A differential inclusion approach for modeling and analysis of dynamical systems under uncertainty

In this paper we deal with the application of differential inclusions to modeling nonlinear dynamical systems under uncertainty in parameters. In this case, differential inclusions seem to be better suited to modeling practical situations under uncertainty and imprecision than formulations by means of fuzzy differential equations. We develop a practical algorithm to approximate the reachable sets of a class of nonlinear differential inclusion, which eludes the computational problems of a previous set-valued version of the Heun’s method. Our algorithm is based on a complete discretization (time and state space) of the differential inclusion and it suits hardware features, handling the memory used by the method in a controlled fashion during all iterations. As a case of study, we formulate a differential inclusion to model an epidemic outbreak of dengue fever under Cuban conditions. The model takes into account interaction of human and mosquito populations as well as vertical transmission in the mosquito population. It is studied from the theoretical point of view to apply the Practical Algorithm. Also, we estimate the temporal evolution of the different human and mosquito populations given by the model in the Dengue 3 epidemic in Havana 2001, through the computation of the reachable sets using the Practical Algorithm.     

Mixture and non-mixture cure fraction models based on the generalized modified Weibull distribution with an application to gastric cancer data

The cure fraction models are usually used to model lifetime time data with long-term survivors. In the present article, we introduce a Bayesian analysis of the four-parameter generalized modified Weibull (GMW) distribution in presence of cure fraction, censored data and covariates. In order to include the proportion of “cured” patients, mixture and non-mixture formulation models are considered. To demonstrate the ability of using this model in the analysis of real data, we consider an application to data from patients with gastric adenocarcinoma. Inferences are obtained by using MCMC (Markov Chain Monte Carlo) methods.     

STATISTICAL LINGUISTIC LAWS IN ECOLOGICAL MODELS

This paper gives the theoretical setup so that an ecological model, as a particular mathematical model, can be considered a text written in a formal language (mathematics), and therefore, statistical linguistic laws can be applied to obtain information parameters in different semantic levels of the same model. The statistical laws will be useful to: a) compare semantic levels, submodels, and different models mutually; b) prove that information temperature parameter is an indirect measure of meaning: the significance or semantic component of information, opposed to significant, or comprehension, on the part of the observer (modeller) of the model text. We will apply these ideas in two practical examples.     

Comparison of four test methods to measure damping properties of materials by using piezoelectric transducers

This article presents the experimental results of damping loss factor and Young’s modulus obtained for stiff and flexible materials through the use of four different methodologies: the Central Impedance Method, the Modified Oberst Method, the Seismic Response Method, and the simply supported beam method. The first three methods are based on the ASTM standard but using different experimental setting and different Frequency Response Functions. The fourth method corresponds to a non-resonant technique used in the characterization of materials at very low frequencies. In this work, the results of damping loss factor and Young’s modulus obtained through these four methods are compared, the variability of results is studied and the sensitivity of each technique when facing controlled temperature variations is verified.     

Introducing concurrency in sequential Java via laws

Nowadays multi-core processors can be found everywhere. It is well known that one way of improving performance is by parallelization. In this paper we propose a parallelization strategy for Java using algebraic laws. We perform an experiment with two benchmarks and show that our strategy produces a gain similar to a specialized parallel version provided by the Java Grande Benchmark (JGB).     

Clipping algorithms for solving the nearest point problem over reduced convex hulls

The nearest point problem (NPP), i.e., finding the closest points between two disjoint convex hulls, has two classical solutions, the Gilbert-Schlesinger-Kozinec (GSK) and Mitchell-Dem’yanov-Malozemov (MDM) algorithms. When the convex hulls do intersect, NPP has to be stated in terms of reduced convex hulls (RCHs), made up of convex pattern combinations whose coefficients are bound by a μ<1 value and that are disjoint for suitable μ. The GSK and MDM methods have recently been extended to solve NPP for RCHs using the particular structure of the extreme points of a RCH. While effective, their reliance on extreme points may make them computationally costly, particularly when applied in a kernel setting. In this work we propose an alternative clipped extension of classical MDM that results in a simpler algorithm with the same classification accuracy than that of the extensions already mentioned, but also with a much faster numerical convergence.     

Static and dynamic analysis of laminated plates based on an unconstrained third order theory and using a radial point interpolator meshless method

The Natural Neighbour Radial Point Interpolation Method (NNRPIM), an improved meshless method, is used in the numerical implementation of an Unconstrained Third-Order Plate Theory applied to laminates. The nodal connectivity and the node dependent integration background mesh are constructed resorting to the Voronoï tessellation and to the Delaunay triangulation. Within NNRPIM the obtained interpolation functions, constructed with the Radial Point Interpolators, pass through all nodes inside the influence-cell providing the interpolation functions with the delta Kronecker property. In order to prove the high accuracy and convergence rate of the proposed meshless method several well-known benchmark static and dynamic laminate examples are solved. The numerical results obtained with the NNRPIM are compared with the Unconstrained Third-Order Plate Theory exact solution, when available, and with exact solutions of other plate deformation theories.