Lower Bounds for Oblivious Subspace Embeddings

An oblivious subspace embedding (OSE) for some $\epsilon$,$\delta \in (0,1/3)$ and d ≤ m ≤ n is a distribution $\mathcal{D}$ over $\mathbb{R}^{m×n}$ such that $\underset {\Pi \sim \mathcal{D}} {Pr} (\forall x \in W, (1−\epsilon)|| x ||_2≤ || \Pi x ||_2≤(1+\epsilon)|| x||_2)≥1−\delta$ for any linear subspace $W \subset \mathbb{R}^n$ of dimension d. We prove any OSE with $\delta < 1/3$ has $m = \Omega((d + log(1/\delta))/\epsilon^2)$, which is optimal. Furthermore, if every $\Pi$ in the support of $\mathcal{D}$ is sparse, having at most s non-zero entries per column, we show tradeoff lower bounds between m and s.Engineering and Applied Science

A Prime Analogue of Roth's Theorem in Function Fields

Abstract. Let Fq[t] denote the polynomial ring over the nite eld Fq, and let PR denote the subset of Fq[t] containing all monic irreducible polynomials of degree R. For non-zero elements r = (r1; r2; r3) of Fq satisfying r1 + r2 + r3 = 0, let D(PR) = Dr(PR) denote the maximal cardinality of a set AR PR which contains no non-trivial solution of r1x1 + r2x2 + r3x3 = 0 with xi 2 AR (1 i 3). By applying the polynomial Hardy-Littlewood circle method, we prove that D(PR) q jPRj=(log log log log jPRj).NSERC Discovery Grant || NSA Young Investigator Grant, #H98230-10-1-0155, #H98230-12-1-0220, #H98230-14-1-0164

Extended Dorsal Preservation in a New Concept of Preservational Rhinoplasty

Background: A dorsal preservation rhinoplasty concept was discussed and the benefits vs. contraindications and limitations were presented. In specific cases of severe nasal septal deformations associated with necessity of major septoplasty, focused on perpendicular plate, a New Concept of Extended Dorsal Preservation Rhinoplasty is presented (New Extended PR-D). PR-D is based on septoplasty, rhinosculpture and partial osteotomies. Goals: The objective of this paper is to present a new approach in some cases of rhinoplasty named as extended dorsal preservation rhinoplasty. Methods and Results: Partial and incomplete osteotomies were introduced as method to avoid disinsertion of nasal pyramid of glabellar area and to avoid bony step in areas off osteotomy cut. Rhinosculpture in its extended mode was promoted for modulation of bony structure with obtaining immediate aesthetic and structural results, minoring a surgical trauma. Conclusion: The principles of Preservation Concept were respected in this New Extended PR-D Concept.info:eu-repo/semantics/publishedVersio

Hadron production measurement from NA61/SHINE

New results of NA61/SHINE on determination of charged hadron yields in proton-carbon interactions are presented. They aim to improve predictions of the neutrino flux in the T2K experiment. The data were recorded using a secondary-proton beam of 31 GeV/$c$ momentum from CERN SPS which impinges on a graphite target. To determine the inclusive production cross section for charged pions, kaons and protons the thin ($0.04\, \lambda_I$) target was exploited. Results of this measurement are used in the T2K beam simulation program to reweight hadron yields in the interaction vertex. At the same time, NA61/SHINE results obtained with the T2K replica target ($1.9\, \lambda_I$) allow to constrain hadron yields at the surface of the target. It would correspond to the constraint up to 90% of the neutrino flux, thus reducing significantly a model dependence of the neutrino beam prediction. All measured spectra are compared to predictions of hadron production models. In addition a status of the analysis of data collected by NA61/SHINE for the NuMI target (Fermilab) is reviewed. These data will be used further in neutrino beam calculations for the MINERvA, MINOS(+) and LBNE experiments.Comment: Presented at EPS-HEP 2013 in Stockholm on July 19, 201

Optimal and efficient crossover designs for comparing test treatments with a control treatment

This paper deals exclusively with crossover designs for the purpose of comparing t test treatments with a control treatment when the number of periods is no larger than t+1. Among other results it specifies sufficient conditions for a crossover design to be simultaneously A-optimal and MV-optimal in a very large and appealing class of crossover designs. It is expected that these optimal designs are highly efficient in the entire class of crossover designs. Some computationally useful tools are given and used to build assorted small optimal and efficient crossover designs. The model robustness of these newly discovered crossover designs is discussed.Comment: Published at http://dx.doi.org/10.1214/009053604000000887 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org