Noether's Theorem for Fractional Optimal Control Problems

We begin by reporting on some recent results of the authors (Frederico and Torres, 2006), concerning the use of the fractional Euler-Lagrange notion to prove a Noether-like theorem for the problems of the calculus of variations with fractional derivatives. We then obtain, following the Lagrange multiplier technique used in (Agrawal, 2004), a new version of Noether's theorem to fractional optimal control systems.Comment: To be presented at FDA'06 - 2nd IFAC Workshop on Fractional Differentiation and its Applications, 19-21 July 2006, Porto, Portugal. Accepted (07-March-2006) for the Conference Proceeding

Fractional Noether's theorem in the Riesz-Caputo sense

We prove a Noether's theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and optimal control are given.Comment: Accepted (25/Jan/2010) for publication in Applied Mathematics and Computatio

Accurate Pulmonary Nodule Detection in Computed Tomography Images Using Deep Convolutional Neural Networks

Early detection of pulmonary cancer is the most promising way to enhance a patient's chance for survival. Accurate pulmonary nodule detection in computed tomography (CT) images is a crucial step in diagnosing pulmonary cancer. In this paper, inspired by the successful use of deep convolutional neural networks (DCNNs) in natural image recognition, we propose a novel pulmonary nodule detection approach based on DCNNs. We first introduce a deconvolutional structure to Faster Region-based Convolutional Neural Network (Faster R-CNN) for candidate detection on axial slices. Then, a three-dimensional DCNN is presented for the subsequent false positive reduction. Experimental results of the LUng Nodule Analysis 2016 (LUNA16) Challenge demonstrate the superior detection performance of the proposed approach on nodule detection(average FROC-score of 0.891, ranking the 1st place over all submitted results).Comment: MICCAI 2017 accepte

A Dual Mesh Method for a Non-Local Thermistor Problem

We use a dual mesh numerical method to study a non-local parabolic problem arising from the well-known thermistor problem.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Numerical analysis of a nonlocal parabolic problem resulting from thermistor problem

We analyze the spatially semidiscrete piecewise linear finite element method for a nonlocal parabolic equation resulting from thermistor problem. Our approach is based on the properties of the elliptic projection defined by the bilinear form associated with the variational formulation of the finite element method. We assume minimal regularity of the exact solution that yields optimal order error estimate. The full discrete backward Euler method and the Crank-Nicolson-Galerkin scheme are also considered. Finally, a simple algorithm for solving the fully discrete problem is proposed

A minimal HIV-AIDS infection model with general incidence rate and application to Morocco data

We study the global dynamics of a SICA infection model with general incidence rate. The proposed model is calibrated with cumulative cases of infection by HIV-AIDS in Morocco from 1986 to 2015. We first prove that our model is biologically and mathematically well-posed. Stability analysis of different steady states is performed and threshold parameters are identified where the model exhibits clearance of infection or maintenance of a chronic infection. Furthermore, we examine the robustness of the model to some parameter values by examining the sensitivity of the basic reproduction number. Finally, using numerical simulations with real data from Morocco, we show that the model predicts well such reality.Comment: This is a preprint of a paper whose final and definite form is with 'Statistics Opt. Inform. Comput.', Vol. 7, No 2 (2019). See [http://www.IAPress.org]. Submitted 16/Sept/2018; Revised 10 & 15/Dec/2018; Accepted 15/Dec/201