[Effect on nonlinear summation of postsynaptic potentials on the average potential and distribution of interspike intervals of a neuron]. / Vliianie nelineinoi summatsii postsinapticheskikh potentsialov na srednii potentsial i raspredelenie mezhimpul'snykh intervalov neirona.

A probability model of the neuron is considered which uses a simple equivalent electric scheme of the synapse suggesting that characteristic time of conductivity change is much less than the time constant of the membrane tau. The model is characterized by the fact that the distribution of potential jumps depends on the accumulated potential u(t). Formula are obtained for the average value and dispersion of the membrane potential. They coincide with the known formula (1) deduced for the contrary case of slow conductivity changes at tau lambda greater than 1 (lambda - frequency of elementary jumps of conductivity). For tau lambda greater than 1 distribution of probability of interimpulse intervals at arbitrary form of distribution function of jumps F (delta u, u) is described.

[Limiting behavior of a model of the impulse activity of a neuron for large frequency of input flow and small contributions of a single synapse (non-diffusion approximation)]. / Predel'noe povedenie modeli impul'snoi aktivnosti neirona dlia bol'shikh chastot vkhodnykh potokov i malykh vkladakh odnogo sinapsa (nediffuzionnoe priblizhenie).

The limit behavior of probability models of neuron's firing, viz. models with exponential decay and constant threshold is considered. These models differ from each other by F(v), distribution of jumps of potential after arrival of input impulse. If average number of input impulses arriving during the decaying time of one impulse in very large and threshold depolarisation, measured by unit of average jump of potential, is large too, than limit density of interspike interval distribution does not depend on form of F(v); and depends on other neuron's parameters mean and variance of F(v). Moreover, the form of this density depends on only one parameter--normalised threshold. Under this condition interspike interval distribution for diffusion model converges to the same limit. Lapase transform for limit distribution is found and results of its numeric inverts are given.

[Model of the impulse activity of a neuron receiving a stationary impulse imput]. / Model' impul'snoi aktivnosti neirona, poluchaiushchego statsionarnyi impul'snyi pritok

The stationary model of spike activity of a single neuron is considered. This model exponential decay and constant threshold can be described as discontinuous one. The problem of calculation of Laplas' transform the probability density function (PDF) of interspike interval (ISI) can be reduced to the boundary problem for the usual differential equation. For the exponential PDF of the magnitude of the PSP the Laplas' transform of ISI PDF is expressed by special functions. The mean and standard deviation of ISI for different combinations of parameters were plotted with the aid of computer. The experiment without intracellular recoding, allowing to estimate the values of certain physiological parameters of a neuron on the basis of the model is proposed.

[Method of evaluating the synaptic input to a single mesencephalic neuron]. / Sposob otsenki sinapticheskogo pritoka k odinochnomu neironu srednego mozga

The mathematical model of the spike activity of a neuron with synaptic input from many other neurons [1], describes adequately the firing of 5 from 7 neurons in the tegmentum of mesencephalic cat and changes of their activity evoked by glutamate iontophoresis. For these 5 neurons the estimates of the PSPs' average frequency of the threshold depolarization and of the constant decay of the EPSP were received. For different neurons the values of these parameters are 4--100 KHz, 100--800 average unitary EPSPs and 4--30 msec correspondingly. The stationary value of the average membrane potential (SVAMP) in all 5 neurons was removed significantly from the resting potential toward the threshold potential. SWAMP could be changed by the glutamate iontophoresis in such a degree to overlap the threshold potential.

[Perception of color and volumetric shape of objects]. / Ob uznavanii okraski i ob''emnoi formy predmetov

The problem of recognition of coloration of volume objects, illuminated simultaneously with bright point ans weak diffuse sources (having arbirary and previously unknown spectra) is considered. A mathematical model, in which a process of recognition of coloration is accompanied by determining orientations of surface elements relatively the point source is described. The information on orientation allows in many cases to calculate the volume shape of objects of the external world form their monocular ""retinal"" image.