Polynomial Invariant of Molecular Circuit Topology

On invariant sets topology

In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

Polynomial Closure and Topology

A Knot Polynomial Invariant for Analysis of Topology of RNA Stems and Protein Disulfide Bonds.

Knot polynomials have been used to detect and classify knots in biomolecules. Computation of knot polynomials in DNA and protein molecules have revealed the existence of knotted structures, and provided important insight into their topological structures. However, conventional knot polynomials are not well suited to study RNA molecules, as RNA structures are determined by stem regions which are...

Subdivision Invariant Polynomial Interpolation

In previous works a polynomial interpolation method for triangular meshes has been introduced. This interpolant can be used to design smooth surfaces of arbitrary topological type. In a design process, it is very useful to be able to locate the deformation made on a geometric model. The previously introduced interpolant has the so-called strict locality property: when a mesh vertex is changed, ...

MOLECULAR ANALYSIS OF THE SULFUR REGULATORY CIRCUIT OF NEUROSPORA CRASSA

The sulfur regulatory circuit of the filamentous fungus, Neurospora crassa, consists of a set of unlinked structural genes which encode sulfur catabolic and two major regulatory genes which govern their expression. The cys-3 regulatory gene encode a transacting regulatory protein which activates the expression of cys-14 and ars, whereas the other regulatory genes Scon-l and Scon-2 appear to...