Maximal total population of species in a diffusive logistic model.

In this paper, we investigate the maximization of the total population of a single species which is governed by a stationary diffusive logistic equation with a fixed amount of resources. For large diffusivity, qualitative properties of the maximizers like symmetry will be addressed. Our results are in line with previous findings which assert that for large diffusion, concentrated resources are favorable for maximizing the total population. Then, an optimality condition for the maximizer is derived based upon rearrangement theory. We develop an efficient numerical algorithm applicable to domains with different geometries in order to compute the maximizer. It is established that the algorithm is convergent. Our numerical simulations give a real insight into the qualitative properties of the maximizer and also lead us to some conjectures about the maximizer.

Subpixel Matching Using Double-Precision Gradient-Based Method for Digital Image Correlation.

Digital image correlation (DIC) for displacement and strain measurement has flourished in recent years. There are integer pixel and subpixel matching steps to extract displacement from a series of images in the DIC approach, and identification accuracy mainly depends on the latter step. A subpixel displacement matching method, named the double-precision gradient-based algorithm (DPG), is proposed in this study. After, the integer pixel displacement is identified using the coarse-fine search algorithm. In order to improve the accuracy and anti-noise capability in the subpixel extraction step, the traditional gradient-based method is used to analyze the data on the speckle patterns using the computer, and the influence of noise is considered. These two nearest integer pixels in one direction are both utilized as an interpolation center. Then, two subpixel displacements are extracted by the five-point bicubic spline interpolation algorithm using these two interpolation centers. A novel combination coefficient considering contaminated noises is presented to merge these two subpixel displacements to obtain the final identification displacement. Results from a simulated speckle pattern and a painted beam bending test show that the accuracy of the proposed method can be improved by four times that of the traditional gradient-based method that reaches the same high accuracy as the Newton-Raphson method. The accuracy of the proposed method efficiently reaches at 92.67%, higher than the Newton-Raphon method, and it has better anti-noise performance and stability.

Automated facial characterization and image retrieval by convolutional neural networks.

Introduction: Developing efficient methods to infer relations among different faces consisting of numerous expressions or on the same face at different times (e.g., disease progression) is an open issue in imaging related research. In this study, we present a novel method for facial feature extraction, characterization, and identification based on classical computer vision coupled with deep learning and, more specifically, convolutional neural networks. Methods: We describe the hybrid face characterization system named FRetrAIval (FRAI), which is a hybrid of the GoogleNet and the AlexNet Neural Network (NN) models. Images analyzed by the FRAI network are preprocessed by computer vision techniques such as the oriented gradient-based algorithm that can extract only the face region from any kind of picture. The Aligned Face dataset (AFD) was used to train and test the FRAI solution for extracting image features. The Labeled Faces in the Wild (LFW) holdout dataset has been used for external validation. Results and discussion: Overall, in comparison to previous techniques, our methodology has shown much better results on k-Nearest Neighbors (KNN) by yielding the maximum precision, recall, F1, and F2 score values (92.00, 92.66, 92.33, and 92.52%, respectively) for AFD and (95.00% for each variable) for LFW dataset, which were used as training and testing datasets. The FRAI model may be potentially used in healthcare and criminology as well as many other applications where it is important to quickly identify face features such as fingerprint for a specific identification target.

Assessment of Gradient-Based Algorithm for Surface Determination in Multi-Material Gap Measurements by X ray Computed Tomography.

X-ray computed tomography is one of the most promising measurement techniques for the dimensional evaluation of industrial components. However, the inherent complexity of this technology also involves important challenges. One of them is to develop surface determination algorithms capable of providing measurement results with better accuracy in any situation-for example, for single and multi-material parts, inner and outer geometries, with and without image artefacts, etc.-and reducing user influence. The surface determination is particularly complex in the case of multi-material parts, especially when they are separated by small air gaps. In previous works, two gradient-based algorithms were presented, that showed less measurement variability throughout the whole part, and reduced the computational cost and operator influence compared to threshold-based algorithms. This work focuses on the evaluation of the performance of these algorithms when used in a scenario so complex that parts of it are made of one or more materials (metal-metal and polymer-metal) with gaps inside. For this purpose, a set of multi-material reference standards is used. The presented gradient-based algorithms show measurement errors comparable to commercial threshold-based algorithms, but with the capability of obtaining accurate measurements in smaller gaps, apart from reducing the user influence on the measurement process.

On-line prediction of ferrous ion concentration in goethite process based on self-adjusting structure RBF neural network.

Outlet ferrous ion concentration is an essential indicator to manipulate the goethite process in the zinc hydrometallurgy plant. However, it cannot be measured on-line, which leads to the delay of this feedback information. In this study, a self-adjusting structure radial basis function neural network (SAS-RBFNN) is developed to predict the outlet ferrous ion concentration on-line. First, a supervised cluster algorithm is proposed to initialize the RBFNN. Then, the network structure is adjusted by the developed self-adjusting structure mechanism. This mechanism can merge or divide the hidden neurons according to the distance of the clusters to achieve the adaptability of the RBFNN. Finally, the connection weights are determined by the gradient-based algorithm. The convergence of the SAS-RBFNN is analyzed by the Lyapunov criterion. A simulation for a benchmark problem shows the effectiveness of the proposed network. The SAS-RBFNN is then applied to predict the outlet ferrous ion concentration in the goethite process. The results demonstrate that this network can provide a more accurate prediction than the mathematical model, even under the fluctuating production condition.

Determination of poroelastic properties of cartilage using constrained optimization coupled with finite element analysis.

The feasibility of determining biphasic material properties using a finite element model of stress relaxation coupled with two types of constrained optimization to match measured data was investigated. Comparison of these two approaches, a zero-order method and a gradient-based algorithm, validated the predicted material properties. Optimizations were started from multiple different initial guesses of material properties (design variables) to establish the robustness of the optimization. Overall, the optimal values are close to those found by Cohen et al. (1998) but these small differences produced a marked improvement in the fit to the measured stress relaxation. Despite the greater deviation in the optimized values obtained from the zero-order method, both optimization procedures produced material properties that gave equally good overall fits to the measured data. Furthermore, optimized values were all within the expected range of material properties. Modeling stress relaxation using the optimized material properties showed an excellent fit to the entire time history of the measured data.