The Elliptic curves in gauge theory, string theory, and cohomology

Elliptic curves play a natural and important role in elliptic cohomology. In earlier work with I. Kriz, thes elliptic curves were interpreted physically in two ways: as corresponding to the intersection of M2 and M5 in the context of (the reduction of M-theory to) type IIA and as the elliptic fiber leading to F-theory for type IIB. In this paper we elaborate on the physical setting for various generalized cohomology theories, including elliptic cohomology, and we note that the above two seemingly unrelated descriptions can be unified using Sen's picture of the orientifold limit of F-theory compactification on K3, which unifies the Seiberg-Witten curve with the F-theory curve, and through which we naturally explain the constancy of the modulus that emerges from elliptic cohomology. This also clarifies the orbifolding performed in the previous work and justifies the appearance of the w_4 condition in the elliptic refinement of the mod 2 part of the partition function. We comment on the cohomology theory needed for the case when the modular parameter varies in the base of the elliptic fibration.Comment: 23 pages, typos corrected, minor clarification

Theory of the propagation of coupled waves in arbitrarily-inhomogeneous stratified media

We generalize the invariant imbedding theory of the wave propagation and derive new invariant imbedding equations for the propagation of arbitrary number of coupled waves of any kind in arbitrarily-inhomogeneous stratified media, where the wave equations are effectively one-dimensional. By doing this, we transform the original boundary value problem of coupled second-order differential equations to an initial value problem of coupled first-order differential equations, which makes the numerical solution of the coupled wave equations much easier. Using the invariant imbedding equations, we are able to calculate the matrix reflection and transmission coefficients and the wave amplitudes inside the inhomogeneous media exactly and efficiently. We establish the validity and the usefulness of our results by applying them to the propagation of circularly-polarized electromagnetic waves in one-dimensional photonic crystals made of isotropic chiral media. We find that there are three kinds of bandgaps in these structures and clarify the nature of these bandgaps by exact calculations.Comment: 7 pages, 1 figure, to appear in Europhys. Let

Lineage A betacoronavirus NS2 proteins and the homologous torovirus Berne pp1a carboxy-terminal domain are phosphodiesterases that antagonize activation of RNase L

Viruses in the family Coronaviridae, within the order Nidovirales, are etiologic agents of a range of human and animal diseases, including both mild and severe respiratory diseases in humans. These viruses encode conserved replicase and structural proteins as well as more diverse accessory proteins, encoded in the 3′ ends of their genomes, that often act as host cell antagonists. We previously showed that 2′,5′-phosphodiesterases (2′,5′-PDEs) encoded by the prototypical Betacoronavirus, mouse hepatitis virus (MHV), and by Middle East respiratory syndrome-associated coronavirus antagonize the oligoadenylate-RNase L (OAS-RNase L) pathway. Here we report that additional coronavirus superfamily members, including lineage A betacoronaviruses and toroviruses infecting both humans and animals, encode 2′,5′-PDEs capable of antagonizing RNase L. We used a chimeric MHV system (MHV(Mut)) in which exogenous PDEs were expressed from an MHV backbone lacking the gene for a functional NS2 protein, the endogenous RNase L antagonist. With this system, we found that 2′,5′-PDEs encoded by the human coronavirus HCoV-OC43 (OC43; an agent of the common cold), human enteric coronavirus (HECoV), equine coronavirus (ECoV), and equine torovirus Berne (BEV) are enzymatically active, rescue replication of MHV(Mut) in bone marrow-derived macrophages, and inhibit RNase L-mediated rRNA degradation in these cells. Additionally, PDEs encoded by OC43 and BEV rescue MHV(Mut) replication and restore pathogenesis in wild-type (WT) B6 mice. This finding expands the range of viruses known to encode antagonists of the potent OAS-RNase L antiviral pathway, highlighting its importance in a range of species as well as the selective pressures exerted on viruses to antagonize it. IMPORTANCE Viruses in the family Coronaviridae include important human and animal pathogens, including the recently emerged viruses severe acute respiratory syndrome-associated coronavirus (SARS-CoV) and Middle East respiratory syndrome-associated coronavirus (MERS-CoV). We showed previously that two viruses within the genus Betacoronavirus, mouse hepatitis virus (MHV) and MERS-CoV, encode 2′,5′-phosphodiesterases (2′,5′-PDEs) that antagonize the OAS-RNase L pathway, and we report here that these proteins are furthermore conserved among additional coronavirus superfamily members, including lineage A betacoronaviruses and toroviruses, suggesting that they may play critical roles in pathogenesis. As there are no licensed vaccines or effective antivirals against human coronaviruses and few against those infecting animals, identifying viral proteins contributing to virulence can inform therapeutic development. Thus, this work demonstrates that a potent antagonist of host antiviral defenses is encoded by multiple and diverse viruses within the family Coronaviridae, presenting a possible broad-spectrum therapeutic target

A Systematic Review of Music Therapy Practice and Outcomes with Acute Adult Psychiatric In-Patients

PMCID: PMC3732280This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Amicable pairs and aliquot cycles for elliptic curves

An amicable pair for an elliptic curve E/Q is a pair of primes (p,q) of good reduction for E satisfying #E(F_p) = q and #E(F_q) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j not 0) have no aliqout cycles of length greater than two. We give conjectural formulas for the frequency of amicable pairs. For CM curves, the derivation of precise conjectural formulas involves a detailed analysis of the values of the Grossencharacter evaluated at a prime ideal P in End(E) having the property that #E(F_P) is prime. This is especially intricate for the family of curves with j = 0.Comment: 53 page

Rest-UV Absorption Lines as Metallicity Estimator: the Metal Content of Star-Forming Galaxies at z~5

We measure a relation between the depth of four prominent rest-UV absorption complexes and metallicity for local galaxies and verify it up to z~3. We then apply this relation to a sample of 224 galaxies at 3.5 = 4.8) in COSMOS, for which unique UV spectra from DEIMOS and accurate stellar masses from SPLASH are available. The average galaxy population at z~5 and log(M/Msun) > 9 is characterized by 0.3-0.4 dex (in units of 12+log(O/H)) lower metallicities than at z~2, but comparable to z~3.5. We find galaxies with weak/no Ly-alpha emission to have metallicities comparable to z~2 galaxies and therefore may represent an evolved sub-population of z~5 galaxies. We find a correlation between metallicity and dust in good agreement with local galaxies and an inverse trend between metallicity and star-formation rate (SFR) consistent with observations at z~2. The relation between stellar mass and metallicity (MZ relation) is similar to z~3.5, however, there are indications of it being slightly shallower, in particular for the young, Ly-alpha emitting galaxies. We show that, within a "bathtub" approach, a shallower MZ relation is expected in the case of a fast (exponential) build-up of stellar mass with an e-folding time of 100-200 Myr. Due to this fast evolution, the process of dust production and metal enrichment as a function of mass could be more stochastic in the first billion years of galaxy formation compared to later times.Comment: 20 pages, 13 figures, 4 tables; Submitted to Ap

Controlled trial of fish oil for regression of human coronary atherosclerosis

AbstractObjectives. This randomized clinical trial tested whether fish oil supplements can improve human coronary atherosclerosis.Background. Epidemiologic studies of populations whose intake of oily fish is high, as well as laboratory studies of the effects of the polyunsaturated fatty acids in fish oil, support the hypothesis that fish oil is antiatherogenic.Methods. Patients with angiographically documented coronary heart disease and normal plasma lipid levels were randomized to receive either fish oil capsules (n = 31), containing 6 g of n-3 fatty acids, or olive oil capsules (n = 28) for an average duration of 28 months. Coronary atherosclerosis on angiography was quantified by computer-assisted image analysis.Results. Mean (±SD) baseline characteristics were age 62 ± 7 years, plasma total cholesterol concentration 187 ± 31 mg/dl (4.83 ± 0.80 mmol/liter) and triglyceride levels 132 ± 70 mg/dl (1.51 ± 0.80 mmol/liter). Fish oil lowered triglyceride levels by 30% (p = 0.007) but had no significant effects on other plasma lipoprotein levels. At the end of the trial, eicosapentaenoic acid in adipose tissue samples was 0.91% in the fish oil group compared with 0.20% in the control group (p < 0.0001). At baseline, the minimal lumen diameter of coronary artery lesions (n = 305) was 1.64 ± 0.76 mm, and percent narrowing was 48 ± 14%. Mean minimal diameter of atherosclerotic coronary arteries decreased by 0.104 and 0.138 mm in the fish oil and control groups, respectively (p = 0.6 between groups), and percent stenosis increased by 2.4% and 2.6%, respectively (p = 0.8). Confidence intervals exclude improvement by fish oil treatment of >0.17 mm, or >2.6%.Conclusions. Fish oil treatment for 2 years does not promote major favorable changes in the diameter of atherosclerotic coronary arteries

A Coherent Study of Emission Lines from Broad-Band Photometry: Specific Star-Formation Rates and [OIII]/H{\beta} Ratio at 3 < z < 6

We measure the H{\alpha} and [OIII] emission line properties as well as specific star-formation rates (sSFR) of spectroscopically confirmed 3<z<6 galaxies in COSMOS from their observed colors vs. redshift evolution. Our model describes consistently the ensemble of galaxies including intrinsic properties (age, metallicity, star-formation history), dust-attenuation, and optical emission lines. We forward-model the measured H{\alpha} equivalent-widths (EW) to obtain the sSFR out to z~6 without stellar mass fitting. We find a strongly increasing rest-frame H{\alpha} EW that is flattening off above z~2.5 with average EWs of 300-600A at z~6. The sSFR is increasing proportional to (1+z)^2.4 at z<2.2 and (1+z)^1.5 at higher redshifts, indicative of a fast mass build-up in high-z galaxies within e-folding times of 100-200Myr at z~6. The redshift evolution at z>3 cannot be fully explained in a picture of cold accretion driven growth. We find a progressively increasing [OIII]{\lambda}5007/H{\beta} ratio out to z~6, consistent with the ratios in local galaxies selected by increasing H{\alpha} EW (i.e., sSFR). This demonstrates the potential of using "local high-z analogs" to investigate the spectroscopic properties and relations of galaxies in the re-ionization epoch.Comment: 18 pages, 11 figures, 3 table

A Multiwavelength Consensus on the Main Sequence of Star-Forming Galaxies at z~2

We compare various star formation rate (SFR) indicators for star-forming galaxies at $1.4<z<2.5$ in the COSMOS field. The main focus is on the SFRs from the far-IR (PACS-Herschel data) with those from the ultraviolet, for galaxies selected according to the BzK criterion. FIR-selected samples lead to a vastly different slope of the SFR-stellar mass ($M_*$) relation, compared to that of the dominant main sequence population as measured from the UV, since the FIR selection picks predominantly only a minority of outliers. However, there is overall agreement between the main sequences derived with the two SFR indicators, when stacking on the PACS maps the BzK-selected galaxies. The resulting logarithmic slope of the SFR-{$M_*$} relation is $\sim0.8-0.9$, in agreement with that derived from the dust-corrected UV-luminosity. Exploiting deeper 24$\mu$m-Spitzer data we have characterized a sub-sample of galaxies with reddening and SFRs poorly constrained, as they are very faint in the $B$ band. The combination of Herschel with Spitzer data have allowed us to largely break the age/reddening degeneracy for these intriguing sources, by distinguishing whether a galaxy is very red in B-z because of being heavily dust reddened, or whether because star formation has been (or is being) quenched. Finally, we have compared our SFR(UV) to the SFRs derived by stacking the radio data and to those derived from the H$\alpha$ luminosity of a sample of star-forming galaxies at $1.4<z<1.7$. The two sets of SFRs are broadly consistent as they are with the SFRs derived from the UV and by stacking the corresponding PACS data in various mass bins.Comment: Accepted for publication in MNRA