Vertex-connectivity in periodic graphs and underlying nets of crystal structures

2016 ◽  
Vol 72 (3) ◽  
pp. 376-384 ◽  
Author(s):  
Jean-Guillaume Eon
Keyword(s):  
Crystal Structures ◽  
Long Range ◽  
Connected Graph ◽  
Three Dimensional ◽  
Topological Properties ◽  
Combinatorial Topology ◽  
Vertex Connectivity ◽  
Quotient Graph ◽  
Periodic Graphs ◽  
Definition Of

Periodic nets used to describe the combinatorial topology of crystal structures have been required to be 3-connected by some authors. A graph isn-connected when deletion of less thannvertices does not disconnect it.n-Connected graphs area fortiarin-coordinated but the converse is not true. This article presents an analysis of vertex-connectivity in periodic graphs characterized through their labelled quotient graph (LQG) and applied to a definition of underlying nets of crystal structures. It is shown that LQGs ofp-periodic graphs (p≥ 2) that are 1-connected or 2-connected, but not 3-connected, arecontractiblein the sense that they display, respectively, singletons or pairs of vertices separating dangling or linker components with zero net voltage over every cycle. The contraction operation that substitutes vertices and edges, respectively, for dangling components and linkers yields a 3-connected graph with the same periodicity. 1-Periodic graphs can be analysed in the same way through their LQGs but the result may not be 3-connected. It is claimed that long-range topological properties of periodic graphs are respected by contraction so that contracted graphs can represent topological classes of crystal structures, be they rods, layers or three-dimensional frameworks.

Application of high-resolution field-emission LVSEM, backscatter imaging, immunogold staining to definition of the spatial distributions of two human neutrophil adherence receptors

1993 ◽  
Vol 51 ◽  
pp. 36-37
Author(s):  
Robert D. Nelson ◽  
Sharon R. Hasslen ◽  
Stanley L. Erlandsen
Keyword(s):  
Cell Surface ◽  
Surface Membrane ◽  
Three Dimensional ◽  
Human Neutrophils ◽  
Spatial Distributions ◽  
Immunogold Staining ◽  
Functional Control ◽  
Neutrophil Adherence ◽  
Definition Of ◽  
Mode Of Attachment

Receptors are commonly defined in terms of number per cell, affinity for ligand, chemical structure, mode of attachment to the cell surface, and mechanism of signal transduction. We propose to show that knowledge of spatial distribution of receptors on the cell surface can provide additional clues to their function and components of functional control.L-selectin and Mac-1 denote two receptor populations on the neutrophil surface that mediate neutrophil-endothelial cell adherence interactions and provide for targeting of neutrophil recruitment to sites of inflammation. We have studied the spatial distributions of these receptors using LVSEM and backscatter imaging of isolated human neutrophils stained with mouse anti-receptor (primary) antibody and goat anti-mouse (secondary) antibody conjugated to 12 nm colloidal gold. This combination of techniques provides for three-dimensional analysis of the expression of these receptors on different surface membrane domains of the neutrophil: the ruffles and microvilli that project from the cell surface, and the cell body between these projecting structures.

scholarly journals Proposing 3D Thermal Technology for Heritage Building Energy Monitoring

2021 ◽  
Vol 13 (8) ◽  
pp. 1537
Author(s):  
Antonio Adán ◽  
Víctor Pérez ◽  
José-Luis Vivancos ◽  
Carolina Aparicio-Fernández ◽  
Samuel A. Prieto
Keyword(s):  
Computer Vision ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Building Energy ◽  
Energy Monitoring ◽  
3D Computer Vision ◽  
Building Monitoring ◽  
Heritage Buildings ◽  
Heritage Building ◽  
Definition Of

The energy monitoring of heritage buildings has, to date, been governed by methodologies and standards that have been defined in terms of sensors that record scalar magnitudes and that are placed in specific positions in the scene, thus recording only some of the values sampled in that space. In this paper, however, we present an alternative to the aforementioned technologies in the form of new sensors based on 3D computer vision that are able to record dense thermal information in a three-dimensional space. These thermal computer vision-based technologies (3D-TCV) entail a revision and updating of the current building energy monitoring methodologies. This paper provides a detailed definition of the most significant aspects of this new extended methodology and presents a case study showing the potential of 3D-TCV techniques and how they may complement current techniques. The results obtained lead us to believe that 3D computer vision can provide the field of building monitoring with a decisive boost, particularly in the case of heritage buildings.

scholarly journals HiChIP and Hi-C Protocol Optimized for Primary Murine T Cells

2021 ◽  
Vol 4 (3) ◽  
pp. 49
Author(s):  
Tomas Zelenka ◽  
Charalampos Spilianakis
Keyword(s):  
T Cells ◽  
Long Range ◽  
Three Dimensional ◽  
Cell Types ◽  
Range Interaction ◽  
Chromatin Interactions ◽  
Optimized Protocol ◽  
Long Range Interaction ◽  
Chromatin Compactness ◽  
Detailed Protocol

The functional implications of the three-dimensional genome organization are becoming increasingly recognized. The Hi-C and HiChIP research approaches belong among the most popular choices for probing long-range chromatin interactions. A few methodical protocols have been published so far, yet their reproducibility and efficiency may vary. Most importantly, the high frequency of the dangling ends may dramatically affect the number of usable reads mapped to valid interaction pairs. Additionally, more obstacles arise from the chromatin compactness of certain investigated cell types, such as primary T cells, which due to their small and compact nuclei, impede limitations for their use in various genomic approaches. Here we systematically optimized all the major steps of the HiChIP protocol in T cells. As a result, we reduced the number of dangling ends to nearly zero and increased the proportion of long-range interaction pairs. Moreover, using three different mouse genotypes and multiple biological replicates, we demonstrated the high reproducibility of the optimized protocol. Although our primary goal was to optimize HiChIP, we also successfully applied the optimized steps to Hi-C, given their significant protocol overlap. Overall, we describe the rationale behind every optimization step, followed by a detailed protocol for both HiChIP and Hi-C experiments.

A Kind Of Conditional Vertex Connectivity Of Cayley Graphs Generated By Wheel Graphs

2019 ◽  
Vol 63 (9) ◽  
pp. 1372-1384
Author(s):  
Zuwen Luo ◽  
Liqiong Xu
Keyword(s):  
Fault Tolerance ◽  
Connected Graph ◽  
Cayley Graphs ◽  
Network Structures ◽  
Vertex Connectivity ◽  
Wheel Graphs

Abstract Let $G=(V(G), E(G))$ be a connected graph. A subset $T \subseteq V(G)$ is called an $R^{k}$-vertex-cut, if $G-T$ is disconnected and each vertex in $V(G)-T$ has at least $k$ neighbors in $G-T$. The cardinality of a minimum $R^{k}$-vertex-cut is the $R^{k}$-vertex-connectivity of $G$ and is denoted by $\kappa ^{k}(G)$. $R^{k}$-vertex-connectivity is a new measure to study the fault tolerance of network structures beyond connectivity. In this paper, we study $R^{1}$-vertex-connectivity and $R^{2}$-vertex-connectivity of Cayley graphs generated by wheel graphs, which are denoted by $AW_{n}$, and show that $\kappa ^{1}(AW_{n})=4n-7$ for $n\geq 6$; $\kappa ^{2}(AW_{n})=6n-12$ for $n\geq 6$.

Anion packing density: a universal quantity for both dense and porous crystalline inorganic phases

2002 ◽  
Vol 58 (3) ◽  
pp. 457-462 ◽  
Author(s):  
F. Liebau ◽  
H. Küppers
Keyword(s):  
High Pressure ◽  
Packing Density ◽  
Three Dimensional ◽  
Ionic Radii ◽  
Generalized Framework ◽  
Molal Volumes ◽  
Definition Of ◽  
Anion Packing ◽  
Very High ◽  
Framework Density

To compare densities of inorganic high-pressure phases their molal volumes or specific gravities are usually employed, whereas for zeolites and other microporous materials the so-called framework density, FD, is applied. The definition of FD, which refers only to phases with three-dimensional tetrahedron frameworks, is extended to a `generalized framework density' d f, which is independent of the dimensionality of the framework and the coordination number(s) of the framework cations. In this paper the anion packing density, d ap, is introduced as a new quantity which is not only applicable to any inorganic phase but, in contrast to FD and d f, also allows quantitative comparisons to be made for crystalline inorganic phases of any kind. The anion packing density can readily be calculated if the volume and content of the unit cell and the radii of the anions of a phase are known. From d ap values calculated for high-pressure silica polymorphs studied under very high pressure, it is concluded that Shannon–Prewitt effective ionic radii do not sufficiently take into account the compressibility of the anions.

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