scholarly journals Variability in higher order structure of noise added to weighted networks

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Ann S. Blevins ◽  
Jason Z. Kim ◽  
Dani S. Bassett
Keyword(s):  
Data Analysis ◽  
Real World ◽  
Higher Order ◽  
Order Structure ◽  
Complex Behavior ◽  
World Systems ◽  
Model Network ◽  
Noise Structure ◽  
Low Weight ◽  
Model Networks

AbstractThe complex behavior of many real-world systems depends on a network of both strong and weak edges. Distinguishing between true weak edges and low-weight edges caused by noise is a common problem in data analysis, and solutions tend to either remove noise or study noise in the absence of data. In this work, we instead study how noise and data coexist, by examining the structure of noisy, weak edges that have been synthetically added to model networks. We find that the structure of low-weight, noisy edges varies according to the topology of the model network to which it is added, that at least three qualitative classes of noise structure emerge, and that these noisy edges can be used to classify the model networks. Our results demonstrate that noise does not present as a monolithic nuisance, but rather as a nuanced, topology-dependent, and even useful entity in characterizing higher-order network interactions.

scholarly journals Higher-order temporal network effects through triplet evolution

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Qing Yao ◽  
Bingsheng Chen ◽  
Tim S. Evans ◽  
Kim Christensen
Keyword(s):  
Real World ◽  
Link Prediction ◽  
Higher Order ◽  
Prediction Algorithm ◽  
Interaction Patterns ◽  
Temporal Networks ◽  
World Systems ◽  
Order Interaction ◽  
Space And Time ◽  
Pairwise Interactions

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.

scholarly journals Topological Information Data Analysis

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 869 ◽  
Author(s):  
Pierre Baudot ◽  
Monica Tapia ◽  
Daniel Bennequin ◽  
Jean-Marc Goaillard
Keyword(s):  
Data Analysis ◽  
Statistical Tests ◽  
Biological Systems ◽  
Higher Order ◽  
Information Storage ◽  
Structure Characteristic ◽  
Order Structure ◽  
Data Set ◽  
Topological Information ◽  
Statistical Interactions

This paper presents methods that quantify the structure of statistical interactions within a given data set, and were applied in a previous article. It establishes new results on the k-multivariate mutual-information ( I k ) inspired by the topological formulation of Information introduced in a serie of studies. In particular, we show that the vanishing of all I k for 2 ≤ k ≤ n of n random variables is equivalent to their statistical independence. Pursuing the work of Hu Kuo Ting and Te Sun Han, we show that information functions provide co-ordinates for binary variables, and that they are analytically independent from the probability simplex for any set of finite variables. The maximal positive I k identifies the variables that co-vary the most in the population, whereas the minimal negative I k identifies synergistic clusters and the variables that differentiate–segregate the most in the population. Finite data size effects and estimation biases severely constrain the effective computation of the information topology on data, and we provide simple statistical tests for the undersampling bias and the k-dependences. We give an example of application of these methods to genetic expression and unsupervised cell-type classification. The methods unravel biologically relevant subtypes, with a sample size of 41 genes and with few errors. It establishes generic basic methods to quantify the epigenetic information storage and a unified epigenetic unsupervised learning formalism. We propose that higher-order statistical interactions and non-identically distributed variables are constitutive characteristics of biological systems that should be estimated in order to unravel their significant statistical structure and diversity. The topological information data analysis presented here allows for precisely estimating this higher-order structure characteristic of biological systems.

scholarly journals Entropy in Dynamic Systems

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 896
Author(s):  
Jan Awrejcewicz ◽  
José A. Tenreiro Machado
Keyword(s):  
Stochastic Processes ◽  
Dynamic Systems ◽  
Real World ◽  
Complex Behavior ◽  
World Systems ◽  
And Control ◽  
Monitor And Control

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor and control complicated chaotic and stochastic processes [...]

scholarly journals Detecting informative higher-order interactions in statistically validated hypergraphs

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Federico Musciotto ◽  
Federico Battiston ◽  
Rosario N. Mantegna
Keyword(s):  
Empirical Evidence ◽  
Real World ◽  
Open Problem ◽  
Null Hypothesis ◽  
Higher Order ◽  
Analytic Approach ◽  
Extensive Literature ◽  
World Systems

AbstractRecent empirical evidence has shown that in many real-world systems, successfully represented as networks, interactions are not limited to dyads, but often involve three or more agents at a time. These data are better described by hypergraphs, where hyperlinks encode higher-order interactions among a group of nodes. In spite of the extensive literature on networks, detecting informative hyperlinks in real world hypergraphs is still an open problem. Here we propose an analytic approach to filter hypergraphs by identifying those hyperlinks that are over-expressed with respect to a random null hypothesis, and represent the most relevant higher-order connections. We apply our method to a class of synthetic benchmarks and to several datasets, showing that the method highlights hyperlinks that are more informative than those extracted with pairwise approaches. Our method provides a first way, to the best of our knowledge, to obtain statistically validated hypergraphs, separating informative connections from noisy ones.

READING EXERCISES FOR VIII GRADE STUDENTS BASED ON BLOOM’S TAXONOMY

2017 ◽  
Vol 6 (3) ◽  
Author(s):  
Intan Permata Sari And Indra Hartoyo
Keyword(s):  
Data Analysis ◽  
Lower Order ◽  
Bloom's Taxonomy ◽  
Higher Order Thinking ◽  
Thinking Skills ◽  
Higher Order ◽  
Critical Thinking Skills ◽  
Thinking Skill ◽  
Level Of Education ◽  
Bloom’S Taxonomy

This study is aimed at (1) analyzing reading exercises based Bloom’s taxonomy for VIII grade in English on Sky textbook. (2) Found the distribution of the lower and higher order thinking skill in reading exercises. (3) To reason for level reading exercises. After analyzed the data, the result of the data analysis also infers that the six levels of Bloom’s taxonomy in reading exercises weren’t applied totally. The creating skill doesn’t have distribution in reading exercise, and the understanding – remembering level more dominant than another levels. The distribution of the higher order thinking level was lower than the lower order thinking level and the six levels are not appropriate with the proportion for each level of education based Bloom’s taxonomy, such as the distribution of the creating level in the reading exercise must be a concern because no question that belong to the creating level. It was concluded that reading exercises in English on Sky textbook cannot improve students' critical thinking skills for VIII grade.

Macrocycles of Higher Ortho-Phenylenes: Assembly and Folding

2019 ◽  
Author(s):  
Zacharias Kinney ◽  
Viraj Kirinda ◽  
Scott Hartley
Keyword(s):  
Chemical Shift ◽  
Higher Order ◽  
Order Structure ◽  
Complex Geometries ◽  
Spatial Relationships ◽  
Predominant Species ◽  
Bite Angle ◽  
Direct Assembly

<p>Higher-order structure in abiotic foldamer systems represents an important but largely unrealized goal. As one approach to this challenge, covalent assembly can be used to assemble macrocycles with foldamer subunits in well-defined spatial relationships. Such systems have previously been shown to exhibit self-sorting, new folding motifs, and dynamic stereoisomerism, yet there remain important questions about the interplay between folding and macrocyclization and the effect of structural confinement on folding behavior. Here, we explore the dynamic covalent assembly of extended <i>ortho</i>-phenylenes (hexamer and decamer) with rod-shaped linkers. Characteristic <sup>1</sup>H chemical shift differences between cyclic and acyclic systems can be compared with computational conformer libraries to determine the folding states of the macrocycles. We show that the bite angle provides a measure of the fit of an <i>o</i>-phenylene conformer within a shape-persistent macrocycle, affecting both assembly and ultimate folding behavior. For the <i>o</i>-phenylene hexamer, the bite angle and conformer stability work synergistically to direct assembly toward triangular [3+3] macrocycles of well-folded oligomers. For the decamer, the energetic accessibility of conformers with small bite angles allows [2+2] macrocycles to be formed as the predominant species. In these systems, the <i>o</i>-phenylenes are forced into unusual folding states, preferentially adopting a backbone geometry with distinct helical blocks of opposite handedness. The results show that simple geometric restrictions can be used to direct foldamers toward increasingly complex geometries.</p>

Macrocycles of Higher ortho-Phenylenes: Assembly and Folding

2019 ◽  
Author(s):  
Zacharias Kinney ◽  
Viraj Kirinda ◽  
Scott Hartley
Keyword(s):  
Chemical Shift ◽  
Higher Order ◽  
Order Structure ◽  
Complex Geometries ◽  
Spatial Relationships ◽  
Predominant Species ◽  
Bite Angle ◽  
Direct Assembly

<p>Higher-order structure in abiotic foldamer systems represents an important but largely unrealized goal. As one approach to this challenge, covalent assembly can be used to assemble macrocycles with foldamer subunits in well-defined spatial relationships. Such systems have previously been shown to exhibit self-sorting, new folding motifs, and dynamic stereoisomerism, yet there remain important questions about the interplay between folding and macrocyclization and the effect of structural confinement on folding behavior. Here, we explore the dynamic covalent assembly of extended <i>ortho</i>-phenylenes (hexamer and decamer) with rod-shaped linkers. Characteristic <sup>1</sup>H chemical shift differences between cyclic and acyclic systems can be compared with computational conformer libraries to determine the folding states of the macrocycles. We show that the bite angle provides a measure of the fit of an <i>o</i>-phenylene conformer within a shape-persistent macrocycle, affecting both assembly and ultimate folding behavior. For the <i>o</i>-phenylene hexamer, the bite angle and conformer stability work synergistically to direct assembly toward triangular [3+3] macrocycles of well-folded oligomers. For the decamer, the energetic accessibility of conformers with small bite angles allows [2+2] macrocycles to be formed as the predominant species. In these systems, the <i>o</i>-phenylenes are forced into unusual folding states, preferentially adopting a backbone geometry with distinct helical blocks of opposite handedness. The results show that simple geometric restrictions can be used to direct foldamers toward increasingly complex geometries.</p>

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