Higher-order models capture changes in controllability of temporal networks

AbstractWe study the evolution of networks through ‘triplets’—three-node graphlets. We develop a method to compute a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order interactions in the evolution of networks, we compare both artificial and real-world data to a model based on pairwise interactions only. The significant differences between the computed matrix and the calculated matrix from the fitted parameters demonstrate that non-pairwise interactions exist for various real-world systems in space and time, such as our data sets. Furthermore, this also reveals that different patterns of higher-order interaction are involved in different real-world situations. To test our approach, we then use these transition matrices as the basis of a link prediction algorithm. We investigate our algorithm’s performance on four temporal networks, comparing our approach against ten other link prediction methods. Our results show that higher-order interactions in both space and time play a crucial role in the evolution of networks as we find our method, along with two other methods based on non-local interactions, give the best overall performance. The results also confirm the concept that the higher-order interaction patterns, i.e., triplet dynamics, can help us understand and predict the evolution of different real-world systems.

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Higher order models for computer-aided circuit design

IEEE Journal of Solid-State Circuits ◽

10.1109/jssc.1972.1050274 ◽

1972 ◽

Vol 7 (2) ◽

pp. 208-211 ◽

Cited By ~ 4

Author(s):

W.E. Drobish

Keyword(s):

Circuit Design ◽

Higher Order ◽

Computer Aided ◽

Higher Order Models

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Higher-order Markov models for metagenomic sequence classification

Bioinformatics ◽

10.1093/bioinformatics/btaa562 ◽

2020 ◽

Vol 36 (14) ◽

pp. 4130-4136

Author(s):

David J Burks ◽

Rajeev K Azad

Keyword(s):

Dna Sequences ◽

Markov Models ◽

Fragment Size ◽

Higher Order ◽

Training Data ◽

Supplementary Information ◽

Local Alignment ◽

Metagenomic Sequence ◽

Higher Order Models

Abstract Motivation Alignment-free, stochastic models derived from k-mer distributions representing reference genome sequences have a rich history in the classification of DNA sequences. In particular, the variants of Markov models have previously been used extensively. Higher-order Markov models have been used with caution, perhaps sparingly, primarily because of the lack of enough training data and computational power. Advances in sequencing technology and computation have enabled exploitation of the predictive power of higher-order models. We, therefore, revisited higher-order Markov models and assessed their performance in classifying metagenomic sequences. Results Comparative assessment of higher-order models (HOMs, 9th order or higher) with interpolated Markov model, interpolated context model and lower-order models (8th order or lower) was performed on metagenomic datasets constructed using sequenced prokaryotic genomes. Our results show that HOMs outperform other models in classifying metagenomic fragments as short as 100 nt at all taxonomic ranks, and at lower ranks when the fragment size was increased to 250 nt. HOMs were also found to be significantly more accurate than local alignment which is widely relied upon for taxonomic classification of metagenomic sequences. A novel software implementation written in C++ performs classification faster than the existing Markovian metagenomic classifiers and can therefore be used as a standalone classifier or in conjunction with existing taxonomic classifiers for more robust classification of metagenomic sequences. Availability and implementation The software has been made available at https://github.com/djburks/SMM. Contact [email protected] Supplementary information Supplementary data are available at Bioinformatics online.

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Is the Lattice Boltzmann Method Applicable to Rarefied Gas Flows? Comprehensive Evaluation of the Higher-Order Models

Journal of Fluids Engineering ◽

10.1115/1.4031000 ◽

2015 ◽

Vol 138 (1) ◽

Cited By ~ 9

Author(s):

Minoru Watari

Keyword(s):

Lattice Boltzmann Method ◽

Lattice Boltzmann ◽

Rarefied Gas ◽

Slip Flow ◽

Higher Order ◽

Gas Flows ◽

Rarefied Gas Flows ◽

Slip Flow Regime ◽

Boltzmann Method ◽

Higher Order Models

Lattice Boltzmann method (LBM) whose equilibrium distribution function contains higher-order terms is called higher-order LBM. It is expected that nonequilibrium physics beyond the Navier–Stokes can be accurately captured using the higher-order LBM. Relationship between the level of higher-order and the simulation accuracy of rarefied gas flows is studied. Theoretical basis for constructing higher-order LBM is presented. On this basis, specific higher-order models are constructed. To confirm that the models have been correctly constructed, verification simulations are performed focusing on the continuum regime: sound wave and supersonic flow in Laval nozzle. With applications to microelectromechanical systems (MEMS) in mind, low Mach number flows are studied. Shear flow and heat conduction between parallel walls in the slip flow regime are investigated to confirm the relaxation process in the Knudsen layer. Problems between concentric cylinders are investigated from the slip flow regime to the free molecule regime to confirm the effect of boundary curvature. The accuracy is discussed comparing the simulation results with pioneers' studies. Models of the fourth-order give sufficient accuracy even for highly rarefied gas flows. Increase of the particle directions is necessary as the Knudsen number increases.

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