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

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

Estimation of protein folding probability from equilibrium simulations

The assumption that similar structures have similar folding probabilities ($p_{fold}$) leads naturally to a procedure to evaluate $p_{fold}$ for every snapshot saved along an equilibrium folding-unfolding trajectory of a structured peptide or protein. The procedure utilizes a structurally homogeneous clustering and does not require any additional simulation. It can be used to detect multiple folding pathways as shown for a three-stranded antiparallel $\beta$-sheet peptide investigated by implicit solvent molecular dynamics simulations.Comment: 7 pages, 4 figures, supplemetary material

On the structure and stability of magnetic tower jets

Modern theoretical models of astrophysical jets combine accretion, rotation, and magnetic fields to launch and collimate supersonic flows from a central source. Near the source, magnetic field strengths must be large enough to collimate the jet requiring that the Poynting flux exceeds the kinetic-energy flux. The extent to which the Poynting flux dominates kinetic energy flux at large distances from the engine distinguishes two classes of models. In magneto-centrifugal launch (MCL) models, magnetic fields dominate only at scales $\lesssim 100$ engine radii, after which the jets become hydrodynamically dominated (HD). By contrast, in Poynting flux dominated (PFD) magnetic tower models, the field dominates even out to much larger scales. To compare the large distance propagation differences of these two paradigms, we perform 3-D ideal MHD AMR simulations of both HD and PFD stellar jets formed via the same energy flux. We also compare how thermal energy losses and rotation of the jet base affects the stability in these jets. For the conditions described, we show that PFD and HD exhibit observationally distinguishable features: PFD jets are lighter, slower, and less stable than HD jets. Unlike HD jets, PFD jets develop current-driven instabilities that are exacerbated as cooling and rotation increase, resulting in jets that are clumpier than those in the HD limit. Our PFD jet simulations also resemble the magnetic towers that have been recently created in laboratory astrophysical jet experiments.Comment: 16 pages, 11 figures, published in ApJ: ApJ, 757, 6

Development of cytomegalovirus (CMV) immune recovery uveitis is associated with Th17 cell depletion and poor systemic CMV-specific T cell responses.

Backgroundthe immune reconstitution inflammatory syndromes (IRIS) are a spectrum of inflammatory conditions associated with opportunistic infections and occurring in approximately16% of human immunodeficiency type 1 (HIV-1)-infected patients given antiretroviral therapy. It has been proposed that these conditions are linked by a dysregulated immune system that is prone to exaggerated responses. However, immunologic studies have been limited by the availability of longitudinal samples from patients with IRIS and appropriate matched control subjects. Cytomegalovirus (CMV) immune recovery uveitis (IRU) is an IRIS occurring in up to 38% of patients with CMV retinitis. Although the pathologic immune responses occur in the eye, immune dysregulation that allows for development of pathologic responses is presumably caused by faulty systemic immune cell reconstitution.Methodswe examined CMV-specific T cell responses, regulatory T (T(reg)) cell function and polyclonal T cell responses, including IL-17 production, in 25 patients with CMV IRU and 49 immunorestored control subjects with CMV retinitis who did not develop IRU.Resultspatients with CMV IRU had poor CMV-specific CD4(+) T cell responses, as compared with control subjects, whereas CD8(+) T cell responses were comparable. Patients with CMV IRU were characterized by smaller numbers of circulating Th17 cells. Deficiency in anti-CMV responses was not associated with differences in T(reg) cell function.Conclusionsthe T(reg) cell compartment is intact in patients with CMV IRU, and these patients do not develop exaggerated systemic CMV-specific or polyclonal immune responses. Cases are instead characterized by more profound depletion of Th17 cells and poor antiviral immune responses. CMV IRU may be most likely to develop in persons experiencing the greatest degree of immune dysfunction before initiating highly active antiretroviral therapy

Astrophysical jets: observations, numerical simulations, and laboratory experiments

This paper provides summaries of ten talks on astrophysical jets given at the HEDP/HEDLA-08 International Conference in St. Louis. The talks are topically divided into the areas of observation, numerical modeling, and laboratory experiment. One essential feature of jets, namely, their filamentary (i.e., collimated) nature, can be reproduced in both numerical models and laboratory experiments. Another essential feature of jets, their scalability, is evident from the large number of astrophysical situations where jets occur. This scalability is the reason why laboratory experiments simulating jets are possible and why the same theoretical models can be used for both observed astrophysical jets and laboratory simulations