Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model

Modeling viral dynamics in HIV/AIDS studies has resulted in a deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS290 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Towards an efficient multiscale modeling of low-dimensional reactive systems: study of numerical closure procedures

In this paper, we present a study on how to develop an efficient multiscale simulation strategy for the dynamics of chemically active systems on low-dimensional supports. Such reactions are encountered in a wide variety of situations, ranging from heterogeneous catalysis to electrochemical or (membrane) biological processes, to cite a few. We analyzed in this context different techniques within the framework of an important multiscale approach known as the equation free method (EFM), which "bridges the multiscale gap" by building microscopic configurations using macroscopic-level information only. We hereby considered two simple reactive processes on a one-dimensional lattice, the simplicity of which allowed for an in-depth understanding of the parameters controlling the efficiency of this approach. We demonstrate in particular that it is not enough to base the EFM on the time evolution of the average concentrations of particles on the lattice, but that the time evolution of clusters of particles has to be included as well. We also show how important it is for the accuracy of this method to carefully choose the procedure with which microscopic states are constructed, starting from the measured macroscopic quantities. As we also demonstrate that some errors cannot be corrected by increasing the number of observed macroscopic variables, this work points towards which procedures should be used in order to generate efficient and reliable multiscale simulations of these systems.Comment: 15 pages, 11 figure

Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure

Dating and localizing an invasion from post-introduction data and a coupled reaction-diffusion-absorption model

Invasion of new territories by alien organisms is of primary concern for environmental and health agencies and has been a core topic in mathematical modeling, in particular in the intents of reconstructing the past dynamics of the alien organisms and predicting their future spatial extents. Partial differential equations offer a rich and flexible modeling framework that has been applied to a large number of invasions. In this article, we are specifically interested in dating and localizing the introduction that led to an invasion using mathematical modeling, post-introduction data and an adequate statistical inference procedure. We adopt a mechanistic-statistical approach grounded on a coupled reaction-diffusion-absorption model representing the dynamics of an organism in an heterogeneous domain with respect to growth. Initial conditions (including the date and site of the introduction) and model parameters related to diffusion, reproduction and mortality are jointly estimated in the Bayesian framework by using an adaptive importance sampling algorithm. This framework is applied to the invasion of \textit{Xylella fastidiosa}, a phytopathogenic bacterium detected in South Corsica in 2015, France

Integration of renewable energy into Nigerian power systems

Many countries are advancing down the road of electricity privatization, deregulation, and competition as a solution to their growing electricity demand and other challenges posed by the monopolistic nature of the existing structure. Presently, Nigeria has a supply deficit of electricity as a result of the growing demand. This imbalance has negatively affected the economy of the country and the social-economic well-being of the population. Hence, there is an urgent need to reform the power sector for greater efficiency and better performance. The objectives of the reform are to meet the growing power demand by increasing the electric power generation and also by increasing competitiveness through the participation of more private sector entities. The renewable energy integration is one way of increasing the electricity generation in the country in order to cater for the growing demand adequately. Examples of the renewable energy that is available in the country include wind, geothermal, solar and hydro. They are considered to be environmentally friendly, replenishable and do not contribute to the climate change phenomena. The country presently generates the bulk of its electricity from both thermal (85%) and hydroelectric (15%) power plants. While electricity generation from the thermal power stations constitutes the largest share of greenhouse emission, this is mostly from burning coal and natural gas. The effect of this high proportion of greenhouse emission causes climate change which is referred to as a variation in the climate system statistical properties over a long period of time. It has been observed that many of the activities of human beings are contributory factors to the release of these greenhouse gases (GHG). But, as the traditional sources of energy continue to threaten the present and future existence on the planet earth, it is, therefore, imperative to increase the integration of the variable renewable energy sources in a sustainable and eco-friendly manner over a long period of time. The variability and the uncertainties of the renewable energy source's output, present a major challenge in the design of an efficient electricity market in a deregulated environment. The system deregulation and the use of renewable sources for the generation of electricity are major changes presently being experienced in power system. In a deregulated power system, the integration of renewable generation and its penetration affects both the physical and the economic operations. The main focus of this research is on the integration of wind energy into Nigerian power systems. Up till now, research on the availability of the wind energy and its economic impacts has been limited in Nigeria. Generally, the previous study of wind energy availability in Nigeria has been limited in scope. The wind energy assessment study has not been detailed enough to be able to ascertain the wind energy potential of the country. To cope with this shortcoming, a detailed statistical wind modeling and forecasting methodology have been used in this thesis to determine the amount of extractable wind energy in six selected locations in Nigeria using historical wind speed data for 30 years. The accuracy test of the statistical models was also carried using the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Chi-Square methods to determine the inherent error margin in the modeling and analysis. It is found that the error margin of the evaluations falls within the expected permissible tolerance range. For a more detailed wind assessment study of the Nigeria weather, the seasonal variation of the weather conditions as it affects the wind speed and availability during the two major seasons of dry and rainy was considered. A Self-Adaptive Differential Evolution (SADE) was used to solve the economic load dispatch problem that considers the valve-point effects and the transmission losses subject to many constraints. The results obtained were compared with those obtained using the "standard" Differential Evolution (DE), Genetic Algorithm (GA), and traditional Gradient Descent method. The results of the SADE obtained when compared with the GA, DE, and Gradient descent show the superiority of SADE over all the other methods. The research work shows that the wind energy is available in commercial quantity for generation of electricity in Nigeria. And, if tapped would help reduce the gap between the demand and supply of electricity in the country. It was also demonstrated that the wind energy integration into the power systems affects the generators total production cost