Modern Statistical Methods for GLAST Event Analysis

We describe a statistical reconstruction methodology for the GLAST LAT. The methodology incorporates in detail the statistics of the interactions of photons and charged particles with the tungsten layers in the LAT, and uses the scattering distributions to compute the full probability distribution over the energy and direction of the incident photons. It uses model selection methods to estimate the probabilities of the possible geometrical configurations of the particles produced in the detector, and numerical marginalization over the energy loss and scattering angles at each layer. Preliminary results show that it can improve on the tracker-only energy estimates for muons and electrons incident on the LAT.Comment: To appear in the proceedings of the First GLAST Symposium (held at Stanford University, 5-8 February 2007

Riesz external field problems on the hypersphere and optimal point separation

We consider the minimal energy problem on the unit sphere $\mathbb{S}^d$ in the Euclidean space $\mathbb{R}^{d+1}$ in the presence of an external field $Q$, where the energy arises from the Riesz potential $1/r^s$ (where $r$ is the Euclidean distance and $s$ is the Riesz parameter) or the logarithmic potential $\log(1/r)$. Characterization theorems of Frostman-type for the associated extremal measure, previously obtained by the last two authors, are extended to the range $d-2 \leq s < d - 1.$ The proof uses a maximum principle for measures supported on $\mathbb{S}^d$. When $Q$ is the Riesz $s$-potential of a signed measure and $d-2 \leq s <d$, our results lead to explicit point-separation estimates for $(Q,s)$-Fekete points, which are $n$-point configurations minimizing the Riesz $s$-energy on $\mathbb{S}^d$ with external field $Q$. In the hyper-singular case $s > d$, the short-range pair-interaction enforces well-separation even in the presence of more general external fields. As a further application, we determine the extremal and signed equilibria when the external field is due to a negative point charge outside a positively charged isolated sphere. Moreover, we provide a rigorous analysis of the three point external field problem and numerical results for the four point problem.Comment: 35 pages, 4 figure

An Electrostatics Problem on the Sphere Arising from a Nearby Point Charge

For a positively charged insulated d-dimensional sphere we investigate how the distribution of this charge is affected by proximity to a nearby positive or negative point charge when the system is governed by a Riesz s-potential 1/r^s, s>0, where r denotes Euclidean distance between point charges. Of particular interest are those distances from the point charge to the sphere for which the equilibrium charge distribution is no longer supported on the whole of the sphere (i.e. spherical caps of negative charge appear). Arising from this problem attributed to A. A. Gonchar are sequences of polynomials of a complex variable that have some fascinating properties regarding their zeros.Comment: 44 pages, 9 figure

Topological superconductivity in the extended Kitaev-Heisenberg model

We study superconducting pairing in the doped Kitaev-Heisenberg model by taking into account the recently proposed symmetric off-diagonal exchange $\Gamma$. By performing a mean-field analysis, we classify all possible superconducting phases in terms of symmetry, explicitly taking into account effects of spin-orbit coupling. Solving the resulting gap equations self-consistently, we map out a phase diagram that involves several topologically nontrivial states. For $\Gamma<0$, we find a competition between a time-reversal symmetry breaking chiral phase with Chern number $\pm1$ and a time-reversal symmetric nematic phase that breaks the rotational symmetry of the lattice. On the other hand, for $\Gamma \geq 0$ we find a time-reversal symmetric phase that preserves all the lattice symmetries, thus yielding clearly distinguishable experimental signatures for all superconducting phases. Both of the time-reversal symmetric phases display a transition to a $\mathbb{Z}_2$ non-trivial phase at high doping levels. Finally, we also include a symmetry-allowed spin-orbit coupling kinetic energy and show that it destroys a tentative symmetry protected topological order at lower doping levels. However, it can be used to tune the time-reversal symmetric phases into a $\mathbb{Z}_2$ non-trivial phase even at lower doping

Theory of strong localization effects of light in disordered loss or gain media

We present a systematical theory for the interplay of strong localization effects and absorption or gain of classical waves in 3-dimensional, disordered dielectrics. The theory is based on the selfconsistent Cooperon resummation, implementing the effects of energy conservation and its absorptive or emissive corrections by an exact, generalized Ward identity. Substantial renormalizations are found, depending on whether the absorption/gain occurs in the scatterers or in the background medium. We find a finite, gain-induced correlation volume which may be significantly smaller than the scale set by the scattering mean free path, even if there are no truly localized modes. Possible consequences for coherent feedback in random lasers as well as the possibility of oscillatory in time behavior induced by sufficiently strong gain are discussed.Comment: Published versio

Quantitative measurement of the surface charge density

We present a method of measuring the charge density on dielectric surfaces. Similar to electrostatic force microscopy we record the electrostatic interaction between the probe and the sample surface, but at large tip-sample distances. For calibration we use a pyroelectric sample which allows us to alter the surface charge density by a known amount via a controlled temperature change. For proof of principle we determined the surface charge density under ambient conditions of ferroelectric lithium niobate

Impact of Electrostatic Forces in Contact Mode Scanning Force Microscopy

In this $\ll$ contribution we address the question to what extent surface charges affect contact-mode scanning force microscopy measurements. % We therefore designed samples where we could generate localized electric field distributions near the surface as and when required. % We performed a series of experiments where we varied the load of the tip, the stiffness of the cantilever and the hardness of the sample surface. % It turned out that only for soft cantilevers could an electrostatic interaction between tip and surface charges be detected, irrespective of the surface properties, i.\,e. basically regardless its hardness. % We explain these results through a model based on the alteration of the tip-sample potential by the additional electric field between charged tip and surface charges

Extraintestinal Pathogenic Escherichia coli: A Combination of Virulence with Antibiotic Resistance

Escherichia coli represents an incredible versatile and diverse enterobacterial species and can be subdivided into the following; (i) intestinal non-pathogenic, commensal isolates. (ii) Intestinal pathogenic isolates and (iii) extraintestinal pathogenic E. coli or ExPEC isolates. The presence to several putative virulence genes has been positively linked with the pathogenicity of ExPEC. E. coli remains one of the most frequent causes of nosocomial and community-acquired bacterial infections including urinary tract infections, enteric infections, and systemic infections in humans. ExPEC has emerged in 2000s as an important player in the resistance to antibiotics including the cephalosporins and fluoroquinolones. Most importantly among ExPEC is the increasing recognition of isolates producing “newer β-lactamases” that consists of plasmid-mediated AmpC β-lactamases (e.g., CMY), extended-spectrum β-lactamases (e.g., CTX-M), and carbapenemases (e.g., NDM). This review will highlight aspects of virulence associated with ExPEC, provide a brief overview of plasmid-mediated resistance to β-lactams including the characteristics of the successful international sequence types such as ST38, ST131, ST405, and ST648 among ExPEC