Copulas with given values on a horizontal and a vertical section

summary:In this paper we study the set of copulas for which both a horizontal section and a vertical section have been given. We give a general construction for copulas of this type and we provide the lower and upper copulas with these sections. Symmetric copulas with given horizontal section are also discussed, as well as copulas defined on a grid of the unit square. Several examples are presented

Construction of admissible linear orders for pairs of intervals

In this work we construct linear orders between pairs of intervals by using aggregation functions. We apply these orders in a decision-making problem where the experts provide their opinions by means of interval-valued fuzzy sets

How do genetic relatedness and spatial proximity shape African swine fever infections in wild boar?

The importance of social and spatial structuring of wildlife populations for disease spread, though widely recognized, is still poorly understood in many host-pathogen systems. In particular, system-specific kin relationships among hosts can create contact heterogeneities and differential disease transmission rates. Here, we investigate how distance-dependent infection risk is influenced by genetic relatedness in a novel host-pathogen system: wild boar (Sus scrofa) and African swine fever (ASF).We hypothesized that infection risk would correlate positively with proximity and relatedness to ASF-infected individuals but expected those relationships to weaken with the distance between individuals due to decay in contact rates and genetic similarity.We genotyped 323 wild boar samples (243 ASF-negative and 80 ASF-positive) collected in north-eastern Poland in 2014–2016 and modelled the effects of geographic distance, genetic relatedness and ASF virus transmission mode (direct or carcass-based) on the probability of ASF infection. Infection risk was positively associated with spatial proximity and genetic relatedness to infected individuals with generally stronger effect of distance. In the high-contact zone (0–2 km), infection risk was shaped by the presence of infected individuals rather than by relatedness to them. In the medium-contact zone (2–5 km), infection risk decreased but was still associated with relatedness and paired infections were more frequent among relatives. At farther distances, infection risk further declined with relatedness and proximity to positive individuals, and was 60% lower among un-related individuals in the no-contact zone (33% in10–20 km) compared among relatives in the high-contact zone (93% in 0–2 km). Transmission mode influenced the relationship between proximity or relatedness and infection risk. Our results indicate that the presence of nearby infected individuals is most important for shaping ASF infection rates through carcass-based transmission, while relatedness plays an important role in shaping transmission rates between live animals

Pre-aggregation functions: construction and an application

In this work we introduce the notion of preaggregation function. Such a function satisfies the same boundary conditions as an aggregation function, but, instead of requiring monotonicity, only monotonicity along some fixed direction (directional monotonicity) is required. We present some examples of such functions. We propose three different methods to build pre-aggregation functions. We experimentally show that in fuzzy rule-based classification systems, when we use one of these methods, namely, the one based on the use of the Choquet integral replacing the product by other aggregation functions, if we consider the minimum or the Hamacher product t-norms for such construction, we improve the results obtained when applying the fuzzy reasoning methods obtained using two classical averaging operators like the maximum and the Choquet integral.This work was supported in part by the Spanish Ministry of Science and Technology under projects TIN2008-06681-C06-01, TIN2010- 15055, TIN2013-40765-P, TIN2011-29520

Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making

In this work we introduce a method for constructing linear orders between pairs of intervals by using aggregation functions. We adapt this method to the case of interval-valued Atanassov intuitionistic fuzzy sets and we apply these sets and the considered orders to a decision making problem.The work has been supported by projects TIN2013-40765-P and MTM2012-37894-C02-02 of the Spanish Ministry of Science and the Research Services of the Universidad Publica de Navarra

Monolithic integration of InP on Si by molten alloy driven selective area epitaxial growth

We report a new approach for monolithic integration of III-V materials into silicon, based on selective area growth and driven by a molten alloy in metal-organic vapor epitaxy. Our method includes elements of both selective area and droplet-mediated growths and combines the advantages of the two techniques. Using this approach, we obtain organized arrays of high crystalline quality InP insertions into (100) oriented Si substrates. Our detailed structural, morphological and optical studies reveal the conditions leading to defect formation. These conditions are then eliminated to optimize the process for obtaining dislocation-free InP nanostructures grown directly on Si and buried below the top surface. The PL signal from these structures exhibits a narrow peak at the InP bandgap energy. The fundamental aspects of the growth are studied by modeling the InP nucleation process. The model is fitted by our x-ray diffraction measurements and correlates well with the results of our transmission electron microscopy and optical investigations. Our method constitutes a new approach for the monolithic integration of active III-V material into Si platform and opens up new opportunities in active Si photonics