An asymptotic formula for the number of non-negative integer matrices with prescribed row and column sums

We count mxn non-negative integer matrices (contingency tables) with prescribed row and column sums (margins). For a wide class of smooth margins we establish a computationally efficient asymptotic formula approximating the number of matrices within a relative error which approaches 0 as m and n grow.Comment: 57 pages, results strengthened, proofs simplified somewha

The number of graphs and a random graph with a given degree sequence

We consider the set of all graphs on n labeled vertices with prescribed degrees D=(d_1, ..., d_n). For a wide class of tame degree sequences D we prove a computationally efficient asymptotic formula approximating the number of graphs within a relative error which approaches 0 as n grows. As a corollary, we prove that the structure of a random graph with a given tame degree sequence D is well described by a certain maximum entropy matrix computed from D. We also establish an asymptotic formula for the number of bipartite graphs with prescribed degrees of vertices, or, equivalently, for the number of 0-1 matrices with prescribed row and column sums.Comment: 52 pages, minor improvement

Forbidden Line Emission in the Eccentric Spectroscopic Binaries DQ Tauri and UZ Tauri E Monitored over an Orbital Period

We present echelle spectroscopy of the close pre-main-sequence binary star systems DQ Tau and UZ Tau-E. Over a 16 day time interval we acquired 14 nights of spectra for DQ Tau and 12 nights of spectra for UZ Tau-E. This represents the entire phase of DQ Tau, and 63 percent of the phase of UZ Tau-E. As expected, photospheric lines such as Li I 6707 clearly split into two components as the primary and secondary orbit one another, as did the permitted line He I 5876. Unlike the photospheric features, the forbidden lines of [O I] 6300 and [O I] 5577, retain the same shape throughout the orbit. Therefore these lines must originate outside of the immediate vicinity of the two stars and any circumstellar disks that participate in the orbital motion of the stars.Comment: 14 pages including 6 figures, aastex preprint, accepted to Astronomical Journa

Laboratory Experiments, Numerical Simulations, and Astronomical Observations of Deflected Supersonic Jets: Application to HH 110

Collimated supersonic flows in laboratory experiments behave in a similar manner to astrophysical jets provided that radiation, viscosity, and thermal conductivity are unimportant in the laboratory jets, and that the experimental and astrophysical jets share similar dimensionless parameters such as the Mach number and the ratio of the density between the jet and the ambient medium. Laboratory jets can be studied for a variety of initial conditions, arbitrary viewing angles, and different times, attributes especially helpful for interpreting astronomical images where the viewing angle and initial conditions are fixed and the time domain is limited. Experiments are also a powerful way to test numerical fluid codes in a parameter range where the codes must perform well. In this paper we combine images from a series of laboratory experiments of deflected supersonic jets with numerical simulations and new spectral observations of an astrophysical example, the young stellar jet HH 110. The experiments provide key insights into how deflected jets evolve in 3-D, particularly within working surfaces where multiple subsonic shells and filaments form, and along the interface where shocked jet material penetrates into and destroys the obstacle along its path. The experiments also underscore the importance of the viewing angle in determining what an observer will see. The simulations match the experiments so well that we can use the simulated velocity maps to compare the dynamics in the experiment with those implied by the astronomical spectra. The experiments support a model where the observed shock structures in HH 110 form as a result of a pulsed driving source rather than from weak shocks that may arise in the supersonic shear layer between the Mach disk and bow shock of the jet's working surface.Comment: Full resolution figures available at http://sparky.rice.edu/~hartigan/pub.html To appear in Ap

A Survey of Irradiated Pillars, Globules, and Jets in the Carina Nebul

We present wide-field, deep narrowband H$_2$, Br$\gamma$, H$\alpha$, [S II], [O III], and broadband I and K-band images of the Carina star formation region. The new images provide a large-scale overview of all the H$_2$ and Br$\gamma$ emission present in over a square degree centered on this signature star forming complex. By comparing these images with archival HST and Spitzer images we observe how intense UV radiation from O and B stars affects star formation in molecular clouds. We use the images to locate new candidate outflows and identify the principal shock waves and irradiated interfaces within dozens of distinct areas of star-forming activity. Shocked molecular gas in jets traces the parts of the flow that are most shielded from the intense UV radiation. Combining the H$_2$ and optical images gives a more complete view of the jets, which are sometimes only visible in H$_2$. The Carina region hosts several compact young clusters, and the gas within these clusters is affected by radiation from both the cluster stars and the massive stars nearby. The Carina Nebula is ideal for studying the physics of young H II regions and PDR's, as it contains multiple examples of walls and irradiated pillars at various stages of development. Some of the pillars have detached from their host molecular clouds to form proplyds. Fluorescent H$_2$ outlines the interfaces between the ionized and molecular gas, and after removing continuum, we detect spatial offsets between the Br$\gamma$ and H$_2$ emission along the irradiated interfaces. These spatial offsets can be used to test current models of PDRs once synthetic maps of these lines become available.Comment: Accepted in the Astronomical Journa

Suppression of SIV-specific CD4+ T cells by infant but not adult macaque regulatory T cells: implications for SIV disease progression.

The impact of regulatory T cells (T reg cells) on the course of HIV and SIV disease is unknown. T reg cells could suppress protective antiviral responses and accelerate disease progression. Alternatively, these cells might block T cell activation and thereby limit viral replication as well as activation-associated immunopathology. Given the higher frequency of T reg cells known to be present during human fetal ontogeny, such influences may be most important in the context of perinatal infection. We found that infant macaques had higher fractions of CD4(+)CD25(+)CD127(low)FoxP3(+) T reg cells in the peripheral blood and in lymphoid tissues, and that these T reg cells showed greater in vitro suppressive activity on a per cell basis. Infant and adult macaques were infected with SIVmac251 to test the influence of the T reg cell compartment on SIV-specific immune responses. After infection with SIV, most (three out of four) infant macaques had persistently high viral loads, weak and transient SIV-specific CD4(+) and CD8(+) T cell responses, and rapid disease progression. T reg cells in the infant but not in the adult directly suppressed SIV-specific CD4(+) T cell responses, which were detectable only after depletion of T reg cells. In the case of both the infant and the adult macaque, T reg cells were not able to directly suppress SIV-specific CD8(+) T cell responses and had no apparent effect on T cell activation. In aggregate, these observations suggest that the T reg cell compartment of the infant macaque facilitates rapid disease progression, at least in part by incapacitating SIV-specific CD4(+) T cell responses