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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)
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)
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)
A device designed specifically for mild to severe concussions was used to produce quantitative experimental blunt brain injury in male Wistar rats. We have examined the effects of varying magnitudes of cerebral trauma on the maximal binding capacity (Bmax) of D1 and D2 dopamine (DA) receptors. The Bmax for each receptor subtype was obtained from Scatchard(More)
Natriuretic peptides inhibit the release and action of many hormones through cyclic guanosine monophosphate (cGMP), but the mechanism of cGMP action is unclear. In frog ventricular muscle and guinea-pig hippocampal neurons, cGMP inhibits voltage-activated Ca2+ currents by stimulating phosphodiesterase activity and reducing intracellular cyclic AMP; however,(More)
The development of fast and accurate methods of photometric redshift estimation is a vital step towards being able to fully utilize the data of next-generation surveys within precision cosmology. In this paper we apply a specific approach to spectral connectivity analysis (SCA; Lee & Wasserman 2009) called diffusion map. SCA is a class of non-linear(More)
To obtain thermostable immunoreagents specific for the spore form of Bacillus anthracis two llamas were immunized with a combination of six different recombinant proteins. These proteins BclA, gerQ, SODA1, SOD15, BxpB and the protein p5303 have all been shown as components of the B. anthracis spore and could potentially serve as targets for the detection of(More)
Testing theories of hierarchical structure formation requires estimating the distribution of galaxy morphologies and its change with redshift. One aspect of this investigation involves identifying galaxies with disturbed morphologies (e.g. merging galaxies). This is often done by summarizing galaxy images using, e.g. the concentration, asymmetry and(More)
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