Sources of path integration error in young and aging humans

Path integration is a vital function in navigation: it enables the continuous tracking of one’s position in space by integrating self-motion cues. Path integration abilities vary across individuals but tend to deteriorate in old age. The specific causes of path integration errors, however, remain poorly characterized. Here, we combined tests of path integration performance with a novel analysis based on the Langevin diffusion equation, which allowed us to decompose errors into distinct causes that can corrupt path integration computations. Across age groups, the dominant errors were due to noise and a bias in speed estimation. Noise-driven errors accumulated with travel distance not elapsed time, suggesting that the dominant noise originates in the velocity input rather than within the integrator. Age-related declines were traced primarily to a growth in this unbiased noise. Together, these findings shed light on the contributors to path integration error and the mechanisms underlying age-related navigational deficits.

Modeling conflict in a social system using diffusion equations

In this paper the problem of modeling social conflicts of various types with the help of diffusion equations is discussed. The main approaches to and methods of mathematical modeling in contemporary humanitarian sciences are outlined. The main concepts of social conflicts, means of their classification and interpretation – including ethnic-social, religious, and other conflicts – are considered. The notion of a conflict in a social system is defined in terms of mathematical modeling. A model based on the Langevin diffusion equation is introduced. The model is based on the idea that all individuals in a society interact by means of a communication field. This field is induced by each individual in the society and forms informational interaction between individuals. An analytical solution of the system of equations is given in the first approximation for a diverging type of diffusion. It is shown that even for a simple case of the interaction of two groups of individuals the developed model makes it possible to discover characteristic laws of a conflict in a social system. It allows determining the effect of social distance in a society on the conditions of generation of such processes, with account of external effects or a random factor. Based on the analysis of the phase portraits for the given system, it has been concluded that there exists a stability region within which the social system is stable and non-conflicting.