Computational algebraic topology-based video restoration

2005 ◽  
Author(s):  
Alban Rochel ◽  
Djemel Ziou ◽  
Marie-Flavie Auclair-Fortier
Keyword(s):  
Algebraic Topology ◽  
Video Restoration ◽  
Computational Algebraic Topology

Global computational algebraic topology approach for diffusion

2004 ◽  
Author(s):  
Marie-Flavie Auclair-Fortier ◽  
Djemel Ziou ◽  
Madjid Allili
Keyword(s):  
Algebraic Topology ◽  
Computational Algebraic Topology

Computational Algebraic Topology

2008 ◽  
pp. 1603-1654
Author(s):  
Gunnar Carlsson ◽  
Dmitry Feichtner-Kozlov
Keyword(s):  
Algebraic Topology ◽  
Computational Algebraic Topology

scholarly journals P systems and computational algebraic topology

2010 ◽  
Vol 52 (11-12) ◽  
pp. 1982-1996 ◽  
Author(s):  
Hepzibah A. Christinal ◽  
Daniel Díaz-Pernil ◽  
Pedro Real
Keyword(s):  
Algebraic Topology ◽  
P Systems ◽  
Computational Algebraic Topology

scholarly journals Disrupted metabolic connectivity in dopaminergic and cholinergic networks at different stages of dementia from 18F-FDG PET brain persistent homology network

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tun-Wei Hsu ◽  
Jong-Ling Fuh ◽  
Da-Wei Wang ◽  
Li-Fen Chen ◽  
Chia-Jung Chang ◽  
...  
Keyword(s):  
Algebraic Topology ◽  
Fdg Pet ◽  
Persistent Homology ◽  
Network Connectivity ◽  
Brain Regions ◽  
Imaging Data ◽  
Cholinergic Pathways ◽  
Positron Emission ◽  
Metabolic Connectivity ◽  
Neurochemical Changes

AbstractDementia is related to the cellular accumulation of β-amyloid plaques, tau aggregates, or α-synuclein aggregates, or to neurotransmitter deficiencies in the dopaminergic and cholinergic pathways. Cellular and neurochemical changes are both involved in dementia pathology. However, the role of dopaminergic and cholinergic networks in metabolic connectivity at different stages of dementia remains unclear. The altered network organisation of the human brain characteristic of many neuropsychiatric and neurodegenerative disorders can be detected using persistent homology network (PHN) analysis and algebraic topology. We used 18F-fluorodeoxyglucose positron emission tomography (18F-FDG PET) imaging data to construct dopaminergic and cholinergic metabolism networks, and used PHN analysis to track the evolution of these networks in patients with different stages of dementia. The sums of the network distances revealed significant differences between the network connectivity evident in the Alzheimer’s disease and mild cognitive impairment cohorts. A larger distance between brain regions can indicate poorer efficiency in the integration of information. PHN analysis revealed the structural properties of and changes in the dopaminergic and cholinergic metabolism networks in patients with different stages of dementia at a range of thresholds. This method was thus able to identify dysregulation of dopaminergic and cholinergic networks in the pathology of dementia.

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