The purpose of these notes is to define an equivalence between the natural homology theories associated to operads and the homology of functors over certain categories of operators (PROPs) related to operads.

as recent advancements in biology shows, the molecular machines specially proteins, rna and complex molecules play the main role of the so called cell functionality. it means a very big part of the system biology is concerned with the interactions of such molecular components. drug industries and research institutes are trying hard to better understand the concepts underlying these interactions...

In the wake of Donaldson’s pioneering work [6], Picard-Lefschetz theory has been extended from its original context in algebraic geometry to (a very large class of) symplectic manifolds. Informally speaking, one can view the theory as analogous to Kirby calculus: one of its basic insights is that one can give a (non-unique) presentation of a symplectic manifold, in terms of a symplectic hypersu...

An adaptive two-step paradigm for the superresolution of optical images is developed in this paper. The procedure locally projects image samples onto a family of kernels that are learned from image data. First, an unsupervised feature extraction is performed on local neighborhood information from a training image. These features are then used to cluster the neighborhoods into disjoint sets for ...

Although genes have specific phenotypic consequences in a given species, this functional relationship can clearly change during the course of evolution. Many cases of evolutionary dissociations between homologous genes and homologous morphological features are now known. These dissociations have interesting and important implications for understanding the genetic basis for evolutionary change i...