An algebraic operator approach to the analysis of Gerber-Shiu functions

We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value problems, amounting to iteratively solving first-order problems. This leads to an explicit expression for the Gerber-Shiu function in terms of the penalty function.

Hardy-Weinberg Equilibrium and the Ternary Plot

The Hardy-Weinberg law, formulated about 100 years ago, states that under certainassumptions, the three genotypes AA, AB and BB at a bi-allelic locus are expected to occur inthe proportions p2, 2pq, and q2 respectively, where p is the allele frequency of A, and q = 1-p.There are many statistical tests being used to check whether empirical marker data obeys theHardy-Weinberg principle. Among these are the classical xi-square test (with or withoutcontinuity correction), the likelihood ratio test, Fisher's Exact test, and exact tests in combinationwith Monte Carlo and Markov Chain algorithms. Tests for Hardy-Weinberg equilibrium (HWE)are numerical in nature, requiring the computation of a test statistic and a p-value.There is however, ample space for the use of graphics in HWE tests, in particular for the ternaryplot. Nowadays, many genetical studies are using genetical markers known as SingleNucleotide Polymorphisms (SNPs). SNP data comes in the form of counts, but from the countsone typically computes genotype frequencies and allele frequencies. These frequencies satisfythe unit-sum constraint, and their analysis therefore falls within the realm of compositional dataanalysis (Aitchison, 1986). SNPs are usually bi-allelic, which implies that the genotypefrequencies can be adequately represented in a ternary plot. Compositions that are in exactHWE describe a parabola in the ternary plot. Compositions for which HWE cannot be rejected ina statistical test are typically “close" to the parabola, whereas compositions that differsignificantly from HWE are “far". By rewriting the statistics used to test for HWE in terms ofheterozygote frequencies, acceptance regions for HWE can be obtained that can be depicted inthe ternary plot. This way, compositions can be tested for HWE purely on the basis of theirposition in the ternary plot (Graffelman & Morales, 2008). This leads to nice graphicalrepresentations where large numbers of SNPs can be tested for HWE in a single graph. Severalexamples of graphical tests for HWE (implemented in R software), will be shown, using SNPdata from different human populations

Operator expansion: definition and molecular integral applications

Es defineix l'expansió general d'operadors com una combinació lineal de projectors i s'exposa la seva aplicació generalitzada al càlcul d'integrals moleculars. Com a exemple numèric, es fa l'aplicació al càlcul d'integrals de repulsió electrònica entre quatre funcions de tipus s centrades en punts diferents, i es mostren tant resultats del càlcul com la definició d'escalat respecte a un valor de referència, que facilitarà el procés d'optimització de l'expansió per uns paràmetres arbitraris. Es donen resultats ajustats al valor exacte

Methods for testing association between uncertain genotypes and quantitative traits.

Interpretability and power of genome-wide association studies can be increased by imputing unobserved genotypes, using a reference panel of individuals genotyped at higher marker density. For many markers, genotypes cannot be imputed with complete certainty, and the uncertainty needs to be taken into account when testing for association with a given phenotype. In this paper, we compare currently available methods for testing association between uncertain genotypes and quantitative traits. We show that some previously described methods offer poor control of the false-positive rate (FPR), and that satisfactory performance of these methods is obtained only by using ad hoc filtering rules or by using a harsh transformation of the trait under study. We propose new methods that are based on exact maximum likelihood estimation and use a mixture model to accommodate nonnormal trait distributions when necessary. The new methods adequately control the FPR and also have equal or better power compared to all previously described methods. We provide a fast software implementation of all the methods studied here; our new method requires computation time of less than one computer-day for a typical genome-wide scan, with 2.5 M single nucleotide polymorphisms and 5000 individuals.

Necessary and sufficient conditions for robust stability using modal intervals

In this paper, robustness of parametric systems is analyzed using a new approach to interval mathematics called Modal Interval Analysis. Modal Intervals are an interval extension that, instead of classic intervals, recovers some of the properties required by a numerical system. Modal Interval Analysis not only simplifies the computation of interval functions but allows semantic interpretation of their results. Necessary, sufficient and, in some cases, necessary and sufficient conditions for robust performance are presented

The prognostic value of health-related quality-of-life data in predicting survival in glioblastoma cancer patients: results from an international randomised phase III EORTC Brain Tumour and Radiation Oncology Groups, and NCIC Clinical Trials Group study.

This is one of the few studies that have explored the value of baseline symptoms and health-related quality of life (HRQOL) in predicting survival in brain cancer patients. Baseline HRQOL scores (from the EORTC QLQ-C30 and the Brain Cancer Module (BN 20)) were examined in 490 newly diagnosed glioblastoma cancer patients for the relationship with overall survival by using Cox proportional hazards regression models. Refined techniques as the bootstrap re-sampling procedure and the computation of C-indexes and R(2)-coefficients were used to try and validate the model. Classical analysis controlled for major clinical prognostic factors selected cognitive functioning (P=0.0001), global health status (P=0.0055) and social functioning (P<0.0001) as statistically significant prognostic factors of survival. However, several issues question the validity of these findings. C-indexes and R(2)-coefficients, which are measures of the predictive ability of the models, did not exhibit major improvements when adding selected or all HRQOL scores to clinical factors. While classical techniques lead to positive results, more refined analyses suggest that baseline HRQOL scores add relatively little to clinical factors to predict survival. These results may have implications for future use of HRQOL as a prognostic factor in cancer patients.

Integral inequalities for algebraic and trigonometric polynomials

Vegeu el resum a l'inici del document del fitxer adjunt.

Diagnosing Patients Combining Principal Components Analysis and Case Based Reasoning

This paper addresses the application of a PCA analysis on categorical data prior to diagnose a patients data set using a Case-Based Reasoning (CBR) system. The particularity is that the standard PCA techniques are designed to deal with numerical attributes, but our medical data set contains many categorical data and alternative methods as RS-PCA are required. Thus, we propose to hybridize RS-PCA (Regular Simplex PCA) and a simple CBR. Results show how the hybrid system produces similar results when diagnosing a medical data set, that the ones obtained when using the original attributes. These results are quite promising since they allow to diagnose with less computation effort and memory storage

Reply to Budowle, Ge, Chakraborty and Gill-King: use of prior odds for missing persons identifications

Prior probabilities represent a core element of the Bayesian probabilistic approach to relatedness testing. This letter opinions on the commentary 'Use of prior odds for missing persons identifications' by Budowle et al. (2011), published recently in this journal. Contrary to Budowle et al. (2011), we argue that the concept of prior probabilities (i) is not endowed with the notion of objectivity, (ii) is not a case for computation and (iii) does not require new guidelines edited by the forensic DNA community - as long as probability is properly considered as an expression of personal belief. Please see related article: http://www.investigativegenetics.com/content/3/1/3

Genetic team composition and level of selection in the evolution of cooperation

In cooperative multiagent systems, agents interac to solve tasks. Global dynamics of multiagent teams result from local agent interactions, and are complex and difficult to predict. Evolutionary computation has proven a promising approach to the design of such teams. The majority of current studies use teams composed of agents with identical control rules ("geneti- cally homogeneous teams") and select behavior at the team level ("team-level selection"). Here we extend current approaches to include four combinations of genetic team composition and level of selection. We compare the performance of genetically homo- geneous teams evolved with individual-level selection, genetically homogeneous teams evolved with team-level selection, genetically heterogeneous teams evolved with individual-level selection, and genetically heterogeneous teams evolved with team-level selection. We use a simulated foraging task to show that the optimal combination depends on the amount of cooperation required by the task. Accordingly, we distinguish between three types of cooperative tasks and suggest guidelines for the optimal choice of genetic team composition and level of selection

Generalized canonical correlation analysis of matrices with different row and column orders

A Method is offered that makes it possible to apply generalized canonicalcorrelations analysis (CANCOR) to two or more matrices of different row and column order. The new method optimizes the generalized canonical correlationanalysis objective by considering only the observed values. This is achieved byemploying selection matrices. We present and discuss fit measures to assessthe quality of the solutions. In a simulation study we assess the performance of our new method and compare it to an existing procedure called GENCOM,proposed by Green and Carroll. We find that our new method outperforms the GENCOM algorithm both with respect to model fit and recovery of the truestructure. Moreover, as our new method does not require any type of iteration itis easier to implement and requires less computation. We illustrate the methodby means of an example concerning the relative positions of the political parties inthe Netherlands based on provincial data.

Estimating uncertainty of alcohol-attributable fractions for infectious and chronic diseases.

Background: Alcohol is a major risk factor for burden of disease and injuries globally. This paper presents a systematic method to compute the 95% confidence intervals of alcohol-attributable fractions (AAFs) with exposure and risk relations stemming from different sources.Methods: The computation was based on previous work done on modelling drinking prevalence using the gamma distribution and the inherent properties of this distribution. The Monte Carlo approach was applied to derive the variance for each AAF by generating random sets of all the parameters. A large number of random samples were thus created for each AAF to estimate variances. The derivation of the distributions of the different parameters is presented as well as sensitivity analyses which give an estimation of the number of samples required to determine the variance with predetermined precision, and to determine which parameter had the most impact on the variance of the AAFs.Results: The analysis of the five Asian regions showed that 150 000 samples gave a sufficiently accurate estimation of the 95% confidence intervals for each disease. The relative risk functions accounted for most of the variance in the majority of cases.Conclusions: Within reasonable computation time, the method yielded very accurate values for variances of AAFs.