About Projections of Solutions for Fuzzy Differential Equations

In this paper we propose the concept of fuzzy projections on subspaces of , obtained from Zadeh's extension of canonical projections in , and we study some of the main properties of such projections. Furthermore, we will review some properties of fuzzy projection solution of fuzzy differential equations. As we will see, the concept of fuzzy projection can be interesting for the graphical representation of fuzzy solutions

Genetic variation and recombination of RdRp and HSP 70h genes of Citrus tristeza virus isolates from orange trees showing symptoms of citrus sudden death disease

<p>Abstract</p> <p>Background</p> <p>Citrus sudden death (CSD), a disease that rapidly kills orange trees, is an emerging threat to the Brazilian citrus industry. Although the causal agent of CSD has not been definitively determined, based on the disease's distribution and symptomatology it is suspected that the agent may be a new strain of <it>Citrus tristeza virus </it>(CTV). CTV genetic variation was therefore assessed in two Brazilian orange trees displaying CSD symptoms and a third with more conventional CTV symptoms.</p> <p>Results</p> <p>A total of 286 RNA-dependent-RNA polymerase (RdRp) and 284 heat shock protein 70 homolog (HSP70h) gene fragments were determined for CTV variants infecting the three trees. It was discovered that, despite differences in symptomatology, the trees were all apparently coinfected with similar populations of divergent CTV variants. While mixed CTV infections are common, the genetic distance between the most divergent population members observed (24.1% for RdRp and 11.0% for HSP70h) was far greater than that in previously described mixed infections. Recombinants of five distinct RdRp lineages and three distinct HSP70h lineages were easily detectable but respectively accounted for only 5.9 and 11.9% of the RdRp and HSP70h gene fragments analysed and there was no evidence of an association between particular recombinant mosaics and CSD. Also, comparisons of CTV population structures indicated that the two most similar CTV populations were those of one of the trees with CSD and the tree without CSD.</p> <p>Conclusion</p> <p>We suggest that if CTV is the causal agent of CSD, it is most likely a subtle feature of population structures within mixed infections and not merely the presence (or absence) of a single CTV variant within these populations that triggers the disease.</p

Molecular epidemiology of Citrus Leprosis Virus C: a new viral lineage and phylodynamic of the main viral subpopulations in the Americas.

Despite the importance of viral strains/variants as agents of emerging diseases, genetic and evolutionary processes affecting their ecology are not fully understood. To get insight into this topic, we assessed the population and spatial dynamic parameters of citrus leprosis virus C (CiLV-C, genus Cilevirus, family Kitaviridae). CiLV-C is the etiological agent of citrus leprosis disease, a non-systemic infection considered the main viral disorder affecting citrus orchards in Brazil. Overall, we obtained 18 complete or near-complete viral genomes, 123 complete nucleotide sequences of the open reading frame (ORF) encoding the putative coat protein, and 204 partial nucleotide sequences of the ORF encoding the movement protein, from 430 infected Citrus spp. samples collected between 1932 and 2020. A thorough examination of the collected dataset suggested that the CiLV-C population consists of the major lineages CRD and SJP, unevenly distributed, plus a third one called ASU identified in this work, which is represented by a single isolate found in an herbarium sample collected in Asuncion, Paraguay, in 1937. Viruses from the three lineages share about 85% nucleotide sequence identity and show signs of inter-clade recombination events. Members of the lineage CRD were identified both in commercial and non-commercial citrus orchards. However, those of the lineages SJP were exclusively detected in samples collected in the citrus belt of São Paulo and Minas Gerais, the leading Brazilian citrus production region, after 2015. The most recent common ancestor of viruses of the three lineages dates back to, at least, ?1500 years ago. Since citrus plants were introduced in the Americas by the Portuguese around the 1520s, the Bayesian phylodynamic analysis suggested that the ancestors of the main CiLV-C lineages likely originated in contact with native vegetation of South America. The intensive expansion of CRD and SJP lineages in Brazil started probably linked to the beginning of the local citrus industry. The high prevalence of CiLV-C in the citrus belt of Brazil likely ensues from the intensive connectivity between orchards, which represents a potential risk toward pathogen saturation across the region