Fast handheld two-photon fluorescence microendoscope with a 475 microm x 475 microm field of view for in vivo imaging

A fast handheld two-photon fiber-optic fluorescence endoscope for three-dimensional (3D) in vivo cellular imaging is developed. The compact handheld probe of the two-photon endoscope can simply be placed into contact with the target tissue to reveal clear 3D surface and subsurface histological images without biopsy. The new system has, to the best of our knowledge, the largest field of view (FOV) of 475 microm x 475 microm and a 3D imaging volume larger than 475 microm x 475 microm x 250 microm. A real-time two-photon fluorescence image is displayed at 0.4 mm(2)/s. The lateral and axial resolutions of the two-photon fluorescence endoscope are better than 1 and 14.5 microm, respectively.     

Domination critical graphs

A set of vertices S is said to dominate the graph G if for each v ? S, there is a vertex u ∈ S with u adjacent to v. The smallest cardinality of any such dominating set is called the domination number of G and is denoted by γ(G). The purpose of this paper is to initiate an investigation of those graphs which are critical in the following sense: For each v, u ∈ V(G) with v not adjacent to u, γ(G + vu) < γ(G). Thus G is k-y-critical if γ(G) = k and for each edge e ? E(G), γ(G + e) = k ?1. The 2-domination critical graphs are characterized the properties of the k-critical graphs with k ≥ 3 are studied. In particular, the connected 3-critical graphs of even order are shown to have a 1-factor and some stringent restrictions on their degree sequences and diameters are obtained.