Input-to-state stability of infinite-dimensional control systems

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs the existence of an ISS-Lyapunov function implies the input-to-state stability of a system. Then for the case of systems described by abstract equations in Banach spaces we develop two methods of construction of local and global ISS-Lyapunov functions. We prove a linearization principle that allows a construction of a local ISS-Lyapunov function for a system which linear approximation is ISS. In order to study interconnections of nonlinear infinite-dimensional systems, we generalize the small-gain theorem to the case of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov function for an entire interconnection, if ISS-Lyapunov functions for subsystems are known and the small-gain condition is satisfied. We illustrate the theory on examples of linear and semilinear reaction-diffusion equations.Comment: 33 page

Polarization due to rotational distortion in the bright star Regulus

This is the full published article (retrieved from the 6 months post-publication posting on arXiv) including the Methods and Supplementary Information sections: 33 pages, 10 figures, 8 tablesPolarization in stars was first predicted by Chandrasekhar [1] who calculated a substantial linear polarization at the stellar limb for a pure electron-scattering atmosphere. This polarization will average to zero when integrated over a spherical star but could be detected if the symmetry is broken, for example by the eclipse of a binary companion. Nearly 50 years ago, Harrington and Collins [2] modeled another way of breaking the symmetry and producing net polarization - the distortion of a rapidly rotating hot star. Here we report the first detection of this effect. Observations of the linear polarization of Regulus, with two different high-precision polarimeters, range from +42 parts-per-million (ppm) at a wavelength of 741 nm to -22 ppm at 395 nm. The reversal from red to blue is a distinctive feature of rotation-induced polarization. Using a new set of models for the polarization of rapidly rotating stars we find that Regulus is rotating at 96.5(+0.6/-0.8)% of its critical angular velocity for breakup, and has an inclination greater than 76.5 degrees. The rotation axis of the star is at a position angle of 79.5+/-0.7 degrees. The conclusions are independent of, but in good agreement with, the results of previously published interferometric observations of Regulus [3]. The accurate measurement of rotation in early-type stars is important for understanding their stellar environments [4], and course of their evolution [5].Peer reviewedFinal Accepted Versio

The efficacy of iron chelator regimes in reducing cardiac and hepatic iron in patients with thalassaemia major: a clinical observational study

<p>Abstract</p> <p>Background</p> <p>Available iron chelation regimes in thalassaemia may achieve different changes in cardiac and hepatic iron as assessed by MR. The aim of this study was to assess the efficacy of four available iron chelator regimes in 232 thalassaemia major patients by assessing the rate of change in repeated measurements of cardiac and hepatic MR.</p> <p>Results</p> <p>For the heart, deferiprone and the combination of deferiprone and deferoxamine significantly reduced cardiac iron at all levels of iron loading. As patients were on deferasirox for a shorter time, a second analysis ("Initial interval analysis") assessing the change between the first two recorded MR results for both cardiac and hepatic iron (minimum interval 12 months) was made. Combination therapy achieved the most rapid fall in cardiac iron load at all levels and deferiprone alone was significantly effective with moderate and mild iron load. In the liver, deferasirox effected significant falls in iron load and combination therapy resulted in the most rapid decline.</p> <p>Conclusion</p> <p>With the knowledge of the efficacy of the different available regimes and the specific iron load in the heart and the liver, appropriate tailoring of chelation therapy should allow clearance of iron. Combination therapy is best in reducing both cardiac and hepatic iron, while monotherapy with deferiprone or deferasirox are effective in the heart and liver respectively. The outcomes of this study may be useful to physicians as to the chelation they should prescribe according to the levels of iron load found in the heart and liver by MR.</p

Search for CP violation in D0 and D+ decays

A high statistics sample of photoproduced charm particles from the FOCUS (E831) experiment at Fermilab has been used to search for CP violation in the Cabibbo suppressed decay modes D+ to K-K+pi+, D0 to K-K+ and D0 to pi-pi+. We have measured the following CP asymmetry parameters: A_CP(K-K+pi+) = +0.006 +/- 0.011 +/- 0.005, A_CP(K-K+) = -0.001 +/- 0.022 +/- 0.015 and A_CP(pi-pi+) = +0.048 +/- 0.039 +/- 0.025 where the first error is statistical and the second error is systematic. These asymmetries are consistent with zero with smaller errors than previous measurements.Comment: 12 pages, 4 figure

A Study of D0 --> K0(S) K0(S) X Decay Channels

Using data from the FOCUS experiment (FNAL-E831), we report on the decay of $D^0$ mesons into final states containing more than one $K^0_S$. We present evidence for two Cabibbo favored decay modes, $D^0\to K^0_SK^0_S K^- \pi^+$ and $D^0\to K^0_SK^0_S K^+ \pi^-$, and measure their combined branching fraction relative to $D^0\to \bar{K} ^0\pi^+\pi^-$ to be $\frac{\Gamma(D^0\to K^0_SK^0_SK^{\pm}\pi^{\mp})}{\Gamma(D^0\to \bar{K} ^0\pi^+\pi^-)}$ = 0.0106 $\pm$ 0.0019 $\pm$ 0.0010. Further, we report new measurements of $\frac{\Gamma(D^0\to K^0_SK^0_SK^0_S)}{\Gamma(D^0\to \bar{K} ^0\pi^+\pi^-)}$ = 0.0179 $\pm$ 0.0027 $\pm$ 0.0026, $\frac{\Gamma(D^0\to K^0\bar{K} ^0)}{\Gamma(D^0\to \bar{K} ^0\pi^+\pi^-)}$ = 0.0144 $\pm$ 0.0032 $\pm$ 0.0016, and $\frac{\Gamma(D^0\to K^0_SK^0_S\pi^+\pi^-)}{\Gamma(D^0\to \bar{K} ^0\pi^+\pi^-)}$ = 0.0208 $\pm$ 0.0035 $\pm$ 0.0021 where the first error is statistical and the second is systematic.Comment: 11 pages, 3 figures, typos correcte

Progesterone after previous preterm birth for prevention of neonatal respiratory distress syndrome (PROGRESS): a randomised controlled trial

Background: Neonatal respiratory distress syndrome, as a consequence of preterm birth, is a major cause of early mortality and morbidity during infancy and childhood. Survivors of preterm birth continue to remain at considerable risk of both chronic lung disease and long-term neurological handicap. Progesterone is involved in the maintenance of uterine quiescence through modulation of the calcium-calmodulin-myosin-light-chain-kinase system in smooth muscle cells. The withdrawal of progesterone, either actual or functional is thought to be an antecedent to the onset of labour. While there have been recent reports of progesterone supplementation for women at risk of preterm birth which show promise in this intervention, there is currently insufficient data on clinically important outcomes for both women and infants to enable informed clinical decision-making. The aims of this randomised, double blind, placebo controlled trial are to assess whether the use of vaginal progesterone pessaries in women with a history of previous spontaneous preterm birth will reduce the risk and severity of respiratory distress syndrome, so improving their infant's health, without increasing maternal risks. Methods Design: Multicentred randomised, double blind, placebo-controlled trial. Inclusion Criteria: pregnant women with a live fetus, and a history of prior preterm birth at less than 37 weeks gestation and greater than 20 weeks gestation in the immediately preceding pregnancy, where onset of labour occurred spontaneously, or in association with cervical incompetence, or following preterm prelabour ruptured membranes. Trial Entry & Randomisation: After obtaining written informed consent, eligible women will be randomised between 18 and 23+6 weeks gestation using a central telephone randomisation service. The randomisation schedule prepared by non clinical research staff will use balanced variable blocks, with stratification according to plurality of the pregnancy and centre where planned to give birth. Eligible women will be randomised to either vaginal progesterone or vaginal placebo. Study Medication & Treatment Schedules: Treatment packs will appear identical. Woman, caregivers and research staff will be blinded to treatment allocation. Primary Study Outcome: Neonatal Respiratory Distress Syndrome (defined by incidence and severity). Sample Size: of 984 women to show a 40% reduction in respiratory distress syndrome from 15% to 9% (p = 0.05, 80% power). Discussion: This is a protocol for a randomised trial.Jodie M. Dodd, Caroline A. Crowther, Andrew J. McPhee, Vicki Flenady, and Jeffrey S. Robinso

T1 at 1.5T and 3T compared with conventional T2* at 1.5T for cardiac siderosis

Background: Myocardial black blood (BB) T2* relaxometry at 1.5T provides robust, reproducible and calibrated non-invasive assessment of cardiac iron burden. In vitro data has shown that like T2*, novel native Modified Look-Locker Inversion recovery (MOLLI) T1 shortens with increasing tissue iron. The relative merits of T1 and T2* are largely unexplored. We compared the established 1.5T BB T2* technique against native T1 values at 1.5T and 3T in iron overload patients and in normal volunteers. Methods: A total of 73 subjects (42 male) were recruited, comprising 20 healthy volunteers (controls) and 53 patients (thalassemia major 22, sickle cell disease 9, hereditary hemochromatosis 9, other iron overload conditions 13). Single mid-ventricular short axis slices were acquired for BB T2* at 1.5T and MOLLI T1 quantification at 1.5T and 3T. Results: In healthy volunteers, median T1 was 1014 ms (full range 939–1059 ms) at 1.5T and modestly increased to 1165ms (full range 1056–1224 ms) at 3T. All patients with significant cardiac iron overload (1.5T T2* values <20 ms) had T1 values <939 ms at 1.5T, and <1056 ms at 3T. Associations between T2* and T1 were found to be moderate with y =377 · x0.282 at 1.5T (R2 = 0.717), and y =406 · x0.294 at 3T (R2 = 0.715). Measures of reproducibility of T1 appeared superior to T2*. Conclusions: T1 mapping at 1.5T and at 3T can identify individuals with significant iron loading as defined by the current gold standard T2* at 1.5T. However, there is significant scatter between results which may reflect measurement error, but it is also possible that T1 interacts with T2*, or is differentially sensitive to aspects of iron chemistry or other biology. Hurdles to clinical implementation of T1 include the lack of calibration against human myocardial iron concentration, no demonstrated relation to cardiac outcomes, and variation in absolute T1 values between scanners, which makes inter-centre comparisons difficult. The relative merits of T1 at 3T versus T2* at 3T require further consideration