Search results for "Path integration"
showing 5 items of 5 documents
Modelling Spatial Memory
2018
Among the different capabilities of animals, the formation of spatial memories is crucial for their life. Living beings able to move, constantly need to orient themselves in the environment to reach a target that might be not always visible. This chapter investigates the process of spatial memory formation as an essential ingredient for orientation in open and unstructured environments. Neural centres devoted to spatial memory and path integration were deeply investigated both in rats and different insect species like ants, bees and fruit flies. In this chapter a neural-inspired model for the formation of a spatial working memory is discussed considering some key elements of the insect neur…
Ideal and physical barrier problems for non-linear systems driven by normal and Poissonian white noise via path integral method
2016
Abstract In this paper, the probability density evolution of Markov processes is analyzed for a class of barrier problems specified in terms of certain boundary conditions. The standard case of computing the probability density of the response is associated with natural boundary conditions, and the first passage problem is associated with absorbing boundaries. In contrast, herein we consider the more general case of partially reflecting boundaries and the effect of these boundaries on the probability density of the response. In fact, both standard cases can be considered special cases of the general problem. We provide solutions by means of the path integral method for half- and single-degr…
Non-linear systems under Levy White Noise Handled by path integration method
2009
Aim of this paper is an investigation on the consistency of the Path Integration (PI) method already proposed by Naess & Johansen, 1991,1993 for non-linear systems driven by α-stable white noise. It is shown that in the limit, as τ→0, the Einstein-Smoluchowsky (ES) equation is fully restored. Once the consistency of the PI is demonstrated for the half oscillator, then the extension of the ES equation for MDOF system is found starting from the PI method.
A spiking network for spatial memory formation: Towards a fly-inspired ellipsoid body model
2013
Neural centers devoted to spatial memory and path integration were largely studied in rats and in different insect species like ants and bees. In this paper a neural-based model for the formation of a spatial working memory is proposed mirroring some peculiarities of the Drosophila central brain and in particular the ellipsoid body. Simulation results are reported opening the way to applications on roving platforms.
Efficient solution of the first passage problem by Path Integration for normal and Poissonian white noise
2015
Abstract In this paper the first passage problem is examined for linear and nonlinear systems driven by Poissonian and normal white noise input. The problem is handled step-by-step accounting for the Markov properties of the response process and then by Chapman–Kolmogorov equation. The final formulation consists just of a sequence of matrix–vector multiplications giving the reliability density function at any time instant. Comparison with Monte Carlo simulation reveals the excellent accuracy of the proposed method.