The Density of States and the Spectral Shift Density of Random Schroedinger Operators

In this article we continue our analysis of Schroedinger operators with a random potential using scattering theory. In particular the theory of Krein's spectral shift function leads to an alternative construction of the density of states in arbitrary dimensions. For arbitrary dimension we show existence of the spectral shift density, which is defined as the bulk limit of the spectral shift function per unit interaction volume. This density equals the difference of the density of states for the free and the interaction theory. This extends the results previously obtained by the authors in one dimension. Also we consider the case where the interaction is concentrated near a hyperplane.Comment: 1 figur

Scattering Theory Approach to Random Schroedinger Operators in One Dimension

Methods from scattering theory are introduced to analyze random Schroedinger operators in one dimension by applying a volume cutoff to the potential. The key ingredient is the Lifshitz-Krein spectral shift function, which is related to the scattering phase by the theorem of Birman and Krein. The spectral shift density is defined as the "thermodynamic limit" of the spectral shift function per unit length of the interaction region. This density is shown to be equal to the difference of the densities of states for the free and the interacting Hamiltonians. Based on this construction, we give a new proof of the Thouless formula. We provide a prescription how to obtain the Lyapunov exponent from the scattering matrix, which suggest a way how to extend this notion to the higher dimensional case. This prescription also allows a characterization of those energies which have vanishing Lyapunov exponent.Comment: 1 figur

Probe method and a Carleman function

A Carleman function is a special fundamental solution with a large parameter for the Laplace operator and gives a formula to calculate the value of the solution of the Cauchy problem in a domain for the Laplace equation. The probe method applied to an inverse boundary value problem for the Laplace equation in a bounded domain is based on the existence of a special sequence of harmonic functions which is called a {\it needle sequence}. The needle sequence blows up on a special curve which connects a given point inside the domain with a point on the boundary of the domain and is convergent locally outside the curve. The sequence yields a reconstruction formula of unknown discontinuity, such as cavity, inclusion in a given medium from the Dirichlet-to-Neumann map. In this paper, an explicit needle sequence in {\it three dimensions} is given in a closed form. It is an application of a Carleman function introduced by Yarmukhamedov. Furthermore, an explicit needle sequence in the probe method applied to the reduction of inverse obstacle scattering problems with an {\it arbitrary} fixed wave number to inverse boundary value problems for the Helmholtz equation is also given.Comment: 2 figures, final versio

A Novel Strategy Involved Anti-Oxidative Defense: The Conversion of NADH into NADPH by a Metabolic Network

The reduced nicotinamide adenine dinucleotide phosphate (NADPH) is pivotal to the cellular anti-oxidative defence strategies in most organisms. Although its production mediated by different enzyme systems has been relatively well-studied, metabolic networks dedicated to the biogenesis of NADPH have not been fully characterized. In this report, a metabolic pathway that promotes the conversion of reduced nicotinamide adenine dinucleotide (NADH), a pro-oxidant into NADPH has been uncovered in Pseudomonas fluorescens exposed to oxidative stress. Enzymes such as pyruvate carboxylase (PC), malic enzyme (ME), malate dehydrogenase (MDH), malate synthase (MS), and isocitrate lyase (ICL) that are involved in disparate metabolic modules, converged to create a metabolic network aimed at the transformation of NADH into NADPH. The downregulation of phosphoenol carboxykinase (PEPCK) and the upregulation of pyruvate kinase (PK) ensured that this metabolic cycle fixed NADH into NADPH to combat the oxidative stress triggered by the menadione insult. This is the first demonstration of a metabolic network invoked to generate NADPH from NADH, a process that may be very effective in combating oxidative stress as the increase of an anti-oxidant is coupled to the decrease of a pro-oxidant

Top Quark Mass Measurement from Dilepton Events at CDF II with the Matrix-Element Method

We describe a measurement of the top quark mass using events with two charged leptons collected by the CDF II detector from $p\bar{p}$ collisions with $\sqrt s = 1.96$ TeV at the Fermilab Tevatron. The likelihood in top mass is calculated for each event by convoluting the leading order matrix element describing $q\bar{q} \to t\bar{t} \to b\ell\nu_{\ell}\bar{b}\ell'\nu_{\ell'}$ with detector resolution functions. The presence of background events in the data sample is modeled using similar calculations involving the matrix elements for major background processes. In a data sample with integrated luminosity of 340 pb$^{-1}$, we observe 33 candidate events and measure $M_{top} = 165.2 \pm 6.1(\textrm{stat.}) \pm 3.4(\textrm{syst.}) \mathrm{~GeV}/c^2.$ This measurement represents the first application of this method to events with two charged leptons and is the most precise single measurement of the top quark mass in this channel.Comment: 21 pages, 14 figure

Precision measurement of the top quark mass from dilepton events at CDF II

We report a measurement of the top quark mass, M_t, in the dilepton decay channel of $t\bar{t}\to b\ell'^{+}\nu_{\ell'}\bar{b}\ell^{-}\bar{\nu}_{\ell}$ using an integrated luminosity of 1.0 fb^{-1} of p\bar{p} collisions collected with the CDF II detector. We apply a method that convolutes a leading-order matrix element with detector resolution functions to form event-by-event likelihoods; we have enhanced the leading-order description to describe the effects of initial-state radiation. The joint likelihood is the product of the likelihoods from 78 candidate events in this sample, which yields a measurement of M_{t} = 164.5 \pm 3.9(\textrm{stat.}) \pm 3.9(\textrm{syst.}) \mathrm{GeV}/c^2, the most precise measurement of M_t in the dilepton channel.Comment: 7 pages, 2 figures, version includes changes made prior to publication by journa

Cross Section Measurements of High-pTp_T Dilepton Final-State Processes Using a Global Fitting Method

We present a new method for studying high-$p_T$ dilepton events ($e^{\pm}e^{\mp}$, $\mu^{\pm}\mu^{\mp}$, $e^{\pm}\mu^{\mp}$) and simultaneously extracting the production cross sections of $p\bar{p} \to t\bar{t}$, $p\bar{p} \to W^+W^-$, and p\bar{p} \to \ztt at a center-of-mass energy of $\sqrt{s} = 1.96$ TeV. We perform a likelihood fit to the dilepton data in a parameter space defined by the missing transverse energy and the number of jets in the event. Our results, which use $360 {\rm pb^{-1}}$ of data recorded with the CDF II detector at the Fermilab Tevatron Collider, are $\sigma(t\bar{t}) = 8.5_{-2.2}^{+2.7}$ pb, $\sigma(W^+W^-) = 16.3^{+5.2}_{-4.4}$ pb, and \sigma(\ztt) =291^{+50}_{-46} pb.Comment: 20 pages, 2 figures, to be submitted to PRD-R

Measurement of the Ratios of Branching Fractions B(Bs -> Ds pi pi pi) / B(Bd -> Dd pi pi pi) and B(Bs -> Ds pi) / B(Bd -> Dd pi)

Using 355 pb^-1 of data collected by the CDF II detector in \ppbar collisions at sqrt{s} = 1.96 TeV at the Fermilab Tevatron, we study the fully reconstructed hadronic decays B -> D pi and B -> D pi pi pi. We present the first measurement of the ratio of branching fractions B(Bs -> Ds pi pi pi) / B(Bd -> Dd pi pi pi) = 1.05 pm 0.10 (stat) pm 0.22 (syst). We also update our measurement of B(Bs -> Ds pi) / B(Bd -> Dd pi) to 1.13 pm 0.08 (stat) pm 0.23 (syst) improving the statistical uncertainty by more than a factor of two. We find B(Bs -> Ds pi) = [3.8 pm 0.3 (stat) pm 1.3 (syst)] \times 10^{-3} and B(Bs -> Ds pi pi pi) = [8.4 pm 0.8 (stat) pm 3.2 (syst)] \times 10^{-3}.Comment: 7 pages, 2 figure

Treating asthma with omega-3 fatty acids: where is the evidence? A systematic review

BACKGROUND: Considerable interest exists in the potential therapeutic value of dietary supplementation with the omega-3 fatty acids. Given the interplay between pro-inflammatory omega-6 fatty acids, and the less pro-inflammatory omega-3 fatty acids, it has been thought that the latter could play a key role in treating or preventing asthma. The purpose was to systematically review the scientific-medical literature in order to identify, appraise, and synthesize the evidence for possible treatment effects of omega-3 fatty acids in asthma. METHODS: Medline, Premedline, Embase, Cochrane Central Register of Controlled Trials, CAB Health, and, Dissertation Abstracts were searched to April 2003. We included randomized controlled trials (RCT's) of subjects of any age that used any foods or extracts containing omega-3 fatty acids as treatment or prevention for asthma. Data included all asthma related outcomes, potential covariates, characteristics of the study, design, population, intervention/exposure, comparators, and co interventions. RESULTS: Ten RCT's were found pertinent to the present report. CONCLUSION: Given the largely inconsistent picture within and across respiratory outcomes, it is impossible to determine whether or not omega-3 fatty acids are an efficacious adjuvant or monotherapy for children or adults. Based on this systematic review we recommend a large randomized controlled study of the effects of high-dose encapsulated omega-3 fatty acids on ventilatory and inflammatory measures of asthma controlling diet and other asthma risk factors. This review was limited because Meta-analysis was considered inappropriate due to missing data; poorly or heterogeneously defined populations, interventions, intervention-comparator combinations, and outcomes. In addition, small sample sizes made it impossible to meaningfully assess the impact on clinical outcomes of co-variables. Last, few significant effects were found