Severity: Warning
Message: Undefined array key "choices"
Filename: controllers/Detail.php
Line Number: 249
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 249
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 249
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 249
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: strpos(): Passing null to parameter #1 ($haystack) of type string is deprecated
Filename: models/Detail_model.php
Line Number: 71
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File: /var/www/html/application/models/Detail_model.php
Line: 71
Function: strpos
File: /var/www/html/application/controllers/Detail.php
Line: 252
Function: insertAPISummary
File: /var/www/html/index.php
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Function: require_once
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Message: str_replace(): Passing null to parameter #3 ($subject) of type array|string is deprecated
Filename: helpers/my_audit_helper.php
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File: /var/www/html/application/helpers/my_audit_helper.php
Line: 8919
Function: str_replace
File: /var/www/html/application/controllers/Detail.php
Line: 255
Function: formatAIDetailSummary
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Undefined array key "choices"
Filename: controllers/Detail.php
Line Number: 256
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 256
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 256
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Undefined array key "usage"
Filename: controllers/Detail.php
Line Number: 257
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 257
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 257
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File: /var/www/html/application/controllers/Detail.php
Line: 257
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Undefined array key "usage"
Filename: controllers/Detail.php
Line Number: 258
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File: /var/www/html/application/controllers/Detail.php
Line: 258
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
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Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Filename: controllers/Detail.php
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Function: _error_handler
File: /var/www/html/index.php
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Filename: controllers/Detail.php
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Function: _error_handler
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Message: Undefined array key "usage"
Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
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Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
Line: 260
Function: _error_handler
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
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Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: file_get_contents(https://...@gmail.com&api_key=61f08fa0b96a73de8c900d749fcb997acc09): Failed to open stream: HTTP request failed! HTTP/1.1 429 Too Many Requests
Filename: helpers/my_audit_helper.php
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File: /var/www/html/application/helpers/my_audit_helper.php
Line: 143
Function: file_get_contents
File: /var/www/html/application/helpers/my_audit_helper.php
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Function: simplexml_load_file_from_url
File: /var/www/html/application/helpers/my_audit_helper.php
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Function: getPubMedXML
File: /var/www/html/application/controllers/Detail.php
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Function: pubMedSearch_Global
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Function: pubMedGetRelatedKeyword
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Filename: helpers/my_audit_helper.php
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File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3100
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File: /var/www/html/application/controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
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Function: pubMedGetRelatedKeyword
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Function: require_once
Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can be unified. Two existing recent theories state that 1) functional networks can be explained by all possible walks in the structural network, which we will refer to as the series expansion approach, and 2) functional networks can be explained by a weighted combination of the eigenmodes of the structural network, the so-called eigenmode approach. To elucidate the unique or common explanatory power of these approaches to estimate functional networks from the structural network, we analysed the relationship between these two existing views. Using linear algebra, we first show that the eigenmode approach can be written in terms of the series expansion approach, i.e., walks on the structural network associated with different hop counts correspond to different weightings of the eigenvectors of this network. Second, we provide explicit expressions for the coefficients for both the eigenmode and series expansion approach. These theoretical results were verified by empirical data from Diffusion Tensor Imaging (DTI) and functional Magnetic Resonance Imaging (fMRI), demonstrating a strong correlation between the mappings based on both approaches. Third, we analytically and empirically demonstrate that the fit of the eigenmode approach to measured functional data is always at least as good as the fit of the series expansion approach, and that errors in the structural data lead to large errors of the estimated coefficients for the series expansion approach. Therefore, we argue that the eigenmode approach should be preferred over the series expansion approach. Results hold for eigenmodes of the weighted adjacency matrices as well as eigenmodes of the graph Laplacian. Taken together, these results provide an important step towards unification of existing theories regarding the structure-function relationships in brain networks.
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Source |
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http://dx.doi.org/10.1016/j.neuroimage.2020.116805 | DOI Listing |
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