It is an open problem to find a good characterization for independence or, more generally, the rank function in the d-dimensional rigidity matroid of a graph when d ≥ 3. In this paper we give a brief survey of existing lower and upper bounds on the rank of the 3-dimensional rigidity matroid of a graph and introduce a new upper bound, which may lead to the desired good characterization.

background: endometriosis is the presence of endometrial tissue outside of the uterine cavity and is the most common gynecologic disorder in women of reproductive age. we have preliminary evidence that in the presence of a 3-dimensional (3-d) fibrin matrix, human endometrial glands, stroma, and neovascularization can develop in vitro, mimicking the earliest stages of endometriosis. the aim of t...

Background Endometriosis is the presence of endometrial tissue outside of the uterine cavity and is the most common gynecologic disorder in women of reproductive age. We have preliminary evidence that in the presence of a 3-dimensional (3-D) fibrin matrix, human endometrial glands, stroma, and neovascularization can develop in vitro, mimicking the earliest stages of endometriosis. The aim of th...

We propose a mesh comparison method using a new attribute deviation metric. The considered meshes contain geometrical and appearance attributes (material color, texture, temperature, etc.). The proposed deviation metric computes local differences between the attributes of two meshes. A mesh comparison assessment can be done easily and quickly using this metric. The techniques proposed are appli...

Abstruct-3-D technology promises higher integration density and lower interconnection complexity and delay. At present, however, not much work on circuit applications has been done due to lack of insight into 3-D circuit architecture and performance. One of the purposes of realizing 3-D integration is to reduce the interconnect complexity and delay of 2-D, which is widely avowed as the harrier ...

Abstract : The goal of this paper is to find a close to isomorphic presentation of 3-manifolds in terms of Hopf algebraic expressions. To this end we define and compare three different braided tensor categories that arise naturally in the study of Hopf algebras and 3-dimensional topology. The first is the category Cob of connected surfaces with one boundary component and 3-dimensional relative ...

In this paper we show that the Inverse problems of HAMILTONIAN CYCLE and 3D-MATCHING are coNP complete. This completes the study of inverse problems of the six natural NP-complete problems from [GJ79] and answers an open question from [Ch03]. We classify the inverse complexity of the natural verifier for HAMILTONIAN CYCLE and 3D-MATCHING by showing coNP-completeness of the corresponding inverse...

In this study, the influence of different physicochemical parameters on the yield of polyhydroxyalkanoates (PHAs) produced by Bacillus cereus FA11 is investigated. The physicochemical factors include pH, temperature, time, inoculum size and its age, agitation speed and composition of the glucose rich peptone deficient (GRPD) medium. During two-stage fermentation, B. cereus FA11 produced a signi...