Lectures on Topics in Finite Element Solution of Elliptic Problems (Lectures on Mathematics and Physics / Tata Institute of Fund)

038709542X......Page 1
Contents......Page 6
Part I: The being of neural cells......Page 18
1.1 Brain straightforward sight......Page 19
1.2 Prediction of future events after learning......Page 29
1.3 Location of functions in the brain......Page 43
1.4 Location of memory in the brain......Page 48
1.5 Memory location in the pre- and postsynaptic structures......Page 54
1.6 Plasticity of excitable membrane......Page 62
1.7 The chemical nature of memory......Page 84
1.8 Preparing of \'a whole\' out of mutual interactions......Page 108
1.9 *Forward propagation of prediction......Page 114
2.1 Neurons and glia operate together......Page 121
2.2 Death through necrosis (murder of cells) and apoptosis (suicide of a cell)......Page 122
2.3 Neural and glial cells assist in survival......Page 127
2.4 Spread of damage within a tissue......Page 131
2.5 Cell coupling through gap junctions......Page 132
2.6 Multiple pathways for cell survival......Page 135
2.7 Nonlinear dependencies of doses, time and reciprocal interactions......Page 152
2.8 Homeostasis as a resetting and reorganization......Page 155
2.9 Long-term potentiation as a form of cell damage......Page 173
3.1 Motivation as the simplest tool for investigation of the objective roots of a subjective life......Page 185
3.2 Chemical nature of motivations......Page 188
3.3 Elemental motivations emerge in a result of transient cell damage......Page 197
3.4 Reward protects neurons from damage......Page 215
3.5 Goal-directed behavior of single cells......Page 227
3.6 Paradoxical properties of instrumental reactions......Page 249
3.7 Trial-and-error at the cellular level during instrumental conditioning......Page 253
4.1 A physiological description of voluntary actions......Page 255
4.2 An origin of agency and voluntary actions......Page 258
4.3 Common decision and the only reaction of the whole brain......Page 260
4.4 Gap junctions enriches a brain with a new quality......Page 262
4.5 Choice of alternatives with respect to the output......Page 265
4.6 Formation of neuronal ensembles during tension......Page 269
4.7 Physiology of free will......Page 274
4.8 The emergence of higher-level organizations from the interactions of lower-level units......Page 288
5. Death as an awareness-rising factor (a single neuron can suffer and delight)......Page 294
5.1 Physiological access to consciousness......Page 295
5.2 Merging of odd information in aware perception......Page 300
5.3 Changeability of consciousness......Page 302
5.4 Recurring change of consciousness during bipolar disorder......Page 304
5.5 Properties of the alive, but unconscious brain......Page 305
5.6 Inhibition in the brain and consciousness......Page 306
5.7 Chemical modulation of consciousness......Page 309
5.8 Materialization of the SELF......Page 311
5.9 Discrete time steps in perception......Page 315
5.10 Common currency for choice: between displeasure and pleasure......Page 316
5.11 What is bad and good for a neuron?......Page 318
Part II: Mathematics of feeling......Page 321
6.1 Phenomenology of a neural cell\'s behavior and fuzzy logic......Page 322
6.2 Perceptions as a Mathematical Object......Page 324
6.3 Mathematical Operations with Fuzzy Quantities and Zadeh\'s Extensional Principle......Page 330
7.1 Fuzzy Dynamics: Evolution of a System with Vague Parameters and Uncertainty in the Dynamics law......Page 340
7.2 Master-Equation of fuzzy dynamics......Page 344
7.3 Fuzzy trajectories......Page 346
7.4 Evolution of uncertainty......Page 361
7.5 Evolution of perceptions......Page 363
8.1 Linguistic variables and linguistic rules of a neuron\'s behavior......Page 366
8.2 Fuzzy dynamics of a neural cell\'s learning......Page 372
9.1 The operation of memory......Page 388
9.2 The verve of injured neurons......Page 391
9.3 Subjective nature of motivation......Page 395
9.4 Goal-directed actions......Page 404
9.6 Fuzzy dynamics model of neuronal behavior......Page 408
9.7 Fuzzy logic of a neural cell......Page 410
9.8 Artificial motivational neurons and feeling robots......Page 416
A.1 *Model of a chemical memory of a neuron......Page 418
A.2 *An alternative type of fuzzy dynamics equations......Page 428
References......Page 433
F......Page 474
P......Page 475
Z......Page 476
List of symbols......Page 477
List of definitions......Page 479