A viable axion from gauged flavor symmetries

We consider a string inspired non-supersymmetric extension of the standard model with gauged anomalous U(1) flavor symmetries. Consistency requires the Green-Schwarz mechanism to cancel mixed anomalies. The additional required scalars provide Stuckelberg masses for the $Z'$ particles associated to the gauged flavor symmetry, so they decouple at low energies. Our models also include a complex scalar field $\phi$ to generate Froggatt-Nielsen mass terms for light particles giving a partial solution to the fermion mass problem. A residual approximate (anomalous) global symmetry survives at low energies. The associated pseudo-Goldstone mode is the phase of the $\phi$ scalar field, and it becomes the dominant contribution to the physical axion. An effective field theory analysis that includes neutrino masses gives a prediction for the axion decay constant. We find a simple modeI where the axion decay constant is in the center of the allowed window.Comment: 4 pages, 1 figure. v2: Couplings of axions to matter revised, other minor revision

Development of a Translator from LLVM to ACL2

In our current work a library of formally verified software components is to be created, and assembled, using the Low-Level Virtual Machine (LLVM) intermediate form, into subsystems whose top-level assurance relies on the assurance of the individual components. We have thus undertaken a project to build a translator from LLVM to the applicative subset of Common Lisp accepted by the ACL2 theorem prover. Our translator produces executable ACL2 formal models, allowing us to both prove theorems about the translated models as well as validate those models by testing. The resulting models can be translated and certified without user intervention, even for code with loops, thanks to the use of the def::ung macro which allows us to defer the question of termination. Initial measurements of concrete execution for translated LLVM functions indicate that performance is nearly 2.4 million LLVM instructions per second on a typical laptop computer. In this paper we overview the translation process and illustrate the translator's capabilities by way of a concrete example, including both a functional correctness theorem as well as a validation test for that example.Comment: In Proceedings ACL2 2014, arXiv:1406.123

X-ray Isophote Shapes and the Mass of NGC 3923

We present analysis of the shape and radial mass distribution of the E4 galaxy NGC 3923 using archival X-ray data from the ROSAT PSPC and HRI. The X-ray isophotes are significantly elongated with ellipticity e_x=0.15 (0.09-0.21) (90% confidence) for semi-major axis a\sim 10h^{-1}_70 kpc and have position angles aligned with the optical isophotes within the estimated uncertainties. Applying the Geometric Test for dark matter, which is independent of the gas temperature profile, we find that the ellipticities of the PSPC isophotes exceed those predicted if M propto L at a marginal significance level of 85% (80%) for oblate (prolate) symmetry. Detailed hydrostatic models of an isothermal gas yield ellipticities for the gravitating matter, e_mass=0.35-0.66 (90% confidence), which exceed the intensity weighted ellipticity of the R-band optical light, = 0.30 (e_R^max=0.39). We conclude that mass density profiles with rho\sim r^{-2} are favored over steeper profiles if the gas is essentially isothermal (which is suggested by the PSPC spectrum) and the surface brightness in the central regions (r<~15") is not modified substantially by a multi-phase cooling flow, magnetic fields, or discrete sources. We argue that these effects are unlikely to be important for NGC 3923. (The derived e_{mass} range is very insensitive to these issues.) Our spatial analysis also indicates that the allowed contribution to the ROSAT emission from a population of discrete sources with Sigma_x propto Sigma_R is significantly less than that indicated by the hard spectral component measured by ASCA.Comment: 14 pages (6 figures), To Appear in MNRA

A Note on Adult Overwintering of Dasymutilla Nigripes in Michigan (Hymenoptera: Mutillidae)

Excerpt: Although Dasymutilla nigripes (Fabricius) is one of the more common Michigan velvet ant species, little is known about its life cycle. In his summary of mutillid life cycles, Michel (1928) indicated that mutillids of northern latitudes probably overwinter in the prepupal stage within the subterranean cells of their hymenopterous hosts. Bohart and McSwain (1939) cited prepupal overwintering as normal for Dasymutilla sackenii (Cresson) in California. However, Potts and Smith (1944), also working in California, collected overwintering adult female Dasymutilla aureola pacifica (Cresson)

X-ray Constraints on the Intrinsic Shape of the Lenticular Galaxy NGC 1332

We have analyzed ROSAT PSPC X-ray data of the optically elongated S0 galaxy NGC 1332 with the purposes of constraining the intrinsic shape of its underlying mass and presenting a detailed investigation of the uncertainties resulting from the assumptions underlying this type of analysis. The X-ray isophotes are elongated with ellipticity $0.10 - 0.27$ (90% confidence) for semi-major axes 75\arcsec -90\arcsec and have orientations consistent with the optical isophotes (ellipticity $\sim 0.43$). The spectrum is poorly constrained by the PSPC data and cannot rule out sizeable radial temperature gradients or an emission component due to discrete sources equal in magnitude to the hot gas. Using (and clarifying) the "geometric test" for dark matter, we determined that the hypothesis that mass-traces-light is not consistent with the X-ray data at 68% confidence and marginally consistent at 90% confidence independent of the gas temperature profile. Detailed modeling gives constraints on the ellipticity of the underlying mass of \epsilon_{mass} = 0.47 - 0.72 (0.31 - 0.83) at 68% (90%) confidence for isothermal and polytropic models. The total mass of the isothermal models within a=43.6 kpc (D = 20h^{-1}_{80} Mpc) is M_{tot} = (0.38 - 1.7) \times 10^{12}M_{\sun} (90% confidence) corresponding to total blue mass-to-light ratio \Upsilon_B = (31.9 - 143) \Upsilon_{\sun}. Similar results are obtained when the dark matter is fit directly using the known distributions of the stars and gas. When possible rotation of the gas and emission from discrete sources are included flattened mass distributions are still required, although the constraints on \epsilon_{mass}$, but not the total mass, are substantially weakened.Comment: 45 pages (figures missing), PostScript, to appear in ApJ on January 20, 199

The Intrinsic Ellipticity of Spiral Disks

We have measured the distribution of intrinsic ellipticities for a sample of 28 relatively face-on spiral disks. We combine H-alpha velocity fields and R and I-band images to determine differences between kinematic and photometric inclination and position angles, from which we estimate intrinsic ellipticities of galaxy disks. Our findings suggest disks have a log-normal distribution of ellipticities (mean epsilon =0.06) and span a range from epsilon= 0 (circular) to epsilon=0.2. We are also able to construct a tight Tully-Fisher relation for our face-on sample. We use this to assess the contribution of disk ellipticity on the observed Tully-Fisher scatter.Comment: 4 pages, 2 figures, to appear in "Disks of Galaxies: Kinematics, Dynamics and Perturbations" (ASP Conference Series), eds E.Athanassoula and A. Bosm

Polynomial treewidth forces a large grid-like-minor

Robertson and Seymour proved that every graph with sufficiently large treewidth contains a large grid minor. However, the best known bound on the treewidth that forces an $\ell\times\ell$ grid minor is exponential in $\ell$. It is unknown whether polynomial treewidth suffices. We prove a result in this direction. A \emph{grid-like-minor of order} $\ell$ in a graph $G$ is a set of paths in $G$ whose intersection graph is bipartite and contains a $K_{\ell}$-minor. For example, the rows and columns of the $\ell\times\ell$ grid are a grid-like-minor of order $\ell+1$. We prove that polynomial treewidth forces a large grid-like-minor. In particular, every graph with treewidth at least $c\ell^4\sqrt{\log\ell}$ has a grid-like-minor of order $\ell$. As an application of this result, we prove that the cartesian product $G\square K_2$ contains a $K_{\ell}$-minor whenever $G$ has treewidth at least $c\ell^4\sqrt{\log\ell}$.Comment: v2: The bound in the main result has been improved by using the Lovasz Local Lemma. v3: minor improvements, v4: final section rewritte