Spectral extrema and Lifshitz tails for non monotonous alloy type models

In the present note, we determine the ground state energy and study the existence of Lifshitz tails near this energy for some non monotonous alloy type models. Here, non monotonous means that the single site potential coming into the alloy random potential changes sign. In particular, the random operator is not a monotonous function of the random variables

Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension

In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These Schr\"odinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.Comment: 9 page

A roof plate-dependent enhancer controls the expression of Homeodomain only protein in the developing cerebral cortex

AbstractThe smallest known homeodomain protein, Homeodomain only protein (Hop), was identified and described here as a temporally and spatially restricted gene in the neurogenic regions of the developing murine CNS including the cerebral cortex. Furthermore, an evolutionarily conserved 418 base pair upstream cis-regulatory DNA sequence was found to confine the Hop expression to the CNS of transgenic mice, but not to the heart which is the second major Hop expressing organ Chen, F., Kook, H., Milewski, R., Gitler, A.D., Lu, M.M., Li, J., Nazarian, R., Schnepp, R., Jen, K., Biben, C., Runke, G., Mackay, J.P., Novotny, J., Schwartz, R.J., Harvey, R.P., Mullins, M.C., Epstein, J.A., 2002. Hop is an unusual homeobox gene that modulates cardiac development. Cell 110, 713–723; Shin, C.H., Liu, Z.P., Passier, R., Zhang, C.L., Wang, D.Z., Harris, T.M., Yamagishi, H., Richardson, J.A., Childs, G., Olson, E.N., 2002. Modulation of cardiac growth and development by HOP, an unusual homeodomain protein. Cell 110, 725–735. The forebrain enhancer activity was successfully reproduced in vitro utilizing a combination of the electroporation and the organotypic brain culture method. Using this approach, the minimal requirement for the forebrain-specific enhancer sequence was delineated down to 200 base pairs. We further demonstrate that the Hop enhancer activity is inducible ectopically in a transgenic tissue by wild-type roof plate transplantation in vitro. Thus Hop is regulated in the forebrain by a so far unidentified paracrine signaling factor from the roof plate. Furthermore, the identified enhancer sequence provides an important tool for the targeted expression of transgenes in the medial cortex and the cortical hem

Inverse Scattering for Gratings and Wave Guides

We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes" given for all frequencies uniquely determine these coefficients. The gratings may contain conductors as well as dielectrics and the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page

A matrix-valued point interactions model

We study a matrix-valued Schr\"odinger operator with random point interactions. We prove the absence of absolutely continuous spectrum for this operator by proving that away from a discrete set its Lyapunov exponents do not vanish. For this we use a criterion by Gol'dsheid and Margulis and we prove the Zariski denseness, in the symplectic group, of the group generated by the transfer matrices. Then we prove estimates on the transfer matrices which lead to the H\"older continuity of the Lyapunov exponents. After proving the existence of the integrated density of states of the operator, we also prove its H\"older continuity by proving a Thouless formula which links the integrated density of states to the sum of the positive Lyapunov exponents

The repulsion between localization centers in the Anderson model

In this note we show that, a simple combination of deep results in the theory of random Schr\"odinger operators yields a quantitative estimate of the fact that the localization centers become far apart, as corresponding energies are close together

Gamma-widths, lifetimes and fluctuations in the nuclear quasi-continuum

Statistical $\gamma$-decay from highly excited states is determined by the nuclear level density (NLD) and the $\gamma$-ray strength function ($\gamma$SF). These average quantities have been measured for several nuclei using the Oslo method. For the first time, we exploit the NLD and $\gamma$SF to evaluate the $\gamma$-width in the energy region below the neutron binding energy, often called the quasi-continuum region. The lifetimes of states in the quasi-continuum are important benchmarks for a theoretical description of nuclear structure and dynamics at high temperature. The lifetimes may also have impact on reaction rates for the rapid neutron-capture process, now demonstrated to take place in neutron star mergers.Comment: CGS16, Shanghai 2017, Proceedings, 5 pages, 3 figure

Anodal transcranial direct current stimulation over S1 differentially modulates proprioceptive accuracy in young and old adults

Background: Proprioception is a prerequisite for successful motor control but declines throughout the lifespan. Brain stimulation techniques such as anodal transcranial direct current stimulation (a-tDCS) are capable of enhancing sensorimotor performance across different tasks and age groups. Despite such growing evidence for a restorative potential of tDCS, its impact on proprioceptive accuracy has not been studied in detail yet. Objective: This study investigated online effects of a-tDCS over S1 on proprioceptive accuracy in young (YA) and old healthy adults (OA). Methods: The effect of 15 min of a-tDCS vs. sham on proprioceptive accuracy was assessed in a cross-over, double blind experiment in both age groups. Performance changes were tested using an arm position matching task in a robotic environment. Electrical field (EF) strengths in the target area S1 and control areas were assessed based on individualized simulations. Results: a-tDCS elicited differential changes in proprioceptive accuracy and EF strengths in the two groups: while YA showed a slight improvement, OA exhibited a decrease in performance during a-tDCS. Stronger EF were induced in target S1 and control areas in the YA group. However, no relationship between EF strength and performance change was found. Conclusion: a-tDCS over S1 elicits opposing effects on proprioceptive accuracy as a function of age, a result that is important for future studies investigating the restorative potential of a-tDCS in healthy aging and in the rehabilitation of neurological diseases that occur at advanced age. Modeling approaches could help elucidate the relationship between tDCS protocols, brain structure and performance modulation