On the optimization of two-class work-conserving parameterized scheduling policies

Numerous scheduling policies are designed to differentiate quality of service for different applications. Service differentiation can in fact be formulated as a generalized resource allocation optimization towards the minimization of some important system characteristics. For complex scheduling policies, however, optimization can be a demanding task, due to the difficult analytical analysis of the system at hand. In this paper, we study the optimization problem in a queueing system with two traffic classes, a work-conserving parameterized scheduling policy, and an objective function that is a convex combination of either linear, convex or concave increasing functions of given performance measures of both classes. In case of linear and concave functions, we show that the optimum is always in an extreme value of the parameter. Furthermore, we prove that this is not necessarily the case for convex functions; in this case, a unique local minimum exists. This information greatly simplifies the optimization problem. We apply the framework to some interesting scheduling policies, such as Generalized Processor Sharing and semi-preemptive priority scheduling. We also show that the well-documented \(c\mu \)-rule is a special case of our framework.     

The diameter of a random subgraph of the hypercube

In this paper we present an estimation for the diameter of random subgraph of a hypercube. In the article by A. V. Kostochka (Random Struct Algorithms 4 (1993) 215–229) the authors obtained lower and upper bound for the diameter. According to their work, the inequalities n + m_p ≤ D(G_n) ≤ n + m_p + 8 almost surely hold as n → ∞, where n is dimension of the hypercube and m_p depends only on sampling probabilities. It is not clear from their work, whether the values of the diameter are really distributed on these 9 values, or whether the inequality can be sharpened. In this paper we introduce several new ideas, using which we are able to obtain an exact result: D(G_n) = n + m_p (almost surely). © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

Direct Likelihood Evaluation for the Renewal Hawkes Process

An interesting extension of the widely applied Hawkes self-exiting point process, the renewal Hawkes (RHawkes) process, was recently proposed by Wheatley, Filimonov, and Sornette, which has the potential to significantly widen the application domains of the self-exciting point processes. However, they claimed that computation of the likelihood of the RHawkes process requires exponential time and therefore is practically impossible. They proposed two expectation–maximization (EM) type algorithms to compute the maximum likelihood estimator (MLE) of the model parameters. Because of the fundamental role of likelihood in statistical inference, a practically feasible method for likelihood evaluation is highly desirable. In this article, we provide an algorithm that evaluates the likelihood of the RHawkes process in quadratic time, a drastic improvement from the exponential time claimed by Wheatley, Filimonov, and Sornette. We demonstrate the superior performance of the resulting MLEs of the model relative to the EM estimators through simulations. We also present a computationally efficient procedure to calculate the Rosenblatt residuals of the process for goodness-of-fit assessment, and a simple yet efficient procedure for future event prediction. The proposed methodologies were applied on real data from seismology and finance. An R package implementing the proposed methodologies is included in the supplementary materials.     

Erbium photoluminescence excitation spectroscopy in Si: Er epitaxial structures

Excitation spectra of erbium photoluminescence in Si: Er epitaxial structures are studied within a broad pump wavelength range (λ_ex = 780–1500 nm). All the structures studied reveal a fairly strong erbium photoluminescence signal at photon energies substantially smaller than the silicon band-gap width (λ = 1060 nm) with no exciton generation. A possible mechanism of erbium ion excitation in silicon without exciton involvement is discussed.     

Moufang sets of mixed type F4

Moufang sets were introduced by Jacques Tits in order to understand isotropic linear algebraic groups of relative rank one, but the notion is more general. We describe a new class of Moufang sets, arising from so‐called mixed groups of type ${\mathsf{F}}_4$ in characteristic 2, obtained as the fixed point set under a suitable involution.     

The Farrell–Jones Conjecture for the solvable Baumslag–Solitar groups

In this paper, we prove the Farrell–Jones Conjecture for the solvable Baumslag–Solitar groups with coefficients in an additive category. We also extend our results to groups of the form, Z[1/p] semidirect product with any virtually cyclic group, where p is a prime number.     

Silver ion dynamics in the Ag5Te2Cl-polymorphs revealed by solid state NMR lineshape and two- and three-time correlation spectroscopies

The relation between structure and ion dynamics in the three polymorphs of Ag(5)Te(2)Cl has been investigated using (109)Ag, (125)Te, and (35)Cl NMR spectroscopies. Specifically, the influence of the structural phase transitions observed near 240 K (P2(1)/c<-->P2(1)/n) and near 332 K (P2(1)/n<-->I4/mcm) upon silver ion mobilities has been studied by temperature dependent (109)Ag NMR lineshapes and spin-lattice relaxation times. While the superionic high temperature phase alpha-Ag(5)Te(2)Cl is characterized by a molten cationic sublattice, fast ion dynamics in the medium-temperature phase beta-Ag(5)Te(2)Cl occurs in spatially restricted regions comprising all the crystallographically distinct silver sites. Temperature dependent magic-angle-spinning linewidths yield an activation energy of 0.38 eV, consistent with 0.44 eV measured from dc electric conductivities. For the low-temperature gamma-modification, results of two- and three-time (109)Ag correlation spectroscopies provide a detailed insight into the nature of the silver ionic hopping motion. Temperature dependent jump rates measured by two-time correlation functions yield an activation energy E(a)= 0.48 eV. (109)Ag NMR three-time correlation functions indicate that the non-exponential relaxation behavior of the silver ions can be attributed to a broad distribution of jump rates rather than correlated forward-backward jumps. Nevertheless, all the silver ions are mobile down to temperatures of about 185 K.     

Intertrimer and intratrimer metallophilic and excimeric bonding in the ground and phosphorescent States of trinuclear coinage metal pyrazolates: a computational study

The interactions present in cyclic trinuclear coinage metal pyrazolates were studied computationally. Cuprophilic interaction was found to bind the singlet ground state of the dimer of trimers [[Cu(Pz)](3)](2), overcoming electrostatic repulsion. The large variation in intertrimer separations found in the literature for coinage metal pyrazolates is consistent with the relatively weak metallophilic interaction. The emissive triplet excited-state geometry of [[M(Pz)](3)](2) is predicted by density functional calculations to show major geometric distortion caused by Jahn-Teller instability and excimeric M-M bonding. Large calculated Stokes' shifts, which are also observed for experimental models, are consistent with significant excited-state distortions for these materials. The major finding derived from the present study is that the intertrimer M...M contraction in the emissive T(1) state is much more than the intratrimer contraction in all [[M(Pz)](3)](2) models, giving rise to a lower T(1) --> S(0) phosphorescence energy in these models than in analogous monomer-of-trimer models. The observations made here point to a great potential for rationally tuning the emission properties of trinuclear coinage metal complexes through choice of the metal and ligands.