73 research outputs found
Free-particle and harmonic-oscillator propagators in two and three dimensions
This contribution illustrates how to construct free-particle and harmonic-oscillator quantum-mechanical propagators in two and three dimensions in cartesian, and in circular and spherical coordinates, respectively, starting from the corresponding one-dimensional propagators in cartesian coordinates
Connection Between Type A and E Factorizations and Construction of Satellite Algebras
Recently, we introduced a new class of symmetry algebras, called satellite
algebras, which connect with one another wavefunctions belonging to different
potentials of a given family, and corresponding to different energy
eigenvalues. Here the role of the factorization method in the construction of
such algebras is investigated. A general procedure for determining an so(2,2)
or so(2,1) satellite algebra for all the Hamiltonians that admit a type E
factorization is proposed. Such a procedure is based on the known relationship
between type A and E factorizations, combined with an algebraization similar to
that used in the construction of potential algebras. It is illustrated with the
examples of the generalized Morse potential, the Rosen-Morse potential, the
Kepler problem in a space of constant negative curvature, and, in each case,
the conserved quantity is identified. It should be stressed that the method
proposed is fairly general since the other factorization types may be
considered as limiting cases of type A or E factorizations.Comment: 20 pages, LaTeX, no figure, to be published in J. Phys.
Generalized Morse Potential: Symmetry and Satellite Potentials
We study in detail the bound state spectrum of the generalized Morse
potential~(GMP), which was proposed by Deng and Fan as a potential function for
diatomic molecules. By connecting the corresponding Schr\"odinger equation with
the Laplace equation on the hyperboloid and the Schr\"odinger equation for the
P\"oschl-Teller potential, we explain the exact solvability of the problem by
an symmetry algebra, and obtain an explicit realization of the latter
as . We prove that some of the generators
connect among themselves wave functions belonging to different GMP's (called
satellite potentials). The conserved quantity is some combination of the
potential parameters instead of the level energy, as for potential algebras.
Hence, belongs to a new class of symmetry algebras. We also stress
the usefulness of our algebraic results for simplifying the calculation of
Frank-Condon factors for electromagnetic transitions between rovibrational
levels based on different electronic states.Comment: 23 pages, LaTeX, 2 figures (on request). one LaTeX problem settle
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
Pan-cancer Alterations of the MYC Oncogene and Its Proximal Network across the Cancer Genome Atlas
Although theMYConcogene has been implicated incancer, a systematic assessment of alterations ofMYC, related transcription factors, and co-regulatoryproteins, forming the proximal MYC network (PMN),across human cancers is lacking. Using computa-tional approaches, we define genomic and proteo-mic features associated with MYC and the PMNacross the 33 cancers of The Cancer Genome Atlas.Pan-cancer, 28% of all samples had at least one ofthe MYC paralogs amplified. In contrast, the MYCantagonists MGA and MNT were the most frequentlymutated or deleted members, proposing a roleas tumor suppressors.MYCalterations were mutu-ally exclusive withPIK3CA,PTEN,APC,orBRAFalterations, suggesting that MYC is a distinct onco-genic driver. Expression analysis revealed MYC-associated pathways in tumor subtypes, such asimmune response and growth factor signaling; chro-matin, translation, and DNA replication/repair wereconserved pan-cancer. This analysis reveals insightsinto MYC biology and is a reference for biomarkersand therapeutics for cancers with alterations ofMYC or the PMN
Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context
Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts
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