Vector cross product in n-dimensional vector space

The definition of vector cross product (VCP) introduced by Eckmann only exists in thethree- and the seven- dimensional vector space. In this paper, according to the orthogonal completeness, magnitude of basis vector cross product and all kinds of combinations of basis vector $\hat{e}_i$, the generalized definition of VCP in the odd n-dimensional vector space is given by introducing a cross term $X_{AB}$. In addition, the definition is validated by reducing the generalization definition to the fundamental three- and seven-dimensional vector space.Comment: 9 pages, 1 figure, comments are welcom

Probing Human Response Times

In a recent preprint \cite{eck}, the temporal dynamics of an e-mail network has been investigated by J.P. Eckmann, E. Moses and D. Sergi. Specifically, the time period between an e-mail message and its reply were recorded. It will be shown here that their data agrees quantitatively with the frame work proposed to explain a recent experiment on the response of ``internauts'' to a news publication \cite{www2} despite differences in communication channels, topics, time-scale and socio-economic characteristics of the two population. This suggest a generalized response time distribution $\sim t^{-1}$ for human populations in the absence of deadlines with important implications for psychological and social studies as well the study of dynamical networks.Comment: 6 pages including 2 figures. Subm. for Proceedings of Frontier Science 200

Experiments on Internet Response

This paper suggests a generalized distribution of response times to new information $\sim t^{-b}$ for human populations in the absence of deadlines. This has important implications for psychological and social studies as well the study of dynamical networks such as the WWW.Comment: 4 figures 6 page

Inertia tensor and cross product In n-dimensions space

We demonstrated using an elementary method that the inertia tensor of a material point and the cross product of two vectors were only possible in a three or seven dimensional space. The representation matrix of the cross product in the seven dimensional space and its properties were given. The relationship between the inertia tensor and the octonions algebra was emphasized for the first time in this work

POOL File Catalog, Collection and Metadata Components

The POOL project is the common persistency framework for the LHC experiments to store petabytes of experiment data and metadata in a distributed and grid enabled way. POOL is a hybrid event store consisting of a data streaming layer and a relational layer. This paper describes the design of file catalog, collection and metadata components which are not part of the data streaming layer of POOL and outlines how POOL aims to provide transparent and efficient data access for a wide range of environments and use cases - ranging from a large production site down to a single disconnected laptops. The file catalog is the central POOL component translating logical data references to physical data files in a grid environment. POOL collections with their associated metadata provide an abstract way of accessing experiment data via their logical grouping into sets of related data objects.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 4 pages, 1 eps figure, PSN MOKT00

A Cheeger-Buser-Type inequality on CW complexes

We extend the definition of boundary expansion to CW complexes and prove a Cheeger-Buser-Type relation between the spectral gap of the Laplacian and the expansion of an orientable CW complex