A hybrid generative/discriminative method for EEG evoked potential detection

I. INTRODUCTION Generative and discriminative learning approaches are two prevailing and powerful, yet different, paradigms in machine leaning. Generative learning models, such as Bayesian inference [1] attempt to model the underlying distributions of the variables in order to compute classification and regression functions. These methods provide a rich framework for learning from prior knowledge. Discriminative learning models, such as support vector machines (SVM) [2] avoid generative modeling by directly optimizing a mapping from the inputs to the desired outputs by adjusting the resulting classification boundary. These latter methods commonly demonstrate superior performance in classification. Recently, researchers have investigated the relationship between these two learning paradigms and have attempted to combine their complementary strength

Local-Oscillator Noise Coupling in Balanced Homodyne Readout for Advanced Gravitational Wave Detectors

The second generation of interferometric gravitational wave detectors are quickly approaching their design sensitivity. For the first time these detectors will become limited by quantum back-action noise. Several back-action evasion techniques have been proposed to further increase the detector sensitivity. Since most proposals rely on a flexible readout of the full amplitude- and phase-quadrature space of the output light field, balanced homodyne detection is generally expected to replace the currently used DC readout. Up to now, little investigation has been undertaken into how balanced homodyne detection can be successfully transferred from its ubiquitous application in table-top quantum optics experiments to large-scale interferometers with suspended optics. Here we derive implementation requirements with respect to local oscillator noise couplings and highlight potential issues with the example of the Glasgow Sagnac Speed Meter experiment, as well as for a future upgrade to the Advanced LIGO detectors.Comment: 7 pages, 5 figure

Effects of static and dynamic higher-order optical modes in balanced homodyne readout for future gravitational waves detectors

With the recent detection of Gravitational waves (GW), marking the start of the new field of GW astronomy, the push for building more sensitive laser-interferometric gravitational wave detectors (GWD) has never been stronger. Balanced homodyne detection (BHD) allows for a quantum noise (QN) limited readout of arbitrary light field quadratures, and has therefore been suggested as a vital building block for upgrades to Advanced LIGO and third generation observatories. In terms of the practical implementation of BHD, we develop a full framework for analyzing the static optical high order modes (HOMs) occurring in the BHD paths related to the misalignment or mode matching at the input and output ports of the laser interferometer. We find the effects of HOMs on the quantum noise limited sensitivity is independent of the actual interferometer configuration, e.g. Michelson and Sagnac interferometers are effected in the same way. We show that misalignment of the output ports of the interferometer (output misalignment) only effects the high frequency part of the quantum noise limited sensitivity (detection noise). However, at low frequencies, HOMs reduce the interferometer response and the radiation pressure noise (back action noise) by the same amount and hence the quantum noise limited sensitivity is not negatively effected in that frequency range. We show that the misalignment of laser into the interferometer (input misalignment) produces the same effect as output misalignment and additionally decreases the power inside the interferometer. We also analyze dynamic HOM effects, such as beam jitter created by the suspended mirrors of the BHD. Our analyses can be directly applied to any BHD implementation in a future GWD. Moreover, we apply our analytical techniques to the example of the speed meter proof of concept experiment under construction in Glasgow. We find that for our experimental parameters, the performance of our seismic isolation system in the BHD paths is compatible with the design sensitivity of the experiment

A BRUTE-FORCE ANALYTICAL FORMULATION OF THE INDEPENDENT COMPONENTS ANALYSIS SOLUTION

ABSTRACT Many algorithms based on information theoretic measures and/or temporal statistics of the signals have been proposed for ICA in the literature. There have also been analytical solutions suggested based on predictive modeling of the signals. In this paper, we show that finding an analytical solution for the ICA problem through solving a system of nonlinear equations is possible. We demonstrate that this solution is robust to decreasing sample size and measurement SNR. Nevertheless, finding the root of the nonlinear function proves to be a challenge. Besides the analytical solution approach, we try finding the solution using a least squares approach with the derived analytical equations. Monte Carlo simulations using the least squares approach are performed to investigate the effect of sample size and measurement noise on the performance

The status of GEO 600

The GEO 600 laser interferometer with 600m armlength is part of a worldwide network of gravitational wave detectors. GEO 600 is unique in having advanced multiple pendulum suspensions with a monolithic last stage and in employing a signal recycled optical design. This paper describes the recent commissioning of the interferometer and its operation in signal recycled mode

Quantum state preparation and macroscopic entanglement in gravitational-wave detectors

Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the new possibility of experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical behavior of objects in the realm of everyday experience - using gravitational-wave detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometer's classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the classical noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum state preparation, and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses, and the performance of the planned Advanced LIGO interferometers in quantum-state preparation

Search of the Orion spur for continuous gravitational waves using a loosely coherent algorithm on data from LIGO interferometers

We report results of a wideband search for periodic gravitational waves from isolated neutron stars within the Orion spur towards both the inner and outer regions of our Galaxy. As gravitational waves interact very weakly with matter, the search is unimpeded by dust and concentrations of stars. One search disk (A) is 6.87° in diameter and centered on 20h10m54.71s+33°33′25.29′′, and the other (B) is 7.45° in diameter and centered on 8h35m20.61s-46°49′25.151′′. We explored the frequency range of 50-1500 Hz and frequency derivative from 0 to -5×10-9 Hz/s. A multistage, loosely coherent search program allowed probing more deeply than before in these two regions, while increasing coherence length with every stage. Rigorous follow-up parameters have winnowed the initial coincidence set to only 70 candidates, to be examined manually. None of those 70 candidates proved to be consistent with an isolated gravitational-wave emitter, and 95% confidence level upper limits were placed on continuous-wave strain amplitudes. Near 169 Hz we achieve our lowest 95% C.L. upper limit on the worst-case linearly polarized strain amplitude h0 of 6.3×10-25, while at the high end of our frequency range we achieve a worst-case upper limit of 3.4×10-24 for all polarizations and sky locations. © 2016 American Physical Society

First low-frequency Einstein@Home all-sky search for continuous gravitational waves in Advanced LIGO data

We report results of a deep all-sky search for periodic gravitational waves from isolated neutron stars in data from the first Advanced LIGO observing run. This search investigates the low frequency range of Advanced LIGO data, between 20 and 100 Hz, much of which was not explored in initial LIGO. The search was made possible by the computing power provided by the volunteers of the Einstein@Home project. We find no significant signal candidate and set the most stringent upper limits to date on the amplitude of gravitational wave signals from the target population, corresponding to a sensitivity depth of 48.7 [1/root Hz]. At the frequency of best strain sensitivity, near 100 Hz, we set 90% confidence upper limits of 1.8 x 10(-25). At the low end of our frequency range, 20 Hz, we achieve upper limits of 3.9 x 10(-24). At 55 Hz we can exclude sources with ellipticities greater than 10(-5) within 100 pc of Earth with fiducial value of the principal moment of inertia of 10(38) kg m(2)