[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-216826-en":3,"doc-seo-216826-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":20,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":14,"update_tm":27,"read_time":28},216826,962084931830,"Jacob","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Granger Causality Between Functional Brain Networks - gVAR methodology","Granger causality is studied between time series of graphs by modeling the dynamics of network structure through the spectral radius, the largest eigenvalue of each graph’s adjacency matrix. A methodology named gVAR fits a vector autoregressive model to spectral-radius sequences derived from brain connectivity measures, enabling statistical testing of directional influence between hemispheres. Results are reported for rs-fMRI/phenotypic autism data from ABIDE I and for paired violinist fNIRS recordings, supporting differential right-to-left effects conditioned by age, sex, and diagnosis.","Granger Causality Between Functional Brain Networks  \nAdèle Helena Ribeiro 1 , João Ricardo Sato 2 , and André Fujita 1  \n[adele@ime.usp.br](adele@ime.usp.br)  \n1-Department of Computer Science, Institute of Mathematics and Statistic, University of São Paulo, São Paulo  \n2-Center of Mathematics Computation and Cognition, Federal University of ABC, São Bernardo do Campo  \nIntroduction  \nDifferential Connectivity Between Brain Hemispheres in Autistim  \nNetworks are everywhere, from social to biological sciences. Usually they are represented by graphs, i.e., mathematical objects composed of a set of vertices and a set of edges. However, a vast number of natural networks are dynamic and current methods typically ignore a key component: time.  \nSupposing that two time series of graphs, yi;t and yj;t are generated by models whose parameters are random variables, we define, inspired by [1], that yi;t does not Granger cause yj;t if the models parameters for yi;t does not Granger cause the model parameters yj;t.  \nAlthough the models and consequently the parameters of graphs are usually unknown, the spectral radius is a function of the models parameters, capturing intrinsic structural and dynamical characteristics of the graph.  \nFigure 1: For (A) Erdös-Rényi, (B) geometric, (C) regular, (D) Watts-Strogatz, and (E) Barabási-Albert random graphs, spectral radius is a function of the parameters.  \nWe propose a methodology, called gVAR, that identifies Granger causality between time series of graphs by fittinga vector autoregressive (VAR) model on the time series of the spectral radii (the largest eigenvalue of the adjacency matrix of the graph) .  \nConsidering that yi;t is the spectral radius of the ith graph at time t, the gVAR(p) model is:  \nK p  \nyi;t = 􀀋 i +X X 􀀀􀀌lj;i yi;t􀀀l􀀁 + ui;t ; for i = 1; : : : ; K  \nj=1 l=1  \nWe analyzed rs-fMRI and phenotypic data from 737 subjects for whom the mean framewise displacement (FD) is not greater than 0.2 from the Autism Brain Imaging Data Exchange I (ABIDE I) dataset [3] . For each subject, we performed the pre-processing steps shown in Figure 3 .  \nW􀀕Right~~ ~~􀀀~~ ~~~~ ~~􀀀~~ ~~1 = 􀀋 + 􀀌F DFD + 􀀌SEX SEX+  \n􀀌 AGE AGE + 􀀌ASDASD + 􀀌SEX 􀀃 AGE SEX 􀀃 AGE+  \n􀀌 AGE 􀀃 ASD AGE 􀀃 ASD + 􀀍 SITE + \"  \nTable 1: Results considering the Wald's test statistic for assessing Granger causality from the right to the left hemisphere, from gVAR with order p = 5 .  \nParameter  \nEstimate  \nStd. Error  \nP-value  \n􀀋  \n2.5270  \n0.2163  \n\u003C 0.0001  \n􀀌 FD  \n􀀌 SEX  \n􀀌 AGE  \n􀀌 ASD  \n􀀌 AGE 􀀃 ASD  \n􀀌 SEX 􀀃 AGE  \n-0.9295  \n0.5956 0.0082 0.2945  \n􀀀0:0204  \n-0.0290  \n0.8893 0.2291 0.0073 0.1731  \n0:0089  \n0.0126  \n0.2963 0.0095 0.2619 0.0893  \n0:0220  \n0.0215  \nFigure 3: (A) For each subject, we mapped the brain regions according to the AAL atlas and excluded 26 cerebellar regions.(B) We obtained 45 regions on each hemisphere of the brain.(C) To preserve the sampling rate, we estimated a Pearson correlation graph for each hemisphere at each time point. (D) Finally, we applied the gVAR method.  \nFigure 4: Significant interaction effect between AGE and diagnostic of ASD for the Granger causality from the right to the left brain hemisphere considering (A) male subjects and (B) female subjects.  \nFigure 5: Differential Granger causality from the right to the left hemisphere in autistic subjects considering only females aged 6 to 13 years (p-value = 0:0147) and considering only males aged 16 to 60 years (p-value = 0:0096) .  \nMean Box−Cox Transformed Wald Statistics for the Granger Causality from Right to Left Brain Hemisphere  \n| |\n| --- |\n| |\n| |\n| |\n\nControl.Male ASD.Male Control.Female ASD.Female  \nBrain   \n-brain interaction of two professional violinists   \n\n| We analyzed 23-channel functional Near Infrared Spectroscopy (fNIRS) signals simultaneously acquired from both violinists while they were playing an 30s excerpt of Antonio Vivaldi's Allegro from the Concerto No 1 in E Major, Op. 8, RV 269,“Spring” [2] . The participants are 50 and 4","cbCaioTNqKqRjfvW","https://ap.wps.com/l/cbCaioTNqKqRjfvW","pdf",1801231,1,"English","en",105,"# Introduction\n## Differential Connectivity Between Brain Hemispheres in Autistim\n## gVAR Methodology\n## Experimental Analyses: ABIDE I and fNIRS Violinists\n# Results and Statistical Testing","[{\"question\":\"What does “spectral radius” represent in the gVAR framework?\",\"answer\":\"For each time-indexed graph, the spectral radius is the largest eigenvalue of its adjacency matrix, used as the dynamic summary to model network evolution over time.\"},{\"question\":\"How does gVAR identify Granger causality between time series of graphs?\",\"answer\":\"gVAR fits a vector autoregressive (VAR) model to the time series of spectral radii and then applies statistical tests (e.g., Wald’s test) to assess whether one graph time series predicts parameters associated with another.\"},{\"question\":\"Which datasets and signals are analyzed in the study?\",\"answer\":\"The autism analysis uses rs-fMRI and phenotypic data from ABIDE I with mean framewise displacement constraints, and the second analysis uses simultaneous 23-channel fNIRS signals from two professional violinists during a short Vivaldi excerpt.\"}]","Granger Causality Between Functional Brain Networks - gVAR methodology | PDF",1788827880,3,{"code":4,"msg":30,"data":31},"ok",{"site_id":23,"language":22,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"granger-causality-between-functional-brain-networks-gvar-methodology","",{"@graph":35,"@context":84},[36,52,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,49],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":28},"https://docshare.wps.com/document/research-report/",{"item":50,"name":13,"@type":42,"position":51},"https://docshare.wps.com/document/granger-causality-between-functional-brain-networks-gvar-methodology/216826/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":22,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":40,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-09-11","2026-09-08",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What does “spectral radius” represent in the gVAR framework?","Question",{"text":74,"@type":75},"For each time-indexed graph, the spectral radius is the largest eigenvalue of its adjacency matrix, used as the dynamic summary to model network evolution over time.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does gVAR identify Granger causality between time series of graphs?",{"text":79,"@type":75},"gVAR fits a vector autoregressive (VAR) model to the time series of spectral radii and then applies statistical tests (e.g., Wald’s test) to assess whether one graph time series predicts parameters associated with another.",{"name":81,"@type":72,"acceptedAnswer":82},"Which datasets and signals are analyzed in the study?",{"text":83,"@type":75},"The autism analysis uses rs-fMRI and phenotypic data from ABIDE I with mean framewise displacement constraints, and the second analysis uses simultaneous 23-channel fNIRS signals from two professional violinists during a short Vivaldi excerpt.","https://schema.org",{"og:url":50,"og:type":86,"og:title":13,"og:site_name":57,"og:description":14},"article",{"robots":88,"canonical":50},"index,follow",{"doc_id":7,"site_id":23},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":51,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":105,"slug":137},19,"General","general"]