An algorithm for the quadratic approximation

The quadratic approximation is a three dimensional analogue of the two dimensional Pade approximation. A determinantal expression for the polynomial coefficients of the quadratic approximation is given. A recursive algorithm for the construction of these coefficients is derived. The algorithm constructs a table of quadratic approximations analogous to the Pade table of rational approximations

An algorithm for the quadratic approximation

The quadratic approximation is a three dimensional analogue of the two dimensional Pade approximation. A determinantal expression for the polynomial coefficients of the quadratic approximation is given. A recursive algorithm for the construction of these coefficients is derived. The algorithm constructs a table of quadratic approximations analogous to the Pade table of rational approximations

Realistic Earth escape strategies for solar sailing

With growing interest in solar sailing comes the requirement to provide a basis for future detailed planetary escape mission analysis by drawing together prior work, clarifying and explaining previously anomalies. Previously unexplained seasonal variations in sail escape times from Earth orbit are explained analytically and corroborated within a numerical trajectory model. Blended-sail control algorithms, explicitly independent of time, which providenear-optimal escape trajectories and maintain a safe minimum altitude and which are suitable as a potential autonomous onboard controller, are then presented. These algorithms are investigated from a range of initial conditions and are shown to maintain the optimality previously demonstrated by the use of a single-energy gain control law but without the risk of planetary collision. Finally, it is shown that the minimum sail characteristic acceleration required for escape from a polar orbit without traversing the Earth shadow cone increases exponentially as initial altitude is decreased

Clinical efficacy, radiographic and safety findings through 2 years of golimumab treatment in patients with active psoriatic arthritis: results from a long-term extension of the randomised, placebo-controlled GO-REVEAL study

Objectives: To assess long-term golimumab efficacy/safety in patients with active psoriatic arthritis (PsA).<p></p> Methods Adult PsA patients (≥3 swollen, ≥3 tender joints, active psoriasis) were randomly assigned to subcutaneous injections of placebo, golimumab 50 mg or 100 mg every 4 weeks (q4wks) through week 20. All patients received golimumab 50 or 100 mg beginning week 24. Findings through 2 years are reported. Efficacy evaluations included ≥20% improvement in American College of Rheumatology (ACR20) response, good/moderate response in Disease Activity Scores incorporating 28 joints and C-reactive protein (DAS28-CRP), ≥75% improvement in Psoriasis Area and Severity Index (PASI75) and changes in PsA-modified Sharp/van der Heijde scores (SHS).<p></p> Results: Golimumab treatment through 2 years was effective in maintaining clinical response (response rates: ACR20 63%–70%, DAS28-CRP 77%–86%, PASI75 56%–72%) and inhibiting radiographic progression (mean change in PsA-modified SHS in golimumab-treated patients: −0.36), with no clear difference between doses. No new safety signals were identified through 2 years. With the study's tuberculosis screening and prophylactic measures, no patient developed active tuberculosis through 2 years.<p></p> Conclusions: Golimumab 50 and 100 mg for up to 2 years yielded sustained clinical and radiographic efficacy when administered to patients with active PsA. Increasing the golimumab dose from 50 to 100 mg q4wks added limited benefit. Golimumab safety through up to 2 years was consistent with other antitumour necrosis factor α agents used to treat PsA. Treatment of patients with latent tuberculosis identified at baseline appeared to be effective in inhibiting the development of active tuberculosis.<p></p&gt

Minimal residual disease in breast cancer: an overview of circulating and disseminated tumour cells

Within the field of cancer research, focus on the study of minimal residual disease (MRD) in the context of carcinoma has grown exponentially over the past several years. MRD encompasses circulating tumour cells (CTCs)—cancer cells on the move via the circulatory or lymphatic system, disseminated tumour cells (DTCs)—cancer cells which have escaped into a distant site (most studies have focused on bone marrow), and resistant cancer cells surviving therapy—be they local or distant, all of which may ultimately give rise to local relapse or overt metastasis. Initial studies simply recorded the presence and number of CTCs and DTCs; however recent advances are allowing assessment of the relationship between their persistence, patient prognosis and the biological properties of MRD, leading to a better understanding of the metastatic process. Technological developments for the isolation and analysis of circulating and disseminated tumour cells continue to emerge, creating new opportunities to monitor disease progression and perhaps alter disease outcome. This review outlines our knowledge to date on both measurement and categorisation of MRD in the form of CTCs and DTCs with respect to how this relates to cancer outcomes, and the hurdles and future of research into both CTCs and DTCs

Electrochromic orbit control for smart-dust devices

Recent advances in MEMS (micro electromechanical systems) technology are leading to spacecraft which are the shape and size of computer chips, so-called SpaceChips, or ‘smart dust devices’. These devices can offer highly distributed sensing when used in future swarm applications. However, they currently lack a feasible strategy for active orbit control. This paper proposes an orbit control methodology for future SpaceChip devices which is based on exploiting the effects of solar radiation pressure using electrochromic coatings. The concept presented makes use of the high area-to-mass ratio of these devices, and consequently the large force exerted upon them by solar radiation pressure, to control their orbit evolution by altering their surface optical properties. The orbital evolution of Space Chips due to solar radiation pressure can be represented by a Hamiltonian system, allowing an analytic development of the control methodology. The motion in the orbital element phase space resembles that of a linear oscillator, which is used to formulate a switching control law. Additional perturbations and the effect of eclipses are accounted for by modifying the linearized equations of the secular change in orbital elements around an equilibrium point in the phase space of the problem. Finally, the effectiveness of the method is demonstrated in a test case scenario

Stringy Stability of Charged Dilaton Black Holes with Flat Event Horizon

Electrically charged black holes with flat event horizon in anti-de Sitter space have received much attention due to various applications in Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, from modeling the behavior of quark-gluon plasma to superconductor. Crucial to the physics on the dual field theory is the fact that when embedded in string theory, black holes in the bulk may become vulnerable to instability caused by brane pair-production. Since dilaton arises naturally in the context of string theory, we study the effect of coupling dilaton to Maxwell field on the stability of flat charged AdS black holes. In particular, we study the stability of Gao-Zhang black holes, which are locally asymptotically anti-de Sitter. We find that for dilaton coupling parameter $\alpha$ > 1, flat black holes are stable against brane pair production, however for 0 < $\alpha$ < 1, the black holes eventually become unstable as the amount of electrical charges is increased. Such instability however, behaves somewhat differently from that of flat Reissner-Nordstr\"om black holes. In addition, we prove that the Seiberg-Witten action of charged dilaton AdS black hole of Gao-Zhang type with flat event horizon (at least in 5-dimension) is always logarithmically divergent at infinity for finite values of $\alpha$, and is finite and positive in the case $\alpha$ tends to infinity . We also comment on the robustness of our result for other charged dilaton black holes that are not of Gao-Zhang type.Comment: Fixed some confusions regarding whether part of the discussions concern electrically charged hole or magnetically charged one. No changes to the result

Squirrelpox virus: assessing prevalence, transmission and environmental degradation

Red squirrels (Sciurus vulgaris) declined in Great Britain and Ireland during the last century, due to habitat loss and the introduction of grey squirrels (Sciurus carolinensis), which competitively exclude the red squirrel and act as a reservoir for squirrelpox virus (SQPV). The disease is generally fatal to red squirrels and their ecological replacement by grey squirrels is up to 25 times faster where the virus is present. We aimed to determine: (1) the seropositivity and prevalence of SQPV DNA in the invasive and native species at a regional scale; (2) possible SQPV transmission routes; and, (3) virus degradation rates under differing environmental conditions. Grey (n = 208) and red (n = 40) squirrel blood and tissues were sampled. Enzyme-linked immunosorbent assay (ELISA) and quantitative real-time polymerase chain reaction (qPCR) techniques established seropositivity and viral DNA presence, respectively. Overall 8% of squirrels sampled (both species combined) had evidence of SQPV DNA in their tissues and 22% were in possession of antibodies. SQPV prevalence in sampled red squirrels was 2.5%. Viral loads were typically low in grey squirrels by comparison to red squirrels. There was a trend for a greater number of positive samples in spring and summer than in winter. Possible transmission routes were identified through the presence of viral DNA in faeces (red squirrels only), urine and ectoparasites (both species). Virus degradation analyses suggested that, after 30 days of exposure to six combinations of environments, there were more intact virus particles in scabs kept in warm (25°C) and dry conditions than in cooler (5 and 15°C) or wet conditions. We conclude that SQPV is present at low prevalence in invasive grey squirrel populations with a lower prevalence in native red squirrels. Virus transmission could occur through urine especially during warm dry summer conditions but, more notably, via ectoparasites, which are shared by both species

Quasinormal modes of a black hole surrounded by quintessence

Using the third-order WKB approximation, we evaluate the quasinormal frequencies of massless scalar field perturbation around the black hole which is surrounded by the static and spherically symmetric quintessence. Our result shows that due to the presence of quintessence, the scalar field damps more rapidly. Moreover, we also note that the quintessential state parameter $\epsilon$ (the ratio of pressure $p_q$ to the energy density $\rho_q$) play an important role for the quasinormal frequencies. As the state parameter $\epsilon$ increases the real part increases and the absolute value of the imaginary part decreases. This means that the scalar field decays more slowly in the larger $\epsilon$ quintessence case.Comment: 7 pages, 3 figure

Phantom scalar emission in the Kerr black hole spacetime

We study the absorption probability and Hawking radiation spectra of a phantom scalar field in the Kerr black hole spacetime. We find that the presence of the negative kinetic energy terms modifies the standard results in the greybody factor, super-radiance and Hawking radiation. Comparing with the usual scalar particle, the phantom scalar emission is enhanced in the black hole spacetime.Comment: 11 pages, 6 figures, a revised version accepted for publication in CQ