We consider in this paper two different types of the weighted geometric means positive definite operators. show component-wise bijection these and give a property spectral mean as metric midpoint. Moreover, several interesting inequalities related with operators will be shown. also see meaning gyrogroup structure finite dimension find formulas 2-by-2 matrices density matrices.

batch Fermentation by Means of Genetic Programming K.D. BETTENHAUSEN , P. MARENBACH , S. FREYER , H. RETTENMAIER and U. NIEKEN Darmstadt University of Technology , Institute of Control Engineering, Department of Control Systems Theory & Robotics, Landgraf-Georg-Strasse 4, D-64283 Darmstadt, Germany BASF AG, D-67056 Ludwigshafen, Germany Abstract. The article at hand describes an approach for th...

In this paper, we address a single-machine scheduling problem with due dates and batch setup times to minimize the weighted number of tardy jobs. We give a pseudo-polynomial dynamic program and a fully-polynomial approximation scheme for the case where the due dates are uniform within a family. 2007 Elsevier Ltd. All rights reserved.

Combining different microarray data sets across platforms has the potential to generally increase statistical power. Distance Weighted Discrimination (DWD) is a powerful tool for solving binary classification problems in high dimensions. It has also been shown to provide an effective approach to binary cross-platform batch adjustment. In this paper, we extend the binary DWD to the multicategory...

In modelling risk management strategies (i.e., within-lot batch testing, statistical process control), two basic assumptions have been normally made: that the true concentration of microorganisms are log-normally distributed within a batch, and that the variance of the samples is the same for a little or highly contaminated lot. These assumptions were evaluated by characterising the between-bat...

To provide statistical guarantees of QoS, the Internet requires a measurement infrastructure for estimating available resources from actual tra c. In this paper, we outline an algorithm that collects a histogram of the occupancy of a single-server FCFS queue at packet arrival times, and infers the loss rate and delay distribution from such measurements. Direct estimation of such QoS parameters ...

We analyze online [5] and mini-batch [16] k-means variants. Both scale up the widely used k-means algorithm via stochastic approximation, and have become popular for large-scale clustering and unsupervised feature learning. We show, for the first time, that starting with any initial solution, they converge to a “local optimum” at rateO( 1t ) (in terms of the k-means objective) under general con...