Small deviations for beta ensembles

We establish various small deviation inequalities for the extremal (soft edge) eigenvalues in the beta-Hermite and beta-Laguerre ensembles. In both settings, upper bounds on the variance of the largest eigenvalue of the anticipated order follow immediately

Metallicity as a criterion to select H2 bearing Damped Lyman-alpha systems

We characterize the importance of metallicity on the presence of molecular hydrogen in damped Lyman-alpha (DLA) systems. We construct a representative sample of 18 DLA/sub-DLA systems with log N(HI)>19.5 at high redshift (zabs>1.8) with metallicities relative to solar [X/H]>-1.3(with[X/H]= logN(X)/N(H)-log(X/H)solar and X either Zn, S or Si). We gather data covering the expected wavelength range of redshifted H2 absorption lines on all systems in the sample from either the literature (10 DLAs), the UVES-archive or new VLT-UVES observations for four of them. The sample is large enough to discuss for the first time the importance of metallicity as a criterion for the presence of molecular hydrogen in the neutral phase at high-z. From the new observations, we report two new detections of molecular hydrogen in the systems at zabs=2.431 toward Q2343+125 and zabs=2.426 toward Q2348-011. We compare the H2 detection fraction in the high-metallicity sample with the detection fraction in the overall sample from Ledoux et al. (2003). We show that the fraction of DLA systems with logf=log 2N(H2)/(2N(H2)+N(HI))>-4 is as large as 50% for [X/H]>-0.7 when it is only about 5% for [X/H]<-1.3 and about 15% in the overall sample (with -2.5<[X/H]<-0.3). This demonstrates that the presence of molecular hydrogen at high redshift is strongly correlated with metallicity.Comment: 4 pages, 3 Postscript figures. Accepted in Astronomy and Astrophysics Lette

Higher-Order Memory Schema and Conscious Experience

In the interesting and thought-provoking article Grazziano and colleagues argue for their Attention Schema Theory (AST) of consciousness. They present AST as a unification of Global Workspace Theory (GWT), Illusionism, and the Higher-Order Thought (HOT) theory. We argue it is a mistake to equate 'subjective experience,' ad related terms, with dualism. They simply denote experience. Also, as presented, AST does not accurately capture the essence of HOT for two reasons. HOT is presented as a version of strong illusionism, which it isn't, and HOT requires that one be aware of one's mental life, and postulates that his consists in a re-representation of what is occurring at at the lower-order levels. However, the authors deny that AST involves re-representing visual stimuli. We close by proposing an alternative unification: GWT and AST provide crucial accounts of how lower-order states are assembled and maintained, but higher-order theory provides the account of subjective experience

Additional material on bounds of ℓ2\ell^2-spectral gap for discrete Markov chains with band transition matrices

We analyse the $\ell^2(\pi)$-convergence rate of irreducible and aperiodic Markov chains with $N$-band transition probability matrix $P$ and with invariant distribution $\pi$. This analysis is heavily based on: first the study of the essential spectral radius $r\_{ess}(P\_{|\ell^2(\pi)})$ of $P\_{|\ell^2(\pi)}$ derived from Hennion's quasi-compactness criteria; second the connection between the spectral gap property (SG$\_2$) of $P$ on $\ell^2(\pi)$ and the $V$-geometric ergodicity of $P$. Specifically, (SG$\_2$) is shown to hold under the condition \alpha\_0 := \sum\_{{m}=-N}^N \limsup\_{i\rightarrow +\infty} \sqrt{P(i,i+{m})\, P^*(i+{m},i)}\ \textless{}\, 1. Moreover $r\_{ess}(P\_{|\ell^2(\pi)}) \leq \alpha\_0$. Simple conditions on asymptotic properties of $P$ and of its invariant probability distribution $\pi$ to ensure that \alpha\_0\textless{}1 are given. In particular this allows us to obtain estimates of the $\ell^2(\pi)$-geometric convergence rate of random walks with bounded increments. The specific case of reversible $P$ is also addressed. Numerical bounds on the convergence rate can be provided via a truncation procedure. This is illustrated on the Metropolis-Hastings algorithm

A Higher-Order Theory of Emotional Consciousness

Emotional states of consciousness, or what are typically called emotional feelings, are traditionally viewed as being innately programed in subcortical areas of the brain, and are often treated as different from cognitive states of consciousness, such as those related to the perception of external stimuli. We argue that conscious experiences, regardless of their content, arise from one system in the brain. On this view, what differs in emotional and non-emotional states is the kind of inputs that are processed by a general cortical network of cognition, a network essential for conscious experiences. Although subcortical circuits are not directly responsible for conscious feelings, they provide non-conscious inputs that coalesce with other kinds of neural signals in the cognitive assembly of conscious emotional experiences. In building the case for this proposal, we defend a modified version of what is known as the higher-order theory of consciousness

Automatic computation of quantum-mechanical bound states and wavefunctions

We discuss the automatic solution of the multichannel Schr\"odinger equation. The proposed approach is based on the use of a CP method for which the step size is not restricted by the oscillations in the solution. Moreover, this CP method turns out to form a natural scheme for the integration of the Riccati differential equation which arises when introducing the (inverse) logarithmic derivative. A new Pr\"ufer type mechanism which derives all the required information from the propagation of the inverse of the log-derivative, is introduced. It improves and refines the eigenvalue shooting process and implies that the user may specify the required eigenvalue by its index

On CP, LP and other piecewise perturbation methods for the numerical solution of the Schrödinger equation

The piecewise perturbation methods (PPM) have proven to be very efficient for the numerical solution of the linear time-independent Schrödinger equation. The underlying idea is to replace the potential function piecewisely by simpler approximations and then to solve the approximating problem. The accuracy is improved by adding some perturbation corrections. Two types of approximating potentials were considered in the literature, that is piecewise constant and piecewise linear functions, giving rise to the so-called CP methods (CPM) and LP methods (LPM). Piecewise polynomials of higher degree have not been used since the approximating problem is not easy to integrate analytically. As suggested by Ixaru (Comput Phys Commun 177:897–907, 2007), this problem can be circumvented using another perturbative approach to construct an expression for the solution of the approximating problem. In this paper, we show that there is, however, no need to consider PPM based on higher-order polynomials, since these methods are equivalent to the CPM. Also, LPM is equivalent to CPM, although it was sometimes suggested in the literature that an LP method is more suited for problems with strongly varying potentials. We advocate that CP schemes can (and should) be used in all cases, since it forms the most straightforward way of devising PPM and there is no advantage in considering other piecewise polynomial perturbation methods