Skew-gradient representation of generalized Birkhoffian system

2015 ◽  
Vol 24 (10) ◽  
pp. 104502 ◽  
Author(s):  
Feng-Xiang Mei ◽  
Hui-Bin Wu
Cognition ◽  
2015 ◽  
Vol 142 ◽  
pp. 266-290 ◽  
Author(s):  
Lilia Rissman ◽  
Kyle Rawlins ◽  
Barbara Landau

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 515 ◽  
Author(s):  
Savin Treanţă

In this paper, by using a vector variable, the procedure of characteristic systems allows us to describe the kernel of a polynomial of scalar derivations by solving Cauchy Problems for the corresponding system of ODEs. Moreover, a gradient representation for the associated Cauchy Problem solution is derived.


2015 ◽  
Vol 64 (23) ◽  
pp. 234501
Author(s):  
Wu Hui-Bin ◽  
Mei Feng-Xiang

2012 ◽  
Vol 61 (2) ◽  
pp. 024502
Author(s):  
Lou Zhi-Mei ◽  
Mei Feng-Xiang

2019 ◽  
Author(s):  
Rocco Chiou ◽  
Gina F. Humphreys ◽  
Matthew A. Lambon Ralph

AbstractThe ‘default network’ (DN) becomes active when the mind is steered internally towards self-generated thoughts but turns dormant when the mind is directed externally towards the outside world. While hypotheses have been proposed to characterise the association and dissociation between different component areas of the DN, it remains unclear how they coalesce into a unitary network and fractionate into different sub-networks. Here we identified two distinct subsystems within the DN – while both subsystems show common disinterest in externally-oriented visuospatial tasks, their functional profiles differ strikingly according to the preferred contents of thoughts, preferred modes of task requirement, and causative neural dynamics among network nodes. Specifically, one subsystem comprises key nodes of the frontotemporal semantic regions. This network shows moderate dislike to visuospatial tasks, shows proclivity for task-contexts with restraints on thoughts and responses, and prefers thoughts that are focused on other people. By contrast, the other subsystem comprises the cortical midline structure and angular gyri. This network shows strong aversion to visuospatial tasks, favours task-contexts allowing free self-generated thoughts without constraints, and prefers thoughts that are focused on self. Furthermore, causative connectivity reveals that task-contexts systematically alter the dynamics within and between subsystems, suggesting flexible adaption to situational demands. This ‘self/inward vs. others/outward’ separation within the broad DN resembles recent discoveries regarding a dyadic structure within the frontoparietal network that comprises regions controlling memories/thoughts vs. regions controlling sensory-motoric processes, and echoes burgeoning views that the brain is organised with a spectrum-like architecture along gradational changes of ‘inward vs. outward’ preferences.SignificanceRather than construing the default network (DN) as ‘task-negative’ regions that passively react to off-task mind-wandering, researchers have begun to acknowledge the active role of the DN in supporting internally-directed cognition. Here we found a striking dichotomy within the DN in terms of the subsystems’ task-driven functional and connectivity profiles, extending beyond previous inferences using meta-analysis and resting-state fMRI. This dichotomy reflects a local manifestation of a macro-scale gradient representation spanning across the broad cerebral cortex. This cortical gradient increases its representational complexity, from primitive sensory and motoric processing, through lexical-semantic codes for language tasks, to abstract self-generated thoughts in task-free contexts. These findings enable a framework where the separate yet related literatures of semantic cognition and default-mode processes converge.


2001 ◽  
Vol 50 (11) ◽  
pp. 2049
Author(s):  
LUO SHAO-KAI ◽  
GUO YONG-XIN ◽  
CHEN XIANG-WEI ◽  
FU JING-LI

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