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We provide a framework for structural multiscale geometric organization of graphs and subsets of R(n). We use diffusion semigroups to generate multiscale geometries in order to organize and represent complex structures. We show that appropriately selected eigenfunctions or scaling functions of Markov matrices, which describe local transitions, lead to(More)
Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) non-Gaussian behavior of image statistics, i.e. high kurtosis, heavy tails, and sharp central cusps. In this paper we review some recent results in statistical modeling of natural images that attempt to explain these patterns.(More)
Sparse low-dimensional matrix factorization methods applied to biological data with latent structure Graphical model selection in high dimensional settings: Practical methods and fundamental limits
In the companion article, a framework for structural multiscale geometric organization of subsets of R(n) and of graphs was introduced. Here, diffusion semigroups are used to generate multiscale analyses in order to organize and represent complex structures. We emphasize the multiscale nature of these problems and build scaling functions of Markov matrices(More)
BACKGROUND Although quality of life (QOL) is generally improved by heart transplantation, medical noncompliance and mental health and QOL limitations often emerge and persist. Transplant teams' ability to address these issues is hampered because many patients reside long distances from the transplant program. We therefore conducted the first empirical(More)
The receptive fields for simple cells in visual cortex show a strong preference for edges of a particular orientation and display adjacent excitatory and inhibitory subfields. These subfields are projections from ON-center and OFF-center lateral geniculate nucleus cells, respectively. Here we present a single-cell model using ON and OFF channels, a natural(More)
Mutations in the dystrophin gene cause Duchenne muscular dystrophy (DMD) most commonly through loss of protein expression. In a small subpopulation of patients, missense mutations can cause DMD, Becker muscular dystrophy, or X-linked cardiomyopathy. Nearly one-half of disease-causing missense mutations are located in actin-binding domain 1 (ABD1) of(More)
Various reports and opinion papers have offered suggestions to alleviate the national and California RN shortages. The methodology of using the report card concept for comparing the number of RN jobs per 100,000 populations regionally with the national database further highlights the severe shortage of RN's in various regions in California. This report card(More)
Proton magnetic resonance spectroscopy (MRS) is being used to evaluate individuals after acute traumatic brain injury. These studies have shown that changes in certain brain metabolites are associated with poor neurologic outcomes. The majority of MRS studies have been obtained relatively late after injury, but there have been a few reports of use early(More)