Nonlinear Compressive Particle Filtering

Many systems for which compressive sensing is used today are dynamical. The common approach is to neglect the dynamics and see the problem as a sequence of independent problems. This approach has two disadvantages. Firstly, the temporal dependency in the state could be used to improve the accuracy of the state estimates. Secondly, having an estimate for the state and its support could be used to reduce the computational load of the subsequent step. In the linear Gaussian setting, compressive sensing was recently combined with the Kalman filter to mitigate above disadvantages. In the nonlinear dynamical case, compressive sensing can not be used and, if the state dimension is high, the particle filter would perform poorly. In this paper we combine one of the most novel developments in compressive sensing, nonlinear compressive sensing, with the particle filter. We show that the marriage of the two is essential and that neither the particle filter or nonlinear compressive sensing alone gives a satisfying solution.Comment: Accepted to CDC 201

Approximative two-flavor framework for neutrino oscillations with nonstandard interactions

In this paper, we develop approximative two-flavor neutrino oscillation formulas including subleading nonstandard interaction effects. Especially, the limit when the small mass-squared difference approaches zero is investigated. The approximate formulas are also tested against numerical simulations in order to determine their accuracy and they will probably be most useful in the GeV energy region, which is the energy region where most upcoming neutrino oscillation experiments will be operating. Naturally, it is important to have analytical formulas in order to interpret the physics behind the degeneracies between standard and nonstandard parameters.Comment: 21 pages, 7 figures, REVTeX4. Final version published in Phys. Rev.

Initial experiments concerning quantum information processing in rare-earth-ion doped crystals

In this paper initial experiments towards constructing simple quantum gates in a solid state material are presented. Instead of using specially tailored materials, the aim is to select a subset of randomly distributed ions in the material, which have the interaction necessary to control each other and therefore can be used to do quantum logic operations. The experimental results demonstrate that part of an inhomogeneously broadened absorption line can be selected as a qubit and that a subset of ions in the material can control the resonance frequency of other ions. This opens the way for the construction of quantum gates in rare-earth-ion doped crystals.Comment: 24 pages, including 12 figure

Nonlinear Basis Pursuit

In compressive sensing, the basis pursuit algorithm aims to find the sparsest solution to an underdetermined linear equation system. In this paper, we generalize basis pursuit to finding the sparsest solution to higher order nonlinear systems of equations, called nonlinear basis pursuit. In contrast to the existing nonlinear compressive sensing methods, the new algorithm that solves the nonlinear basis pursuit problem is convex and not greedy. The novel algorithm enables the compressive sensing approach to be used for a broader range of applications where there are nonlinear relationships between the measurements and the unknowns

Robust Subspace System Identification via Weighted Nuclear Norm Optimization

Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework to handle outliers. The proposed framework takes the form of a convex optimization problem with an objective that trades off fit, rank and sparsity. As in robust PCA, it can be problematic to find a suitable regularization parameter. We show how the space in which a suitable parameter should be sought can be limited to a bounded open set of the two dimensional parameter space. In practice, this is very useful since it restricts the parameter space that is needed to be surveyed.Comment: Submitted to the IFAC World Congress 201

Energy Disaggregation via Adaptive Filtering

The energy disaggregation problem is recovering device level power consumption signals from the aggregate power consumption signal for a building. We show in this paper how the disaggregation problem can be reformulated as an adaptive filtering problem. This gives both a novel disaggregation algorithm and a better theoretical understanding for disaggregation. In particular, we show how the disaggregation problem can be solved online using a filter bank and discuss its optimality.Comment: Submitted to 51st Annual Allerton Conference on Communication, Control, and Computin

Blind Identification via Lifting

Blind system identification is known to be an ill-posed problem and without further assumptions, no unique solution is at hand. In this contribution, we are concerned with the task of identifying an ARX model from only output measurements. We phrase this as a constrained rank minimization problem and present a relaxed convex formulation to approximate its solution. To make the problem well posed we assume that the sought input lies in some known linear subspace.Comment: Submitted to the IFAC World Congress 2014. arXiv admin note: text overlap with arXiv:1303.671

Matter Enhanced Neutrino Oscillations with a Realistic Earth Density Profile

We have investigated matter enhanced neutrino oscillations with a mantle-core-mantle step function and a realistic Earth matter density profile in both a two and a three neutrino scenario. We found that the realistic Earth matter density profile can be well approximated with the mantle-core-mantle step function and that there could be an influence on the oscillation channel $\nu_\mu \to \nu_\tau$ due to resonant enhancement of one of the mixing angles.Comment: 8 pages, 5 figures (PostScript), MPLA LaTe