Optimal Approximations of the Frequency Moments

We give a one-pass, O~(m^{1-2/k})-space algorithm for estimating the k-th frequency moment of a data stream for any real k>2. Together with known lower bounds, this resolves the main problem left open by Alon, Matias, Szegedy, STOC'96. Our algorithm enables deletions as well as insertions of stream elements.

Time-Frequency Representations for Speech Signals

This work addresses two related questions. The first question is what joint time-frequency energy representations are most appropriate for auditory signals, in particular, for speech signals in sonorant regions. The quadratic transforms of the signal are examined, a large class that includes, for example, the spectrograms and the Wigner distribution. Quasi-stationarity is not assumed, since this would neglect dynamic regions. A set of desired properties is proposed for the representation: (1) shift-invariance, (2) positivity, (3) superposition, (4) locality, and (5) smoothness. Several relations among these properties are proved: shift-invariance and positivity imply the transform is a superposition of spectrograms; positivity and superposition are equivalent conditions when the transform is real; positivity limits the simultaneous time and frequency resolution (locality) possible for the transform, defining an uncertainty relation for joint time-frequency energy representations; and locality and smoothness tradeoff by the 2-D generalization of the classical uncertainty relation. The transform that best meets these criteria is derived, which consists of two-dimensionally smoothed Wigner distributions with (possibly oriented) 2-D guassian kernels. These transforms are then related to time-frequency filtering, a method for estimating the time-varying 'transfer function' of the vocal tract, which is somewhat analogous to ceptstral filtering generalized to the time-varying case. Natural speech examples are provided. The second question addressed is how to obtain a rich, symbolic description of the phonetically relevant features in these time-frequency energy surfaces, the so-called schematic spectrogram. Time-frequency ridges, the 2-D analog of spectral peaks, are one feature that is proposed. If non-oriented kernels are used for the energy representation, then the ridge tops can be identified, with zero-crossings in the inner product of the gradient vector and the direction of greatest downward curvature. If oriented kernels are used, the method can be generalized to give better orientation selectivity (e.g., at intersecting ridges) at the cost of poorer time-frequency locality. Many speech examples are given showing the performance for some traditionally difficult cases: semi-vowels and glides, nasalized vowels, consonant-vowel transitions, female speech, and imperfect transmission channels.

The Geometry of Frequency Squares

Mavron, Vassili; Jungnickel, D.; McDonough, T.P., (2001) 'The Geometry of Frequency Squares', Journal of Combinatorial Theory, Series A 96, pp.376-387 RAE2008

Frequency of word-use predicts rates of lexical evolution throughout Indo-European history

Mark Pagel, Quentin D. Atkinson & Andrew Meade (2007). Frequency of word-use predicts rates of lexical evolution throughout Indo-European history. Nature, 449,717-720. RAE2008

Frequency-Dependent Phase Transitions in the Coordination of Human Bimanual Tasks

The 2-channel Ellias-Grossberg neural pattern generator of Cohen, Grossberg, and Pribe [1] is shown to simulate data from human bimanual coordination tasks in which anti-phase oscillations at low frequencies spontaneously switch to in-phase oscillations at high frequencies, in-phase oscillations can be performed at both low and high frequencies, phase fluctuations occur at the anti-phase to in-phase transition, and a "seagull effect" of larger errors occurs at intermediate phases.

A Neural Pattern Generator that Exhibits Frequency-Dependent In-Phase and Anti-Phase Oscillations

This article describes a. neural pattern generator based on a cooperative-competitive feedback neural network. The two-channel version of the generator supports both in-phase and anti-phase oscillations. A scalar arousal level controls both the oscillation phase and frequency. As arousal increases, oscillation frequency increases and bifurcations from in-phase to anti-phase, or anti-phase to in-phase oscillations can occur. Coupled versions of the model exhibit oscillatory patterns which correspond to the gaits used in locomotion and other oscillatory movements by various animals.

Dual-layer frequency-selective grid polarizers on thin-film substrates for THz applications

Dual-layer frequency-selective subwavelength grid polarizers on thin-film dielectric substrates are proposed for THz and sub-THz applications. The dual-layer grids possess enhanced (squared) polarizing efficiency at a sequence of discrete frequencies in reflection and within extended frequency bands in transmission as compared to conventional single grids.

The influence of thermal plasma profiles on low-frequency Alfvén eigenmode dynamics in a tokamak

The confinement of fast particles, present in a tokamak plasma as nuclear fusion products and through external heating, will be essential for any future fusion reactor. Fast particles can be expelled from the plasma through their interaction with Alfvén eigenmode (AE) instabilities. AEs can exist in gaps in the Alfvén continuum created by plasma equilibrium non-uniformities. In the ASDEX Upgrade tokamak, low-frequency modes in the frequency range from f ≈ 10 − 90kHz, including beta-induced Alfvén eigenmodes (BAEs) and lower frequency modes with mixed Alfvén and acoustic polarisations, have been observed. These exist in gaps in the Alfvén continuum opened up by geodesic curvature and finite plasma compressibility. In this thesis, a kinetic dispersion relation is solved numerically to investigate the influence of thermal plasma profiles on the evolution of these low-frequency modes during the sawtooth cycle. Using information gained from various experimental sources to constrain the equilibrium reconstructions, realistic safety factor profiles are obtained for the analysis using the CLISTE code. The results for the continuum accumulation point evolution are then compared with experimental results from ASDEX Upgrade during periods of ICRH only as well as for periods with both ICRH and ECRH applied simultaneously. It is found that the diamagnetic frequency plays an important role in influencing the dynamics of BAEs and low-frequency acoustic Alfvén eigenmodes, primarily through the presence of gradients in the thermal plasma profiles. Different types of modes that are observed during discharges heated almost exclusively by ECRH were also investigated. These include electron internal transport barrier (eITB) driven modes, which are observed to coincide with the occurrence of an eITB in the plasma during the low-density phase of the discharge. Also observed are BAE-like modes and edge-TAEs, both of which occur during the H-mode phase of the discharge.

Correcting the errors: Volatility forecast evaluation using high-frequency data and realized volatilities

We develop general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit recent nonparametric asymptotic distributional results, are both easy-to-implement and highly accurate in empirically realistic situations. We also illustrate that properly accounting for the measurement errors in the volatility forecast evaluations reported in the existing literature can result in markedly higher estimates for the true degree of return volatility predictability.