IFS approximations of distribution functions and related optimization problems.
Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients⋆⋆⋆
In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product. We consider then the Stochastic Collocation method, and use the previous estimates to introduce...
Improved discrepancy bounds for hybrid sequences involving Halton sequences
Improvement of Fisher's test of periodicity
Fisher's test of periodicity in time series and Siegel's version of this test for compound periodicities are investigated in the paper. An improvement increasing the power of the test is suggested and demonstrated by means of numerical simulations.
Improving feature selection process resistance to failures caused by curse-of-dimensionality effects
The purpose of feature selection in machine learning is at least two-fold - saving measurement acquisition costs and reducing the negative effects of the curse of dimensionality with the aim to improve the accuracy of the models and the classification rate of classifiers with respect to previously unknown data. Yet it has been shown recently that the process of feature selection itself can be negatively affected by the very same curse of dimensionality - feature selection methods may easily over-fit...
Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators
Incomplete time series prediction using max-margin classification of data with absent features.
Individual Cell-Based Model for In-Vitro Mesothelial Invasion of Ovarian Cancer
In vitro transmesothelial migration assays of ovarian cancer cells, isolated or aggregated in multicellular spheroids, are reproduced deducing suitable Cellular Potts Models (CPM). We show that the simulations are in good agreement with the experimental evidence and that the overall process is regulated by the activity of matrix metalloproteinases (MMPs) and by the interplay of the adhesive properties of the cells with the extracellular matrix and...
Inference in linear models with inequality constrained parameters
In many econometric applications there is prior information available for some or all parameters of the underlying model which can be formulated in form of inequality constraints. Procedures which incorporate this prior information promise to lead to improved inference. However careful application seems to be necessary. In this paper we will review some methods proposed in the literature. Among these there are inequality constrained least squares (ICLS), constrained maximum likelihood (CML) and...
Inference on overlap coefficients under the Weibull distribution : equal shape parameter
In this paper we consider three measures of overlap, namely Matusia’s measure , Morisita’s measure and Weitzman’s measure . These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible life distribution model with two parameters. Monte Carlo evaluations are used to study the bias and precision...
Inference on overlap coefficients under the Weibull distribution: Equal shape parameter
In this paper we consider three measures of overlap, namely Matusia's measure ρ, Morisita's measure λ and Weitzman's measure Δ. These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible life distribution model with two parameters. Monte Carlo evaluations are used to study the bias and precision...
Inferences for joint modelling of repeated ordinal scores and time to event data.
Infinite pseudo-random sequences of high algorithmic complexity
Influence of preconditioning and blocking on accuracy in solving Markovian models
The article considers the effectiveness of various methods used to solve systems of linear equations (which emerge while modeling computer networks and systems with Markov chains) and the practical influence of the methods applied on accuracy. The paper considers some hybrids of both direct and iterative methods. Two varieties of the Gauss elimination will be considered as an example of direct methods: the LU factorization method and the WZ factorization method. The Gauss-Seidel iterative method...
Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics
We study the influence of time delays on the dynamics of the general Hahnfeldt et al. model of an angiogenesis process. We analyse the dynamics of the system for different values of the parameter α which reflects the strength of stimulation of the vessel formation process. Time delays are introduced in three subprocesses: tumour growth, stimulation and inhibition of vessel formation (represented by endothelial cell dynamics). We focus on possible destabilisation of the positive steady state due...
Influenza Transmission in Preschools: Modulation by contact landscapes and interventions
Epidemiologic data suggest that schools and daycare facilities likely play a major role in the dissemination of influenza. Pathogen transmission within such small, inhomogenously mixed populations is difficult to model using traditional approaches. We developed simulation based mathematical tool to investigate the effects of social contact networks on pathogen dissemination in a setting analogous to a daycare center or grade school. Here we show...
Information contained in design points of experiments with correlated observations
A random process (field) with given parametrized mean and covariance function is observed at a finite number of chosen design points. The information about its parameters is measured via the Fisher information matrix (for normally distributed observations) or using information functionals depending on that matrix. Conditions are stated, under which the contribution of one design point to this information is zero. Explicit expressions are obtained for the amount of information coming from a selected...
Information denoising and quantization by diffusion reaction model.
Insensitivity region for variance components in general linear model
In linear regression models the estimator of variance components needs a suitable choice of a starting point for an iterative procedure for a determination of the estimate. The aim of this paper is to find a criterion for a decision whether a linear regression model enables to determine the estimate reasonably and whether it is possible to do so when using the given data.
Interval estimation for the Poisson distribution parameter with a single observation.