Convergence of continuous-time quantum walks on the line

The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that depends on the initial state of the particle. This convergence behavior has recently been demonstrated for the simplest continuous-time random walk [see quant-ph/0408140]. In this brief report, we use a different technique to establish the same convergence for a very large class of continuous-time quantum walks, and we identify the limit distribution in the general case.Comment: Version to appear in Phys. Rev.

Smear correction of highly-variable, frame-transfer-CCD images with application to polarimetry

Image smear, produced by the shutter-less operation of frame transfer CCD detectors, can be detrimental for many imaging applications. Existing algorithms used to numerically remove smear, do not contemplate cases where intensity levels change considerably between consecutive frame exposures. In this report we reformulate the smearing model to include specific variations of the sensor illumination. The corresponding desmearing expression and its noise properties are also presented and demonstrated in the context of fast imaging polarimetry.Comment: Article accepted for publication in Applied Optics on 08 Jun 201

Instrumentation for solar spectropolarimetry: state of the art and prospects

Given its unchallenged capabilities in terms of sensitivity and spatial resolution, the combination of imaging spectropolarimetry and numeric Stokes inversion represents the dominant technique currently used to remotely sense the physical properties of the solar atmosphere and, in particular, its important driving magnetic field. Solar magnetism manifests itself in a wide range of spatial, temporal, and energetic scales. The ubiquitous but relatively small and weak fields of the so-called quiet Sun are believed today to be crucial for answering many open questions in solar physics, some of which have substantial practical relevance due to the strong Sun?Earth connection. However, such fields are very challenging to detect because they require spectropolarimetric measurements with high spatial (sub-arcsec), spectral (<100  mÅ), and temporal (<10  s) resolution along with high polarimetric sensitivity (<0.1  %   of the intensity). We collect and discuss both well-established and upcoming instrumental solutions developed during the last decades to push solar observations toward the above-mentioned parameter regime. This typically involves design trade-offs due to the high dimensionality of the data and signal-to-noise-ratio considerations, among others. We focus on the main three components that form a spectropolarimeter, namely, wavelength discriminators, the devices employed to encode the incoming polarization state into intensity images (polarization modulators), and the sensor technologies used to register them. We consider the instrumental solutions introduced to perform this kind of measurements at different optical wavelengths and from various observing locations, i.e., ground-based, from the stratosphere or near space.Fil: Iglesias, Francisco Andres. Universidad Tecnológica Nacional. Facultad Regional de Mendoza; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; ArgentinaFil: Feller, Alex. Max Planck Institut Fur Sonnensystemforschung; Alemani

Estimating the effects of a California gun control program with Multitask Gaussian Processes

Gun violence is a critical public safety concern in the United States. In 2006 California implemented a unique firearm monitoring program, the Armed and Prohibited Persons System (APPS), to address gun violence in the state. The APPS program first identifies those firearm owners who become prohibited from owning one due to federal or state law, then confiscates their firearms. Our goal is to assess the effect of APPS on California murder rates using annual, state-level crime data across the US for the years before and after the introduction of the program. To do so, we adapt a non-parametric Bayesian approach, multitask Gaussian Processes (MTGPs), to the panel data setting. MTGPs allow for flexible and parsimonious panel data models that nest many existing approaches and allow for direct control over both dependence across time and dependence across units, as well as natural uncertainty quantification. We extend this approach to incorporate non-Normal outcomes, auxiliary covariates, and multiple outcome series, which are all important in our application. We also show that this approach has attractive Frequentist properties, including a representation as a weighting estimator with separate weights over units and time periods. Applying this approach, we find that the increased monitoring and enforcement from the APPS program substantially decreased homicides in California. We also find that the effect on murder is driven entirely by declines in gun-related murder with no measurable effect on non-gun murder. Estimated cost per murder avoided are substantially lower than conventional estimates of the value of a statistical life, suggesting a very high benefit-cost ratio for this enforcement effort

Covers of acts over monoids II

In 1981 Edgar Enochs conjectured that every module has a flat cover and finally proved this in 2001. Since then a great deal of effort has been spent on studying different types of covers, for example injective and torsion free covers. In 2008, Mahmoudi and Renshaw initiated the study of flat covers of acts over monoids but their definition of cover was slightly different from that of Enochs. Recently, Bailey and Renshaw produced some preliminary results on the `other' type of cover and it is this work that is extended in this paper. We consider free, divisible, torsion free and injective covers and demonstrate that in some cases the results are quite different from the module case

Structural origin of the weak germanate anomaly in lead germanate glass properties

Binary PbO–GeO2 glasses have been studied in detail from 5 to 75 mol% PbO using high-resolution neutron diffraction, high-energy X-ray diffraction, 207-Pb NMR, pycnometry, and thermal analysis. The Ge–O coordination number displays a broad maximum nGeO = 4.14(3) close to 27 mol% PbO. This is smaller than the maximum nGeO = 4.3 reported in CaO–GeO2 glasses but occurs at a similar composition. This structural behavior appears to explain the relatively weak germanate anomaly manifest in lead germanate glasses, for example as a maximum in the measured atom number density and a plateau in the glass transition temperatures. The structural role of Pb(II) is complex. On the one hand, short covalent Pb–O bonds and small Pb–O coordination numbers of ∼3 to 4 indicate glass network former character for Pb(II), associated with a stereochemically active electron lone pair. On the other hand, the presence of some GeO5 or GeO6 units, in addition to the majority GeO4 tetrahedral species, indicates some modifier character of Pb(II) at low PbO contents, giving rise to the observed weak germanate anomaly, as well as elongation and enhanced ionicity of the Pb–O bonds. Overall, the observed structural behavior of Pb(II) in lead germanate glasses appears as intermediate between that observed in lead silicate and lead borate glasses. Despite rapid quenching, at low PbO contents, the glasses studied exhibited nanoscale heterogeneity, evidenced by small-angle X-ray scattering consistent with the early stages of spinodal decomposition

Electromagnetic navigation transthoracic needle aspiration for the diagnosis of pulmonary nodules: A safety and feasibility pilot study

BACKGROUND: Pulmonary nodules remain a diagnostic challenge for physicians. Minimally invasive biopsy methods include bronchoscopy and CT guided transthoracic needle aspiration (TTNA). A novel electromagnetic guidance transthoracic needle aspiration (ETTNA) procedure which can be combined with navigational bronchoscopy (NB) and endobronchial ultrasound (EBUS) in a single setting has become available. METHODS: A prospective pilot study examining the safety, feasibility and diagnostic yield of ETTNA in a single procedural setting. All patients enrolled underwent EBUS for lung cancer staging followed by NB and ETTNA. Feasibility of performing ETTNA and a safety assessment by recording procedural related complications including pneumothorax or bleeding was performed. Diagnostic yield of ETTNA defined by a definitive pathologic tissue diagnosis was recorded. An additional diagnostic yield analysis was performed using a cohort analysis of combined interventions (EBUS + NB + ETTNA). All non-diagnostic biopsies were either followed with radiographic imaging or a surgical biopsy was performed. RESULTS: Twenty-four subjects were enrolled. ETTNA was feasible in 96% of cases. No bleeding events occurred. There were five pneumothoraces (21%) of which only two (8%) subjects required drainage. The diagnostic yield for ETTNA alone was 83% and increased to 87% (P=0.0016) when ETTNA was combined with NB. When ETTNA and NB were performed with EBUS for complete staging, the diagnostic yield increased further to 92% (P=0.0001). CONCLUSIONS: This is the first human pilot study demonstrating an acceptable safety and feasibility profile with a novel ETTNA system. Further studies are needed to investigate the increased diagnostic yield from this pilot study

MAS-NMR Studies of Carbonate Retention in a Very Wide Range of Na2O-SiO2 Glasses

Glasses that contain carbon are of geological interest, and the form of that carbon can be probed by Magic-Angle Spinning Nuclear Magnetic Resonance (MAS-NMR) spectroscopy. Previous studies of the Na2O-SiO2 glass system could only reach 56 mol% Na2O. Here we reproduce and extend those studies to cover a very wide compositional range, from 20 to 70 mol% Na2O, by using a combination of conventional melt-quench and twin roller quenching technologies on natural and 99% 13C-enriched sodium silicate glasses. 13C MAS-NMR reveals that measurable levels of carbon retention occur above at least 40 mol% Na2O,and takes the form of CO32- ions incorporated in the glass structure. These CO32- anions are surrounded by Na+ cations, forming nanoscale domains in a sodium silicate glass network. 23Na MAS-NMR showed a linear decrease in mean Na—O bond length with increasing Na2O content, up to 60 mol% Na2O, above which the mean Na—O bond length increased. Elemental analysis detected significant (>5%) carbonate by mass in the 65 and 70 mol% Na2O glasses. For the 70 mol% Na2O glass, 13C and 23Na MAS-NMR detected ordered nanoscale domains composed of only Na2O and CO2. These results have shown the quantity and nature of carbon retention in the archetypal sodium silicate glass system, which will better inform structural models and carbonate solubility limits

Lead silicate glass structure : new insights from diffraction and modeling of probable lone pair locations

Structures of binary PbO‐SiO2 glasses have been studied in detail over the compositional range 35 to 80 mol% PbO using high‐resolution neutron diffraction, high‐energy X‐ray diffraction, static 207Pb NMR, and structural modeling. The changes in the local environment of Pb(II) are subtle; it has a low coordination to oxygen (∼3 to 4) plus a stereochemically active electron lone pair and, thus, behaves as a glass network forming (or intermediate) cation over the entire composition range. This conclusion contradicts previous reports that Pb(II) is a network modifier at low concentrations, and is supported by an analysis of lead and alkaline earth silicate glass molar volumes. The Pb‐O peak bond length shortens by 0.04 Å with increasing PbO content, indicating stronger, more covalent bonding, and consistent with an increase in the number of short (≤ 2.70 Å) Pb‐O bonds, from 3.3 to 3.6. This is accompanied by increased axial symmetry of the Pb(II) sites, and is interpreted as a gradual transition toward square pyramidal [PbO4] sites such as those found in crystalline PbO polymorphs. An attendant decrease in the periodicity associated with the first sharp diffraction peak (FSDP) toward that of β‐PbO, accompanied by increases in the correlation lengths associated with the plumbite network (FSDP) and silicate anions (neutron prepeak), provides evidence of increased intermediate‐range order and has implications for the glass forming limit imposed by crystallization. Pb(II) electron lone pairs occupy the natural voids within the silicate network at low PbO contents, while at high PbO contents they aggregate to create voids that form part of the plumbite network, analogous to the open channels in Pb11Si3O17 and the layered structures of α‐ and β‐PbO. Si‐O and Pb‐O bond lengths have been correlated with 29Si and 207Pb NMR chemical shifts, respectively. This is the first time that such correlations have been demonstrated for glasses and attests to the accuracy with which pulsed neutron total scattering can measure average bond lengths