A branch-and-price algorithm for a hierarchical crew scheduling problem.

We describe a real-life problem arising at a crane rental company. This problem is a generalization of the basic crew scheduling problem given in Mingozzi et al. and Beasley and Cao. We formulate the problem as an integer programming problem and establish ties with the integer multicommodity flow problem and the hierarchical interval scheduling problem. After establishing the complexity of the problem we propose a branch-and-price algorithm to solve it. We test this algorithm on a limited number of real-life instances.Scheduling;

Efficient analysis and representation of geophysical processes using localized spherical basis functions

While many geological and geophysical processes such as the melting of icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or the surface displacement remaining after large earthquakes are spatially localized, many of these naturally admit spectral representations, or they may need to be extracted from data collected globally, e.g. by satellites that circumnavigate the Earth. Wavelets are often used to study such nonstationary processes. On the sphere, however, many of the known constructions are somewhat limited. And in particular, the notion of `dilation' is hard to reconcile with the concept of a geological region with fixed boundaries being responsible for generating the signals to be analyzed. Here, we build on our previous work on localized spherical analysis using an approach that is firmly rooted in spherical harmonics. We construct, by quadratic optimization, a set of bandlimited functions that have the majority of their energy concentrated in an arbitrary subdomain of the unit sphere. The `spherical Slepian basis' that results provides a convenient way for the analysis and representation of geophysical signals, as we show by example. We highlight the connections to sparsity by showing that many geophysical processes are sparse in the Slepian basis.Comment: To appear in the Proceedings of the SPIE, as part of the Wavelets XIII conference in San Diego, August 200

Connectivity measures for internet topologies.

The topology of the Internet has initially been modelled as an undirected graph, where vertices correspond to so-called Autonomous Systems (ASs),and edges correspond to physical links between pairs of ASs. However, in order to capture the impact of routing policies, it has recently become apparent that one needs to classify the edges according to the existing economic relationships (customer-provider, peer-to-peer or siblings) between the ASs. This leads to a directed graph model in which traffic can be sent only along so-called valley-free paths. Four different algorithms have been proposed in the literature for inferring AS relationships using publicly available data from routing tables. We investigate the differences in the graph models produced by these algorithms, focussing on connectivity measures. To this aim, we compute the maximum number of vertex-disjoint valley-free paths between ASs as well as the size of a minimum cut separating a pair of ASs. Although these problems are solvable in polynomial time for ordinary graphs, they are NP-hard in our setting. We formulate the two problems as integer programs, and we propose a number of exact algorithms for solving them. For the problem of finding the maximum number of vertex-disjoint paths, we discuss two algorithms; the first one is a branch-and-price algorithm based on the IP formulation, and the second algorithm is a non LP based branch-and-bound algorithm. For the problem of finding minimum cuts we use a branch-and-cut algo rithm, based on the IP formulation of this problem. Using these algorithms, we obtain exact solutions for both problems in reasonable time. It turns out that there is a large gap in terms of the connectivity measures between the undirected and directed models. This finding supports our conclusion that economic relationships need to be taken into account when building a topology of the Internet.Research; Internet;

A Two-Step Approach for Offset and Position Estimation from Pseudo-Ranges Applied to Multilateration Tracking

In multilateration tracking, an object, e.g., an airplane, emits a known reference signal, which is received by several base stations (sensors) located at known positions. The receiving times of the signal at the sensors correspond to the times of arrival (TOA) plus an unknown offset, because the emission time is unknown. Usually, for estimating the position of the object, the receiving times are converted to a larger number of time differences of arrival (TDOA) in order to eliminate the unknown offset. To avoid this conversion, the proposed approach directly uses the receiving times. This is achieved by 1. determining the optimal offset from the redundant measurements in closed form and 2. by considering a modified measurement equation. As a result, position estimation can be performed by optimal stochastic linearization

Disambiguating the role of blood flow and global signal with partial information decomposition

Global signal (GS) is an ubiquitous construct in resting state functional magnetic resonance imaging (rs-fMRI), associated to nuisance, but containing by definition most of the neuronal signal. Global signal regression (GSR) effectively removes the impact of physiological noise and other artifacts, but at the same time it alters correlational patterns in unpredicted ways. Performing GSR taking into account the underlying physiology (mainly the blood arrival time) has been proven to be beneficial. From these observations we aimed to: 1) characterize the effect of GSR on network-level functional connectivity in a large dataset; 2) assess the complementary role of global signal and vessels; and 3) use the framework of partial information decomposition to further look into the joint dynamics of the global signal and vessels, and their respective influence on the dynamics of cortical areas. We observe that GSR affects intrinsic connectivity networks in the connectome in a non-uniform way. Furthermore, by estimating the predictive information of blood flow and the global signal using partial information decomposition, we observe that both signals are present in different amounts across intrinsic connectivity networks. Simulations showed that differences in blood arrival time can largely explain this phenomenon, while using hemodynamic and calcium mouse recordings we were able to confirm the presence of vascular effects, as calcium recordings lack hemodynamic information. With these results we confirm network-specific effects of GSR and the importance of taking blood flow into account for improving de-noising methods. Additionally, and beyond the mere issue of data denoising, we quantify the diverse and complementary effect of global and vessel BOLD signals on the dynamics of cortical areas

Conformations of confined biopolymers

Nanoscale and microscale confinement of biopolymers naturally occurs in cells and has been recently achieved in artificial structures designed for nanotechnological applications. Here, we present an extensive theoretical investigation of the conformations and shape of a biopolymer with varying stiffness confined to a narrow channel. Combining scaling arguments, analytical calculations, and Monte Carlo simulations, we identify various scaling regimes where master curves quantify the functional dependence of the polymer conformations on the chain stiffness and strength of confinement.Comment: 5 pages, 4 figures, minor correction

Fluctuation-Dissipation Theorem for the Microcanonical Ensemble

A derivation of the Fluctuation-Dissipation Theorem for the microcanonical ensemble is presented using linear response theory. The theorem is stated as a relation between the frequency spectra of the symmetric correlation and response functions. When the system is not in the thermodinamic limit, this result can be viewed as an extension of the fluctuation-dissipation relations to a situation where dynamical fluctuations determine the response. Therefore, the relation presented here between equilibrium fluctuations and response can have a very different physical nature from the usual one in the canonical ensemble. These considerations imply that the Fluctuation-Dissipation Theorem is not restricted to the context of thermal equilibrium, where it is usually derived. Dispersion relations and sum rules are also obtained and discussed in the present case. Although analogous to the Kramers-Kronig relations, they are not related to the frequency spectrum but to the energy dependence of the response function.Comment: 15 pages, v3: final version, new text added, new reference

Gaussian Filtering using State Decomposition Methods

State estimation for nonlinear systems generally requires approximations of the system or the probability densities, as the occurring prediction and filtering equations cannot be solved in closed form. For instance, Linear Regression Kalman Filters like the Unscented Kalman Filter or the considered Gaussian Filter propagate a small set of sample points through the system to approximate the posterior mean and covariance matrix. To reduce the number of sample points, special structures of the system and measurement equation can be taken into account. In this paper, two principles of system decomposition are considered and applied to the Gaussian Filter. One principle exploits that only a part of the state vector is directly observed by the measurement. The second principle separates the system equations into linear and nonlinear parts in order to merely approximate the nonlinear part of the state. The benefits of both decompositions are demonstrated on a real-world example

Anisotropic Reversible-Jump McMC Shear-Velocity Tomography of the Eastern Alpine Crust

The eastern Alpine crust has been shaped by the continental collision of the European and Adriatic plates beginning at 35 Ma and was affected by a major reorganization after 20 Ma. To better understand how the eastern Alpine surface structures link with deep seated processes, we analyze the depth-dependent seismic anisotropy based on Rayleigh wave propagation. Ambient noise recordings are evaluated to extract Rayleigh wave phase dispersion measurements. These are inverted in a two step approach for the azimuthally anisotropic shear velocity structure. Both steps are performed with a reversible jump Markov chain Monte Carlo (rj-McMC) approach that estimates data errors and propagates the modeled uncertainties from the phase velocity maps into the depth inversion. A two layer structure of azimuthal anisotropy is imaged in the Alpine crust, with an orogen-parallel upper crust and approximately orogen-perpendicular layer in the lower crust and the uppermost mantle. In the upper layer, the anisotropy tends to follow major fault lines and may thus be an apparent, structurally driven anisotropy. The main foliation and fold axis orientations might contribute to the anisotropy. In the lower crust, the N-S orientation of the fast axis is mostly confined to regions north of the Periadriatic Fault and may be related to European subduction. Outside the orogen, no clearly layered structure is identified. The anisotropy pattern in the northern Alpine foreland is found to be similar compared to SKS studies which is an indication of very homogeneous fast axis directions throughout the crust and the upper mantle