Logarithmic Picard groups, chip firing, and the combinatorial rank

Illusie has suggested that one should think of the classifying group of M_X^{gp}-torsors on a logarithmically smooth curve $X$ over a standard logarithmic point as a logarithmic analogue of the Picard group of $X$. This logarithmic Picard group arises naturally as a quotient of the algebraic Picard group by lifts of the chip firing relations of the associated dual graph. We connect this perspective to Baker and Norine’s theory of ranks of divisors on a finite graph, and to Amini and Baker’s metrized complexes of curves. Moreover, we propose a definition of a combinatorial rank for line bundles on $X$ and prove that an analogue of the Riemann–Roch formula holds for our combinatorial rank. Our proof proceeds by carefully describing the relationship between the logarithmic Picard group on a logarithmic curve and the Picard group of the associated metrized complex. This approach suggests a natural categorical framework for metrized complexes, namely the category of logarithmic curves

Using baseline-dependent window functions for data compression and field-of-interest shaping in radio interferometry

In radio interferometry, observed visibilities are intrinsically sampled at some interval in time and frequency. Modern interferometers are capable of producing data at very high time and frequency resolution; practical limits on storage and computation costs require that some form of data compression be imposed. The traditional form of compression is a simple averaging of the visibilities over coarser time and frequency bins. This has an undesired side effect: the resulting averaged visibilities "decorrelate", and do so differently depending on the baseline length and averaging interval. This translates into a non-trivial signature in the image domain known as "smearing", which manifests itself as an attenuation in amplitude towards off-centre sources. With the increasing fields of view and/or longer baselines employed in modern and future instruments, the trade-off between data rate and smearing becomes increasingly unfavourable. In this work we investigate alternative approaches to low-loss data compression. We show that averaging of the visibility data can be treated as a form of convolution by a boxcar-like window function, and that by employing alternative baseline-dependent window functions a more optimal interferometer smearing response may be induced. In particular, we show improved amplitude response over a chosen field of interest, and better attenuation of sources outside the field of interest. The main cost of this technique is a reduction in nominal sensitivity; we investigate the smearing vs. sensitivity trade-off, and show that in certain regimes a favourable compromise can be achieved. We show the application of this technique to simulated data from the Karl G. Jansky Very Large Array (VLA) and the European Very-long-baseline interferometry Network (EVN)

Lower Bounds on Mutual Information

We correct claims about lower bounds on mutual information (MI) between real-valued random variables made in A. Kraskov {\it et al.}, Phys. Rev. E {\bf 69}, 066138 (2004). We show that non-trivial lower bounds on MI in terms of linear correlations depend on the marginal (single variable) distributions. This is so in spite of the invariance of MI under reparametrizations, because linear correlations are not invariant under them. The simplest bounds are obtained for Gaussians, but the most interesting ones for practical purposes are obtained for uniform marginal distributions. The latter can be enforced in general by using the ranks of the individual variables instead of their actual values, in which case one obtains bounds on MI in terms of Spearman correlation coefficients. We show with gene expression data that these bounds are in general non-trivial, and the degree of their (non-)saturation yields valuable insight.Comment: 4 page

A First Step Towards Automatically Building Network Representations

To fully harness Grids, users or middlewares must have some knowledge on the topology of the platform interconnection network. As such knowledge is usually not available, one must uses tools which automatically build a topological network model through some measurements. In this article, we define a methodology to assess the quality of these network model building tools, and we apply this methodology to representatives of the main classes of model builders and to two new algorithms. We show that none of the main existing techniques build models that enable to accurately predict the running time of simple application kernels for actual platforms. However some of the new algorithms we propose give excellent results in a wide range of situations

M-grid: Using Ubiquitous Web Technologies to create a Computational Grid

There are many potential users and uses for grid computing. However, the concept of sharing computing resources excites security concerns and, whilst being powerful and flexible, at least for novices, existing systems are complex to install and use. Together these represent a significant barrier to potential users who are interested to see what grid computing can do. This paper describes m-grid, a system for building a computational grid which can accept tasks from any user with access to a web browser and distribute them to almost any machine with access to the internet and manages to do this without the installation of additional software or interfering with existing security arrangements

Optical implementation of systolic array processing

Algorithms for matrix vector multiplication are implemented using acousto-optic cells for multiplication and input data transfer and using charge coupled devices detector arrays for accumulation and output of the results. No two dimensional matrix mask is required; matrix changes are implemented electronically. A system for multiplying a 50 component nonnegative real vector by a 50 by 50 nonnegative real matrix is described. Modifications for bipolar real and complex valued processing are possible, as are extensions to matrix-matrix multiplication and multiplication of a vector by multiple matrices

Surface roughness interpretation of 730 kg days CRESST-II results

The analysis presented in the recent publication of the CRESST-II results finds a statistically significant excess of registered events over known background contributions in the acceptance region and attributes the excess to a possible Dark Matter signal, caused by scattering of relatively light WIMPs. We propose a mechanism which explains the excess events with ion sputtering caused by 206Pb recoils and alpha particles from 210Po decay, combined with realistic surface roughness effects.Comment: 15 pages, 6 figures. v2: corrected quenching factor discussion. v3: corrected references. v4: added reference

A Phenomenology of Spiritual Experiences in Wilderness: Relating Self, Culture and Wilderness

Abstract This study uses thirty-two semi-structured interviews of overnight visitors to a northern wilderness to question, update, and improve our understanding of spiritual experiences in wilderness. The resulting narrative further develops the inputs, processes and outcomes of spiritual experiences in wilderness, and advances our understanding of: a) visitor definitions of wilderness and spirituality; b) the significance of wilderness spirituality mentors; and c) the growing impact cultural changes have on spiritual experiences in wilderness. Participants described wilderness as a setting where they can manage the information they are required to process and engage in rituals that support contemplation of spiritual themes. This study uncovers new threads such as the role of the numerous teachers of wilderness spirituality and the impact of escaping information technology

XMM-Newton, Chandra, and CGPS observations of the Supernova Remnants G85.4+0.7 and G85.9-0.6

We present an XMM-Newton detection of two low radio surface brightness SNRs, G85.4+0.7 and G85.9-0.6, discovered with the Canadian Galactic Plane Survey (CGPS). High-resolution XMM-Newton images revealing the morphology of the diffuse emission, as well as discrete point sources, are presented and correlated with radio and Chandra images. The new data also permit a spectroscopic analysis of the diffuse emission regions, and a spectroscopic and timing analysis of the point sources. Distances have been determined from HI and CO data to be 3.5 +/- 1.0 kpc for SNR G85.4+0.7 and 4.8 +/- 1.6 kpc for SNR G85.9-0.6. The SNR G85.4+0.7 is found to have a temperature of ~12-13 MK and a 0.5-2.5 keV luminosity of ~1-4 x 10^33 D(3.5)^2 erg/s (where D(3.5) is the distance in units of 3.5 kpc), with an electron density n_e of ~0.07-0.16(fD(3.5))^-1/2 cm^-3 (where f is the volume filling factor), and a shock age of ~9-49(fD(3.5))^1/2 kyr. The SNR G85.9-0.6 is found to have a temperature of ~15-19 MK and a 0.5-2.5 keV luminosity of ~1-4 x 10^34 D(4.8)^2 erg/s (where D(4.8) is the distance in units of 4.8 kpc), with an electron density n_e of ~0.04-0.10(fD(4.8))^-1/2 cm^-3 and a shock age of ~12-42(fD(4.8))^1/2 kyr. Based on the data presented here, none of the point sources appears to be the neutron star associated with either SNR.Comment: 30 pages using emulateapj, 16 figures with quality reduced for astro-ph only. The original version with high-resolution figures can be downloaded from: http://www.physics.umanitoba.ca/~samar/astro-ph/G85s-ms09102007.pdf To appear in ApJ (Jan 20 2008 issue, v673, n1