Severity: Warning
Message: fopen(/var/lib/php/sessions/ci_sessionn6a3pnofabgiru3tdo3pn8a90qc5dmfh): Failed to open stream: No space left on device
Filename: drivers/Session_files_driver.php
Line Number: 177
Backtrace:
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: session_start(): Failed to read session data: user (path: /var/lib/php/sessions)
Filename: Session/Session.php
Line Number: 137
Backtrace:
File: /var/www/html/index.php
Line: 316
Function: require_once
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
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
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
Severity: 8192
Message: strpos(): Passing null to parameter #1 ($haystack) of type string is deprecated
Filename: models/Detail_model.php
Line Number: 71
Backtrace:
File: /var/www/html/application/models/Detail_model.php
Line: 71
Function: strpos
File: /var/www/html/application/controllers/Detail.php
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Function: insertAPISummary
File: /var/www/html/index.php
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Function: require_once
Severity: 8192
Message: str_replace(): Passing null to parameter #3 ($subject) of type array|string is deprecated
Filename: helpers/my_audit_helper.php
Line Number: 8919
Backtrace:
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
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: 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
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: Undefined array key "usage"
Filename: controllers/Detail.php
Line Number: 258
Backtrace:
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
Line Number: 258
Backtrace:
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: Undefined array key "usage"
Filename: controllers/Detail.php
Line Number: 259
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 259
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
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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: Undefined array key "usage"
Filename: controllers/Detail.php
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Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 260
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
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File: /var/www/html/application/controllers/Detail.php
Line: 260
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
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File: /var/www/html/application/controllers/Detail.php
Line: 260
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
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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Backtrace:
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
Line: 3098
Function: getPubMedXML
File: /var/www/html/application/controllers/Detail.php
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Function: pubMedSearch_Global
File: /var/www/html/application/controllers/Detail.php
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Function: pubMedGetRelatedKeyword
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Function: require_once
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Message: Attempt to read property "Count" on bool
Filename: helpers/my_audit_helper.php
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File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3100
Function: _error_handler
File: /var/www/html/application/controllers/Detail.php
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Function: pubMedSearch_Global
File: /var/www/html/application/controllers/Detail.php
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Function: pubMedGetRelatedKeyword
File: /var/www/html/index.php
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Function: require_once
Networks studied in many disciplines, including neuroscience and mathematical biology, have connectivity that may be stochastic about some underlying mean connectivity represented by a non-normal matrix. Furthermore, the stochasticity may not be independent and identically distributed (iid) across elements of the connectivity matrix. More generally, the problem of understanding the behavior of stochastic matrices with nontrivial mean structure and correlations arises in many settings. We address this by characterizing large random N×N matrices of the form A=M+LJR, where M,L, and R are arbitrary deterministic matrices and J is a random matrix of zero-mean iid elements. M can be non-normal, and L and R allow correlations that have separable dependence on row and column indices. We first provide a general formula for the eigenvalue density of A. For A non-normal, the eigenvalues do not suffice to specify the dynamics induced by A, so we also provide general formulas for the transient evolution of the magnitude of activity and frequency power spectrum in an N-dimensional linear dynamical system with a coupling matrix given by A. These quantities can also be thought of as characterizing the stability and the magnitude of the linear response of a nonlinear network to small perturbations about a fixed point. We derive these formulas and work them out analytically for some examples of M,L, and R motivated by neurobiological models. We also argue that the persistence as N→∞ of a finite number of randomly distributed outlying eigenvalues outside the support of the eigenvalue density of A, as previously observed, arises in regions of the complex plane Ω where there are nonzero singular values of L(-1)(z1-M)R(-1) (for z∈Ω) that vanish as N→∞. When such singular values do not exist and L and R are equal to the identity, there is a correspondence in the normalized Frobenius norm (but not in the operator norm) between the support of the spectrum of A for J of norm σ and the σ pseudospectrum of M.
Download full-text PDF |
Source |
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4745946 | PMC |
http://dx.doi.org/10.1103/PhysRevE.91.012820 | DOI Listing |
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