In this paper, we consider stochastic coverage of bounded domains by a diffusing swarm of robots that take local measurements of an underlying scalar field. We introduce three control methodologies with diffusion, advection, and reaction as independent control inputs. We analyze the diffusionbased control strategy using standard operator semigrouptheoretic arguments. We show that the diffusion coefficient can be chosen to be dependent only on the robots' local measurements to ensure that the swarm density converges to a function proportional to the scalar field. The boundedness of the domain precludes the need to impose assumptions on decaying properties of the scalar field at infinity. Moreover, exponential convergence of the swarm density to the equilibrium follows from properties of the spectrum of the semigroup generator. In addition, we use the proposed coverage method to construct a time-inhomogenous diffusion process and apply the observability of the heat equation to reconstruct the scalar field over the entire domain from observations of the robots' random motion over a small subset of the domain. We verify our results through simulations of the coverage scenario on a 2D domain and the field estimation scenario on a 1D domain.
Parenting children with autism in countries with limited professional and financial resources can be overwhelming. Parent training led by non-governmental organizations may help alleviate some of these burdens. The present pilot study was conducted in the Republic of Macedonia, a country located in Southeastern Europe. The purpose of the study was to evaluate a parent training model for disseminating evidence-based practices through didactic and pyramidal training strategies. Results indicated that children improved on a number of different behaviors and results provide some evidence that parenting confidence and distress improved.
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