Boundary Element Method for the Mixed BBM-KdV Equation Compared to Non Standard Boundary Conditions

In this chapter, we are interested in the numerical resolution of the mixed BBM-KdV equation defined in unbounded domain. Boundary Element Method (BEM) are introduced to truncate the equation into a considered bounded domain. BEM uses domain decomposition techniques to construct Boundary Condition (BC) as transmission between the bounded domain and its complementary. We then present a suitable approximation of these BC using Discrete Galerkin Method. Numerical simulations are made to show the efficiency of these BC. We also compare with another method that truncates the equation from unbounded to bounded domain, called Non Standard Boundary Conditions (NSBC) which introduces new variables to catch information at the boundary and compose a system to connect all these variables in the bounded domain. Further discussions are made to highlight the advantages of each method as well as the difficulties encountered in the numerical resolution

Comprehensive miscarriage dataset for an early miscarriage prediction

We present risk factors for predicting miscarriage. Our data is created through an android mobile application that collects automatically real-time data about the pregnant woman. This process is done every 60 s while the mobile application is on active mode. We distinguish two types of data: data from mobile phone and data from healthcare sensors. Data generated is real and concerns real pregnant women to test and validate the proposed system and assess its performance and effectiveness

Existence of global attractor for one-dimensional weakly damped nonlinear Schrödinger equation with Dirac interaction and artificial boundary condition in half-line

Abstract We consider a nonlinear Schrödinger equation with Dirac interaction defect. Moreover, non-standard boundary conditions are introduced in connection to the behavior of the solutions. First, we prove that this kind of Schrödinger equation can be characterized by an autonomous dynamical system. Then, based on this result, we show that such an equation possesses a maximal compact attractor in the weak topology of H 1 $\mathbf{H}^{\mathbf{1}}$

Artificial boundary condition for one-dimensional nonlinear Schrödinger problem with Dirac interaction: existence and uniqueness results

Abstract We consider the nonlinear Schrödinger equation with Dirac interaction in a half-line domain of R $\mathbb{R}$. Endowed with artificial boundary condition, we discuss the global well-posedness of the equation

A constructive method for convex solutions of a class of nonlinear Black-Scholes equations

In this work, we are concerned with the theoretical study of a nonlinear Black-Scholes equation resulting from market frictions. We will focus our attention on Barles and Soner’s model where the volatility is enlarged due to the presence of transaction costs. The aim of this paper is to give a constructive mathematical approach for proving the existence of convex solutions to a non degenerate fully nonlinear deterministic problem with nonlinear dependence upon the highest derivative. The existence of a strong solution to the original equation is shown by considering a monotone sequence satisfying an abstract Barenblatt equation and converging toward the solution of a limit problem

Using Machine Learning Algorithms for Breast Cancer Risk Prediction and Diagnosis

AbstractBreast cancer represents one of the diseases that make a high number of deaths every year. It is the most common type of all cancers and the main cause of women's deaths worldwide. Classification and data mining methods are an effective way to classify data. Especially in medical field, where those methods are widely used in diagnosis and analysis to make decisions. In this paper, a performance comparison between different machine learning algorithms: Support Vector Machine (SVM), Decision Tree (C4.5), Naive Bayes (NB) and k Nearest Neighbors (k-NN) on the Wisconsin Breast Cancer (original) datasets is conducted. The main objective is to assess the correctness in classifying data with respect to efficiency and effectiveness of each algorithm in terms of accuracy, precision, sensitivity and specificity. Experimental results show that SVM gives the highest accuracy (97.13%) with lowest error rate. All experiments are executed within a simulation environment and conducted in WEKA data mining tool