Primer for the algebraic geometry of sandpiles

The Abelian Sandpile Model (ASM) is a game played on a graph realizing the dynamics implicit in the discrete Laplacian matrix of the graph. The purpose of this primer is to apply the theory of lattice ideals from algebraic geometry to the Laplacian matrix, drawing out connections with the ASM. An extended summary of the ASM and of the required algebraic geometry is provided. New results include a characterization of graphs whose Laplacian lattice ideals are complete intersection ideals; a new construction of arithmetically Gorenstein ideals; a generalization to directed multigraphs of a duality theorem between elements of the sandpile group of a graph and the graph's superstable configurations (parking functions); and a characterization of the top Betti number of the minimal free resolution of the Laplacian lattice ideal as the number of elements of the sandpile group of least degree. A characterization of all the Betti numbers is conjectured.Comment: 45 pages, 14 figures. v2: corrected typo

A Magnetohydrodynamic Model of the M87 Jet I: Superluminal Knot Ejections from HST-1 as Trails of Quad Relativistic MHD Shocks

This is the first in a series of papers that introduces a new paradigm for understanding the jet in M87: a collimated relativistic flow in which strong magnetic fields play a dominant dynamical role. Here wefocus on the flow downstream of HST-1 - an essentially stationary flaring feature that ejects trails of superluminal components. We propose that these components are quad relativistic magnetohydrodynamic shock fronts (forward/reverse fast and slow modes) in a narrow jet with a helically twisted magnetic structure. And we demonstrate the properties of such shocks with simple one-dimensional numerical simulations. Quasi-periodic ejections of similar component trails may be responsible for the M87 jet substructures observed further downstream on 100 - 1,000 pc scales. This new paradigm requires the assimilation of some new concepts into the astrophysical jet community, particularly the behavior of slow/fast-mode waves/shocks and of current-driven helical kink instabilities. However, the prospects of these ideas applying to a large number of other jet systems may make this worth the effort.Comment: 7 pages, 4 figures, Accepted for Publication in Ap

New Constraints on Quantum Gravity from X-ray and Gamma-Ray Observations

One aspect of the quantum nature of spacetime is its "foaminess" at very small scales. Many models for spacetime foam are defined by the accumulation power $\alpha$, which parameterizes the rate at which Planck-scale spatial uncertainties (and thephase shifts they produce) may accumulate over large path-lengths. Here $\alpha$ is defined by theexpression for the path-length fluctuations, $\delta \ell$, of a source at distance $\ell$, wherein $\delta \ell \simeq \ell^{1 - \alpha} \ell_P^{\alpha}$, with $\ell_P$ being the Planck length. We reassess previous proposals to use astronomical observations ofdistant quasars and AGN to test models of spacetime foam. We show explicitly how wavefront distortions on small scales cause the image intensity to decay to the point where distant objects become undetectable when the path-length fluctuations become comparable to the wavelength of the radiation. We use X-ray observations from {\em Chandra} to set the constraint $\alpha \gtrsim 0.58$, which rules out the random walk model (with $\alpha = 1/2$). Much firmer constraints canbe set utilizing detections of quasars at GeV energies with {\em Fermi}, and at TeV energies with ground-based Cherenkovtelescopes: $\alpha \gtrsim 0.67$ and $\alpha \gtrsim 0.72$, respectively. These limits on $\alpha$ seem to rule out $\alpha = 2/3$, the model of some physical interest.Comment: 11 pages, 9 figures, ApJ, in pres

A survey of X-ray emission from 100 kpc radio jets

We have completed a Chandra snapshot survey of 54 radio jets that are extended on arcsec scales. These are associated with flat spectrum radio quasars spanning a redshift range z=0.3 to 2.1. X-ray emission is detected from the jet of approximately 60% of the sample objects. We assume minimum energy and apply conditions consistent with the original Felten-Morrison calculations in order to estimate the Lorentz factors and the apparent Doppler factors. This allows estimates of the enthalpy fluxes, which turn out to be comparable to the radiative luminosities.Comment: Conference Proceedings IAU Symposium No. 313, Extragalactic jets from every angle, pp. 219-224, 4 figure

Peripheral blood gene expression reveals an inflammatory transcriptomic signature in Friedreich's ataxia patients.

Transcriptional changes in Friedreich's ataxia (FRDA), a rare and debilitating recessive Mendelian neurodegenerative disorder, have been studied in affected but inaccessible tissues-such as dorsal root ganglia, sensory neurons and cerebellum-in animal models or small patient series. However, transcriptional changes induced by FRDA in peripheral blood, a readily accessible tissue, have not been characterized in a large sample. We used differential expression, association with disability stage, network analysis and enrichment analysis to characterize the peripheral blood transcriptome and identify genes that were differentially expressed in FRDA patients (n = 418) compared with both heterozygous expansion carriers (n = 228) and controls (n = 93 739 individuals in total), or were associated with disease progression, resulting in a disease signature for FRDA. We identified a transcriptional signature strongly enriched for an inflammatory innate immune response. Future studies should seek to further characterize the role of peripheral inflammation in FRDA pathology and determine its relevance to overall disease progression

The Warped Nuclear Disk of Radio Galaxy 3C 449

Among radio galaxies containing nuclear dust disks, the bipolar jet axis is generally observed to be perpendicular to the disk major axis. The FR I radio source 3C 449 is an outlier to this statistical majority, as it possesses a nearly parallel jet/disk orientation on the sky. We examine the 600 pc dusty disk in this galaxy with images from the Hubble Space Telescope. We find that a colormap of the disk exhibits a twist in its isocolor contours (isochromes). We model the colormap by integrating galactic starlight through an absorptive disk, and find that the anomalous twist in the isochromes can be reproduced in the model with a vertically thin, warped disk. The model predicts that the disk is nearly perpendicular to the jet axis within 100 pc of the nucleus. We discuss physical mechanisms capable of causing such a warp. We show that precessional models or a torque on the disk arising from a possible binary black hole in the AGN causes precession on a timescale that is too long to account for the predicted disk morphology. However, we estimate that the pressure in the X-ray emitting interstellar medium is large enough to perturb the disk, and argue that jet-driven anisotropy in the excited ISM may be the cause of the warp. In this way, the warped disk in 3C 449 may be a new manifestation of feedback from an active galactic nucleus.Comment: Accepted for publication in Ap