The geometry and topology of the region in which a director field is embedded impose limitations on kind supported orientational order. These manifest as compatibility conditions that relate quantities describing to embedding space. For example, two dimensions (2D) splay bend fields suffice determine uniquely (up rigid motions) must comply with one relation linear Gaussian curvature manifold. I...

Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map from space visual so as preserve some dissimilarity (similarity) measure, such the Euclidean distance example. In fact, although adopting distinct mathematical formulations favor different aspects of data, most multidimensio...

An efficient compression algorithm for multi-view video sequences, which are captured by two-dimensional (2D) camera arrays, is proposed in this work. First, we propose a novel prediction structure, called three-dimensional hierarchical B prediction (3DHBP), which can efficiently reduce horizontal inter-view redundancies, vertical inter-view redundancies, and temporal redundancies in multi-view...

Oversampled filter banks can be used to enhance resilience to erasures in communication systems in much the same way that finite-dimensional frames have previously been applied. This paper extends previous finite dimensional treatments to frames and signals in l2(Z) with frame expansions that can be implemented efficiently with filter banks. It is shown that tight frames attain best performance...