A family of Schr\"odinger operators whose spectrum is an interval

By approximation, I show that the spectrum of the Schr\"odinger operator with potential $V(n) = f(n\rho \pmod 1)$ for f continuous and $\rho > 0$, $\rho \notin \N$ is an interval.Comment: Comm. Math. Phys. (to appear

A quantitative central limit theorem for linear statistics of random matrix eigenvalues

It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate of convergence of order almost $1/n$ can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein's method of exchangeable pairs.Comment: Title modified; main result stated under slightly weaker conditions; accepted for publication in the Journal of Theoretical Probabilit

An enrichment of KK-theory over the category of symmetric spectra

In [6] Higson showed that the formal properties of the Kasparov KK-theory groups are best understood if one regards KK(A,B) for separable C*-algebras A,B as the morphism set of a category KK. In category language the composition and exterior KKproduct give KK the structure of a symmetric monoidal category which is enriched over abelian groups. We show that the enrichment of KK can be lifted to an enrichment over the category of symmetric spectra

Reciprocal Inhibition of Adiponectin and Innate Lung Immune Responses to Chitin and Aspergillus fumigatus

Chitin is a structural biopolymer found in numerous organisms, including pathogenic fungi, and recognized as an immune-stimulating pathogen associated molecular pattern by pattern recognition molecules of the host immune system. However, programming and regulation of lung innate immunity to chitin inhalation in the context of inhalation of fungal pathogens such as Aspergillus fumigatus is complex and our understanding incomplete. Here we report that the systemic metabolism-regulating cytokine adiponectin is decreased in the lungs and serum of mice after chitin inhalation, with a concomitant decrease in surface expression of the adiponectin receptor AdipoR1 on lung leukocytes. Constitutive lung expression of acidic mammalian chitinase resulted in decreased inflammatory cytokine gene expression and neutrophil recruitment, but did not significantly affect lung adiponectin transcription. Exogenous recombinant adiponectin specifically dampened airway chitin-mediated eosinophil recruitment, while adiponectin deficiency resulted in increased airway eosinophils. The presence of adiponectin also resulted in decreased CCL11-mediated migration of bone marrow-derived eosinophils. In contrast to purified chitin, aspiration of viable conidia from the high chitin-expressing A. fumigatus isolate Af5517 resulted in increased neutrophil recruitment and inflammatory cytokine gene expression in adiponectin-deficient mice, while no significant changes were observed in response to the isolate Af293. Our results identify a novel role for the adiponectin pathway in inhibition of lung inflammatory responses to chitin and A. fumigatus inhalation

Dissociable feedback valence effects on frontal midline theta during reward gain versus threat avoidance learning

While frontal midline theta (FMθ) has been associated with threat processing, with cognitive control in the context of anxiety, and with reinforcement learning, most reinforcement learning studies on FMθ have used reward rather than threat-related stimuli as reinforcer. Accordingly, the role of FMθ in threat-related reinforcement learning is largely unknown. Here, n = 23 human participants underwent one reward-, and one punishment-, based reversal learning task, which differed only with regard to the kind of reinforcers that feedback was tied to (i.e., monetary gain vs. loud noise burst, respectively). In addition to single-trial EEG, we assessed single-trial feedback expectations based on both a reinforcement learning computational model and trial-by-trial subjective feedback expectation ratings. While participants' performance and feedback expectations were comparable between the reward and punishment tasks, FMθ was more reliably amplified to negative vs. positive feedback in the reward vs. punishment task. Regressions with feedback valence, computationally derived, and self-reported expectations as predictors and FMθ as criterion further revealed that trial-by-trial variations in FMθ specifically relate to reward-related feedback-valence and not to threat-related feedback or to violated expectations/prediction errors. These findings suggest that FMθ as measured in reinforcement learning tasks may be less sensitive to the processing of events with direct relevance for fear and anxiety