Benchmarking parallel eigen decomposition for residuals analysis of very large graphs

2012 ◽  
Author(s):  
Edward M. Rutledge ◽  
Benjamin A. Miller ◽  
Michelle S. Beard
Keyword(s):  
Large Graphs ◽  
Residuals Analysis ◽  
Eigen Decomposition

scholarly journals What are the Most Widely Used and Effective Attack Coverage Systems in Men’s Volleyball?

2018 ◽  
Vol 62 (1) ◽  
pp. 111-121
Author(s):  
Raúl Hileno ◽  
Antonio García-de-Alcaraz ◽  
Bernat Buscà ◽  
Cristòfol Salas ◽  
Oleguer Camerino
Keyword(s):  
Mean Difference ◽  
First Line ◽  
Chi Square ◽  
Residuals Analysis ◽  
Specific Position ◽  
Pan American ◽  
Guiding Principles ◽  
High Level ◽  
Tests For Independence ◽  
Chi Square Tests

Abstract In volleyball, attack coverage is one of the play actions most neglected in coaching and research. The purpose of this study was to find out which attack coverage systems are used by high-level men’s teams in different game situations and the characteristics of the most effective systems. We analysed 15 matches from the 2010 Men’s Pan-American Volleyball Cup, with a total of 1,415 coverage actions. Chi-square tests for independence, adjusted residuals analysis and calculations of standardised mean difference were performed. The results show that high-level men’s volleyball uses many coverage systems other than the traditional 3-2-0 and 2-3-0. At this level of play, the most frequent systems were 1-3-1 and 1-2-2, which occurred significantly often at the culmination of a third-tempo attack at the wing. The most effective systems consisted of three coverage lines, with fewer than five players covering the spiker and at least one player in the first coverage line, in both the attack and counterattack phases. Given the large number of coverage systems identified in different game situations, we recommend flexible, loosely structured training in these systems, based on a set of guiding principles that all players on a team must internalise for the specific position they are playing. Regarding the systems’ efficacy, the main watchword is that on each coverage line there should always be at least one player, but the first line should not be exposed.

VColor*: a practical approach for coloring large graphs

2021 ◽  
Vol 15 (4) ◽  
Author(s):  
Yun Peng ◽  
Xin Lin ◽  
Byron Choi ◽  
Bingsheng He
Keyword(s):  
Practical Approach ◽  
Large Graphs

scholarly journals Faster Motif Counting via Succinct Color Coding and Adaptive Sampling

2021 ◽  
Vol 15 (6) ◽  
pp. 1-27
Author(s):  
Marco Bressan ◽  
Stefano Leucci ◽  
Alessandro Panconesi
Keyword(s):  
Adaptive Sampling ◽  
Relative Frequency ◽  
State Of The Art ◽  
Color Coding ◽  
Input Graph ◽  
Large Graphs ◽  
Running Time ◽  
Uniform Sampling ◽  
Current State ◽  
Connected Subgraphs

We address the problem of computing the distribution of induced connected subgraphs, aka graphlets or motifs , in large graphs. The current state-of-the-art algorithms estimate the motif counts via uniform sampling by leveraging the color coding technique by Alon, Yuster, and Zwick. In this work, we extend the applicability of this approach by introducing a set of algorithmic optimizations and techniques that reduce the running time and space usage of color coding and improve the accuracy of the counts. To this end, we first show how to optimize color coding to efficiently build a compact table of a representative subsample of all graphlets in the input graph. For 8-node motifs, we can build such a table in one hour for a graph with 65M nodes and 1.8B edges, which is times larger than the state of the art. We then introduce a novel adaptive sampling scheme that breaks the “additive error barrier” of uniform sampling, guaranteeing multiplicative approximations instead of just additive ones. This allows us to count not only the most frequent motifs, but also extremely rare ones. For instance, on one graph we accurately count nearly 10.000 distinct 8-node motifs whose relative frequency is so small that uniform sampling would literally take centuries to find them. Our results show that color coding is still the most promising approach to scalable motif counting.

Tiered Sampling

2021 ◽  
Vol 15 (5) ◽  
pp. 1-52
Author(s):  
Lorenzo De Stefani ◽  
Erisa Terolli ◽  
Eli Upfal
Keyword(s):  
Large Scale ◽  
Analysis Of Algorithms ◽  
Base Layer ◽  
Single Edge ◽  
Real World Data ◽  
High Quality ◽  
Large Graphs ◽  
Massive Graphs ◽  
Variance Estimate ◽  
Low Probability

We introduce Tiered Sampling , a novel technique for estimating the count of sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size M , which can be magnitudes smaller than the number of edges. Our methods address the challenging task of counting sparse motifs—sub-graph patterns—that have a low probability of appearing in a sample of M edges in the graph, which is the maximum amount of data available to the algorithms in each step. To obtain an unbiased and low variance estimate of the count, we partition the available memory into tiers (layers) of reservoir samples. While the base layer is a standard reservoir sample of edges, other layers are reservoir samples of sub-structures of the desired motif. By storing more frequent sub-structures of the motif, we increase the probability of detecting an occurrence of the sparse motif we are counting, thus decreasing the variance and error of the estimate. While we focus on the designing and analysis of algorithms for counting 4-cliques, we present a method which allows generalizing Tiered Sampling to obtain high-quality estimates for the number of occurrence of any sub-graph of interest, while reducing the analysis effort due to specific properties of the pattern of interest. We present a complete analytical analysis and extensive experimental evaluation of our proposed method using both synthetic and real-world data. Our results demonstrate the advantage of our method in obtaining high-quality approximations for the number of 4 and 5-cliques for large graphs using a very limited amount of memory, significantly outperforming the single edge sample approach for counting sparse motifs in large scale graphs.

scholarly journals Functional Form Model Specification: An Application to Hedonic Pricing

1995 ◽  
Vol 24 (2) ◽  
pp. 166-173 ◽  
Author(s):  
Jeff E. Brown ◽  
Don E. Ethridge
Keyword(s):  
Functional Form ◽  
Hedonic Pricing ◽  
Hedonic Model ◽  
Model Specification ◽  
Estimation Accuracy ◽  
Hedonic Price ◽  
Partial Regression ◽  
Cotton Price ◽  
Residuals Analysis ◽  
Form Model

A combination of conceptual analysis and empirical analysis—partial regression and residuals analysis—was used to derive an appropriate functional form hedonic price model. These procedures are illustrated in the derivation of a functional form hedonic model for an automated, econometric daily cotton price reporting system for the Texas-Oklahoma cotton market. Following conceptualization to deduce the general shapes of relationships, the appropriate specific functional form was found by testing particular attribute transformations identified from partial regression analysis. Minimizing structural errors across attribute levels and estimation accuracy were used in determining when an appropriate functional form for both implicit and explicit prices was found.

scholarly journals Isoscattering strings of concatenating graphs and networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Michał Ławniczak ◽  
Adam Sawicki ◽  
Małgorzata Białous ◽  
Leszek Sirko
Keyword(s):  
Trace Function ◽  
Quantum Graphs ◽  
Mathematical Approach ◽  
Large Graphs ◽  
Graphs And Networks ◽  
Scattering Matrices ◽  
Theoretical Predictions ◽  
Infinite Strings ◽  
Microwave Networks ◽  
Insight Into

AbstractWe identify and investigate isoscattering strings of concatenating quantum graphs possessing n units and 2n infinite external leads. We give an insight into the principles of designing large graphs and networks for which the isoscattering properties are preserved for $$n \rightarrow \infty $$ n → ∞ . The theoretical predictions are confirmed experimentally using $$n=2$$ n = 2 units, four-leads microwave networks. In an experimental and mathematical approach our work goes beyond prior results by demonstrating that using a trace function one can address the unsettled until now problem of whether scattering properties of open complex graphs and networks with many external leads are uniquely connected to their shapes. The application of the trace function reduces the number of required entries to the $$2n \times 2n $$ 2 n × 2 n scattering matrices $${\hat{S}}$$ S ^ of the systems to 2n diagonal elements, while the old measures of isoscattering require all $$(2n)^2$$ ( 2 n ) 2 entries. The studied problem generalizes a famous question of Mark Kac “Can one hear the shape of a drum?”, originally posed in the case of isospectral dissipationless systems, to the case of infinite strings of open graphs and networks.

Topological Fisheye Views for Visualizing Large Graphs

2005 ◽  
Vol 11 (4) ◽  
pp. 457-468 ◽  
Author(s):  
E.R. Gansner ◽  
Y. Koren ◽  
S.C. North
Keyword(s):  
Large Graphs
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