Topological data analysis of contagion maps for examining spreading processes on networks

Taylor, Dane; Klimm, Florian; Harrington, Heather A.; Kramar, Miroslav; Mischaikow, Konstantin; Porter, Mason A.; Mucha, Peter J.

doi:10.1038/ncomms8723

Cited by 143 publications

(145 citation statements)

References 64 publications

(99 reference statements)

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“…Similarity measures have many uses due to the current widespread use of networks in social sciences, medicine, biology, physics and so on192021222324252627282930. They can help, among many other examples, to discriminate between neurological disorders by quantifying functional and topological similarities31, to find structurally more similar molecules that are more likely to exhibit similar properties, for drug design32, and to quantify changes in temporal evolving networks22.…”

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confidence: 99%

Quantification of network structural dissimilarities

et al. 2017

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Identifying and quantifying dissimilarities among graphs is a fundamental and challenging problem of practical importance in many fields of science. Current methods of network comparison are limited to extract only partial information or are computationally very demanding. Here we propose an efficient and precise measure for network comparison, which is based on quantifying differences among distance probability distributions extracted from the networks. Extensive experiments on synthetic and real-world networks show that this measure returns non-zero values only when the graphs are non-isomorphic. Most importantly, the measure proposed here can identify and quantify structural topological differences that have a practical impact on the information flow through the network, such as the presence or absence of critical links that connect or disconnect connected components.

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confidence: 99%

Quantification of network structural dissimilarities

et al. 2017

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“…Topological Data Analysis (TDA) is a collection of computational tools derived from the mathematical subject of Algebraic Topology, that can help in identifying the behaviour of a biological system from a global perspective, guide detailed quantitative investigations and aid tailor further experimental settings. In fact, algorithms from topological data analysis have started to play important roles in novel interdisciplinary fields in biomedical sciences, including cancer genomics [12] , diabetes [13] , neuroscience [14] , infectious diseases [15,16] , and in biology in general [17,18] .…”

Section: Introductionmentioning

confidence: 99%

Topological data analysis to model the shape of immune responses during co-infections

Sasaki

Bruder

Hernandez‐Vargas

2020

Communications in Nonlinear Science and Numerical Simulation

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a b s t r a c tCo-infections by multiple pathogens have important implications in many aspects of health, epidemiology and evolution. However, how to disentangle the non-linear dynamics of the immune response when two infections take place at the same time is largely unexplored. Using data sets of the immune response during influenza-pneumococcal coinfection in mice, we employ here topological data analysis to simplify and visualise high dimensional data sets.We identified persistent shapes of the simplicial complexes of the data in the three infection scenarios: single viral infection, single bacterial infection, and co-infection. The immune response was found to be distinct for each of the infection scenarios and we uncovered that the immune response during the co-infection has three phases and two transition points. During the first phase, its dynamics is inherited from its response to the primary (viral) infection. The immune response has an early shift (few hours post coinfection) and then modulates its response to react against the secondary (bacterial) infection. Between 18 and 26 h post co-infection the nature of the immune response changes again and does no longer resembles either of the single infection scenarios.

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“…Topological data analysis (TDA) is able to extract such information [9–14]; currently, it has been used for the analysis of EEG signals [15] within the TOPDRIM project [16]. The key-concept in TDA is persistent homology : a procedure for counting, through a process called filtration , the higher dimensional persistent holes of topological spaces.…”

Section: Introductionmentioning

confidence: 99%

Topological classifier for detecting the emergence of epileptic seizures

Piangerelli

Rucco²,

Tesei

et al. 2018

BMC Res Notes

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ObjectiveAn innovative method based on topological data analysis is introduced for classifying EEG recordings of patients affected by epilepsy. We construct a topological space from a collection of EEGs signals using Persistent Homology; then, we analyse the space by Persistent entropy, a global topological feature, in order to classify healthy and epileptic signals.ResultsThe performance of the resulting one-feature-based linear topological classifier is tested by analysing the Physionet dataset. The quality of classification is evaluated in terms of the Area Under Curve (AUC) of the receiver operating characteristic curve. It is shown that the linear topological classifier has an AUC equal to while the performance of a classifier based on Sample Entropy has an AUC equal to 62.0%.

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Topological data analysis of contagion maps for examining spreading processes on networks

Cited by 143 publications

References 64 publications

Quantification of network structural dissimilarities

Quantification of network structural dissimilarities

Topological data analysis to model the shape of immune responses during co-infections

Topological classifier for detecting the emergence of epileptic seizures

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