We prove the universality of the β-ensembles with convex analytic potentials and for any β > 0, i.e. we show that the spacing distributions of log-gases at any inverse temperature β coincide with those of the Gaussian β-ensembles. AMS Subject Classification (2010): 15B52, 82B44

• Explicit expression of MMSE estimator is derived from noisy measurements with many missing entries. MSE for and asymptotic results are discussed. This paper considers the task estimating l 2 norm a n -dimensional random Gaussian vector taken after entries missed only K (0 ? ) retained while rest erased set to 0. Specifically, we evaluate minimum mean square error (MMSE) unknown performing und...

We study rotational surfaces with constant Minkowski Gaussian curvature and mean in a 3-dimensional normed space rotationally symmetric norm. have generalization of the catenoid, pseudo-sphere Delaunay surfaces.

A parametric mean length is defined as the quantity L R = R R−1 [ 1 − ∑N i=1 p β i D −ni( R−1 R ) ∑N j=1 p β j ] where R > 0 ( 1) , β > 0, pi > 0, ∑ pi = 1, i = 1, 2, . . . ,N. This being the mean length of code words. Lower and upper bounds for L R are derived in terms of R-norm information measure for the incomplete power distribution. AMS Subject classification. 94A15, 94A17, 94A24, 26D15.

We here provide additional proofs, definitions, lemmas and derivations omitted in the paper. Note that material contained in the latter are referred to by the captions used there (e.g. Theorem 1), whereas auxiliary statements contained exclusively in this supplement are preceded by a capital Roman letter (e.g. Theorem A.1). A Sub-Gaussian random variables and concentration inequalities A random...

We provide a Laakso construction to prove that the property of having an equivalent norm with the property (β) of Rolewicz is qualitatively preserved via surjective uniform quotient mappings between separable Banach spaces. On the other hand, we show that the (β)-modulus is not quantitatively preserved via such a map by exhibiting two uniformly homeomorphic Banach spaces that do not have (β)-mo...

OBJECTIVES While shared decision making (SDM) promotes health-related decisions that are informed, value-based and adhered to, few studies report on theory-based approaches to SDM adoption by healthcare professionals. We aimed to identify the factors influencing dietitians' intentions to adopt two SDM behaviours: 1) present dietary treatment options to patients and 2) help patients clarify thei...

Maximum (or `∞) norm minimization subject to an underdetermined system of linear equations finds use in a large number of practical applications, such as vector quantization, peak-to-average power ratio (PAPR) (or “crest factor”) reduction in wireless communication systems, approximate neighbor search, robotics, and control. In this paper, we analyze the fundamental properties of signal represe...

We consider a finite horizon linear discrete time varying system whose input is a random noise with an imprecisely known probability law. The statistical uncertainty is described by a nonnegative parameter a which constrains the anisotropy of the noise as an entropy theoretic measure of deviation of the actual noise distribution from Gaussian white noise laws with scalar covariance matrices. Th...

We introduce a plane, which we call the delta-sigma plane, that is indexed by the norm of the estimator bias gradient and the variance of the estimator. The norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space. Using a uniform Cramer-Rao (CR) bound on estimator variance a delta-sigma tradeoo curve is speciied which d...