Virtual reality as a new approach to assess cognitive decline in the elderly

Brain aging is a natural process that leads to a change in cognitive functions. Mild Cognitive Impairment (MCI) is a condition in which a person has cognitive functions that are below normal for his age. However, these deficits are not pronounced enough to confirm for the diagnosis of dementia. It is therefore important to develop new ways to assess cognitive functions in the elderly. This would indeed lead to a better identification of the cognitive losses that are related to normal or pathological aging. The objective of this study was to investigate the relevance of virtual reality as a new evaluation approach in psychology. To do this, 10 elderly people with Mild Cognitive Impairment, and 20 elderly people without cognitive problems, were compared using tests of prospective memory that were presented in a traditional way and in virtual reality. The diagnosis of MCI was made using the Montreal Cognitive Assessment (MoCA). Significant differences between the two groups were noted in virtual reality. Nevertheless, no difference was observed between the two groups with the traditional task. A significant positive correlation between the virtual reality task and the MoCA, but not between the traditional task and the MoCA, was observed. An evaluative approach based on virtual reality seems more sensitive to cognitive impairment associated with aging than an approach based on traditional neuropsychological tests.

Boundary rules and breaking of self-organized criticality in 2D frozen percolation

We study frozen percolation on the (planar) triangular lattice, where connected components stop growing (“freeze”) as soon as their “size” becomes at least N, for some parameter N ≥ 1. The size of a connected component can be measured in several natural ways, and we consider the two particular cases of diameter and volume (i.e. number of sites). Diameter-frozen and volume-frozen percolation have been studied in previous works ([5, 15] and [6, 4], resp.), and they display radically different behaviors. These works adopt the rule that the boundary of a frozen cluster stays vacant forever, and we investigate the influence of these “boundary rules” in the present paper. We prove the (somewhat surprising) result that they strongly matter in the diameter case, and we discuss briefly the volume case

Boundary rules and breaking of self-organized criticality in 2D frozen percolation

We study frozen percolation on the (planar) triangular lattice, where connected components stop growing ("freeze") as soon as their "size" becomes at least N, for some parameter N ≥ 1. The size of a connected component can be measured in several natural ways, and we consider the two particular cases of diameter and volume (i.e. number of sites). Diameter-frozen and volume-frozen percolation have been studied in previous works ([25, 11] and [27, 26], resp.), and they display radically different behaviors. These works adopt the rule that the boundary of a frozen cluster stays vacant forever, and we investigate the influence of these "boundary conditions" in the present paper. We prove the (somewhat surprising) result that they strongly matter in the diameter case, and we discuss briefly the volume case

Two-dimensional volume-frozen percolation: deconcentration and prevalence of mesoscopic clusters

Frozen percolation on the binary tree was introduced by Aldous [1], inspired by sol-gel transitions. We investigate a version of the model on the triangular lattice, where connected components stop growing (freeze) as soon as they contain at least N vertices, where N is a (typically large) parameter. For the process in certain +nite domains, we show a Òseparation of scalesÓ and use this to prove a deconcentration property. Then, for the full-plane process, we prove an accurate comparison to the process in suitable +nite domains, and obtain that, with high probability (as N→), the origin belongs in the nal con+guration to a mesoscopic cluster, i.e., a cluster which contains many, but much fewer than N, vertices (and hence is non-frozen). For this work we develop new interesting properties for near-critical percolation, including asymp-totic formulas involving the percolation probability θ(p) and the characteristic length L(p) as p → pc