Regularly Varying Measures on Metric Spaces: Hidden Regular Variation and Hidden Jumps

We develop a framework for regularly varying measures on complete separable metric spaces $\mathbb{S}$ with a closed cone $\mathbb{C}$ removed, extending material in Hult & Lindskog (2006), Das, Mitra & Resnick (2013). Our framework provides a flexible way to consider hidden regular variation and allows simultaneous regular variation properties to exist at different scales and provides potential for more accurate estimation of probabilities of risk regions. We apply our framework to iid random variables in $\mathbb{R}_+^\infty$ with marginal distributions having regularly varying tails and to c\`adl\`ag L\'evy processes whose L\'evy measures have regularly varying tails. In both cases, an infinite number of regular variation properties coexist distinguished by different scaling functions and state spaces.Comment: 40 page

Spin-Hall Effect in A Symmetric Quantum Wells by A Random Rashba Field

Changes dopant ion concentrations in the sides of a symmetric quantum well are known to create a random Rashba-type spin-orbit coupling. Here we demonstrate that, as a consequence, a finite size spin-Hall effect is also present. Our numerical algorithm estimates the result of the Kubo formula for the spin-Hall conductivity, by using a tight-binding approximation of the Hamiltonian in the framework of a time-dependent Green's function formalism, well suited for very large systems.Comment: 4 pages, 4 figures in eps forma

TBC of the thoracic wall with fistulisation through the breast

A 53-year-old North African woman presented with a longstanding history of ulcerations of the right breast. Physical examination showed (Fig. 1 subfigure) an ulcer of 1.5 cm in the outer inferior quadrant, another smaller areolar ulcer and a discharging sinus tract in the inframammary sulcus. Apart from female genital mutilation, her past medical history was negative. Laboratory work up was essentially normal, culture of the ulcers were taken. Mammography showed infra-areolar skin retraction, associated with irregular, high density distortion of the breast tissue. Ultrasound (Fig. 1) revealed communicating sinus tracts coming from an intercostal mass with central necrosis. Mobile internal echoes were suggestive for abscess formation and a truecut biopsy was taken. An important granulomatous inflammatory pattern and fibrosis were found. Axillary lymphadenopathy was present

Rethinking our understanding of the pathogenesis of necrotic enteritis in chickens

For decades, low doses of antibiotics have been used widely in animal production to promote growth. However, there is a trend to reduce this use of antibiotics in feedstuffs, and legislation is now in place in Europe to prohibit their use in this way. As a consequence, economically important diseases, such as necrotic enteritis (NE) of chickens, that are caused by Clostridium perfringens have become more prevalent. Recent research is creating a paradigm shift in our understanding of the pathogenesis of NE and is now providing information that will be necessary to monitor and control the incidence of NE in poultry

Homodyne locking of a squeezer

We report on the successful implementation of a new approach to locking the frequencies of an OPO-based squeezed-vacuum source and its driving laser. The technique allows the simultaneous measurement of the phase-shifts induced by a cavity, which may be used for the purposes of frequency-locking, as well as the simultaneous measurement of the sub-quantum-noise-limited (sub-QNL) phase quadrature output of the OPO. The homodyne locking technique is cheap, easy to implement and has the distinct advantage that subsequent homodyne measurements are automatically phase-locked. The homodyne locking technique is also unique in that it is a sub-QNL frequency discriminator.Comment: Accepted to Optics Letter

Nonergodic measurements of qubit frequency noise

Slow fluctuations of a qubit frequency are one of the major problems faced by quantum computers. To understand their origin it is necessary to go beyond the analysis of their spectra. We show that characteristic features of the fluctuations can be revealed using comparatively short sequences of periodically repeated Ramsey measurements, with the sequence duration smaller than needed for the noise to approach the ergodic limit. The outcomes distribution and its dependence on the sequence duration are sensitive to the nature of noise. The time needed for quantum measurements to display quasi-ergodic behavior can strongly depend on the measurement parameters