A Bayesian model for measurements on a set of instruments

A Bayesian model is proposed based on randomizing the systematic errors of the instruments. Conditions are identified under which the randomization reduces the expected bias in estimating a measured quantity. __________ Translated from Izmeritel’naya Tekhnika, No. 3, pp. 22–25, March, 2007.     

Three Types of Mathematical Uncertainty Models

Mathematical models have been constructed for three types of uncertainty (interval, stochastic, and Bayesian), and the application of these models is discussed for describing measurements in the presence of unmonitored fluctuations leading to ambiguities in the results. __________ Translated from Izmeritel'naya Tekhnika, No. 9, pp. 39–44, September, 2005.     

Mutual synchronization and desynchronization of Lorenz systems

The dynamics of two symmetrically coupled Lorenz systems is investigated by means of a numerical experiment. A bifurcation analysis of the synchronization process is presented. The results are compared with numerical experiments. It is shown that changing the coupling can synchronize or desynchronize the subsystems. Pis’ma Zh. Tekh. Fiz. 24, 22–30 (April 12, 1998)     

The activation law for one-dimensional maps

The activation dynamics of one-dimensional maps is considered. It is shown that the activation law describing the average time required for attaining a given boundary has the form of the error function (erfc), whereas approximation using the exponential law gives much worse results. In addition, it is demonstrated that linear analysis can be applied to a substantially nonlinear problem.     

Phase synchronization of switchings in stochastic and chaotic bistable systems

We study synchronization of switching processes in stochastic and chaotic bistable systems driven by a periodic signal in terms of phase synchronization. By introduction of instantaneous phases of transitions between metastable states and of the periodic forcing we show explicitly the effect of phase locking. The dynamics of phase difference appears to be qualitatively equivalent to that of a synchronized classical self-sustained oscillator. We have found that the degree of phase coherence between the input signal and the response estimated employing the effective diffusion constant is maximal at an optimal noise level in a stochastic bistable system or at an optimal value of a control parameter in a purely deterministic case. We also consider the effect of mutual synchronization of the switching processes in coupled stochastic and chaotic bistable systems.     

Mutual synchronization of switching processes in coupled Lorenz systems

A numerical analysis is made of the synchronization of the mean switching frequencies in two symmetrically coupled Lorenz systems functioning in a chaotic regime. The observed effect on the coupling-mismatch parameter plane corresponds to a region of synchronization of the switching processes, within which the mean switching frequencies coincide to a given accuracy. Pis’ma Zh. Tekh. Fiz. 23, 14–19 (April 26, 1997)     

The effect of spatiotemporal fluctuations on the pulse propagation

We have studied the influence of uncorrelated Gaussian fluctuations on the propagation of pulses in an excitable medium modeled by the FitzHugh-Nagumo system under an external point action. Depending on the properties of this medium, one of the two possible scenarios is realized in the noise-induced suppression of propagating pulses. The first scenario can be classified as the noise-induced incoherence (breakage of the links) between adjacent elements of the medium. The second scenario is related to a spontaneous generation of pulses in the medium under the action of fluctuations. These models are applied to analysis of some recent biological experiments devoted to the dynamics of calcium waves.     

Measurement of a Discrete Indicator Utilizing Nonnumerical,Inaccurate, and Incomplete Information

In accordance with the requirements of the international Guide to the Expression of Uncertainty in Measurement, a new Bayes model has been developed for estimating the mathematical expectation and variance of a random quantity modeling the uncertainty of the result of a measurement of a discrete indicator. The model makes it possible to utilize nonnumerical, inaccurate, and incomplete information concerning the probability distribution of this random quantity.     

Forecast with the use of statistical and expert methods

Consideration is given to a combination of different methods for the forecast of values of the social-economic index. One group of methods estimate the value of the index in the future by econometric analysis basing on its dynamics in the past. A new notion of optimal initial vector of forecast is introduced. Other methods are based on experts’ forecast whose conclusions accumulate nonnumerical, incomplete, and inexact information. The final estimate is delivered by a combination of econometric and expert forecasts with weighting coefficients; they are chosen by a researcher taking the volume and quality of the used expert and statistical information into account.