Let (DS, QS, sim) be a retrieval system consisting of a document space DS, a query space QS, and a function sim, expressing the similarity between a document and a query. Following Everett and Cater, we introduce topologies on the document space. These topologies are generated by the similarity function sim and the query space QS. Three topolgies will be studied : the retrieval topology, the si...

We define the similarity boundary of a self-similar set and use it to analyze the properties of self-similar sets in the general setting of any complete metric space. The similarity boundary is an attempt at extending the concept of the topological boundary in a way that is consistent with our intuitive understanding of the term boundary. We also show how with the analysis of the similarity bou...

This account summarizes Dr. Subhash Basak’s work in the field of molecular similarity. In particular, it looks at the development and application of quantitative molecular similarity analysis (QMSA) techniques using physicochemical properties, topological indices, and atom pairs as descriptors for developing structureor property-based similarity spaces and the use of a k-nearest neighbors (kNN)...

Self-similarity of plants has attracted the attention of biologists for at least 50 years, yet its formal treatment is rare, and no measure for quantifying the degree of self-similarity currently exists. We propose a formal definition and measures of self-similarity, tailored to branching plant structures. To evaluate self-similarity, we make use of an algorithm for computing topological distan...

In this paper, we present a novel scheme for archival and retrieval of symbolic images from a symbolic image database based on Triangular Spatial Relationship [1]. Conventionally, Triangular Spatial Relationship was designed to preserve only spatial relationship among the components in a symbolic image neglecting the topological relationship existing between them, where topological relationship...

Two real entried (respectively: orthogonal) n x n matrices^! andB are said to be linearly similar if there is an invertible real (resp. orthogonal) n x n matrix C with CAC~ = B. Of course, A, B and C may be regarded as linear functions from R (resp. isometries from S~) to itself. The matrices A and B are said to be (resp. homogeneously differentiably) differentiably similar if there is a diffeo...

In this paper we present a method for the multi-resolution comparison of biomolecular electrostatic potentials without the need for global structural alignment of the biomolecules. The underlying computational geometry algorithm uses multi-resolution attributed contour trees (MACTs) to compare the topological features of volumetric scalar fields. We apply the MACTs to compute electrostatic simi...