Jacobi-Predictor-Corrector Approach for the Fractional Ordinary Differential Equations

We present a novel numerical method, called {\tt Jacobi-predictor-corrector approach}, for the numerical solution of fractional ordinary differential equations based on the polynomial interpolation and the Gauss-Lobatto quadrature w.r.t. the Jacobi-weight function $\omega(s)=(1-s)^{\alpha-1}(1+s)^0$. This method has the computational cost O(N) and the convergent order $IN$, where $N$ and $IN$ are, respectively, the total computational steps and the number of used interpolating points. The detailed error analysis is performed, and the extensive numerical experiments confirm the theoretical results and show the robustness of this method.Comment: 24 pages, 5 figure

EB Ford revisited: assessing the long-term stability of wing-spot patterns and population genetic structure of the meadow brown butterfly on the Isles of Scilly

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.Data files of wing spot sizes and AFLP genotypes available from the Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.j7v42.Understanding selection in the wild remains a major aim of evolutionary ecology and work by Ford and colleagues on the meadow brown butterfly Maniola jurtina did much to ignite this agenda. A great deal of their work was conducted during the 1950s on the Isles of Scilly. They documented island-specific wing-spot patterns that remained consistent over about a decade, but patterns on some islands changed after environmental perturbation. It was suggested that these wing-spot patterns reflected island-specific selection and that there was little migration between islands. However, genetic studies to test the underlying assumption of restricted migration are lacking and it is also unknown whether the originally described wing-spot patterns have persisted over time. We therefore collected female butterflies from five of Ford's original study locations, including three large islands (St Mary's, St Martin's and Tresco) and two small islands (Tean and St Helen's). Wing-spot patterns had not changed appreciably over time on three of the islands (two large and one small), but were significantly different on the other two. Furthermore, analysis of 176 amplified fragment length polymorphisms revealed significant genome-wide differentiation among the five islands. Our findings are consistent with Ford's conclusions that despite the close proximity of these islands, there is restricted gene flow among them.Heredity advance online publication, 2 November 2016; doi:10.1038/hdy.2016.94.We thank the Genetics Society for a fieldwork grant (to DJH) that funded the collection trip and DJH thanks Mike Johnson for sparking interest in this area. SWB is supported by the Australian Research Council and a Ramsay Fellowship, NW by a Royal Society Wolfson Fellowship and NERC and DJH by the Leverhulme Trust

Tolerability and safety of novel half milliliter formulation of glatiramer acetate for subcutaneous injection: an open-label, multicenter, randomized comparative study

Daily glatiramer acetate (GA) 20 mg/1.0 mL is a first-line treatment for relapsing-remitting multiple sclerosis (RRMS). To reduce the occurrence of injection pain and local injection site reactions (LISRs), a reduced volume formulation of GA was developed. This study compared pain and LISRs after injecting the marketed and the novel formulations. RRMS patients currently injecting GA participated in this multicenter, randomized, crossover comparative study. All patients administered once-daily subcutaneous injections of GA 20 mg/1.0 mL (marketed formulation) or GA 20 mg/0.5 mL (reduced volume formulation) for 14 days. Patients were crossed-over to the alternate treatment for an additional 14 days. Using a Visual Analog Scale (VAS), patients recorded in daily diaries the severity of injection pain immediately and 5 min post-injection, and the presence and severity of LISRs (swelling, redness, itching, lump) within 5 min and 24 h post-injection. VAS pain scores were ranked significantly lower immediately and 5 min after GA 20 mg/0.5 mL injections (p < 0.0001). Although LISRs were rare for both preparations, the severity of reactions ranked significantly lower and fewer symptoms occurred within 5 min and 24 h of using the reduced volume formulation (p < 0.0001). GA injected subcutaneously in a reduced volume formulation is a more tolerable option

Justification of the symmetric damping model of the dynamical Casimir effect in a cavity with a semiconductor mirror

A "microscopic" justification of the "symmetric damping" model of a quantum oscillator with time-dependent frequency and time-dependent damping is given. This model is used to predict results of experiments on simulating the dynamical Casimir effect in a cavity with a photo-excited semiconductor mirror. It is shown that the most general bilinear time-dependent coupling of a selected oscillator (field mode) to a bath of harmonic oscillators results in two equal friction coefficients for the both quadratures, provided all the coupling coefficients are proportional to a single arbitrary function of time whose duration is much shorter than the periods of all oscillators. The choice of coupling in the rotating wave approximation form leads to the "mimimum noise" model of the quantum damped oscillator, introduced earlier in a pure phenomenological way.Comment: 9 pages, typos corrected, corresponds to the published version, except for the reference styl

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel.In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime: we compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole.Comment: 75 pages, no figures, submitted to Living Reviews in Relativit

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol

New instability of non-extremal black holes: spitting out supertubes

We search for stable bound states of non-extremal rotating three-charge black holes in five dimensions (Cvetic-Youm black holes) and supertubes. We do this by studying the potential of supertube probes in the non-extremal black hole background and find that generically the marginally bound state of the supersymmetric limit becomes metastable and disappears with non-extremality (higher temperature). However near extremality there is a range of parameters allowing for stable bound states, which have lower energy than the supertube-black hole merger. Angular momentum is crucial for this effect. We use this setup in the D1-D5 decoupling limit to map a thermodynamic instability of the CFT (a new phase which is entropically dominant over the black hole phase) to a tunneling instability of the black hole towards the supertube-black hole bound state. This generalizes the results of ArXiv:1108.0411 [hep-th], which mapped an entropy enigma in the bulk to the dual CFT in a supersymmetric setup.Comment: 28 pages + appendix, 15 figures, v2: References added, typos corrected. Version published in JHE

Ferritins: furnishing proteins with iron

Ferritins are a superfamily of iron oxidation, storage and mineralization proteins found throughout the animal, plant, and microbial kingdoms. The majority of ferritins consist of 24 subunits that individually fold into 4-α-helix bundles and assemble in a highly symmetric manner to form an approximately spherical protein coat around a central cavity into which an iron-containing mineral can be formed. Channels through the coat at inter-subunit contact points facilitate passage of iron ions to and from the central cavity, and intrasubunit catalytic sites, called ferroxidase centers, drive Fe2+ oxidation and O2 reduction. Though the different members of the superfamily share a common structure, there is often little amino acid sequence identity between them. Even where there is a high degree of sequence identity between two ferritins there can be major differences in how the proteins handle iron. In this review we describe some of the important structural features of ferritins and their mineralized iron cores and examine in detail how three selected ferritins oxidise Fe2+ in order to explore the mechanistic variations that exist amongst ferritins. We suggest that the mechanistic differences reflect differing evolutionary pressures on amino acid sequences, and that these differing pressures are a consequence of different primary functions for different ferritins

Quality of Care in Humanitarian Surgery

Humanitarian surgical programs are set up de novo, within days or hours in emergency or disaster settings. In such circumstances, insuring quality of care is extremely challenging. Basic structural inputs such as a safe structure, electricity, clean water, a blood bank, sterilization equipment, a post-anesthesia recovery unit, appropriate medications should be established. Currently, no specific credentials are needed for surgeons to operate in a humanitarian setting; the training of more humanitarian surgeons is desperately needed. Standard perioperative protocols for the humanitarian setting after common procedures such as Cesarean section, burn care, open fractures, and amputations and antibiotic prophylaxis, and post-operative pain management must be developed. Outcome data, especially long-term outcomes, are difficult to collect as patients often do not return for follow-up and may be difficult to trace; standard databases for post-operative infections and mortality rates should be established. Checklists have recently received significant attention as an instrument to support the improvement of surgical quality; knowing which items are most applicable to humanitarian settings remains unknown. In conclusion, the quality of surgical services in humanitarian settings must be regulated. Many other core medical activities of humanitarian organizations such as therapeutic feeding, mass vaccination, and the treatment of infectious diseases, such as tuberculosis and human immunodeficiency virus, are subject to rigorous reporting of quality indicators. There is no reason why surgery should be exempted from quality oversight. The surgical humanitarian community should pull together before the next disaster strikes

The Expanding Fireball of Nova Delphini 2013

A classical nova occurs when material accreting onto the surface of a white dwarf in a close binary system ignites in a thermonuclear runaway. Complex structures observed in the ejecta at late stages could result from interactions with the companion during the common envelope phase. Alternatively, the explosion could be intrinsically bipolar, resulting from a localized ignition on the surface of the white dwarf or as a consequence of rotational distortion. Studying the structure of novae during the earliest phases is challenging because of the high spatial resolution needed to measure their small sizes. Here we report near-infrared interferometric measurements of the angular size of Nova Delphini 2013, starting from one day after the explosion and continuing with extensive time coverage during the first 43 days. Changes in the apparent expansion rate can be explained by an explosion model consisting of an optically thick core surrounded by a diffuse envelope. The optical depth of the ejected material changes as it expands. We detect an ellipticity in the light distribution, suggesting a prolate or bipolar structure that develops as early as the second day. Combining the angular expansion rate with radial velocity measurements, we derive a geometric distance to the nova of 4.54 +/- 0.59 kpc from the Sun.Comment: Published in Nature. 32 pages. Final version available at http://www.nature.com/nature/journal/v515/n7526/full/nature13834.htm