Improving Sparsity in Kernel Adaptive Filters Using a Unit-Norm Dictionary

Kernel adaptive filters, a class of adaptive nonlinear time-series models, are known by their ability to learn expressive autoregressive patterns from sequential data. However, for trivial monotonic signals, they struggle to perform accurate predictions and at the same time keep computational complexity within desired boundaries. This is because new observations are incorporated to the dictionary when they are far from what the algorithm has seen in the past. We propose a novel approach to kernel adaptive filtering that compares new observations against dictionary samples in terms of their unit-norm (normalised) versions, meaning that new observations that look like previous samples but have a different magnitude are not added to the dictionary. We achieve this by proposing the unit-norm Gaussian kernel and define a sparsification criterion for this novel kernel. This new methodology is validated on two real-world datasets against standard KAF in terms of the normalised mean square error and the dictionary size.Comment: Accepted at the IEEE Digital Signal Processing conference 201

Gravitational Wave Detection with High Frequency Phonon Trapping Acoustic Cavities

There are a number of theoretical predictions for astrophysical and cosmological objects, which emit high frequency ($10^6-10^9$~Hz) Gravitation Waves (GW) or contribute somehow to the stochastic high frequency GW background. Here we propose a new sensitive detector in this frequency band, which is based on existing cryogenic ultra-high quality factor quartz Bulk Acoustic Wave cavity technology, coupled to near-quantum-limited SQUID amplifiers at $20$~mK. We show that spectral strain sensitivities reaching $10^{-22}$ per $\sqrt{\text{Hz}}$ per mode is possible, which in principle can cover the frequency range with multiple ($>100$) modes with quality factors varying between $10^6-10^{10}$ allowing wide bandwidth detection. Due to its compactness and well established manufacturing process, the system is easily scalable into arrays and distributed networks that can also impact the overall sensitivity and introduce coincidence analysis to ensure no false detections.Comment: appears in Phys. Rev. D, (2014

Rotating Resonator-Oscillator Experiments to Test Lorentz Invariance in Electrodynamics

In this work we outline the two most commonly used test theories (RMS and SME) for testing Local Lorentz Invariance (LLI) of the photon. Then we develop the general framework of applying these test theories to resonator experiments with an emphasis on rotating experiments in the laboratory. We compare the inherent sensitivity factors of common experiments and propose some new configurations. Finally we apply the test theories to the rotating cryogenic experiment at the University of Western Australia, which recently set new limits in both the RMS and SME frameworks [hep-ph/0506074].Comment: Submitted to Lecture Notes in Physics, 36 pages, minor modifications, updated list of reference