It is well documented that natural images are compressible in wavelet bases and tend to exhibit fractal properties. In this paper, we investigate statistical models that mimic these behaviors. We then use our models to make predictions on the statistics of the wavelet coefficients. Following an innovation modeling approach, we identify a general class of finite-variance self-similar sparse rand...

The purpose of this study was to test the hypothesis that endothelium-dependent dilation (flow-induced dilation and ACh-induced dilation) in rat soleus muscle arterioles is impaired by hindlimb unweighting (HLU). Male Sprague-Dawley rats (approximately 300 g) were exposed to HLU or weight-bearing control (Con) conditions for 14 days. Soleus first-order (1A) and second-order (2A) arterioles were...

We show that the commutant lifting theorem for n-tuples of commuting contractions with regular dilations fails to be true. A positive answer is given for operators which ”double intertwine” given n-tuples of contractions. The commutant lifting theorem is one of the most important results of the Sz. Nagy—Foias dilation theory. It is usually stated in the following way: Theorem. Let T and T ′ be ...

This model ties gravitation and celestial mechanics kinematics directly to time dilation. It is a new theory of cosmology the evolution galaxies. Space are not two separate things, but aspects single thing, “spacetime”. Whatever affects space, time, vice-versa. If speeds up, space must contract maintain speed light, c, when thickens into mass, it harder evolve forward, appears slow. spatial eve...

w)I2 + [G(w + :)I' = 1. Its periodic extension then satisfies +*(w) 2 1 and hence a sampling function with q w) = +(w)/G*(w) belongs to L2(Z2). 5) Daubechies Wavelets: The scaling function for the simplest class of Daubechies wavelets, those with support on [0, 31, are defined by the dilation equations REFERENCES [ 11 I. Daubechies, " Orthonormal bases of compactly supported wavelets, " Comm. c...

Sparse exchangeable graphs on R+, and the associated graphex framework for sparse graphs, generalize exchangeable graphs on N, and the associated graphon framework for dense graphs. We develop the graphex framework as a tool for statistical network analysis by identifying the sampling scheme that is naturally associated with the models of the framework, and by introducing a general consistent e...