From Computer to Brain: Foundations of Computational Neuroscience

From Computer to Brain: Foundations of Computational Neuroscience

William W. Lytton

Language: English

Pages: 364


Format: PDF / Kindle (mobi) / ePub

Biology undergraduates, medical students and life-science graduate students often have limited mathematical skills. Similarly, physics, math and engineering students have little patience for the detailed facts that make up much of biological knowledge. Teaching computational neuroscience as an integrated discipline requires that both groups be brought forward onto common ground. This book does this by making ancillary material available in an appendix and providing basic explanations without becoming bogged down in unnecessary details. The book will be suitable for undergraduates and beginning graduate students taking a computational neuroscience course and also to anyone with an interest in the uses of the computer in modeling the nervous system.

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not flour) and broccoli.” In Boolean notation, using the first letter of each word as the symbol, this is (∼ (S ∨F ))∧B or, equivalently, (∼ S∧ ∼ F )∧B. The needle always pulls out cards that don’t use that ingredient (False) and leave behind cards that do use it (True). Complex Boolean operations can be performed using the proper combination of needles. This recipe card scheme was marketed as a practical database management technique in the 1960s. Although it has been made obsolete with the

that it refers to the base 10 number system, the word is used to refer to any equipment that uses discrete rather than continuous states. Thus, the modern computer is a digital computer that uses binary representations. This is likely to be a major difference from brain function. Although Von Neumann and other early computationalists took the all-ornone nature of the axonal spike as evidence that the brain was primarily a binary digital device, this viewpoint is not currently popular. Binary means

(reduced weight), and positive state (increased rate) times negative weight (inhibitory input) produces negative state (reduced rate). A major appeal of the rate coding model is that it gives us the simplicity and modeling tractability of a scalar state. However, there are neurobiological as well as computational reasons to believe that rate coding is important in the nervous system. There is clearly a frequency/strength relationship in the efferent (motor) peripheral nervous system. Increased

the brainstem reflex that stabilizes the eyes in the head when the head is moved. Then, in a more speculative vein, I go still higher in the brain, looking at how artificial neural networks can be used to emulate aspects of human memory. This will involve an explicit compare-and-contrast with computer memory design. Following this, I turn bottom-up, more seriously exploring the biological concepts of nervous system function. I start with a detailed description of the neuron with some ideas of how

attraction for the remembered vector. This basin is the upper-left quadrant of state space. The limit cycle has a basin of attraction consisting of the upperright and lower-left quadrants of state space. Then there is the spurious attractor at 1 −1 with its basin in the lower-right quadrant. Since we restrict ourselves to binary inputs to the network, these basins don’t have much meaning. The only binary point in each basin is the attractor itself. We can present the network with analog vectors

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