D-modules on Smooth Toric Varieties

Let X be a smooth toric variety. David Cox introduced the homogeneous coordinate ring S of X and its irrelevant ideal B. Extending well-known results on projective space, Cox established the following: (1) the category of quasi-coherent sheaves on X is equivalent to the category of graded S-modules modulo B-torsion, (2) the variety X is a geometric quotient of Spec(S) V(B) by a suitable torus action. We provide the D-module version of these results. More specifically, let A denote the ring of differential operators on Spec(S). We show that the category of D-modules on X is equivalent to a subcategory of graded A-modules modulo B-torsion. Additionally, we prove that the characteristic variety of a D-module is a geometric quotient of an open subset of the characteristic variety of the associated A-module and that holonomic D-modules correspond to holonomic A-modules.Comment: AMS-LaTeX, 28 page

Single microwave photon detection in the micromaser

High efficiency single photon detection is an interesting problem for many areas of physics, including low temperature measurement, quantum information science and particle physics. For optical photons, there are many examples of devices capable of detecting single photons with high efficiency. However reliable single photon detection of microwaves is very difficult, principally due to their low energy. In this paper we present the theory of a cascade amplifier operating in the microwave regime that has an optimal quantum efficiency of 93%. The device uses a microwave photon to trigger the stimulated emission of a sequence of atoms where the energy transition is readily detectable. A detailed description of the detector's operation and some discussion of the potential limitations of the detector are presented.Comment: 8 pages, 5 figure

Dichotomy results for delay differential equations with negative Schwarzian

We gain further insight into the use of the Schwarzian derivative to obtain new results for a family of functional differential equations including the famous Wright's equation and the Mackey-Glass type delay differential equations. We present some dichotomy results, which allow us to get easily computable bounds of the global attractor. We also discuss related conjectures, and formulate new open problems.Comment: 16 pages, submitted to Chaos,Solitons,Fractal

Problems with Fitting to the Power-Law Distribution

This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood estimation (MLE) is far more robust. Finally, it presents a new table for performing the Kolmogorov-Smirnof test for goodness-of-fit tailored to power-law distributions in which the power-law exponent is estimated using MLE. The techniques presented here will advance the application of complex network theory by allowing reliable estimation of power-law models from data and further allowing quantitative assessment of goodness-of-fit of proposed power-law models to empirical data.Comment: 4 pages, 1 figure, 2 table

Service based comparison of group cognitive behavior therapy to waiting list control for chronic fatigue syndrome with regard to symptom reduction and positive psychological dimensions

Background: Although chronic fatigue syndrome (CFS) sometimes referred to as myalgic encephalomyelitis (ME) is a very challenging condition to treat, there is evidence that individual cognitive behavioral therapy (ICBT) can be effective for treatment and management of its symptoms. Furthermore, group cognitive behavioral therapy (GCBT) is emerging as promising treatment for the condition. The aim of the present study was to explore further the effectiveness of GCBT in a routine clinical setting and to investigate associated positive psychological effects related to GCBT. Methods: In this pragmatic, non-randomized, controlled trial, 28 people acted as their own waiting list control by completing a range of measures 8 weeks prior to taking part in the GCBT. The intervention consisted of 8 consecutive weeks of 2.5-hour sessions. Results: Repeated measures analysis of covariance revealed significant improvements in physical fatigue (F = 28.31, P < .01, effect size d = 0.52), mental fatigue (F = 7.72, P < .01, effect size d = 0.22), and depressive symptoms (Beck depression inventory-fast screen for medical individuals [BDI-FS]: F = 11.43, P < .01, effect size d = 0.30; hospital anxiety and depression scale [HADS-D]: F = 16.72, P < .01, effect size d = 0.38) compared with the waiting list. Improvements in quality of life (F = 7.56, P < .01, effect size d = 0.23), hope (F = 15.15, P < .01, effect size d = 0.36), and optimism (F = 8.17, P < .01, effect size d = 0.23) were also identified, but no change was reported for anxiety levels. Global outcome measures revealed that the majority of the individuals found the treatment beneficial and were satisfied with the results. Conclusion: GCBT is a beneficial and cost-effective treatment that individuals find amenable in routine clinical practice for CFS. Additionally we have described important effects emerged on positive psychological dimensions such as hope and optimism potentially enhancing the overall benefit

Myelination of the right parahippocampal cingulum is associated with physical activity in young healthy adults

Recent evidence suggests that individual differences in physical activity (PA) may be associated with individual differences in white matter microstructure and with grey matter volume of the hippocampus. Therefore, this study investigated the association between PA and white matter microstructure of pathways connecting to the hippocampus. A total of 33 young, healthy adults underwent magnetic resonance imaging (MRI). High angular resolution diffusion-weighted imaging and multi-component relaxometry MRI scans (multi-component driven equilibrium pulse observation of T1 and T2) were acquired for each participant. Activity levels (AL) of participants were calculated from 72-h actigraphy recordings. Tractography using the damped Richardson Lucy algorithm was used to reconstruct the fornix and bilateral parahippocampal cinguli (PHC). The mean fractional anisotropy (FA) and the myelin water fraction (MWF), a putative marker of myelination, were determined for each pathway. A positive correlation between both AL and FA and between AL and MWF were hypothesized for the three pathways. There was a selective positive correlation between AL and MWF in the right PHC (r = 0.482, p = 0.007). Thus, our results provide initial in vivo evidence for an association between myelination of the right PHC and PA in young healthy adults. Our results suggest that MWF may not only be more specific, but also more sensitive than FA to detect white matter microstructural alterations. If PA was to induce structural plasticity of the right PHC this may contribute to reverse structural alterations of the right PHC in neuropsychiatric disorder with hippocampal pathologies

Macroscopic Entanglement of a Bose Einstein Condensate on a Superconducting Atom Chip

We propose and analyse a practically implementable scheme to generate macroscopic entanglement of a Bose-Einstein condensate in a micro-magnetic trap magnetically coupled to a superconducting loop. We treat the superconducting loop in a quantum superposition of two different flux states coupled with the magnetic trap to generate macroscopic entanglement. Our scheme also provides a platform to realise interferometry of entangled atoms through the Bose-Einstein condensate and to explore physics at the quantum-classical interface.Comment: 4 Pages, Two figure

Development of an In Vitro Ocular Platform to Test Contact Lenses

The definitive version of Development of an in Vitro Ocular Platform to Test Contact Lenses was published by Emerald www.emeraldinsight.com in Journal of Visualized Experiments, (110) (2016) https://doi.org/10.3791/53907Currently, in vitro evaluations of contact lenses (CLs) for drug delivery are typically performed in large volume vials,1-6 which fail to mimic physiological tear volumes.7 The traditional model also lacks the natural tear flow component and the blinking reflex, both of which are defining factors of the ocular environment. The development of a novel model is described in this study, which consists of a unique 2-piece design, eyeball and eyelid piece, capable of mimicking physiological tear volume. The models are created from 3-D printed molds (Polytetrafluoroethylene or Teflon molds), which can be used to generate eye models from various polymers, such as polydimethylsiloxane (PDMS) and agar. Further modifications to the eye pieces, such as the integration of an explanted human or animal cornea or human corneal construct, will permit for more complex in vitro ocular studies. A commercial microfluidic syringe pump is integrated with the platform to emulate physiological tear secretion. Air exposure and mechanical wear are achieved using two mechanical actuators, of which one moves the eyelid piece laterally, and the other moves the eyeballeyepiece circularly. The model has been used to evaluate CLs for drug delivery and deposition of tear components on CLs

Insights to Using Contact Lenses for Drug Delivery

Phan, C.-M. (2013). Insights to Using Contact Lenses for Drug Delivery. Clinical & Experimental Pharmacology, 04(01). https://doi.org/10.4172/2161-1459.1000145There has been considerable interest in the potential application of contact lenses for ocular drug delivery. This short communication provides an overview of the challenges faced by delivering drugs using contact lenses, highlights the solutions to limitations that have already been achieved, and describes the barriers that remain before commercial application can be realized.NSERC 20/20 Network for the Development of Advanced Ophthalmic Material

Evolutionary Optimization of State Selective Field Ionization for Quantum Computing

State selective field ionization detection techniques in physics require a specific progression through a complicated atomic state space to optimize state selectivity and overall efficiency. For large principle quantum number n, the theoretical models become computationally intractable and any results are often rendered irrelevant by small deviations from ideal experimental conditions, for example external electromagnetic fields. Several different proposals for quantum information processing rely heavily upon the quality of these detectors. In this paper, we show a proof of principle that it is possible to optimize experimental field profiles in situ by running a genetic algorithm to control aspects of the experiment itself. A simple experiment produced novel results that are consistent with analyses of existing results.Comment: 9 pages, 5 figure