Hyperorthogonal well-folded Hilbert curves

R-trees can be used to store and query sets of point data in two or more dimensions. An easy way to construct and maintain R-trees for two-dimensional points, due to Kamel and Faloutsos, is to keep the points in the order in which they appear along the Hilbert curve. The R-tree will then store bounding boxes of points along contiguous sections of the curve, and the efficiency of the R-tree depends on the size of the bounding boxes---smaller is better. Since there are many different ways to generalize the Hilbert curve to higher dimensions, this raises the question which generalization results in the smallest bounding boxes. Familiar methods, such as the one by Butz, can result in curve sections whose bounding boxes are a factor $\Omega(2^{d/2})$ larger than the volume traversed by that section of the curve. Most of the volume bounded by such bounding boxes would not contain any data points. In this paper we present a new way of generalizing Hilbert's curve to higher dimensions, which results in much tighter bounding boxes: they have at most 4 times the volume of the part of the curve covered, independent of the number of dimensions. Moreover, we prove that a factor 4 is asymptotically optimal.Comment: Manuscript submitted to Journal of Computational Geometry. An abstract appeared in the 31st Int Symp on Computational Geometry (SoCG 2015), LIPIcs 34:812-82

The CantiClever: a dedicated probe for magnetic force microscopy

We present a new cantilever for magnetic-force microscopy (MFM), the CantiClever, which is not derived from atomic-force microscopy (AFM) probes but optimized for MFM. Our design integrates the cantilever and the magnetic tip in a single manufacturing process with the use of silicon micromachining techniques, which allows for batch fabrication of the probes. This manufacturing process enables precise control on all dimensions of the magnetic tip, resulting in a very thin magnetic element with a very high aspect ratio. Using. the CantiClever, magnetic features down to 30 nm could be observed in a CAMST reference sample

On the variation of hedging decisions in daily currency risk management

Internationally operating firms naturally face the decision whether or not to hedge the currency risk implied by foreign investments. In a recent paper, Bos, Mahieu and van Dijk evaluate the returns from optimal and alternative currency hedging strategies, for a series of 7 models, using Bayesian inference and decision analysis. The models differ in the way time-varying means, variances or the unconditional error distributions are incorporated. In this extension, we compare the hedging decisions and financial returns and utilities as they result from the modelling assumptions and the attitudes towards risk

Daily exchange rate behaviour and hedging of currency risk

Exchange rates typically exhibit time-varying patterns in both means and variances. The histograms of such series indicate heavy tails. In this paper we construct models which enable a decision-maker to analyze the implications of such time series patterns for currency risk management. Our approach is Bayesian where extensive use is made of Markov chain Monte Carlo methods. The effects of several model characteristics (unit roots, GARCH, stochastic volatility, heavy tailed disturbance densities) are investigated in relation to the hedging decision strategies. Consequently, we can make a distinction between statistical relevance of model specifications, and the economic consequences from a risk management point of view. The empirical results suggest that econometric modelling of heavy tails and time-varying means and variances pays off compared to a efficient markets model. The different ways to measure persistence and changing volatilities appear to strongly influence the hedging decision the investor faces

Daily Exchange Rate Behaviour and Hedging of Currency Risk

Exchange rates typically exhibit time-varying patterns in both means and variances. The histograms of such series indicate heavy tails. In this paper we construct models which enable a decision-maker to analyze the implications of such time series patterns for currency risk management. Our approach is Bayesian where extensive use is made of Markov chain Monte Carlo methods. The effects of several model characteristics (unit roots, GARCH, stochastic volatility, heavy tailed disturbance densities) are investigated in relation to the hedging decision strategies. Consequently, we can make a distinction between statistical relevance of model specifications, and the economic consequences from a risk management point of view. The empirical results suggest that econometric modelling of heavy tails and time-varying means and variances pays off compared to a efficient markets model. The different ways to measure persistence and changing volatilities appear to strongly influence the hedging decision the investor faces.

Explaining Adaptive Radial-Based Direction Sampling

In this short paper we summarize the computational steps of Adaptive Radial-Based Direction Sampling (ARDS), which can be used for Bayesian analysis of ill behaved target densities. We consider one simulation experiment in order to illustrate the good performance of ARDS relative to the independence chain MH algorithm and importance sampling

Adaptive polar sampling, a class of flexibel and robust Monte Carlo integration methods

Adaptive Polar Sampling (APS) algorithms are proposed for Bayesian analysis of models with nonelliptical, possibly, multimodal posterior distributions. A location-scale transformation and a transformation to polar coordinates are used. After the transformation to polar coordinates, a Metropolis-Hastings method or, alternatively, an importance sampling method is applied to sample directions and, conditionally on these, distances are generated by inverting the cumulative distribution function. A sequential procedure is applied to update the initial location and scaling matrix in order to sample directions in an efficient way. Tested on a set of canonical mixture models that feature multimodality, strong correlation, and skewness, the APS algorithms compare favourably with the standard Metropolis-Hastings and importance samplers in terms of flexibility and robustness. APS is applied to several econometric and statistical examples. The empirical results for a regression model with scale contamination, an ARMA-GARCH-Student t model with near cancellation of roots and heavy tails, a mixture model for economic growth, and a nonlinear threshold model for industrial production growth confirm the practical flexibility and robustness of APS