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

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

A uniform Berry--Esseen theorem on MM-estimators for geometrically ergodic Markov chains

Let $\{X_n\}_{n\ge0}$ be a $V$-geometrically ergodic Markov chain. Given some real-valued functional $F$, define $M_n(\alpha):=n^{-1}\sum_{k=1}^nF(\alpha,X_{k-1},X_k)$, $\alpha\in\mathcal{A}\subset \mathbb {R}$. Consider an $M$ estimator $\hat{\alpha}_n$, that is, a measurable function of the observations satisfying $M_n(\hat{\alpha}_n)\leq \min_{\alpha\in\mathcal{A}}M_n(\alpha)+c_n$ with $\{c_n\}_{n\geq1}$ some sequence of real numbers going to zero. Under some standard regularity and moment assumptions, close to those of the i.i.d. case, the estimator $\hat{\alpha}_n$ satisfies a Berry--Esseen theorem uniformly with respect to the underlying probability distribution of the Markov chain.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ347 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

The VLT-UVES survey for molecular hydrogen in high-redshift damped Lyman-alpha systems

We have searched for molecular hydrogen in damped Lyman-alpha (DLA) and sub-DLA systems at z>1.8 using UVES at the VLT. Out of the 33 systems in our sample, 8 have firm and 2 have tentative detections of associated H2 absorption lines. Considering that 3 detections were already known from past searches, H2 is detected in 13 to 20 percent of the newly-surveyed systems. We report new detections of molecular hydrogen at z=2.087 and 2.595 toward, respectively, Q 1444+014 and Q 0405-443, and also reanalyse the system at z=3.025 toward Q 0347-383. We find that there is a correlation between metallicity and depletion factor in both our sample and also the global population of DLA systems (60 systems in total). The DLA and sub-DLA systems where H2 is detected are usually amongst those having the highest metallicities and the largest depletion factors. Moreover, the individual components where H2 is detected have depletion factors systematically larger than other components in the profiles. In two different systems, one of the H2-detected components even has [Zn/Fe]>=1.4. These are the largest depletion factors ever seen in DLA systems. All this clearly demonstrates the presence of dust in a large fraction of the DLA systems. The mean H2 molecular fraction is generally small in DLA systems and similar to what is observed in the Magellanic Clouds. From 58 to 75 percent of the DLA systems have log f<-6. This can be explained if the formation rate of H2 onto dust grains is reduced in those systems, probably because the gas is warm (T>1000 K) and/or the ionizing flux is enhanced relative to what is observed in our Galaxy.Comment: 21 pages, 16 figures, MNRA

CREOLE: a Universal Language for Creating, Requesting, Updating and Deleting Resources

In the context of Service-Oriented Computing, applications can be developed following the REST (Representation State Transfer) architectural style. This style corresponds to a resource-oriented model, where resources are manipulated via CRUD (Create, Request, Update, Delete) interfaces. The diversity of CRUD languages due to the absence of a standard leads to composition problems related to adaptation, integration and coordination of services. To overcome these problems, we propose a pivot architecture built around a universal language to manipulate resources, called CREOLE, a CRUD Language for Resource Edition. In this architecture, scripts written in existing CRUD languages, like SQL, are compiled into Creole and then executed over different CRUD interfaces. After stating the requirements for a universal language for manipulating resources, we formally describe the language and informally motivate its definition with respect to the requirements. We then concretely show how the architecture solves adaptation, integration and coordination problems in the case of photo management in Flickr and Picasa, two well-known service-oriented applications. Finally, we propose a roadmap for future work.Comment: In Proceedings FOCLASA 2010, arXiv:1007.499

Regular perturbation of V -geometrically ergodic Markov chains

In this paper, new conditions for the stability of V-geometrically ergodic Markov chains are introduced. The results are based on an extension of the standard perturbation theory formulated by Keller and Liverani. The continuity and higher regularity properties are investigated. As an illustration, an asymptotic expansion of the invariant probability measure for an autoregressive model with i.i.d. noises (with a non-standard probability density function) is obtained

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

Understanding the Higher-Order Approach to Consciousness

Critics have often misunderstood the higher-order theory (HOT) of consciousness. Here we clarify its position on several issues, and distinguish it from other views such as the global The higher-order theory (HOT) of consciousness has often been misunderstood by critics. Here we clarify its position on several issues, and distinguish it from other views such as the global workspace theory (GWT) and early sensory models (e.g. first-order local recurrency theories). For example, HOT has been criticized for over-intellectualizing consciousness. We show that while higher-order states are cognitively assembled, the requirements are actually considerably less than often presumed. In this sense HOT may be viewed as an intermediate position between GWT and early sensory views. Also, we clarify that most proponents of HOT do not stipulate consciousness as equivalent to metacognition or confidence. Further, compared to other existing theories, HOT can arguably account better for complex everyday experiences, such as of emotions and episodic memories. This makes HOT particularly useful as a framework for conceptualizing pathological mental states