Local regularity for parabolic nonlocal operators

Weak solutions to parabolic integro-differential operators of order $\alpha \in (\alpha_0, 2)$ are studied. Local a priori estimates of H\"older norms and a weak Harnack inequality are proved. These results are robust with respect to $\alpha \nearrow 2$. In this sense, the presentation is an extension of Moser's result in 1971.Comment: 31 pages, 3 figure

Quantitative Determination of Temperature in the Approach to Magnetic Order of Ultracold Fermions in an Optical Lattice

We perform a quantitative simulation of the repulsive Fermi-Hubbard model using an ultracold gas trapped in an optical lattice. The entropy of the system is determined by comparing accurate measurements of the equilibrium double occupancy with theoretical calculations over a wide range of parameters. We demonstrate the applicability of both high-temperature series and dynamical mean-field theory to obtain quantitative agreement with the experimental data. The reliability of the entropy determination is confirmed by a comprehensive analysis of all systematic errors. In the center of the Mott insulating cloud we obtain an entropy per atom as low as 0.77k(B) which is about twice as large as the entropy at the Neel transition. The corresponding temperature depends on the atom number and for small fillings reaches values on the order of the tunneling energy

The effects of peripheral and central high insulin on brain insulin signaling and amyloid-β in young and old APP/PS1 mice

Hyperinsulinemia is a risk factor for late-onset Alzheimer's disease (AD). In vitro experiments describe potential connections between insulin, insulin signaling, and amyloid-β (Aβ), but in vivo experiments are needed to validate these relationships under physiological conditions. First, we performed hyperinsulinemic-euglycemic clamps with concurrent hippocampal microdialysis in young, awake, behaving APP(swe)/PS1(dE9) transgenic mice. Both a postprandial and supraphysiological insulin clamp significantly increased interstitial fluid (ISF) and plasma Aβ compared with controls. We could detect no increase in brain, ISF, or CSF insulin or brain insulin signaling in response to peripheral hyperinsulinemia, despite detecting increased signaling in the muscle. Next, we delivered insulin directly into the hippocampus of young APP/PS1 mice via reverse microdialysis. Brain tissue insulin and insulin signaling was dose-dependently increased, but ISF Aβ was unchanged by central insulin administration. Finally, to determine whether peripheral and central high insulin has differential effects in the presence of significant amyloid pathology, we repeated these experiments in older APP/PS1 mice with significant amyloid plaque burden. Postprandial insulin clamps increased ISF and plasma Aβ, whereas direct delivery of insulin to the hippocampus significantly increased tissue insulin and insulin signaling, with no effect on Aβ in old mice. These results suggest that the brain is still responsive to insulin in the presence of amyloid pathology but increased insulin signaling does not acutely modulate Aβ in vivo before or after the onset of amyloid pathology. Peripheral hyperinsulinemia modestly increases ISF and plasma Aβ in young and old mice, independent of neuronal insulin signaling. SIGNIFICANCE STATEMENT The transportation of insulin from blood to brain is a saturable process relevant to understanding the link between hyperinsulinemia and AD. In vitro experiments have found direct connections between high insulin and extracellular Aβ, but these mechanisms presume that peripheral high insulin elevates brain insulin significantly. We found that physiological hyperinsulinemia in awake, behaving mice does not increase CNS insulin to an appreciable level yet modestly increases extracellular Aβ. We also found that the brain of aged APP/PS1 mice was not insulin resistant, contrary to the current state of the literature. These results further elucidate the relationship between insulin, the brain, and AD and its conflicting roles as both a risk factor and potential treatment

Evolutionary biology for the 21st century

New theoretical and conceptual frameworks are required for evolutionary biology to capitalize on the wealth of data now becoming available from the study of genomes, phenotypes, and organisms - including humans - in their natural environments.Molecular and Cellular BiologyOrganismic and Evolutionary Biolog

Color Doppler imaging of the superior ophthalmic vein in patients with Graves' orbitopathy before and after treatment of congestive disease

OBJECTIVE: To compare superior ophthalmic vein blood flow parameters measured with color Doppler imaging in patients with congestive Graves' orbitopathy before and after treatment and in normal controls. METHODS: Twenty-two orbits from 12 patients with Graves' orbitopathy in the congestive stage and 32 orbits from 16 normal controls underwent color Doppler imaging studies. Color Doppler imaging was repeated after treatment in the group of patients with Graves' orbitopathy, which included orbital decompression in 16 orbits and corticosteroids in six orbits. The findings for each group were compared. RESULTS: In the group of orbits with congestive disease, superior ophthalmic vein flow was detected in 17 orbits (anteroposteriorally in 13 and in the opposite direction in four) and was undetectable in five. After treatment, superior ophthalmic vein flow was detected and anteroposterior in 21 and undetected in one orbit. In normals, superior ophthalmic vein flow was detected anteroposterior in 29 orbits and undetectable in three orbits, indicating a significant difference between groups. There was also a significant difference between controls and congestive Graves' orbits and between congestive orbits before and after treatment, but not between controls and patients after treatment. A comparison of superior ophthalmic vein flow parameters revealed a significant difference between the groups. The superior ophthalmic vein flow was significantly reduced in the congestive stage compared with the flow parameters following treatment and in the untreated controls. CONCLUSIONS: Superior ophthalmic vein flow was significantly reduced in the orbits affected with congestive Graves' orbitopathy and returned to normal following treatment. Congestion appears to be a contributing pathogenic factor in the active inflammatory stage of Graves' orbitopathy.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Magnetic ordering of Mn sublattice, dense Kondo lattice behavior of Ce in (RPd3)8Mn (R = La, Ce)

We have synthesized two new interstitial compounds (RPd3)8Mn (R = La and Ce). The Mn ions present in "dilute" concentration of just 3 molar percent form a sublattice with an unusually large Mn-Mn near neighbor distance of ~ 85 nm. While the existence of (RPd3)8M (where M is a p-block element) is already documented in the literature, the present work reports for the first time the formation of this phase with M being a 3d element. In (LaPd3)8Mn, the Mn sub-lattice orders antiferromagnetically as inferred from the peaks in low-field magnetization at 48 K and 23 K. The latter peak progressively shifts towards lower temperatures in increasing magnetic field and disappears below 1.8 K in a field of ~ 8 kOe. On the other hand in (CePd3)8Mn the Mn sublattice undergoes a ferromagnetic transition around 35 K. The Ce ions form a dense Kondo-lattice and are in a paramagnetic state at least down to 1.5 K. A strongly correlated electronic ground state arising from Kondo effect is inferred from the large extrapolated value of C/T = 275 mJ/Ce-mol K^2 at T = 0 K. In contrast, the interstitial alloys RPd3Mnx (x = 0.03 and 0.06), also synthesized for the first time, have a spin glass ground state due to the random distribution of the Mn ions over the available "1b" sites in the parent RPd3 crystal lattice.Comment: 18 figures and 20 pages of text documen

Surface Geometry of C60 on Ag(111)

The geometry of adsorbed C60 influences its collective properties. We report the first dynamical low-energy electron diffraction study to determine the geometry of a C60 monolayer, Ag(111)-(23×23)30°-C60, and related density functional theory calculations. The stable monolayer has C60 molecules in vacancies that result from the displacement of surface atoms. C60 bonds with hexagons down, with their mirror planes parallel to that of the substrate. The results indicate that vacancy structures are the rule rather than the exception for C60 monolayers on close-packed metal surfaces. © 2009 The American Physical Society

Dispersion, damping, and intensity of spin excitations in the single-layer (Bi,Pb)2_{2}(Sr,La)2_{2}CuO6+δ_{6+\delta} cuprate superconductor family

Using Cu-$L_3$ edge resonant inelastic x-ray scattering (RIXS) we measured the dispersion and damping of spin excitations (magnons and paramagnons) in the high-$T_\mathrm{c}$ superconductor (Bi,Pb)$_{2}$(Sr,La)$_{2}$CuO$_{6+\delta}$ (Bi2201), for a large doping range across the phase diagram ($0.03\lesssim p\lesssim0.21$). Selected measurements with full polarization analysis unambiguously demonstrate the spin-flip character of these excitations, even in the overdoped sample. We find that the undamped frequencies increase slightly with doping for all accessible momenta, while the damping grows rapidly, faster in the (0,0)$\rightarrow$(0.5,0.5) nodal direction than in the (0,0)$\rightarrow$(0.5,0) antinodal direction. We compare the experimental results to numerically exact determinant quantum Monte Carlo (DQMC) calculations that provide the spin dynamical structure factor $S(\textbf{Q},\omega)$ of the three-band Hubbard model. The theory reproduces well the momentum and doping dependence of the dispersions and spectral weights of magnetic excitations. These results provide compelling evidence that paramagnons, although increasingly damped, persist across the superconducting dome of the cuprate phase diagram; this implies that long range antiferromagnetic correlations are quickly washed away, while short range magnetic interactions are little affected by doping.Comment: 11 pages, 9 figure