Image Restoration: A General Wavelet Frame Based Model and Its Asymptotic Analysis

Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a generic wavelet frame based image restoration model, called the "general model", which includes most of the existing wavelet frame based models as special cases. Moreover, the general model also includes examples that are new to the literature. Motivated by our earlier studies [1-3], We provide an asymptotic analysis of the general model as image resolution goes to infinity, which establishes a connection between the general model in discrete setting and a new variatonal model in continuum setting. The variational model also includes some of the existing variational models as special cases, such as the total generalized variational model proposed by [4]. In the end, we introduce an algorithm solving the general model and present one numerical simulation as an example

A multi-protein receptor-ligand complex underlies combinatorial dendrite guidance choices in C. elegans.

Ligand receptor interactions instruct axon guidance during development. How dendrites are guided to specific targets is less understood. The C. elegans PVD sensory neuron innervates muscle-skin interface with its elaborate dendritic branches. Here, we found that LECT-2, the ortholog of leukocyte cell-derived chemotaxin-2 (LECT2), is secreted from the muscles and required for muscle innervation by PVD. Mosaic analyses showed that LECT-2 acted locally to guide the growth of terminal branches. Ectopic expression of LECT-2 from seam cells is sufficient to redirect the PVD dendrites onto seam cells. LECT-2 functions in a multi-protein receptor-ligand complex that also contains two transmembrane ligands on the skin, SAX-7/L1CAM and MNR-1, and the neuronal transmembrane receptor DMA-1. LECT-2 greatly enhances the binding between SAX-7, MNR-1 and DMA-1. The activation of DMA-1 strictly requires all three ligands, which establishes a combinatorial code to precisely target and pattern dendritic arbors

Nonlinear analysis of dynamical complex networks

Copyright © 2013 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Complex networks are composed of a large number of highly interconnected dynamical units and therefore exhibit very complicated dynamics. Examples of such complex networks include the Internet, that is, a network of routers or domains, the World Wide Web (WWW), that is, a network of websites, the brain, that is, a network of neurons, and an organization, that is, a network of people. Since the introduction of the small-world network principle, a great deal of research has been focused on the dependence of the asymptotic behavior of interconnected oscillatory agents on the structural properties of complex networks. It has been found out that the general structure of the interaction network may play a crucial role in the emergence of synchronization phenomena in various fields such as physics, technology, and the life sciences