Search results for " math"
showing 10 items of 11183 documents
Modelling and assessing public health policies to counteract Italian measles outbreaks
2021
This study aims to understand, through explanatory research, the key factors that led to the 2017 measles outbreak in Italy, the causes of the low level of immunisation and the causes of possible cyclical phenomena of measles epidemics. This topic's comprehension has required a holistic approach, merging epidemiological aspects, socioeconomic aspects (including the evolution of mistrust in vaccinations, infodemy and fake news) and health law constraints. A specific SIR System Dynamics (SD) model was built to reproduce the relevant cause-and-effect relationships between social interactions, the public institutions behaviour and the measles outbreaks. SD results permit the assessment of the h…
How many longitudinal covariate measurements are needed for risk prediction?
2014
Abstract Objective In epidemiologic follow-up studies, many key covariates, such as smoking, use of medication, blood pressure, and cholesterol, are time varying. Because of practical and financial limitations, time-varying covariates cannot be measured continuously, but only at certain prespecified time points. We study how the number of these longitudinal measurements can be chosen cost-efficiently by evaluating the usefulness of the measurements for risk prediction. Study Design and Setting The usefulness is addressed by measuring the improvement in model discrimination between models using different amounts of longitudinal information. We use simulated follow-up data and the data from t…
A new approach for estimating a nonlinear growth component in multilevel modeling
2011
This study presents a new approach to estimation of a nonlinear growth curve component with fixed and random effects in multilevel modeling. This approach can be used to estimate change in longitudinal data, such as day-of-the-week fluctuation. The motivation of the new approach is to avoid spurious estimates in a random coefficient regression model due to the synchronized periodical effect (e.g., day-of-the-week fluctuation) appearing both in independent and dependent variables. First, the new approach is introduced. Second, a Monte Carlo simulation study is carried out to examine the functioning of the proposed new approach in the case of small sample sizes. Third, the use of the approac…
Numerical Recovery of Source Singularities via the Radiative Transfer Equation with Partial Data
2013
The inverse source problem for the radiative transfer equation is considered, with partial data. Here we demonstrate numerical computation of the normal operator $X_{V}^{*}X_{V}$ where $X_{V}$ is the partial data solution operator to the radiative transfer equation. The numerical scheme is based in part on a forward solver designed by F. Monard and G. Bal. We will see that one can detect quite well the visible singularities of an internal optical source $f$ for generic anisotropic $k$ and $\sigma$, with or without noise added to the accessible data $X_{V}f$. In particular, we use a truncated Neumann series to estimate $X_{V}$ and $X_{V}^{*}$, which provides a good approximation of $X_{V}^{*…
A Cooperative Coevolution Framework for Parallel Learning to Rank
2015
We propose CCRank, the first parallel framework for learning to rank based on evolutionary algorithms (EA), aiming to significantly improve learning efficiency while maintaining accuracy. CCRank is based on cooperative coevolution (CC), a divide-and-conquer framework that has demonstrated high promise in function optimization for problems with large search space and complex structures. Moreover, CC naturally allows parallelization of sub-solutions to the decomposed sub-problems, which can substantially boost learning efficiency. With CCRank, we investigate parallel CC in the context of learning to rank. We implement CCRank with three EA-based learning to rank algorithms for demonstration. E…
On shape differentiation of discretized electric field integral equation
2013
Abstract This work presents shape derivatives of the system matrix representing electric field integral equation discretized with Raviart–Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries of the original system matrix. The results are compared to derivatives computed with automatic differentiation technique and finite differences, and are found to be in an excellent agreement. Furthermore, the derived formulas are employed to analyze shape sensitivity of the input impedance of a planar inverted F-antenna, and the results are compared to those obtained using a finite difference approximation.
A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality
2015
We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.
Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
2017
Abstract European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like the Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a give…
Reduced Order Models for Pricing American Options under Stochastic Volatility and Jump-diffusion Models
2016
American options can be priced by solving linear complementary problems (LCPs) with parabolic partial(-integro) differential operators under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. These operators are discretized using finite difference methods leading to a so-called full order model (FOM). Here reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD) and non negative matrix factorization (NNMF) in order to make pricing much faster within a given model parameter variation range. The numerical experiments demonstrate orders of magnitude faster pricing with ROMs. peerReviewed
Synchronous R-NSGA-II: An Extended Preference-Based Evolutionary Algorithm for Multi-Objective Optimization
2015
Classical evolutionary multi-objective optimization algorithms aim at finding an approx- imation of the entire set of Pareto optimal solutions. By considering the preferences of a decision maker within evolutionary multi-objective optimization algorithms, it is possible to focus the search only on those parts of the Pareto front that satisfy his/her preferences. In this paper, an extended preference-based evolutionary algorithm has been proposed for solving multi-objective optimiza- tion problems. Here, concepts from an interactive synchronous NIMBUS method are borrowed and combined with the R-NSGA-II algorithm. The proposed synchronous R-NSGA-II algorithm uses preference information provid…