Critical interfaces of the Ashkin-Teller model at the parafermionic point

We present an extensive study of interfaces defined in the Z_4 spin lattice representation of the Ashkin-Teller (AT) model. In particular, we numerically compute the fractal dimensions of boundary and bulk interfaces at the Fateev-Zamolodchikov point. This point is a special point on the self-dual critical line of the AT model and it is described in the continuum limit by the Z_4 parafermionic theory. Extending on previous analytical and numerical studies [10,12], we point out the existence of three different values of fractal dimensions which characterize different kind of interfaces. We argue that this result may be related to the classification of primary operators of the parafermionic algebra. The scenario emerging from the studies presented here is expected to unveil general aspects of geometrical objects of critical AT model, and thus of c=1 critical theories in general.Comment: 15 pages, 3 figure

Smooth 2D Coordinate Systems on Discrete Surfaces

International audienceWe introduce a new method to compute conformal param- eterizations using a recent definition of discrete conformity, and estab- lish a discrete version of the Riemann mapping theorem. Our algorithm can parameterize triangular, quadrangular and digital meshes. It can be adapted to preserve metric properties. To demonstrate the efficiency of our method, many examples are shown in the experiment section

Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

Discrete exterior calculus (DEC) for the surface Navier-Stokes equation

We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on staggered grids in flat space for which we demonstrate second order convergence. We compare computational results with a vorticity-stream function approach for surfaces with genus 0 and demonstrate the interplay between topology, geometry and flow properties. Our discretization also allows to handle harmonic vector fields, which we demonstrate on a torus.Comment: 21 pages, 9 figure

Comparison of the confidence in freedom from infection based on different control programmes between EU member states: STOC free

The STOC free project constructed a generic framework that allows a standardised and harmonised description of different control programmes (CP) for cattle diseases. The STOC free model can be used to determine the confidence of freedom from infection that has been achieved in disease CPs, in support of an ongoing assessment of progress towards output-based standards as outlined in the EU Animal Health Law. With this information, and as required, further CP actions can be taken to mitigate the risks of persistence and (re-)introduction on the probability of freedom from infection. Bovine viral diarrhoea virus (BVDV) was chosen as the case disease because of the diversity in CPs in the six participating countries. A Bayesian hidden Markov model was considered the best modelling method. Detailed BVDVCP information was collected in the participating countries and the key aspects for inclusion in the STOCfree model were identified. A first version of STOC free model was developed and tested on simulated data. The risk factors for BVDV infection that needed to be included in the model were defined and default values for these risk factors were quantified. A data collection tool was finalised with which the data for the STOC free model was collected. Subsequently, the developed model was tested and validated using real BVDV CP data from partner countries. Based on the feedback, the model was finalised and the report and corresponding computer code were made publicly available. There were roughly three different BVDV situations that occurred in the partner countries: 1. Endemic situation with a CP operating at herd level, 2. Endemic situation with a CP operating at animal level and 3. BVD free situation. The STOC free model is able to include herd level data only and animal level data has to be aggregated to herd level before the model can be applied. The STOC free model is not applicable for a country that is completely BVDV free given that it needs some infections to estimate its parameters and converge. In the latter situation, a scenario tree model could be a better suited tool, and this was evaluated in the Swedish case study. Further work is needed for generalisation of the method to other diseases and expansion of the method to include socioeconomic aspects of CPs <br/

Genomic diversity, linkage disequilibrium and selection signatures in European local pig breeds assessed with a high density SNP chip

Genetic characterization of local breeds is essential to preserve their genomic variability, to advance conservation policies and to contribute to their promotion and sustainability. Genomic diversity of twenty European local pig breeds and a small sample of Spanish wild pigs was assessed using high density SNP chips. A total of 992 DNA samples were analyzed with the GeneSeek Genomic Profiler (GGP) 70 K HD porcine genotyping chip. Genotype data was employed to compute genetic diversity, population differentiation and structure, genetic distances, linkage disequilibrium and effective population size. Our results point out several breeds, such as Turopolje, Apulo Calabrese, Casertana, Mora Romagnola and Lithuanian indigenous wattle, having the lowest genetic diversity, supported by low heterozygosity and very small effective population size, demonstrating the need of enhanced conservation strategies. Principal components analysis showed the clustering of the individuals of the same breed, with few breeds being clearly isolated from the rest. Several breeds were partially overlapped, suggesting genetic closeness, which was particularly marked in the case of Iberian and Alentejana breeds. Spanish wild boar was also narrowly related to other western populations, in agreement with recurrent admixture between wild and domestic animals. We also searched across the genome for loci under diversifying selection based on FST outlier tests. Candidate genes that may underlie differences in adaptation to specific environments and productive systems and phenotypic traits were detected in potentially selected genomic regions

Diversity across major and candidate genes in European local pig breeds

The aim of this work was to analyse the distribution of causal and candidate mutations associated to relevant productive traits in twenty local European pig breeds. Also, the potential of the SNP panel employed for elucidating the genetic structure and relationships among breeds was evaluated. Most relevant genes and mutations associated with pig morphological, productive, meat quality, reproductive and disease resistance traits were prioritized and analyzed in a maximum of 47 blood samples from each of the breeds (Alentejana, Apulo-Calabrese, Basque, Bísara, Majorcan Black, Black Slavonian (Crna slavonska), Casertana, Cinta Senese, Gascon, Iberian, Krskopolje (Krskopoljski), Lithuanian indigenous wattle, Lithuanian White Old Type, Mora Romagnola, Moravka, Nero Siciliano, Sarda, Schwa-bisch-Hallisches Schwein (Swabian Hall pig), Swallow-Bellied Mangalitsa and Turopolje). We successfully analyzed allelic variation in 39 polymorphisms, located in 33 candidate genes. Results provide relevant information regarding genetic diversity and segregation of SNPs associated to production and quality traits. Coat color and morphological trait-genes that show low level of segregation, and fixed SNPs may be useful for traceability. On the other hand, we detected SNPs which may be useful for association studies as well as breeding programs. For instance, we observed predominance of alleles that might be unfavorable for disease resistance and boar taint in most breeds and segregation of many alleles involved in meat quality, fatness and growth traits. Overall, these findings provide a detailed catalogue of segregating candidate SNPs in 20 European local pig breeds that may be useful for traceability purposes, for association studies and for breeding schemes. Population genetic analyses based on these candidate genes are able to uncover some clues regarding the hidden genetic substructure of these populations, as the extreme genetic closeness between Iberian and Alentejana breeds and an uneven admixture of the breeds studied. The results are in agreement with available knowledge regarding breed history and management, although largest panels of neutral markers should be employed to get a deeper understanding of the population’s structure and relationships

Genome‐wide detection of copy number variants in European autochthonous and commercial pig breeds by whole‐genome sequencing of DNA pools identified breed‐characterising copy number states

In this study, we identified copy number variants (CNVs) in 19 European autochthonous pig breeds and in two commercial breeds (Italian Large White and Italian Duroc) that represent important genetic resources for this species. The genome of 725 pigs was sequenced using a breed‐specific DNA pooling approach (30–35 animals per pool) obtaining an average depth per pool of 42×. This approach maximised CNV discovery as well as the related copy number states characterising, on average, the analysed breeds. By mining more than 17.5 billion reads, we identified a total of 9592 CNVs (~683 CNVs per breed) and 3710 CNV regions (CNVRs; 1.15% of the reference pig genome), with an average of 77 CNVRs per breed that were considered as private. A few CNVRs were analysed in more detail, together with other information derived from sequencing data. For example, the CNVR encompassing the KIT gene was associated with coat colour phenotypes in the analysed breeds, confirming the role of the multiple copies in determining breed‐specific coat colours. The CNVR covering the MSRB3 gene was associated with ear size in most breeds. The CNVRs affecting the ELOVL6 and ZNF622 genes were private features observed in the Lithuanian Indigenous Wattle and in the Turopolje pig breeds respectively. Overall, the genome variability unravelled here can explain part of the genetic diversity among breeds and might contribute to explain their origin, history and adaptation to a variety of production systems.info:eu-repo/semantics/acceptedVersio

Output-based assessment of herd-level freedom from infection in endemic situations:Application of a Bayesian Hidden Markov model

International audienceCountries have implemented control programmes (CPs) for cattle diseases such as bovine viral diarrhoea virus (BVDV) that are tailored to each country-specific situation. Practical methods are needed to assess the output of these CPs in terms of the confidence of freedom from infection that is achieved. As part of the STOC free project, a Bayesian Hidden Markov model was developed, called STOC free model, to estimate the probability of infection at herd-level. In the current study, the STOC free model was applied to BVDV field data in four study regions, from CPs based on ear notch samples. The aim of this study was to estimate the probability of herd-level freedom from BVDV in regions that are not (yet) free. We additionally evaluated the sensitivity of the parameter estimates and predicted probabilities of freedom to the prior distributions for the different model parameters. First, default priors were used in the model to enable comparison of model outputs between study regions. Thereafter, country-specific priors based on expert opinion or historical data were used in the model, to study the influence of the priors on the results and to obtain country-specific estimates.The STOC free model calculates a posterior value for the model parameters (e.g. herd-level test sensitivity and specificity, probability of introduction of infection) and a predicted probability of infection. The probability of freedom from infection was computed as one minus the probability of infection. For dairy herds that were considered free from infection within their own CP, the predicted probabilities of freedom were very high for all study regions ranging from 0.98 to 1.00, regardless of the use of default or country-specific priors. The priors did have more influence on two of the model parameters, herd-level sensitivity and the probability of remaining infected, due to the low prevalence and incidence of BVDV in the study regions. The advantage of STOC free model compared to scenario tree modelling, the reference method, is that actual data from the CP can be used and estimates are easily updated when new data becomes availabl