Matrix trace inequalities are finding increased use in many areas such as analysis, where they can be used to generalise several well known classical inequalities, and computational statistics, where they can be applied, for example, to data fitting problems. In this paper we give simple proofs of two useful matrix trace inequalities and provide applications to orthogonal regression and matrix ...

Many scientific computing algorithms (in various domains, such as weather prediction, structural analysis, or electrical network analysis) strongly rely on solving fundamental matrix computation problems (such as linear system solving, eigenvalue decomposition, singular value decomposition, matrix nearness problems, joint diagonalization of matrices...). These problems are often solved using it...

Several features of subfitness are analyzed. Isbell’s Spatiality Theorem leads to the concept of T1-spatiality which is compared with the TD-spatiality. Subfitness is put into relation with other weak separation axioms (and with the existence of nearness), both in spaces and locales, and seeming discrepancies are explained. A new characteristic of subfitness by means of codensity is presented.

Machine learning can be described as the discipline of automatically “learning” concepts from data eitherwith, or without human guidance. The goal ofmostmachine learning applications is to discover patterns within data so that properties of hitherto unseen data can be predicted reliably. However, the task of learning from data can often be very challenging (naturally contingent upon the concept...

This study was designed to assess in situ the effects of sediment nearness on Crassostrea gigas metabolism. One year-old oysters were reared for 5 months (April-August) in plastic bags on metallic frames at 10 and 60 cm off the sediment at the beginning of April. The management of the energetic resources (storage, consumption) was estimated with respect to biochemical changes of proteins, lipid...

BACKGROUND Standard measures of dyspnea rely on self-report. Cognitive impairment and nearness to death may interfere with symptom distress reporting leading to underrecognition and overtreatment or undertreatment. Previous psychometric testing of the Respiratory Distress Observation Scale (RDOS) demonstrated internal consistency and convergent validity with dyspnea self-report and discriminant...

2 State of the art in robot motion algorithms 3 2.1 Global path-planners . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Grid methods (cell decomposition) . . . . . . . . . . . . . 3 2.1.2 Roadmap methods . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Local and reactive algorithms . . . . . . . . . . . . . . . . . . . . 4 2.2.1 Potential Field Methods (PF) . . . . . . . . . . . . ....

A formula for the distance of a Toeplitz matrix to the subspace of {e}-circulant matrices is presented, and applications of {e}-circulant matrices to preconditioning of linear systems of equations with a Toeplitz matrix are discussed. Copyright c © 2006 John Wiley & Sons, Ltd. key words: Toeplitz matrix, circulant matrix, {e}-circulant, matrix nearness problem, distance to normality, preconditi...

This paper introduces two new matrix nearness problems that are intended to generalize the distance to instability and the distance to stability. They are named the distance to delocalization and the distance to localization due to their applicability in analyzing the robustness of eigenvalues with respect to arbitrary localization sets (domains) in the complex plane. For the open left-half pla...