Existence and uniqueness of global solutions to fully nonlinear second order elliptic systems

We consider the problem of existence and uniqueness of strong a.e. solutions u:Rn⟶RNu:Rn⟶RN to the fully nonlinear PDE system F(⋅,D2u)=f, a.e. on Rn,(1) F(⋅,D2u)=f, a.e. on Rn,(1) when f∈L2(Rn)Nf∈L2(Rn)N and F is a Carathéodory map. (1) has not been considered before. The case of bounded domains has been studied by several authors, firstly by Campanato and under Campanato’s ellipticity condition on F. By introducing a new much weaker notion of ellipticity, we prove solvability of (1) in a tailored Sobolev “energy” space and a uniqueness estimate. The proof is based on the solvability of the linearised problem by Fourier transform methods, together with a “perturbation device” which allows to use Campanato’s near operators. We also discuss our hypothesis via counterexamples and give a stability theorem of strong global solutions for systems of the form (1)

Four conjectures in Nonlinear Analysis

In this chapter, I formulate four challenging conjectures in Nonlinear Analysis. More precisely: a conjecture on the Monge-Amp\`ere equation; a conjecture on an eigenvalue problem; a conjecture on a non-local problem; a conjecture on disconnectedness versus infinitely many solutions.Comment: arXiv admin note: text overlap with arXiv:1504.01010, arXiv:1409.5919, arXiv:1612.0819

The first endogenous herpesvirus, identified in the tarsier genome, and novel sequences from primate rhadinoviruses and lymphocryptoviruses

Herpesviridae is a diverse family of large and complex pathogens whose genomes are extremely difficult to sequence. This is particularly true for clinical samples, and if the virus, host, or both genomes are being sequenced for the first time. Although herpesviruses are known to occasionally integrate in host genomes, and can also be inherited in a Mendelian fashion, they are notably absent from the genomic fossil record comprised of endogenous viral elements (EVEs). Here, we combine paleovirological and metagenomic approaches to both explore the constituent viral diversity of mammalian genomes and search for endogenous herpesviruses. We describe the first endogenous herpesvirus from the genome of the Philippine tarsier, belonging to the Roseolovirus genus, and characterize its highly defective genome that is integrated and flanked by unambiguous host DNA. From a draft assembly of the aye-aye genome, we use bioinformatic tools to reveal over 100,000 bp of a novel rhadinovirus that is the first lemur gammaherpesvirus, closely related to Kaposi's sarcoma-associated virus. We also identify 58 genes of Pan paniscus lymphocryptovirus 1, the bonobo equivalent of human Epstein-Barr virus. For each of the viruses, we postulate gene function via comparative analysis to known viral relatives. Most notably, the evidence from gene content and phylogenetics suggests that the aye-aye sequences represent the most basal known rhadinovirus, and indicates that tumorigenic herpesviruses have been infecting primates since their emergence in the late Cretaceous. Overall, these data show that a genomic fossil record of herpesviruses exists despite their extremely large genomes, and expands the known diversity of Herpesviridae, which will aid the characterization of pathogenesis. Our analytical approach illustrates the benefit of intersecting evolutionary approaches with metagenomics, genetics and paleovirology

Dynamically generated embeddings of spacetime

We discuss how embeddings in connection with the Campbell-Magaard (CM) theorem can have a physical interpretation. We show that any embedding whose local existence is guaranteed by the CM theorem can be viewed as a result of the dynamical evolution of initial data given in a four-dimensional spacelike hypersurface. By using the CM theorem, we establish that for any analytic spacetime, there exist appropriate initial data whose Cauchy development is a five-dimensional vacuum space into which the spacetime is locally embedded. We shall see also that the spacetime embedded is Cauchy stable with respect these the initial data.Comment: (8 pages, 1 figure). A section on Cauchy Stability of the embedding was added. (To appear in Class. Quant. Grav.

Inverse optical tomography through PDE constrained optimisation in L∞

Fluorescent Optical Tomography (FOT) is a new bio-medical imaging method with wider industrial applications. It is currently intensely researched since it is very precise and with no side effects for humans, as it uses non-ionising red and infrared light. Mathematically, FOT can be modelled as an inverse parameter identification problem, associated with a coupled elliptic system with Robin boundary conditions. Herein we utilise novel methods of Calculus of Variations in L∞ to lay the mathematical foundations of FOT which we pose as a PDE-constrained minimisation problem in Lp and L∞

The extraordinary evolutionary history of the reticuloendotheliosis viruses

The reticuloendotheliosis viruses (REVs) comprise several closely related amphotropic retroviruses isolated from birds. These viruses exhibit several highly unusual characteristics that have not so far been adequately explained, including their extremely close relationship to mammalian retroviruses, and their presence as endogenous sequences within the genomes of certain large DNA viruses. We present evidence for an iatrogenic origin of REVs that accounts for these phenomena. Firstly, we identify endogenous retroviral fossils in mammalian genomes that share a unique recombinant structure with REVs—unequivocally demonstrating that REVs derive directly from mammalian retroviruses. Secondly, through sequencing of archived REV isolates, we confirm that contaminated Plasmodium lophurae stocks have been the source of multiple REV outbreaks in experimentally infected birds. Finally, we show that both phylogenetic and historical evidence support a scenario wherein REVs originated as mammalian retroviruses that were accidentally introduced into avian hosts in the late 1930s, during experimental studies of P. lophurae, and subsequently integrated into the fowlpox virus (FWPV) and gallid herpesvirus type 2 (GHV-2) genomes, generating recombinant DNA viruses that now circulate in wild birds and poultry. Our findings provide a novel perspective on the origin and evolution of REV, and indicate that horizontal gene transfer between virus families can expand the impact of iatrogenic transmission events

Disease-associated XMRV sequences are consistent with laboratory contamination

BACKGROUND: Xenotropic murine leukaemia viruses (MLV-X) are endogenous gammaretroviruses that infect cells from many species, including humans. Xenotropic murine leukaemia virus-related virus (XMRV) is a retrovirus that has been the subject of intense debate since its detection in samples from humans with prostate cancer (PC) and chronic fatigue syndrome (CFS). Controversy has arisen from the failure of some studies to detect XMRV in PC or CFS patients and from inconsistent detection of XMRV in healthy controls. RESULTS: Here we demonstrate that Taqman PCR primers previously described as XMRV-specific can amplify common murine endogenous viral sequences from mouse suggesting that mouse DNA can contaminate patient samples and confound specific XMRV detection. To consider the provenance of XMRV we sequenced XMRV from the cell line 22Rv1, which is infected with an MLV-X that is indistinguishable from patient derived XMRV. Bayesian phylogenies clearly show that XMRV sequences reportedly derived from unlinked patients form a monophyletic clade with interspersed 22Rv1 clones (posterior probability >0.99). The cell line-derived sequences are ancestral to the patient-derived sequences (posterior probability >0.99). Furthermore, pol sequences apparently amplified from PC patient material (VP29 and VP184) are recombinants of XMRV and Moloney MLV (MoMLV) a virus with an envelope that lacks tropism for human cells. Considering the diversity of XMRV we show that the mean pairwise genetic distance among env and pol 22Rv1-derived sequences exceeds that of patient-associated sequences (Wilcoxon rank sum test: p = 0.005 and p < 0.001 for pol and env, respectively). Thus XMRV sequences acquire diversity in a cell line but not in patient samples. These observations are difficult to reconcile with the hypothesis that published XMRV sequences are related by a process of infectious transmission. CONCLUSIONS: We provide several independent lines of evidence that XMRV detected by sensitive PCR methods in patient samples is the likely result of PCR contamination with mouse DNA and that the described clones of XMRV arose from the tumour cell line 22Rv1, which was probably infected with XMRV during xenografting in mice. We propose that XMRV might not be a genuine human pathogen

Conformational adaptation of Asian macaque TRIMCyp directs lineage specific antiviral activity

TRIMCyps are anti-retroviral proteins that have arisen independently in New World and Old World primates. All TRIMCyps comprise a CypA domain fused to the tripartite domains of TRIM5α but they have distinct lentiviral specificities, conferring HIV-1 restriction in New World owl monkeys and HIV-2 restriction in Old World rhesus macaques. Here we provide evidence that Asian macaque TRIMCyps have acquired changes that switch restriction specificity between different lentiviral lineages, resulting in species-specific alleles that target different viruses. Structural, thermodynamic and viral restriction analysis suggests that a single mutation in the Cyp domain, R69H, occurred early in macaque TRIMCyp evolution, expanding restriction specificity to the lentiviral lineages found in African green monkeys, sooty mangabeys and chimpanzees. Subsequent mutations have enhanced restriction to particular viruses but at the cost of broad specificity. We reveal how specificity is altered by a scaffold mutation, E143K, that modifies surface electrostatics and propagates conformational changes into the active site. Our results suggest that lentiviruses may have been important pathogens in Asian macaques despite the fact that there are no reported lentiviral infections in current macaque populations

The bornavirus-derived human protein EBLN1 promotes efficient cell cycle transit, microtubule organisation and genome stability.

It was recently discovered that vertebrate genomes contain multiple endogenised nucleotide sequences derived from the non-retroviral RNA bornavirus. Strikingly, some of these elements have been evolutionary maintained as open reading frames in host genomes for over 40 million years, suggesting that some endogenised bornavirus-derived elements (EBL) might encode functional proteins. EBLN1 is one such element established through endogenisation of the bornavirus N gene (BDV N). Here, we functionally characterise human EBLN1 as a novel regulator of genome stability. Cells depleted of human EBLN1 accumulate DNA damage both under non-stressed conditions and following exogenously induced DNA damage. EBLN1-depleted cells also exhibit cell cycle abnormalities and defects in microtubule organisation as well as premature centrosome splitting, which we attribute in part, to improper localisation of the nuclear envelope protein TPR. Our data therefore reveal that human EBLN1 possesses important cellular functions within human cells, and suggest that other EBLs present within vertebrate genomes may also possess important cellular functions