Efficient elementary and restricted non-elementary route pricing

Column generation is involved in the current most efficient approaches to routing problems. Set partitioning formulations model routing problems by considering all possible routes and selecting a subset that visits all customers. These formulations often produce tight lower bounds and require column generation for their pricing step. The bounds in the resulting branch-and-price are tighter when elementary routes are considered, but this approach leads to a more difficult pricing problem. Balancing the pricing with route relaxations has become crucial for the efficiency of the branch-and-price for routing problems. Recently, the ng-routes relaxation was proposed as a compromise between elementary and non-elementary routes. The ng-routes are non-elementary routes with the restriction that when following a customer, the route is not allowed to visit another customer that was visited before if they belong to a dynamically computed set. The larger the size of these sets, the closer the ng-route is to an elementary route. This work presents an efficient pricing algorithm for ng-routes and extends this algorithm for elementary routes. Therefore, we address the Shortest Path Problem with Resource Constraint (SPPRC) and the Elementary Shortest Path Problem with Resource Constraint (ESPPRC). The proposed algorithm combines the Decremental State-Space Relaxation technique (DSSR) with completion bounds. We apply this algorithm for the Generalized Vehicle Routing Problem (GVRP) and for the Capacitated Vehicle Routing Problem (CVRP), demonstrating that it is able to price elementary routes for instances up to 200 customers, a result that doubles the size of the ESPPRC instances solved to date.     

Convergence to equilibrium of biased plane Partitions

We study a single‐flip dynamics for the monotone surface in (2 + 1) dimensions obtained from a boxed plane partition. The surface is analyzed as a system of non‐intersecting simple paths. When the flips have a non‐zero bias we prove that there is a positive spectral gap uniformly in the boundary conditions and in the size of the system. Under the same assumptions, for a system of size M, the mixing time is shown to be of order M up to logarithmic corrections. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 83–114, 2011     

Impact of PDL-induced crosstalk on 100-Gb/s polarization-multiplexed RZ-DQPSK in PMD-affected metro networks

The impact of PDL-induced crosstalk on 100-Gb/s polarization-multiplexed RZ-DQPSK performance in direct detection systems is experimentally assessed in presence of a moderate amount of PMD. In particular, RZ-interleaving and RZ-overlapping schemes have shown opposite behaviours towards PMD and PDL. Measurements carried out confirm the less robustness of RZ-interleaving than RZ-overlapping towards PMD, but highlight a much stronger tolerance of RZ-interleaving to PDL with respect to RZ-overlapping. When PDL combines with moderate PMD, as in metro networks, it is shown that RZ-overlapping high tolerance to PMD drastically fails, RZ-interleaving proving more efficient to deal with polarization issues in case of direct detection of polarization-multiplexed signals.     

Parton densities from deep inelastic scattering to hadronic processes at super collider energies

We give several sets of parton densities derived from recent measurements of structure functions in deep inelastic scattering. The difference among these densities reflects the uncertainties from deep inelastic data of different experiments, allowing an estimate of the error band for the predictions one may obtain for any given hadronic process at higher energy. The densities are available at any scaleQ ²≦5.10⁹ GeV² andx≧5.10^?5 and include next-to-leading corrections as well as threshold effects due to heavy flavours. A comparison with a large set of data in a wide range of scales (Drell-Yan,W andZ production, etc.) is also presented.     

Fast mixing for independent sets,colorings, and other models on trees

We study the mixing time of the Glauber dynamics for general spin systems on the regular tree, including the Ising model, the hard‐core model (independent sets), and the antiferromagnetic Potts model at zero temperature (colorings). We generalize a framework, developed in our recent paper (Martinelli, Sinclair, and Weitz, Tech. Report UCB//CSD‐03‐1256, Dept. of EECS, UC Berkeley, July 2003) in the context of the Ising model, for establishing mixing time O(nlog n), which ties this property closely to phase transitions in the underlying model. We use this framework to obtain rapid mixing results for several models over a significantly wider range of parameter values than previously known, including situations in which the mixing time is strongly dependent on the boundary condition. We also discuss applications of our framework to reconstruction problems on trees. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

Stochastic resonance in paramagnetic resonance systems

Experimental evidence of the stochastic resonance phenomenon in an electron paramagnetic resonance (EPR) system is reported. The amplitude and phase response of the EPR system operating in bistable conditions are measured for increasing values of the noise intensity. Theoretical predictions based on a simple dynamical model for the relevant system observables are shown to be in good agreement with experimental results.     

Laser-noise-induced correlations and anti-correlations in electromagnetically induced transparency

High degrees of intensity correlation between two independent lasers were observed after propagation through a rubidium vapor cell in which they generate Electromagnetically Induced Transparency (EIT). As the optical field intensities are increased, the correlation changes sign (becoming anti-correlation). The experiment was performed in a room temperature rubidium cell, using two diode lasers tuned to the ⁸⁵Rb D₂ line (λ= 780 nm). The cross-correlation spectral function for the pump and probe fields is numerically obtained by modeling the temporal dynamics of both field phases as diffusing processes. We explored the dependence of the atomic response on the atom-field Rabi frequencies, optical detuning and Doppler width. The results show that resonant phase-noise to amplitude-noise conversion is at the origin of the observed signal and the change in sign for the correlation coefficient can be explained as a consequence of the competition between EIT and Raman resonance processes.     

Amplitude modulated transversal and longitudinal EPR spectroscopy

The amplitude modulated EPR spectroscopy is analyzed both in the time and the frequency domain. The results of numerical calculations and analytical approximate treatments indicate that the signal lineshape is differently affected by relaxation mechanisms when transversal or longitudinal detection is used in spectroscopies with variable frequencies of modulation. Measurements of longitudinally detected electron-spin double resonance obtained in dependence on the frequency of modulation confirm the lineshape expected by the theoretical analysis.