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Asymptotic Analysis of Equivalences and Core-Structures in Kronecker-Style Graph Models [article]

Alex J. Chin, Timothy D. Goodrich, Michael P. O'Brien, Felix Reidl, Blair D. Sullivan, Andrew van der Poel
2016 arXiv   pre-print
Kronecker-style models (SKG and R-MAT) are often used due to their scalability and ability to mimic key properties of real-world networks.  ...  In this work, we prove several results using asymptotic analysis which illustrate that empirical studies may not fully capture the true behavior of the models.  ...  Kronecker-style Models We now define the Kronecker-style models, including a new formulation R-MAT $ used in our analysis.  ... 
arXiv:1609.05081v1 fatcat:c76g6dyhvfg2jhwavosj5xrmsa

A survey of statistical network models [article]

Anna Goldenberg, Alice X Zheng, Stephen E Fienberg, Edoardo M Airoldi
2009 arXiv   pre-print
Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation.  ...  Probability models on graphs date back to 1959.  ...  Airoldi was a postdoctoral fellow in the Department of Computer Science and the Lewis-Sigler Institute for Integrative Genomics at Princeton University when a large portion of this work was carried out  ... 
arXiv:0912.5410v1 fatcat:mcr4pzkvxrhcxo2w3j42fz7ry4

A Survey of Statistical Network Models

Anna Goldenberg
2009 Foundations and Trends® in Machine Learning  
Airoldi was a postdoctoral fellow in the Department of Computer Science and the Lewis-Sigler Institute for Integrative Genomics at Princeton University when a large portion of this work was carried out  ...  We thank Joseph Blitzstein and Pavel Krivitsky for a careful reading and the correction of a number of infelicities.  ...  More recently this style of statistical physics models have been used to detect community structure in networks, e.g., see Girvan and Newman [122] and Backstrom et al.  ... 
doi:10.1561/2200000005 fatcat:psbbsr4hgbdfhjx5wr6hky7mc4

Structural Equation Models as Computation Graphs [article]

Erik-Jan van Kesteren, Daniel L. Oberski
2019 arXiv   pre-print
Structural equation modeling (SEM) is a popular tool in the social and behavioural sciences, where it is being applied to ever more complex data types.  ...  In this paper, we consider each SEM as a computation graph, a flexible method of specifying objective functions borrowed from the field of deep learning.  ...  We thank Rogier Kievit for his comments on an earlier version of this manuscript, and Maksim Rudnev for his helpful questions regarding tensorsem.  ... 
arXiv:1905.04492v2 fatcat:3spoe7li2za75cjlzhnpk5crai

Design of the dynamic stability properties of the collective behavior of articulated bipeds

Albert Mukovskiy, Jean-Jacques Slotine, Martin A. Giese
2010 2010 10th IEEE-RAS International Conference on Humanoid Robots  
and walking styles.  ...  The analysis and design of the stability properties of such complex multi-component systems is a largely unsolved problem.  ...  For the case of asymmetric coupling graphs with more general structure including negative feedback links some results on asymptotic stability have been provided in [45] .  ... 
doi:10.1109/ichr.2010.5686311 dblp:conf/humanoids/MukovskiySG10 fatcat:lw2r63c7nrb2jkehtxvwyhpe7i

Linear latent variable models: the lava-package

Klaus Kähler Holst, Esben Budtz-Jørgensen
2012 Computational statistics (Zeitschrift)  
The model and software are demonstrated in data of measurements of the serotonin transporter in the human brain.  ...  The philosophy of the implementation is to separate the model specification from the actual data, which leads to a dynamic and easy way of modeling complex hierarchical structures.  ...  Graphics Function Task plot Plots path diagram of model labels Defines labels for variables edgelabels Defines labels and style for edges of the graph nodecolor Defines color and style of nodes/variables  ... 
doi:10.1007/s00180-012-0344-y fatcat:mnow4wcn5jd5tj4q24ib4xsiii

Shape, connectedness percolation and electrical conductivity of clusters in suspensions of hard platelets [article]

Arshia Atashpendar, Tim Ingenbrand, Tanja Schilling
2020 arXiv   pre-print
On the contrary, using an anisotropic conductance model, the network conductivity decreases with increasing volume fraction in the isotropic, and further diminishes at the onset of the nematic.  ...  and in the respective stable phases.  ...  ACKNOWLEDGMENTS The authors acknowledge support by the state of Baden-Württemberg through bwHPC and the German Research Foundation (DFG) through grants no INST 39/963-1 FUGG and SCHI 853/4-1 648689.  ... 
arXiv:2001.09894v1 fatcat:rew2dznr4rchtgie6cfcolh75y

Graph Signal Processing – Part III: Machine Learning on Graphs, from Graph Topology to Applications [article]

Ljubisa Stankovic, Danilo Mandic, Milos Dakovic, Milos Brajovic, Bruno Scalzo, Shengxi Li, Anthony G. Constantinides
2020 arXiv   pre-print
This part of monograph concludes with two emerging applications in financial data processing and underground transportation networks modeling.  ...  Tensor representation of lattice-structured graphs is next considered, and it is shown that tensors (multidimensional data arrays) are a special class of graph signals, whereby the graph vertices reside  ...  In this way, the associated adjacency matrix exhibits a desirable structured form, referred to as Kronecker summable, which effectively reduces the number of parameters required to model the entire graph  ... 
arXiv:2001.00426v1 fatcat:t7323epqsve2na7q7imuyhlkeq

SISA: Set-Centric Instruction Set Architecture for Graph Mining on Processing-in-Memory Systems [article]

Maciej Besta, Raghavendra Kanakagiri, Grzegorz Kwasniewski, Rachata Ausavarungnirun, Jakub Beránek, Konstantinos Kanellopoulos, Kacper Janda, Zur Vonarburg-Shmaria, Lukas Gianinazzi, Ioana Stefan, Juan Gómez Luna, Marcin Copik (+6 others)
2021 arXiv   pre-print
In this work, we address this problem with a simple yet surprisingly powerful observation: operations on sets of vertices, such as intersection or union, form a large part of many complex graph mining  ...  Simple graph algorithms such as PageRank have been the target of numerous hardware accelerators.  ...  ACKNOWLEDGMENTS We thank Mark Klein, Hussein Harake, Colin McMurtrie, Angelo Mangili, and the whole CSCS team granting access to the Ault and Daint machines, and for their excellent technical support.  ... 
arXiv:2104.07582v2 fatcat:vxkku5ytrjggbher45qthnv564

Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures

Toshikazu Kuniya, Yoshiaki Muroya, Yoichi Enatsu
2014 Mathematical Biosciences and Engineering  
In this paper, we formulate an SIR epidemic model with hybrid of multigroup and patch structures, which can be regarded as a model for the geographical spread of infectious diseases or a multi-group model  ...  We show that if a threshold value, which corresponds to the well-known basic reproduction number R 0 , is less than or equal to unity, then the disease-free equilibrium of the model is globally asymptotically  ...  Acknowledgments The authors greatly appreciate the Editor and anonymous referees for their helpful comments and valuable suggestions which improved the quality of this paper in the present style.  ... 
doi:10.3934/mbe.2014.11.1375 pmid:25365599 fatcat:vrafn2hbybdi3opne37sntymky

Community detection and tracking on networks from a data fusion perspective [article]

James P. Ferry, J. Oren Bumgarner
2012 arXiv   pre-print
Community structure in networks has been investigated from many viewpoints, usually with the same end result: a community detection algorithm of some kind.  ...  This results in a method for directly estimating the probabilities that pairs of nodes are in the same community.  ...  The authors thank Andrea Lancichinetti for the LFR benchmark data shown in Figure 3 .  ... 
arXiv:1201.1512v1 fatcat:r5uzvrqgirhrznyceyuk6qbubm

Prospects for Declarative Mathematical Modeling of Complex Biological Systems [article]

Eric Mjolsness
2018 arXiv   pre-print
Examples of such computations on models include model analysis, relatively general-purpose model-reduction maps, and the initial phases of model implementation, all of which should preserve or approximate  ...  Multiscale modeling benefits from both the expressive power of declarative modeling languages and the application of model reduction methods to link models across scale.  ...  The author wishes to acknowledge the hospitality of the Sainsbury Laboratory Cambridge University, and funding from the Leverhulme Trust, NIH grant R01HD073179, and USAF/DARPA FA8750-14-C-0011.  ... 
arXiv:1804.11044v1 fatcat:57pjcv7b3ngtdo3zp35grn6a5m

Single Machine Graph Analytics on Massive Datasets Using Intel Optane DC Persistent Memory [article]

Gurbinder Gill, Ramesh Peri Intel Corporation)
2020 arXiv   pre-print
In this paper, we present key runtime and algorithmic principles to consider when performing graph analytics on extreme-scale graphs on large-memory platforms of this sort.  ...  Our results show that frameworks based on the runtime and algorithmic principles advocated in this paper (i) perform significantly better than the others, and (ii) are competitive with graph analytics  ...  However, they only use artificial Kronecker [35] and RMAT [11] generated graphs, which, as we have shown in this work, exhibit different structural properties compared to real-world graphs.  ... 
arXiv:1904.07162v3 fatcat:ocdffoxm2vcdnniggqfzlwuhgm

Optimizing Neural Networks with Kronecker-factored Approximate Curvature [article]

James Martens, Roger Grosse
2020 arXiv   pre-print
K-FAC is based on an efficiently invertible approximation of a neural network's Fisher information matrix which is neither diagonal nor low-rank, and in some cases is completely non-sparse.  ...  It is derived by approximating various large blocks of the Fisher (corresponding to entire layers) as being the Kronecker product of two much smaller matrices.  ...  Acknowledgments We gratefully acknowledge support from Google, NSERC, and the University of Toronto.  ... 
arXiv:1503.05671v7 fatcat:ilwuai2ssrauzkxsxljdjdvf3e

PageRank Beyond the Web

David F. Gleich
2015 SIAM Review  
The mathematics of PageRank, however, are entirely general and apply to any graph or network in any domain.  ...  Thus, PageRank is now regularly used in bibliometrics, social and information network analysis, and for link prediction and recommendation.  ...  for carefully reading several early drafts and Yongyang Yu for assistance with the literature review.  ... 
doi:10.1137/140976649 fatcat:odab3aoaqbfddidyh653kn4oem
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