scholarly journals Spherical codes, maximal local packing density, and the golden ratio

2010 ◽  
Vol 51 (4) ◽  
pp. 043302 ◽  
Author(s):  
Adam B. Hopkins ◽  
Frank H. Stillinger ◽  
Salvatore Torquato
Keyword(s):  
Packing Density ◽  
Golden Ratio ◽  
Spherical Codes ◽  
Local Packing Density

scholarly journals Local Packing Density Is the Main Structural Determinant of the Rate of Protein Sequence Evolution at Site Level

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
So-Wei Yeh ◽  
Tsun-Tsao Huang ◽  
Jen-Wei Liu ◽  
Sung-Huan Yu ◽  
Chien-Hua Shih ◽  
...  
Keyword(s):  
Packing Density ◽  
Protein Sequence ◽  
Solvent Accessibility ◽  
Sequence Evolution ◽  
Relative Solvent Accessibility ◽  
Sequence Variability ◽  
Substitution Rates ◽  
Contact Number ◽  
Local Packing Density ◽  
Structural Determinant

Functional and biophysical constraints result in site-dependent patterns of protein sequence variability. It is commonly assumed that the key structural determinant of site-specific rates of evolution is the Relative Solvent Accessibility (RSA). However, a recent study found that amino acid substitution rates correlate better with two Local Packing Density (LPD) measures, the Weighted Contact Number (WCN) and the Contact Number (CN), than with RSA. This work aims at a more thorough assessment. To this end, in addition to substitution rates, we considered four other sequence variability scores, four measures of solvent accessibility (SA), and other CN measures. We compared all properties for each protein of a structurally and functionally diverse representative dataset of monomeric enzymes. We show that the best sequence variability measures take into account phylogenetic tree topology. More importantly, we show that both LPD measures (WCN and CN) correlate better than all of the SA measures, regardless of the sequence variability score used. Moreover, the independent contribution of the best LPD measure is approximately four times larger than that of the best SA measure. This study strongly supports the conclusion that a site’s packing density rather than its solvent accessibility is the main structural determinant of its rate of evolution.

Variation in the local packing density near the wall of a randomly packed bed of equal spheres

1978 ◽  
Vol 20 (2) ◽  
pp. 257-260 ◽  
Author(s):  
Keishi Gotoh ◽  
W.S. Jodrey ◽  
E.M. Tory
Keyword(s):  
Packing Density ◽  
Packed Bed ◽  
Local Packing Density

scholarly journals Experiment on compaction of air-dried soil under drop shocks

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0250076
Author(s):  
Jianbo Wang ◽  
Tiansheng Hong ◽  
Zhen Li ◽  
Xiuyun Xue ◽  
Shilei Lyu
Keyword(s):  
Shock Intensity ◽  
Packing Density ◽  
Soil Compaction ◽  
Local Density ◽  
Drop Height ◽  
Nursery Culture ◽  
Straight Line ◽  
Dimensional Distribution ◽  
Line Slope ◽  
Local Packing Density

For the requirement in container nursery culture that growing media should be achieved the appropriate degree compaction, this paper presents an experiment on the compaction dynamics of air-dried soil under repetitive drop shocks, as a preliminary step toward the mechanization of this compaction method. The drop height used to adjust the shock intensity included 2 mm, 4 mm, 5 mm and 6 mm. And the overall packing density of soil in a vertically stratified cylinder vessel and the local packing density in each layer were taken as indicators of soil compaction states. The stretched exponential function derived from KWW law than the empirical inverse-logarithmic function has been found to be more suitable for expressing the temporal evolution of soil compaction, according to the results of curve-fitting to test values of the overall and local density. It is inherent in this experimental configuration that the drop shock intensity even at a constant drop height varies with drop times, owing to the interaction between the soil packing itself and drop shocks caused by the combination of the packing and the container. But the function t/τf(t,H) is manifested as a straight line on the drop times t with the line slope related to the drop height H, so the soil compaction dynamics caused by its drop shocks and that under the condition with actively controlled intensity actually share the common relaxation law. In addition, the soil’s one-dimensional distribution of local packing density showed a slight positive gradient as similar as monodisperse particles did.

scholarly journals Dissecting the roles of local packing density and longer-range effects in protein sequence evolution

2015 ◽  
Author(s):  
Amir Shahmoradi ◽  
Claus O Wilke
Keyword(s):  
Packing Density ◽  
Solvent Accessibility ◽  
Voronoi Cell ◽  
Sequence Evolution ◽  
Relative Importance ◽  
Site Specific ◽  
Contact Number ◽  
Evolutionary Variation ◽  
Local Packing Density ◽  
Protein Sequence Evolution

What are the structural determinants of protein sequence evolution? A number of site-specific structural characteristics have been proposed, most of which are broadly related to either the density of contacts or the solvent accessibility of individual residues. Most importantly, there has been disagreement in the literature over the relative importance of solvent accessibility and local packing density for explaining site-specific sequence variability in proteins. We show here that this discussion has been confounded by the definition of local packing density. The most commonly used measures of local packing, such as the contact number and the weighted contact number, represent by definition the combined effects of local packing density and longer-range effects. As an alternative, we here propose a truly local measure of packing density around a single residue, based on the Voronoi cell volume. We show that the Voronoi cell volume, when calculated relative to the geometric center of amino-acid side chains, behaves nearly identically to the relative solvent accessibility, and both can explain, on average, approximately 34\% of the site-specific variation in evolutionary rate in a data set of 209 enzymes. An additional 10\% of variation can be explained by non-local effects that are captured in the weighted contact number. Consequently, evolutionary variation at a site is determined by the combined action of the immediate amino-acid neighbors of that site and of effects mediated by more distant amino acids. We conclude that instead of contrasting solvent accessibility and local packing density, future research should emphasize the relative importance of immediate contacts and longer-range effects on evolutionary variation.

Low-Dielectric-Constant Materials for ULSI Interlayer-Dielectric Applications

MRS Bulletin ◽  
1997 ◽  
Vol 22 (10) ◽  
pp. 19-27 ◽  
Author(s):  
Wei William Lee ◽  
Paul S. Ho
Keyword(s):  
Packing Density ◽  
Propagation Delay ◽  
Single Chip ◽  
Crosstalk Noise ◽  
Metal Line ◽  
Total Delay ◽  
Interlayer Dielectric ◽  
Low Dielectric ◽  
Interconnect Delay ◽  
Interconnect Technology

Continuing improvement of microprocessor performance historically involves a decrease in the device size. This allows greater device speed, an increase in device packing density, and an increase in the number of functions that can reside on a single chip. However higher packing density requires a much larger increase in the number of interconnects. This has led to an increase in the number of wiring levels and a reduction in the wiring pitch (sum of the metal line width and the spacing between the metal lines) to increase the wiring density. The problem with this approach is that—as device dimensions shrink to less than 0.25 μm (transistor gate length)—propagation delay, crosstalk noise, and power dissipation due to resistance-capacitance (RC) coupling become significant due to increased wiring capacitance, especially interline capacitance between the metal lines on the same metal level. The smaller line dimensions increase the resistivity (R) of the metal lines, and the narrower interline spacing increases the capacitance (C) between the lines. Thus although the speed of the device will increase as the feature size decreases, the interconnect delay becomes the major fraction of the total delay and limits improvement in device performance.To address these problems, new materials for use as metal lines and interlayer dielectrics (ILD) as well as alternative architectures have been proposed to replace the current Al(Cu) and SiO2 interconnect technology.

Data visualization quality in a geographic information system using golden ratio properties

2018 ◽  
pp. 46-57
Author(s):  
A. V. Voronin ◽  
G. N. Maltsev ◽  
M. Yu. Sokhen
Keyword(s):  
Information System ◽  
Geographic Information System ◽  
Data Visualization ◽  
Golden Ratio ◽  
Quality Criterion ◽  
Geographic Information ◽  
Control Device ◽  
Video Data ◽  
Geoinformation Systems ◽  
System Operator

Introduction:Data visualization quality is important for the work of a geographic information system operator, determining the conditions under which he or she makes decisions concerning the displayed data. Visual perception patterns associated with the golden ratio properties allow us to formulate a criterion for data visualization quality which would characterize the possibilities of the operator’s complex perception of the video data displayed on a control device screen in the form of an electronic card.Purpose:Substantiation of a data visualization quality criterion for geoinformation systems using the golden ratio properties, and the study of the conditions for providing good visualization quality for geodata and metadata on a video control device screen in accordance with the proposed criterion.Methods:A formal definition of the data visualization quality criterion in geoinformation systems using the coefficient of the screen area information coverage as an index whose optimal value corresponds to the mathematical definition of the golden ratio; and the study of the properties of this criterion. Results: Based on the conducted analysis of visual perception of video data and golden ratio properties during the data visualization, a criterion is proposed for data visualization quality, which uses the golden ratio properties and characterizes the possibilities of complex perception of video data in an electronic map form by a geographic information system operator. Iteration algorithms for choosing the video data display scale are developed, based on the visualization quality criterion and related to the golden ratio properties. These are the basic algorithm used for each geodata layer represented on the electronicmap, and an algorithm of successive analysis of various layers of the displayed geodata. The choice of a video data display scale in accordance with the developed algorithms can be preliminarily carried out by the system operator using the parameters of standard electronic maps and geodata/metadata sets typical for the current applied problem. We have studied how the scale of the geodata and metadata displayed on an electronic map affects their visualization quality on screens of various sizes. For the considered standard volumes of displayed geodata and metadata, the best visualization quality was achieved when they were displayed on a standard computer monitor, as opposed to a portable notebook or visualization screen.Practical relevance:The proposed criterion and the recommendations for choosing a screen size for the video monitoring device or the structures of the displayed geo-objects and metadata can be used in the design of geoinformation systems, or for preliminary choice of the displayed data structure by a geoinformation system operator.

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