Publications

We study the Cooper instability in jellium model in the controlled regime of small to intermediate values of the Coulomb parameter r

Visual information arriving at the retina is transmitted to the brain by signals in the optic nerve, and the brain must rely solely on these signals to make inferences about the visual world. Previous work has probed the content of these signals by directly reconstructing images from retinal activity using linear regression or nonlinear regression with neural networks. Maximum a posteriori (MAP) reconstruction using retinal encoding models and separately-trained natural image priors offers a more general and principled approach. We develop a novel method for approximate MAP reconstruction that combines a generalized linear model for retinal responses to light, including their dependence on spike history and spikes of neighboring cells, with the image prior implicitly embedded in a deep convolutional neural network trained for image denoising. We use this method to reconstruct natural images from ex vivo simultaneously-recorded spikes of hundreds of retinal ganglion cells uniformly sampling a region of the retina. The method produces reconstructions that match or exceed the state-of-the-art in perceptual similarity and exhibit additional fine detail, while using substantially fewer model parameters than previous approaches. The use of more rudimentary encoding models (a linear-nonlinear-Poisson cascade) or image priors (a 1/f spectral model) significantly reduces reconstruction performance, indicating the essential role of both components in achieving high-quality reconstructed images from the retinal signal.

Attentional gating is a core mechanism supporting behavioral flexibility, but its biological implementation remains uncertain. Gain modulation of neural responses is likely to play a key role, but simply boosting relevant neural responses can be insufficient for improving behavioral outputs, especially in hierarchical circuits. Here we propose a variation of attentional gating that relies on stochastic gain modulation as a dedicated indicator of task relevance. We show that targeted stochastic modulation can be effectively learned and used to fine-tune hierarchical architectures, without reorganization of the underlying circuits. Simulations of such networks demonstrate improvements in learning efficiency and performance in novel tasks, relative to traditional attentional mechanisms based on deterministic gain increases. The effectiveness of this approach relies on the availability of representational bottlenecks in which the task relevant information is localized in small subpopulations of neurons. Overall, this work provides a new mechanism for constructing intelligent systems that can flexibly and robustly adapt to changes in task structure.

New SARS-CoV-2 variants causing COVID-19 are a major risk to public health worldwide due to the potential for phenotypic change and increases in pathogenicity, transmissibility and/or vaccine escape. Recognising signatures of new variants in terms of replacing growth and severity are key to informing the public health response. To assess this, we aimed to investigate key time periods in the course of infection, hospitalisation and death, by variant. We linked datasets on contact tracing (Contact Tracing Advisory Service), testing (the Second-Generation Surveillance System) and hospitalisation (the Admitted Patient Care dataset) for the entire length of contact tracing in the England - from March 2020 to March 2022. We modelled, for England, time delay distributions using a Bayesian doubly interval censored modelling approach for the SARS-CoV-2 variants Alpha, Delta, Delta Plus (AY.4.2), Omicron BA.1 and Omicron BA.2. This was conducted for the incubation period, the time from infection to hospitalisation and hospitalisation to death. We further modelled the growth of novel variant replacement using a generalised additive model with a negative binomial error structure and the relationship between incubation period length and the risk of a fatality using a Bernoulli generalised linear model with a logit link. The mean incubation periods for each variant were: Alpha 4.19 (95% credible interval (CrI) 4.13-4.26) days; Delta 3.87 (95% CrI 3.82-3.93) days; Delta Plus 3.92 (95% CrI 3.87-3.98) days; Omicron BA.1 3.67 (95% CrI 3.61-3.72) days and Omicron BA.2 3.48 (95% CrI 3.43-3.53) days. The mean time from infection to hospitalisation was for Alpha 11.31 (95% CrI 11.20-11.41) days, Delta 10.36 (95% CrI 10.26-10.45) days and Omicron BA.1 11.54 (95% CrI 11.38-11.70) days. The mean time from hospitalisation to death was, for Alpha 14.31 (95% CrI 14.00-14.62) days; Delta 12.81 (95% CrI 12.62-13.00) days and Omicron BA.2 16.02 (95% CrI 15.46-16.60) days. The 95th percentile of the incubation periods were: Alpha 11.19 (95% CrI 10.92-11.48) days; Delta 9.97 (95% CrI 9.73-10.21) days; Delta Plus 9.99 (95% CrI 9.78-10.24) days; Omicron BA.1 9.45 (95% CrI 9.23-9.67) days and Omicron BA.2 8.83 (95% CrI 8.62-9.05) days. Shorter incubation periods were associated with greater fatality risk when adjusted for age, sex, variant, vaccination status, vaccination manufacturer and time since last dose with an odds ratio of 0.83 (95% confidence interval 0.82-0.83) (P value < 0.05). Variants of SARS-CoV-2 that have replaced previously dominant variants have had shorter incubation periods. Conversely co-existing variants have had very similar and non-distinct incubation period distributions. Shorter incubation periods reflect generation time advantage, with a reduction in the time to the peak infectious period, and may be a significant factor in novel variant replacing growth. Shorter times for admission to hospital and death were associated with variant severity - the most severe variant, Delta, led to significantly earlier hospitalisation, and death. These measures are likely important for future risk assessment of new variants, and their potential impact on population health.

We develop efficient and accurate sum-of-exponential (SOE) approximations for the Gaussian using rational approximation of the exponential function on the negative real axis. Six digit accuracy can be obtained with eight terms and ten digit accuracy can be obtained with twelve terms. This representation is of potential interest in approximation theory but we focus here on its use in accelerating the fast Gauss transform (FGT) in one and two dimensions. The one-dimensional scheme is particularly straightforward and easy to implement, requiring only twenty-four lines of MATLAB code. The two-dimensional version requires some care with data structures, but is significantly more efficient than existing FGTs. Following a detailed presentation of the theoretical foundations, we demonstrate the performance of the fast transforms with several numerical experiments.

We discuss the challenges of motivating, constructing, and quantising a canonically-normalised inflationary perturbation in spatially curved universes. We show that this has historically proved challenging due to the interaction of non-adiabaticity with spatial curvature. We propose a novel curvature perturbation which is canonically normalised, unique up to a single scalar parameter. This corrected quantisation has potentially observational consequences via modifications to the primordial power spectrum at large angular scales, as well as theoretical implications for quantisation procedures in curved cosmologies filled with a scalar field.

Polynomial spectral methods provide fast, accurate, and flexible solvers for broad ranges of PDEs with one bounded dimension, where the incorporation of general boundary conditions is well understood. However, automating extensions to domains with multiple bounded dimensions is challenging because of difficulties in implementing boundary conditions and imposing compatibility conditions at shared edges and corners. Past work has included various workarounds, such as the anisotropic inclusion of partial boundary data at shared edges or approaches that only work for specific boundary conditions. Here we present a general system for imposing boundary and compatibility conditions for elliptic equations on hypercubes. We take an approach based on the generalized tau method, which allows for a wide range of boundary conditions for many types of spectral methods. The generalized tau method has the distinct advantage that the specified polynomial residual determines the exact algebraic solution; afterwards, any stable numerical scheme will find the same result. We can, therefore, provide one-to-one comparisons to traditional collocation and Galerkin methods within the tau framework. As an essential requirement, we add specific tau corrections to the boundary conditions in addition to the bulk PDE. We then impose additional mutual compatibility conditions to ensure boundary conditions match at shared subsurfaces. Our approach works with general boundary conditions that commute on intersecting subsurfaces, including Dirichlet, Neumann, Robin, and any combination of these on all boundaries. The tau corrections and compatibility conditions can be fully isotropic and easily incorporated into existing solvers. We present the method explicitly for the Poisson equation in two and three dimensions and describe its extension to arbitrary elliptic equations (e.g. biharmonic) in any dimension.

We present results of an all-sky search for continuous gravitational waves which can be produced by spinning neutron stars with an asymmetry around their rotation axis, using data from the third observing run of the Advanced LIGO and Advanced Virgo detectors. Four different analysis methods are used to search in a gravitational-wave frequency band from 10 to 2048 Hz and a first frequency derivative from −10−8 to 10−9 Hz/s. No statistically-significant periodic gravitational-wave signal is observed by any of the four searches. As a result, upper limits on the gravitational-wave strain amplitude h0 are calculated. The best upper limits are obtained in the frequency range of 100 to 200 Hz and they are ∼1.1×10−25 at 95\% confidence-level. The minimum upper limit of 1.10×10−25 is achieved at a frequency 111.5 Hz. We also place constraints on the rates and abundances of nearby planetary- and asteroid-mass primordial black holes that could give rise to continuous gravitational-wave signals.

We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than evaluating the volume potential over the given domain, we first extend the source data to a geometrically simpler region with high order accuracy. This allows us to accelerate the evaluation of the volume potential using an efficient, geometry-unaware fast multipole-based algorithm. To impose the desired boundary condition, it remains only to solve the Laplace equation with suitably modified boundary data. This is accomplished with existing fast and accurate boundary integral methods. The novelty of our solver is the scheme used for creating the source extension, assuming it is provided on an adaptive quad-tree. For leaf boxes intersected by the boundary, we construct a universal "stencil" and require that the data be provided at the subset of those points that lie within the domain interior. This universality permits us to precompute and store an interpolation matrix which is used to extrapolate the source data to an extended set of leaf nodes with full tensor-product grids on each. We demonstrate the method's speed, robustness and high-order convergence with several examples, including domains with piecewise smooth boundaries.

Marine recruits training at Parris Island experienced an unexpectedly high rate of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection, despite preventive measures including a supervised, 2-week, pre-entry quarantine. We characterize SARS-CoV-2 transmission in this cohort.