Discontinuities in pattern inference

This paper deals with the inferrability of classes of E-pattern languages—also referred to as extended or erasing pattern languages—from positive data in Gold’s model of identification in the limit. The first main part of the paper shows that the recently presented negative result on terminal-free E-pattern languages over binary alphabets does not hold for other alphabet sizes, so that the full class of these languages is inferrable from positive data if and only if the corresponding terminal alphabet does not consist of exactly two distinct letters. The second main part yields the insight that the positive result on terminal-free E-pattern languages over alphabets with three or four letters cannot be extended to the class of general E-pattern languages. With regard to larger alphabets, the extensibility remains open. The proof methods developed for these main results do not directly discuss the (non-)existence of appropriate learning strategies, but they deal with structural properties of classes of E-pattern languages, and, in particular, with the problem of finding telltales for these languages. It is shown that the inferrability of classes of E-pattern languages is closely connected to some problems on the ambiguity of morphisms so that the technical contributions of the paper largely consist of combinatorial insights into morphisms in word monoids

Discontinuities in pattern inference

This paper deals with the inferrability of classes of E-pattern languages—also referred to as extended or erasing pattern languages—from positive data in Gold’s model of identification in the limit. The first main part of the paper shows that the recently presented negative result on terminal-free E-pattern languages over binary alphabets does not hold for other alphabet sizes, so that the full class of these languages is inferrable from positive data if and only if the corresponding terminal alphabet does not consist of exactly two distinct letters. The second main part yields the insight that the positive result on terminal-free E-pattern languages over alphabets with three or four letters cannot be extended to the class of general E-pattern languages. With regard to larger alphabets, the extensibility remains open. The proof methods developed for these main results do not directly discuss the (non-)existence of appropriate learning strategies, but they deal with structural properties of classes of E-pattern languages, and, in particular, with the problem of finding telltales for these languages. It is shown that the inferrability of classes of E-pattern languages is closely connected to some problems on the ambiguity of morphisms so that the technical contributions of the paper largely consist of combinatorial insights into morphisms in word monoids

Using prior information to identify boundaries in disease risk maps

Disease maps display the spatial pattern in disease risk, so that high-risk clusters can be identified. The spatial structure in the risk map is typically represented by a set of random effects, which are modelled with a conditional autoregressive (CAR) prior. Such priors include a global spatial smoothing parameter, whereas real risk surfaces are likely to include areas of smooth evolution as well as discontinuities, the latter of which are known as risk boundaries. Therefore, this paper proposes an extension to the class of CAR priors, which can identify both areas of localised spatial smoothness and risk boundaries. However, allowing for this localised smoothing requires large numbers of correlation parameters to be estimated, which are unlikely to be well identified from the data. To address this problem we propose eliciting an informative prior about the locations of such boundaries, which can be combined with the information from the data to provide more precise posterior inference. We test our approach by simulation, before applying it to a study of the risk of emergency admission to hospital in Greater Glasgow, Scotland

Non-stationary patterns of isolation-by-distance: inferring measures of local genetic differentiation with Bayesian kriging

Patterns of isolation-by-distance arise when population differentiation increases with increasing geographic distances. Patterns of isolation-by-distance are usually caused by local spatial dispersal, which explains why differences of allele frequencies between populations accumulate with distance. However, spatial variations of demographic parameters such as migration rate or population density can generate non-stationary patterns of isolation-by-distance where the rate at which genetic differentiation accumulates varies across space. To characterize non-stationary patterns of isolation-by-distance, we infer local genetic differentiation based on Bayesian kriging. Local genetic differentiation for a sampled population is defined as the average genetic differentiation between the sampled population and fictive neighboring populations. To avoid defining populations in advance, the method can also be applied at the scale of individuals making it relevant for landscape genetics. Inference of local genetic differentiation relies on a matrix of pairwise similarity or dissimilarity between populations or individuals such as matrices of FST between pairs of populations. Simulation studies show that maps of local genetic differentiation can reveal barriers to gene flow but also other patterns such as continuous variations of gene flow across habitat. The potential of the method is illustrated with 2 data sets: genome-wide SNP data for human Swedish populations and AFLP markers for alpine plant species. The software LocalDiff implementing the method is available at http://membres-timc.imag.fr/Michael.Blum/LocalDiff.htmlComment: In press, Evolution 201

Gap Filling of 3-D Microvascular Networks by Tensor Voting

We present a new algorithm which merges discontinuities in 3-D images of tubular structures presenting undesirable gaps. The application of the proposed method is mainly associated to large 3-D images of microvascular networks. In order to recover the real network topology, we need to fill the gaps between the closest discontinuous vessels. The algorithm presented in this paper aims at achieving this goal. This algorithm is based on the skeletonization of the segmented network followed by a tensor voting method. It permits to merge the most common kinds of discontinuities found in microvascular networks. It is robust, easy to use, and relatively fast. The microvascular network images were obtained using synchrotron tomography imaging at the European Synchrotron Radiation Facility. These images exhibit samples of intracortical networks. Representative results are illustrated

Dispersal and population structure at different spatial scales in the subterranean rodent Ctenomys australis

This study was funded by grants from Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET, PIP5838), Agencia de Promoción Científica y Tecnológica de la Argentina (PICTO1-423, BID-1728/OC-AR), and the programme ECOS-Sud France/Argentina (A05B01).Background: The population genetic structure of subterranean rodent species is strongly affected by demographic (e.g. rates of dispersal and social structure) and stochastic factors (e.g. random genetic drift among subpopulations and habitat fragmentation). In particular, gene flow estimates at different spatial scales are essential to understand genetic differentiation among populations of a species living in a highly fragmented landscape. Ctenomys australis (the sand dune tuco-tuco) is a territorial subterranean rodent that inhabits a relatively secure, permanently sealed burrow system, occurring in sand dune habitats on the coastal landscape in the south-east of Buenos Aires province, Argentina. Currently, this habitat is threatened by urban development and forestry and, therefore, the survival of this endemic species is at risk. Here, we assess population genetic structure and patterns of dispersal among individuals of this species at different spatial scales using 8 polymorphic microsatellite loci. Furthermore, we evaluate the relative importance of sex and habitat configuration in modulating the dispersal patterns at these geographical scales. Results: Our results show that dispersal in C. australis is not restricted at regional spatial scales (similar to 4 km). Assignment tests revealed significant population substructure within the study area, providing support for the presence of two subpopulations from three original sampling sites. Finally, male-biased dispersal was found in the Western side of our study area, but in the Eastern side no apparent philopatric pattern was found, suggesting that in a more continuous habitat males might move longer distances than females. Conclusions: Overall, the assignment-based approaches were able to detect population substructure at fine geographical scales. Additionally, the maintenance of a significant genetic structure at regional (similar to 4 km) and small (less than 1 km) spatial scales despite apparently moderate to high levels of gene flow between local sampling sites could not be explained simply by the linear distance among them. On the whole, our results support the hypothesis that males disperse more frequently than females; however they do not provide support for strict philopatry within females.Publisher PDFPeer reviewe