Limit distributions for the maxima of stationary Gaussian processes

AbstractLet {Xn} be a stationary Gaussian sequence with E{X0} = 0, {X20} = 1 and E{X0Xn} = rn n Let cn = (2ln n)built12, bn = cn− 12c-1n ln(4π ln n), and set Mn = max0 ⩽k⩽nXk. A classical result for independent normal random variables is that P[cn(Mn−bn)⩽x]→exp[-e-x] as n → ∞ for all x. Berman has shown that (1) applies as well to dependent sequences provided rnlnn = o(1). Suppose now that {rn} is a convex correlation sequence satisfying rn = o(1), (rnlnn)-1 is monotone for large n and o(1). Then P[rn-12(Mn − (1−rn)12bn)⩽x] → Ф(x) for all x, where Ф is the normal distribution function. While the normal can thus be viewed as a second natural limit distribution for {Mn}, there are others. In particular, the limit distribution is given below when rn is (sufficiently close to) γ/ln n. We further exhibit a collection of limit distributions which can arise when rn decays to zero in a nonsmooth manner. Continuous parameter Gaussian processes are also considered. A modified version of (1) has been given by Pickands for some continuous processes which possess sufficient asymptotic independence properties. Under a weaker form of asymptotic independence, we obtain a version of (2)

Photonic Anomalous Quantum Hall Effect

We experimentally realize a photonic analogue of the anomalous quantum Hall insulator using a two-dimensional (2D) array of coupled ring resonators. Similar to the Haldane model, our 2D array is translation invariant, has zero net gauge flux threading the lattice, and exploits next-nearest neighbor couplings to achieve a topologically non-trivial bandgap. Using direct imaging and on-chip transmission measurements, we show that the bandgap hosts topologically robust edge states. We demonstrate a topological phase transition to a conventional insulator by frequency detuning the ring resonators and thereby breaking the inversion symmetry of the lattice. Furthermore, the clockwise or the counter-clockwise circulation of photons in the ring resonators constitutes a pseudospin degree of freedom. We show that the two pseudospins acquire opposite hopping phases and their respective edge states propagate in opposite directions. These results are promising for the development of robust reconfigurable integrated nanophotonic devices for applications in classical and quantum information processing

Magnetic order in CaFe1-xCoxAsF (x = 0, 0.06, 0.12) superconductor compounds

A Neutron Powder Diffraction (NPD) experiment has been performed to investigate the structural phase transition and magnetic order in CaFe1-xCoxAsF superconductor compounds (x = 0, 0.06, 0.12). The parent compound CaFeAsF undergoes a tetragonal to orthorhombic phase transition at 134(3) K, while the magnetic order in form of a spin-density wave (SDW) sets in at 114(3) K. The antiferromagnetic structure of the parent compound has been determined with a unique propagation vector k = (1,0,1) and the Fe saturation moment of 0.49(5)uB aligned along the long a-axis. With increasing Co doping, the long range antiferromagnetic order has been observed to coexist with superconductivity in the orthorhombic phase of the underdoped CaFe0.94Co0.06AsF with a reduced Fe moment (0.15(5)uB). Magnetic order is completely suppressed in optimally doped CaFe0.88Co0.12AsF. We argue that the coexistence of SDW and superconductivity might be related to mesoscopic phase separation.Comment: 4pages, 4figure

Magnetisation distribution in the tetragonal phase of BaFe2As2

We have determined the spatial distribution of the magnetisation induced by a field of 9 T in the tetragonal phase of BaFe2As2 using polarised neutron diffraction. Magnetic structure factors derived from the polarisation dependence of the intensities of Bragg reflections were used to make a maximum entropy reconstruction of the distribution projected on the 110 plane. The reconstruction shows clearly that the magnetisation is confined to the region around the iron atoms and that there is no significant magnetisation associated with either the As or Ba atoms. The distribution of magnetisation around the Fe atom is significantly non-spherical with a shape which is extended in the directions in the projection. These results show that the electrons which give rise to the paramagnetic susceptibility are confined to the Fe atoms their distribution suggests that they occupy 3d t_2g type orbitals with about 60% in those of xy symmetry

FHL2 regulates hematopoietic stem cell functions under stress conditions.

FHL2, a member of the four and one half LIM domain protein family, is a critical transcriptional modulator. Here, we identify FHL2 as a critical regulator of hematopoietic stem cells (HSCs) that is essential for maintaining HSC self-renewal under regenerative stress. We find that Fhl2 loss has limited effects on hematopoiesis under homeostatic conditions. In contrast, Fhl2-null chimeric mice reconstituted with Fhl2-null bone marrow cells developed abnormal hematopoiesis with significantly reduced numbers of HSCs, hematopoietic progenitor cells (HPCs), red blood cells and platelets as well as hemoglobin levels. In addition, HSCs displayed a significantly reduced self-renewal capacity and were skewed toward myeloid lineage differentiation. We find that Fhl2 loss reduces both HSC quiescence and survival in response to regenerative stress, probably as a consequence of Fhl2-loss-mediated downregulation of cyclin-dependent kinase-inhibitors, including p21(Cip) and p27(Kip1). Interestingly, FHL2 is regulated under the control of a tissue-specific promoter in hematopoietic cells and it is downregulated by DNA hypermethylation in the leukemia cell line and primary leukemia cells. Furthermore, we find that downregulation of FHL2 frequently occurs in myelodysplastic syndrome and acute myeloid leukemia patients, raising a possibility that FHL2 downregulation has a role in the pathogenesis of myeloid malignancies

Ab initio lattice dynamics simulations and inelastic neutron scattering spectra for studying phonons in BaFe2As2: Effect of structural phase transition, structural relaxation and magnetic ordering

We have performed extensive ab initio calculations to investigate phonon dynamics and their possible role in superconductivity in BaFe2As2 and related systems. The calculations are compared to inelastic neutron scattering data that offer improved resolution over published data [Mittal et al., PRB 78 104514 (2008)], in particular at low frequencies. Effects of structural phase transition and full/partial structural relaxation, with and without magnetic ordering, on the calculated vibrational density of states are reported. Phonons are best reproduced using either the relaxed magnetic structures or the experimental cell. Several phonon branches are affected by the subtle structural changes associated with the transition from the tetragonal to the orthorhombic phase. Effects of phonon induced distortions on the electronic and spin structure have been investigated. It is found that for some vibrational modes, there is a significant change of the electronic distribution and spin populations around the Fermi level. A peak at 20 meV in the experimental data falls into the pseudo-gap region of the calculation. This was also the case reported in our recent work combined with an empirical parametric calculation [Mittal et al., PRB 78 104514 (2008)]. The combined evidence for the coupling of electronic and spin degrees of freedom with phonons is relevant to the current interest in superconductivity in BaFe2As2 and related systems

Neutron diffraction study on phase transition and thermal expansion of SrFeAsF

The magnetic ordering and crystal structure of iron pnictide SrFeAsF was investigated by using neutron powder diffraction method. With decreasing temperature, the tetragonal to orthorhombic phase transition is found at 180 K, while the paramagnetic to antiferromagnetic phase transition set in at 133 K. Similar to the parent compound of other iron pnictide system, the striped Fe magnetism is confirmed in antiferromagnetic phase and the Fe moment of 0.58(6) uB aligned along long a axis. The thermal expansion of orthorhombic phase of SrFeAsF is also investigated. Based on the Grueneisen approximation and Debye approximation for internal energy, the volume of SrFeAsF can be well fitted with Debye temperature of 347(5) K. The experimental atomic displacement parameters for different crystallographic sites in SrFeAsF are analyzed with Debye model. The results suggested that the expansion of FeAs layers plays an important role in determining the thermal expansion coefficient.Comment: 4 pages, 3 figure