The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski’s coagulation equations in which the number of aggregations is limited. The latter models the deterministic evolution of concentrations of particles in a medium where particles coalesce pairwise as time passes and each particle can only perform a given number of aggregation...

Bridging levels of "granularity" and "scale" are frequently cited as key problems for biomedical informatics. However, detailed accounts of what is meant by these terms are sparse in the literature. We argue for distinguishing two notions: "size range," which deals with physical size, and "collectivity," which deals with aggregations of individuals into collections, which have emergent properti...

Dielectric data in volcanic ash at weather radar wavelengths (centimeter range) are extremely sparse and are crucial for radar sensing of ash clouds and for imaging of volcanic terrains. This study extends previous data to include a wavelength range of 1.5-7.5 cm and volcanic ash compositions of 50-75 % silica. The real part of the complex permittivity, 2′, of volcanic ash is 6± 0.5 (1σ) for al...

Bridging levels of “granularity” and “scale” are frequently cited as key problems for biomedical informatics. However, detailed accounts of what is meant by these terms are sparse in the literature. We argue for distinguishing two notions: “size range”, which deals with physical size, and “collectivity”, which deals with aggregations of individuals into collections which have emergent propertie...

The recently proposed sparse shape composition (SSC) opens a new avenue for shape prior modeling. Instead of assuming any parametric model of shape statistics, SSC incorporates shape priors on-the-fly by approximating a shape instance (usually derived from appearance cues) by a sparse combination of shapes in a training repository. Theoretically, one can increase the modeling capability of SSC ...

“Shape” and “appearance”, the two pillars of a deformable model, complement each other in object segmentation. In many medical imaging applications, while the low-level appearance information is weak or mis-leading, shape priors play a more important role to guide a correct segmentation. The recently proposed Sparse Shape Composition (SSC) 49,51 opens a new avenue for shape prior modeling. Inst...

The dry landscape garden at Ryoanji Temple in Kyoto, Japan, a UNESCO world heritage site, intrigues hundreds of thousands of visitors every year with its abstract, sparse and seemingly random composition of rocks and moss on an otherwise empty rectangle of raked gravel. Here we apply a model of shape analysis in early visual processing to show that the 'empty' space of the garden is implicitly ...

A common problem with OnLine Analytical Processing (OLAP) databases is data explosion data size multiplies, when it is loaded from the source data into multidimensional cubes. Data explosion is not an issue for small databases, but can be serious problems with large databases. In this paper we discuss the sparsity and data explosion phenomenon in multidimensional data model, which lie at the co...

Background: Microarray experiments can simultaneously determine the expression of thousands of genes. Identification of potential genes from microarray data for diagnosis of cancer is important. This study aimed to identify genes for the diagnosis of acute myeloid and lymphoblastic leukemia using a sparse feature selection method. Materials and Methods: In this descriptive study, the expressio...