Prefix Codes: Equiprobable Words, Unequal Letter Costs

Describes a near-linear-time algorithm for a variant of Huffman coding, in which the letters may have non-uniform lengths (as in Morse code), but with the restriction that each word to be encoded has equal probability. [See also ``Huffman Coding with Unequal Letter Costs'' (2002).]Comment: proceedings version in ICALP (1994

Hydrodynamic Simulations of the Interaction between an AGB Star and a Main Sequence Companion in Eccentric Orbits

The Rotten Egg Nebula has at its core a binary composed of a Mira star and an A-type companion at a separation >10 au. It has been hypothesized to have formed by strong binary interactions between the Mira and a companion in an eccentric orbit during periastron passage ~800 years ago. We have performed hydrodynamic simulations of an asymptotic giant branch star interacting with companions with a range of masses in orbits with a range of initial eccentricities and periastron separations. For reasonable values of the eccentricity, we find that Roche lobe overflow can take place only if the periods are <<100 years. Moreover, mass transfer causes the system to enter a common envelope phase within several orbits. Since the central star of the Rotten Egg nebula is an AGB star, we conclude that such a common envelope phase must have lead to a merger, so the observed companion must have been a tertiary companion of a binary that merged at the time of nebula ejection. Based on the mass and timescale of the simulated disc formed around the companion before the common envelope phase, we analytically estimate the properties of jets that could be launched. Allowing for super-Eddington accretion rates, we find that jets similar to those observed are plausible, provided that the putative lost companion was relatively massive.Comment: accepted for publication in MNRA

Mixing Time Scales in a Supernova-Driven Interstellar Medium

We study the mixing of chemical species in the interstellar medium (ISM). Recent observations suggest that the distribution of species such as deuterium in the ISM may be far from homogeneous. This raises the question of how long it takes for inhomogeneities to be erased in the ISM, and how this depends on the length scale of the inhomogeneities. We added a tracer field to the three-dimensional, supernova-driven ISM model of Avillez (2000) to study mixing and dispersal in kiloparsec-scale simulations of the ISM with different supernova (SN) rates and different inhomogeneity length scales. We find several surprising results. Classical mixing length theory fails to predict the very weak dependence of mixing time on length scale that we find on scales of 25--500 pc. Derived diffusion coefficients increase exponentially with time, rather than remaining constant. The variance of composition declines exponentially, with a time constant of tens of Myr, so that large differences fade faster than small ones. The time constant depends on the inverse square root of the supernova rate. One major reason for these results is that even with numerical diffusion exceeding physical values, gas does not mix quickly between hot and cold regions.Comment: 23 pages, 14 figures that include 7 simulation images and 19 plots, accepted for publication at Ap

Variations in Arterial Blood Pressure after Kidney Transplantation

The course of hypertension within the first 2 months after kidney transplantation was correlated with renal function, plasma renin activity (PRA), and the daily maintenance dose of prednisone in 18 homograft recipients. During acute rejection blood pressure (BP) closely correlated with PRA. Patients with normal homograft function showed an increase in BP early after transplantation which in most returned to normal 3-8 weeks later. In the latter group no correlation could be found between the level of BP and PRA, however the BP correlated closely with the dose of prednisone. These observations suggest that during acute rejection the increase in BP may at least partly be mediated by a renal pressor mechanism, whereas with normal renal function the high dose of glucocorticoids may play an important role in the development of hypertension.</jats:p

Recovery from Hepatorenal Syndrome after Orthotopic Liver Transplantation

Three patients with progressive renal failure and advanced hepatic insufficiency due to cirrhosis of the liver underwent orthotopic liver transplantation. All three patients had immediate improvement in hepatic function and within two weeks after liver replacement regained nearly normal kidney function. However, the renal recovery was delayed in each case, and its course was not uniform. Plasma renin activity was high, and renin substrate was low before transplantation in one case in which these measurements were obtained; both returned to normal soon after liver replacement. (N Engl J Med 289:1155–1159, 1973). © 1973, Massachusetts Medical Society. All rights reserved

HST Images Flash Ionization of Old Ejecta by the 2011 Eruption of Recurrent Nova T Pyxidis

T Pyxidis is the only recurrent nova surrounded by knots of material ejected in previous outbursts. Following the eruption that began on 2011 April 14.29, we obtained seven epochs (from 4 to 383 days after eruption) of Hubble Space Telescope narrowband Ha images of T Pyx . The flash of radiation from the nova event had no effect on the ejecta until at least 55 days after the eruption began. Photoionization of hydrogen located north and south of the central star was seen 132 days after the beginning of the eruption. That hydrogen recombined in the following 51 days, allowing us to determine a hydrogen atom density of at least 7e5 cm^-3 - at least an order of magnitude denser than the previously detected, unresolved [NII] knots surrounding T Pyx. Material to the northwest and southeast was photoionized between 132 and 183 days after the eruption began. 99 days later that hydrogen had recombined. Both then (282 days after outburst) and 101 days later, we detected almost no trace of hydrogen emission around T Pyx. There is a large reservoir of previously unseen, cold diffuse hydrogen overlapping the previously detected, [NII] - emitting knots of T Pyx ejecta. The mass of this newly detected hydrogen is probably an order of magnitude larger than that of the [NII] knots. We also determine that there is no significant reservoir of undetected ejecta from the outer boundaries of the previously detected ejecta out to about twice that distance, near the plane of the sky. The lack of distant ejecta is consistent with the Schaefer et al (2010) scenario for T Pyx, in which the star underwent its first eruption within five years of 1866 after many millennia of quiescence, followed by the six observed recurrent nova eruptions since 1890. This lack of distant ejecta is not consistent with scenarios in which T Pyx has been erupting continuously as a recurrent nova for many centuries or millennia.Comment: 27 pages, 10 figures, submitted to the Astrophysical Journa