The Relativistic Levinson Theorem in Two Dimensions

In the light of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation in two dimensions is established as a relation between the total number $n_{j}$ of the bound states and the sum of the phase shifts $\eta_{j}(\pm M)$ of the scattering states with the angular momentum $j$: $$\eta_{j}(M)+\eta_{j}(-M)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$$ $$~~~=\left\{\begin{array}{ll} (n_{j}+1)\pi &{\rm when~a~half~bound~state~occurs~at}~E=M ~~{\rm and}~~ j=3/2~{\rm or}~-1/2\\ (n_{j}+1)\pi &{\rm when~a~half~bound~state~occurs~at}~E=-M~~{\rm and}~~ j=1/2~{\rm or}~-3/2\\ n_{j}\pi~&{\rm the~rest~cases} . \end{array} \right.$$ \noindent The critical case, where the Dirac equation has a finite zero-momentum solution, is analyzed in detail. A zero-momentum solution is called a half bound state if its wave function is finite but does not decay fast enough at infinity to be square integrable.Comment: Latex 14 pages, no figure, submitted to Phys.Rev.A; Email: [email protected], [email protected]

Levinson's Theorem for the Klein-Gordon Equation in Two Dimensions

The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V(r)$ is established. It is shown that $N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})= [\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$, where $N_{m}$ denotes the difference between the number of bound states of the particle $n_{m}^{+}$ and the ones of antiparticle $n_{m}^{-}$ with a fixed angular momentum $m$, and the $\delta_{m}$ is named phase shifts. The constants $\beta_{1}$ and $\beta_{2}$ are introduced to symbol the critical cases where the half bound states occur at $E=\pm M$.Comment: Revtex file 14 pages, submitted to Phys. Rev.

Interstellar abundances in the neutral and ionized gas of NGC604

We present FUSE spectra of the giant HII region NGC604 in the spiral galaxy M33. Chemical abundances are derived from far-UV absorption lines and are compared to those derived from optical emission lines. We derived the column densities of HI, NI, OI, SiII, PII, ArI, and FeII, fitting the line profiles with either a single component or several components. Our net results, assuming a single component, show that N, O, Si, and Ar are apparently underabundant in the neutral phase by a factor of 10 or more with respect to the ionized phase, while Fe is the same. However, we discuss the possibility that the absorption lines are made of individual unresolved components, and find that only PII, ArI, and FeII lines should not be affected by the presence of hidden saturated components, while NI, OI, and SiII might be much more affected. If N, O, and Si are actually underabundant in the neutral gas of NGC604 with respect to the ionized gas, this would confirm earlier results obtained for the blue compact dwarfs. However, a deeper analysis focused on P, Ar, and Fe mitigates the above conclusion and indicates that the neutral gas and ionized gas could have similar abundances.Comment: Accepted for publication in A&

The nuclear starburst in Arp 299-A: From the 5.0 GHz VLBI radio light-curves to its core-collapse supernova rate

The nuclear region of the Luminous Infra-red Galaxy Arp 299-A hosts a recent ($\simeq 10$ Myr), intense burst of massive star formation which is expected to lead to numerous core-collapse supernovae (CCSNe). Previous VLBI observations, carried out with the EVN at 5.0 GHz and with the VLBA at 2.3 and 8.4 GHz, resulted in the detection of a large number of compact, bright, non-thermal sources in a region \lsim150 pc in size. We aim at establishing the nature of all non-thermal, compact components in Arp 299-A, as well as estimating its core-collapse supernova rate. We use multi-epoch European VLBI Network (EVN) observations taken at 5.0 GHz to image with milliarcsecond resolution the compact radio sources in the nuclear region of Arp 299-A. We also use one single-epoch 5.0 GHz Multi-Element Radio Linked Interferometer Network (MERLIN) observation to image the extended emission in which the compact radio sources --traced by our EVN observations-- are embedded. Twenty-six compact sources are detected, 8 of them are new objects not previously detected. The properties of all detected objects are consistent with them being a mixed population of CCSNe and SNRs. We find clear evidence for at least two new CCSNe, implying a lower limit to the CCSN rate of \nu_{\rm SN}\gsim0.80 SN/yr indicating that the bulk of the current star formation in Arp 299-A is taking place in the innermost $\sim 150$ pc. Our MERLIN observations trace a region of diffuse, extended emission which is co-spatial to the region where all compact sources are found. From this diffuse, non-thermal radio emission we obtain an independent estimate for the core-collapse supernova rate, which is in the range $\nu_{\rm SN}=0.40$ - 0.65 SN/yr, roughly in agreement with previous estimates and our direct estimate of the CCSN rate from the compact radio emission.Comment: 13 pages, 5 figures, accepted for publication on Astronomy & Astrophysic

Levinson's theorem and scattering phase shift contributions to the partition function of interacting gases in two dimensions

We consider scattering state contributions to the partition function of a two-dimensional (2D) plasma in addition to the bound-state sum. A partition function continuity requirement is used to provide a statistical mechanical heuristic proof of Levinson's theorem in two dimensions. We show that a proper account of scattering eliminates singularities in thermodynamic properties of the nonideal 2D gas caused by the emergence of additional bound states as the strength of an attractive potential is increased. The bound-state contribution to the partition function of the 2D gas, with a weak short-range attraction between its particles, is found to vanish logarithmically as the binding energy decreases. A consistent treatment of bound and scattering states in a screened Coulomb potential allowed us to calculate the quantum-mechanical second virial coefficient of the dilute 2D electron-hole plasma and to establish the difference between the nearly ideal electron-hole gas in GaAs and the strongly correlated exciton/free-carrier plasma in wide-gap semiconductors such as ZnSe or GaN.Comment: 10 pages, 3 figures; new version corrects some minor typo

Association of MC1R Variants and host phenotypes with melanoma risk in CDKN2A mutation carriers: a GenoMEL study

<p><b>Background</b> Carrying the cyclin-dependent kinase inhibitor 2A (CDKN2A) germline mutations is associated with a high risk for melanoma. Penetrance of CDKN2A mutations is modified by pigmentation characteristics, nevus phenotypes, and some variants of the melanocortin-1 receptor gene (MC1R), which is known to have a role in the pigmentation process. However, investigation of the associations of both MC1R variants and host phenotypes with melanoma risk has been limited.</p> <p><b>Methods</b> We included 815 CDKN2A mutation carriers (473 affected, and 342 unaffected, with melanoma) from 186 families from 15 centers in Europe, North America, and Australia who participated in the Melanoma Genetics Consortium. In this family-based study, we assessed the associations of the four most frequent MC1R variants (V60L, V92M, R151C, and R160W) and the number of variants (1, ≥2 variants), alone or jointly with the host phenotypes (hair color, propensity to sunburn, and number of nevi), with melanoma risk in CDKN2A mutation carriers. These associations were estimated and tested using generalized estimating equations. All statistical tests were two-sided.</p> <p><b>Results</b> Carrying any one of the four most frequent MC1R variants (V60L, V92M, R151C, R160W) in CDKN2A mutation carriers was associated with a statistically significantly increased risk for melanoma across all continents (1.24 × 10−6 ≤ P ≤ .0007). A consistent pattern of increase in melanoma risk was also associated with increase in number of MC1R variants. The risk of melanoma associated with at least two MC1R variants was 2.6-fold higher than the risk associated with only one variant (odds ratio = 5.83 [95% confidence interval = 3.60 to 9.46] vs 2.25 [95% confidence interval = 1.44 to 3.52]; Ptrend = 1.86 × 10−8). The joint analysis of MC1R variants and host phenotypes showed statistically significant associations of melanoma risk, together with MC1R variants (.0001 ≤ P ≤ .04), hair color (.006 ≤ P ≤ .06), and number of nevi (6.9 × 10−6 ≤ P ≤ .02).</p> <p><b>Conclusion</b> Results show that MC1R variants, hair color, and number of nevi were jointly associated with melanoma risk in CDKN2A mutation carriers. This joint association may have important consequences for risk assessments in familial settings.</p&gt

Markov Chain Ontology Analysis (MCOA)

<p>Abstract</p> <p>Background</p> <p>Biomedical ontologies have become an increasingly critical lens through which researchers analyze the genomic, clinical and bibliographic data that fuels scientific research. Of particular relevance are methods, such as enrichment analysis, that quantify the importance of ontology classes relative to a collection of domain data. Current analytical techniques, however, remain limited in their ability to handle many important types of structural complexity encountered in real biological systems including class overlaps, continuously valued data, inter-instance relationships, non-hierarchical relationships between classes, semantic distance and sparse data.</p> <p>Results</p> <p>In this paper, we describe a methodology called Markov Chain Ontology Analysis (MCOA) and illustrate its use through a MCOA-based enrichment analysis application based on a generative model of gene activation. MCOA models the classes in an ontology, the instances from an associated dataset and all directional inter-class, class-to-instance and inter-instance relationships as a single finite ergodic Markov chain. The adjusted transition probability matrix for this Markov chain enables the calculation of eigenvector values that quantify the importance of each ontology class relative to other classes and the associated data set members. On both controlled Gene Ontology (GO) data sets created with Escherichia coli, Drosophila melanogaster and Homo sapiens annotations and real gene expression data extracted from the Gene Expression Omnibus (GEO), the MCOA enrichment analysis approach provides the best performance of comparable state-of-the-art methods.</p> <p>Conclusion</p> <p>A methodology based on Markov chain models and network analytic metrics can help detect the relevant signal within large, highly interdependent and noisy data sets and, for applications such as enrichment analysis, has been shown to generate superior performance on both real and simulated data relative to existing state-of-the-art approaches.</p

Comparative genomics of proteins involved in RNA nucleocytoplasmic export

Background: The establishment of the nuclear membrane resulted in the physical separation of transcription and translation, and presented early eukaryotes with a formidable challenge: how to shuttle RNA from the nucleus to the locus of protein synthesis. In prokaryotes, mRNA is translated as it is being synthesized, whereas in eukaryotes mRNA is synthesized and processed in the nucleus, and it is then exported to the cytoplasm. In metazoa and fungi, the different RNA species are exported from the nucleus by specialized pathways. For example, tRNA is exported by exportin-t in a RanGTP-dependent fashion. By contrast, mRNAs are associated to ribonucleoproteins (RNPs) and exported by an essential shuttling complex (TAP-p15 in human, Mex67-mtr2 in yeast) that transports them through the nuclear pore. The different RNA export pathways appear to be well conserved among members of Opisthokonta, the eukaryotic supergroup that includes Fungi and Metazoa. However, it is not known whether RNA export in the other eukaryotic supergroups follows the same export routes as in opisthokonts. Methods: Our objective was to reconstruct the evolutionary history of the different RNA export pathways across eukaryotes. To do so, we screened an array of eukaryotic genomes for the presence of homologs of the proteins involved in RNA export in Metazoa and Fungi, using human and yeast proteins as queries. Results: Our genomic comparisons indicate that the basic components of the RanGTP-dependent RNA pathways are conserved across eukaryotes, and thus we infer that these are traceable to the last eukaryotic common ancestor (LECA). On the other hand, several of the proteins involved in RanGTP-independent mRNA export pathways are less conserved, which would suggest that they represent innovations that appeared later in the evolution of eukaryotes. Conclusions: Our analyses suggest that the LECA possessed the basic components of the different RNA export mechanisms found today in opisthokonts, and that these mechanisms became more specialized throughout eukaryotic evolution

Tuning fresh: radiation through rewiring of central metabolism in streamlined bacteria

Most free-living planktonic cells are streamlined and in spite of their limitations in functional flexibility, their vast populations have radiated into a wide range of aquatic habitats. Here we compared the metabolic potential of subgroups in the Alphaproteobacteria lineage SAR11 adapted to marine and freshwater habitats. Our results suggest that the successful leap from marine to freshwaters in SAR11 was accompanied by a loss of several carbon degradation pathways and a rewiring of the central metabolism. Examples for these are C1 and methylated compounds degradation pathways, the Entner–Doudouroff pathway, the glyoxylate shunt and anapleuretic carbon fixation being absent from the freshwater genomes. Evolutionary reconstructions further suggest that the metabolic modules making up these important freshwater metabolic traits were already present in the gene pool of ancestral marine SAR11 populations. The loss of the glyoxylate shunt had already occurred in the common ancestor of the freshwater subgroup and its closest marine relatives, suggesting that the adaptation to freshwater was a gradual process. Furthermore, our results indicate rapid evolution of TRAP transporters in the freshwater clade involved in the uptake of low molecular weight carboxylic acids. We propose that such gradual tuning of metabolic pathways and transporters toward locally available organic substrates is linked to the formation of subgroups within the SAR11 clade and that this process was critical for the freshwater clade to find and fix an adaptive phenotype.This work was supported by the Swedish Research Council (Grant Numbers 2012-4592 to AE and 2012-3892 to SB) and the Communiy Sequencing Programme of the US Department of Energy Joint Genome Institute. The work conducted by the US Department of Energy Joint Genome Institute, a DOE Office of Science User Facility, is supported under Contract No. DE-AC02-05CH11231

Attaching and effacing (A/E) lesion formation by enteropathogenic E. coli on human intestinal mucosa is dependent on non-LEE effectors

Enteropathogenic E. coli (EPEC) is a human pathogen that causes acute and chronic pediatric diarrhea. The hallmark of EPEC infection is the formation of attaching and effacing (A/E) lesions in the intestinal epithelium. Formation of A/E lesions is mediated by genes located on the pathogenicity island locus of enterocyte effacement (LEE), which encode the adhesin intimin, a type III secretion system (T3SS) and six effectors, including the essential translocated intimin receptor (Tir). Seventeen additional effectors are encoded by genes located outside the LEE, in insertion elements and prophages. Here, using a stepwise approach, we generated an EPEC mutant lacking the entire effector genes (EPEC0) and intermediate mutants. We show that EPEC0 contains a functional T3SS. An EPEC mutant expressing intimin but lacking all the LEE effectors but Tir (EPEC1) was able to trigger robust actin polymerization in HeLa cells and mucin-producing intestinal LS174T cells. However, EPEC1 was unable to form A/E lesions on human intestinal in vitro organ cultures (IVOC). Screening the intermediate mutants for genes involved in A/E lesion formation on IVOC revealed that strains lacking non-LEE effector/s have a marginal ability to form A/E lesions. Furthermore, we found that Efa1/LifA proteins are important for A/E lesion formation efficiency in EPEC strains lacking multiple effectors. Taken together, these results demonstrate the intricate relationships between T3SS effectors and the essential role non-LEE effectors play in A/E lesion formation on mucosal surfaces