Let E and F be Banach lattices and assume E∗ has no atoms. Let T : E → F be a norm bounded disjointness preserving operator from E into F . Then β(T ) = α(T ) = ‖T‖e = ‖T‖.

We consider the macroscopic large N limit of Circular beta-Ensemble at high temperature, and its weighted version as well, in regime where inverse temperature scales β/N for some parameter β>0. More precisely, N→∞, equilibrium measure this particle system is described unique minimizer a functional which interpolates between relative entropy (β=0) logarithmic energy (β=∞). The purpose work to sh...

Guo Wenqiang, Qiu Tianshuang, and Li Fan 1. Dalian University of Technology, Dalian , China , 116024 2. Xinjiang Institute of Finance and Economics, Urumchi 830012,China Tel: +86-0411-84706009-3038 Summary: Evoked potentials (EPs) have been widely used to quantify neurological system properties. Traditional EP analyses are developed under the condition that the background noises in EP are Gauss...

in this study, functionalized β-cyclodextrin (β-cd) by aldehyde group was investigated as an oxidase enzyme mimic for the amino phenol oxidation. all calculations were performed by gaussian 09 package using two layers oniom method at the oniom (mpw1pw91/6-311++g(d,p)/uff) level. in the first step, h2o2 is encapsulated in the hydrophobic cavity. in the second step, h2o2 molecule oxidized the ald...

Quantifying coherence is an essential endeavor for both quantum mechanical foundations and technologies. We present a bona fide measure of by utilizing the Tsallis relative operator (α,β)-entropy. first prove that proposed fulfills all criteria well defined measure, including strong monotonicity in resource theories coherence. then study ordering (α,β)-entropy coherence, α-entropies Rényi α-ent...

This article studies the estimation of precision matrix a high-dimensional Gaussian network. We investigate graphical selector operator with shrinkage, GSOS for short, to maximize penalized likelihood function where elastic net-type penalty is considered as combination norm-one and targeted Frobenius norm penalty. Numerical illustrations demonstrate that our proposed methodology competitive can...

We prove the results stated in the main paper. We start by providing a brief summary of the notations used in the paper. Set [p] = {1, . . . , p} and for a subset J ⊂ [p], let |J | be its cardinality. Bold upper (resp. lower) case letters denote matrices (resp. vectors), and the same letter not bold represents its coefficients, e.g. aj denotes the jth entry of a. For an n × p matrix A with colu...

In the recent past Kernelized Fuzzy C-Means clustering technique has earned popularity especially in the machine learning community. This technique has been derived from the conventional Fuzzy C-Means clustering technique of Bezdek by defining the vector norm with the Gaussian Radial Basic Function instead of a Euclidean distance. Subsequently the fuzzy cluster centroids and the partition matri...

In recent years analysis of complexity of learning Gaussian mixture models from sampled data has received significant attention in computational machine learning and theory communities. In this paper we present the first result showing that polynomial time learning of multidimensional Gaussian Mixture distributions is possible when the separation between the component means is arbitrarily small...

Principal Component Analysis (PCA) is widely used for identifying the major components of statistically distributed point clouds. Robust versions of PCA, often based in part on the l norm (rather than the l norm), are increasingly used, especially for point clouds with many outliers. Neither standard PCA nor robust PCAs can provide, without additional assumptions, reliable information for outli...