Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.

Viral metagenomic analysis of feces of wild small carnivores

Background: Recent studies have clearly demonstrated the enormous virus diversity that exists among wild animals. This exemplifies the required expansion of our knowledge of the virus diversity present in wildlife, as well as the potential transmission of these viruses to domestic animals or humans. Methods: In the present study we evaluated the viral diversity of fecal samples (n = 42) collected from 10 different species of wild small carnivores inhabiting the northern part of Spain using random PCR in combination with next-generation sequencing. Samples were collected from American mink (Neovison vison), European mink (Mustela lutreola), European polecat (Mustela putorius), European pine marten (Martes martes), stone marten (Martes foina), Eurasian otter (Lutra lutra) and Eurasian badger (Meles meles) of the family of Mustelidae; common genet (Genetta genetta) of the family of Viverridae; red fox (Vulpes vulpes) of the family of Canidae and European wild cat (Felis silvestris) of the family of Felidae. Results: A number of sequences of possible novel viruses or virus variants were detected, including a theilovirus, phleboviruses, an amdovirus, a kobuvirus and picobirnaviruses. Conclusions: Using random PCR in combination with next generation sequencing, sequences of various novel viruses or virus variants were detected in fecal samples collected from Spanish carnivores. Detected novel viruses highlight the viral diversity that is present in fecal material of wild carnivores.

Human Endogenous Retrovirus HERV-Fc1 Association with Multiple Sclerosis Susceptibility: A Meta-Analysis

Background: Human endogenous retroviruses (HERVs) are repetitive sequences derived from ancestral germ-line infections by exogenous retroviruses and different HERV families have been integrated in the genome. HERV-Fc1 in chromosome X has been previously associated with multiple sclerosis (MS) in Northern European populations. Additionally, HERV-Fc1 RNA levels of expression have been found increased in plasma of MS patients with active disease. Considering the North-South latitude gradient in MS prevalence, we aimed to evaluate the role of HERV-Fc1on MS risk in three independent Spanish cohorts. Methods: A single nucleotide polymorphism near HERV-Fc1, rs391745, was genotyped by Taqman chemistry in a total of 2473 MS patients and 3031 ethnically matched controls, consecutively recruited from: Northern (569 patients and 980 controls), Central (883 patients and 692 controls) and Southern (1021 patients and 1359 controls) Spain. Our results were pooled in a meta-analysis with previously published data. Results: Significant associations of the HERV-Fc1 polymorphism with MS were observed in two Spanish cohorts and the combined meta-analysis with previous data yielded a significant association [rs391745 C-allele carriers: p(M-H) = 0.0005; ORM-H (95% CI) = 1.27 (1.11-1.45)]. Concordantly to previous findings, when the analysis was restricted to relapsing remitting and secondary progressive MS samples, a slight enhancement in the strength of the association was observed [p(M-H) = 0.0003, ORM-H (95% CI) = 1.32 (1.14-1.53)]. Conclusion: Association of the HERV-Fc1 polymorphism rs391745 with bout-onset MS susceptibility was confirmed in Southern European cohorts.