36 37 38
Potassium “turn-on” variable      73 76 95—96 105 319
Potassium “turn-on” variable conductivity      36 62 70 72—73 75
Potassium “turn-on” variable current, components of      62 70 71
Potassium “turn-on” variable ion concentration (in periaxonal space)      87 219
potential energy      29 30 34
Power balance      80 127—129 136 194
Power, definition of      318
Precursor (“skirt”)      119 122
Prediction      30 32
Presynaptic membrane      36 37
Pritchard, R.M.      263
Propagation speed on squid nerve      33 83 84 97—98
Protein Data Bank      30
Proteins      29 300
Proteins immense numbers of      297
Proteins intrinsic      10 53 57 61 76 153
Protobiological molecules      14 15
Psychological time      310
Purkinje cell      207 208
Pyramidal cells      189 215 217 278
Quantum theory      31 34 58
Quick, D.C.      219
Rabbit sciatic nerve      6 7 139 152
Rail, Wilfred      196 205 221
Raminsky, M.      158
Ramon y Cajal, Santiago      8 11 12 208 224
Ramon, F.      167
Ranvier, nodes of      see Active nodes
Rapid eye movement (REM) sleep in rats      287
rat      264 285—287
Rayleigh, Lord (John William Strutt)      50
Reaction diffusion equation      see Nonlinear diffusion
Reaction time      3 154
Reciprocity theorem      198
Recovery      105 249
Recovery models      115—124
Recovery variable      5 123—124 143
Reductionism, cognitive      306
Reductive materialism      293 294—296
Reductive materialism arguments against      296—305
Reentry      14
Refractory zones      3 5 87—89 91 127
Relative dielectric constant      55
Resting conductance      188
Resting conductance potential      31 63—64 70
Retinal light intensity      13
Retrodiction      30 32
Richer, Ira      146
Rinzel, John      126 221
Rochester, N.      272
Rosenblatt, Frank      12 233 237
Royal Institution of London      2—3
Rudin, Donald      52
Rushton, W.A.H.      153 159
Sabah, N.H.      91
Safety factor for nerve impulse      33 87 111 204
Safety factor in cell assemblies      267 268
Safety factor in cell assemblies Markin—Chizmadzhev model      122
Safety factor in cell assemblies multiplex neuron      10 210
Saltatory conduction      7 139 140 158
Sattinger, D.H.      328
Schmitt, F.O.      44 45
Schmitt, O.H.      166 169
Schrodinger, Erwin      31 35
Schrodinger’s equation      295
Schuster, Peter      309
Sciatic nerve(s)      139—159
Sciatic nerve(s) of cat      149 150 157
Sciatic nerve(s) of frog      1 2 74 142—143 149 150
Sciatic nerve(s) of rabbit      6 7 139
Sciatic nerve(s) ofother vertebrates      152 157 158
Sears, T.A.      158
Senden, Marius von      258 262
Separation of variables      134 325
Sherrington, Charles Scott      8 11 257 311
Shooting method      82 101—102 111
Shot noise      40
Sigma-Pi model of dendrites      214—215
Sigmoid umction      214 245—246 249 267
Silberstein, P.T.      90
Single neuron recording      257
Skou, Jens Christian      64
Smith, B.H.      44 45
Smith, Dean      218 219
Sneyd, James      199
Soap bubble      49 50—51
Soap bubble film      50—51 65
Soap bubble film black      51
Social assemblies      17 261 274
Social assemblies time      310
Sodium channels conductance      36 61—62 64 72—75
Sodium channels current      61—62 70 71
Sodium channels “turn-on” and “turn-off”      72 76 95—96 105 110 154 319—320
Sodium channels, genetic variations of      153
Sodium-potassium pump      63—64 65
solder      243—244
Soliton(s)      80 248
Southampton — Duke Morphological Archive      188 189 220
Soviet Union      5 10 207
Space clamp(ed)      67 68 69 71 91 249 269
Space clamp(ed) squid membrane      71—72 74—77
Space constant      190 191
Space constant active      224
Speed of impulse propagation, myelinated nerve      1 2 7 142 145—147 149 158
Speed of impulse propagation, smooth nerve      3 83 84 97—98 121
Spike response model      42 116
Spin-glass brain model      234 248 252
Spira, M.E.      219
Spreading resistance      40
Spruston, Nelson      45
Squid giant axon      3 4 6—7 27 32 40
Squid giant axon branching GR for      218
Squid giant axon H-H model of      9 77—78 83—84 120
Squid giant axon membrane currents      69 70—74
Squid giant axon membrane currents oscillatory behavior of      90—91
Squid giant axon membrane currents permeabilities      63 70—74
Squid giant axon nerve impulse, stability      83—84 86
Squid giant axon, impulse speed for      83 97—98
Squid giant axon, refractory zones of      87—89
Stability      14 323—330
Stability Lyapunov      246
Stability of attractor neural network      245
Stability of attractor neural network M-C impulses      121
Stability of attractor neural network, axonal impulses      323—330
Stability of attractor neural network, cell assemblies      268 272 273—274
Stability of attractor neural network, F-N impulses      132—136
Stability of attractor neural network, H-H impulse      83 84
Stability of attractor neural network, leading edges      108—109
Stampfli, R.      158
State diagrams      241—242
Statistical models of neural nets      18
Statistical models of neurons      222
Stimulus-response problems      321
Stochastic behavior of synapses      38
Stuart, Greg      45
Studies of Artificial Neural Systems (SANS)      278 284
Subjective experience      311
Subthreshold resonance      91
Superposition theorem      193
Supervenience      295 296
Synapses      8 10 27 248
Synapses active and passive      215—216
1 2 3 4
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