For a given class F of uniform frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation |〈fk, fl〉| among all frames {fk}k∈I ∈ F . We first analyze finite-dimensional Grassmannian frames. Using links to packings in Grassmannian spaces and antipodal spherical codes we derive bounds on the minimal achievable correlation for Grassmannian frames. These ...

Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. In this paper, we introduce the notion of a sparse fusion frame, that is, a fusion frame whose subspaces are generated by orthonormal basis vectors that are sparse in a ‘uniform basis’ over all subspaces, thereby enabling low-complexity fusion frame decomposition...

Nowhere dense classes of graphs [21, 22] are very general classes of uniformly sparse graphs with several seemingly unrelated characterisations. From an algorithmic perspective, a characterisation of these classes in terms of uniform quasi-wideness, a concept originating in finite model theory, has proved to be particularly useful. Uniform quasi-wideness is used in many fpt-algorithms on nowher...

The purpose of this note is to report the main results obtained by the authors in [8] and [9], respectively. The notion of a Smyth completable quasi-uniform space provides an efficient tool to give a topological foundation for many kinds of spaces which arise naturally in Theoretical Computer Science; in particular in Domain Theory (e.g. [5], [13] and [14]) and Complexity Theory (e.g. [9] and [...

When a live streaming video is delivered over a peer-to-peer (P2P) network, the video is divided into several chunks and distributed to peers. Each chunk has its own playback time deadline. A chunk delay can be a problem of great concern because a serious chunk delay can produce obvious discontinuity of the streaming video, resulting in low satisfaction for a viewer. The playback time of a dela...

This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as reproduction of second-degree polynomials, approximation order, conditions for convexity preservation. In particular, σ quasi-uniform grids with σ≤4, get quasi C3 that maintains properties initia...

In this paper 1 we describe in precise the structure of all rigid modal rooted frames of depth 2. The interest to rigid frames came from the paper [5] where it has been showed that any given quasi-characterizing inference rule is self-admissible if and only if the frame of the algebra generated that rule is not rigid. The study of admissibility of inference rules was, in particular, motivated b...

Conventionally, the inverse problem of gated cardiac SPECT is solved by reconstructing the images frame-by-frame, ignoring the inter-frame correlation along the time dimension. To compensate for the non-uniform attenuation for quantitative cardiac imaging, iterative image reconstruction has been a choice which could utilize an a priori constraint on the inter-frame correlation for a penalized m...