scholarly journals On the Connectivity and Giant Component Size of Random K-out Graphs Under Randomly Deleted Nodes

2021 ◽  
Author(s):  
Eray Can Elumar ◽  
Mansi Sood ◽  
Osman Yagan
Keyword(s):  
Giant Component ◽  
Component Size

The configuration model

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Degree Sequence ◽  
Graph Model ◽  
Network Models ◽  
Clustering Coefficient ◽  
Giant Component ◽  
Configuration Model ◽  
Bipartite Networks ◽  
Small Component ◽  
Random Graph Model ◽  
Average Size

A discussion of the most fundamental of network models, the configuration model, which is a random graph model of a network with a specified degree sequence. Following a definition of the model a number of basic properties are derived, including the probability of an edge, the expected number of multiedges, the excess degree distribution, the friendship paradox, and the clustering coefficient. This is followed by derivations of some more advanced properties including the condition for the existence of a giant component, the size of the giant component, the average size of a small component, and the expected diameter. Generating function methods for network models are also introduced and used to perform some more advanced calculations, such as the calculation of the distribution of the number of second neighbors of a node and the complete distribution of sizes of small components. The chapter ends with a brief discussion of extensions of the configuration model to directed networks, bipartite networks, networks with degree correlations, networks with high clustering, and networks with community structure, among other possibilities.

Random graphs

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Large Scale ◽  
Random Network ◽  
Graph Model ◽  
Clustering Coefficient ◽  
Giant Component ◽  
Random Graph Model ◽  
Definition Of ◽  
Average Size

An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties like the mean degree, degree distribution, and clustering coefficient. This is followed with a detailed derivation of the large-scale structural properties of random graphs, including the position of the phase transition at which a giant component appears, the size of the giant component, the average size of the small components, and the expected diameter of the network. The chapter ends with a discussion of some of the shortcomings of the random graph model.

scholarly journals Techno-Economic Planning and Operation of the Microgrid Considering Real-Time Pricing Demand Response Program

Energies ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4597
Author(s):  
Zi-Xuan Yu ◽  
Meng-Shi Li ◽  
Yi-Peng Xu ◽  
Sheraz Aslam ◽  
Yuan-Kang Li
Keyword(s):  
Real Time ◽  
Demand Response ◽  
Positive Impact ◽  
Environmental Aspects ◽  
Component Size ◽  
Cost Of Energy ◽  
Four Seasons ◽  
Demand Response Program ◽  
Real Time Pricing

The optimal planning of grid-connected microgrids (MGs) has been extensively studied in recent years. While most of the previous studies have used fixed or time-of-use (TOU) prices for the optimal sizing of MGs, this work introduces real-time pricing (RTP) for implementing a demand response (DR) program according to the national grid prices of Iran. In addition to the long-term planning of MG, the day-ahead operation of MG is also analyzed to get a better understanding of the DR program for daily electricity dispatch. For this purpose, four different days corresponding to the four seasons are selected for further analysis. In addition, various impacts of the proposed DR program on the MG planning results, including sizing and best configuration, net present cost (NPC) and cost of energy (COE), and emission generation by the utility grid, are investigated. The optimization results show that the implementation of the DR program has a positive impact on the technical, economic, and environmental aspects of MG. The NPC and COE are reduced by about USD 3700 and USD 0.0025/kWh, respectively. The component size is also reduced, resulting in a reduction in the initial cost. Carbon emissions are also reduced by 185 kg/year.

scholarly journals Electrodeposited Hydroxyapatite-Based Biocoatings: Recent Progress and Future Challenges

Coatings ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 110
Author(s):  
Mir Saman Safavi ◽  
Frank C. Walsh ◽  
Maria A. Surmeneva ◽  
Roman A. Surmenev ◽  
Jafar Khalil-Allafi
Keyword(s):  
Recent Progress ◽  
Tribological Behavior ◽  
Metallic Materials ◽  
Industrial Processing ◽  
Component Size ◽  
Polymeric Particles ◽  
Operational Variables ◽  
Wide Range ◽  
Future Challenges ◽  
Coating Methods

Hydroxyapatite has become an important coating material for bioimplants, following the introduction of synthetic HAp in the 1950s. The HAp coatings require controlled surface roughness/porosity, adequate corrosion resistance and need to show favorable tribological behavior. The deposition rate must be sufficiently fast and the coating technique needs to be applied at different scales on substrates having a diverse structure, composition, size, and shape. A detailed overview of dry and wet coating methods is given. The benefits of electrodeposition include controlled thickness and morphology, ability to coat a wide range of component size/shape and ease of industrial processing. Pulsed current and potential techniques have provided denser and more uniform coatings on different metallic materials/implants. The mechanism of HAp electrodeposition is considered and the effect of operational variables on deposit properties is highlighted. The most recent progress in the field is critically reviewed. Developments in mineral substituted and included particle, composite HAp coatings, including those reinforced by metallic, ceramic and polymeric particles; carbon nanotubes, modified graphenes, chitosan, and heparin, are considered in detail. Technical challenges which deserve further research are identified and a forward look in the field of the electrodeposited HAp coatings is taken.

scholarly journals Minor influence of humeral component size on torsional stiffness of the Souter-Strathclyde total elbow prosthesis

2009 ◽  
Vol 34 (8) ◽  
pp. 1213-1218 ◽  
Author(s):  
Joris C. T. van der Lugt ◽  
Daniel R. Suarez ◽  
Tim J. van der Steenhoven ◽  
Rob G. H. H. Nelissen
Keyword(s):  
Torsional Stiffness ◽  
Elbow Prosthesis ◽  
Component Size ◽  
Humeral Component ◽  
Minor Influence ◽  
Total Elbow Prosthesis

scholarly journals Implications of component size and calibration error on digital templating for total hip arthroplasty. A visual matrix from a simple mathematical model

2021 ◽  
Author(s):  
Christoph Kolja Boese ◽  
Tim Rolvien ◽  
Matthias Trost ◽  
Michael Frink ◽  
Jan Hubert ◽  
...  
Keyword(s):  
Total Hip Arthroplasty ◽  
Hip Arthroplasty ◽  
Standard Procedure ◽  
Calibration Error ◽  
Optimal Size ◽  
Linear Calibration ◽  
Component Size ◽  
Digital Templating ◽  
Total Hip ◽  
Implant Size

Abstract Objective Preoperative digital templating is a standard procedure in total hip arthroplasty. Deviations between template size and final implant size may result from inaccurate calibration, templating as well as intraoperative decisions. So far, the explicit effect of calibration errors on templating has not been addressed adequately. Materials and Methods A mathematical simulation of calibration errors up to ± 24% was applied to the templating of acetabular cups (38 to 72 mm diameter). The effect of calibration errors on template component size as deviation from optimal size was calculated. Results The relationship between calibration error and component size deviation is inverse and linear. Calibration errors have a more pronounced effect on larger component sizes. Calibration errors of 2–6% result in templating errors of up to two component sizes. Common errors of up to 12% may result in templating errors of 3–4 sizes for common implant sizes. A tabular matrix visualizes the effect. Conclusion Calibration errors play a significant role in component size selection during digital templating. Orthopedic surgeons should be aware of this effect and try to identify and address this source of error.

The Cognitive Social Network in Dreams: Transitivity, Assortativity, and Giant Component Proportion Are Monotonic

2015 ◽  
Vol 40 (3) ◽  
pp. 671-696 ◽  
Author(s):  
Hye Joo Han ◽  
Richard Schweickert ◽  
Zhuangzhuang Xi ◽  
Charles Viau-Quesnel
Keyword(s):  
Social Network ◽  
Giant Component
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