Properties of Random Graphs with Hidden Color

We investigate in some detail a recently suggested general class of ensembles of sparse undirected random graphs based on a hidden stub-coloring, with or without the restriction to nondegenerate graphs. The calculability of local and global structural properties of graphs from the resulting ensembles is demonstrated. Cluster size statistics are derived with generating function techniques, yielding a well-defined percolation threshold. Explicit rules are derived for the enumeration of small subgraphs. Duality and redundancy is discussed, and subclasses corresponding to commonly studied models are identified.Comment: 14 pages, LaTeX, no figure

An iterative procedure to obtain inverse response functions for thick-target correction of measured charged-particle spectra

A new method for correcting charged-particle spectra for thick target effects is described. Starting with a trial function, inverse response functions are found by an iterative procedure. The variances corresponding to the measured spectrum are treated similiarly and in parallel. Oscillations of the solution are avoided by rebinning the data to finer bins during a correction iteration and back to the original or wider binning after each iteration. This thick-target correction method has been used for data obtained with the MEDLEY facility at the The Svedberg Laboratory, Uppsala, Sweden, and is here presented in detail and demonstrated for two test cases.Comment: 14 pages, 8 figures, submitted to NIM

Analysis of complex contagions in random multiplex networks

We study the diffusion of influence in random multiplex networks where links can be of $r$ different types, and for a given content (e.g., rumor, product, political view), each link type is associated with a content dependent parameter $c_i$ in $[0,\infty]$ that measures the relative bias type-$i$ links have in spreading this content. In this setting, we propose a linear threshold model of contagion where nodes switch state if their "perceived" proportion of active neighbors exceeds a threshold \tau. Namely, a node connected to $m_i$ active neighbors and $k_i-m_i$ inactive neighbors via type-$i$ links will turn active if $\sum{c_i m_i}/\sum{c_i k_i}$ exceeds its threshold \tau. Under this model, we obtain the condition, probability and expected size of global spreading events. Our results extend the existing work on complex contagions in several directions by i) providing solutions for coupled random networks whose vertices are neither identical nor disjoint, (ii) highlighting the effect of content on the dynamics of complex contagions, and (iii) showing that content-dependent propagation over a multiplex network leads to a subtle relation between the giant vulnerable component of the graph and the global cascade condition that is not seen in the existing models in the literature.Comment: Revised 06/08/12. 11 Pages, 3 figure

Complex Probabilities on R^N as Real Probabilities on C^N and an Application to Path Integrals

We establish a necessary and sufficient condition for averages over complex valued weight functions on R^N to be represented as statistical averages over real, non-negative probability weights on C^N. Using this result, we show that many path-integrals for time-ordered expectation values of bosonic degrees of freedom in real-valued time can be expressed as statistical averages over ensembles of paths with complex-valued coordinates, and then speculate on possible consequences of this result for the relation between quantum and classical mechanics.Comment: 4 pages, 0 figure

A Variational Approach for Minimizing Lennard-Jones Energies

A variational method for computing conformational properties of molecules with Lennard-Jones potentials for the monomer-monomer interactions is presented. The approach is tailored to deal with angular degrees of freedom, {\it rotors}, and consists in the iterative solution of a set of deterministic equations with annealing in temperature. The singular short-distance behaviour of the Lennard-Jones potential is adiabatically switched on in order to obtain stable convergence. As testbeds for the approach two distinct ensembles of molecules are used, characterized by a roughly dense-packed ore a more elongated ground state. For the latter, problems are generated from natural frequencies of occurrence of amino acids and phenomenologically determined potential parameters; they seem to represent less disorder than was previously assumed in synthetic protein studies. For the dense-packed problems in particular, the variational algorithm clearly outperforms a gradient descent method in terms of minimal energies. Although it cannot compete with a careful simulating annealing algorithm, the variational approach requires only a tiny fraction of the computer time. Issues and results when applying the method to polyelectrolytes at a finite temperature are also briefly discussed.Comment: 14 pages, uuencoded compressed postscript fil

The effect of microstructure on mechanical properties of HVOF sprayed WC-CoCr composite coatings

This study aims for deeper understanding of the composition and phase changes occurring during HVOF spraying of the powder to WC-CoCr coatings. Also, the effect of lamellar microstructure on the mechanical properties is studied. Compositional and microstructural features are studied by means of X-ray diffraction, XRF, FE-SEM and TEM (EDX, EELS). Mechanical properties are mainly studied by different instrumented indentation and nanoindentation techniques. The use of two new fracture parameters, complementing the fracture toughness value of the coating, are proposed and examined. Higher load range indentations are used to measure cross-sectional and surface hardness, elastic modulus and fracture toughness of the coatings. Mechanical properties of individual phases are studied by nanoindentation. To our knowledge this is the first time that the mechanical properties of this amorphous/nanocrystalline matrix are studied. ICP (In-situ Coating Property) sensor, developed for quality control and residual stress evaluation, is also used to measure the elastic modulus and coefficient of thermal expansion (CTE) of the coatings. Abrasion wear resistance of the coatings are studied according to standard ASTM G 65D. Because of the brittle nature of HVOF coatings, the main focus of this study is in the effects of coating microstructure on fracture toughness, and on crack initiation and propagation resistance. It is shown that even when two similar coatings have equal indentation fracture toughness values, the critical crack initiation loads may be very different. This new parameter is expected to be extremely useful in the evaluation of the coating performance under loading conditions

Complex Langevin Equation and the Many-Fermion Problem

We study the utility of a complex Langevin (CL) equation as an alternative for the Monte Carlo (MC) procedure in the evaluation of expectation values occurring in fermionic many-body problems. We find that a CL approach is natural in cases where non-positive definite probability measures occur, and remains accurate even when the corresponding MC calculation develops a severe ``sign problem''. While the convergence of CL averages cannot be guaranteed in principle, we show how convergent results can be obtained in three examples ranging from simple one-dimensional integrals over quantum mechanical models to a schematic shell model path integral.Comment: 19 pages, 10 PS figures embedded in tex