The edge-disjoint path problem on random graphs by message-passing

We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an exponential computational cost in the number of paths. To overcome this obstacle we propose an efficient implementation by mapping the equations onto a weighted combinatorial matching problem over an auxiliary graph. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behaviour of both the number of paths to be accommodated and their minimum total length.Comment: 14 pages, 8 figure

Stochastic Optimization of Service Provision with Selfish Users

We develop a computationally efficient technique to solve a fairly general distributed service provision problem with selfish users and imperfect information. In particular, in a context in which the service capacity of the existing infrastructure can be partially adapted to the user load by activating just some of the service units, we aim at finding the configuration of active service units that achieves the best trade-off between maintenance (e.g.\ energetic) costs for the provider and user satisfaction. The core of our technique resides in the implementation of a belief-propagation (BP) algorithm to evaluate the cost configurations. Numerical results confirm the effectiveness of our approach.Comment: paper presented at NETSTAT Workshop, Budapest - June 201

Stochastic optimization by message passing

Most optimization problems in applied sciences realistically involve uncertainty in the parameters defining the cost function, of which only statistical information is known beforehand. In a recent work we introduced a message passing algorithm based on the cavity method of statistical physics to solve the two-stage matching problem with independently distributed stochastic parameters. In this paper we provide an in-depth explanation of the general method and caveats, show the details of the derivation and resulting algorithm for the matching problem and apply it to a stochastic version of the independent set problem, which is a computationally hard and relevant problem in communication networks. We compare the results with some greedy algorithms and briefly discuss the extension to more complicated stochastic multi-stage problems.Comment: 31 pages, 8 figure

Small x resummation of rapidity distributions: the case of Higgs production

We provide a method for the all order computation of small x contributions at the leading logarithmic level to cross-sections which are differential in rapidity. The method is based on a generalization to rapidity distributions of the high energy (or k_T) factorization theorem hitherto proven for inclusive cross-sections. We apply the method to Higgs production in gluon-gluon fusion, both with finite top mass and in the infinite mass limit: in both cases, we determine all-order resummed expressions, as well as explicit expressions for the leading small x terms up to NNLO. We use our result to construct an explicit approximate analytic expression of the finite-mass NLO rapidity distribution and an estimate of finite-mass corrections at NNLO.Comment: 53 pages, 6 figures. Several typos corrected. Final version, to be published in NP

HERA data and DGLAP evolution: theory and phenomenology

We examine critically the evidence for deviations from next-to-leading order perturbative DGLAP evolution in HERA data. We briefly review the status of perturbative small-x resummation and of global determinations of parton distributions. We show that the geometric scaling properties of HERA data are consistent with DGLAP evolution, which is also strongly supported by the double asymptotic scaling properties of the data. However, backward--evolution of parton distributions into the low x, low Q^2 region does show evidence of deviations between the observed behaviour and the next-to-leading order predictions. These deviations cannot be explained by missing next-to-next-to-leading order perturbative terms, and are consistent with perturbative small-x resummation.Comment: Fig. 8 corrected. Published in NP

Deviations from NLO QCD evolution in inclusive HERA data

We search for deviations from next-to-leading order QCD evolution in HERA structure function data. We compare to data predictions for structure functions in the small x region, obtained by evolving backwards to low Q^2 the results of a parton fit performed in the large Q^2 region, where fixed-order perturbative QCD is certainly reliable. We find evidence for deviations which are qualitatively consistent with the behaviour predicted by small x perturbative resummation, and possibly also by nonlinear evolution effects, but incompatible with next-to-next-to leading order corrections.Comment: Final version (to be published in PLB), new plots in fig. 5 and new column in tab. 4 added, fig. 10 added, discussion on distances on pag. 8 added, typos correcte

X-Ray Resonant Scattering as a Direct Probe of Orbital Ordering in Transition-Metal Oxides

X-ray resonant scattering at the K-edge of transition metal oxides is shown to measure the orbital order parameter, supposed to accompany magnetic ordering in some cases. Virtual transitions to the 3d-orbitals are quadrupolar in general. In cases with no inversion symmetry, such as V$_2$O$_3$, treated in detail here, a dipole component enhances the resonance. Hence, we argue that the detailed structure of orbital order in V$_2$O$_3$ is experimentally accessible.Comment: LaTex using RevTex, 4 pages and two included postscript figure

Search for CP Violation in the Decay Z -> b (b bar) g

About three million hadronic decays of the Z collected by ALEPH in the years 1991-1994 are used to search for anomalous CP violation beyond the Standard Model in the decay Z -> b \bar{b} g. The study is performed by analyzing angular correlations between the two quarks and the gluon in three-jet events and by measuring the differential two-jet rate. No signal of CP violation is found. For the combinations of anomalous CP violating couplings, ${\hat{h}}_b = {\hat{h}}_{Ab}g_{Vb}-{\hat{h}}_{Vb}g_{Ab}$ and $h^{\ast}_b = \sqrt{\hat{h}_{Vb}^{2}+\hat{h}_{Ab}^{2}}$, limits of \hat{h}_b < 0.59$and$h^{\ast}_{b} < 3.02$ are given at 95\% CL.Comment: 8 pages, 1 postscript figure, uses here.sty, epsfig.st