Spectral methods for growth curve clustering

Central European Journal of Operations Research - The growth curve clustering problem is analyzed and its connection with the spectral relaxation method is described. For a given set of growth...     

Semi-stable extensions over 1-dimensional bases

Given a family of Calabi-Yau varieties over the punctured disc or over the field of Laurent series, we show that, after a finite base change, the family can be extended across the origin while keeping the canonical class trivial. More generally, we prove similar extension results for families whose log-canonical class is semi-ample. We use these to show that the Berkovich and essential skeleta agree for smooth varieties over C((t)) with semi-ample canonical class.     

First steps in tropical intersection theory

We establish first parts of a tropical intersection theory. Namely, we define cycles, Cartier divisors and intersection products between these two (without passing to rational equivalence) and discuss push-forward and pull-back. We do this first for fans in \mathbbRⁿ{\mathbb{R}^{n}} and then for “abstract” cycles that are fans locally. With regard to applications in enumerative geometry, we finally have a look at rational equivalence and intersection products of cycles and cycle classes in \mathbbRⁿ{\mathbb{R}^{n}} .     

The arithmetic-geometric scaling spectrum for continued fractions

To compare continued fraction digits with the denominators of the corresponding approximants we introduce the arithmetic-geometric scaling. We will completely determine its multifractal spectrum by means of a number-theoretical free-energy function and show that the Hausdorff dimension of sets consisting of irrationals with the same scaling exponent coincides with the Legendre transform of this free-energy function. Furthermore, we identify the asymptotic of the local behaviour of the spectrum at the right boundary point and discuss a connection to the set of irrationals with continued-fraction digits exceeding a given number which tends to infinity.     

Co9S8 as a catalyst for electroreduction of O2: quantum chemistry predictions

The slab band quantum computational approach in the Vienna ab initio simulation package (VASP) is used to calculate the adsorption energies of reactants, reaction intermediates, and products in O2 reduction and in water oxidation in acid on three crystallographic surfaces of pentlandite structure Co9S8. Reversible potentials for the reaction steps involving electron and proton transfer are determined by using the energies in a linear Gibbs free energy relationship. On the basis of these results, we find that the partially OH-covered (202) surface is active toward O2 reduction and should have overpotential behavior similar to that observed for platinum electrodes. One structure in the predicted four-electron reduction mechanism is novel: S2- provides an adsorption site for O following O-O bond scission, which, unlike the case of platinum electrodes, takes place prior to the first reduction step.     

Parity-breaking bifurcation and global oscillation in patterns of ion channels

Stationary spatiotemporal pattern formation emerging from the electric activity of biological membranes is widespread in cells and tissues. A known key instability comes from the self-aggregation of membrane channels. In a two-dimensional geometry, we show that the primary pattern undergoes four secondary instabilities: Eckhaus-like, period-halving, drift instabilities, and a global oscillation. The stability diagram is determined. The parity-breaking (drift) bifurcation of channel density is characterized analytically and numerically.     

Synthesis and properties of a functionalized heterobimetallic Re(I)–Gd(III) complex as a potential dual-contrast agent for molecular imaging

In the design of dual-imaging probes, the first functionalized and neutral heterobimetallic Re(I)–Gd(III) complex, highly soluble in aqueous solutions, has been prepared. This system exhibits interesting photophysical properties (λ_em = 578 nm, ? = 1.4%) for optical imaging and substantial higher relaxivity (r₁ = 6.6 mM⁻¹ s⁻¹ at 0.47 T and 37 °C) than the clinically used MRI contrast agents. Moreover, this system incorporates an aromatic ester functionality suitable for bioconjugation.     

Mutually disjoint designs and new 5‐designs derived from groups and codes

The article gives constructions of disjoint 5‐designs obtained from permutation groups and extremal self‐dual codes. Several new simple 5‐designs are found with parameters that were left open in the table of 5‐designs given in (G. B. Khosrovshahi and R. Laue, t‐Designs with t⩾3, in “Handbook of Combinatorial Designs”, 2nd edn, C. J. Colbourn and J. H. Dinitz (Editors), Chapman & Hall/CRC, Boca Raton, FL, 2007, pp. 79–101), namely, 5−(v, k, λ) designs with (v, k, λ)=(18, 8, 2m) (m=6, 9), (19, 9, 7m) (m=6, 9), (24, 9, 6m) (m=3, 4, 5), (25, 9, 30), (25, 10, 24m) (m=4, 5), (26, 10, 126), (30, 12, 440), (32, 6, 3m) (m=2, 3, 4), (33, 7, 84), and (36, 12, 45n) for 2⩽n⩽17. These results imply that a simple 5−(v, k, λ) design with (v, k)=(24, 9), (25, 9), (26, 10), (32, 6), or (33, 7) exists for all admissible values of λ. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 305–317, 2010     

A Three-Dimensional Model for Fiber Lay-Down Processes

We present an improved stochastic model concerning the lay-down of fibers on a conveyor belt in the production of nonwovens. The model is based on stochastic differential equations describing the resulting position of the fiber on the belt having regard to its motion in the deposition region under influence of turbulent air flow. Our aim is to generalize an existing model to 3D. By introducing a parameter we have an alternative to consider both isotropic and anisotropic orientation of the fibers generating the nonwoven. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-central limit theorems for random selections

Selection from finite sets is a basic procedure of statistics and the partial sum behavior of selected elements is completely known under the “uniform asymptotic negligibility” condition of central limit theory. The purpose of the present paper is to determine the asymptotic behavior of partial sums when the central limit theorem fails. As an application, we describe the limiting properties of permutation and bootstrap statistics in case of infinite variance.