Informatica

In this paper, the nonlinear neural network FitzHugh–Nagumo model with an expansion by the excited neuronal kernel function has been investigated. The mean field approximation of neuronal potentials and recovery currents inside neuron ensembles was used. The biologically more realistic nonlinear sodium ionic current–voltage characteristic and kernel functions were applied. A possibility to present the nonlinear integral differential equations with kernel functions under the Fourier transformation by partial differential equations allows us to overcome the analytical and numerical modeling difficulties. An equivalence of two kinds solutions was confirmed basing on the errors analysis. The approach of the equivalent partial differential equations was successfully employed to solve the system with the heterogeneous synaptic functions as well as the FitzHugh–Nagumo nonlinear time-delayed differential equations in the case of the Hopf bifurcation and stability of stationary states. The analytical studies are corroborated by many numerical modeling experiments.

In the presented paper, some issues of the fundamental classical mechanics theory in the sense of Ising physics are introduced into the applied neural network area. The expansion of the neural networks theory is based primarily on introducing Hebb postulate into the mean field theory as an instrument of analysis of complex systems. Appropriate propositions and a theorem with proofs were proposed. In addition, some computational background is presented and discussed.

In the present paper, the neural networks theory based on presumptions of the Ising model is considered. Indirect couplings, the Dirac distributions and the corrected Hebb rule are introduced and analyzed. The embedded patterns memorized in a neural network and the indirect couplings are considered as random. Apart from the complex theory based on Dirac distributions the simplified stationary mean field equations and their solutions taking into account an ergodicity of the average overlap and the indirect order parameter are presented. The modeling results are demonstrated to corroborate theoretical statements and applied aspects.

In this paper the immune network system was presented by the sequence of species with new immunological components allowing more plausible to reflect the immune response processes. The mathematical model oriented to the describing of the more realistic immune processes in the dynamics allowed to organize the computational experiment in the first to demonstrate a possible very complex behavior including chaotic regimes. The results of modeling of dynamic immunological processes with chaotic behavior are represented and considered.

In this paper, the information theory interpreted as the neural network systems of the brain is considered for information conveying and storing. Using the probability theory and specific properties of the neural systems, some foundations are presented. The neural network model proposed and computational experiments allow us to draw a conclusion that such an approach can be applied in storing, coding, and transmission of information.

In this paper, the main measure, an amount of information, of the information theory is analyzed and corrected. The three conceptions of the theory on the microstate, dissipation pathways, and self‐organization levels with a tight connection to the statistical physics are discussed. The concepts of restricted information were introduced as well as the proof of uniqueness of the entropy function, when the probabilities are rational numbers, is presented.

We consider a generalized model of neural network with a fuzziness and chaos. The origin of the fuzzy signals lies in complex biochemical and electrical processes of the synapse and dendrite membrane excitation and the inhibition mechanism. The mathematical operations included into fuzzy neural network modeling are: the scalar product between inputs of layers and synaptic weights is replaced by a fuzzy logic multiplication, the sum of products changes to the fuzzy logic sums, and the operators such as supremum, maximum, and minimum are presented for a fuzzy description. The algorithm of varying membership functions, built basing on a backpropagation paradigm and a method of fuzzy neural optimization, has been considered. Both fuzzy properties and a chaos phenomenon are analyzed basing upon experimental computations.

In this paper, the hexagonal approach was proposed for modeling the functioning of cerebral cortex, especially, the processes of learning and recognition of visual information. This approach is based on the real neurophysiological data of the structure and functions of cerebral cortex. Distinctive characteristic of the proposed neural network is the hexagonal arrangement of excitatory connections between neurons that enable the spreading or cloning of information on the surface of neuronal layer. Cloning of information and modification of the weight of connections between neurons are used as the basic principles for learning and recognition processes. Computer simulation of the hexagonal neural network indicated a suitability and prospectiveness of proposed approach in the creation, together with other modern concepts, of artificial neural network which will realize the most complicated processes that take place in the brain of living beings, such as short-term and long-term memory, episodic and declarative memory, recall, recognition, categorisation, thinking, and others.

Comparative study of the recognition of nonsemantic geometrical figures by the human subjects and ART neural network was carried out. The results of computer simulation experiments with ART neural network showed well correspondence with the psychophysical data on the recognition of different complexity visual patterns: in both cases the patterns of medium complexity were recognized with the highest accuracy. On the contrary, the recognition of the patterns by their informative fragments demonstrated different recognition strategies employed by natural and artificial neural systems. For biological systems, it is necessary the presence of not only distinctive features in visual patterns but the redundant features as well for successive recognition. ART neural network ignores redundant features and recognizes visual patterns with equal accuracy whether the whole pattern or only the informative fragment of any completeness is present.

The nonlinearities play a crucial role in the brain processes. They take place in neuronal system elements: synapses, dendrite membranes, soma of neurons, axons. It is established that the soma nonlinearity, which is of sigmoidal shape, is not so strong as compared with the electric current-voltage relation of a dendrite membrane. The relation is N-shaped with two stable and one unstable points. In dynamics, this leads to the appearance of a switch wave or formation of some logic functions. We present some artificial logic circuits based on an electrical analogy of dendritic membrane characteristics in static and dynamic cases. The nonlinear cable theory and the numerical simulation were used. Basing on the logic circuit construction proposed, we suppose that the dendritic membrane processes are able not only to gather and transfer information but also to transform and classify knowledge.