Christopher Thron

Pade - Z(2) estimator of determinants

We introduce the Pade-Z2 (PZ) stochastic estimator for calculating determinants and determinant ratios. The estimator is applied to the calculation of fermion determi- nants from the two ends of the Hybrid Monte Carlo trajectories with pseudofermions. Our results on the 8 3 × 12 lattice with Wilson action show that the statistical errors from the stochastic estimator can be reduced by more than an order of magnitude by employing an unbiased variational subtraction scheme which utilizes the off-diagonal matrices from the hopping expansion. Having been able to reduce the error of the determinant ratios to about 20 % with a relatively small number of noise vectors, this may become a feasible algorithm for simulating dynamical fermions in full QCD. We also discuss the application to the density of states in Hamiltonian systems.

Efficient scalable sensor node placement algorithm for fixed target coverage applications of wireless sensor networks

Large applications of sensor networks, such as environmental risk monitoring, require the deployment of hundreds or even thousands of nodes. This study proposes and implements a novel stochastic physics-based optimisation algorithm that is both efficient (guarantees full target coverage with a reduced number of sensors) and scalable (meaning that it can be executed for very large-scale problems in a reasonable computation time). The algorithm employs ‘virtual sensors’ which move, merge, recombine, and ‘explode’ during the course of the algorithm, where the process of merging and recombining virtual sensors reduces the number of actual sensors while maintaining full coverage. The parameters which control sensor merging and explosion are varied during the algorithm to perform the same function as an annealing schedule in simulated annealing. Simulation results illustrate the rapidity and the effectiveness of the proposed method.

Linearized Robust Beamforming for Two-Way Relay Systems

In beamforming, channel state information (CSI) is used to design the beamforming vector (or matrix). Since in a practical system the CSI always needs to be estimated, channel estimation (CE) errors are inevitable, which could severely affect the performance of a beamforming scheme. In this paper, we present a novel beamforming method for two-way relay (TWR) systems that is robust against CE errors. The proposed method obtains a sub-optimal solution for the associated non-convex robust optimization problem by solving a set of closed-form linear equations. Simulations show a considerable performance gain over the rank-one relaxation-based semidefinite programming (SDP) solutions, especially for the cases where the relaxed problem becomes infeasible. In addition, there is significant reduction in complexity, making this method very attractive for practical implementation.

Padé-Z2estimator of determinants

We introduce the Pade-Z2 (PZ) stochastic estimator for calculating determinants and determinant ratios. The estimator is applied to the calculation of fermion determi- nants from the two ends of the Hybrid Monte Carlo trajectories with pseudofermions. Our results on the 8 3 × 12 lattice with Wilson action show that the statistical errors from the stochastic estimator can be reduced by more than an order of magnitude by employing an unbiased variational subtraction scheme which utilizes the off-diagonal matrices from the hopping expansion. Having been able to reduce the error of the determinant ratios to about 20 % with a relatively small number of noise vectors, this may become a feasible algorithm for simulating dynamical fermions in full QCD. We also discuss the application to the density of states in Hamiltonian systems.

Mathematical Modelling and Optimal Control of Anthracnose

In this paper we propose two nonlinear models for the control of anthracnose disease. The first one is an ordinary differential equation (ODE) model which represents the whithin host evolution of the disease. The second model includes spatial diffusion of the disease in a bounded domain Ω. We show well formulation of those models checking existence of solutions for given initial conditions and positive invariance of positive cone. Considering a quadratic cost functional and applying maximum principle we construct a feedback optimal control for the EDO model which is evaluated through numerical simulations with scientific software Scilab®. For the diffusion model we establish under some conditions existence of unique optimal control with respect to a generalized version of cost functional mentioned before. We also provide a characterization for existing optimal control. Finally we discuss a family of nonlinear controlled systems.

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 [15]. 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). For comparative purposes, we perform our analyses for a spatially-averaged model as well as the space-dependent diffusion model. Under weak smoothness conditions on parameters we demonstrate the well-posedness of both models by verifying existence and uniqueness of the solution for the growth inhibition rate for given initial conditions. We also show that the set [0, 1] is positively invariant. We first study control by impulsive strategies, then analyze the simultaneous use of mixed continuous and pulse strategies. In each case we specify a cost functional to be minimized, and we demonstrate the existence of optimal control strategies. In the case of pulse-only strategies, we provide explicit algorithms for finding the optimal control strategies for both the spatially-averaged model and the space-dependent model. We verify the algorithms for both models via simulation, and discuss properties of the optimal solutions.

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).

“Frogs in a Pot”: An Agent-Based Model of Well-Being versus Prosperity

Surveys of rapidly-developing countries have shown that huge increases in average personal wealth are frequently accompanied by little or no increase in average (self-reported) happiness. We propose a simple agent-based model that may help to explain this phenomenon. The model shows that under certain conditions, the cumulative effect of individuals’ free choices of employment that maximizes their (self-perceived) personal well-being may actually produce a continuing decrease in the population’s average well-being. Like the proverbial “frog in a pot”, the eventual effect is worse when the onset of the decrease is more gradual. More generally, the model indicates that there is a natural tendency in free-market societies for well-being to become defined in increasingly materialistic terms. We discuss the implications of our model on the issue of incentive pay for teachers, and argue that our model may also provide insight into other situations where individuals’ free-market choices lead to progressive worsening of the population’s average well-being.

Affinity and Hostility in Divided Communities: A Mathematical Model

We propose, develop, and analyze a mathematical model of the probability distribution of intergroup attitudes (measured on a linear scale) in a community that is divided between two distinct social groups (which may be distinguished by religion, ethnicity, or some other socially distinguishing factor). The model is based on very simple premises that are both intuitive and justified by sociological research. Under certain assumptions, we derive analytical equations to approximate the evolution of the probability distribution of affinities. We investigate the behavior of the model in various special cases, for various model configurations. We conclude that the analytical approximations do substantially capture the behavior of the system. According to the model, social pressures cause individuals in each group to tend towards extremes of hostility or affinity towards the other group. Under some conditions, groups can have stable extremist and moderate factions; but a very small change in system parameters can upset the stability, and the entire group is driven to unanimous extremism or moderation. Groups with intermediate affinity may end up unanimously extremist or unanimously moderate, depending on model parameters and random factors; a small change in parameters can have a huge effect on the likely outcome. Interpersonal cohesion (the degree to which individuals influence each other ’s opinions) plays a significant role in controlling within-group polarization. We show that programs to improve intergroup relations that target subpopulations of each group have greatly reduced effectiveness when cohesion is low. There is a narrow changeover range in which a small reduction in cohesion produces a much larger tendency towards within-group polarization.

Algebraic method for optimal beamforming in two-way relay systems with analog network coding

The problem of optimal beamforming for two-way relay (TWR) systems with perfect channel state information (CSI) that use analog network coding (ANC) is reduced to a pair of algebraic equations in two variables that can be solved very inexpensively using the conjugate gradient algorithm. The solution has greatly reduced complexity compared to previous optimal solutions via semidefinite programming (SDP). Together with a previously-designed linearized algorithm for beamforming in the robust (imperfect CSI) case, it provides a high-performance, low-complexity robust beamforming solution for 2-way relays.