Molecular similarity is a pervasive concept in chemistry. It is essential to many aspects of chemical reasoning and analysis and is perhaps the fundamental assumption underlying medicinal chemistry. Dissimilarity, the complement of similarity, also plays a major role in a growing number of applications of molecular diversity in combinatorial chemistry, high-throughput screening, and related fie...

AbstractThe boundary layer flow over a horizontal plate with power law variations in the freestream velocity and wall temperature of the form Ue ∼ x and Tw − T∞ ∼ x and with viscous dissipation, is studied. The boundary layer equations are transformed to a dimensionless system of equations using a non–similarity variable ξ(x) and a pseudo-similarity variable η(x, y). The effects of the various ...

Method of creating sketch from available photograph is known as sketch synthesis. To synthesize face sketch, similarity between different photograph patches is evaluated. Existing patch level method requires huge computational time and space for finding candidate photograph patches. Photograph patches are replaced by sparse coefficients using sparse coding. Sparse representation is used to sele...

When one sees a printout of Pascal’s triangle of binomial coefficients computed modulo the prime 2 (Figure 1, where all zeros have been replaced by blanks), one is immediately struck by the pleasing self-similarity in the picture. Modulo a prime p which is different from 2 (Figure 2), the self-similarity is a little more complicated, if no less striking. Another striking feature of the mod 2 tr...

In this extended abstract we introduce a new method for eliciting experts, prior knowledge about the similarity of the roles of features in the prediction task. The key idea is to use an interactive multidimensional-scaling-type scatterplot display of the features to elicit the similarity relationships, and then use the elicited relationships in the prior distribution of prediction parameters. ...

A diagram for Bianchi spaces with vanishing vector of structure constants (type A in the Ellis-MacCallum classification) illustrates the relations among their different types under similarity transformations. The Ricci coefficients and the Ricci tensor are related by a Cremona transformation.

Many similarity coefficients for binary data are defined as fractions. For certain resemblance measures the denominator may become zero. If the denominator is zero the value of the coefficient is indeterminate. It is shown that the seriousness of the indeterminacy problem differs with the resemblance measures. Following Batagelj and Bren (1995) we remove the indeterminacies by defining appropri...

$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, w...

This paper presents a novel robust digital image watermarking scheme using subsampling and nonnegative matrix factorization. Firstly, subsampling is used to construct a subimage sequence. Then, based on the column similarity of the subimage sequence, nonnegative matrix factorization (NMF) is applied to decompose the sequence. A Gaussian pseudo-random watermark sequence is embedded in the factor...