Sparse and stable Markowitz portfolios

We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the sum of the absolute values of the portfolio weights. This penalty regularizes (stabilizes) the optimization problem, encourages sparse portfolios (i.e. portfolios with only few active positions), and allows to account for transaction costs. Our approach recovers as special cases the no-short-positions portfolios, but does allow for short positions in limited number. We implement this methodology on two benchmark data sets constructed by Fama and French. Using only a modest amount of training data, we construct portfolios whose out-of-sample performance, as measured by Sharpe ratio, is consistently and significantly better than that of the naive evenly-weighted portfolio which constitutes, as shown in recent literature, a very tough benchmark.Comment: Better emphasis of main result, new abstract, new examples and figures. New appendix with full details of algorithm. 17 pages, 6 figure

The repetition threshold for binary rich words

A word of length $n$ is rich if it contains $n$ nonempty palindromic factors. An infinite word is rich if all of its finite factors are rich. Baranwal and Shallit produced an infinite binary rich word with critical exponent $2+\sqrt{2}/2$ ($\approx 2.707$) and conjectured that this was the least possible critical exponent for infinite binary rich words (i.e., that the repetition threshold for binary rich words is $2+\sqrt{2}/2$). In this article, we give a structure theorem for infinite binary rich words that avoid $14/5$-powers (i.e., repetitions with exponent at least 2.8). As a consequence, we deduce that the repetition threshold for binary rich words is $2+\sqrt{2}/2$, as conjectured by Baranwal and Shallit. This resolves an open problem of Vesti for the binary alphabet; the problem remains open for larger alphabets.Comment: 16 page

A rapid procedure for the extraction of genomic DNA from intact Aspergillus spores

Genomic DNA of different species of Aspergillus was prepared from intact spores using the Nucleon MiY kit of Amersham. The method is rapid, does not involve mechanical disruption of the spores nor the use of phenol-chloroform extractions and yields DNA that is suitable for PCR amplification and Southern analysis. The method is also applicable to mycelium ground with glass beads

Geological resource management of the future: Drilling down the possibilities

Management of geological resources is based, ideally, on information on the quality and quantity of surface and subsurface litho-stratigraphical properties. Increasingly, these data become available for the offshore realm, though the integration into manageable and user-friendly applications is still at its infancy. Building on expertise from on-land data mining, we are now in the phase of creating 3D voxel models allowing for multi criteria resource volume calculations. The underlying data will be subdued to uncertainty modelling, a necessary step to produce data products with confidence limits. Anticipating on the dynamic nature of the marine environment, we aim at coupling the voxel model to environmental impact models to calculate resource depletion and regeneration, based on geological boundary conditions. In combination with anticipated impacts on fauna and flora, mining thresholds will be defined. All of the information is integrated into a decision support system for easy querying and online visualizations . The main aim is to provide long-term predictions on resource quantities to ensure future developments for the benefit of society and our future generations