41 research outputs found
Statistics of pre-localized states in disordered conductors
The distribution function of local amplitudes of single-particle states in
disordered conductors is calculated on the basis of the supersymmetric
-model approach using a saddle-point solution of its reduced version.
Although the distribution of relatively small amplitudes can be approximated by
the universal Porter-Thomas formulae known from the random matrix theory, the
statistics of large amplitudes is strongly modified by localization effects. In
particular, we find a multifractal behavior of eigenstates in 2D conductors
which follows from the non-integer power-law scaling for the inverse
participation numbers (IPN) with the size of the system. This result is valid
for all fundamental symmetry classes (unitary, orthogonal and symplectic). The
multifractality is due to the existence of pre-localized states which are
characterized by power-law envelopes of wave functions, , . The pre-localized states in short quasi-1D wires have the
power-law tails , too, although their IPN's
indicate no fractal behavior. The distribution function of the
largest-amplitude fluctuations of wave functions in 2D and 3D conductors has
logarithmically-normal asymptotics.Comment: RevTex, 17 twocolumn pages; revised version (several misprint
corrected
New insights into the genetic etiology of Alzheimer's disease and related dementias
Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele
Education and self‐regulation of learning for gifted pupils: systemic design and development
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