Regularity of multifractal spectra of conformal iterated function systems

We investigate multifractal regularity for infinite conformal iterated function systems (cIFS). That is we determine to what extent the multifractal spectrum depends continuously on the cIFS and its thermodynamic potential. For this we introduce the notion of regular convergence for families of cIFS not necessarily sharing the same index set, which guarantees the convergence of the multifractal spectra on the interior of their domain. In particular, we obtain an Exhausting Principle for infinite cIFS allowing us to carry over results for finite to infinite systems, and in this way to establish a multifractal analysis without the usual regularity conditions. Finally, we discuss the connections to the $\lambda$-topology introduced by Roy and Urbas{\'n}ki.Comment: 16 pages; 3 figure

Bounding the Heat Trace of a Calabi-Yau Manifold

The SCHOK bound states that the number of marginal deformations of certain two-dimensional conformal field theories is bounded linearly from above by the number of relevant operators. In conformal field theories defined via sigma models into Calabi-Yau manifolds, relevant operators can be estimated, in the point-particle approximation, by the low-lying spectrum of the scalar Laplacian on the manifold. In the strict large volume limit, the standard asymptotic expansion of Weyl and Minakshisundaram-Pleijel diverges with the higher-order curvature invariants. We propose that it would be sufficient to find an a priori uniform bound on the trace of the heat kernel for large but finite volume. As a first step in this direction, we then study the heat trace asymptotics, as well as the actual spectrum of the scalar Laplacian, in the vicinity of a conifold singularity. The eigenfunctions can be written in terms of confluent Heun functions, the analysis of which gives evidence that regions of large curvature will not prevent the existence of a bound of this type. This is also in line with general mathematical expectations about spectral continuity for manifolds with conical singularities. A sharper version of our results could, in combination with the SCHOK bound, provide a basis for a global restriction on the dimension of the moduli space of Calabi-Yau manifolds.Comment: 32 pages, 3 figure

Thermodynamic formalism for transient dynamics on the real line

We develop a new thermodynamic formalism to investigate the transient behaviour of maps on the real line which are skew-periodic $\mathbb{Z}$-extensions of expanding interval maps. Our main focus lies in the dimensional analysis of the recurrent and transient sets as well as in determining the whole dimension spectrum with respect to $\alpha$-escaping sets. Our results provide a one-dimensional model for the phenomenon of a dimension gap occurring for limit sets of Kleinian groups. In particular, we show that a dimension gap occurs if and only if we have non-zero drift and we are able to precisely quantify its width as an application of our new formalism.Comment: 23 pages, 5 figure

A Minimal Model of Burst-Noise Induced Bistability

We investigate the influence of intrinsic noise on stable states of a one-dimensional dynamical system that shows in its deterministic version a saddle-node bifurcation between monostable and bistable behaviour. The system is a modified version of the Schl\"ogl model, which is a chemical reaction system with only one type of molecule. The strength of the intrinsic noise is varied without changing the deterministic description by introducing bursts in the autocatalytic production step. We study the transitions between monostable and bistable behavior in this system by evaluating the number of maxima of the stationary probability distribution. We find that changing the size of bursts can destroy and even induce saddle-node bifurcations. This means that a bursty production of molecules can qualitatively change the dynamics of a chemical reaction system even when the deterministic description remains unchanged.Comment: 7 pages, 9 figure

On adaptive posterior concentration rates

We investigate the problem of deriving posterior concentration rates under different loss functions in nonparametric Bayes. We first provide a lower bound on posterior coverages of shrinking neighbourhoods that relates the metric or loss under which the shrinking neighbourhood is considered, and an intrinsic pre-metric linked to frequentist separation rates. In the Gaussian white noise model, we construct feasible priors based on a spike and slab procedure reminiscent of wavelet thresholding that achieve adaptive rates of contraction under $L^2$ or $L^{\infty}$ metrics when the underlying parameter belongs to a collection of H\"{o}lder balls and that moreover achieve our lower bound. We analyse the consequences in terms of asymptotic behaviour of posterior credible balls as well as frequentist minimax adaptive estimation. Our results are appended with an upper bound for the contraction rate under an arbitrary loss in a generic regular experiment. The upper bound is attained for certain sieve priors and enables to extend our results to density estimation.Comment: Published at http://dx.doi.org/10.1214/15-AOS1341 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Estimating the effects of oil price shockson the Kazakh economy

This paper explores the role of oil for the Kazakh economy. In order to assess thedegree of volatility the oil price features, it, firstly, discusses the literature on oil price behaviour. Secondly, it analyzes the effect of oil price declines on key macroeconomicvariables such as real GDP, inflation and real exchange rates using vectorautoregressive (VAR) models. In this respect, the paper deviates from a large number of papers on oil price effects as it considers a transition rather than a developed economy and an oil exporting rather than an oil importing country. The key findings to emerge from this paper are, first, that the price of oil is influenced by a large number of factors, which results in a considerable degree of volatility. Secondly, all variables considered in theVAR model exhibit a strong negative significant reaction on oil price declines, and, thirdly, a standard linear VAR model is appropriate for capturing the Kazakh oil-macro relationship.Oil price, VAR-Models, oil exporting economy.

Climate change

Knowledge of factors that trigger human response to climate change is crucial for effective climate change policy communication. Climate change has been claimed to have low salience as a risk issue because it cannot be directly experienced. Still, personal factors such as strength of belief in local effects of climate change have been shown to correlate strongly with responses to climate change and there is a growing literature on the hypothesis that personal experience of climate change (and/or its effects) explains responses to climate change. Here we provide, using survey data from 845 private forest owners operating in a wide range of bio-climatic as well as economic-social-political structures in a latitudinal gradient across Europe, the first evidence that the personal strength of belief and perception of local effects of climate change, highly significantly explain human responses to climate change. A logistic regression model was fitted to the two variables, estimating expected probabilities ranging from 0.07 (SD +/-0.01) to 0.81 (SD +/-0.03) for self-reported adaptive measures taken. Adding socio-demographic variables improved the fit, estimating expected probabilities ranging from 0.022 (SD +/-0.008) to 0.91 (SD +/-0.02). We conclude that to explain and predict adaptation to climate change, the combination of personal experience and belief must be considered