Neuroscience: Pattern Recognition with Neural Networks

Neuroscience: Pattern Recognition with Neural Networks

Retinal ganglion cells, that is, the output cells of the retina, have concentric on-center or off-center receptive fields. The on-center receptive field consists of an excitatory circular region surrounded by an inhibitory annular region, while the off-center receptive field has the opposite structure. These cells are supposed to extract contrast components from patterns projected onto the retina. Photoreceptors and ganglion cells are not directly connected in an actual biological retina. There are several kinds of cells in between and the information is processed by the interactions of such cells. Engineers in pattern recognition often classify the process of self-organization into supervised learning (or learning-with-a-teacher) and unsupervised learning (or learning-without-a-teacher). A famous example of a classical network that can be trained by supervised learning is the three-layered perceptron. Although the perceptron has a three-layered hierarchical structure, it is only in the highest stage that the cells have variable input connections.

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Psychology, Neurobiology and Modeling: The Science of Hebbian Reverberations

Psychology, Neurobiology and Modeling: The Science of Hebbian Reverberations

This chapter discusses introspective considerations for the necessity of having attractors, which neuropsychology has termed as reverberations. There exist experimental evidences for reverberations and attractors exist and are observable in neurophysiology. Attractors that are observed neurophysiologically, which appear to be required for mental processing, are very informative both for describing the functioning of the brain and for measuring information about computation processes. There are other phenomena in cognitive psychology whose interpretation in terms of correlated attractors is quite simple. For example, there is a well known phenomenon called false alarm in which subjects are shown a set of objects and then a sublist is defined. Patterns are shown very quickly, at random, and the subject has to respond after each presentation whether the stimulus belongs to the sublist. If the pattern shown is correlated with one belonging to the sublist, then the number of errors grows. In attractor language, it happens because each one of the patterns carries information of the fact that it was seen very often in temporal proximity to a pattern that belongs to the sublist.

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Neuroscience: Towards a Kinetic Theory of Cortical-like Neural Fields

Neuroscience: Towards a Kinetic Theory of Cortical-like Neural Fields

The kinetic theory of neural fields is based fundamentally on the description of electrical properties of single neurons and on some statistical hypotheses about their connecting network. This chapter discusses the basis of this theory and its main results. It discusses a basilar, minimal set of biological neural features, except those linked to neural plasticity. Such characteristics are utilized for the construction, through statistical-physics methods, of a general mathematical model, which does not refer to particular brain regions. The chapter discusses some results of the application of the theory to cortical-like neural fields and to attention and learning. Neural systems are considered as finite regions of the three-dimensional space filled with two different types of particles. Neurons, characterized by an inner excitation corresponding to the subthreshold membrane potential, constitute a kind of motionless, solid background. They, under some conditions, emit impulses in space.

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Neuroscience: Qualitative Overview of Population Neurodynamics

Neuroscience: Qualitative Overview of Population Neurodynamics

The estimates of the number of neurons in a cubic millimeter of cortex range from 104 to 106 and from 103 to 105 for the number of synaptic connections on each dendritic tree. The typical sensory input for a conditioned stimulus is carried by a parallel array of an immeasurably large number of receptor axons and the motor outflow for a typical conditioned response, a fraction of a second later, is carried in parallel by an immeasurably large number of motor axons. The networks of model neurons are constructed by induction that represent the actions of a small subset of neurons on the implicit assumption that what the other (unobserved) neurons are doing during a perceptual act or a conditioned reflex is not important for the activity of the observed subset. This approach might be called statistical mechanics of brain function, comparable to the study of molecules in an ideal gas in terms of their kinetic energy, position, and collision rates.

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Neuroscience:Noise and Chaos in Neural Systems

Neuroscience:Noise and Chaos in Neural Systems

This chapter discusses two questions (1) how to characterize the dendritic arborization patterns and what could be the mechanism of the generation of dendritic branching trees and (2) what can be the role of environmental noise in the ontogenetic formation of ordered cortical structures. The dendritic arborization can be classified based on (1) randomness versus regularity in regard to branching of the various dendritic segments, resulting in a continuous spectrum ranging from the “radiate” to the “tufted” types of arborization and (2) the degree of deviation of the individual branches from a radiated and rectilinear course. A three-variable extension of the Turing-Gierer-Meinhardt (TGM) model describes network formation based on the diffusible morphogen concept. This model leads to uniform behavior. Accepting the view that neural dendritic branching might have a self-similar character, its development can be modeled by fractal generating growth models.

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Neuroscience: Diffusion Models of Single Neurones' Activity

Neuroscience: Diffusion Models of Single Neurones' Activity

This chapter presents a survey of one-dimensional stochastic diffusion models for the membrane potential of a single neuron, with emphasis on the probabilistic properties of the models and on the related first-passage-time (FPT) problems, namely, on the determination of the neuronal output. It discusses how the much celebrated Ornstein-Uhlenbeck (OU) neuronal model can be obtained as the limit of a Markov process with discrete state space in continuous time. The stochastic models of neuronal activity rank among the most advanced applications of the theory of stochastic processes to biology. There are several reasons why many of these neuronal models stem out of the theory of diffusion processes: (1) the theory of diffusion processes is well developed and hence, it allows the neural modelers to apply many general results to the specific application area, (2) for neurons with many synaptic inputs, there is a rather good correspondence between the models and the biological reality, (3) even when some of the assumptions underlying the model may be somewhat questionable, the output behavior of the neuron can often be well approximated by that of a suitably chosen diffusion process, which is, for instance, strikely true for the well-known Gerstein-Mandelbrot diffusion model, and (4) from a biophysical point of view, the neuronal models of single cells reflect the electrical properties of the membrane via electric circuit models that contain energy storage elements.

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Neuroscience: Mechanisms Responsible for Epilepsy in Hippocampal Slices Predispose the Brain to Collective Oscillations

Neuroscience: Mechanisms Responsible for Epilepsy in Hippocampal Slices Predispose the Brain to Collective Oscillations

About 90% of the neurons in the CA3 region are pyramidal cells, the principal neurons that supply CA3 output to other parts of the brain (including, in particular, the CA1 hippocampal region and the opposite CA3 region—there is one hippocampus in each cerebral hemisphere). Of particular relevance to epilepsy and probably to normal brain function is the fact that CA3 neurons synaptically excite one another. These connections are called recurrent. The remaining neurons, generally nonpyramidal in shape, are probably all inhibitory and most or all of them use γ-aminobutyric acid (GABA) as their transmitter. Pyramidal neurons have two sets of dendrites, called basilar and apical, with recurrent synaptic connections into both sets of dendrites. Presynaptic neurons release transmitters onto a given postsynaptic neuron causing membrane synaptic currents to flow and possibly initiating intracellular secondary metabolic processes that in turn influence the membrane. There are also synaptic receptors whose primary function is to couple to intracellular biochemical processes. As metabolic processes are, in general, slower than voltage-gated membrane processes, the different receptor coupling mechanisms introduce a range of time scales into neuronal function.

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Neuroscience: An Introduction to Neural Oscillators

Neuroscience: An Introduction to Neural Oscillators

Neurons and neural regions communicate to other cells and regions through a variety of means. The simplest means that is seen in early development is through gap junctions. The transport of ions or potential is done via diffusion resulting in a coupling term that depends on the difference between the two coupled entities. The most common communication is via chemical synapses. Other ways of communication are via pooled substances that can accumulate in the extracellular space such as ions (Ca2+, K+) and second messengers (such as, NO, cAMP). This chapter discusses a number of properties of chains of oscillators that have local connectivity and depend only on phase-differences. These arise from the averaging reduction and have been used to understand the central pattern generator of the lamprey. Periodically forced chains have been exploited to provide information on the structure of the lamprey spinal cord central pattern generator.

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Neuroscience:Single Neuron Dynamics: an Introduction

Neuroscience:Single Neuron Dynamics: an Introduction

This chapter discusses the mathematical descriptions of neuronal behavior. The potential in the bath surrounding a neuron is relatively constant under normal circumstances, and it is conventionally taken to be zero. The potential inside the cell is then, by definition, the membrane potential. It can be measured by inserting a hollow glass electrode filled with an electrolytic solution through the cell membrane. At rest, the membrane potential is typically around −70 mV and during the normal course of cell activity, it may vary from about −80 mV to +50 mV. These variations are caused by changes in the conductances of channels that allow ions to cross the cell membrane. The neuron is polarized at rest because of its negative membrane potential. Making the membrane potential more negative is termed hyperpolarization and moving it in the positive direction is termed depolarization. The electrical currents that affect the membrane potential of a neuron arise from the flow of ions, principally potassium, sodium, calcium, and chloride, across the cell membrane.

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Neuroscience:Analysis of Single-Unit Activity in the Cerebral Cortex

Neuroscience:Analysis of Single-Unit Activity in the Cerebral Cortex

The extracellular spiking activity of single units is usually recorded by inserting a very fine needle (micro-electrode) into the cortex while recording the voltage at the tip of the electrode. Living cells are characterized by having a potential difference across their membranes with the inside negative relative to the outside. Active nerve cells are characterized by having different membrane potential at different sites. Such differences result in currents flowing through the salt solutions both inside and outside the cell. The currents, in the extracellular fluid, set potential differences that can be recorded by a micro-electrode. The electric field induced by a surface dipole depends on the dipole moment, the area, the orientation of the surface, and the distance from the dipole. The statistics of the activity of a single unit is most commonly studied by means of the renewal density function. This function describes the rate of firing of a single unit as a function of time that has elapsed since it fired.

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Neuroscience:Models of Visuomotor Coordination in Frog and Monkey

Neuroscience: Models of Visuomotor Coordination in Frog and Monkey

The escape direction in response to the approach of a large moving object may be briefly characterized as a compromise between the forward direction of the animal and the direction immediately away from the looming stimulus. Barriers can modify avoidance behavior, just as they modify approach behavior. If a barrier is interposed to block the preferred direction of escape for a stimulus coming from a particular direction, then the behavior of the animal changes and it tends to jump just to the left or just to the right of the barrier. When a limb moves, it needs a burst of agonist contraction to accelerate the limb in the desired direction, followed by an appropriately timed antagonist burst to decelerate it to rest at the desired position (with a possible small agonist correction thereafter). A new resting level of muscle contraction holds the limb in its new position. By contrast, the eye has little inertia and therefore, no antagonist burst is required; the eye has no changing load to require feedback.

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Neuroscience:Anatomical Bases of Neural Network Modeling

Neuroscience:Anatomical Bases of Neural Network Modeling

Neuronal connectivity in most neural centers is sufficiently specific to permit the disassembly of the whole network into distinct pieces (or units) of characteristic internal connectivity that are arranged into larger structures by repetition of similar architectural units. These units have been termed neuronal modules and the architectural principle is referred to by the modular architectonic principle of neural centers. This chapter discusses the modular architectonic principle as it can be recognized in various parts of the central nervous system (CNS) of the vertebrates, starting with the spinal cord. The upper diencephalic and telencephalic (striatum and putamen) part of the brainstem does not retain anything resembling the quasi-segmental arrangement of the lower neuraxis. There is, however, a small part of the diencephalon—the so called hypothalamus, that is, the ventralmost part of the diencephalon—in which the elements of the basic architectural principle of the neuraxis are preserved longitudinally oriented fiber tracts and transversally oriented (coronal) quasi-discs of neuropil.

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