Spectral properties of random graphs with fixed equitable partition

We define a graph to be $S$-regular if it contains an equitable partition given by a matrix $S$. These graphs are generalizations of both regular and bipartite, biregular graphs. An $S$-regular matrix is defined then as a matrix on an $S$-regular graph consistent with the graph's equitable partition. In this paper we derive the limiting spectral density for large, random $S$-regular matrices as well as limiting functions of certain statistics for their eigenvector coordinates as a function of eigenvalue. These limiting functions are defined in terms of spectral measures on $S$-regular trees. In general, these spectral measures do not have a closed-form expression; however, we provide a defining system of polynomials for them. Finally, we explore eigenvalue bounds of $S$-regular graph, proving an expander mixing lemma, Alon-Bopana bound, and other eigenvalue inequalities in terms of the eigenvalues of the matrix $S$.Comment: 24 pages, 3 figure

Inactivation of a CRF-dependent amygdalofugal pathway reverses addiction-like behaviors in alcohol-dependent rats.

The activation of a neuronal ensemble in the central nucleus of the amygdala (CeA) during alcohol withdrawal has been hypothesized to induce high levels of alcohol drinking in dependent rats. In the present study we describe that the CeA neuronal ensemble that is activated by withdrawal from chronic alcohol exposure contains ~80% corticotropin-releasing factor (CRF) neurons and that the optogenetic inactivation of these CeA CRF+ neurons prevents recruitment of the neuronal ensemble, decreases the escalation of alcohol drinking, and decreases the intensity of somatic signs of withdrawal. Optogenetic dissection of the downstream neuronal pathways demonstrates that the reversal of addiction-like behaviors is observed after the inhibition of CeA CRF projections to the bed nucleus of the stria terminalis (BNST) and that inhibition of the CRFCeA-BNST pathway is mediated by inhibition of the CRF-CRF1 system and inhibition of BNST cell firing. These results suggest that the CRFCeA-BNST pathway could be targeted for the treatment of excessive drinking in alcohol use disorder

SparsePak: A Formatted Fiber Field-Unit for The WIYN Telescope Bench Spectrograph. II. On-Sky Performance

We present a performance analysis of SparsePak and the WIYN Bench Spectrograph for precision studies of stellar and ionized gas kinematics of external galaxies. We focus on spectrograph configurations with echelle and low-order gratings yielding spectral resolutions of ~10000 between 500-900nm. These configurations are of general relevance to the spectrograph performance. Benchmarks include spectral resolution, sampling, vignetting, scattered light, and an estimate of the system absolute throughput. Comparisons are made to other, existing, fiber feeds on the WIYN Bench Spectrograph. Vignetting and relative throughput are found to agree with a geometric model of the optical system. An aperture-correction protocol for spectrophotometric standard-star calibrations has been established using independent WIYN imaging data and the unique capabilities of the SparsePak fiber array. The WIYN point-spread-function is well-fit by a Moffat profile with a constant power-law outer slope of index -4.4. We use SparsePak commissioning data to debunk a long-standing myth concerning sky-subtraction with fibers: By properly treating the multi-fiber data as a ``long-slit'' it is possible to achieve precision sky subtraction with a signal-to-noise performance as good or better than conventional long-slit spectroscopy. No beam-switching is required, and hence the method is efficient. Finally, we give several examples of science measurements which SparsePak now makes routine. These include H$\alpha$ velocity fields of low surface-brightness disks, gas and stellar velocity-fields of nearly face-on disks, and stellar absorption-line profiles of galaxy disks at spectral resolutions of ~24,000.Comment: To appear in ApJSupp (Feb 2005); 19 pages text; 7 tables; 27 figures (embedded); high-resolution version at http://www.astro.wisc.edu/~mab/publications/spkII_pre.pd

A Transgenic Rat for Investigating the Anatomy and Function of Corticotrophin Releasing Factor Circuits.

Corticotrophin-releasing factor (CRF) is a 41 amino acid neuropeptide that coordinates adaptive responses to stress. CRF projections from neurons in the central nucleus of the amygdala (CeA) to the brainstem are of particular interest for their role in motivated behavior. To directly examine the anatomy and function of CRF neurons, we generated a BAC transgenic Crh-Cre rat in which bacterial Cre recombinase is expressed from the Crh promoter. Using Cre-dependent reporters, we found that Cre expressing neurons in these rats are immunoreactive for CRF and are clustered in the lateral CeA (CeL) and the oval nucleus of the BNST. We detected major projections from CeA CRF neurons to parabrachial nuclei and the locus coeruleus, dorsal and ventral BNST, and more minor projections to lateral portions of the substantia nigra, ventral tegmental area, and lateral hypothalamus. Optogenetic stimulation of CeA CRF neurons evoked GABA-ergic responses in 11% of non-CRF neurons in the medial CeA (CeM) and 44% of non-CRF neurons in the CeL. Chemogenetic stimulation of CeA CRF neurons induced Fos in a similar proportion of non-CRF CeM neurons but a smaller proportion of non-CRF CeL neurons. The CRF1 receptor antagonist R121919 reduced this Fos induction by two-thirds in these regions. These results indicate that CeL CRF neurons provide both local inhibitory GABA and excitatory CRF signals to other CeA neurons, and demonstrate the value of the Crh-Cre rat as a tool for studying circuit function and physiology of CRF neurons

Time-lapse synchrotron X-ray diffraction to monitor conservation coatings for heritage lead in atmospheres polluted with oak-emitted volatile organic compounds

We discuss the effectiveness of a lead tetradecanoate coating on lead to protect against harmful volatile organic compounds emitted from oak. The oak volatile organic compounds were characterized by GCMS and the major constituent was found to be acetic acid. Under the test conditions, the coating decreases the rate of corrosion by up to 75% compared to bare lead. The thickness of corrosion products on the sample was also calculated thus demonstrating the power of the time-lapse synchrotron radiation X-ray diffraction technique to deliver a quantitative estimate of the effectiveness of the coating

Total Galaxy Magnitudes and Effective Radii from Petrosian Magnitudes and Radii

Petrosian magnitudes were designed to help with the difficult task of determining a galaxy's total light. Although these magnitudes (taken here as the flux within 2R_P, with the inverted Petrosian index 1/eta(R_P)=0.2) can represent most of an object's flux, they do of course miss the light outside of the Petrosian aperture (2R_P). The size of this flux deficit varies monotonically with the shape of a galaxy's light-profile, i.e., its concentration. In the case of a de Vaucouleurs R^{1/4} profile, the deficit is 0.20 mag; for an R^{1/8} profile this figure rises to 0.50 mag. Here we provide a simple method for recovering total (Sersic) magnitudes from Petrosian magnitudes using only the galaxy concentration (R_90/R_50 or R_80/R_20) within the Petrosian aperture. The corrections hold to the extent that Sersic's model provides a good description of a galaxy's luminosity profile. We show how the concentration can also be used to convert Petrosian radii into effective half-light radii, enabling a robust measure of the mean effective surface brightness. Our technique is applied to the SDSS DR2 Petrosian parameters, yielding good agreement with the total magnitudes, effective radii, and mean effective surface brightnesses obtained from the NYU--VAGC Sersic R^{1/n} fits by Blanton et al. (2005). Although the corrective procedure described here is specifically applicable to the SDSS DR2 and DR3, it is generally applicable to all imaging data where any Petrosian index and concentration can be constructed.Comment: AJ, in press after minor additions to the text (7 pages of text, plus 6 of figures and tables

Long-term Earth-Moon evolution with high-level orbit and ocean tide models

Tides and Earth‐Moon system evolution are coupled over geological time. Tidal energy dissipation on Earth slows [Formula: see text] rotation rate, increases obliquity, lunar orbit semi‐major axis and eccentricity, and decreases lunar inclination. Tidal and core‐mantle boundary dissipation within the Moon decrease inclination, eccentricity and semi‐major axis. Here we integrate the Earth‐Moon system backwards for 4.5 Ga with orbital dynamics and explicit ocean tide models that are “high‐level” (i.e., not idealized). To account for uncertain plate tectonic histories, we employ Monte Carlo simulations, with tidal energy dissipation rates (normalized relative to astronomical forcing parameters) randomly selected from ocean tide simulations with modern ocean basin geometry and with 55, 116, and 252 Ma reconstructed basin paleogeometries. The normalized dissipation rates depend upon basin geometry and [Formula: see text] rotation rate. Faster Earth rotation generally yields lower normalized dissipation rates. The Monte Carlo results provide a spread of possible early values for the Earth‐Moon system parameters. Of consequence for ocean circulation and climate, absolute (un‐normalized) ocean tidal energy dissipation rates on the early Earth may have exceeded [Formula: see text] rate due to a closer Moon. Prior to [Formula: see text] , evolution of inclination and eccentricity is dominated by tidal and core‐mantle boundary dissipation within the Moon, which yield high lunar orbit inclinations in the early Earth‐Moon system. A drawback for our results is that the semi‐major axis does not collapse to near‐zero values at 4.5 Ga, as indicated by most lunar formation models. Additional processes, missing from our current efforts, are discussed as topics for future investigation