285,890 research outputs found
The Cauchy Operator for Basic Hypergeometric Series
We introduce the Cauchy augmentation operator for basic hypergeometric
series. Heine's transformation formula and Sears'
transformation formula can be easily obtained by the symmetric property of some
parameters in operator identities. The Cauchy operator involves two parameters,
and it can be considered as a generalization of the operator . Using
this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy
integral, Sears' two-term summation formula, as well as the -analogues of
Barnes' lemmas. Finally, we find that the Cauchy operator is also suitable for
the study of the bivariate Rogers-Szeg\"o polynomials, or the continuous big
-Hermite polynomials.Comment: 21 pages, to appear in Advances in Applied Mathematic
Online Matrix Completion Through Nuclear Norm Regularisation
It is the main goal of this paper to propose a novel method to perform matrix
completion on-line. Motivated by a wide variety of applications, ranging from
the design of recommender systems to sensor network localization through
seismic data reconstruction, we consider the matrix completion problem when
entries of the matrix of interest are observed gradually. Precisely, we place
ourselves in the situation where the predictive rule should be refined
incrementally, rather than recomputed from scratch each time the sample of
observed entries increases. The extension of existing matrix completion methods
to the sequential prediction context is indeed a major issue in the Big Data
era, and yet little addressed in the literature. The algorithm promoted in this
article builds upon the Soft Impute approach introduced in Mazumder et al.
(2010). The major novelty essentially arises from the use of a randomised
technique for both computing and updating the Singular Value Decomposition
(SVD) involved in the algorithm. Though of disarming simplicity, the method
proposed turns out to be very efficient, while requiring reduced computations.
Several numerical experiments based on real datasets illustrating its
performance are displayed, together with preliminary results giving it a
theoretical basis.Comment: Corrected a typo in the affiliatio
Combined SIRT3 and SIRT5 deletion is associated with inner retinal dysfunction in a mouse model of type 1 diabetes
Abstract Diabetic retinopathy (DR) is a major cause of blindness in working adults in the industrialized world. In addition to vision loss caused by macular edema and pathological angiogenesis, DR patients often exhibit neuronal dysfunction on electrophysiological testing, suggesting that there may be an independent neuronal phase of disease that precedes vascular disease. Given the tremendous metabolic requirements of the retina and photoreceptors in particular, we hypothesized that derangements in metabolic regulation may accelerate retinal dysfunction in diabetes. As such, we induced hyperglycemia with streptozotocin in mice with monoallelic Nampt deletion from rod photoreceptors, mice lacking SIRT3, and mice lacking SIRT5 and tested multiple components of retinal function with electroretinography. None of these mice exhibited accelerated retinal dysfunction after induction of hyperglycemia, consistent with normal-appearing retinal morphology in hyperglycemic Sirt3 −/− or Sirt5 −/− mice. However, mice lacking both SIRT3 and SIRT5 (Sirt3 −/− Sirt5 −/− mice) exhibited significant evidence of inner retinal dysfunction after induction of hyperglycemia compared to hyperglycemic littermate controls, although this dysfunction was not accompanied by gross morphological changes in the retina. These results suggest that SIRT3 and SIRT5 may be involved in regulating neuronal dysfunction in DR and provide a foundation for future studies investigating sirtuin-based therapies
Electro-optic scanning of light coupled from a corrugated LiNbO3 waveguide
Light diffracted from a grating output coupler in a Ti-diffused LiNbO3 waveguide is scanned electro-optically. Using a coupling length of 2.5 mm in our arrangement we have demonstrated a scanning capability of one resolved spot per 3 V/µm applied field
Consistency of Markov chain quasi-Monte Carlo on continuous state spaces
The random numbers driving Markov chain Monte Carlo (MCMC) simulation are
usually modeled as independent U(0,1) random variables. Tribble [Markov chain
Monte Carlo algorithms using completely uniformly distributed driving sequences
(2007) Stanford Univ.] reports substantial improvements when those random
numbers are replaced by carefully balanced inputs from completely uniformly
distributed sequences. The previous theoretical justification for using
anything other than i.i.d. U(0,1) points shows consistency for estimated means,
but only applies for discrete stationary distributions. We extend those results
to some MCMC algorithms for continuous stationary distributions. The main
motivation is the search for quasi-Monte Carlo versions of MCMC. As a side
benefit, the results also establish consistency for the usual method of using
pseudo-random numbers in place of random ones.Comment: Published in at http://dx.doi.org/10.1214/10-AOS831 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Two-flux Colliding Plane Waves in String Theory
We construct the two-flux colliding plane wave solutions in higher
dimensional gravity theory with dilaton, and two complementary fluxes. Two
kinds of solutions has been obtained: Bell-Szekeres(BS) type and homogeneous
type. After imposing the junction condition, we find that only Bell-Szekeres
type solution is physically well-defined. Furthermore, we show that the future
curvature singularity is always developed for our solutions.Comment: 16 pages, Latex; typoes corrected; references added, minor
modification
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