The matrix rate of return

In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This allows us for simultaneous analysis of evolution of baskets parameterized by complex variables in both continuous and discrete time models.     

An investigation into EMI-induced noise in nanometer multi-quantum well InGaN LEDs

This study investigates the low-frequency noise induced by electromagnetic radiation interference (EMI) in a nanometer multi-quantum well InGaN LED (NMQLED). Theoretical models of the noise spectra and the EMI are constructed. In general, a good agreement is identified between the experimental and theoretical results. Both sets of results reveal that the magnitude of the EMI-induced noise is related to the pulse height, the output load, the parasitic capacitance, the interference frequency and the interference amplitude. It is shown that the harmonic noise increases with an increasing interference amplitude and frequency. The techniques presented in this study provide a systematic approach for obtaining the interference noise and signal-to-noise ratio (SNR) in LEDs and similar wavelength-based semiconductor devices.     

A note on the disjunctive index of joined a-perfect graphs

In this paper we present a lower bound of the disjunctive rank of the facets describing the stable set polytope of joined a-perfect graphs. This class contains near-bipartite, t-perfect, h-perfect and complement of fuzzy interval graphs, among others. The stable set polytope of joined a-perfect graphs is described by means of full rank constraints of its node induced prime antiwebs. As a first step, we completely determine the disjunctive rank of all these constraints. Using this result we obtain a lower bound of the disjunctive index of joined a-perfect graphs and prove that this bound can be achieved. In addition, we completely determine the disjunctive index of every antiweb and observe that it does not always coincide with the disjunctive rank of its full rank constraint.     

Snarks and Flow-Critical Graphs

It is well-known that a 2-edge-connected cubic graph has a 3-edge-colouring if and only if it has a 4-flow. Snarks are usually regarded to be, in some sense, the minimal cubic graphs without a 3-edge-colouring. We defined the notion of 4-flow-critical graphs as an alternative concept towards minimal graphs. It turns out that every snark has a 4-flow-critical snark as a minor. We verify, surprisingly, that less than 5% of the snarks with up to 28 vertices are 4-flow-critical. On the other hand, there are infinitely many 4-flow-critical snarks, as every flower-snark is 4-flow-critical. These observations give some insight into a new research approach regarding Tutteʼs Flow Conjectures.     

Coloring plane graphs with independent crossings

We show that every plane graph with maximum face size four in which all faces of size four are vertex‐disjoint is cyclically 5‐colorable. This answers a question of Albertson whether graphs drawn in the plane with all crossings independent are 5‐colorable. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 184–205, 2010     

Schemata, Distributions and Graphical Models in Evolutionary Optimization

In this paper the optimization of additively decomposed discrete functions is investigated. For these functions genetic algorithms have exhibited a poor performance. First the schema theory of genetic algorithms is reformulated in probability theory terms. A schema defines the structure of a marginal distribution. Then the conceptual algorithm BEDA is introduced. BEDA uses a Boltzmann distribution to generate search points. From BEDA a new algorithm, FDA, is derived. FDA uses a factorization of the distribution. The factorization captures the structure of the given function. The factorization problem is closely connected to the theory of conditional independence graphs. For the test functions considered, the performance of FDA—in number of generations till convergence—is similar to that of a genetic algorithm for the OneMax function. This result is theoretically explained.     

A family of regular graphs of girth 5

Murty [A generalization of the Hoffman-Singleton graph, Ars Combin. 7 (1979) 191-193.] constructed a family of (p^m+2)-regular graphs of girth five and order 2p^2m, where p?5 is a prime, which includes the Hoffman-Singleton graph [A.J. Hoffman, R.R. Singleton, On Moore graphs with diameters 2 and 3, IBM J. (1960) 497-504]. This construction gives an upper bound for the least number f(k) of vertices of a k-regular graph with girth 5. In this paper, we extend the Murty construction to k-regular graphs with girth 5, for each k. In particular, we obtain new upper bounds for f(k), k?16.     

Phosphorous disulfide and its ions in the electronic ground state: a gas phase theoretical study

Ab initio molecular orbital theory and density functional theory calculations were performed on the electronic ground states of the open-shell PS₂ molecule and its singly charged ions. A comparison of the optimized molecular structures indicates as the stepwise one-electron reduction of the PS₂⁺ ion, to yield PS₂ and PS₂⁻, provokes a symmetric elongation of both PS bonds along with a bending of its linear equilibrium geometry. The ionization potential (IP), adiabatic electron affinity (EA_ad), and atomization energy (AE) of the open-shell PS₂ molecule were calculated at different levels of theory. The following values were obtained at the more realistic UMP4SDTQ/6-311+G(3df)//UHF/6-311+G(3df) level of theory: IP=8.32 eV, EA_ad=3.03 eV and AE=12.40 eV. At the same level of theory, the calculated vertical detachment energy (VDE) of the PS₂⁻ anion is 3.22 eV. The donor–acceptor complexes formed in the gas-phase upon interaction of either one or two ammonia molecules with PS₂⁺ were also investigated. The calculated gas-phase binding energies indicate that the formation of the bis-adduct is favored over that of the mono-adduct by a binding energy gain of about 20 kcal/mol.