On matrices of neural nets

The structure of a complete or incomplete neural net is represented here by several matrices. The activity equation of the net follows in a general form. A chain or cycle is defined as a neural structure whose connection matrix is unitary. We can compute the number of simple chains by a recurrent formula. Academia Sinica     

Memory topology of neural nets

Aiming at a topology of memory-growth, a computer-simulated mechanism is developed here, based on the probabilistic neural model previously developed by Anninos, Csermeley & Harth.The essential topology of this mechanism reflects the generally accepted idea that memory growth is achieved by means of association processes, i.e. through the cross-referencing of new inputs with already acquired information. In terms of computer-simulation such mechanism is developed by following the formalism of Set Theory. So the memory units, i.e. the neural netlets are equated to subsets of a set which represents a larger memory-system. Consistently with this formalism, association is a necessary, although non-sufficient condition for the growth of memory and the Boolean overlap of two subsets, i.e. of two netlets, is identified with the cross-reference mechanism which we assume to be the basis of memory growth.     

A statistical consequence of the logical calculus of nervous nets

A formal method is derived for converting logical relations among the actions of neurons in a net into statistical relations among the frequencies of their impulses.     

CDMA and TDMA based neural nets

CDMA and TDMA telecommunication techniques were established long time ago, but they have acquired a renewed presence due to the rapidly increasing mobile phones demand. In this paper, we are going to see they are suitable for neural nets, if we leave the concept "connection" between processing units and we adopt the concept "messages" exchanged between them. This may open the door to neural nets with a higher number of processing units and flexible configuration.     

The neural mechanism of logical thinking

A theory of such neural circuits is developed which provide for formal logical thinking. As a by-product of this study, a neural mechanism is indicated which provides for the conception of ordinal numbers. A quantitative theory of the probability of erroneous reasoning and of the speed of reasoning in its relations to other psychological phenomena is suggested.     

Methods of analysis of neural nets

The properties of isotropy, smoothness, minimum curvature and locality suggest the shape of filled-in contours between two boundary edges. The contours are composed of the arcs of two circles tangent to the given edges, meeting smoothly, and minimizing the total curvature. It is shown that shapes meeting all the above requirement can be generated by a network which performs simple, local computations. It is suggested that the filling-in process plays an important role in the early processing of visual information.     

The wiring-in of neural nets revisited

Earlier and some recent ideas about the possible modes of specification of the wiring-in of nervous systems are reviewed in the light of older and several recent experiments, and some new ideas are suggested. It is argued that certain general principles, notably the postulated ‘principle of alternative matching’ (PALMA) and a suggested and related ‘kaleidoscopic effect’ (KALEF), as well as the notion of an ‘extracellular guidance network’ (ECGN), are in good agreement with recent and older findings concerning axonal guidance during neural wiring-in. It seems possible that by means of genetically programmed processes, neurons become systematically combinatorially labelled to such a degree that possibly all neurons areuniquely specified, as regards the combination oftypes of cell labels they make. Yet, there remains considerable freedom as regards the modes of arrangements of cell labels within cell surface membranes and the KALEF permits to overcome apparent difficulties that confronted earlier versions of the cell labelling hypotheses (cf. Edelman,Science 219, 450–457, 1983, for mention of such difficulties). Apart from label specification, neural development seems to depend on trophic factors, which are also essential for the maintenance of the developed nervous system. The systematic programmes for cell labelling, apart from generating all the required neurons, also produces inappropriate neurons and synaptic connections. These are got rid of by systematic cell death and/or atrophy of inappropriate synapses and/or elimination of inappropriate axon collaterals. The resulting neural net seems then very specifically wired-in for each species, apparently without redundant neurons.     

Mathematical biophysics of some neural nets

Methods are considered for constructing neural nets of the McCulloch-Pitts type giving arbitrary time delays between stimuli and their responses. By introducing cycles of neurons, the problem is treated from the standpoint of economizing on the number of neurons required. A generalization is effect that will realize any unique temporal response pattern from a unique stimulus.     

Influence of music on the solution of mathematical logical tasks

Musical accompaniment (of different styles and intensities) of the solution of mathematical logical tasks influenced the time required for their solution. Classical music 35 and 65 dB and rock music 65 and 85 dB in terms of loudness decreased the time of the solution. Louder classical music (85 dB) did not have this effect. Solution of tasks without musical accompaniment led to an increase in coherent values, especially in ??₁, ??₂, and ?? the frequency bands in the EEG of the occipital cortex. The intrahemispheric and interhemispheric coherences of frontal EEG increased and EEG asymmetry (in the number of Coh connections in the left and right hemispheres) arose during the solution of the tasks accompanied by music. Classical music (35 and 65 dB) caused left-side asymmetry in the EEG. The use of more powerful classical or rock music led to a prevalence of the number of Coh connections in the right hemisphere.     

The group structure of some neural nets

A method is given for using a set of disjoint cycles as the main body of a neural net that will given rise to more than one temporal response pattern for different afferent stimuli. The method arises out of considering the correspondence between this type of net and certain Abelian groups of finite order. The consideration also gives rise to a possible definition of the “complexity” of this type of neural net.     

A diffusion model of a neuron and neural nets

In the paper a diffusion model of a neuron is treated. A new, less restrictive than usually, condition of applicability of a diffusion model is presented. As a result the point-process-to-point-process model of a neuron is obtained, which produces an output signal of the same kind as the accepted input signals.     

Stabilization of Hebbian neural nets by inhibitory learning

In Hebbian neural models synaptic reinforcement occurs when the pre- and post-synaptic neurons are simultaneously active. This causes an instability toward unlimited growth of excitatory synapses. The system can be stabilized by recurrent inhibition via modifiable inhibitory synapses. When this process is included, it is possible to dispense with the non-linear normalization or cut-off conditions which were necessary for stability in previous models. The present formulation is response-linear if synaptic changes are slow. It is self-consistent because the stabilizing effects will tend to keep most neural activity in the middle range, where neural response is approximately linear. The linearized equations are tensor invariant under a class of rotations of the state space. Using this, the response to stimulation may be derived as a set of independent modes of activity distributed over the net, which may be identified with cell assemblies. A continuously infinite set of equivalent solutions exists.     

Outline of a matrix calculus for neural nets

The activity of a neural net is represented in terms of a matrix vector equation with a normalizing operator in which the matrix represents only the complete structure of the net, and the normalized vector-matrix product represents the activity of all the non-afferent neurons. The activity vectors are functions of a quantized time variable whose elements are zero (no activity) or one (activity). Certain properties of the structure matrix are discussed and the computational procedure which results from the matrix vector equation is illustrated by a specific example.     

Conditions for periodic and aperiodic behavior of formal neural nets

Formal neural networks (FNN) can display dynamical behaviours, more or less different from each other depending on their units, the functions attributed to these units, interconnections, parameters, state spaces and initial states, etc. Whatever is 'chaos' - of which several practical and more exact definitions exist -, it used to be emerging at special conditions. Its prediction most often requires an individual analysis of the dynamical system (DS) in question. A study of such conditions is usually necessary in order to reach suitable control, which now seems to become a new trend in chaos theory. In chaos control tasks quick commands and at least short-term foresight of trends are required. It is a primary question also to define in advance what is regarded to be a controlled case of chaos. Possible importance of these general considerations at molecular scale is also discussed, avoiding not well-founded speculations.     

Psychological and stabilographic features of healthy persons with different capabilities of performing dual tasks

A dual task study including control of postural balance and counting was conducted on 40 healthy subjects (with an average age of 29.8 ± 2.47 years) along with a psychological examination that included estimation of the working memory, attention, and the time of attention switch. Three types of dual task performance were observed: worsening of either one or both components of the dual task, improvement of one component, and improvement of both components of the dual task. 30% of participants performed a dual task better than isolated tasks. Successful performance in the dual task correlated with the higher volume of spatial and working memory, attention, and a rapid switch of attention. The speed of sway of the center of pressure (CoP) negatively correlated with the speed of attention switch, while the amplitude of the CoP shift in the frontal plane negatively correlated with the volume of spatial and working memory. These data suggest involvement of the cognitive resources in controlling the upright balance and a high degree of motor automatism when the dual tasks are successfully performed. Our experimental paradigm is expected to be helpful in predicting individual performance in situations with high information loads.     

Decision of mathematical logical tasks in sensory enriched environment (classical music)

The time of a decision of mathematical logical tasks (MLT) was decreased during classical musical accompaniment (power 35 and 65 dB). Music 85 dB did not influence on the process of decision of MLT. Decision without the musical accompaniment led to increasing of coherent function values in beta1, beta2, gamma frequency ranges in EEG of occipital areas with prevalence in a left hemisphere. A coherence of potentials was decreased in EEG of frontal cortex. Music decreasing of making-decision time enhanced left-sided EEG asymmetry The intrahemispheric and the interhemispheric coherences of frontal cortex were increased during the decision of MLT accompanied by music. Using of musical accompaniment 85 dB produced a right-side asymmetry in EEG and formed a focus of coherent connections in EEG of temporal area of a right hemisphere.     

Limited forearm motion compensated by thoracohumeral kinematics when performing tasks requiring pronation and supination

This study investigates the altered thoracohumeral kinematics when forearm rotation is restricted while performing five activities requiring pronation and supination. Two splints simulated both a fixed-supinated or fixed-neutral forearm in six healthy subjects; the three-dimensional coupled relationship among motion about the forearm, elbow, and shoulder were analyzed. In using a screwdriver, the normal range of forearm rotation of 77.6° (SD = 30.8°) was reduced in the fixed-supinated to 11.3° (SD = 2.9°) and fixed-neutral to 18.2° (SD = 6.2°). This restriction from the fixed-supinated and fixed-neutral forearms was compensated at the shoulder by a significant increase in the total range of (1) ad/abduction by 57.3° and 62.8° respectively (p < .001), (2) forward-reverse flexion (24.3° and 18.2° respectively; p < .05) and (3) internal-external rotation (37.1° and 44.2° respectively; p < .001). A similar result was demonstrated for the doorknob activity. The elbow did not significantly contribute to forearm rotation (p = .14), and is believed to be due to the elbow axis being orthogonal and oblique to the forearm axis. For open kinetic-chain activities, with a fixed-supinated forearm performing there was a significant coupled increase in ad/abduction (p < .05) and int/external rotation (p < .05) for the phone and feeding tasks, with the phone task also having a significantly increased forward shoulder flexion (p < .05). For the fixed-neutral forearm, significant compensatory movement was only seen in the feeding task with increased ad/abduction and internal-external shoulder rotation (p < .05) and the card inserting task with increased ad/abduction and forward-reverse shoulder flexion. Limited forearm function requires compensatory motion from adjacent joints to perform activities that require pronation and supination.     

Discussion: McCulloch-Pitts and related neural nets from 1943 to 1989

The McCulloch-Pitts paper “A Logical Calculus of the Ideas Immanent in Nervous Activity” was published in theBulletin of Mathematical Biophysics in 1943, a decade before the work of Hodgkin, Huxley, Katz and Eccles. The McCulloch-Pitts neuron is an extremely simplified representation of neural properties, based simply on the existence of a threshold for the activation of an action potential. This work has been supported in part by Grants from the University of Chicago Brain Research Foundation, and the U.S. Department of the Navy, Office of Naval Research (Grant No. N 00014-89J-1099).