arXiv subjects

Timothy Roberts

Publications and source records attributed to Timothy Roberts.

5 recordsLinked to original sources

arXiv2024

Homoclinic snaking of contact defects in reaction-diffusion equations

We apply spatial dynamical-systems techniques to prove that certain spatiotemporal patterns in reversible reaction-diffusion equations undergo snaking bifurcations. That is, in a narrow region of parameter space, countably many branches of patterned states coexist that connect at towers of saddle-node bifurcations. Our patterns of interest are contact defects, which are 1-dimensional time-periodic patterns with a spatially oscillating core region that at large distances from the origin in space resemble pure temporally oscillatory states and arise as natural analogues of spiral and target waves in one spatial dimension. We show that these solutions lie on snaking branches that have a more complex structure than has been seen in other contexts. In particular, we predict the existence of families of asymmetric travelling defect solutions with arbitrary background phase offsets, in addition to symmetric standing target and spiral patterns. We prove the presence of these additional patterns by reconciling results in classic ODE studies with results from the spatial-dynamics study of patterns in PDEs and using geometrical information contained in the stable and unstable manifolds of the background wavetrains and their natural equivariance structure.

math.DS↗

arXiv2020

Deep Learning-Based Single-Ended Objective Quality Measures for Time-Scale Modified Audio

Objective evaluation of audio processed with Time-Scale Modification (TSM) is seeing a resurgence of interest. Recently, a labelled time-scaled audio dataset was used to train an objective measure for TSM evaluation. This DE measure was an extension of Perceptual Evaluation of Audio Quality, and required reference and test signals. In this paper, two single-ended objective quality measures for time-scaled audio are proposed that do not require a reference signal. Data driven features are created by either a convolutional neural network (CNN) or a bidirectional gated recurrent unit (BGRU) network and fed to a fully-connected network to predict subjective mean opinion scores. The proposed CNN and BGRU measures achieve an average Root Mean Squared Error of 0.608 and 0.576, and a mean Pearson correlation of 0.771 and 0.794, respectively. The proposed measures are used to evaluate TSM algorithms, and comparisons are provided for 16 TSM implementations. The objective measure is available at https://www.github.com/zygurt/TSM.

eess.AS↗

arXiv2020

An Objective Measure of Quality for Time-Scale Modification of Audio

Objective evaluation of audio processed with Time-Scale Modification (TSM) remains an open problem. Recently, a dataset of time-scaled audio with subjective quality labels was published and used to create an initial objective measure of quality. In this paper, an improved objective measure of quality for time-scaled audio is proposed. The measure uses hand-crafted features and a fully connected network to predict subjective mean opinion scores. Basic and Advanced Perceptual Evaluation of Audio Quality features are used in addition to nine features specific to TSM artefacts. Six methods of alignment are explored, with interpolation of the reference magnitude spectrum to the length of the test magnitude spectrum giving the best performance. The proposed measure achieves a mean Root Mean Squared Error of 0.487 and a mean Pearson correlation of 0.865, equivalent to 98th and 82nd percentiles of subjective sessions respectively. The proposed measure is used to evaluate time-scale modification algorithms, finding that Elastique gives the highest objective quality for Solo instrument and voice signals, while the Identity Phase-Locking Phase Vocoder gives the highest objective quality for music signals and the best overall quality. The objective measure is available at https://www.github.com/zygurt/TSM.

eess.AS↗

arXiv2020

A time-scale modification dataset with subjective quality labels

Time Scale Modification (TSM) is a well-researched field; however, no effective objective measure of quality exists. This paper details the creation, subjective evaluation, and analysis of a dataset for use in the development of an objective measure of quality for TSM. Comprised of two parts, the training component contains 88 source files processed using six TSM methods at 10 time scales, while the testing component contains 20 source files processed using three additional methods at four time scales. The source material contains speech, solo harmonic and percussive instruments, sound effects, and a range of music genres. Ratings (42 529) were collected from 633 sessions using laboratory and remote collection methods. Analysis of results shows no correlation between age and quality of rating; expert and non-expert listeners to be equivalent; minor differences between participants with and without hearing issues; and minimal differences between testing modalities. A comparison of published objective measures and subjective scores shows the objective measures to be poor indicators of subjective quality. Initial results for a retrained objective measure of quality are presented with results approaching average root mean squared error loss and Pearson correlation values of subjective sessions. The labeled dataset is available at http://ieee-dataport.org/1987.

eess.AS↗

arXiv2014

A spectral-timing model for ULXs in the super-critical regime

Ultraluminous X-ray sources (ULXs) with luminosities lying between ~3x10^{39} - 2x10^{40} erg/s represent a contentious sample of objects as their brightness, together with a lack of unambiguous mass estimates for the vast majority of the central objects, leads to a degenerate scenario where the accretor could be a stellar remnant (black hole or neutron star) or intermediate mass black hole (IMBH). Recent, high-quality observations imply that the presence of IMBHs in the majority of these objects is unlikely unless the accretion flow somehow deviates strongly from expectation based on objects with known masses. On the other-hand, physically motivated models for super-critical inflows can re-create the observed X-ray spectra and their evolution, although have been lacking a robust explanation for their variability properties. In this paper we include the effect of a partially inhomogeneous wind that imprints variability onto the X-ray emission via two distinct methods. The model is heavily dependent on both inclination to the line-of-sight and mass accretion rate, resulting in a series of qualitative and semi-quantitative predictions. We study the time-averaged spectra and variability of a sample of well-observed ULXs, finding that the source behaviours can be explained by our model in both individual cases as well as across the entire sample, specifically in the trend of hardness-variability power. We present the covariance spectra for these sources for the first time, which shed light on the correlated variability and issues associated with modelling broad ULX spectra.

astro-ph.HE↗