Conformal mapping of unbounded multiply connected regions onto canonical slit regions

We present a boundary integral equation method for conformal mapping of unbounded multiply connected regions onto five types of canonical slit regions. For each canonical region, three linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unboundedmultiply connected region. The integral equations are uniquely solvable. The kernels involved in these integral equations are the modified Neumann kernels and the adjoint generalized Neumann kernels

Innovation systems in regions of Europe: A comparative perspective

The understanding of the innovation process has changed considerably in the past years. Models have shifted from linear and firm based conceptions towards interdependent and systemic approaches. Both national and regional innovation systems have been discussed in recent literature. The present paper investigates on the basis of data for eight European regions, collected in the course of a European project, to which extent companies engage into networks in their innovation process. Also, the types of partners, their respective locations (regional, national, European) as well as differences between the regions are explored. First results show, that for many firms innovation is still a rather internal process. Reliance on internal competence, lack of trust to other firms and fear of losing economic benefits to others are among the reasons. Nevertheless, for another group of companies networks are much more relevant. They draw on ideas, know-how and complementary assets from customers, suppliers, consultants, universities, funding and training institutions. With regard to the spatial reach of networks, we find considerable differences between company types and regions, however.

High Redshift Standard Candles: Predicted Cosmological Constraints

We investigate whether future measurements of high redshift standard candles (HzSCs) will be a powerful probe of dark energy, when compared to other types of planned dark energy measurements. Active galactic nuclei and gamma ray bursts have both been proposed as potential HzSC candidates. Due to their high luminosity, they can be used to probe unexplored regions in the expansion history of the universe. Information from these regions can help constrain the properties of dark energy, and in particular, whether it varies over time. We consider both linear and piecewise parameterizations of the dark energy equation of state, $w(z)$, and assess the optimal redshift distribution a high-redshift standard-candle survey could take to constrain these models. The more general the form of the dark energy equation of state $w(z)$ being tested, the more useful high-redshift standard candles become. For a linear parameterization of $w(z)$, HzSCs give only small improvements over planned supernova and baryon acoustic oscillation measurements; a wide redshift range with many low redshift points is optimal to constrain this linear model. However to constrain a general, and thus potentially more informative, form of $w(z)$, having many HzSCs can significantly improve limits on the nature of dark energy.Comment: Accepted MNRAS, 27 Pages, 15 figures, matches published versio

A Knowledge Gradient Policy for Sequencing Experiments to Identify the Structure of RNA Molecules Using a Sparse Additive Belief Model

We present a sparse knowledge gradient (SpKG) algorithm for adaptively selecting the targeted regions within a large RNA molecule to identify which regions are most amenable to interactions with other molecules. Experimentally, such regions can be inferred from fluorescence measurements obtained by binding a complementary probe with fluorescence markers to the targeted regions. We use a biophysical model which shows that the fluorescence ratio under the log scale has a sparse linear relationship with the coefficients describing the accessibility of each nucleotide, since not all sites are accessible (due to the folding of the molecule). The SpKG algorithm uniquely combines the Bayesian ranking and selection problem with the frequentist $\ell_1$ regularized regression approach Lasso. We use this algorithm to identify the sparsity pattern of the linear model as well as sequentially decide the best regions to test before experimental budget is exhausted. Besides, we also develop two other new algorithms: batch SpKG algorithm, which generates more suggestions sequentially to run parallel experiments; and batch SpKG with a procedure which we call length mutagenesis. It dynamically adds in new alternatives, in the form of types of probes, are created by inserting, deleting or mutating nucleotides within existing probes. In simulation, we demonstrate these algorithms on the Group I intron (a mid-size RNA molecule), showing that they efficiently learn the correct sparsity pattern, identify the most accessible region, and outperform several other policies

Remark on the Potential Function of the Linear Sigma Model

It is shown that the potential functions for the ordinary linear sigma model can be divided into two topographically different types depending on whether the quantity $R\equiv(m_\sigma/m_\pi)^2$ is greater than or less than nine. Since the Wigner-Weyl mode (R=1) and the Nambu-Goldstone mode ($R=\infty$ belong to different regions, we speculate that this classification may provide a generalization to the broken symmetry situation, which could be convenient for roughly characterizing different possible applications of the model. It is noted that a more complicated potential does not so much change this picture as add different new regions.Comment: 26 pages, 11 figures (gzipped