Optimally Sparse Frames

Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of the frame measurements of a signal typically requires a large number of additions and multiplications, and this makes a frame decomposition intractable in applications with limited computing budget. To address this problem, in this paper, we focus on frames in finite-dimensional Hilbert spaces and introduce sparsity for such frames as a new paradigm. In our terminology, a sparse frame is a frame whose elements have a sparse representation in an orthonormal basis, thereby enabling low-complexity frame decompositions. To introduce a precise meaning of optimality, we take the sum of the numbers of vectors needed of this orthonormal basis when expanding each frame vector as sparsity measure. We then analyze the recently introduced algorithm Spectral Tetris for construction of unit norm tight frames and prove that the tight frames generated by this algorithm are in fact optimally sparse with respect to the standard unit vector basis. Finally, we show that even the generalization of Spectral Tetris for the construction of unit norm frames associated with a given frame operator produces optimally sparse frames

Cohesion and Repulsion in Bayesian Distance Clustering

Clustering in high-dimensions poses many statistical challenges. While traditional distance-based clustering methods are computationally feasible, they lack probabilistic interpretation and rely on heuristics for estimation of the number of clusters. On the other hand, probabilistic model-based clustering techniques often fail to scale and devising algorithms that are able to effectively explore the posterior space is an open problem. Based on recent developments in Bayesian distance-based clustering, we propose a hybrid solution that entails defining a likelihood on pairwise distances between observations. The novelty of the approach consists in including both cohesion and repulsion terms in the likelihood, which allows for cluster identifiability. This implies that clusters are composed of objects which have small "dissimilarities" among themselves (cohesion) and similar dissimilarities to observations in other clusters (repulsion). We show how this modelling strategy has interesting connection with existing proposals in the literature as well as a decision-theoretic interpretation. The proposed method is computationally efficient and applicable to a wide variety of scenarios. We demonstrate the approach in a simulation study and an application in digital numismatics.Comment: 1 supplementary PDF attached. To view the supplementary PDF, please download the attachment under "Ancilliary Files

A user material interface for the Peridynamic Peridigm framework.

User materials (UMAT) in finite element codes allow the researchers or engineers to apply their own material routines. Simple software interfaces are specified to represent the material behavior in software. In order to use these already existing and often validated models to Peridynamics a UMAT interface is presented. It allows the simplified use of already existing material routines in the peridynamic framework Peridigm. The interface is based on the Abaqus UMAT definition and allows the integration of Fortran routines directly into Peridigm. The integration of already existing UMAT routines based in Peridigm eliminates the need for redevelopment and reprogramming material models from classical continuum mechanics theory. In addition, the same material model implementations are applicable in finite element as well as peridynamic simulations. This opens up new possibilities for analysis, verification and comparison. With this interface many material routines can be reused and applied to progressive failure analysis. The source code is stored in a GitHub repository

Effects of Hepatitis B Surface Antigen on Virus-specific and Global T Cells in Patients With Chronic HBV infection

10.1053/j.gastro.2020.04.019Gastroenterolog