Finite-state Markov Chains obey Benford's Law

A sequence of real numbers (x_n) is Benford if the significands, i.e. the fraction parts in the floating-point representation of (x_n) are distributed logarithmically. Similarly, a discrete-time irreducible and aperiodic finite-state Markov chain with probability transition matrix P and limiting matrix P* is Benford if every component of both sequences of matrices (P^n - P*) and (P^{n+1}-P^n) is Benford or eventually zero. Using recent tools that established Benford behavior both for Newton's method and for finite-dimensional linear maps, via the classical theories of uniform distribution modulo 1 and Perron-Frobenius, this paper derives a simple sufficient condition (nonresonant) guaranteeing that P, or the Markov chain associated with it, is Benford. This result in turn is used to show that almost all Markov chains are Benford, in the sense that if the transition probabilities are chosen independently and continuously, then the resulting Markov chain is Benford with probability one. Concrete examples illustrate the various cases that arise, and the theory is complemented with several simulations and potential applications.Comment: 31 pages, no figure

Vascular rings: A rare cause of common respiratory symptoms

Upper airway symptoms or dysphagia may be caused by vascular anomalies, forming a ring around the trachea, oesophagus or both. To analyse the clinical presentation, use of various diagnostic techniques, treatment and follow-up we carried out a retrospective study of 38 children who had been diagnosed with a vascular ting between 1981 and 1996. We found 74% of the vascular tings to be symptomatic, with inspiratory stridor and wheezing as the main complaints. The delay between the onset of symptoms and diagnosis of a vascular ting in patients without associated anomalies ranged from 1 to 84 mo. Associated anomalies were found in 53% of cases and 80% of these anomalies consisted of associated cardiovascular malformations. Oesophagography proved to be a valuable diagnostic technique when a vascular ting was suspected. Echocardiography appeared to be of little value for the diagnosis of a vascular ring, but was essential to exclude associated cardiovascular malformations. Although angiography has always been considered to be the gold standard in the determination of the exact anatomy of vascular tings, increasing evidence is available that CT scan or MRI may replace this role. Mortality was related to co-existent tracheal deformities in 5/6 cases. Of the remaining, preoperatively symptomatic patients, relief of symptoms was achieved immediately after surgery in 43% and within 4y after surgery in 57%. Prolonged and recurrent respiratory complaints or dysphagia in infancy or childhood should alert the paediatrician to the possibility of a vascular ring

The Einstein-Vlasov sytem/Kinetic theory

The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades where the main focus has been on nonrelativistic- and special relativistic physics, e.g. to model the dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In 1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (e.g. fluid models). The first part of this paper gives an introduction to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental in order to get a good comprehension of kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity (http://www.livingreviews.org

Prospects for Spin Physics at RHIC

Colliding beams of 70% polarized protons at up to $\sqrt{s}$=500 GeV, with high luminosity, L=2$\times10^{{\rm 32}}$ cm$^{-2}$sec$^{-1}$, will represent a new and unique laboratory for studying the proton. RHIC-Spin will be the first polarized-proton collider and will be capable of copious production of jets, directly produced photons, and $W$ and $Z$ bosons. Features will include direct and precise measurements of the polarization of the gluons and of $\bar{u}$, $\bar{d}$, $u$, and $d$ quarks in a polarized proton. Parity violation searches for physics beyond the standard model will be competitive with unpolarized searches at the Fermilab Tevatron. Transverse spin will explore transversity for the first time, as well as quark-gluon correlations in the proton. Spin dependence of the total cross section and in the Coulomb nuclear interference region will be measured at collider energies for the first time. These qualitatively new measurements can be expected to deepen our understanding of the structure of matter and of the strong interaction.Comment: 51 pages, 22 figures. Scheduled to appear in the Annual Review of Nuclear and Particle Science Vol. 50, to be published in December 2000 by Annual Reviews, http://AnnualReviews.or

Surface modification of hydrophobic polymers for improvement of endothelial cell-surface interactions

The aim of this study is to improve the interaction of endothelial cells with polymers used in vascular prostheses. Polytetrafluoroethylene (PTFE; Teflon) films were treated by means of nitrogen and oxygen plasmas. Depending on the plasma exposure time, modified PTFE surfaces showed water-contact angles of 15¿58° versus 96° for unmodified PTFE. Electron spectroscopy in chemical analysis (ESCA) measurements revealed incorporation of both nitrogenand oxygen-containing groups into the PTFE surfaces, dependent on the plasma composition and exposure time. In-vitro biological evaluation of unmodified and modified PTFE surfaces showed that human endothelial cells, seeded from 20% human serum-containing culture medium, adhered well on to modified PTFE surfaces, but not on to unmodified films. Adhesion of endothelial cells on to expanded PTFE graft material (Gore-Tex) was also stimulated by plasma treatment of this substrate. On plasma-treated expanded PTFE, the adhering endothelial cells formed a monolayer, which covered the textured surface. The latter observation is important in view of the hemocompatibility of vascular grafts seeded with endothelial cells before implantation

Next-to-leading order QCD predictions for W+W+jj production at the LHC

Because the LHC is a proton-proton collider, sizable production of two positively charged W-bosons in association with two jets is possible. This process leads to a distinct signature of same sign high-pt leptons, missing energy and jets. We compute the NLO QCD corrections to the QCD-mediated part of pp -> W+W+jj. These corrections reduce the dependence of the production cross-section on the renormalization and factorization scale to about +- 10 percent. We find that a large number of W+W+jj events contain a relatively hard third jet. The presence of this jet should help to either pick up the W+W+jj signal or to reject it as an unwanted background.Comment: 15 pages, 5 (lovely) figures, v3 accepted for publication in JHEP, corrects tables in appendi

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

A powerful bursting radio source towards the Galactic Centre

Transient astronomical sources are typically powered by compact objects and usually signify highly explosive or dynamic events. While radio astronomy has an impressive record of obtaining high time resolution observations, usually it is achieved in quite narrow fields-of-view. Consequently, the dynamic radio sky is poorly sampled, in contrast to the situation in the X- and gamma-ray bands in which wide-field instruments routinely detect transient sources. Here we report a new transient source, GCRT J1745-3009, detected in 2002 during a moderately wide-field radio transient monitoring program of the Galactic center (GC) region at 0.33 GHz. The characteristics of its bursts are unlike those known for any other class of radio transient. If located in or near the GC, its brightness temperature (~10^16 K) and the implied energy density within GCRT J1745-3009 vastly exceeds that observed in most other classes of radio astronomical sources, and is consistent with coherent emission processes rarely observed. We conclude that GCRT J1745-3009 is the first member of a new class of radio transient sources, the first of possibly many new classes to be identified through current and upcoming radio surveys.Comment: 16 pages including 3 figures. Appears in Nature, 3 March 200