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David A. Smith

Publications and source records attributed to David A. Smith.

At least 55 records · Page 3Linked to original sources
arXiv2016

Evolution PDEs and augmented eigenfunctions. Half-line

The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the complex (spectral) plane. This representation is obtained by the {\em unified transform} introduced by Fokas in the 90's. On the other hand, it is known that many initial-boundary value problems can be solved via a classical transform pair, constructed via the spectral analysis of the associated spatial operator. For example, the Dirichlet problem for the heat equation can be solved by applying the Fourier sine transform pair. However, for many other initial-boundary value problems there is {\em no} suitable transform pair in the classical literature. Here we pose and answer two related questions: Given any well-posed initial-boundary value problem, does there exist a (non-classical) transform pair suitable for solving that problem? If so, can this transform pair be constructed via the spectral analysis of a differential operator? The answer to both of these questions is positive and given in terms of {\em augmented eigenfunctions}, a novel class of spectral functionals. These are eigenfunctions of a suitable differential operator in a certain generalised sense, they provide an effective spectral representation of the operator, and are associated with a transform pair suitable to solve the given initial-boundary value problem.

math.AP↗
arXiv2016

Automatic Construction of Evaluation Sets and Evaluation of Document Similarity Models in Large Scholarly Retrieval Systems

Retrieval systems for scholarly literature offer the ability for the scientific community to search, explore and download scholarly articles across various scientific disciplines. Mostly used by the experts in the particular field, these systems contain user community logs including information on user specific downloaded articles. In this paper we present a novel approach for automatically evaluating document similarity models in large collections of scholarly publications. Unlike typical evaluation settings that use test collections consisting of query documents and human annotated relevance judgments, we use download logs to automatically generate pseudo-relevant set of similar document pairs. More specifically we show that consecutively downloaded document pairs, extracted from a scholarly information retrieval (IR) system, could be utilized as a test collection for evaluating document similarity models. Another novel aspect of our approach lies in the method that we employ for evaluating the performance of the model by comparing the distribution of consecutively downloaded document pairs and random document pairs in log space. Across two families of similarity models, that represent documents in the term vector and topic spaces, we show that our evaluation approach achieves very high correlation with traditional performance metrics such as Mean Average Precision (MAP), while being more efficient to compute.

cs.IR↗
arXiv2015

First-fit coloring on interval graphs has performance ratio at least 5

First-fit is the online graph coloring algorithm that considers vertices one at a time in some order and assigns each vertex the least positive integer not used already on a neighbor. The maximum number of colors used by first-fit on graph G over all vertex orders is denoted χ_{FF}(G). The exact value of R := \sup_G [χ_{FF}(G) / ω(G)] over interval graphs G is unknown. Pemmaraju, Raman, and Varadarajan (2004) proved R <= 10, and this can be improved to 8. Witsenhausen (1976) and Chrobak and Ślusarek (1988) showed R >= 4, and Ślusarek (1993) improved this to 4.45. We prove R >= 5.

math.CO↗
arXiv2014

The unified transform method for linear initial-boundary value problems: a spectral interpretation

It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods such as Fourier series and transform techniques may only be used to solve certain problems. The solution representation obtained by such a classical method is known to be an expansion in the eigenfunctions or generalised eigenfunctions of the self-adjoint ordinary differential operator associated with the spatial part of the initial-boundary value problem. In this work, we emphasise that the unified transform method may be viewed as the natural extension of Fourier transform techniques for non-self-adjoint operators. Moreover, we investigate the spectral meaning of the transform pair used in the new method; we discuss the recent definition of a new class of spectral functionals and show how it permits the diagonalisation of certain non-self-adjoint spatial differential operators.

math.SP↗
arXiv2013

Beyond the 2nd Fermi Pulsar Catalog

Over thirteen times more gamma-ray pulsars have now been studied with the Large Area Telescope on NASA's Fermi satellite than the ten seen with the Compton Gamma-Ray Observatory in the nineteen-nineties. The large sample is diverse, allowing better understanding both of the pulsars themselves and of their roles in various cosmic processes. Here we explore the prospects for even more gamma-ray pulsars as Fermi enters the 2nd half of its nominal ten-year mission. New pulsars will naturally tend to be fainter than the first ones discovered. Some of them will have unusual characteristics compared to the current population, which may help discriminate between models. We illustrate a vision of the future with a sample of six pulsars discovered after the 2nd Fermi Pulsar Catalog was written.

astro-ph.HE↗
arXiv2012

Well-posedness and conditioning of 3rd and higher order two-point initial-boundary value problems

We discuss initial-boundary value problems of arbitrary spatial order subject to arbitrary boundary conditions. We formalise the concept of the conditioning of such a problem and show that it represents a necessary criterion for well-posedness. The other requirement for well-posedness, the convergence of certain series, is also analysed. We illustrate these results with a full classification of 3rd order problems having non-Robin boundary conditions. Part of this work is devoted to correcting an oversight in the author's earlier work Well-posed two-point initial-boundary value problems with arbitrary boundary conditions in volume 152 of Math. Proc. Camb. Philos. Soc.

math.AP↗
arXiv2012

SPAN512: A new mid-latitude pulsar survey with the Nancay Radio Telescope

We present an ongoing survey with the Nançay Radio Telescope at L-band. The targeted area is $74^\circ \lesssim l <150^\circ$ and $3.5^\circ < |b| < 5^\circ$. This survey is characterized by a long integration time (18 min), large bandwidth (512 MHz) and high time and frequency resolution (64 $μ$s and 0.5 MHz) giving a nominal sensitivity limit of 0.055 mJy for long period pulsars. This is about 2 times better than the mid-latitude HTRU survey, and is designed to be complementary with current large scale surveys. This survey will be more sensitive to transients (RRATs, intermittent pulsars), distant and faint millisecond pulsars as well as scintillating sources (or any other kind of radio faint sources) than all previous short-integration surveys.

astro-ph.HE↗
arXiv2012

Relaxation and Pre-thermalization in an Isolated Quantum System

Understanding relaxation processes is an important unsolved problem in many areas of physics. A key challenge in studying such non-equilibrium dynamics is the scarcity of experimental tools for characterizing their complex transient states. We employ measurements of full quantum mechanical probability distributions of matter-wave interference to study the relaxation dynamics of a coherently split one-dimensional Bose gas and obtain unprecedented information about the dynamical states of the system. Following an initial rapid evolution, the full distributions reveal the approach towards a thermal-like steady state characterized by an effective temperature that is independent from the initial equilibrium temperature of the system before the splitting process. We conjecture that this state can be described through a generalized Gibbs ensemble and associate it with pre-thermalization.

cond-mat.quant-gas↗
arXiv2012

Inference by Minimizing Size, Divergence, or their Sum

We speed up marginal inference by ignoring factors that do not significantly contribute to overall accuracy. In order to pick a suitable subset of factors to ignore, we propose three schemes: minimizing the number of model factors under a bound on the KL divergence between pruned and full models; minimizing the KL divergence under a bound on factor count; and minimizing the weighted sum of KL divergence and factor count. All three problems are solved using an approximation of the KL divergence than can be calculated in terms of marginals computed on a simple seed graph. Applied to synthetic image denoising and to three different types of NLP parsing models, this technique performs marginal inference up to 11 times faster than loopy BP, with graph sizes reduced up to 98%-at comparable error in marginals and parsing accuracy. We also show that minimizing the weighted sum of divergence and size is substantially faster than minimizing either of the other objectives based on the approximation to divergence presented here.

cs.LG↗
arXiv2011

Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed problems using Fokas' transform method. We also give a sufficient condition guaranteeing that the solution can be represented using a series. The relevant condition, the analyticity at infinity of certain meromorphic functions within particular sectors, is significantly more concrete and easier to test than the previous criterion, based on the existence of admissible functions.

math.AP↗
arXiv2011

Absorption Imaging of Ultracold Atoms on Atom Chips

Imaging ultracold atomic gases close to surfaces is an important tool for the detailed analysis of experiments carried out using atom chips. We describe the critical factors that need be considered, especially when the imaging beam is purposely reflected from the surface. In particular we present methods to measure the atom-surface distance, which is a prerequisite for magnetic field imaging and studies of atom surface-interactions.

physics.atom-ph↗
arXiv2008

Experimental single-impulse magnetic focusing of launched cold atoms

Single-impulse three-dimensional magnetic focusing of vertically launched cold atoms has been observed. Four different configurations of the lens were used to vary the relative radial and axial focusing properties. Compact focused clouds of 85Rb were seen for all four configurations. It is shown that an atom-optical ray matrix approach for describing the lensing action is insufficient. Numerical simulation using a full approximation to the lens's magnetic field shows very good agreement with the radial focusing properties of the lens. However, the axial (vertical direction) focusing properties are less well described and the reasons for this are discussed.

physics.atom-ph↗
arXiv2006

Review of the Solar Array Telescopes

For several years the only experiments sensitive to astrophysical gamma rays with energies beyond the reach of EGRET but below that of the Cherenkov imaging telescopes have been the "solar tower" detectors. They use >2000 m2 mirror areas to sample the Cherenkov wavefront generated by <100 GeV gamma rays, obtaining Crab sensitivities of more than 6$σ$ in one ON-source hour. I will review the history of the solar tower Cherenkov experiments from 1992 to the present and their key design features. I will describe some successful analysis strategies, then summarize the principal results obtained.

astro-ph↗
arXiv2006

The Cavity of Cygnus A

In this paper, we focus on the limb-brightened, prolate spheroidal cavity of the radio galaxy Cygnus A, as revealed by the Chandra X-ray Observatory. We use the shock heated, thermal intracluster medium around the expanding cavity to infer the properties of the radio synchrotron-emitting gas inside the cavity. The gas along the N and S edges of the cavity is found to have an average temperature of 6.0 keV, which is hotter than the temperature (4.6 keV) of the adjacent intracluster gas. It is proposed that this hotter gas is intracluster gas shocked by the expanding cavity. The shock is thus inferred to be weak (Mach number 1.3, a value also inferred from the density jump at the cavity edge) and its velocity 1,460 km/s. The total kinetic power of the expansion is found to be 1.2 x 10^{46} erg/s, which is larger than both the total radio power and the power emitted by the entire intracluster medium in the 2 -- 10 keV band. It appears that most of the power of the jets in Cygnus A is currently going into heating the intracluster medium. From the derived pressure inside the cavity, there is no conclusive evidence for a component contributing pressure additional to the magnetic fields and relativistic particles responsible for the synchrotron radio emission. Further, the ratio of energy densities in positive to negative cosmic rays in Cygnus A is between 1 and 100 (the value in our Galaxy).

astro-ph↗
arXiv2004

Confronting the Superbubble Model with X-ray Observations of 30 Dor C

We present an analysis of XMM-Newton observations of the superbubble 30 Dor C and compare the results with the predictions from the standard wind-blown bubble model. We find that the observed X-ray spectra cannot be fitted satisfactorily with the model alone and that there is evidence for nonthermal X-ray emission, which is particularly important at > 4 keV. The total unabsorbed 0.1-10 keV luminosities of the eastern and western parts of the bubble are ~3 10^36 erg/s and ~5 10^36 erg/s, respectively. The unabsorbed 0.1-10 keV luminosity of the bubble model is 4 10^36 erg/s and so the power-law component contributes between 1/3 and 1/2 to the total unabsorbed luminosity in this energy band. The nature of the hard nonthermal emission is not clear, although recent supernovae in the bubble may be responsible. We expect that about one or two core-collapse supernovae could have occured and are required to explain the enrichment of the hot gas, as evidenced by the overabundance of alpha-elements by a factor of 3, compared to the mean value of 0.5 solar for the interstellar medium in the Large Magellanic Cloud. As in previous studies of various superbubbles, the amount of energy currently present in 30 Dor C is significantly less than the expected energy input from the enclosed massive stars over their lifetime. We speculate that a substantial fraction of the input energy may be radiated in far-infrared by dust grains, which are mixed with the hot gas because of the thermal conduction and/or dynamic mixing.

astro-ph↗
arXiv2003

A Chandra X-ray Study of NGC 1068: II. The Luminous X-ray Source Population

We present an analysis of the compact X-ray source population in the Seyfert~2 galaxy NGC 1068, imaged with Chandra. We find a total of 84 compact sources, of which 66 are projected onto the galactic disk of NGC 1068. Spectra of the brightest sources have been modeled with both multi-color disk blackbody and power-law models. The power-law model provides the better description of the spectrum for most of these sources. Five sources have 0.4-8 keV intrinsic luminosities greater than 10^{39} erg/s, assuming that their emission is isotropic and that they are associated with NGC 1068. We refer to these sources as Intermediate Luminosity X-ray Objects (IXOs). If these five sources are X-ray binaries accreting with luminosities that are both sub-Eddington and isotropic, then the implied source masses are >7 solar masses, and so they are inferred to be black holes. The brightest source has a much harder spectrum (Gamma = 0.9\pm0.1) than that found in Galactic black hole candidates and other IXOs. It also shows large-amplitude variability on both short-term and long-term timescales. The ratio of the number of sources with luminosities greater than 2.1 x 10^{38} erg/s in the 0.4-8 keV band to the rate of massive star formation is the same, to within a factor of two, for NGC 1068, the Antennae, NGC 5194 (the main galaxy in M51), and the Circinus galaxy. This suggests that the rate of production of X-ray binaries per massive star is approximately the same for galaxies with currently active star formation, including ``starbursts''.

astro-ph↗
arXiv2001

A Chandra X-ray Study of Cygnus A - II. The Nucleus

We report Chandra ACIS and quasi-simultaneous RXTE observations of the nearby, powerful radio galaxy Cygnus A, with the present paper focusing on the properties of the active nucleus. In the Chandra observation, the hard (> a few keV) X-ray emission is spatially unresolved with a size \approxlt 1 arcsec (1.5 kpc, H_0 = 50 km s^-1 Mpc^-1) and coincides with the radio and near infrared nuclei. In contrast, the soft (< 2 keV) emission exhibits a bi-polar nebulosity that aligns with the optical bi-polar continuum and emission-line structures and approximately with the radio jet. In particular, the soft X-ray emission corresponds very well with the [O III] λ5007 and Hα+ [N II] λλ6548, 6583 nebulosity imaged with HST. At the location of the nucleus there is only weak soft X-ray emission, an effect that may be intrinsic or result from a dust lane that crosses the nucleus perpendicular to the source axis. The spectra of the various X-ray components have been obtained by simultaneous fits to the 6 detectors. The compact nucleus is detected to 100 keV and is well described by a heavily absorbed power law spectrum with Γ_h = 1.52^{+0.12}_{-0.12} (similar to other narrow line radio galaxies) and equivalent hydrogen column N_H (nuc) = 2.0^{+0.1}_{-0.2} \times 10^{23} cm^-2. (Abstract truncated).

astro-ph↗