Zeta Functions of Finite Graphs and Coverings, Part II

AbstractGalois theory for normal unramified coverings of finite irregular graphs (which may have multiedges and loops) is developed. Using Galois theory we provide a construction of intermediate coverings which generalizes the classical Cayley and Schreier graph constructions. Three different analogues of Artin L-functions are attached to these coverings. These three types are based on vertex variables, edge variables, and path variables. Analogues of all the standard Artin L-functions results for number fields are proved here for all three types of L-functions. In particular, we obtain factorization formulas for the zeta functions introduced in Part I as a product of L-functions. It is shown that the path L-functions, which depend only on the rank of the graph, can be specialized to give the edge L-functions, and these in turn can be specialized to give the vertex L-functions. The method of Bass is used to show that Ihara type quadratic formulas hold for vertex L-functions. Finally, we use the theory to give examples of two regular graphs (without multiple edges or loops) having the same vertex zeta functions. These graphs are also isospectral but not isomorphic

Detectability of non-differentiable generalized synchrony

Generalized synchronization of chaos is a type of cooperative behavior in directionally-coupled oscillators that is characterized by existence of stable and persistent functional dependence of response trajectories from the chaotic trajectory of driving oscillator. In many practical cases this function is non-differentiable and has a very complex shape. The generalized synchrony in such cases seems to be undetectable, and only the cases, in which a differentiable synchronization function exists, are considered to make sense in practice. We show that this viewpoint is not always correct and the non-differentiable generalized synchrony can be revealed in many practical cases. Conditions for detection of generalized synchrony are derived analytically, and illustrated numerically with a simple example of non-differentiable generalized synchronization.Comment: 8 pages, 8 figures, submitted to PR

The orientation of elliptical galaxies

We determine the orientations of the light distribution of individual elliptical galaxies by combining the profiles of photometric data from the literature with triaxial models. The orientation is given by a Bayesian probability distribution. The likelihood of obtaining the data from a model is a function of the parameters describing the intrinsic shape and the orientation. Integrating the likelihood over the shape parameters, we obtain the estimates of the orientation. We find that the position angle difference between the two suitably chosen points from the profiles of the photometric data plays a key role in constraining the orientation of the galaxy. We apply the methodology to a sample of ten galaxies. The alignment of the intrinsic principle axes of the NGC 3379, 4486 and NGC 5638 are studied.Comment: accepted in Astrophysics and Space Scienc

Detecting the Most Distant (z>7) Objects with ALMA

Detecting and studying objects at the highest redshifts, out to the end of Cosmic Reionization at z>7, is clearly a key science goal of ALMA. ALMA will in principle be able to detect objects in this redshift range both from high-J (J>7) CO transitions and emission from ionized carbon, [CII], which is one of the main cooling lines of the ISM. ALMA will even be able to resolve this emission for individual targets, which will be one of the few ways to determine dynamical masses for systems in the Epoch of Reionization. We discuss some of the current problems regarding the detection and characterization of objects at high redshifts and how ALMA will eliminate most (but not all) of them.Comment: to appear in Astrophysics and Space Science, "Science with ALMA: a new era for Astrophysics", ed. R. Bachille

Temporal fluctuations of waves in weakly nonlinear disordered media

We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short correlation times. A self-consistent calculation shows that for nonlinearities exceeding a certain threshold value, the multiple-scattering speckle pattern becomes unstable and exhibits spontaneous fluctuations even in the absence of scatterer motion. The instability is due to a distributed feedback in the system "coherent wave + nonlinear disordered medium". The feedback is provided by the multiple scattering. The development of instability is independent of the sign of nonlinearity.Comment: RevTeX, 15 pages (including 5 figures), accepted for publication in Phys. Rev.

The baryonic collapse efficiency of galaxy groups in the RESOLVE and ECO surveys

We examine the z = 0 group-integrated stellar and cold baryonic (stars + cold atomic gas) mass functions (group SMF and CBMF) and the baryonic collapse efficiency (group cold baryonic to dark matter halo mass ratio) using the RESOLVE and ECO survey galaxy group catalogs and a GALFORM semi-analytic model (SAM) mock catalog. The group SMF and CBMF fall off more steeply at high masses and rise with a shallower low-mass slope than the theoretical halo mass function (HMF). The transition occurs at the group-integrated cold baryonic mass Mbary cold ~ 1011 M. The SAM, however, has significantly fewer groups at the transition mass ∼1011 M and a steeper low-mass slope than the data, suggesting that feedback is too weak in low-mass halos and conversely too strong near the transition mass. Using literature prescriptions to include hot halo gas and potential unobservable galaxy gas produces a group BMF with a slope similar to the HMF even below the transition mass. Its normalization is lower by a factor of ∼2, in agreement with estimates of warm-hot gas making up the remaining difference. We compute baryonic collapse efficiency with the halo mass calculated two ways, via halo abundance matching (HAM) and via dynamics (extended all the way to three-galaxy groups using stacking). Using HAM, we find that baryonic collapse efficiencies reach a flat maximum for groups across the halo mass range of Mhalo ~ 1011.4 - 12 M, which we label “nascent groups.” Using dynamics, however, we find greater scatter in baryonic collapse efficiencies, likely indicating variation in group hot-to-cold baryon ratios. Similarly, we see higher scatter in baryonic collapse efficiencies in the SAM when using its true groups and their group halo masses as opposed to friends-of-friends groups and HAM masses

Void galaxies follow a distinct evolutionary path in the environmental context catalog

We measure the environmental dependence, where environment is defined by the distance to the third nearest neighbor, of multiple galaxy properties inside the Environmental COntext (ECO) catalog. We focus primarily on void galaxies, which we define as the 10% of galaxies having the lowest local density. We compare the properties of void and non-void galaxies: baryonic mass, color, fractional stellar mass growth rate (FSMGR), morphology, and gas-to-stellar-mass ratio (estimated from a combination of H I data and photometric gas fractions calibrated with the REsolved Spectroscopy Of a Local VolumE survey). Our void galaxies typically have lower baryonic masses than galaxies in denser environments, and they display the properties expected of a lower mass population: they have more late types, are bluer, have a higher FSMGR, and are more gas-rich. We control for baryonic mass and investigate the extent to which void galaxies are different at fixed mass. Void galaxies are bluer, more gas-rich, and more star-forming at fixed mass than non-void galaxies, which is a possible signature of galaxy assembly bias. Furthermore, we show that these trends persist even at fixed mass and morphology, and we find that voids host a distinct population of early types that are bluer and more star-forming than the typical red and quenched early types. In addition to these empirical observational results, we also present theoretical results from mock catalogs with built-in galaxy assembly bias. We show that a simple matching of galaxy properties to (sub)halo properties, such as mass and age, can recover the observed environmental trends in ECO galaxies

Low-Dose Imaging in a New Preclinical Total-Body PET/CT Scanner.

Ionizing radiation constitutes a health risk to imaging scientists and study animals. Both PET and CT produce ionizing radiation. CT doses in pre-clinical in vivo imaging typically range from 50 to 1,000 mGy and biological effects in mice at this dose range have been previously described. [ <sup>18</sup> F]FDG body doses in mice have been estimated to be in the range of 100 mGy for [ <sup>18</sup> F]FDG. Yearly, the average whole body doses due to handling of activity by PET technologists are reported to be 3-8 mSv. A preclinical PET/CT system is presented with design features which make it suitable for small animal low-dose imaging. The CT subsystem uses a X-source power that is optimized for small animal imaging. The system design incorporates a spatial beam shaper coupled with a highly sensitive flat-panel detector and very fast acquisition (<10 s) which allows for whole body scans with doses as low as 3 mGy. The mouse total-body PET subsystem uses a detector architecture based on continuous crystals, coupled to SiPM arrays and a readout based in rows and columns. The PET field of view is 150 mm axial and 80 mm transaxial. The high solid-angle coverage of the sample and the use of continuous crystals achieve a sensitivity of 9% (NEMA) that can be leveraged for use of low tracer doses and/or performing rapid scans. The low-dose imaging capabilities of the total-body PET subsystem were tested with NEMA phantoms, in tumor models, a mouse bone metabolism scan and a rat heart dynamic scan. The CT imaging capabilities were tested in mice and in a low contrast phantom. The PET low-dose phantom and animal experiments provide evidence that image quality suitable for preclinical PET studies is achieved. Furthermore, CT image contrast using low dose scan settings was suitable as a reference for PET scans. Total-body mouse PET/CT studies could be completed with total doses of <10 mGy

A Symmetry-induced Model of Elliptical Galaxy Patterns

S\'ersic (1968) generalized the de Vaucouleurs law which follows the projected (observed) one dimensional radial profile of elliptical galaxies closely and Dehnen (1993) proposed an analytical formula of the 3-dimensional light distributions whose projected line profile resembles the de Vaucouleurs law. This paper is involved to recover the Dehnen model and generalize the model to account for galaxy elliptical shapes by means of curvilinear coordinate systems and employing a symmetry principle. The symmetry principle maps an orthogonal coordinate system to a light distribution pattern. The coordinate system for elliptical galaxy patterns turns out to be the one which is formed by the complex-plane reciprocal transformation $Z=1/W$. The resulting spatial (3-dimensional) light distribution is spherically symmetric and has infinite gradient at its centre, which is called spherical-nucleus solution and is used to model galaxy central area. We can make changes of the coordinate system by cutting out some column areas of its definition domain, the areas containing the galaxy centre. The resulting spatial (3-dimensional) light distributions are axisymmetric or triaxial and have zero gradient at the centre, which are called elliptical-shape solutions and are used to model global elliptical patterns. The two types of logarithmic light distributions are added together to model full elliptical galaxy patterns. The model is a generalization of the Dehnen model. One of the elliptical-shape solutions permits realistic numerical calculation and is fitted to all R-band elliptical images from the Frei {\it et al.}(1996)'s galaxy sample. The fitting is satisfactory. This suggests that elliptical galaxy patterns can be represented in terms of a few basic parameters.Comment: 20 pages, 7 figure

Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events

The $B^0$-$\bar B^0$ oscillation frequency has been measured with a sample of 23 million \B\bar B pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives $\Delta m_d = 0.493 \pm 0.012{(stat)}\pm 0.009{(syst)}$ ps$^{-1}$.Comment: 7 pages, 1 figure, submitted to Physical Review Letter