Spectral fluctuations of tridiagonal random matrices from the beta-Hermite ensemble

A time series delta(n), the fluctuation of the nth unfolded eigenvalue was recently characterized for the classical Gaussian ensembles of NxN random matrices (GOE, GUE, GSE). It is investigated here for the beta-Hermite ensemble as a function of beta (zero or positive) by Monte Carlo simulations. The fluctuation of delta(n) and the autocorrelation function vary logarithmically with n for any beta>0 (1<<n<<N). The simple logarithmic behavior reported for the higher-order moments of delta(n) for the GOE (beta=1) and the GUE (beta=2) is valid for any positive beta and is accounted for by Gaussian distributions whose variances depend linearly on ln(n). The 1/f noise previously demonstrated for delta(n) series of the three Gaussian ensembles, is characterized by wavelet analysis both as a function of beta and of N. When beta decreases from 1 to 0, for a given and large enough N, the evolution from a 1/f noise at beta=1 to a 1/f^2 noise at beta=0 is heterogeneous with a ~1/f^2 noise at the finest scales and a ~1/f noise at the coarsest ones. The range of scales in which a ~1/f^2 noise predominates grows progressively when beta decreases. Asymptotically, a 1/f^2 noise is found for beta=0 while a 1/f noise is the rule for beta positive.Comment: 35 pages, 10 figures, corresponding author: G. Le Cae

Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach

We solve the loop equations of the $\beta$-ensemble model analogously to the solution found for the Hermitian matrices $\beta=1$. For \beta=1$, the solution was expressed using the algebraic spectral curve of equation$y^2=U(x)$. For arbitrary$\beta$, the spectral curve converts into a Schr\"odinger equation$((\hbar\partial)^2-U(x))\psi(x)=0$with$\hbar\propto (\sqrt\beta-1/\sqrt\beta)/N$. This paper is similar to the sister paper~I, in particular, all the main ingredients specific for the algebraic solution of the problem remain the same, but here we present the second approach to finding a solution of loop equations using sectorwise definition of resolvents. Being technically more involved, it allows defining consistently the B-cycle structure of the obtained quantum algebraic curve (a D-module of the form$y^2-U(x)$, where$[y,x]=\hbar$) and to construct explicitly the correlation functions and the corresponding symplectic invariants$F_h$, or the terms of the free energy, in 1/N^2$-expansion at arbitrary $\hbar$. The set of "flat" coordinates comprises the potential times $t_k$ and the occupation numbers \widetilde{\epsilon}_\alpha$. We define and investigate the properties of the A- and B-cycles, forms of 1st, 2nd and 3rd kind, and the Riemann bilinear identities. We use these identities to find explicitly the singular part of$\mathcal F_0$that depends exclusively on$\widetilde{\epsilon}_\alpha$.Comment: 58 pages, 7 figure

On Poincare and logarithmic Sobolev inequalities for a class of singular Gibbs measures

This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular pair interaction. The functional inequalities come from convexity. We prove and characterize optimality in the case of quadratic confinement via a factorization of the measure. This optimality phenomenon holds for all beta Hermite ensembles including the Gaussian unitary ensemble, a famous exactly solvable model of random matrix theory. We further explore exact solvability by reviewing the relation to Dyson-Ornstein-Uhlenbeck diffusion dynamics admitting the Hermite-Lassalle orthogonal polynomials as a complete set of eigenfunctions. We also discuss the consequence of the log-Sobolev inequality in terms of concentration of measure for Lipschitz functions such as maxima and linear statistics.Comment: Minor improvements. To appear in Geometric Aspects of Functional Analysis -- Israel Seminar (GAFA) 2017-2019", Lecture Notes in Mathematics 225

Dnmt3a regulates emotional behavior and spine plasticity in the nucleus accumbens.

Despite abundant expression of DNA methyltransferases (Dnmts) in brain, the regulation and behavioral role of DNA methylation remain poorly understood. We found that Dnmt3a expression was regulated in mouse nucleus accumbens (NAc) by chronic cocaine use and chronic social defeat stress. Moreover, NAc-specific manipulations that block DNA methylation potentiated cocaine reward and exerted antidepressant-like effects, whereas NAc-specific Dnmt3a overexpression attenuated cocaine reward and was pro-depressant. On a cellular level, we found that chronic cocaine use selectively increased thin dendritic spines on NAc neurons and that DNA methylation was both necessary and sufficient to mediate these effects. These data establish the importance of Dnmt3a in the NAc in regulating cellular and behavioral plasticity to emotional stimuli

Ab initio calculation of the 66 low lying electronic states of HeH+^+: adiabatic and diabatic representations

We present an ab initio study of the HeH$^+$ molecule. Using the quantum chemistry package MOLPRO and a large adapted basis set, we have calculated the adiabatic potential energy curves of the first 20 $^1 \Sigma^+$, 19 $^3\Sigma^+$, 12 $^1\Pi$, 9 $^3\Pi$, 4 $^1\Delta$ and 2 $^3\Delta$ electronic states of the ion in CASSCF and CI approaches. The results are compared with previous works. The radial and rotational non-adiabatic coupling matrix elements as well as the dipole moments are also calculated. The asymptotic behaviour of the potential energy curves and of the various couplings between the states is also studied. Using the radial couplings, the diabatic representation is defined and we present an example of our diabatization procedure on the $^1\Sigma^+$ states.Comment: v2. Minor text changes. 28 pages, 18 figures. accepted in J. Phys.

739 observed NEAs and new 2-4m survey statistics within the EURONEAR network

We report follow-up observations of 477 program Near-Earth Asteroids (NEAs) using nine telescopes of the EURONEAR network having apertures between 0.3 and 4.2 m. Adding these NEAs to our previous results we now count 739 program NEAs followed-up by the EURONEAR network since 2006. The targets were selected using EURONEAR planning tools focusing on high priority objects. Analyzing the resulting orbital improvements suggests astrometric follow-up is most important days to weeks after discovery, with recovery at a new opposition also valuable. Additionally we observed 40 survey fields spanning three nights covering 11 sq. degrees near opposition, using the Wide Field Camera on the 2.5m Isaac Newton Telescope (INT), resulting in 104 discovered main belt asteroids (MBAs) and another 626 unknown one-night objects. These fields, plus program NEA fields from the INT and from the wide field MOSAIC II camera on the Blanco 4m telescope, generated around 12,000 observations of 2,000 minor planets (mostly MBAs) observed in 34 square degrees. We identify Near Earth Object (NEO) candidates among the unknown (single night) objects using three selection criteria. Testing these criteria on the (known) program NEAs shows the best selection methods are our epsilon-miu model which checks solar elongation and sky motion and the MPC's NEO rating tool. Our new data show that on average 0.5 NEO candidates per square degree should be observable in a 2m-class survey (in agreement with past results), while an average of 2.7 NEO candidates per square degree should be observable in a 4m-class survey (although our Blanco statistics were affected by clouds). At opposition just over 100 MBAs (1.6 unknown to every 1 known) per square degree are detectable to R=22 in a 2m survey based on the INT data, while our two best ecliptic Blanco fields away from opposition lead to 135 MBAs (2 unknown to every 1 known) to R=23.Comment: Published in Planetary and Space Sciences (Sep 2013

Local semicircle law at the spectral edge for Gaussian β\beta-ensembles

We study the local semicircle law for Gaussian $\beta$-ensembles at the edge of the spectrum. We prove that at the almost optimal level of $n^{-2/3+\epsilon}$, the local semicircle law holds for all $\beta \geq 1$ at the edge. The proof of the main theorem relies on the calculation of the moments of the tridiagonal model of Gaussian $\beta$-ensembles up to the $p_n$-moment where $p_n = O(n^{2/3-\epsilon})$. The result is the analogous to the result of Sinai and Soshnikov for Wigner matrices, but the combinatorics involved in the calculations are different.Comment: 16 pages, 2 figure

First πK\pi K atom lifetime and πK\pi K scattering length measurements

The results of a search for hydrogen-like atoms consisting of $\pi^{\mp}K^{\pm}$ mesons are presented. Evidence for $\pi K$ atom production by 24 GeV/c protons from CERN PS interacting with a nickel target has been seen in terms of characteristic $\pi K$ pairs from their breakup in the same target ($178 \pm 49$) and from Coulomb final state interaction ($653 \pm 42$). Using these results the analysis yields a first value for the $\pi K$ atom lifetime of $\tau=(2.5_{-1.8}^{+3.0})$ fs and a first model-independent measurement of the S-wave isospin-odd $\pi K$ scattering length $\left|a_0^-\right|=\frac{1}{3}\left|a_{1/2}-a_{3/2}\right|= \left(0.11_{-0.04}^{+0.09} \right)M_{\pi}^{-1}$ ($a_I$ for isospin $I$).Comment: 14 pages, 8 figure