The late infall of cold dark matter onto an isolated galaxy, such as our own, produces streams and caustics in its halo. The outer caustics are topological spheres whereas the inner caustics are rings. The self-similar model of galactic halo formation predicts that the caustic ring radii an follow the approximate law an ∼ 1/n. In a study of 32 extended and well-measured external galactic rotati...

We discuss the relation between (topological) transitivity and strong transitivity of dynamical systems. We show that a transitive and open self-map of a compact metric space satisfying a certain expanding condition is strongly transitive. We also prove a couple of results for interval maps; for example it is shown that a transitive piecewise monotone interval map is strongly transitive.

The fact that the properties of a molecule are tightly connected to its structural  characteristics  is one of the fundamental concepts in chemistry. In this connection,  graph theory has been successfully applied in developing some relationships between topological indices and some thermodynamic properties. So ,  a novel method for computing the new descriptors to construct a quantitative rela...

To determine topological similarity between two nodes in different networks, we use the similarity measure of nodes’ local neighborhoods, as described by Milenković and Pržulj1. This measure generalizes the degree of a node, which counts the number of edges that the node touches, into the vector of graphlet degrees, that counts the number of graphlets that the node touches, for all 2-5-node gra...

We argue that in order to reason with similarity we need to model the concept of discriminating power. We offer a simple topological notion called resolution space that provides a rich mathematical framework for reasoning with limited discriminating power avoiding the vagueness paradox.

the fact that the properties of a molecule are tightly connected to its structural  characteristics  is one of the fundamental concepts in chemistry. in this connection,  graph theory has been successfully applied in developing some relationships between topological indices and some thermodynamic properties. so ,  a novel method for computing the new descriptors to construct a quantitative rela...

in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...

Statistical clustering technique is extensively employed in molecular similarity analysis where molecules can be clustered on the basis of Euclidean distances derived from rules measures. Such clusters extremely useful quantitative structure–property relations as any representative within a cluster would have properties similar to other members cluster. Consequently, topological techniques for ...

Real networks show nontrivial topological properties such as community structure and long-tail degree distribution. Moreover, many network analysis applications are based on topological comparison of complex networks. Classification and clustering of networks, model selection, and anomaly detection are just some applications of network comparison. In these applications, an effective similarity ...

Let the patch of a partner in a protein complex be the collection of atoms accounting for the interaction. To improve our understanding of the structure-function relationship, we present a patch model decoupling the topological and geometric properties. While the geometry is classically encoded by the atomic positions, the topology is recorded in a graph encoding the relative position of concen...