W. L. Bynum introduced the weakly convergent sequence coefficient WCS(A') of the Banach space X as WCS(Jf) = sup{M: for each weakly convergent sequence {xn} in X , there is some y e co({x«}) such that M • lim sup ||x,, y\\ < A({x„})} . We consider the weakly convergent sequence coefficient of the /^-product space Z = (fTjLi Xi)t of tne finite non-Schur space Xx, ... , X„ and show that WCS(Z) = ...

This paper describes MEXAR2, a software tool that is currently used to synthesize the operational commands for data downlink from the on-board memory of an interplanetary space mission spacecraft to the ground stations. The tool has been in daily use by the Mission Planning Team of MARS EXPRESS at the European Space Agency since early 2005. Goal of this paper is to present a quick overview of h...

Product quantization [1] is a popular technique for compactly encoding high dimensional vectors to facilitate scalable approximate nearest neighbor (ANN) search on massive datasets. In this paper, we present a general extension to product quantization and its recent variants [2, 3]. Rather than learning a single global product quantizer in the original ambient space, our method partitions the s...

In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how to compute different types of observables, and discuss the concept of a tangent space. We explain how to optimize ground-state approximations, implement real-time evolution and describe elementary ...

The information capacities of two-dimensional optical low-pass channels are discussed. Coherent and incoherent systems operating under finite optical power and area constraints are characterized in terms of two criteria:spacebandwidth product (SBP; the number of pixels required for achieving maximum information capacity) and resolution (G(min); the smallest spot size capable of supporting posit...

It is shown that Witten's star product in string field theory, defined as the overlap of half strings, is equivalent to the Moyal star product involving the relativistic phase space of even string modes. The string field ψ A (x µ [σ]) can be rewritten as a phase space field of the even modes A (x µ 2n , x 0 , p µ 2n) , where x µ 2n are the positions of the even string modes, and p µ 2n are rela...

B.Y. Chen [3] established a sharp inequality for the warping function of a warped product submanifold in a Riemannian space form in terms of the squared mean curvature. For a survey on warped product submanifolds we refer to [4]. In [8], we established a similar relationship between the warping function f (intrinsic structure) and the squared mean curvature and the holomorphic sectional curvatu...

A good distance function is an essential tool in applications which involve querying large databases, such as image retrieval and bioinformatics. We describe a non-parametric algorithm for distance function learning which is based on the boosting of low grade weak learners in a product space. The algorithm learns a function defined over pairs of points, using supervision in the form of equivale...