997 research outputs found

    Near-optimal bounds for phase synchronization

    Full text link
    The problem of phase synchronization is to estimate the phases (angles) of a complex unit-modulus vector zz from their noisy pairwise relative measurements C=zz+σWC = zz^* + \sigma W, where WW is a complex-valued Gaussian random matrix. The maximum likelihood estimator (MLE) is a solution to a unit-modulus constrained quadratic programming problem, which is nonconvex. Existing works have proposed polynomial-time algorithms such as a semidefinite relaxation (SDP) approach or the generalized power method (GPM) to solve it. Numerical experiments suggest both of these methods succeed with high probability for σ\sigma up to O~(n1/2)\tilde{\mathcal{O}}(n^{1/2}), yet, existing analyses only confirm this observation for σ\sigma up to O(n1/4)\mathcal{O}(n^{1/4}). In this paper, we bridge the gap, by proving SDP is tight for σ=O(n/logn)\sigma = \mathcal{O}(\sqrt{n /\log n}), and GPM converges to the global optimum under the same regime. Moreover, we establish a linear convergence rate for GPM, and derive a tighter \ell_\infty bound for the MLE. A novel technique we develop in this paper is to track (theoretically) nn closely related sequences of iterates, in addition to the sequence of iterates GPM actually produces. As a by-product, we obtain an \ell_\infty perturbation bound for leading eigenvectors. Our result also confirms intuitions that use techniques from statistical mechanics.Comment: 34 pages, 1 figur

    Particle Physics at the LHC Start

    Full text link
    I present a concise review of where we stand in particle physics today. First, I will discuss the status of the Standard Model, its open problems and the expected answers from the LHC. Then I will briefly review the avenues for New Physics that can be revealed by the LHC.Comment: 25 pages, 7 figures. Talk given at the Conference "The Legacy of Edoardo Amaldi in Science and Society", Rome, Italy, October 23-25, 200

    Risk-Averse Model Predictive Operation Control of Islanded Microgrids

    Full text link
    In this paper we present a risk-averse model predictive control (MPC) scheme for the operation of islanded microgrids with very high share of renewable energy sources. The proposed scheme mitigates the effect of errors in the determination of the probability distribution of renewable infeed and load. This allows to use less complex and less accurate forecasting methods and to formulate low-dimensional scenario-based optimisation problems which are suitable for control applications. Additionally, the designer may trade performance for safety by interpolating between the conventional stochastic and worst-case MPC formulations. The presented risk-averse MPC problem is formulated as a mixed-integer quadratically-constrained quadratic problem and its favourable characteristics are demonstrated in a case study. This includes a sensitivity analysis that illustrates the robustness to load and renewable power prediction errors

    New Physics and the LHC

    Get PDF
    In these lectures I start by briefly reviewing the status of the electroweak theory, in the Standard Model and beyond. I then discuss the motivation and the possible avenues for new physics, on the brink of the LHC start.Comment: 35 pages, 8 figures. Lectures given at the Lake Louise Winter Institute, Lake Louise, Alberta, Canada, 18-23 February 200
    corecore