arXiv subjects

Tom Kimpson

Publications and source records attributed to Tom Kimpson.

At least 19 recordsLinked to original sources

arXiv2026

Temporal Memory in Repeating Fast Radio Bursts: Epsilon-Machine Reconstruction of Causal Structure in Burst Timing

The emission mechanism of fast radio bursts (FRBs) remains unknown. Whether the bursts from a repeating FRB arrive at random or in a structured sequence is a key constraint on that mechanism. We apply $\varepsilon$-machine reconstruction, a tool from computational mechanics that infers the minimal model capturing all predictive information in a stochastic process. Applied to the waiting-time sequences of three repeating FRBs (FRB~20121102A and FRB~20201124A from FAST; FRB~20220912A from CHIME), the method yields the statistical complexity $C_\mu$, the minimum number of bits required for optimal prediction. Both FAST sources carry roughly one bit of temporal memory (significant against permutation surrogates, $p \leq 0.01$; per-source false-discovery-rate-adjusted $p \leq 0.028$), while FRB~20220912A is consistent with memoryless emission. FRB~20201124A's memory spans hours-to-days across four sessions, FRB~20121102A's spans hours-to-weeks across thirty-nine, and neither source shows defensible within-session predictive memory. For FRB~20121102A the ordering of those sessions is itself predictive (session-shuffle $p = 0.02$), whereas FRB~20201124A's signal reflects the contrast between heterogeneous sessions rather than their order. A simulated windowing test shows that CHIME's short transit observations would suppress comparable structure in the FAST data, leaving FRB~20220912A's null result ambiguous. This first application of $\varepsilon$-machine reconstruction to astrophysical transients yields a model-independent constraint: the bursting of at least two of these repeaters is not memoryless, but is governed by a hidden state that occupies distinct activity-rate regimes varying across observing sessions, behaviour that any viable physical model must reproduce.

astro-ph.HE↗

arXiv2026

Reduced-Precision Stochastic Simulation for Mathematical Biology

The stochastic simulation algorithm (SSA) is widely used to perform exact forward simulation of discrete stochastic processes in biology. However, the computational cost, driven by sequential event-by-event sampling across large ensembles, remains a computational barrier. We investigate whether reduced-precision floating-point arithmetic can accelerate SSA without degrading statistical fidelity, drawing on the success of reduced-precision methods in weather and climate modelling. We evaluate two strategies across five canonical models (birth--death, Schl\"{o}gl, Telegraph, dimerisation, repressilator): (i) mixed precision, computing propensities in 16-bit while maintaining accumulators in 32-bit; and (ii) uniform precision, performing all arithmetic in 16-bit. Mixed-precision SSA produces ensemble statistics that closely match the 64-bit reference for all models, as measured by Kolmogorov--Smirnov tests and Wasserstein distances. Under uniform precision, deterministic rounding introduces systematic biases across several models, with catastrophic failures in some cases. Stochastic rounding (SR) and propensity normalisation eliminate these biases, restoring distributional fidelity across all models tested (KS $p > 0.05$). Our results establish mixed-precision SSA with SR as a viable acceleration strategy for mathematical biology: 16-bit formats shrink per-variable data size by $2$--$4\times$ relative to \texttt{fp32}/\texttt{fp64}, yielding comparable reductions in memory footprint and up to $\sim 1.5\times$ wall-clock speedup on CPU hardware that lacks native 16-bit arithmetic. As a hardware-level acceleration, mixed-precision SSA complements algorithmic methods such as tau-leaping and maps naturally onto modern GPU and TPU architectures with native 16-bit arithmetic.

q-bio.QM↗

arXiv2026

Search for continuous gravitational waves from neutron stars in five globular clusters in the first part of the fourth LIGO-Virgo-KAGRA observing run

We present the results of directed searches for continuous gravitational waves from unknown neutron stars in five Milky Way globular clusters. We carry out these searches in the LIGO data from the first eight months of the fourth LIGO-Virgo-KAGRA observing run using the WEAVE semicoherent program, which sums matched-filter detection-statistic values over many time segments spanning the observation period. No gravitational wave signal is detected in the search band of 20-475 Hz. Injections of simulated continuous wave signals in the data indicate that we achieve the most sensitive results to date across most of the explored parameter space volume, obtaining median 95% confidence level upper limits as low as $\sim 4.2 \times 10^{-26}$ near 282 Hz for NGC 6397. We also derive upper limits on neutron star ellipticity and $r$-mode amplitudes, reaching $\lesssim 10^{-5}$ and $\lesssim 10^{-3}$, respectively, at frequencies above 200 Hz.

gr-qc↗

arXiv2026

Multiscale Modelling of Birth-Death Processes

Many biological systems exhibit multiscale dynamics, where some species occur in high copy numbers while others remain rare. This heterogeneity necessitates hybrid modelling approaches: deterministic models are computationally efficient but inaccurate for low-count species, while fully stochastic simulations are accurate but prohibitively expensive. Threshold-based hybrid methods, such as the Jump--Switch--Flow (JSF) algorithm, address this by simulating low-count species stochastically and high-count species deterministically, switching at a user-chosen threshold $\Omega$. In such methods, the choice of $\Omega$ controls the trade-off between computational cost and accuracy, but is typically made by trial-and-error: there is no principled way to choose $\Omega$ a priori for a given observable of interest. We close this gap for extinction probability. Our contribution is a computable, method-agnostic error bound that quantifies the discrepancy introduced by the threshold and yields an explicit rule for selecting $\Omega$ to meet a user-specified error tolerance. We formalise JSF as a piecewise-deterministic Markov process and derive backward equations for extinction under exact and hybrid dynamics. Near extinction boundaries, the complex nonlinear dynamics reduce to tractable time-inhomogeneous linear birth--death processes; this structure yields a rigorous error decomposition into early and late excursions, whose dominant term becomes a fast, actionable heuristic requiring only the solution of a scalar Riccati equation. Monte Carlo studies on a stochastic Lotka--Volterra model confirm that the heuristic reliably upper-bounds the empirical error in extinction probability across a wide parameter range. The framework depends only on the birth and death rates near extinction, not on the specific simulation method, and therefore applies beyond JSF to any threshold-based hybrid scheme.

q-bio.PE↗

arXiv2025

Is there a retrograde accretion disk around 4U 1626$-$67? Tracking torque reversals with a state-space model

X-ray timing studies of the persistent, Galactic, accretion-powered pulsar 4U 1626$-$67 reveal torque reversals, during which the pulse frequency $\nu(t)$ alternates between multiyear episodes of secular acceleration and deceleration, separated by transitions lasting $\lesssim 150 \, \rm{days}$. Here an unscented Kalman filter is applied to track the $\nu(t)$ fluctuations observed in 22.7 years (3340 samples) of publicly available Compton Gamma-Ray Observatory and Fermi Gamma-Ray Space Telescope data to test the canonical picture of magnetocentrifugal accretion for consistency with prograde-prograde and retrograde-prograde accretion disk configurations on either side of the 2008 torque reversal. It is found that the retrograde-prograde model is preferred, with a log Bayes factor equal to 0.44 and maximum a posteriori log likelihood ratio equal to 2.5. The mass accretion rate $Q(t)$ and magnetocentrifugal fastness $\omega(t)$ transition smoothly between episodes of deceleration and acceleration; $Q(t)$ shifts by $\leq 0.34 \, {\rm dex}$ across the reversal, and one measures $\omega(t) \approx 0.25$ and $\omega(t) \approx 0.30$ during deceleration and acceleration, respectively. The angular acceleration $\dot{\Omega}(t)$ satisfies $-9 \lesssim \dot{\Omega}(t)/(10^{-12} \, \rm{rad \, s^{-2}}) \lesssim -5$ and $2 \lesssim \dot{\Omega}(t)/(10^{-12} \, \rm{rad \, s^{-2}}) \lesssim 9$ before and after the 2008 reversal, respectively, compared to $\dot{\Omega} \approx -3.0 \times 10^{-12} \, \rm{rad \, s^{-2}}$ before reversal and $\dot{\Omega} \approx 2.5 \times 10^{-12} \, \rm{rad \, s^{-2}}$ after reversal, as inferred from previous long-term X-ray timing and spectral analysis of 4U 1626$-$67.

astro-ph.HE↗

arXiv2025

Argus: JAX state-space filtering for gravitational wave detection with a pulsar timing array

Argus is a high-performance Python package for detecting and characterising nanohertz gravitational waves in pulsar timing array data. The package provides a complete Bayesian inference framework based on state-space models, using Kalman filtering for efficient likelihood evaluation. Argus leverages JAX for just-in-time compilation, GPU acceleration, and automatic differentiation, facilitating rapid Bayesian inference with gradient-based samplers. The state-space approach provides a computationally efficient alternative to traditional frequency-domain methods, offering linear scaling with the number of pulse times-of-arrival, and natural handling of non-stationary processes.

astro-ph.IM↗

arXiv2025

Observing Rayleigh-Taylor stable and unstable accretion through a Kalman filter analysis of X-ray pulsars in the Small Magellanic Cloud

Global, three-dimensional, magnetohydrodynamic simulations of Rayleigh-Taylor instabilities at the disk-magnetosphere boundary of rotating, magnetized, compact stellar objects reveal that accretion occurs in three regimes: the stable regime, the chaotic unstable regime, and the ordered unstable regime. Here we track stochastic fluctuations in the pulse period $P(t)$ and aperiodic X-ray luminosity $L(t)$ time series of 24 accretion-powered pulsars in the Small Magellanic Cloud using an unscented Kalman filter to analyze Rossi X-ray Timing Explorer data. We measure time-resolved histories of the magnetocentrifugal fastness parameter $\omega(t)$ and we connect $\omega(t)$ with the three Rayleigh-Taylor accretion regimes. The 24 objects separate into two distinct groups, with 10 accreting in the stable regime, and 14 accreting in the ordered unstable regime. None of the 24 objects except SXP 293 visit the chaotic unstable regime for sustained intervals, although several objects visit it sporadically. The Kalman filter output also reveals a positive temporal cross-correlation between $\omega(t)$ and the independently measured pulse amplitude $A(t)$, which agrees with simulation predictions regarding the pulse-forming behavior of magnetospheric funnel flows in the three accretion regimes.

astro-ph.HE↗

arXiv2025

State-space algorithm for detecting the nanohertz gravitational wave background

The stochastic gravitational wave background (SGWB) can be observed in the nanohertz band using a pulsar timing array (PTA). Here a computationally efficient state-space framework is developed for analysing SGWB data, in which the stochastic gravitational wave strain at Earth is tracked with a non-linear Kalman filter and separated simultaneously from intrinsic, achromatic pulsar spin wandering. The filter is combined with a nested sampler to estimate the parameters of the model, and to calculate a Bayes factor for selecting between models with and without a SGWB. The procedure extends previous state-space formulations of PTA data analysis applied to individually resolvable binary black hole sources. The performance of the new algorithm is tested on synthetic data from the first International PTA Mock Data Challenge. It is shown that the algorithm distinguishes a SGWB from pure noise for $A_{\rm gw} \geq 3 \times 10^{-14}$, where $A_{\rm gw}$ denotes the standard normalization factor for a power spectral density with power-law exponent $-13/3$. Additional, systematic validation tests are also performed with synthetic data generated independently by adjusting the injected parameters to cover astrophysically plausible ranges. Full posterior distributions are recovered and tested for accuracy. The state-space procedure is memory-light and evaluates the likelihood for a standard-sized PTA dataset in $\lesssim 10^{-1}$ s without optimization on a standard central processing unit.

astro-ph.IM↗

arXiv2024

Adaptive cancellation of mains power interference in continuous gravitational wave searches with a hidden Markov model

Continuous gravitational wave searches with terrestrial, long-baseline interferometers are hampered by long-lived, narrowband features in the power spectral density of the detector noise, known as lines. Candidate GW signals which overlap spectrally with known lines are typically vetoed. Here we demonstrate a line subtraction method based on adaptive noise cancellation, using a recursive least squares algorithm, a common approach in electrical engineering applications such as audio and biomedical signal processing. We validate the line subtraction method by combining it with a hidden Markov model (HMM), a standard continuous wave search tool, to detect an injected continuous wave signal with an unknown and randomly wandering frequency, which overlaps with the mains power line at $60 \, {\rm Hz}$ in the Laser Interferometer Gravitational Wave Observatory (LIGO). The performance of the line subtraction method is tested on an injected continuous wave signal obscured by (a) synthetic noise data with both Gaussian and non-Gaussian components, and (b) real noise data obtained from the LIGO Livingston detector. In both cases, before applying the line subtraction method the HMM does not detect the injected continuous wave signal. After applying the line subtraction method the mains power line is suppressed by 20--40 dB, and the HMM detects the underlying signal, with a time-averaged root-mean-square error in the frequency estimate of $\sim 0.05 $ Hz. The performance of the line subtraction method with respect to the characteristics of the 60 Hz line and the control parameters of the recursive least squares algorithm is quantified in terms of receiver operating characteristic curves.

gr-qc↗

arXiv2024

State-space analysis of a continuous gravitational wave source with a pulsar timing array: inclusion of the pulsar terms

Pulsar timing arrays can detect continuous nanohertz gravitational waves emitted by individual supermassive black hole binaries. The data analysis procedure can be formulated within a time-domain, state-space framework, in which the radio timing observations are related to a temporal sequence of latent states, namely the intrinsic pulsar spin frequency. The achromatic wandering of the pulsar spin frequency is tracked using a Kalman filter concurrently with the pulse frequency modulation induced by a gravitational wave from a single source. The modulation is the sum of terms proportional to the gravitational wave strain at the Earth and at every pulsar in the array. Here we generalize previous state-space formulations of the pulsar timing array problem to include the pulsar terms; that is, we copy the pulsar terms from traditional, non-state-space analyses over to the state-space framework. The performance of the generalized Kalman filter is tested using astrophysically representative software injections in Gaussian measurement noise. It is shown that including the pulsar terms corrects for previously identified biases in the parameter estimates (especially the sky position of the source) which also arise in traditional matched-filter analyses that exclude the pulsar terms. Additionally, including the pulsar terms decreases the minimum detectable strain by $14\%$. Overall, the study verifies that the pulsar terms do not raise any special extra impediments for the state-space framework, beyond those studied in traditional analyses. The inspiral-driven evolution of the wave frequency at the Earth and at the retarded time at every pulsar in the array is also investigated.

astro-ph.HE↗

arXiv2024

Kalman tracking and parameter estimation of continuous gravitational waves with a pulsar timing array

Continuous nanohertz gravitational waves from individual supermassive black hole binaries may be detectable with pulsar timing arrays. A novel search strategy is developed, wherein intrinsic achromatic spin wandering is tracked simultaneously with the modulation induced by a single gravitational wave source in the pulse times of arrival. A two-step inference procedure is applied within a state-space framework, such that the modulation is tracked with a Kalman filter, which then provides a likelihood for nested sampling. The procedure estimates the static parameters in the problem, such as the sky position of the source, without fitting for ensemble-averaged statistics such as the power spectral density of the timing noise, and therefore complements traditional parameter estimation methods. It also returns the Bayes factor relating a model with a single gravitational wave source to one without, complementing traditional detection methods. It is shown via astrophysically representative software injections in Gaussian measurement noise that the procedure distinguishes a gravitational wave from pure noise down to a characteristic wave strain of $h_0 \approx 2 \times 10^{-15}$. Full posterior distributions of model parameters are recovered and tested for accuracy. There is a bias of $\approx 0.3$ rad in the marginalised one-dimensional posterior for the orbital inclination $\iota$, introduced by dropping the so-called `pulsar terms'. Smaller biases $\lesssim 10 \%$ are also observed in other static parameters.

astro-ph.HE↗

arXiv2024

Measuring the magnetic dipole moment and magnetospheric fluctuations of accretion-powered pulsars in the Small Magellanic Cloud with an unscented Kalman filter

Many accretion-powered pulsars rotate in magnetocentrifugal disequilibrium, spinning up or down secularly over multi-year intervals. The magnetic dipole moment $\mu$ of such systems cannot be inferred uniquely from the time-averaged aperiodic X-ray flux $\langle L(t) \rangle$ and pulse period $\langle P(t) \rangle$, because the radiative efficiency of the accretion is unknown and degenerate with the mass accretion rate. Here we circumvent the degeneracy by tracking the fluctuations in the unaveraged time series $L(t)$ and $P(t)$ using an unscented Kalman filter, whereupon $\mu$ can be estimated uniquely, up to the uncertainties in the mass, radius and distance of the star. The analysis is performed on Rossi X-ray Timing Explorer observations for $24$ X-ray transients in the Small Magellanic Cloud, which have been monitored regularly for $\sim 16$ years. As well as independent estimates of $\mu$, the analysis yields time-resolved histories of the mass accretion rate and the Maxwell stress at the disk-magnetosphere boundary for each star, and hence auto- and cross-correlations involving the latter two state variables. The inferred fluctuation statistics convey important information about the complex accretion physics at the disk-magnetosphere boundary.

astro-ph.HE↗

arXiv2023

RelativisticDynamics.jl: Relativistic Spin-Orbital Dynamics in Julia

RelativisticDynamics.jl is an open-source Julia package for relativistic spin-orbital dynamics in the gravitational strong-field of a Kerr spacetime. Existing codes for modelling the dynamics of spinning objects like pulsars in the strong-field regime are generally lacking, since such systems occupy an intermediate regime that is generally overlooked. At the "low" end of this regime there are post-Newtonian descriptions which neglect the influence of the pulsar spin on the underlying spacetime metric ("spin-curvature" coupling). At the "high" end there are the full numerical relativity solutions which are primarily applicable toe two black holes with a mass ratio $\mathcal{O}(1)$, and are computationally intractable for pulsar systems observed over a large number of orbital cycles. RelativisticDynamics.jl aims to bridge this gap by providing a modern, fast code for accurate numerical evolution of spinning relativistic systems via the Mathisson-Papetrou-Dixon formalism. Julia is a modern language that solves the "two language problem", enabling fast dynamic typing and JIT compilation on conjunction with petaflop performance, comparable with numerical languages that are better known in the astrophysics community such as C or Fortran. RelativisticDynamics.jl is written to be fully type flexible, being able to support arbitrary number formats, and fully differentiable via automatic differentiation.

astro-ph.HE↗

arXiv2022

Deep learning for quality control of surface physiographic fields using satellite Earth observations

A purposely built deep learning algorithm for the Verification of Earth-System ParametERisation (VESPER) is used to assess recent upgrades of the global physiographic datasets underpinning the quality of the Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF), which is used both in numerical weather prediction and climate reanalyses. A neural network regression model is trained to learn the mapping between the surface physiographic dataset plus the meteorology from ERA5, and the MODIS satellite skin temperature observations. Once trained, this tool is applied to rapidly assess the quality of upgrades of the land-surface scheme. Upgrades which improve the prediction accuracy of the machine learning tool indicate a reduction of the errors in the surface fields used as input to the surface parametrisation schemes. Conversely, incorrect specifications of the surface fields decrease the accuracy with which VESPER can make predictions. We apply VESPER to assess the accuracy of recent upgrades of the permanent lake and glaciers covers as well as planned upgrades to represent seasonally varying water bodies (i.e. ephemeral lakes). We show that for grid-cells where the lake fields have been updated, the prediction accuracy in the land surface temperature (i.e mean absolute error difference between updated and original physiographic datasets) improves by 0.37 K on average, whilst for the subset of points where the lakes have been exchanged for bare ground (or vice versa) the improvement is 0.83 K. We also show that updates to the glacier cover improve the prediction accuracy by 0.22 K. We highlight how neural networks such as VESPER can assist the research and development of surface parameterizations and their input physiography to better represent Earth's surface couples processes in weather and climate models.

physics.ao-ph↗

arXiv2022

Climate Change Modelling at Reduced Float Precision with Stochastic Rounding

Reduced precision floating point arithmetic is now routinely deployed in numerical weather forecasting over short timescales. However the applicability of these reduced precision techniques to longer timescale climate simulations - especially those which seek to describe a dynamical, changing climate - remains unclear. We investigate this question by deploying a global atmospheric, coarse resolution model known as SPEEDY to simulate a changing climate system subject to increased $\text{CO}_2$ concentrations, over a 100 year timescale. Whilst double precision is typically the operational standard for climate modelling, we find that reduced precision solutions (Float32, Float16) are sufficiently accurate. Rounding the finite precision floats stochastically, rather than using the more common ``round-to-nearest" technique, notably improves the performance of the reduced precision solutions. Over 100 years the mean bias error (MBE) in the global mean surface temperature (precipitation) relative to the double precision solution is $+2 \times 10^{-4}$K ($-8 \times 10^{-5}$ mm/6hr) at single precision and $-3.5\times 10^{-2}$ K($-1 \times 10^{-2}$ mm/6hr) at half precision, whilst the inclusion of stochastic rounding reduced the half precision error to +1.8 $\times 10^{-2}$ K ($-8 \times10^{-4}$ mm/6hr). By examining the resultant climatic distributions that arise after 100 years, the difference in the expected value of the global surface temperature, relative to the double precision solution is $\leq 5 \times 10^{-3}$ K and for precipitation $8 \times 10^{-4}$ mm/6h when numerically integrating at half precision with stochastic rounding. Areas of the model which notably improve due to the inclusion of stochastic over deterministic rounding are also explored and discussed. [abridged]

physics.ao-ph↗

arXiv2021

Towards Machine Learning-Based Meta-Studies: Applications to Cosmological Parameters

We develop a new model for automatic extraction of reported measurement values from the astrophysical literature, utilising modern Natural Language Processing techniques. We use this model to extract measurements present in the abstracts of the approximately 248,000 astrophysics articles from the arXiv repository, yielding a database containing over 231,000 astrophysical numerical measurements. Furthermore, we present an online interface (Numerical Atlas) to allow users to query and explore this database, based on parameter names and symbolic representations, and download the resulting datasets for their own research uses. To illustrate potential use cases we then collect values for nine different cosmological parameters using this tool. From these results we can clearly observe the historical trends in the reported values of these quantities over the past two decades, and see the impacts of landmark publications on our understanding of cosmology.

astro-ph.IM↗

arXiv2020

Radio timing in a millisecond pulsar-extreme/intermediate mass ratio binary system

Radio timing observations of a millisecond pulsar in orbit around the Galactic centre black hole (BH) or a BH at the centre of globular clusters could answer foundational questions in astrophysics and fundamental physics. Pulsar radio astronomy typically employs the post-Keplerian approximation to determine the system parameters. However, in the strong gravitational field around the central BH, higher order relativistic effects may become important. We compare the pulsar timing delays given by the post-Keplerian approximation with those given by a relativistic timing model. We find significant discrepancies between the solutions derived for the Einstein delay and the propagation delay (i.e. Roemer and Sharpiro delay) compared to the fully relativistic solutions. Correcting for these higher order relativistic effects is essential in order to construct accurate radio timing models for pulsar systems at the Galactic centre and the centre of globular clusters and informing issues related to their detection.

astro-ph.HE↗

arXiv2020

Orbital spin dynamics of a millisecond pulsar around a massive black hole with an general mass quadrupole

We investigate the spin dynamics of a millisecond pulsar (MSP) in compact orbit around a Kerr-like massive black hole with an general mass quadrupole. We use the Mathisson-Papetrou-Dixon formulation to compute the orbital and spin evolution of the MSP, accounting for the non-linear interaction of the pulsar's energy-momentum tensor on the background spacetime metric. We investigate how the MSP spin and BH quadrupole moment manifest in the pulsar spin-orbital dynamics. We discuss the astrophysical observational implications of these spin and orbital dynamics on the timing of a radio pulsar in an Extreme Mass Ratio Binary, e.g. a Galactic Centre pulsar. In particular, notable timing variations in the Einstein delay and Roemer delay are observed, along with modifications to the pulsar pulse profile.

astro-ph.HE↗