Analysis of brain functional connectivity (FC) could provide insight in how and why cognitive functions decline even in healthy aging (HA). Despite FC being established as fluctuating over time even in the resting state (RS), dynamic functional connectivity (DFC) studies involving healthy elderly individuals and assessing how these patterns relate to cognitive performance are yet scarce. In our recent study we showed that fractal temporal scaling of functional connections in RS is not only reduced in HA, but also predicts increased response latency and reduced task solving accuracy. However, in that work we did not address changes in the dynamics of fractal connectivity (FrC) strength itself and its plausible relationship with mental capabilities. Therefore, here we analyzed RS electroencephalography recordings of the same subject cohort as previously, consisting of 24 young and 19 healthy elderly individuals, who also completed 7 different cognitive tasks after data collection. Dynamic fractal connectivity (dFrC) analysis was carried out via sliding-window detrended cross-correlation analysis (DCCA). A machine learning method based on recursive feature elimination was employed to select the subset of connections most discriminative between the two age groups, identifying 56 connections that allowed for classifying participants with an accuracy surpassing 92%. Mean of DCCA was found generally increased, while temporal variability of FrC decreased in the elderly when compared to the young group. Finally, dFrC indices expressed an elaborate pattern of associations-assessed via Spearman correlation-with cognitive performance scores in both groups, linking fractal connectivity strength and variance to increased response latency and reduced accuracy in the elderly population. Our results provide further support for the relevance of FrC dynamics in understanding age-related cognitive decline and might help to identify potential targets for future intervention strategies.
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http://dx.doi.org/10.1007/s11357-023-01022-x | DOI Listing |
Chaos
January 2025
Emergent Complexity in Physical Systems Laboratory (ECPS), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.
The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, for three-dimensional systems. In certain cases, the fractal dimension of a chaotic attractor in a partial differential equation (PDE) is less than three, even though that attractor is embedded within an infinite-dimensional space. Here, we study the Kuramoto-Sivashinsky PDE at the onset of chaos.
View Article and Find Full Text PDFPLoS One
December 2024
School of Geoscience and Technology, Southwest Petroleum University, Chengdu, China.
Clarifying the pore-throat size and pore size distribution of tight sandstone reservoirs, quantitatively characterizing the heterogeneity of pore-throat structures, is crucial for evaluating reservoir effectiveness and predicting productivity. Through a series of rock physics experiments including gas measurement of porosity and permeability, casting thin sections, scanning electron microscopy, and high-pressure mercury injection, the quality of reservoir properties and microscopic pore-throat structure characteristics were systematically studied. Combined with fractal geometry theory, the effects of different pore throat types, geometric shapes and scale sizes on the fractal characteristics and heterogeneity of sandstone pore throat structure are clarified.
View Article and Find Full Text PDFPhys Rev E
November 2024
Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, California 90089-2531, USA.
Statistics of diffusion, modeled by random walks, such as the mean number of distinct sites visited S(t) at time t, the mean probability P_{0}(t) of being at the origin of the walk, and the mean-squared displacements 〈R^{2}(t)〉 of the random walkers have been studied extensively in the past in both regular lattices and such disordered media as percolation clusters and other fractal structures, and universal power laws for such quantities have been derived. S(t) provides insight into reaction properties of geological formations, while P_{0}(t) is directly linked with the problem of back diffusion in remediation of groundwater aquifers. In all such studies, it was assumed that the conductances of the bonds that connect nearest-neighbor sites of the lattices are equal.
View Article and Find Full Text PDFMethodsX
June 2024
Department of Mathematics, Near East Boulevard, Mathematics Research Center, Near East University, PC: 99138, Mersin, Nicosia 10, Turkey.
Numerous special functions, including the beta function, hypergeometric functions, and other orthogonal polynomials, are closely connected to the gamma function. Recently, gamma function has been enhanced by adding a new parameter. As a consequence, this gamma is called the parametric gamma function or b-gamma function.
View Article and Find Full Text PDFAngew Chem Int Ed Engl
December 2024
University of Michigan, COMPASS, UNITED STATES OF AMERICA.
Self-replication of molecules and microdroplets have been explored as models in prebiotic chemistry. An analogous process for inorganic nanomaterials would involve the autocatalytic nucleation of nanoparticles-an area that remains largely uncharted. Demonstrating such systems would be both fundamentally intriguing and practically relevant, especially if the resulting particles self-assemble.
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