Kalman filter design for atmospheric tip/tilt, tip/tilt anisoplanatism and focus filtering on extremely large telescopes

This paper discusses Kalman filter design to correct for atmospheric tip/tilt, tip/tilt anisoplanatism and focus disturbances in laser guide star multi-conjugate adaptive optics. Model identification, controller design and computation, command oversampling and disturbance rejection are discussed via time domain analysis and control performance evaluation. End-to-end high-fidelity sky-coverage simulations are presented by Wang and co-authors in a companion paper

A note on the Mittag–Leffler condition for Bredon-modules

In this note we show the Bredon-analogue of a result by Emmanouil and Talelli, which gives a criterion when the homological and cohomological dimensions of a countable group $G$ agree. We also present some applications to groups of Bredon-homological dimension $1$.Comment: 10 page

Oscillatory instability in super-diffusive reaction -- diffusion systems: fractional amplitude and phase diffusion equations

Nonlinear evolution of a reaction--super-diffusion system near a Hopf bifurcation is studied. Fractional analogues of complex Ginzburg-Landau equation and Kuramoto-Sivashinsky equation are derived, and some of their analytical and numerical solutions are studied

Synthetic Lethality of Chk1 Inhibition Combined with p53 and/or p21 Loss During a DNA Damage Response in Normal and Tumor Cells

Cell cycle checkpoints ensure genome integrity and are frequently compromised in human cancers. A therapeutic strategy being explored takes advantage of checkpoint defects in p53-deficient tumors in order to sensitize them to DNA-damaging agents by eliminating Chk1-mediated checkpoint responses. Using mouse models, we demonstrated that p21 is a key determinant of how cells respond to the combination of DNA damage and Chk1 inhibition (combination therapy) in normal cells as well as in tumors. Loss of p21 sensitized normal cells to the combination therapy much more than did p53 loss and the enhanced lethality was partially blocked by CDK inhibition. In addition, basal pools of p21 (p53 independent) provided p53 null cells with protection from the combination therapy. Our results uncover a novel p53-independent function for p21 in protecting cells from the lethal effects of DNA damage followed by Chk1 inhibition. As p21 levels are low in a significant fraction of colorectal tumors, they are predicted to be particularly sensitive to the combination therapy. Results reported in this study support this prediction

On a Conjecture of Rapoport and Zink

In their book Rapoport and Zink constructed rigid analytic period spaces $F^{wa}$ for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of $p$-divisible groups to some of these period spaces. They conjectured the existence of an \'etale bijective morphism $F^a \to F^{wa}$ of rigid analytic spaces and of a universal local system of $Q_p$-vector spaces on $F^a$. For Hodge-Tate weights $n-1$ and $n$ we construct in this article an intrinsic Berkovich open subspace $F^0$ of $F^{wa}$ and the universal local system on $F^0$. We conjecture that the rigid-analytic space associated with $F^0$ is the maximal possible $F^a$, and that $F^0$ is connected. We give evidence for these conjectures and we show that for those period spaces possessing PEL period morphisms, $F^0$ equals the image of the period morphism. Then our local system is the rational Tate module of the universal $p$-divisible group and enjoys additional functoriality properties. We show that only in exceptional cases $F^0$ equals all of $F^{wa}$ and when the Shimura group is $GL_n$ we determine all these cases.Comment: v2: 48 pages; many new results added, v3: final version that will appear in Inventiones Mathematica

Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting

A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields

Let R be a regular local ring, containing an infinite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R.Comment: Section "Formal loops and affine Grassmannians" is removed as this is now covered in arXiv:1308.3078. Exposition is improved and slightly restructured. Some minor correction

An optimized multi-proxy, multi-site Antarctic ice and gas orbital chronology (AICC2012): 120-800 ka

An accurate and coherent chronological framework is essential for the interpretation of climatic and environmental records obtained from deep polar ice cores. Until now, one common ice core age scale had been developed based on an inverse dating method (Datice), combining glaciological modelling with absolute and stratigraphic markers between 4 ice cores covering the last 50 ka (thousands of years before present) (Lemieux-Dudon et al., 2010). In this paper, together with the companion paper of Veres et al. (2013), we present an extension of this work back to 800 ka for the NGRIP, TALDICE, EDML, Vostok and EDC ice cores using an improved version of the Datice tool. The AICC2012 (Antarctic Ice Core Chronology 2012) chronology includes numerous new gas and ice stratigraphic links as well as improved evaluation of background and associated variance scenarios. This paper concentrates on the long timescales between 120–800 ka. In this framework, new measurements of δ18Oatm over Marine Isotope Stage (MIS) 11–12 on EDC and a complete δ18Oatm record of the TALDICE ice cores permit us to derive additional orbital gas age constraints. The coherency of the different orbitally deduced ages (from δ18Oatm, δO2/N2 and air content) has been verified before implementation in AICC2012. The new chronology is now independent of other archives and shows only small differences, most of the time within the original uncertainty range calculated by Datice, when compared with the previous ice core reference age scale EDC3, the Dome F chronology, or using a comparison between speleothems and methane. For instance, the largest deviation between AICC2012 and EDC3 (5.4 ka) is obtained around MIS 12. Despite significant modifications of the chronological constraints around MIS 5, now independent of speleothem records in AICC2012, the date of Termination II is very close to the EDC3 one

A phase I trial of the selective oral cyclin-dependent kinase inhibitor seliciclib (CYC202; R-Roscovitine), administered twice daily for 7 days every 21 days

Seliciclib (CYC202; R-roscovitine) is the first selective, orally bioavailable inhibitor of cyclin-dependent kinases 1, 2, 7 and 9 to enter clinical trial. Preclinical studies showed antitumour activity in a broad range of human tumour xenografts. A phase I trial was performed with a 7-day b.i.d. p.o. schedule. Twenty-one patients (median age 62 years, range: 39–73 years) were treated with doses of 100, 200 and 800 b.i.d. Dose-limiting toxicities were seen at 800 mg b.i.d.; grade 3 fatigue, grade 3 skin rash, grade 3 hyponatraemia and grade 4 hypokalaemia. Other toxicities included reversible raised creatinine (grade 2), reversible grade 3 abnormal liver function and grade 2 emesis. An 800 mg portion was investigated further in 12 patients, three of whom had MAG3 renograms. One patient with a rapid increase in creatinine on day 3 had a reversible fall in renal perfusion, with full recovery by day 14, and no changes suggestive of renal tubular damage. Further dose escalation was precluded by hypokalaemia. Seliciclib reached peak plasma concentrations between 1 and 4 h and elimination half-life was 2–5 h. Inhibition of retinoblastoma protein phosphorylation was not demonstrated in peripheral blood mononuclear cells. No objective tumour responses were noted, but disease stabilisation was recorded in eight patients; this lasted for a total of six courses (18 weeks) in a patient with ovarian cancer