Nonnegative Minimum Biased Quadratic Estimation in the Linear Regression Models

AbstractIn the paper the problem of nonnegative estimation of β′Hβ + hσ2 in the linear model E(y) = Xβ, Var(y)= σ2I is discussed. Here H is a nonnegative definite matrix while h is a nonnegative scalar. An iterative procedure for the nonnegative minimum biased quadratic estimator is described. Moreover, in the case that H and X′X commute, an explicit formula for this estimator is given. Admissibility of the estimator is proved. The results are applied to nonnegative estimation of the total mean squared error of a linear biased estimator

MAGIC MOORE-PENROSE INVERSES AND PHILATELIC MAGIC SQUARES WITH SPECIAL EMPHASIS ON THE DANIELS–ZLOBEC MAGIC SQUARE

We study singular magic matrices in which the numbers in the rows and columns and in the two main diagonals all add up to the same sum. Our interest focuses on such magic matrices for which the Moore– Penrose inverse is also magic. Special attention is given to the “Daniels–Zlobec magic square’’ introduced by the British magician and television performer Paul Daniels (b. 1938) and considered by Zlobec (2001); see also Murray (1989, pp. 30–32). We introduce the concept of a “philatelic magic square” as a square arrangement of images of postage stamps so that the associated nominal values form a magic square. Three philatelic magic squares with stamps especially chosen for Sanjo Zlobec are presented in celebration of his 70th birthday; most helpful in identifying these stamps was an Excel checklist by Männikkö (2009)

Depth-dependent ordering, two-length-scale phenomena and crossover behavior in a crystal featuring a skin-layer with defects

Structural defects in a crystal are responsible for the "two length-scale" behavior, in which a sharp central peak is superimposed over a broad peak in critical diffuse X-ray scattering. We have previously measured the scaling behavior of the central peak by scattering from a near-surface region of a V2H crystal, which has a first-order transition in the bulk. As the temperature is lowered toward the critical temperature, a crossover in critical behavior is seen, with the temperature range nearest to the critical point being characterized by mean field exponents. Near the transition, a small two-phase coexistence region is observed. The values of transition and crossover temperatures decay with depth. An explanation of these experimental results is here proposed by means of a theory in which edge dislocations in the near-surface region occur in walls oriented in the two directions normal to the surface. The strain caused by the dislocation lines causes the ordering in the crystal to occur as growth of roughly cylindrically shaped regions. After the regions have reached a certain size, the crossover in the critical behavior occurs, and mean field behavior prevails. At a still lower temperature, the rest of the material between the cylindrical regions orders via a weak first-order transition.Comment: 12 pages, 8 figure

The lattice of the CERN Large Hadron Collider

The lattice of the CERN Large Hadron Collider is designed with 23 regular cells per arc, each containing 6 tightly packed 14.2 m long dipoles. This allows to reach 7 TeV per beam with a dipole field of 8.4 Tesla. There are four experimental insertions, two of which are devoted to high luminosity experiments with ± 23 m of free space for the detector. The other two experimental insertions are combined with injection. The value of ß* at the interaction points is tunable from 6 m at injection to 0.5 m in collision. The energy deposition in the inner triplets is carefully reduced to sustain the nominal luminosity of 1034 cm-2s-1. Two insertions are devoted to collect the halo particles with large emittance and momentum spread surrounding the beam core: escaping rates of the protons are estimated to be less than 4·106 sec-1m-1. Finally, one insertion is used to extract the particles in the vertical direction with a minimized deflecting strength

X-ray scattering study of two length scales in the critical fluctuations of CuGeO3

The critical fluctuations of CuGeO$_3$ have been measured by synchrotron x-ray scattering, and two length scales are clearly observed. The ratio between the two length scales is found to be significantly different along the $a$ axis, with the $a$ axis along the surface normal direction. We believe that such a directional preference is a clear sign that surface random strains, especially those caused by dislocations, are the origin of the long length scale fluctuations.Comment: 5 pages, 4 figures, submitted to PR

Evaluation of the Temporal Muscle Thickness as an Independent Prognostic Biomarker in Patients with Primary Central Nervous System Lymphoma.

In this study, we assessed the prognostic relevance of temporal muscle thickness (TMT), likely reflecting patient's frailty, in patients with primary central nervous system lymphoma (PCNSL). In 128 newly diagnosed PCNSL patients TMT was analyzed on cranial magnetic resonance images. Predefined sex-specific TMT cutoff values were used to categorize the patient cohort. Survival analyses, using a log-rank test as well as Cox models adjusted for further prognostic parameters, were performed. The risk of death was significantly increased for PCNSL patients with reduced muscle thickness (hazard ratio of 3.189, 95% CI: 2-097-4.848, p < 0.001). Importantly, the results confirmed that TMT could be used as an independent prognostic marker upon multivariate Cox modeling (hazard ratio of 2.504, 95% CI: 1.608-3.911, p < 0.001) adjusting for sex, age at time of diagnosis, deep brain involvement of the PCNSL lesions, Eastern Cooperative Oncology Group (ECOG) performance status, and methotrexate-based chemotherapy. A TMT value below the sex-related cutoff value at the time of diagnosis is an independent adverse marker in patients with PCNSL. Thus, our results suggest the systematic inclusion of TMT in further translational and clinical studies designed to help validate its role as a prognostic biomarker