The concepts of wavelet and multiresolution analysis has been extended to many different setups. One can replace the dilation factor 2 by an integer and one needs to construct wavelets to generate the whole space . In general, in higher dimensions, it can be replaced by a dilation matrix , in which case the number of wavelets required is . But in all these cases, the translation set is always a...

In this paper we use the concept of wavelet sets as introduced by X. Dai and D. Larson, to decompose the wavelet representation of the discrete group associated to an arbitrary n×n integer dilation matrix as a direct integral of irreducible monomial representations. In so doing we generalize a result of F. Martin and A. Valette in which they show that the wavelet representation is weakly equiva...

In this paper, we develop a method to construct non-redundant directional wavelet filter banks. Our method uses a special class of filters called Neville filters and can construct non-redundant wavelet filter banks in any dimension for any dilation matrix. The resulting filter banks have directional analysis highpass filters, thus can be used in extracting directional contents in multi-D signal...

We introduce the concept of the modular function for a shiftinvariant subspace that can be represented by normalized tight frame generators for the shift-invariant subspace and prove that it is independent of the selections of the frame generators for the subspace. We shall apply it to study the connections between the dimension functions of wavelet frames for any expansive integer matrix A and...

Cytokine and extracellular matrix (ECM) homeostasis are distinct systems that are each dysregulated in heart failure. Here we show that tissue inhibitor of metalloproteinase (TIMP)-3 is a critical regulator of both systems in a mouse model of left ventricular (LV) dilation and dysfunction. Timp-3 / mice develop precipitous LV dilation and dysfunction reminiscent of dilated cardiomyopathy (DCM),...

The water leak-off during hydraulic fracturing in shale gas reservoirs is a complicated transport behavior involving thermal (T), hydrodynamic (H), mechanical (M) and chemical (C) processes. Although many leak-off models have been published, none of the models fully coupled the transient fluid flow modeling with heat transfer, chemical-potential equilibrium and natural-fracture dilation phenome...

OBJECTIVE Aortic aneurysm, focal dilation of the aorta, results from impaired integrity of aortic extracellular matrix (ECM). Matrix metalloproteinases (MMPs) are traditionally known as ECM-degrading enzymes. MMP2 has been associated with aneurysm in patients and in animal models. We investigated the role of MMP2 in thoracic aortic aneurysm using 2 models of aortic remodeling and aneurysm. AP...

We provide a method for constructing regular sampling lattices in arbitrary dimensions together with an integer dilation matrix. Subsampling using this dilation matrix leads to a similarity-transformed version of the lattice with a chosen density reduction. These lattices are interesting candidates for multidimensional wavelet constructions with a limited number of subbands. 1. Primer on sampli...