An extremal problem for the Bergman kernel of orthogonal polynomials

Let $\Gamma \subset \mathbb C$ be a curve of class $C(2,\alpha)$. For $z_{0}$ in the unbounded component of ${\mathbb C}\setminus \Gamma$, and for $n=1,2,...$, let $\nu_n$ be a probability measure with supp$(\nu_{n})\subset \Gamma$ which minimizes the Bergman function $B_{n}(\nu,z):=\sum_{k=0}^{n}|q_{k}^{\nu}(z)|^{2}$ at $z_{0}$ among all probability measures $\nu$ on $\Gamma$ (here, $\{q_{0}^{\nu},\ldots,q_{n}^{\nu}\}$ are an orthonormal basis in $L^2(\nu)$ for the holomorphic polynomials of degree at most $n$). We show that $\{\nu_{n}\}_n$ tends weak-* to $\hat\delta_{z_{0}}$, the balayage of the point mass at $z_0$ onto $\Gamma$, by relating this to an optimization problem for probability measures on the unit circle. Our proof makes use of estimates for Faber polynomials associated to $\Gamma$.Comment: To appear in Constructive Approximatio

Cellular and molecular mechanisms underlying blood vessel lumen formation

The establishment of a functional vascular system requires multiple complex steps throughout embryogenesis, from endothelial cell (EC) specification to vascular patterning into venous and arterial hierarchies. Following the initial assembly of ECs into a network of cord-like structures, vascular expansion and remodeling occur rapidly through morphogenetic events including vessel sprouting, fusion, and pruning. In addition, vascular morphogenesis encompasses the process of lumen formation, critical for the transformation of cords into perfusable vascular tubes. Studies in mouse, zebrafish, frog, and human endothelial cells have begun to outline the cellular and molecular requirements underlying lumen formation. Although the lumen can be generated through diverse mechanisms, the coordinated participation of multiple conserved molecules including transcription factors, small GTPases, and adhesion and polarity proteins remains a fundamental principle, leading us closer to a more thorough understanding of this complex event

Simulation Application for the LHCb Experiment

We describe the LHCb detector simulation application (Gauss) based on the Geant4 toolkit. The application is built using the Gaudi software framework, which is used for all event-processing applications in the LHCb experiment. The existence of an underlying framework allows several common basic services such as persistency, interactivity, as well as detector geometry description or particle data to be shared between simulation, reconstruction and analysis applications. The main benefits of such common services are coherence between different event-processing stages as well as reduced development effort. The interfacing to Geant4 toolkit is realized through a facade (GiGa) which minimizes the coupling to the simulation engine and provides a set of abstract interfaces for configuration and event-by-event communication. The Gauss application is composed of three main blocks, i.e. event generation, detector response simulation and digitization which reflect the different stages performed during the simulation job. We describe the overall design as well as the details of Gauss application with a special emphasis on the configuration and control of the underlying simulation engine. We also briefly mention the validation strategy and the planing for the LHCb experiment simulation.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 6 pages, LaTeX, 9 eps figures. PSN TUMT00

Quantum nature of the critical points of substances

Thermodynamics of chemical elements, based on the two-component electron-nuclear plasma model shows that the critical parameters for the liquid-vapor transition are the quantum values for which the classical limit is absent.Comment: 4 pages, no figure

Valuation of knowledge and ignorance in mesolimbic reward circuitry

The pursuit of knowledge is a basic feature of human nature. However, in domains ranging from health to finance people sometimes choose to remain ignorant. Here, we show that valence is central to the process by which the human brain evaluates the opportunity to gain information, explaining why knowledge may not always be preferred. We reveal that the mesolimbic reward circuitry selectively treats the opportunity to gain knowledge about future favorable outcomes, but not unfavorable outcomes, as if it has positive utility. This neural coding predicts participants’ tendency to choose knowledge about future desirable outcomes more often than undesirable ones, and to choose ignorance about future undesirable outcomes more often than desirable ones. Strikingly, participants are willing to pay both for knowledge and ignorance as a function of the expected valence of knowledge. The orbitofrontal cortex (OFC), however, responds to the opportunity to receive knowledge over ignorance regardless of the valence of the information. Connectivity between the OFC and mesolimbic circuitry could contribute to a general preference for knowledge that is also modulated by valence. Our findings characterize the importance of valence in information seeking and its underlying neural computation. This mechanism could lead to suboptimal behavior, such as when people reject medical screenings or monitor investments more during bull than bear markets

Influence of Topological Edge States on the Properties of Al/Bi2Se3/Al Hybrid Josephson Devices

In superconductor-topological insulator-superconductor hybrid junctions, the barrier edge states are expected to be protected against backscattering, to generate unconventional proximity effects, and, possibly, to signal the presence of Majorana fermions. The standards of proximity modes for these types of structures have to be settled for a neat identification of possible new entities. Through a systematic and complete set of measurements of the Josephson properties we find evidence of ballistic transport in coplanar Al-Bi2Se3-Al junctions that we attribute to a coherent transport through the topological edge state. The shunting effect of the bulk only influences the normal transport. This behavior, which can be considered to some extent universal, is fairly independent of the specific features of superconducting electrodes. A comparative study of Shubnikov - de Haas oscillations and Scanning Tunneling Spectroscopy gave an experimental signature compatible with a two dimensional electron transport channel with a Dirac dispersion relation. A reduction of the size of the Bi2Se3 flakes to the nanoscale is an unavoidable step to drive Josephson junctions in the proper regime to detect possible distinctive features of Majorana fermions.Comment: 11 pages, 14 figure

Citation

Second-order dipolar order in magic-angle spinning nuclear magnetic resonance J. Chem. Phys. 135, 154507 (2011) Single crystal nuclear magnetic resonance in spinning powders J. Chem. Phys. 135, 144201 (2011) Resistive detection of optically pumped nuclear polarization with spin phase transition peak at Landau level filling factor 2/3 Appl. Phys. Lett. 99, 112106 (2011) High-resolution 13C nuclear magnetic resonance evidence of phase transition of Rb,Cs-intercalated singlewalled nanotubes J. Appl. Phys. 110, 054306 (2011) Distribution of non-uniform demagnetization fields in paramagnetic bulk solids J. Appl. Phys. 110, 013902 (2011) Additional information on J. Chem. Phys. In this article, we present an alternative expansion scheme called Floquet-Magnus expansion (FME) used to solve a time-dependent linear differential equation which is a central problem in quantum physics in general and solid-state nuclear magnetic resonance (NMR) in particular. The commonly used methods to treat theoretical problems in solid-state NMR are the average Hamiltonian theory (AHT) and the Floquet theory (FT), which have been successful for designing sophisticated pulse sequences and understanding of different experiments. To the best of our knowledge, this is the first report of the FME scheme in the context of solid state NMR and we compare this approach with other series expansions. We present a modified FME scheme highlighting the importance of the (timeperiodic) boundary conditions. This modified scheme greatly simplifies the calculation of higher order terms and shown to be equivalent to the Floquet theory (single or multimode time-dependence) but allows one to derive the effective Hamiltonian in the Hilbert space. Basic applications of the FME scheme are described and compared to previous treatments based on AHT, FT, and static perturbation theory. We discuss also the convergence aspects of the three schemes (AHT, FT, and FME) and present the relevant references

Using Mussel Isotope Ratios to Assess Anthropogenic Nitrogen Inputs to Freshwater Ecosystems

Stable nitrogen isotope ratios (δ15N) of freshwater mussels from a series of lakes and ponds were related to watershed land use characteristics to assess their utility in determining the source of nitrogen inputs to inland water bodies. Nitrogen isotope ratios measured in freshwater mussels from 19 lakes and ponds in Rhode Island, U.S.A., ranged from 4.9–12.6% and were found to significantly correlate with the fraction of residential development in 100 and 200 m buffer zones around the ponds. Mussel δ15N values in 12 of the 19 ponds also showed significant correlation with average dissolved nitrate concentrations, which ranged from 23–327 μg L-1. These observations, in light of previous studies which link elevated δ15N values of nitrogen derived from septic wastewater with those seen in biota, suggest that mussel isotope ratios may reflect nitrogen source in freshwater ecosystems. We followed an iterative approach using multiple regression analysis to assess the relationship between mussel δ15N and the land use categories fraction residential development, fraction feedlot agriculture, fraction row-crop agriculture, and fraction natural vegetation in 100 and 200 m buffer zones and pond watersheds. From this we developed a simple regression model to predict mussel δ15N from the fraction of residential development in the 200 m buffer zone around the pond. Subsequent testing with data from 16 additional sites in the same ecoregion led us to refine the model by incorporating the fraction of natural vegetation. The overall average absolute difference between measured and predicted δ15N values using the two-parameter model was 1.6%. Potential sources of error in the model include differences in the scale and categorization of land-use data used to generate and test the model, differences in physical characteristics, such as retention time and range of residential development, and exclusion of sources of enriched nitrogen such as runoff from feedlot operations or increased nitrogen loading from inefficient or failed septic systems