Trees and Matchings

In this article, Temperley's bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on the other, is extended to the setting of general planar directed (and undirected) graphs, where edges carry nonnegative weights that induce a weighting on the set of spanning trees. We show that the weighted, directed spanning trees (often called arborescences) of any planar graph G can be put into a one-to-one weight-preserving correspondence with the perfect matchings of a related planar graph H. One special case of this result is a bijection between perfect matchings of the hexagonal honeycomb lattice and directed spanning trees of a triangular lattice. Another special case gives a correspondence between perfect matchings of the ``square-octagon'' lattice and directed weighted spanning trees on a directed weighted version of the cartesian lattice. In conjunction with results of Kenyon, our main theorem allows us to compute the measures of all cylinder events for random spanning trees on any (directed, weighted) planar graph. Conversely, in cases where the perfect matching model arises from a tree model, Wilson's algorithm allows us to quickly generate random samples of perfect matchings.Comment: 32 pages, 19 figures (minor revisions from version 1

Critical current of a Josephson junction containing a conical magnet

We calculate the critical current of a superconductor/ferromagnetic/superconductor (S/FM/S) Josephson junction in which the FM layer has a conical magnetic structure composed of an in-plane rotating antiferromagnetic phase and an out-of-plane ferromagnetic component. In view of the realistic electronic properties and magnetic structures that can be formed when conical magnets such as Ho are grown with a polycrystalline structure in thin-film form by methods such as direct current sputtering and evaporation, we have modeled this situation in the dirty limit with a large magnetic coherence length ($\xi_f$). This means that the electron mean free path is much smaller than the normalized spiral length $\lambda/2\pi$ which in turn is much smaller than $\xi_f$ (with $\lambda$ as the length a complete spiral makes along the growth direction of the FM). In this physically reasonable limit we have employed the linearized Usadel equations: we find that the triplet correlations are short ranged and manifested in the critical current as a rapid oscillation on the scale of $\lambda/2\pi$. These rapid oscillations in the critical current are superimposed on a slower oscillation which is related to the singlet correlations. Both oscillations decay on the scale of $\xi_f$. We derive an analytical solution and also describe a computational method for obtaining the critical current as a function of the conical magnetic layer thickness.Comment: Extended version of the published paper. Additional information about the computational method is included in the appendi

A first direct measurement of the intergalactic medium temperature around a quasar at z=6

The thermal state of the intergalactic medium (IGM) provides an indirect probe of both the HI and HeII reionisation epochs. Current constraints on the IGM temperature from the Lya forest are restricted to the redshift range 2<z<4.5, limiting the ability to probe the thermal memory of HI reionisation toward higher redshift. In this work, we present the first direct measurement of the IGM temperature around a z=6 quasar by analysing the Doppler widths of Lya absorption lines in the proximity zone of SDSS J0818+1722. We use a high resolution (R= 40000) Keck/HIRES spectrum in combination with detailed numerical modelling to obtain the temperature at mean density, T_0=23600\pm^5000_6900K (\pm^9200_9300K) at 68 (95) per cent confidence assuming a prior probability 13500K<T_0<38500 K following HI and HeII reionisation. This enables us to place an upper limit on the redshift of HI reionisation, z_H, within 33 comoving Mpc of SDSS J0818+1722. If the quasar reionises the HeII in its vicinity, then in the limit of instantaneous reionisation we infer z_H<9.0 (11.0) at 68 (95) per cent confidence assuming photoheating is the dominant heat source and that HI reionisation is driven by ionising sources with soft spectra, typical of population II stars. If the HI and HeII in the IGM around SDSS J0818+1722 are instead reionised simultaneously by a population of massive metal-free stars, characterised by very hard ionising spectra, we obtain a tighter upper limit of z_H<8.4 (9.4). Initiating reionisation at higher redshifts produces temperatures which are too low with respect to our constraint unless the HI ionising sources or the quasar itself have spectra significantly harder than typically assumed.Comment: 15 pages, 9 figures, accepted to MNRA

Parallel Self-Consistent-Field Calculations via Chebyshev-Filtered Subspace Acceleration

Solving the Kohn-Sham eigenvalue problem constitutes the most computationally expensive part in self-consistent density functional theory (DFT) calculations. In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace iteration method, which avoids computing explicit eigenvectors except at the first SCF iteration. The method may be viewed as an approach to solve the original nonlinear Kohn-Sham equation by a nonlinear subspace iteration technique, without emphasizing the intermediate linearized Kohn-Sham eigenvalue problem. It reaches self-consistency within a similar number of SCF iterations as eigensolver-based approaches. However, replacing the standard diagonalization at each SCF iteration by a Chebyshev subspace filtering step results in a significant speedup over methods based on standard diagonalization. Here, we discuss an approach for implementing this method in multi-processor, parallel environment. Numerical results are presented to show that the method enables to perform a class of highly challenging DFT calculations that were not feasible before

Prediction and Generation of Binary Markov Processes: Can a Finite-State Fox Catch a Markov Mouse?

Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov process. This is a class of processes whose predictive model is well known. Surprisingly, the generative model requires three distinct topologies for different regions of parameter space. We show that a previously proposed generator for a particular set of binary Markov processes is, in fact, not minimal. Our results shed the first quantitative light on the relative (minimal) costs of prediction and generation. We find, for instance, that the difference between prediction and generation is maximized when the process is approximately independently, identically distributed.Comment: 12 pages, 12 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/gmc.ht

Neuropsychological evaluation of blast-related concussion: Illustrating the challenges and complexities through OEF/OIF case studies

Background/objective: Soldiers of Operations Enduring Freedom (OEF) and Iraqi Freedom (OIF) sustain blast-related mild traumatic brain injury (concussion) with alarming regularity. This study discusses factors in addition to concussion, such as co-morbid psychological difficulty (e.g. post-traumatic stress) and symptom validity concerns that may complicate neuropsychological evaluation in the late stage of concussive injury. Case report: The study presents the complexities that accompany neuropsychological evaluation of blast concussion through discussion of three case reports of OEF/OIF personnel. Discussion: The authors emphasize uniform assessment of blast concussion, the importance of determining concussion severity according to acute-injury characteristics and elaborate upon non-concussion-related factors that may impact course of cognitive limitation. The authors conclude with a discussion of the need for future research examining the impact of blast concussion (particularly recurrent concussion) and neuropsychological performance

Evaluation Context Impacts Neuropsychological Performance of OEF/OIF Veterans with Reported Combat-Related Concussion

Although soldiers of Operations Iraqi Freedom (OIF) and Enduring Freedom (OEF) encounter combat-related concussion at an unprecedented rate, relatively few studies have examined how evaluation context, insufficient effort, and concussion history impact neuropsychological performances in the years following injury. The current study explores these issues in a sample of 119 U.S. veterans (OEF/OIF forensic concussion, n = 24; non-OEF/OIF forensic concussion, n = 20; OEF/OIF research concussion, n = 38; OEF/OIF research without concussion, n = 37). The OEF/OIF forensic concussion group exhibited significantly higher rates of insufficient effort relative to the OEF/OIF research concussion group, but a comparable rate of insufficient effort relative to the non-OEF/OIF forensic concussion group. After controlling for effort, the research concussion and the research non-concussion groups demonstrated comparable neuropsychological performance. Results highlight the importance of effort assessment among OEF/OIF and other veterans with concussion history, particularly in forensic contexts

Counts and Colors of Faint Galaxies in the U and R Bands

Ground-based counts and colors of faint galaxies in the U and R bands in one field at high Galactic latitude are presented. Integrated over flux, a total of 1.2x10^5 sources per square degree are found to U=25.5 mag and 6.3x10^5 sources per square degree to R=27 mag, with d log N/dm ~ 0.5 in the U band and d log N/dm ~ 0.3 in the R band. Consistent with these number-magnitude curves, sources become bluer with increasing magnitude to median U-R=0.6 mag at 24<U<25 mag and U-R=1.2 mag at 25 < R < 26 mag. Because the Lyman break redshifts into the U band at z~3, at least 1.2x10^5 sources per square degree must be at redshifts z<3. Measurable U-band fluxes of 73 percent of the 6.3x10^5 sources per square degree suggest that the majority of these also lie at z < 3. These results require an enormous space density of objects in any cosmological model.Comment: 17 pages, MNRAS in pres

A Simple Model for r-Process Scatter and Halo Evolution

Recent observations of heavy elements produced by rapid neutron capture (r-process) in the halo have shown a striking and unexpected behavior: within a single star, the relative abundances of r-process elements heavier than Eu are the same as the same as those of solar system matter, while across stars with similar metallicity Fe/H, the r/Fe ratio varies over two orders of magnitude. In this paper we present a simple analytic model which describes a star's abundances in terms of its ``ancestry,'' i.e., the number of nucleosynthesis events (e.g., supernova explosions) which contributed to the star's composition. This model leads to a very simple analytic expression for the abundance scatter versus Fe/H, which is in good agreement with the data and with more sophisticated numerical models. We investigate two classes of scenarios for r-process nucleosynthesis, one in which r-process synthesis events occur in only \sim 4% of supernovae but iron synthesis is ubiquitous, and one in which iron nucleosynthesis occurs in only about 9% of supernovae. (the Wasserburg- Qian model). We find that the predictions in these scenarios are similar for [Fe/H] \ga -2.5, but that these models can be readily distinguished observationally by measuring the dispersion in r/Fe at [Fe/H] \la -3.Comment: AASTeX, 21 pages, includes 4 figure

The Radial Extent and Warp of the Ionized Galactic Disk. I. A VLBA Survey of Extragalactic Sources Toward the Anticenter

We report multifrequency Very Long Baseline Array observations of twelve active galactic nuclei seen toward the Galactic anticenter. All of the sources are at |b| < 10 degrees and seven have |b| < 0.5 degrees. Our VLBA observations can detect an enhancement in the angular broadening of these sources due to an extended H II disk, if the orientation of the H II disk in the outer Galaxy is similar to that of the H I disk. Such an extended H II disk is suggested by the C IV absorption in a quasar's spectrum, the appearance of H I disks of nearby spiral galaxies, and models of Ly-alpha cloud absorbers and the Galactic fountain. We detect eleven of the twelve sources at one or more frequencies; nine of the sources are compact and suitable for an angular broadening analysis. A preliminary analysis of the observed angular diameters suggests that the H II disk does not display considerable warping or flaring and does not extend to large Galactocentric distances (R >~ 100 kpc). A companion paper (Lazio & Cordes 1997) combines these observations with those in the literature and presents a more comprehensive analysis.Comment: 19 pages, LaTeX2e with AASTeX macro aaspp4, accepted for publication in ApJS, Vol. 115, 1998 April; Figures 1, 3, and 4 included, for figures of individual sources see http://astrosun.tn.cornell.edu/students/lazio/Anticenter/anticenterI.htm