A cutting plane algorithm for a clustering problem

In this paper we consider a clustering problem that arises in qualitative data analysis. This problem can be transformed to a combinatorial optimization problem, the clique partitioning problem. We have studied the latter problem from a polyhedral point of view and determined large classes of facets of the associated polytope. These theoretical results are utilized in this paper. We describe a cutting plane algorithm that is based on the simplex method and uses exact and heuristic separation routines for some of the classes of facets mentioned before. We discuss some details of the implementation of our code and present our computational results. We mention applications from, e.g., zoology, economics, and the political sciences.     

Diffusion-limited annihilation in inhomogeneous environments

We study diffusion-limited (on-site) pair annihilation A + A → 0 and (on-site) fusion A + A → A which we show to be equivalent for arbitrary space-dependent diffusion and reaction rates. For one-dimensional lattices with nearest neighbour hopping we find that in the limit of infinite reaction rate the time-dependent n-point density correlations for many-particle initial states are determined by the correlation functions of a dual diffusion-limited annihilation process with at most 2n particles initially. Furthermore, by reformulating general properties of annihilating random walks in one dimension in terms of fermionic anticommutation relations we derive an exact representation for these correlation functions in terms of conditional probabilities for a single particle performing a random walk with dual hopping rates. This allows for the exact and explicit calculation of a wide range of universal and non-universal types of behaviour for the decay of the density and density correlations.     

Theory of Non-Equilibrium Stationary States as a Theory of Resonances

We study a small quantum system (e.g., a simplified model for an atom or molecule) interacting with two bosonic or fermionic reservoirs (say, photon or phonon fields). We show that the combined system has a family of stationary states parametrized by two numbers, T ₁ and T ₂ (‘reservoir temperatures’). If T ₁ ≠ T ₂, then these states are non-equilibrium stationary states (NESS). In the latter case we show that they have nonvanishing heat fluxes and positive entropy production and are dynamically asymptotically stable. The latter means that the evolution with an initial condition, normal with respect to any state where the reservoirs are in equilibria at temperatures T ₁ and T ₂, converges to the corresponding NESS. Our results are valid for the temperatures satisfying the bound min (T ₁,T ₂) > g ^{2 + α}, where g is the coupling constant and 0 < α < 1 is a power related to the infra-red behaviour of the coupling functions. Submitted: March 20, 2006. Revised: March 19, 2007. Accepted: May 11, 2007. Marco Merkli: Partly supported by an NSERC PDF, the Institute of Theoretical Physics of ETH Zürich, Switzerland, the Departments of Mathematics of McGill University and the University of Toronto, Canada. Matthias Mück: Supported by DAAD under grant HSP III. Israel Michael Sigal: Supported by NSERC under grant NA7901.     

Numerical treatment of an asset price model with non-stochastic uncertainty

In contrast to stochastic differential equation models used for the calculation of the term structure of interest rates, we develop an approach based on linear dynamical systems under non-stochastic uncertainty with perturbations. The uncertainty is described in terms of known feasible sets of varying parameters. Observations are used in order to estimate these parameters by minimizing the maximum of the absolute value of measurement errors, which leads to a linear or nonlinear semi-infinite programming problem. A regularized logarithmic barrier method for solving (ill-posed) convex semi-infinite programming problems is suggested. In this method a multi-step proximal regularization is coupled with an adaptive discretization strategy in the framework of an interior point approach. A special deleting rule permits one to use only a part of the constraints of the discretized problems. Convergence of the method and its stability with respect to data perturbations in the cone of convexC ¹-functions are studied. On the basis of the solutions of the semi-infinite programming problems a technical trading system for future contracts of the German DAX is suggested and developed. Supported by the Stiftung Rheinland/Pfalz für Innovation, No. 8312-386261/307.     

Quasiparticle and Cooper pair tenneling in small capacitance Josephson junctions

The tunneling of single electrons in small capacitance tunnel junctions is influenced by charging effects and by the fluctuations of the elecromagnetic environment. We study the effect of an external circuit with arbitrary impedance on the tunneling of quasiparticles and Cooper pairs in voltage driven Josephson junctions. We present results at finite temperatures and also consider an acdriven system.     

Paramagnetic defects in BaTiO3 and their role in light-induced charge transport — Optical studies

On the basis of a previous identification of paramagnetic defects in nominally undoped as grown BaTiO₃ single crystals, we have investigated the changes of the concentrations of these centers and their optical absorptions under illumination with light of varying wavelengths. The most pronounced charge transfers occur by hole ionization of Fe⁴⁺ and — to a lesser extent — of Cr⁵⁺ and Cr⁴⁺. At low temperatures the created holes are trapped in the form of O^–-ions next to Al³⁺ or unknown acceptor defects. Corresponding Fe⁴⁺ and O^– absorptions have been identified.     

The experimental structure of199Au and the interacting boson-fermion model

Gamma rays of¹⁹⁹Au obtained after double neutron capture in¹⁹⁷Au were measured at the ILL high flux reactor. A level scheme up to 1770 keV excitation energy is established. The result is compared with IBFM and Boson-Fermion-Symmetry calculations.