Non-commutative extensions of the MacMahon Master Theorem

We present several non-commutative extensions of the MacMahon Master Theorem, further extending the results of Cartier-Foata and Garoufalidis-Lê-Zeilberger. The proofs are combinatorial and new even in the classical cases. We also give applications to the β-extension and Krattenthaler-Schlosser's q-analogue.     

Oxide and nitride protective layers on stainless steel studied by AES,WDS and XPS

Protective surface layers on AISI 321 stainless steel were prepared by thermal treatments at two different temperatures in air and two controlled atmospheres. Different oxide and/or nitride layers were formed. Surface morphology of the layers was investigated by scanning electron microscopy (SEM). Auger electron spectroscopy (AES) depth profiling of the samples was performed. Since depth profiling suggested layer thicknesses of the order of hundreds of nanometres, an attempt was made to obtain some fast, averaged information about the layer compositions using wavelength dispersive spectroscopy (WDS) at two different beam energies to obtain probing depths best suited to the layer thickness. X‐ray photoelectron spectroscopy (XPS) profiling of one layer was also performed to obtain information about the chemical states of the elements inside the layer. The analysed samples showed considerable differences with respect to their surface morphology, oxide/nitride layer thicknesses, compositions and layer–metal interface thickness. Copyright © 2007 John Wiley & Sons, Ltd.     

Correlations between the activities of a gamma-ray emitter calculated from different peaks in the spectrum

A model for calculating correlations between the activities of the same gamma-ray emitter calculated from different peaks in its spectrum is presented. The correlation coefficients can be expressed by the relative uncertainties of the input quantities. The use of this model in the calculation of the mean activity prevents the calculation of an excessively small uncertainty of the mean, since averaging of correlated uncertainty components is avoided.     

Stochastic resonance on Newman-Watts networks of Hodgkin-Huxley neurons with local periodic driving

We study the phenomenon of stochastic resonance on Newman-Watts small-world networks consisting of biophysically realistic Hodgkin-Huxley neurons with a tunable intensity of intrinsic noise via voltage-gated ion channels embedded in neuronal membranes. Importantly thereby, the subthreshold periodic driving is introduced to a single neuron of the network, thus acting as a pacemaker trying to impose its rhythm on the whole ensemble. We show that there exists an optimal intensity of intrinsic ion channel noise by which the outreach of the pacemaker extends optimally across the whole network. This stochastic resonance phenomenon can be further amplified via fine-tuning of the small-world network structure, and depends significantly also on the coupling strength among neurons and the driving frequency of the pacemaker. In particular, we demonstrate that the noise-induced transmission of weak localized rhythmic activity peaks when the pacemaker frequency matches the intrinsic frequency of subthreshold oscillations. The implications of our findings for weak signal detection and information propagation across neural networks are discussed.     

Separation of magnetic particles in channel flows by BEM

In-line separation of suspensions can become difficult in case of particles with comparable values of densities. For flows in micro devices in such cases gravitational settling is inefficient, and other separation techniques must be applied. In case of magneto active particles, the action of Kelvin magnetic force in a non-uniform magnetic field could be used in order to achieve a higher degree of particles separation. The contribution therefore deals with Euler-Lagrangian formulation of dilute two-phase flows. The Boundary element based computational algorithm solves the incompressible Navier-Stokes equations written in velocity-vorticity formulation. The non-uniform magnetic field is defined analytically for the case of a set of long thin wires. The particle trajectories are computed by applying the 4th order Runge-Kutta method. The computed test case consists of a narrow channel with laminar flow of suspension under Re = 1 − 10. Particle trajectories under the influence of a non-uniform magnetic field are computed for the case of magnetite and aluminium particles suspended in water. The efficiency of separation on basis of particle trajectories for different values of Re number and magnetic field strength is performed, clearly indicating superior separation of magneto active particles. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Quantum Immanants and the Cycle Basis of the Quantum Permutation Space

There are many combinatorial expressions for evaluating characters of the Hecke algebra of type A. However, with rare exceptions, they give simple results only for permutations that have minimal length in their conjugacy class. For other permutations, a recursive formula has to be applied. Consequently, quantum immanants are complicated objects when expressed in the standard basis of the quantum permutation space. In this paper, we introduce another natural basis of the quantum permutation space, and we prove that coefficients of quantum immanants in this basis are class functions.     

On the remoteness function in median graphs

A profile on a graph G is any nonempty multiset whose elements are vertices from G. The corresponding remoteness function associates to each vertex x∈V(G) the sum of distances from x to the vertices in the profile. Starting from some nice and useful properties of the remoteness function in hypercubes, the remoteness function is studied in arbitrary median graphs with respect to their isometric embeddings in hypercubes. In particular, a relation between the vertices in a median graph G whose remoteness function is maximum (antimedian set of G) with the antimedian set of the host hypercube is found. While for odd profiles the antimedian set is an independent set that lies in the strict boundary of a median graph, there exist median graphs in which special even profiles yield a constant remoteness function. We characterize such median graphs in two ways: as the graphs whose periphery transversal number is 2, and as the graphs with the geodetic number equal to 2. Finally, we present an algorithm that, given a graph G on n vertices and m edges, decides in O(mlogn) time whether G is a median graph with geodetic number 2.     

Retracts of Products of Chordal Graphs

In this article, we characterize the graphs G that are the retracts of Cartesian products of chordal graphs. We show that they are exactly the weakly modular graphs that do not contain K_{2, 3}, the 4‐wheel minus one spoke , and the k‐wheels (for as induced subgraphs. We also show that these graphs G are exactly the cage‐amalgamation graphs as introduced by Bre?ar and Tepeh Horvat (Cage‐amalgamation graphs, a common generalization of chordal and median graphs, Eur J Combin 30 (2009), 1071–1081); this solves the open question raised by these authors. Finally, we prove that replacing all products of cliques of G by products of Euclidean simplices, we obtain a polyhedral cell complex which, endowed with an intrinsic Euclidean metric, is a CAT(0) space. This generalizes similar results about median graphs as retracts of hypercubes (products of edges) and median graphs as 1‐skeletons of CAT(0) cubical complexes. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 161–180, 2013