On Selecting and Scheduling Assembly Plans Using Constraint Programming

This work presents the application of Constraint Programming to the problem of selecting and sequencing assembly operations. The set of all feasible assembly plans for a single product is represented using an And/Or graph. This representation embodies some of the constraints involved in the planning problem, such as precedence of tasks, and the constraints due to the completion of a correct assembly plan. The work is focused on the selection of tasks and their optimal ordering, taking into account their execution in a generic multi-robot system. In order to include all different constraints of the problem, the And/Or graph representation is extended, so that links between nodes corresponding to assembly tasks are added, taking into account the resource constraints. The resultant problem is mapped to a Constraint Satisfaction Problem (CSP), and is solved using Constraint Programming, a powerful programming paradigm that is increasingly used to model and solve many hard real-life problems

Superconducting properties of the attractive Hubbard model

A self-consistent set of equations for the one-electron self-energy in the ladder approximation is derived for the attractive Hubbard model in the superconducting state. The equations provide an extension of a T-matrix formalism recently used to study the effect of electron correlations on normal-state properties. An approximation to the set of equations is solved numerically in the intermediate coupling regime, and the one-particle spectral functions are found to have four peaks. This feature is traced back to a peak in the self-energy, which is related to the formation of real-space bound states. For comparison we extend the moment approach to the superconducting state and discuss the crossover from the weak (BCS) to the intermediate coupling regime from the perspective of single-particle spectral densities.Comment: RevTeX format, 8 figures. Accepted for publication in Z.Phys.

R-matrix theory of driven electromagnetic cavities

Resonances of cylindrical symmetric microwave cavities are analyzed in R-matrix theory which transforms the input channel conditions to the output channels. Single and interfering double resonances are studied and compared with experimental results, obtained with superconducting microwave cavities. Because of the equivalence of the two-dimensional Helmholtz and the stationary Schroedinger equations, the results present insight into the resonance structure of regular and chaotic quantum billiards.Comment: Revtex 4.

Dynamical model and nonextensive statistical mechanics of a market index on large time windows

The shape and tails of partial distribution functions (PDF) for a financial signal, i.e. the S&P500 and the turbulent nature of the markets are linked through a model encompassing Tsallis nonextensive statistics and leading to evolution equations of the Langevin and Fokker-Planck type. A model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log-returns for such a financial market index, for small and large time windows, both for small and large log-returns. These turbulent market volatility (of normalized log-returns) distributions can be sufficiently well fitted with a $\chi^2$-distribution. The transition between the small time scale model of nonextensive, intermittent process and the large scale Gaussian extensive homogeneous fluctuation picture is found to be at $ca.$ a 200 day time lag. The intermittency exponent ($\kappa$) in the framework of the Kolmogorov log-normal model is found to be related to the scaling exponent of the PDF moments, -thereby giving weight to the model. The large value of $\kappa$ points to a large number of cascades in the turbulent process. The first Kramers-Moyal coefficient in the Fokker-Planck equation is almost equal to zero, indicating ''no restoring force''. A comparison is made between normalized log-returns and mere price increments.Comment: 40 pages, 14 figures; accepted for publication in Phys Rev

Convergence of the critical attractor of dissipative maps: Log-periodic oscillations, fractality and nonextensivity

For a family of logistic-like maps, we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space. We found that the phase space volume occupied by the ensemble W(t) depicts a power-law decay with log-periodic oscillations reflecting the multifractal character of the critical attractor. We explore the parametric dependence of the power-law exponent and the amplitude of the log-periodic oscillations with the attractor's fractal dimension governed by the inflexion of the map near its extremal point. Further, we investigate the temporal evolution of W(t) for the circle map whose critical attractor is dense. In this case, we found W(t) to exhibit a rich pattern with a slow logarithmic decay of the lower bounds. These results are discussed in the context of nonextensive Tsallis entropies.Comment: 8 pages and 8 fig

Quantum phase properties of two-mode Jaynes-Cummings model for Schr\"odinger-cat states: interference and entanglement

In this paper we investigate the quantum phase properties for the coherent superposition states (Schr\"odinger-cat states) for two-mode multiphoton Jaynes-Cummings model in the framework of the Pegg-Barnett formalism. We also demonstrate the behavior of the Wigner ($W$) function at the phase space origin. We obtain many interesting results such as there is a clear relationship between the revival-collapse phenomenon occurring in the atomic inversion (as well as in the evolution of the $W$ function) and the behavior of the phase distribution of both the single-mode and two-mode cases. Furthermore, we find that the phase variances of the single-mode case can exhibit revival-collapse phenomenon about the long-time behavior. We show that such behavior occurs for interaction time several times smaller than that of the single-mode Jaynes-Cummings model.Comment: 23, 8 figure

A closer look at the uncertainty relation of position and momentum

We consider particles prepared by the von Neumann-L\"uders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviations are not exceptions but rather typical. A necessary and sufficient condition for finite standard deviations is given. Finally, a new uncertainty relation is derived and it is shown that the latter cannot be improved.Comment: 3 pages, introduction shortened, content unchange

Acclimation to short-term low temperatures in two Eucalyptus globulus clones with contrasting drought resistance

We tested the hypothesis that Eucalyptus globulus Labill. genotypes that are more resistant to dry environments might also exhibit higher cold tolerances than drought-sensitive plants. The effect of low temperatures was evaluated in acclimated and unacclimated ramets of a drought-resistant clone (CN5) and a drought-sensitive clone (ST51) of E. globulus. We studied the plants’ response via leaf gas exchanges, leaf water and osmotic potentials, concentrations of soluble sugars, several antioxidant enzymes and leaf electrolyte leakage. Progressively lowering air temperatures (from 24/16 to 10/ 2 C, day/night) led to acclimation of both clones. Acclimated ramets exhibited higher photosynthetic rates, stomatal conductances and lower membrane relative injuries when compared to unacclimated ramets. Moreover, low temperatures led to significant increases of soluble sugars and antioxidant enzymes activity (glutathione reductase, ascorbate peroxidase and superoxide dismutases) of both clones in comparison to plants grown at control temperature (24/16 C). On the other hand, none of the clones, either acclimated or not, exhibited signs of photoinhibition under low temperatures and moderate light. The main differences in the responses to low temperatures between the two clones resulted mainly from differences in carbon metabolism, including a higher accumulation of soluble sugars in the drought-resistant clone CN5 as well as a higher capacity for osmotic regulation, as compared to the droughtsensitive clone ST51. Although membrane injury data suggested that both clones had the same inherent freezing tolerance before and after cold acclimation, the results also support the hypothesis that the droughtresistant clone had a greater cold tolerance at intermediate levels of acclimation than the drought-sensitive clone. A higher capacity to acclimate in a short period can allow a clone to maintain an undamaged leaf surface area along sudden frost events, increasing growt

Tensor completion in hierarchical tensor representations

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the reconstruction of tensors of low multi-linear rank in recently introduced hierarchical tensor formats from a small number of measurements. Hierarchical tensors are a flexible generalization of the well-known Tucker representation, which have the advantage that the number of degrees of freedom of a low rank tensor does not scale exponentially with the order of the tensor. While corresponding tensor decompositions can be computed efficiently via successive applications of (matrix) singular value decompositions, some important properties of the singular value decomposition do not extend from the matrix to the tensor case. This results in major computational and theoretical difficulties in designing and analyzing algorithms for low rank tensor recovery. For instance, a canonical analogue of the tensor nuclear norm is NP-hard to compute in general, which is in stark contrast to the matrix case. In this book chapter we consider versions of iterative hard thresholding schemes adapted to hierarchical tensor formats. A variant builds on methods from Riemannian optimization and uses a retraction mapping from the tangent space of the manifold of low rank tensors back to this manifold. We provide first partial convergence results based on a tensor version of the restricted isometry property (TRIP) of the measurement map. Moreover, an estimate of the number of measurements is provided that ensures the TRIP of a given tensor rank with high probability for Gaussian measurement maps.Comment: revised version, to be published in Compressed Sensing and Its Applications (edited by H. Boche, R. Calderbank, G. Kutyniok, J. Vybiral