Recent studies has revealed that Microtubules (MTs) exhibit three transition states of growth, shrinkage and pause. In this paper, we first introduce a three states random evolution model as a framework for studying MTs dynamics in three transition states of growth, pause and shrinkage. Then, we introduce a nontraditional stack run encoding scheme with 5 symbols for detecting transition states ...

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to...

A weakly admissible mesh (WAM) on a continuum real-valued domain is sequence of discrete grids such that the maximum norm polynomials grid comparable to supremum domain. The asymptotic rate growth sizes and comparability constants must grow in controlled manner. In this paper, we recognize notion WAM can be generalized hierarchical subspaces not necessarily polynomial functions, analyze particu...