Pub Date : 2023-01-26DOI: 10.1088/2632-072X/acb67d
Lewis Higgins, T. Galla, Brian Prestidge, T. Wyatt
We study pitch control in football, using data from six complete seasons of the English Premier League. Our objective is to investigate features of pitch control in the data. We process the data to ensure consistency of the tracking and event datasets. This represents the largest coherent dataset analysed in the literature and allows the observation of consistent patterns across several seasons’ data. We demonstrate that teams playing in front of a crowd at home control on average 2.9±0.2% more of the pitch than teams playing away, which reduces to 1.5±0.6% in matches played behind closed doors. We observe that match by match the difference in pitch control between the teams has a weak, positive correlation with the difference in expected goals (Pearson correlation R = 0.38). As a further manifestation of home advantage we find that in games which the two teams have equal pitch control, on average the home team accumulates greater expected goals ( 0.16±0.03 ). The concept of weighted pitch control is introduced, by assigning a weight to regions of the pitch. We demonstrate that pitch control of the penalty box of the out-of-possession team is negatively correlated with expected goals in each of the six seasons, and interpret this apparently counter-intuitive result.
{"title":"Measuring the pitch control of professional football players using spatiotemporal tracking data","authors":"Lewis Higgins, T. Galla, Brian Prestidge, T. Wyatt","doi":"10.1088/2632-072X/acb67d","DOIUrl":"https://doi.org/10.1088/2632-072X/acb67d","url":null,"abstract":"We study pitch control in football, using data from six complete seasons of the English Premier League. Our objective is to investigate features of pitch control in the data. We process the data to ensure consistency of the tracking and event datasets. This represents the largest coherent dataset analysed in the literature and allows the observation of consistent patterns across several seasons’ data. We demonstrate that teams playing in front of a crowd at home control on average 2.9±0.2% more of the pitch than teams playing away, which reduces to 1.5±0.6% in matches played behind closed doors. We observe that match by match the difference in pitch control between the teams has a weak, positive correlation with the difference in expected goals (Pearson correlation R = 0.38). As a further manifestation of home advantage we find that in games which the two teams have equal pitch control, on average the home team accumulates greater expected goals ( 0.16±0.03 ). The concept of weighted pitch control is introduced, by assigning a weight to regions of the pitch. We demonstrate that pitch control of the penalty box of the out-of-possession team is negatively correlated with expected goals in each of the six seasons, and interpret this apparently counter-intuitive result.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45813186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-16DOI: 10.1088/2632-072X/ac7f75
G. Bianconi, A. Arenas, J. Biamonte, L. Carr, B. Kahng, J. Kertész, Jürgen Kurths, Linyuan Lü, C. Masoller, A. Motter, M. Perc, F. Radicchi, R. Ramaswamy, Francisco A Rodrigues, M. Sales-Pardo, M. San Miguel, S. Thurner, T. Yasseri
The 2021 Nobel Prize in Physics recognized the fundamental role of complex systems in the natural sciences. In order to celebrate this milestone, this editorial presents the point of view of the editorial board of JPhys Complexity on the achievements, challenges, and future prospects of the field. To distinguish the voice and the opinion of each editor, this editorial consists of a series of editor perspectives and reflections on few selected themes. A comprehensive and multi-faceted view of the field of complexity science emerges. We hope and trust that this open discussion will be of inspiration for future research on complex systems.
{"title":"Complex systems in the spotlight: next steps after the 2021 Nobel Prize in Physics","authors":"G. Bianconi, A. Arenas, J. Biamonte, L. Carr, B. Kahng, J. Kertész, Jürgen Kurths, Linyuan Lü, C. Masoller, A. Motter, M. Perc, F. Radicchi, R. Ramaswamy, Francisco A Rodrigues, M. Sales-Pardo, M. San Miguel, S. Thurner, T. Yasseri","doi":"10.1088/2632-072X/ac7f75","DOIUrl":"https://doi.org/10.1088/2632-072X/ac7f75","url":null,"abstract":"The 2021 Nobel Prize in Physics recognized the fundamental role of complex systems in the natural sciences. In order to celebrate this milestone, this editorial presents the point of view of the editorial board of JPhys Complexity on the achievements, challenges, and future prospects of the field. To distinguish the voice and the opinion of each editor, this editorial consists of a series of editor perspectives and reflections on few selected themes. A comprehensive and multi-faceted view of the field of complexity science emerges. We hope and trust that this open discussion will be of inspiration for future research on complex systems.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46478710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1088/2632-072X/acadc8
Chloe F. Norris, A. Maltsev
The sinoatrial node (SAN) is the pacemaker of the heart. Recently calcium signals, believed to be crucially important in rhythm generation, have been imaged in intact SAN and shown to be heterogeneous in various regions of the SAN with a lot of analysis relying on visual inspection rather than mathematical tools. Here we apply methods of random matrix theory (RMT) developed for financial data and various biological data sets including β-cell collectives and electroencephalograms (EEG) to analyse correlations in SAN calcium signals using eigenvalues and eigenvectors of the correlation matrix. We use principal component analysis to locate signalling modules corresponding to localization properties the eigenvectors corresponding to high eigenvalues. We find that the top eigenvector captures the global behaviour of the SAN i.e. action potential (AP) induced calcium transient. In some cases, the eigenvector corresponding to the second highest eigenvalue yields a pacemaker region whose calcium signals predict the AP. Furthermore, using new analytic methods, we study the relationship between covariance coefficients and distance, and find that even inside the central zone, there are non-trivial long range correlations, indicating intercellular interactions in most cases. Lastly, we perform an analysis of nearest-neighbour eigenvalue distances and find that it coincides with universal Wigner surmise under all available experimental conditions, while the number variance, which captures eigenvalue correlations, is sensitive to experimental conditions. Thus RMT application to SAN allows to remove noise and the global effects of the AP-induced calcium transient and thereby isolate the local and meaningful correlations in calcium signalling.
{"title":"Meaningful local signalling in sinoatrial node identified by random matrix theory and PCA","authors":"Chloe F. Norris, A. Maltsev","doi":"10.1088/2632-072X/acadc8","DOIUrl":"https://doi.org/10.1088/2632-072X/acadc8","url":null,"abstract":"The sinoatrial node (SAN) is the pacemaker of the heart. Recently calcium signals, believed to be crucially important in rhythm generation, have been imaged in intact SAN and shown to be heterogeneous in various regions of the SAN with a lot of analysis relying on visual inspection rather than mathematical tools. Here we apply methods of random matrix theory (RMT) developed for financial data and various biological data sets including β-cell collectives and electroencephalograms (EEG) to analyse correlations in SAN calcium signals using eigenvalues and eigenvectors of the correlation matrix. We use principal component analysis to locate signalling modules corresponding to localization properties the eigenvectors corresponding to high eigenvalues. We find that the top eigenvector captures the global behaviour of the SAN i.e. action potential (AP) induced calcium transient. In some cases, the eigenvector corresponding to the second highest eigenvalue yields a pacemaker region whose calcium signals predict the AP. Furthermore, using new analytic methods, we study the relationship between covariance coefficients and distance, and find that even inside the central zone, there are non-trivial long range correlations, indicating intercellular interactions in most cases. Lastly, we perform an analysis of nearest-neighbour eigenvalue distances and find that it coincides with universal Wigner surmise under all available experimental conditions, while the number variance, which captures eigenvalue correlations, is sensitive to experimental conditions. Thus RMT application to SAN allows to remove noise and the global effects of the AP-induced calcium transient and thereby isolate the local and meaningful correlations in calcium signalling.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"4 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61190590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-19DOI: 10.1088/2632-072X/acace0
Pietro De Lellis, Manuel Ruiz Marín, M. Porfiri
Pairwise interactions are critical to collective dynamics of natural and technological systems. Information theory is the gold standard to study these interactions, but recent work has identified pitfalls in the way information flow is appraised through classical metrics—time-delayed mutual information and transfer entropy. These pitfalls have prompted the introduction of intrinsic mutual information to precisely measure information flow. However, little is known regarding the potential use of intrinsic mutual information in the inference of directional influences to diagnose interactions from time-series of individual units. We explore this possibility within a minimalistic, mathematically tractable leader–follower model, for which we document an excess of false inferences of intrinsic mutual information compared to transfer entropy. This unexpected finding is linked to a fundamental limitation of intrinsic mutual information, which suffers from the same sins of time-delayed mutual information: a thin tail of the null distribution that favors the rejection of the null-hypothesis of independence.
{"title":"Inferring directional interactions in collective dynamics: a critique to intrinsic mutual information","authors":"Pietro De Lellis, Manuel Ruiz Marín, M. Porfiri","doi":"10.1088/2632-072X/acace0","DOIUrl":"https://doi.org/10.1088/2632-072X/acace0","url":null,"abstract":"Pairwise interactions are critical to collective dynamics of natural and technological systems. Information theory is the gold standard to study these interactions, but recent work has identified pitfalls in the way information flow is appraised through classical metrics—time-delayed mutual information and transfer entropy. These pitfalls have prompted the introduction of intrinsic mutual information to precisely measure information flow. However, little is known regarding the potential use of intrinsic mutual information in the inference of directional influences to diagnose interactions from time-series of individual units. We explore this possibility within a minimalistic, mathematically tractable leader–follower model, for which we document an excess of false inferences of intrinsic mutual information compared to transfer entropy. This unexpected finding is linked to a fundamental limitation of intrinsic mutual information, which suffers from the same sins of time-delayed mutual information: a thin tail of the null distribution that favors the rejection of the null-hypothesis of independence.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43585095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-19DOI: 10.1088/2632-072X/acacdf
K. Nakazato
Generative adversarial networks are popular deep neural networks for generative modeling in the field of artificial intelligence. In the generative modeling, we want to output a sample with some random numbers as an input. We train the artificial neural network with a training data set for the purpose. The network is known with astonishingly fruitful demonstrations, but we know the difficulty in the training because of the complex training dynamics. Here, we introduce an ecological analogy for the training dynamics. With the simple ecological model, we can understand the dynamics. Furthermore, a controller for the training can be designed based on the understanding. We then demonstrate how the network and the controller work with an ideal case, MNIST.
{"title":"Ecological Analogy for Generative Adversarial Networks and Diversity Control","authors":"K. Nakazato","doi":"10.1088/2632-072X/acacdf","DOIUrl":"https://doi.org/10.1088/2632-072X/acacdf","url":null,"abstract":"Generative adversarial networks are popular deep neural networks for generative modeling in the field of artificial intelligence. In the generative modeling, we want to output a sample with some random numbers as an input. We train the artificial neural network with a training data set for the purpose. The network is known with astonishingly fruitful demonstrations, but we know the difficulty in the training because of the complex training dynamics. Here, we introduce an ecological analogy for the training dynamics. With the simple ecological model, we can understand the dynamics. Furthermore, a controller for the training can be designed based on the understanding. We then demonstrate how the network and the controller work with an ideal case, MNIST.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45131649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-19DOI: 10.1088/2632-072X/acace1
K. Peralta-Martinez, J. A. Méndez-Bermúdez
In this work we analyze structural and spectral properties of a model of directed random geometric graphs: given n vertices uniformly and independently distributed on the unit square, a directed edge is set between two vertices if their distance is smaller than the connection radius ℓ , which is randomly drawn from a Pareto distribution. This Pareto distribution is characterized by the power-law decay α and the lower bound of its support ℓ0 ; thus the graphs depend on three parameters G(n,α,ℓ0) . By increasing ℓ0 , for fixed (n,α) , the model transits from isolated vertices ( ℓ0≈0 ) to complete graphs ( ℓ0=2 ). We first propose a phenomenological expression for the average degree ⟨k(G)⟩ which works well for α > 3, when k is a self-averaging quantity. Then we numerically demonstrate that 〈Vx(G)〉≈n[1−exp(−〈k〉] , for all α, where Vx(G) is the number of nonisolated vertices of G. Finally, we explore the spectral properties of G(n,α,ℓ0) by the use of adjacency matrices represented by diluted random matrix ensembles; a non-Hermitian and a Hermitian one. We find that ⟨k⟩ is a good scaling parameter of spectral and eigenvector properties of G mainly for large α.
{"title":"Directed random geometric graphs: structural and spectral properties","authors":"K. Peralta-Martinez, J. A. Méndez-Bermúdez","doi":"10.1088/2632-072X/acace1","DOIUrl":"https://doi.org/10.1088/2632-072X/acace1","url":null,"abstract":"In this work we analyze structural and spectral properties of a model of directed random geometric graphs: given n vertices uniformly and independently distributed on the unit square, a directed edge is set between two vertices if their distance is smaller than the connection radius ℓ , which is randomly drawn from a Pareto distribution. This Pareto distribution is characterized by the power-law decay α and the lower bound of its support ℓ0 ; thus the graphs depend on three parameters G(n,α,ℓ0) . By increasing ℓ0 , for fixed (n,α) , the model transits from isolated vertices ( ℓ0≈0 ) to complete graphs ( ℓ0=2 ). We first propose a phenomenological expression for the average degree ⟨k(G)⟩ which works well for α > 3, when k is a self-averaging quantity. Then we numerically demonstrate that 〈Vx(G)〉≈n[1−exp(−〈k〉] , for all α, where Vx(G) is the number of nonisolated vertices of G. Finally, we explore the spectral properties of G(n,α,ℓ0) by the use of adjacency matrices represented by diluted random matrix ensembles; a non-Hermitian and a Hermitian one. We find that ⟨k⟩ is a good scaling parameter of spectral and eigenvector properties of G mainly for large α.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46182837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-06DOI: 10.1088/2632-072X/acc91f
Chengyuan Han, Malte Schröder, D. Witthaut, Philipp C. Böttcher
Understanding the structure and formation of networks is a central topic in complexity science. Economic networks are formed by decisions of individual agents and thus not properly described by established random graph models. In this article, we establish a model for the emergence of trade networks that is based on rational decisions of individual agents. The model incorporates key drivers for the emergence of trade, comparative advantage and economic scale effects, but also the heterogeneity of agents and the transportation or transaction costs. Numerical simulations show three macroscopically different regimes of the emerging trade networks. Depending on the specific transportation costs and the heterogeneity of individual preferences, we find centralized production with a star-like trade network, distributed production with all-to-all trading or local production and no trade. Using methods from statistical mechanics, we provide an analytic theory of the transitions between these regimes and estimates for critical parameters values.
{"title":"Formation of trade networks by economies of scale and product differentiation","authors":"Chengyuan Han, Malte Schröder, D. Witthaut, Philipp C. Böttcher","doi":"10.1088/2632-072X/acc91f","DOIUrl":"https://doi.org/10.1088/2632-072X/acc91f","url":null,"abstract":"Understanding the structure and formation of networks is a central topic in complexity science. Economic networks are formed by decisions of individual agents and thus not properly described by established random graph models. In this article, we establish a model for the emergence of trade networks that is based on rational decisions of individual agents. The model incorporates key drivers for the emergence of trade, comparative advantage and economic scale effects, but also the heterogeneity of agents and the transportation or transaction costs. Numerical simulations show three macroscopically different regimes of the emerging trade networks. Depending on the specific transportation costs and the heterogeneity of individual preferences, we find centralized production with a star-like trade network, distributed production with all-to-all trading or local production and no trade. Using methods from statistical mechanics, we provide an analytic theory of the transitions between these regimes and estimates for critical parameters values.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49083968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-06DOI: 10.1088/2632-072X/aca94a
Alex S O Toledo, Riccardo Silini, L. Carpi, C. Masoller
Reliable anomaly/outlier detection algorithms have practical applications in many fields. For instance, anomaly detection allows to filter and clean the data used to train machine learning algorithms, improving their performance. However, outlier mining is challenging when the data is high-dimensional, and different approaches have been proposed for different types of data (temporal, spatial, network, etc). Here we propose a methodology to mine outliers in generic datasets in which it is possible to define a meaningful distance between elements of the dataset. The methodology is based on defining a fully connected, undirected graph, where the nodes are the elements of the dataset and the links have weights that are the distances between the nodes. Outlier scores are defined by analyzing the structure of the graph, in particular, by using the Jensen–Shannon (JS) divergence to compare the distributions of weights of different nodes. We demonstrate the method using a publicly available database of credit-card transactions, where some of the transactions are labeled as frauds. We compare with the performance obtained when using Euclidean distances and graph percolation, and show that the JS divergence leads to performance improvement, but increases the computational cost.
{"title":"Outlier mining in high-dimensional data using the Jensen–Shannon divergence and graph structure analysis","authors":"Alex S O Toledo, Riccardo Silini, L. Carpi, C. Masoller","doi":"10.1088/2632-072X/aca94a","DOIUrl":"https://doi.org/10.1088/2632-072X/aca94a","url":null,"abstract":"Reliable anomaly/outlier detection algorithms have practical applications in many fields. For instance, anomaly detection allows to filter and clean the data used to train machine learning algorithms, improving their performance. However, outlier mining is challenging when the data is high-dimensional, and different approaches have been proposed for different types of data (temporal, spatial, network, etc). Here we propose a methodology to mine outliers in generic datasets in which it is possible to define a meaningful distance between elements of the dataset. The methodology is based on defining a fully connected, undirected graph, where the nodes are the elements of the dataset and the links have weights that are the distances between the nodes. Outlier scores are defined by analyzing the structure of the graph, in particular, by using the Jensen–Shannon (JS) divergence to compare the distributions of weights of different nodes. We demonstrate the method using a publicly available database of credit-card transactions, where some of the transactions are labeled as frauds. We compare with the performance obtained when using Euclidean distances and graph percolation, and show that the JS divergence leads to performance improvement, but increases the computational cost.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47136226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-01DOI: 10.1088/2632-072X/ac9171
G. Parisi
The Nobel Laureate Giorgio Parisi is interviewed by JPhys Complexity Editor-in-Chief, Ginestra Bianconi, on themes related to the 2021 Nobel Prize in Physics awarded to him for research on complex systems.
{"title":"Thoughts on complex systems: an interview with Giorgio Parisi","authors":"G. Parisi","doi":"10.1088/2632-072X/ac9171","DOIUrl":"https://doi.org/10.1088/2632-072X/ac9171","url":null,"abstract":"The Nobel Laureate Giorgio Parisi is interviewed by JPhys Complexity Editor-in-Chief, Ginestra Bianconi, on themes related to the 2021 Nobel Prize in Physics awarded to him for research on complex systems.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47373951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-01DOI: 10.1088/2632-072X/aca57c
L. da Fontoura Costa
The concepts of auto- and cross-correlation play a key role in several areas, including signal processing and analysis, pattern recognition, multivariate statistics, as well as physics in general, as these operations underlie several real-world structures and dynamics. In the present work, the concept of multiset similarity, more specifically the coincidence similarity index, is used as the basis for defining operations between a same network, or two distinct networks, which will be respectively called autorrelation and cross-relation. In analogous manner to the autocorrelation and cross-correlation counterparts, which are defined in terms of inner products between signals, the two operations suggested here allow the comparison of the similarity of nodes and graphs respectively to successive displacements along the neighborhoods of each of the constituent nodes, which therefore plays a role that is analogue to the lag in the class correlation. In addition to presenting these approaches, this work also illustrates their potential respectively to applications for the characterization of several model-theoretic and real world networks, providing a comprehensive description of the specific properties of each analyzed structure. The possibility of analyzing the obtained individual autorrelation signatures in terms of their respective coincidence similarity networks is also addressed and illustrated.
{"title":"Autorrelation and cross-relation of graphs and networks","authors":"L. da Fontoura Costa","doi":"10.1088/2632-072X/aca57c","DOIUrl":"https://doi.org/10.1088/2632-072X/aca57c","url":null,"abstract":"The concepts of auto- and cross-correlation play a key role in several areas, including signal processing and analysis, pattern recognition, multivariate statistics, as well as physics in general, as these operations underlie several real-world structures and dynamics. In the present work, the concept of multiset similarity, more specifically the coincidence similarity index, is used as the basis for defining operations between a same network, or two distinct networks, which will be respectively called autorrelation and cross-relation. In analogous manner to the autocorrelation and cross-correlation counterparts, which are defined in terms of inner products between signals, the two operations suggested here allow the comparison of the similarity of nodes and graphs respectively to successive displacements along the neighborhoods of each of the constituent nodes, which therefore plays a role that is analogue to the lag in the class correlation. In addition to presenting these approaches, this work also illustrates their potential respectively to applications for the characterization of several model-theoretic and real world networks, providing a comprehensive description of the specific properties of each analyzed structure. The possibility of analyzing the obtained individual autorrelation signatures in terms of their respective coincidence similarity networks is also addressed and illustrated.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46042397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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