Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

A Bayesian network approach to the database serch problem in criminal proceedings

Background The 'database search problem', that is, the strengthening of a case - in terms of probative value - against an individual who is found as a result of a database search, has been approached during the last two decades with substantial mathematical analyses, accompanied by lively debate and centrally opposing conclusions. This represents a challenging obstacle in teaching but also hinders a balanced and coherent discussion of the topic within the wider scientific and legal community. This paper revisits and tracks the associated mathematical analyses in terms of Bayesian networks. Their derivation and discussion for capturing probabilistic arguments that explain the database search problem are outlined in detail. The resulting Bayesian networks offer a distinct view on the main debated issues, along with further clarity. Methods As a general framework for representing and analyzing formal arguments in probabilistic reasoning about uncertain target propositions (that is, whether or not a given individual is the source of a crime stain), this paper relies on graphical probability models, in particular, Bayesian networks. This graphical probability modeling approach is used to capture, within a single model, a series of key variables, such as the number of individuals in a database, the size of the population of potential crime stain sources, and the rarity of the corresponding analytical characteristics in a relevant population. Results This paper demonstrates the feasibility of deriving Bayesian network structures for analyzing, representing, and tracking the database search problem. The output of the proposed models can be shown to agree with existing but exclusively formulaic approaches. Conclusions The proposed Bayesian networks allow one to capture and analyze the currently most well-supported but reputedly counter-intuitive and difficult solution to the database search problem in a way that goes beyond the traditional, purely formulaic expressions. The method's graphical environment, along with its computational and probabilistic architectures, represents a rich package that offers analysts and discussants with additional modes of interaction, concise representation, and coherent communication.

The subjectivist interpretation of probability and the problem of individualisation in forensic science

This paper presents and discusses further aspects of the subjectivist interpretation of probability (also known as the 'personalist' view of probabilities) as initiated in earlier forensic and legal literature. It shows that operational devices to elicit subjective probabilities - in particular the so-called scoring rules - provide additional arguments in support of the standpoint according to which categorical claims of forensic individualisation do not follow from a formal analysis under that view of probability theory.

Surdités légères et surdités unilatérales chez l'enfant: quelle importance [Minimal or unilateral hearing loss in children: is it a problem?].

The word "minimal" or "mild" hearing loss seems to imply that their effects are mild or negligible. The literature supports that they can have a significant impact on educative end educational development of young children and contribute to problems in fields of social function, communication and educational achievement. Unilateral hearing loss in children has been considered for long to be of little consequence. In fact it causes problems in speech and language development, speech understanding, especially in noisy environments, and school results. Early diagnosis, follow-up during preschool and school ages are mandatory.