An iterative Multiscale Finite-Volume algorithm converging to the exact solution

The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).

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.

Do we truly see what we think we see? The role of cognitive bias in pathological interpretation.

In the histomorphological grading of prostate carcinoma, pathologists have regularly assigned comparable scores for the architectural Gleason and the now-obsolete nuclear World Health Organization (WHO) grading systems. Although both systems demonstrate good correspondence between grade and survival, they are based on fundamentally different biological criteria. We tested the hypothesis that this apparent concurrence between the two grading systems originates from an interpretation bias in the minds of diagnostic pathologists, rather than reflecting a biological reality. Three pathologists graded 178 prostatectomy specimens, assigning Gleason and WHO scores on glass slides and on digital images of nuclei isolated out of their architectural context. The results were analysed with respect to interdependencies among the grading systems, to tumour recurrence (PSA relapse > 0.1 ng/ml at 48 months) and robust nuclear morphometry, as assessed by computer-assisted image analysis. WHO and Gleason grades were strongly correlated (r = 0.82) and demonstrated identical prognostic power. However, WHO grades correlated poorly with nuclear morphology (r = 0.19). Grading of nuclei isolated out of their architectural context significantly improved accuracy for nuclear morphology (r = 0.55), but the prognostic power was virtually lost. In conclusion, the architectural organization of a tumour, which the pathologist cannot avoid noticing during initial slide viewing at low magnification, unwittingly influences the subsequent nuclear grade assignment. In our study, the prognostic power of the WHO grading system was dependent on visual assessment of tumour growth pattern. We demonstrate for the first time the influence a cognitive bias can have in the generation of an error in diagnostic pathology and highlight a considerable problem in histopathological tumour grading.

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.

When should clinicians search for GLUT1 deficiency syndrome in childhood generalized epilepsies?

UNLABELLED: GLUT1 deficiency (GLUT1D) has recently been identified as an important cause of generalized epilepsies in childhood. As it is a treatable condition, it is crucial to determine which patients should be investigated. METHODS: We analyzed SLC2A1 for mutations in a group of 93 unrelated children with generalized epilepsies. Fasting lumbar puncture was performed following the identification of a mutation. We compared our results with a systematic review of 7 publications of series of patients with generalized epilepsies screened for SLC2A1 mutations. RESULTS: We found 2/93 (2.1%) patients with a SLC2A1 mutation. One, carrying a novel de novo deletion had epilepsy with myoclonic-atonic seizures (MAE), mild slowing of head growth, choreiform movements and developmental delay. The other, with a paternally inherited missense mutation, had childhood absence epilepsy with atypical EEG features and paroxysmal exercise-induced dyskinesia (PED) initially misdiagnosed as myoclonic seizures. Out of a total of 1110 screened patients with generalized epilepsies from 7 studies, 2.4% (29/1110) had GLUT1D. This rate was higher (5.6%) among 303 patients with early onset absence epilepsy (EOAE) from 4 studies. About 50% of GLUT1D patients had abnormal movements and 41% a family history of seizures, abnormal movements or both. CONCLUSION: GLUT1D is most likely to be found in MAE and in EOAE. The probability of finding GLUT1D in the classical idiopathic generalized epilepsies is very low. Pointers to GLUT1D include an increase in seizures before meals, cognitive impairment, or PED which can easily be overlooked.

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.

Generalized food-deceptive orchid species flower earlier and occur at lower altitudes than rewarding ones

Aims Food-deceptive pollination, in which plants do not offer any food reward to their pollinators, is common within the Orchidaceae. As food-deceptive orchids are poorer competitors for pollinator visitation than rewarding orchids, their occurrence in a given habitat may be more constrained than that of rewarding orchids. In particular, the success of deceptive orchids strongly relies on several biotic factors such as interactions with co-flowering rewarding species and pollinators, which may vary with altitude and over time. Our study compares generalized food-deceptive (i.e. excluding sexually deceptive) and rewarding orchids to test whether (i) deceptive orchids flower earlier compared to their rewarding counterparts and whether (ii) the relative occurrence of deceptive orchids decreases with increasing altitude. Methods To compare the flowering phenology of rewarding and deceptive orchids, we analysed data compiled from the literature at the species level over the occidental Palaearctic area. Since flowering phenology can be constrained by the latitudinal distribution of the species and by their phylogenetic relationships, we accounted for these factors in our analysis. To compare the altitudinal distribution of rewarding and deceptive orchids, we used field observations made over the entire Swiss territory and over two Swiss mountain ranges. Important Findings We found that deceptive orchid species start flowering earlier than rewarding orchids do, which is in accordance with the hypotheses of exploitation of naive pollinators and/or avoidance of competition with rewarding co-occurring species. Also, the relative frequency of deceptive orchids decreases with altitude, suggesting that deception may be less profitable at high compared to low altitude.