Positive approximations of the inverse of fractional powers of SPD M-matrices

This study is motivated by the recent development in the fractional calculus and its applications. During last few years, several different techniques are proposed to localize the nonlocal fractional diffusion operator. They are based on transformation of the original problem to a local elliptic or pseudoparabolic problem, or to an integral representation of the solution, thus increasing the dimension of the computational domain. More recently, an alternative approach aimed at reducing the computational complexity was developed. The linear algebraic system $\cal A^\alpha \bf u=\bf f$, $0< \alpha <1$ is considered, where $\cal A$ is a properly normalized (scalded) symmetric and positive definite matrix obtained from finite element or finite difference approximation of second order elliptic problems in $\Omega\subset\mathbb{R}^d$, $d=1,2,3$. The method is based on best uniform rational approximations (BURA) of the function $t^{\beta-\alpha}$ for $0 < t \le 1$ and natural $\beta$. The maximum principles are among the major qualitative properties of linear elliptic operators/PDEs. In many studies and applications, it is important that such properties are preserved by the selected numerical solution method. In this paper we present and analyze the properties of positive approximations of $\cal A^{-\alpha}$ obtained by the BURA technique. Sufficient conditions for positiveness are proven, complemented by sharp error estimates. The theoretical results are supported by representative numerical tests

Direct Observation of the Dynamics of Latex Particles Confined inside Thinning Water-Air Films

The dynamics of micrometer-size polystyrene latex particles confined in thinning foam films was investigated by microscopic interferometric observation. The behavior of the entrapped particles depends on the mobility of the film surfaces, the particle concentration, hydrophobicity, and rate of film formation. When the films were stabilized by sodium dodecyl sulfate, no entrapment of particles between the surfaces was possible. When protein was used as a stabilizer, a limited number of particles were caught inside the film area due to the decreased mobility of the interfaces. In this case, extraordinary long-ranged (>100 Ìm) capillary attraction leads to two-dimensional (2D) particle aggregation. A major change occurs when the microspheres are partially hydrophobized by the presence of cationic surfactant. After the foam films are opened and closed a few times, a layer of particles simultaneously adsorbed to the two interfaces is formed, which sterically inhibits any further film opening and thinning. The particles within this layer show an excellent 2D hexagonal ordering. The experimental data are relevant to the dynamics of defects in coating films, Pickering emulsions, and particle assembly into 2D arrays

Atomic and electronic structure of twin growth defects in magnetite

We report the existence of a stable twin defect in Fe3O4 thin films. By using aberration corrected scanning transmission electron microscopy and spectroscopy the atomic structure of the twin boundary has been determined. The boundary is confined to the (111) growth plane and it is non-stoichiometric due to a missing Fe octahedral plane. By first principles calculations we show that the local atomic structural configuration of the twin boundary does not change the nature of the superexchange interactions between the two Fe sublattices across the twin grain boundary. Besides decreasing the half-metallic band gap at the boundary the altered atomic stacking at the boundary does not change the overall ferromagnetic (FM) coupling between the grains

Atomic and electronic structure of twin growth defects in magnetite

We report the existence of a stable twin defect in Fe3O4 thin films. By using aberration corrected scanning transmission electron microscopy and spectroscopy the atomic structure of the twin boundary has been determined. The boundary is confined to the (111) growth plane and it is non-stoichiometric due to a missing Fe octahedral plane. By first principles calculations we show that the local atomic structural configuration of the twin boundary does not change the nature of the superexchange interactions between the two Fe sublattices across the twin grain boundary. Besides decreasing the half-metallic band gap at the boundary the altered atomic stacking at the boundary does not change the overall ferromagnetic (FM) coupling between the grains

Short-Term Environmental Enrichment Rescues Adult Neurogenesis and Memory Deficits in APPSw,Ind Transgenic Mice

Epidemiological studies indicate that intellectual activity prevents or delays the onset of Alzheimer's disease (AD). Similarly, cognitive stimulation using environmental enrichment (EE), which increases adult neurogenesis and functional integration of newborn neurons into neural circuits of the hippocampus, protects against memory decline in transgenic mouse models of AD, but the mechanisms involved are poorly understood. To study the therapeutic benefits of cognitive stimulation in AD we examined the effects of EE in hippocampal neurogenesis and memory in a transgenic mouse model of AD expressing the human mutant β-amyloid (Aβ) precursor protein (APPSw,Ind). By using molecular markers of new generated neurons (bromodeoxiuridine, NeuN and doublecortin), we found reduced neurogenesis and decreased dendritic length and projections of doublecortin-expressing cells of the dentate gyrus in young APPSw,Ind transgenic mice. Moreover, we detected a lower number of mature neurons (NeuN positive) in the granular cell layer and a reduced volume of the dentate gyrus that could be due to a sustained decrease in the incorporation of new generated neurons. We found that short-term EE for 7 weeks efficiently ameliorates early hippocampal-dependent spatial learning and memory deficits in APPSw,Ind transgenic mice. The cognitive benefits of enrichment in APPSw,Ind transgenic mice were associated with increased number, dendritic length and projections to the CA3 region of the most mature adult newborn neurons. By contrast, Aβ levels and the total number of neurons in the dentate gyrus were unchanged by EE in APPSw,Ind mice. These results suggest that promoting the survival and maturation of adult generated newborn neurons in the hippocampus may contribute to cognitive benefits in AD mouse models

Magnetic profile of proximity-coupled (Dy,Bi)2Te3/(Cr,Sb)2Te3 topological insulator heterostructures

Magnetic topological insulators (TIs) are an ideal playground for the study of novel quantum phenomena building on time-reversal symmetry-broken topological surface states. By combining different magnetic TIs in a heterostructure, their magnetic and electronic properties can be precisely tuned. Recently, we have combined high-moment Dy:Bi2Te3 with high transition temperature Cr:Sb2Te3 in a superlattice, and we found, using x-ray magnetic circular dichroism (XMCD), that long-range magnetic order can be introduced in the Dy:Bi2Te3 layers. Accompanying first-principles calculations indicated that the origin of the long-range magnetic order is a strong antiferromagnetic coupling between Dy and Cr magnetic moments at the interface extending over several layers. However, based on XMCD alone, which is either averaging over the entire thin-film stack or is surface-sensitive, this coupling scenario could not be fully confirmed. Here we use polarized neutron reflectometry, which is ideally suited for the detailed study of superlattices, to retrieve the magnetization in a layer- and interface-resolved way. We find that the magnetization is, in contrast to similar recent studies, homogeneous throughout the individual layers, with no apparent interfacial effects. This finding demonstrates that heterostructure engineering is a powerful way of controlling the magnetic properties of entire layers, with the effects of coupling reaching beyond the interface region

Postsynaptic dysfunction is associated with spatial and object recognition memory loss in a natural model of Alzheimer's disease

Alzheimer’s disease (AD) is an age-related neurodegenerative disorder associated with progressive memory loss, severe dementia, and hallmark neuropathological markers, such as deposition of amyloid-β (Aβ) peptides in senile plaques and accumulation of hyperphosphorylated tau proteins in neurofibrillary tangles. Recent evidence obtained from transgenic mouse models suggests that soluble, nonfibrillar Aβ oligomers may induce synaptic failure early in AD. Despite their undoubted value, these transgenic models rely on genetic manipulations that represent the inherited and familial, but not the most abundant, sporadic form of AD. A nontransgenic animal model that still develops hallmarks of AD would be an important step toward understanding how sporadic AD is initiated. Here we show that starting between 12 and 36 mo of age, the rodent Octodon degus naturally develops neuropathological signs of AD, such as accumulation of Aβ oligomers and phosphorylated tau proteins. Moreover, age-related changes in Aβ oligomers and tau phosphorylation levels are correlated with decreases in spatial and object recognition memory, postsynaptic function, and synaptic plasticity. These findings validate O. degus as a suitable natural model for studying how sporadic AD may be initiated

Unconventional Transcriptional Response to Environmental Enrichment in a Mouse Model of Rett Syndrome

Background: Rett syndrome (RTT) is an X-linked postnatal neurodevelopmental disorder caused by mutations in the gene encoding methyl-CpG binding protein 2 (MeCP2) and one of the leading causes of mental retardation in females. RTT is characterized by psychomotor retardation, purposeless hand movements, autistic-like behavior and abnormal gait. We studied the effects of environmental enrichment (EE) on the phenotypic manifestations of a RTT mouse model that lacks MeCP2 (Mecp2 2/y). Principal Findings: We found that EE delayed and attenuated some neurological alterations presented by Mecp2 2/y mice and prevented the development of motor discoordination and anxiety-related abnormalities. To define the molecular correlate of this beneficial effect of EE, we analyzed the expression of several synaptic marker genes whose expression is increased by EE in several mouse models. Conclusions/Significance: We found that EE induced downregulation of several synaptic markers, suggesting that th