Multistep collocation methods for Volterra Integral Equations

We introduce multistep collocation methods for the numerical integration of Volterra Integral Equations, which depend on the numerical solution in a fixed number of previous time steps. We describe the constructive technique, analyze the order of the resulting methods and their linear stability properties. Numerical experiments confirm the theoretical expectations

Two-step almost collocation methods for Volterra integral equations

In this paper we construct a new class of continuous methods for Volterra integral equations. These methods are obtained by using a collocation technique and by relaxing some of the collocation conditions in order to obtain good stability properties

Two classes of linearly implicit numerical methods for stiff problems: analysis and MATLAB software

The purpose of this work lies in the writing of efficient and optimized Matlab codes to implement two classes of promising linearly implicit numerical schemes that can be used to accurately and stably solve stiff Ordinary Differential Equations (ODEs), and also Partial Differential Equations (PDEs) through the Method Of Lines (MOL). Such classes of methods are the Runge-Kutta (RK) [28] and the Peer [17], and have been constructed using a variant of the Exponential-Fitting (EF) technique [27]. We carry out numerical tests to compare the two methods with each other, and also with the well known and very used Gaussian RK method, by the point of view of stability, accuracy and computational cost, in order to show their convenience

Some new uses of the η_m(Z) functions

We present a procedure and a MATHEMATICA code for the conversion of formulae expressed in terms of the trigonometric functions sin(omega x), cos(omega x) or hyperbolic functions sinh(lambda x), cosh(lambda x) to forms expressed in terms of eta(m)(Z) functions. The possibility of such a conversion is important in the evaluation of the coefficients of the approximation rules derived in the frame of the exponential fitting. The converted expressions allow, among others, a full elimination of the 0/0 undeterminacy, uniform accuracy in the computation of the coefficients, and an extended area of validity for the corresponding approximation formulae

Exponentially-fitted Gauss-Laguerre quadrature rule for integrals over an unbounded interval

New quadrature formulae are introduced for the computation of integrals over the whole positive semiaxis when the integrand has an oscillatory behavior with decaying envelope. The new formulae are derived by exponential fitting, and they represent a generalization of the usual Gauss-Laguerre formulae. Their weights and nodes depend on the frequency of oscillation in the integrand, and thus the accuracy is massively increased. Rules with one up to six nodes are treated with details. Numerical illustrations are also presented

Optimal control of system governed by nonlinear volterra integral and fractional derivative equations

AbstractThis work presents a novel formulation for the numerical solution of optimal control problems related to nonlinear Volterra fractional integral equations systems. A spectral approach is implemented based on the new polynomials known as Chelyshkov polynomials. First, the properties of these polynomials are studied to solve the aforementioned problems. The operational matrices and the Galerkin method are used to discretize the continuous optimal control problems. Thereafter, some necessary conditions are defined according to which the optimal solutions of discrete problems converge to the optimal solution of the continuous ones. The applicability of the proposed approach has been illustrated through several examples. In addition, a comparison is made with other methods for showing the accuracy of the proposed one, resulting also in an improved efficiency

Recommender systems: a novel approach based on singular value decomposition

Due to modern information and communication technologies (ICT), it is increasingly easier to exchange data and have new services available through the internet. However, the amount of data and services available increases the difficulty of finding what one needs. In this context, recommender systems represent the most promising solutions to overcome the problem of the so-called information overload, analyzing users' needs and preferences. Recommender systems (RS) are applied in different sectors with the same goal: to help people make choices based on an analysis of their behavior or users' similar characteristics or interests. This work presents a different approach for predicting ratings within the model-based collaborative filtering, which exploits singular value factorization. In particular, rating forecasts were generated through the characteristics related to users and items without the support of available ratings. The proposed method is evaluated through the MovieLens100K dataset performing an accuracy of 0.766 and 0.951 in terms of mean absolute error and root-mean-square error

Deep Generative Models: The winning key for large and easily accessible ECG datasets?

Large high-quality datasets are essential for building powerful artificial intelligence (AI) algorithms capable of supporting advancement in cardiac clinical research. However, researchers working with electrocardiogram (ECG) signals struggle to get access and/or to build one. The aim of the present work is to shed light on a potential solution to address the lack of large and easily accessible ECG datasets. Firstly, the main causes of such a lack are identified and examined. Afterward, the potentials and limitations of cardiac data generation via deep generative models (DGMs) are deeply analyzed. These very promising algorithms have been found capable not only of generating large quantities of ECG signals but also of supporting data anonymization processes, to simplify data sharing while respecting patients' privacy. Their application could help research progress and cooperation in the name of open science. However several aspects, such as a standardized synthetic data quality evaluation and algorithm stability, need to be further explored

Deep sedation versus minimal sedation during endobronchial ultrasound transbronchial needle aspiration

The sedation plays an important role in the endobronchial ultrasound transbronchial needle aspiration (EBUS-TBNA) procedure. The sedation can be Minimal (anxiolysis), Moderate (conscious sedation) or Deep. The ACCP guidelines suggest that moderate or deep sedation (DS) is an acceptable approach. In fact, several studies compare moderate versus deep sedation, but no study has been carried out to compare deep sedation versus minimal. We carried out a retrospective study to compare the Deep versus Minimal sedation (MiS) in patients undergoing EBUS-TBNA.  The primary end point was the diagnostic accuracy. The secondary end points were adequacy and sensitivity. We evaluated the LN size sampling, procedural time, complications and patient tolerance. Thirty-six patients underwent EBUS-TBNA, 16 under DS and 20 under MiS. The overall diagnostic accuracy for correct diagnosis was 92.9% in DS group and 94.1% in MiS group (p=0.554). Sample adequacy, defined as the percentage of patients with a specific diagnosis by EBUS-TBNA, was 87.5% (14 of 16) and 85% (17 of 20) for the DS group and MiS group, respectively, (p=0.788); the sensitivity was 92.9% in the DS group (95% CI, 73-100%) and 92.9% in the MiS group (95% CI, 77-100%) (p=0.463). There were no major complications in either group. Minor complications were 4 in MiS and 1 in DS (p=0.355).  The patients in the MiS group recalled the procedure more often compared to the other group (p=0.041). The majority of the patients would agree to undergo the same procedure again in the future in both groups (p=0.766).  In our experience EBUS-TBNA performed under MiS has comparable accuracy, adequacy, sensitivity, complications and patient satisfaction to DS, even if the sample was small.  Future prospective multicenter studies are needed to confirm our results