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Christopher Thron

Publications and source records attributed to Christopher Thron.

22 records · Page 2Linked to original sources
arXiv2015

A Metropolis Approach for Mesh Router Nodes placement in Rural Wireless Mesh Networks

Wireless mesh networks appear as an appealing solution to reduce the digital divide between rural and urban regions. However the placement of router nodes is still a critical issue when planning this type of network, especially in rural regions where we usually observe low density and sparse population. In this paper, we firstly provide a network model tied to rural regions by considering the area to cover as decomposed into a set of elementary areas which can be required or optional in terms of coverage and where a node can be placed or not. Afterwards, we try to determine an optimal number and positions of mesh router nodes while maximizing the coverage of areas of interest, minimizing the coverage of optional areas and ensuring connectivity of all mesh router nodes. For that we propose a particularized algorithm based on Metropolis approach to ensure an optimal coverage and connectivity with an optimal number of routers. The proposed algorithm is evaluated on different region instances. We obtained a required coverage between 94% and 97% and a coverage percentage of optional areas less than 16% with an optimal number of routers nr_max2 =1.3*nr_min , (nr_min being the minimum number of router which is the ratio between the total area requiring coverage and the area which can be covered by a router).

cs.NI↗
arXiv2015

Optimal control of anthracnose using mixed strategies

In this paper we propose and study a spatial diffusion model for the control of anthracnose disease in a bounded domain. The model is a generalization of the one previously developed in [14]. We use the model to simulate two different types of control strategies against anthracnose disease. Strategies that employ chemical fungicides are modeled using a continuous control function; while strategies that rely on cultivational practices (such as pruning and removal of mummified fruits) are modeled with a control function which is discrete in time (though not in space). Under weak smoothness conditions on parameters we demonstrate the well-posedness of the model by verifying existence and uniqueness of the solution for given initial conditions. We also show that the set [0; 1] is positively invariant. We first study control by pulse strategy only, then analyze the simultaneous use of continuous and pulse strategies. In each case we specify a cost functional to be minimized, and we demonstrate the existence of optimal control strategies that can be evaluated numerically using the gradient method presented in [1]. We discuss the results of numerical simulations both for a spatially averaged version of the model and for the full model.

math.OC↗
arXiv2014

Mathematical modelling and optimal control of anthracnose

In this paper we propose two nonlinear models for the control of anthracnose disease. The first is an ordinary differential equation (ODE) model which represents the within-host evolution of the disease. The second includes spatial diffusion of the disease in a bounded domain. We demonstrate the well-posedness of those models by verifying the existence of solutions for given initial conditions and positive invariance of the positive cone. By considering a quadratic cost functional and applying a maximum principle, we construct a feedback optimal control for the ODE model which is evaluated through numerical simulations with the scientific software Scilab. For the diffusion model we establish under some conditions the existence of an optimal control with respect to a generalized version of the cost functional mentioned above. We also provide a characterization for this optimal control.

math.OC↗