Transition between metastable equilibria: Applications to binary-choice games.

Transitions between metastable equilibria in the low-temperature phase of dynamical Ising game with activity spillover are studied in the infinite time limit. It is shown that exponential enhancement due to activity spillover, which takes place in finite-time transitions, is absent in the infinite time limit. In order to demonstrate that, the analytical description for infinite time trajectory is developed. An analytical approach to estimate the probability of transition between metastable equilibria in the infinite time limit is introduced and its results are compared with those of kinetic Monte Carlo simulation. Our study sheds light on the dynamics of the Ising game and has implications for the understanding of transitions between metastable states in complex systems.

Interconnected Evolution of Epidemic and Public Vaccination Opinion.

A new model of interconnected coevolving SIRS epidemic and public vaccination opinion pattern is presented. The underlying two-layer network contains strata corresponding to physical interactions in real space and social communications. The layer corresponding to physical interactions is constructed based on data on a real network representing communications between high school students. The evolution of people vaccination attitude is described using an Ising-type model. The model describes a non-trivial dependence of resulting epidemic dynamics on (1) noise amplitude, (2) initial opinion pattern and (3) influence of external information.

[Model of control of diurnal melatonin secretion by the solar radiation].

The mathematical model of the control process of diurnal melatonin secretion under the influence of solar radiation on retina photoreceptors is proposed. Invariant relations for calculating melatonin secretion rate and its concentration in blood plasma are obtained. Spectral, time and energy characteristics of solar radiation synchronizing diurnal melatonin secretion and circadian rhythms in human are defined. A possibility of using the relations obtained is shown for arbitrary combination of calendar dates, local time of any time zone and geographical coordinates of a calculated point on earth surface. The adequacy of model is confirmed by coincidence of the calculation data with the results of independent experimental studies on diurnal secretion of melatonin and circadian rhythm in human. The model proposed can be used during investigation of diurnal secretion of melatonin and circadian rhythm in human.

[A stochastic approach to solving the problem of sensory system thresholds]. / Stokhasticheskii podkhod k resheniiu problemy porogov sensornykh sistem.

On the basis of an analysis of mathematical models realizing concept of discrete and signal detection probability of the threshold it is shown that utilization for describing the discrete model concepts of probability and the apparatus of Dirac delta functions and root-mean-square of noise distribution being reduced to zero in the continuous model the analytical expressions of the models are identical. The evidence obtained shows inner unity of the examined thresholds models and universal nature of the thresholds model of Swets, Tanner and Birdsall built on the basis of the statistical theory of signal detectability. It provides solution of one of the central problems of psychophysics--that of the threshold of the sensory systems.

[One solution to the problem of basic psychophysical law and sensory scaling]. / Ob odnom reshenii problemy osnovnogo psikhofizicheskogo zakon i shkalirovaniia oshchushchenii.

One of the central problems of psychophysics has been considered, namely, the problem of existence and uniqueness of the fundamental psychophysical law and direct sensory scaling. Based on the stochastical model of stimulus processing it was concluded that the Stevens' law should be regarded as the fundamental psychophysical law. A method for analytical description of direct sensory scales has been suggested. It is shown that two principal branches of psychophysical research--sensory sensitivity and psychophysical scaling--are naturally combined by the proposed stochastical perception model forming a unified psychophysical science.

[Statistical model of the inherent noise in the visual system]. / Statisticheskaia model' sobstvennogo shuma zritel'noi sistemy.

A concept of intrinsic noise of the visual system has been formulated. It has been shown that the intrinsic noise is realized in the form of the stochastic (from simple chance to complicated pithy) visual images. On the basis of the suggested concept in the limits of a normal approach, taking into account several obvious suppositions, two identical forms have been obtained of representations of probability density of own noise--the mathematical model of own noise. This model includes, as a particular case, the model of Swets, Tanner and Birdsall and has no inherent limitations.