Random Block Operators

We study fundamental spectral properties of random block operators that are common in the physical modelling of mesoscopic disordered systems such as dirty superconductors. Our results include ergodic properties, the location of the spectrum, existence and regularity of the integrated density of states, as well as Lifshits tails. Special attention is paid to the peculiarities arising from the block structure such as the occurrence of a robust gap in the middle of the spectrum. Without randomness in the off-diagonal blocks the density of states typically exhibits an inverse square-root singularity at the edges of the gap. In the presence of randomness we establish a Wegner estimate that is valid at all energies. It implies that the singularities are smeared out by randomness, and the density of states is bounded. We also show Lifshits tails at these band edges. Technically, one has to cope with a non-monotone dependence on the random couplings.Comment: 22 pages, 3 figure

Towards the Human Genotope

The human genotope is the convex hull of all allele frequency vectors that can be obtained from the genotypes present in the human population. In this paper we take a few initial steps towards a description of this object, which may be fundamental for future population based genetics studies. Here we use data from the HapMap Project, restricted to two ENCODE regions, to study a subpolytope of the human genotope. We study three different approaches for obtaining informative low-dimensional projections of this subpolytope. The projections are specified by projection onto few tag SNPs, principal component analysis, and archetypal analysis. We describe the application of our geometric approach to identifying structure in populations based on single nucleotide polymorphisms

Credit securitization and credit derivatives : financial instruments and the credit risk management of middle market commercial loan portfolios

Banks increasingly recognize the need to measure and manage the credit risk of their loans on a portfolio basis. We address the subportfolio "middle market". Due to their specific lending policy for this market segment it is an important task for banks to systematically identify regional and industrial credit concentrations and reduce the detected concentrations through diversification. In recent years, the development of markets for credit securitization and credit derivatives has provided new credit risk management tools. However, in the addressed market segment adverse selection and moral hazard problems are quite severe. A potential successful application of credit securitization and credit derivatives for managing credit risk of middle market commercial loan portfolios depends on the development of incentive-compatible structures which solve or at least mitigate the adverse selection and moral hazard problems. In this paper we identify a number of general requirements and describe two possible solution concepts

A two parameter ratio-product-ratio estimator using auxiliary information

We propose a two parameter ratio-product-ratio estimator for a finite population mean in a simple random sample without replacement following the methodology in Ray and Sahai (1980), Sahai and Ray (1980), Sahai and Sahai (1985) and Singh and Ruiz Espejo (2003). The bias and mean square error of our proposed estimator are obtained to the first degree of approximation. We derive conditions for the parameters under which the proposed estimator has smaller mean square error than the sample mean, ratio and product estimators. We carry out an application showing that the proposed estimator outperforms the traditional estimators using groundwater data taken from a geological site in the state of Florida.Comment: 13 pages, 2 figures, 4 table