Induced Minor Free Graphs: Isomorphism and Clique-width

Given two graphs $G$ and $H$, we say that $G$ contains $H$ as an induced minor if a graph isomorphic to $H$ can be obtained from $G$ by a sequence of vertex deletions and edge contractions. We study the complexity of Graph Isomorphism on graphs that exclude a fixed graph as an induced minor. More precisely, we determine for every graph $H$ that Graph Isomorphism is polynomial-time solvable on $H$-induced-minor-free graphs or that it is GI-complete. Additionally, we classify those graphs $H$ for which $H$-induced-minor-free graphs have bounded clique-width. These two results complement similar dichotomies for graphs that exclude a fixed graph as an induced subgraph, minor, or subgraph.Comment: 16 pages, 5 figures. An extended abstract of this paper previously appeared in the proceedings of the 41st International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2015

Bayesian Lower Bounds for Dense or Sparse (Outlier) Noise in the RMT Framework

Robust estimation is an important and timely research subject. In this paper, we investigate performance lower bounds on the mean-square-error (MSE) of any estimator for the Bayesian linear model, corrupted by a noise distributed according to an i.i.d. Student's t-distribution. This class of prior parametrized by its degree of freedom is relevant to modelize either dense or sparse (accounting for outliers) noise. Using the hierarchical Normal-Gamma representation of the Student's t-distribution, the Van Trees' Bayesian Cram\'er-Rao bound (BCRB) on the amplitude parameters is derived. Furthermore, the random matrix theory (RMT) framework is assumed, i.e., the number of measurements and the number of unknown parameters grow jointly to infinity with an asymptotic finite ratio. Using some powerful results from the RMT, closed-form expressions of the BCRB are derived and studied. Finally, we propose a framework to fairly compare two models corrupted by noises with different degrees of freedom for a fixed common target signal-to-noise ratio (SNR). In particular, we focus our effort on the comparison of the BCRBs associated with two models corrupted by a sparse noise promoting outliers and a dense (Gaussian) noise, respectively

Joint ML calibration and DOA estimation with separated arrays

This paper investigates parametric direction-of-arrival (DOA) estimation in a particular context: i) each sensor is characterized by an unknown complex gain and ii) the array consists of a collection of subarrays which are substantially separated from each other leading to a structured noise covariance matrix. We propose two iterative algorithms based on the maximum likelihood (ML) estimation method adapted to the context of joint array calibration and DOA estimation. Numerical simulations reveal that the two proposed schemes, the iterative ML (IML) and the modified iterative ML (MIML) algorithms for joint array calibration and DOA estimation, outperform the state of the art methods and the MIML algorithm reaches the Cram\'er-Rao bound for a low number of iterations

Relaxed concentrated MLE for robust calibration of radio interferometers

In this paper, we investigate the calibration of radio interferometers in which Jones matrices are considered to model the interaction between the incident electromagnetic field and the antennas of each station. Specifically, perturbation effects are introduced along the signal path, leading to the conversion of the plane wave into an electric voltage by the receptor. In order to design a robust estimator, the noise is assumed to follow a spherically invariant random process (SIRP). The derived algorithm is based on an iterative relaxed concentrated maximum likelihood estimator (MLE), for which closed-form expressions are obtained for most of the unknown parameters

On the concept of sloped motion for free-floating wave energy converters

A free-floating wave energy converter (WEC) concept whose power take-off (PTO) system reacts against water inertia is investigated herein. The main focus is the impact of inclining the PTO direction on the system performance. The study is based on a numerical model whose formulation is first derived in detail. Hydrodynamics coefficients are obtained using the linear boundary element method package WAMIT. Verification of the model is provided prior to its use for a PTO parametric study and a multi-objective optimization based on a multi-linear regression method. It is found that inclining the direction of the PTO at around 50. to the vertical is highly beneficial for the WEC performance in that it provides a high capture width ratio over a broad region of the wave period range

An Oriented Convergent Mutation Operator for Solving a Scalable Convergent Demand Responsive Transport Problem

International audienceThis paper presents a method for solving the convergence demand responsive transport problem, by using a stochastic approach based on a steady state genetic algorithm for enumerating a set of optimizing sprawling spanning trees, which constitute the best solutions to this problem. Specifically designed to speed up the convergence to optimal solutions, we introduce an oriented convergent mutation operator, allowing multi-objective considerations. So this solution lays the first stakes for considering real-time solving of such a problem. Led by computer science and geography laboratories, this study is provided with a set of experimental results evaluating the approach

Comparison of three algorithms for solving the convergent demand responsive transportation problem

International audienceLed by computer science and geography laboratories, this paper presents three algorithms for solving the Convergent Demand Responsive Transport Problem (CDRTP). Two of them are exact: the first one is based on a dynamic programming algorithm to enumerate exhaustively the sprawling spanning trees and the second one is based on a depth first search algorithm. The third one is stochastic and uses a steady state genetic algorithm. These approaches address the problems of scalability and flexibility, are compared and discussed

Electron quantum optics in quantum Hall edge channels

In this paper, we review recent developments in the emerging field of electron quantum optics, stressing analogies and differences with the usual case of photon quantum optics. Electron quantum optics aims at preparing, manipulating and measuring coherent single electron excitations propagating in ballistic conductors such as the edge channels of a 2DEG in the integer quantum Hall regime. Because of the Fermi statistics and the presence of strong interactions, electron quantum optics exhibits new features compared to the usual case of photon quantum optics. In particular, it provides a natural playground to understand decoherence and relaxation effects in quantum transport.Comment: 13 pages, 6 figures. To appear in the proceedings of StatPhys 24 satellite conference on "International Conference on Frustrated Spin Systems, Cold Atoms and Nanomaterials" held in Hanoi (14-16 July 2010

Аналіз сучасних підходів до визначення поняття “регіон”

Мета статті. Дослідити основні підходи до трактування поняття “регіон”