Various researchers have shown that the binary n-cube (or hypercube) can embed any r-ary m-cubes, having the same number of nodes, with dilation 1. Their construction method is primarily based on the reflected Gray code. We present a different embedding method based on matrix transformations' schemes that achieves the same results. In addition, this method has a nice property that makes it suit...

The simplicial rook graph SR(d, n) is the graph whose vertices are the lattice points in the nth dilate of the standard simplex in R, with two vertices adjacent if they differ in exactly two coordinates. We prove that the adjacency and Laplacian matrices of SR(3, n) have integral spectra for every n. We conjecture that SR(d, n) is integral for all d and n, and give a geometric construction of a...

Abstract. Let A be a square matrix or a linear operator on a Hilbert space H. A dilation of A is a linear operator M on a larger space K ⊃ H such that A = PHM |H, where PH is orthogonal projection onto H. Often it is required additionally that M be a dilation of A for all or a range of positive integer powers k. While much work has been aimed at proving existence of dilations with various prope...

achalasia is a well- defined esophageal motor disorder. graded pneumatic dilation using rigiflex ballon is one of the therapeutic modalities that had not been evaluated in a large long-term study. we aimed at evaluating long-term efficacy of graded rigiflex pneumatic dilation in the treatment of achalasia. symptomatic patients with achalasia who had been referred to our center were consecutivel...

When a Cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L2 = L2(IR) with dilation integer factor M ≥ 2, the standard “matrix extension” approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate any polynomial except the constant. The not...

When a Cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L = L(IR) with dilation integer factor M ≥ 2, the standard “matrix extension” approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate any polynomial except the constant. The notio...

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 (DC...

The fractional Laplacian (−�)γ/2 commutes with the primary coordination transformations in the Euclidean space Rd: dilation, translation and rotation, and has tight link to splines, fractals and stable Levy processes. For 0 < γ < d, its inverse is the classical Riesz potential Iγ which is dilationinvariant and translation-invariant. In this work, we investigate the functional properties (contin...

RATIONALE Aging represents a major risk factor for coronary artery disease and aortic aneurysm formation. MicroRNAs (miRs) have emerged as key regulators of biological processes, but their role in age-associated vascular pathologies is unknown. OBJECTIVE We aim to identify miRs in the vasculature that are regulated by age and play a role in age-induced vascular pathologies. METHODS AND RESU...

BACKGROUND RECS1 is a mechanical stress responsive gene and RECS1 knockout (KO) mice (older than 14 months) are prone to cystic medial degeneration (CMD). The present study was designed to assess whether RECS1 KO mice have altered gelatinase (matrix metalloproteinase (MMP)-2 and MMP-9) levels and whether they are prone to aortic dilation. METHODS AND RESULTS Aortic and plasma gelatinase level...