Publications (31)
The Rise and Fall of the King: The Correlation between FO Aquarii's Low States and the White Dwarf's Spindown
Colin Littlefield, Peter Garnavich, Mark R. Kennedy +45
The intermediate polar FO Aquarii (FO Aqr) experienced its first-reported low-accretion states in 2016, 2017, and 2018, and using newly available photographic plates, we identify p…
Single-seed generation of Brownian paths and integrals for adaptive and high order SDE solvers
Andraž JelinÄiÄ, James Foster, Patrick Kidger
Despite the success of adaptive time-stepping in ODE simulation, it has so far seen few applications for Stochastic Differential Equations (SDEs). To simulate SDEs adaptively, meth…
Neural SDEs as Infinite-Dimensional GANs
Patrick Kidger, James Foster, Xuechen Li +2
Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics. However, a fundamental limitation has been that such models have typically bee…
HD 5501: A Rapidly Evolving Interacting Eclipsing Binary with a Variable Light Curve and H Emission
Richard O. Gray, Christopher. J. Corbally, Sean Curry +19
HD~5501, a hitherto little studied eclipsing binary with an early A-type primary, has been caught in a short-lived, astrophysically interesting phase of its binary evolution. Recen…
Spectral evolution of the narrow emission line components in optical during the 2022 nova eruption of U Scorpii
Katsuki Muraoka, Naoto Kojiguchi, Junpei Ito +20
There remains debate over whether the accretion disk survives or is entirely disrupted after the nova eruption. In our previous paper, Muraoka et al. (2024, PASJ, 76, 293) have pho…
Reachability Aware Capture Regions with Time Adjustment and Cross-Over for Step Recovery
Robert Griffin, James Foster, Stefan Fasano +2
For humanoid robots to live up to their potential utility, they must be able to robustly recover from instabilities. In this work, we propose a number of balance enhancements to en…
An optimal polynomial approximation of Brownian motion
James Foster, Terry Lyons, Harald Oberhauser
In this paper, we will present a strong (or pathwise) approximation of standard Brownian motion by a class of orthogonal polynomials. The coefficients that are obtained from the ex…
The shifted ODE method for underdamped Langevin MCMC
James Foster, Terry Lyons, Harald Oberhauser
In this paper, we consider the underdamped Langevin diffusion (ULD) and propose a numerical approximation using its associated ordinary differential equation (ODE). When used as a…
Underdamped Langevin MCMC with third order convergence
Maximilian Scott, Dáire O'Kane, Andraž JelinÄiÄ +1
In this paper, we propose a new numerical method for the underdamped Langevin diffusion (ULD) and present a non-asymptotic analysis of its sampling error in the 2-Wasserstein dista…
Improving Optimal Power Flow Relaxations Using 3-Cycle Second-Order Cone Constraints
Frederik Geth, James Foster
This paper develops a novel second order cone relaxation of the semidefinite programming formulation of optimal power flow, that does not imply the `angle relaxation'. We build on…
Approximating the signature of Brownian motion for high order SDE simulation
James Foster
The signature is a collection of iterated integrals describing the "shape" of a path. It appears naturally in the Taylor expansions of controlled differential equations and, as a c…
An asymptotic radius of convergence for the Loewner equation and simulation of traces via splitting
James Foster, Terry Lyons, Vlad Margarint
In this paper, we shall study the convergence of Taylor approximations for the backward Loewner differential equation (driven by Brownian motion) near the origin. More concretely,…
Strong Stochastic Flow Maps
Sam McCallum, Zander W. Blasingame, Timothy Herschell +3
Flow and diffusion models generate high-quality samples in many modalities; however, many network evaluations are required during inference due to numerical integration of an under…
Physically Consistent Online Inertial Adaptation for Humanoid Loco-manipulation
James Foster, Stephen McCrory, Christian DeBuys +2
The ability to accomplish manipulation and locomotion tasks in the presence of significant time-varying external loads is a remarkable skill of humans that has yet to be replicated…
Spectroscopic Analysis of the 2025 Eclipse of the Symbiotic Binary V1413 Aquilae
David Boyd, James Foster, Forrest Sims +12
We report on a coordinated campaign by amateur astronomers using a combination of high and low resolution spectroscopy to observe the 2025 eclipse of the symbiotic binary V1413 Aql…
TESS photometry of the nova eruption in V606 Vul: asymmetric photosphere and multiple ejections?
Kirill V. Sokolovsky, Elias Aydi, Konstantin Malanchev +70
Lightcurves of many classical novae deviate from the canonical "fast rise - smooth decline" pattern and display complex variability behavior. We present the first TESS-space-photom…
Efficient, Dynamic Locomotion through Step Placement with Straight Legs and Rolling Contacts
Stefan Fasano, James Foster, Sylvain Bertrand +2
For humans, fast, efficient walking over flat ground represents the vast majority of locomotion that an individual experiences on a daily basis, and for an effective, real-world hu…
On the convergence of adaptive approximations for stochastic differential equations
James Foster, Andraž JelinÄiÄ
In this paper, we study numerical approximations for stochastic differential equations (SDEs) that use adaptive step sizes. In particular, we consider a general setting where decis…
Brownian bridge expansions for Lévy area approximations and particular values of the Riemann zeta function
James Foster, Karen Habermann
We study approximations for the Lévy area of Brownian motion which are based on the Fourier series expansion and a polynomial expansion of the associated Brownian bridge. Comparin…
Efficient and Accurate Gradients for Neural SDEs
Patrick Kidger, James Foster, Xuechen Li +1
Neural SDEs combine many of the best qualities of both RNNs and SDEs: memory efficient training, high-capacity function approximation, and strong priors on model space. This makes…
The Signature Kernel is the solution of a Goursat PDE
Cristopher Salvi, Thomas Cass, James Foster +2
Recently, there has been an increased interest in the development of kernel methods for learning with sequential data. The signature kernel is a learning tool with potential to han…
Neural Rough Differential Equations for Long Time Series
James Morrill, Cristopher Salvi, Patrick Kidger +2
Neural controlled differential equations (CDEs) are the continuous-time analogue of recurrent neural networks, as Neural ODEs are to residual networks, and offer a memory-efficient…
Neural Controlled Differential Equations for Irregular Time Series
Patrick Kidger, James Morrill, James Foster +1
Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equat…
Realistic Differentially-Private Transmission Power Flow Data Release
David Smith, Frederik Geth, Elliott Vercoe +5
For the modeling, design and planning of future energy transmission networks, it is vital for stakeholders to access faithful and useful power flow data, while provably maintaining…
Generative Modelling of Lévy Area for High Order SDE Simulation
Andraž JelinÄiÄ, Jiajie Tao, William F. Turner +3
It is well understood that, when numerically simulating SDEs with general noise, achieving a strong convergence rate better than (where h is the step size) requires t…
Reversible Deep Equilibrium Models
Sam McCallum, Kamran Arora, James Foster
Deep Equilibrium Models (DEQs) are an interesting class of implicit model where the model output is implicitly defined as the fixed point of a learned function. These models have b…
Holistic Cube Analysis: A Query Framework for Data Insights
Xi Wu, Shaleen Deep, Joe Benassi +11
Many data insight questions can be viewed as searching in a large space of tables and finding important ones, where the notion of importance is defined in some adhoc user defined m…
ARCANE: Scalable high-degree cubature formulae for simulating SDEs without Monte Carlo error
Peter Koepernik, Thomas Coxon, James Foster
Monte Carlo sampling is the standard approach for estimating properties of solutions to stochastic differential equations (SDEs), but accurate estimates require huge sample sizes.…
Efficient, Accurate and Stable Gradients for Neural ODEs
Sam McCallum, James Foster
Training Neural ODEs requires backpropagating through an ODE solve. The state-of-the-art backpropagation method is recursive checkpointing that balances recomputation with memory c…
Photometry and Spectroscopy of the Symbiotic Binary V1413 Aquilae during the 2024 Eclipse
David Boyd, David Cejudo, James Foster +2
We report our photometric and spectroscopic observations and analysis of the 2024 eclipse of the symbiotic binary V1413 Aquilae. We found the system in a visually bright state and…
High order splitting methods for SDEs satisfying a commutativity condition
James Foster, Goncalo dos Reis, Calum Strange
In this paper, we introduce a new simple approach to developing and establishing the convergence of splitting methods for a large class of stochastic differential equations (SDEs),…