Near-Optimal Recovery of Linear and N-Convex Functions on Unions of Convex Sets

In this paper we build provably near-optimal, in the minimax sense, estimates of linear forms and, more generally, "$N$-convex functionals" (the simplest example being the maximum of several fractional-linear functions) of unknown "signal" known to belong to the union of finitely many convex compact sets from indirect noisy observations of the signal. Our main assumption is that the observation scheme in question is good in the sense of A. Goldenshluger, A. Juditsky, A. Nemirovski, Electr. J. Stat. 9(2) (2015), arXiv:1311.6765, the simplest example being the Gaussian scheme where the observation is the sum of linear image of the signal and the standard Gaussian noise. The proposed estimates, same as upper bounds on their worst-case risks, stem from solutions to explicit convex optimization problems, making the estimates "computation-friendly.

Michael H.R. Tolkien (1920-84): a research travelogue

This article will attempt to put together a portrait of Michael H.R. Tolkien’s life through recent archival and research visits to various locations related to him in the United Kingdom. These visits were conducted during the Spring and Fall of 2015, and while much still needs to be compiled the information as it is currently known, along with the photographs and video footage, provide a unique portrait of Michael H.R. Tolkien never before known. The presentation of the information as it was uncovered is given chronologically, because the volume of research began as an avalanche that affected subsequent tangents and visits, and also because the reader will appreciate the unraveling of the documentation in this manner (almost like a detective story)

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Brotherton Collection MS 501 : a Middle English anthology reconsidered

Brotherton Collection MS 501, in Leeds University Library, is a fifteenth-century anthology of Middle English religious verse and prose, best known for the Prick of Conscience with which it begins. It received its first proper description in 1952,' and it has recently been described in detail by Ralph Hanna (1982) and N. R. Ker (1983).2 Nevertheless the published descriptions are unsatisfactory in one way or another, and the manuscript's special character has not been brought out

Interplay between spin-density-wave and superconducting states in quasi-one-dimensional conductors

The interference between spin-density-wave and superconducting instabilities in quasi-one-dimensional correlated metals is analyzed using the renormalization group method. At the one-loop level, we show how the interference leads to a continuous crossover from a spin-density-wave state to unconventional superconductivity when deviations from perfect nesting of the Fermi surface exceed a critical value. Singlet pairing between electrons on neighboring stacks is found to be the most favorable symmetry for superconductivity. The consequences of non uniform spin-density-wave pairing on the structure of phase diagram within the crossover region is also discussed.Comment: 10 pages RevTex,4 Figures, submitted to EPJ

Effects of electrospinning parameters on polyacrylonitrile nanofiber diameter: an investigation by response surface methodology

Effects of material and process parameters on the diameter of electrospun polyacrylonitrile fibers were experimentally investigated. Response surface methodology (RSM) was utilized to design the experiments at the settings of solution concentration, voltage and the collector distance. It also imparted the evaluation of the significance of each parameter on the resultant fiber diameter. The investigations were carried out in the two-variable process domains of several collector distances as applied voltage and the solution concentration were varied at a fixed polymer molecular weight. The mean diameter and coefficient of variation were modeled by polynomial response surfaces as functions of solution concentration and voltage at each collector distance. Effect of applied voltage in micron-scale fiber diameter was observed to be almost negligible when solution concentration and collector distance were high. However, all three factors were found statistically significant in the production of nano-scale fibers. The response surface predictions revealed the parameter interactions for the resultant fiber diameter, and showed that there is a negative correlation between the mean diameter and coefficient of variation for the fiber diameter. A sub-domain of the parameter space consisting of the solution concentration, applied voltage and collector distance, was suggested for the potential nano-scale fiber production

Plasma Oscillation in Semiconductor Superlattice Structure

The statistical properties of two-dimensional systems of charges in semiconductor superlattices are analyzed and the dispersion relation of the plasma oscillation is calculated. The possibility to excite these oscillations by applying the electric field parallel to the structure is discussed

Coadjoint Poisson actions of Poisson-Lie groups

A Poisson-Lie group acting by the coadjoint action on the dual of its Lie algebra induces on it a non-trivial class of quadratic Poisson structures extending the linear Poisson bracket on the coadjoint orbits