Positive harmonic functions on comb-like domains

This paper investigates positive harmonic functions on a domain which contains an infinite cylinder, and whose boundary is contained in the union of parallel hyperplanes. (In the plane its boundary consists of two sets of vertical semi-infinite lines.) It characterizes, in terms of the spacing between the hyperplanes, those domains for which there exist minimal harmonic functions with a certain exponential growth.Comment: 18 page

Model based Monte Carlo pricing of energy and temperature quanto options

Weather derivatives have become very popular tools in weather risk management in recent years. One of the elements supporting their diffusion has been the increase in volatility observed on many energy markets. Among the several available contracts, Quanto options are now becoming very popular for a simple reason: they take into account the strong correlation between energy consumption and certain weather conditions, so enabling price and weather risk to be controlled at the same time. These products are more efficient and, in many cases, significantly cheaper than simpler plain vanilla options. Unfortunately, the specific features of energy and weather time series do not enable the use of analytical formulae based on the Black-Scholes pricing approach, nor other more advanced continuous time methods that extend the Black-Scholes approach, unless under strong and unrealistic assumptions. In this study, we propose a Monte Carlo pricing framework based on a bivariate time series model. Our approach takes into account the average and variance interdependence between temperature and energy price series. Furthermore, our approach includes other relevant empirical features, such as periodic patterns in average, variance, and correlations. The model structure enables a more appropriate pricing of Quanto options compared to traditional methods.weather derivatives; Quanto options pricing; derivative pricing; model simulation; forecast

Fitting Prediction Rule Ensembles with R Package pre

Prediction rule ensembles (PREs) are sparse collections of rules, offering highly interpretable regression and classification models. This paper presents the R package pre, which derives PREs through the methodology of Friedman and Popescu (2008). The implementation and functionality of package pre is described and illustrated through application on a dataset on the prediction of depression. Furthermore, accuracy and sparsity of PREs is compared with that of single trees, random forest and lasso regression in four benchmark datasets. Results indicate that pre derives ensembles with predictive accuracy comparable to that of random forests, while using a smaller number of variables for prediction

Symmetries and physically realizable ensembles for open quantum systems

A $D$-dimensional Markovian open quantum system will undergo stochastic evolution which preserves pure states, if one monitors without loss of information the bath to which it is coupled. If a finite ensemble of pure states satisfies a particular set of constraint equations then it is possible to perform the monitoring in such a way that the (discontinuous) trajectory of the conditioned system state is, at all long times, restricted to those pure states. Finding these physically realizable ensembles (PREs) is typically very difficult, even numerically, when the system dimension is larger than 2. In this paper, we develop symmetry-based techniques that potentially greatly reduce the difficulty of finding a subset of all possible PREs. The two dynamical symmetries considered are an invariant subspace and a Wigner symmetry. An analysis of previously known PREs using the developed techniques provides us with new insights and lays the foundation for future studies of higher dimensional systems.Comment: 30 pages, 4 figures, comments welcome. Published versio

Posterior Reversible Encephalopathy Syndrome and Azathioprine

Posterior reversible encephalopathy syndrome (PRES) is a rare syndrome that presents with neurological manifestations, often associated with arterial hypertension. Magnetic resonance imaging (MRI) shows bilateral white matter oedema in the posterior vascular territories. Immunosuppression, (pre) eclampsia and autoimmune diseases can be implicated. A 27-year-old woman, with mixed connective tissue disease under azathioprine, was admitted in the emergency room in status epilepticus and with severe hypertension. The MRI showed bilateral oedema in a pattern compatible with PRES. There was clinical improvement after azathioprine suspension. PRES is typically reversible with prompt recognition of the syndrome and its trigger. The association with azathioprine is rare. LEARNING POINTS: Posterior reversible encephalopathy syndrome should be considered in patients with sudden onset of headache, altered consciousness and seizures.Recognition of this entity and identification of the trigger are essential for reversal of the clinical picture.Autoimmune diseases and some immunosuppressive drugs have been identified as causative, but reports of an association with azathioprine are very rare.info:eu-repo/semantics/publishedVersio

Understanding social exclusion

This CASEbrief summarises 'Understanding Social Exclusion' edited by John Hills, Julian Le Grand and David Piachaud, published by Oxford University Pres