Adaptation in a heterogeneous environment II: To be three or not to be

We propose a model to describe the adaptation of a phenotypically structured population in a $H$-patch environment connected by migration, with each patch associated with a different phenotypic optimum, and we perform a rigorous mathematical analysis of this model. We show that the large-time behaviour of the solution (persistence or extinction) depends on the sign of a principal eigenvalue, $\lambda_H$, and we study the dependency of $\lambda_H$ with respect to $H$. This analysis sheds new light on the effect of increasing the number of patches on the persistence of a population, which has implications in agroecology and for understanding zoonoses; in such cases we consider a pathogenic population and the patches correspond to different host species. The occurrence of a springboard effect, where the addition of a patch contributes to persistence, or on the contrary the emergence of a detrimental effect by increasing the number of patches on the persistence, depends in a rather complex way on the respective positions in the phenotypic space of the optimal phenotypes associated with each patch. From a mathematical point of view, an important part of the difficulty in dealing with $H\ge 3$, compared to $H=1$ or $H=2$, comes from the lack of symmetry. Our results, which are based on a fixed point theorem, comparison principles, integral estimates, variational arguments, rearrangement techniques, and numerical simulations, provide a better understanding of these dependencies. In particular, we propose a precise characterisation of the situations where the addition of a third patch increases or decreases the chances of persistence, compared to a situation with only two patches

Discounting in LTL

In recent years, there is growing need and interest in formalizing and reasoning about the quality of software and hardware systems. As opposed to traditional verification, where one handles the question of whether a system satisfies, or not, a given specification, reasoning about quality addresses the question of \emph{how well} the system satisfies the specification. One direction in this effort is to refine the "eventually" operators of temporal logic to {\em discounting operators}: the satisfaction value of a specification is a value in $[0,1]$, where the longer it takes to fulfill eventuality requirements, the smaller the satisfaction value is. In this paper we introduce an augmentation by discounting of Linear Temporal Logic (LTL), and study it, as well as its combination with propositional quality operators. We show that one can augment LTL with an arbitrary set of discounting functions, while preserving the decidability of the model-checking problem. Further augmenting the logic with unary propositional quality operators preserves decidability, whereas adding an average-operator makes some problems undecidable. We also discuss the complexity of the problem, as well as various extensions

BV formulation of higher form gauge theories in a superspace

We discuss the extended BRST and anti-BRST symmetry (including shift symmetry) in the Batalin-Vilkovisky (BV) formulation for two and three form gauge theories. Further we develop the superspace formulation for the BV actions for these theories. We show that the extended BRST invariant BV action for these theories can be written manifestly covariant manner in a superspace with one Grassmann coordinate. On the hand a superspace with two Grassmann coordinates are required for a manifestly covariant formulation of the extended BRST and extended anti-BRST invariant BV actions for higher form gauge theories.Comment: 30 pages, No figure, version to appear in EPJ

Real-time reverse transcription polymerase chain reaction development for rapid detection of Tomato brown rugose fruit virus and comparison with other techniques

Background: Tomato brown rugose fruit virus (ToBRFV) is a highly infectious tobamovirus that causes severe disease in tomato (Solanum lycopersicum L.) crops. In Italy, the first ToBRFV outbreak occurred in 2018 in several provinces of the Sicily region. ToBRFV outbreak represents a serious threat for tomato crops in Italy and the Mediterranean Basin. Methods: Molecular and biological characterisation of the Sicilian ToBRFV ToB-SIC01/19 isolate was performed, and a sensitive and specific Real-time RT-PCR TaqMan minor groove binder probe method was developed to detect ToBRFV in infected plants and seeds. Moreover, four different sample preparation procedures (immunocapture, total RNA extraction, direct crude extract and leaf-disk crude extract) were evaluated. Results: The Sicilian isolate ToB-SIC01/19 (6,391 nt) showed a strong sequence identity with the isolates TBRFV-P12-3H and TBRFV-P12-3G from Germany, Tom1-Jo from Jordan and TBRFV-IL from Israel. The ToB-SIC01/19 isolate was successfully transmitted by mechanical inoculations in S. lycopersicum L. and Capsicum annuum L., but no transmission occurred in S. melongena L. The developed real-time RT-PCR, based on the use of a primer set designed on conserved sequences in the open reading frames3, enabled a reliable quantitative detection. This method allowed clear discrimination of ToBRFV from other viruses belonging to the genus Tobamovirus, minimising false-negative results. Using immunocapture and total RNA extraction procedures, the real-time RT-PCR and end-point RT-PCR gave the same comparable results. Using direct crude extracts and leaf-disk crude extracts, the end-point RT-PCR was unable to provide a reliable result. This developed highly specific and sensitive real-time RT-PCR assay will be a particularly valuable tool for early ToBRFV diagnosis, optimising procedures in terms of costs and time

Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we are focused in the study of the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some new directions for a future research are formulated.Comment: Changed content; 34 pages, 41 reference

Environmental effects on galaxy evolution. II: quantifying the tidal features in NIR-images of the cluster Abell 85

This work is part of a series of papers devoted to investigate the evolution of cluster galaxies during their infall. In the present article we imaged in NIR a selected sample of galaxies through- out the massive cluster Abell 85 (z = 0.055). We obtained (JHK) photometry for 68 objects, reaching 1 mag/arcsec^2 deeper than 2MASS. We use these images to unveil asymmetries in the outskirts of a sample of bright galaxies and develop a new asymmetry index, alpha_An, which allows to quantify the degree of disruption by the relative area occupied by the tidal features on the plane of the sky. We measure the asymmetries for a subsample of 41 large area objects finding clear asymmetries in ten galaxies, most of them being in groups and pairs projected at different clustercentric distances, some of them located beyond R500 . Combining information on the Hi-gas content of blue galaxies and the distribution of sub-structures across Abell 85, with the present NIR asymmetry analysis, we obtain a very powerful tool to confirm that tidal mechanisms are indeed present and are currently affecting a fraction of galaxies in Abell 85. However, when comparing our deep NIR images with UV-blue images of two very disrupted (jellyfish) galaxies in this cluster, we discard the presence of tidal 1 interactions down to our detection limit. Our results suggest that ram-pressure stripping is at the origin of such spectacular disruptions. We conclude that across a complex cluster like Abell 85, environment mechanisms, both gravitational and hydrodynamical, are playing an active role in driving galaxy evolution.Comment: 30 pages, 13 figures, Accepted for Publication in A