We present what to our knowledge is a new method of optimized torsion-angle normal-mode analysis, in which the normal modes move along curved paths in Cartesian space. We show that optimized torsion-angle normal modes reproduce protein conformational changes more accurately than Cartesian normal modes. We also show that orthogonalizing the displacement vectors from torsion-angle normal-mode ana...

It is proved that equations between arrows assumed for cartesian categories are maximal in the sense that extending them with any new equation in the language of free cartesian categories collapses a cartesian category into a preorder. An analogous result holds for categories with binary products, which may lack a terminal object. The proof is based on a coherence result for cartesian categorie...

The Cartesian product of graphs was introduced more than 50 years ago and many fundamental results were obtained since then. Nevertheless, in the last years several basic problems on the Cartesian product were solved and interesting theorems proved on topics of contemporary interest in graph theory. Here we survey recent developments on the structure of the Cartesian product with emphasis on th...

In this paper, the Hyper - Zagreb index of the Cartesian product, composition and corona product of graphs are computed. These corrects some errors in G. H. Shirdel et al.[11].

The neural basis of pattern recognition is a central problem in visual neuroscience. Responses of single cells were recorded in area V4 of macaque monkey to three classes of periodic stimuli that are based on spatial derivative operators: polar (concentric and radial), hyperbolic, and conventional sinusoidal (Cartesian) gratings. Of 118 cells tested, 16 percent responded significantly more to p...

Under suitable conditions of connectivity or non-bipartiteness, each of the three standard graph products (the Cartesian product, the direct product and the strong product) satisfies the unique prime factorization property, and there are polynomial algorithms to determine the prime factors. This is most easily proved for the Cartesian product. For the other products, current proofs involve a no...

The aim of this paper is to develop a rich set of visual primitives that can be used by a camera-endowed robot as it is exploring a scene and thus generating an attentional sequence––spatio-temporally related sets of visual features. Our starting point is inspired by the work of Gallant et al. on the area V4 response of the macaque monkeys to Cartesian and non-Cartesian stimuli. The novelty of ...

Introduction THE study of topologies on X x Y is motivated by some outstanding deficiencies of the cartesian, that is the usual, topology on the product of spaces. (Throughout this paper all spaces will be assumed to be Hausdorff.) Firstly, the cartesian product of identification maps is not, in general, an identification map. As a consequence certain natural products such as the join and smash...