Publications

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.

Explaining the currently observed magnetic fields in galaxies requires relatively strong seeding in the early Universe. One theory proposes that magnetic fields of the order of μG were expelled by supernova (SN) explosions after primordial, nG or weaker fields were amplified in stellar interiors. In this work, we calculate the maximum magnetic energy that can be injected in the interstellar medium by a stellar cluster of mass Mcl based on what is currently known about stellar magnetism. We consider early-type stars and adopt either a Salpeter or a top-heavy IMF. For their magnetic fields, we adopt either a Gaussian or a bimodal distribution. The Gaussian model assumes that all massive stars are magnetized with 103<⟨B∗⟩<104 G, while the bimodal, consistent with observations of Milky Way stars, assumes only 5-10 per cent of OB stars have 103<⟨B∗⟩<104 G, while the rest have 10<⟨B∗⟩<102 G. We find that the maximum magnetic energy that can be injected by a stellar population is between 10−10−10−7 times the total SN energy. The highest end of these estimates is about five orders of magnitude lower than what is usually employed in cosmological simulations, where about 10−2 of the SN energy is injected as magnetic. Pure advection of the stellar magnetic field by SN explosions is a good candidate for seeding a dynamo, but not enough to magnetize galaxies. Assuming SNe as main mechanism for galactic magnetization, the magnetic field cannot exceed an intensity of 10−7 G in the best-case scenario for a population of 105 solar masses in a superbubble of 300 pc radius, while more typical values are between 10−10−10−9~G. Therefore, other scenarios for galactic magnetization at high redshift need to be explored.

Rapid advances in deep learning have brought not only myriad powerful neural networks, but also breakthroughs that benefit established scientific research. In particular, automatic differentiation (AD) tools and computational accelerators like GPUs have facilitated forward modeling of the Universe with differentiable simulations. Current differentiable cosmological simulations are limited by memory, thus are subject to a trade-off between time and space/mass resolution. They typically integrate for only tens of time steps, unlike the standard non-differentiable simulations. We present a new approach free of such constraints, using the adjoint method and reverse time integration. It enables larger and more accurate forward modeling, and will improve gradient based optimization and inference. We implement it in a particle-mesh (PM) N-body library pmwd (particle-mesh with derivatives). Based on the powerful AD system JAX, pmwd is fully differentiable, and is highly performant on GPUs.

The formation of the large-scale structure, the evolution and distribution of galaxies, quasars, and dark matter on cosmological scales, requires numerical simulations. Differentiable simulations provide gradients of the cosmological parameters, that can accelerate the extraction of physical information from statistical analyses of observational data. The deep learning revolution has brought not only myriad powerful neural networks, but also breakthroughs including automatic differentiation (AD) tools and computational accelerators like GPUs, facilitating forward modeling of the Universe with differentiable simulations. Because AD needs to save the whole forward evolution history to backpropagate gradients, current differentiable cosmological simulations are limited by memory. Using the adjoint method, with reverse time integration to reconstruct the evolution history, we develop a differentiable cosmological particle-mesh (PM) simulation library pmwd (particle-mesh with derivatives) with a low memory cost. Based on the powerful AD library JAX, pmwd is fully differentiable, and is highly performant on GPUs.

Astrocytes have been shown to play a central role in Alzheimer’s Disease (AD). However, the genes and biological pathways underlying disease manifestation are unknown, and it is unclear whether regional molecular differences among astrocytes contribute to regional specificity of disease. Here, we began to address these challenges with integrated experimental and computational approaches. We constructed a human astrocyte-specific functional gene network using Bayesian integration of a large compendium of human functional genomics data, as well as regional astrocyte gene expression profiles we generated in the mouse. This network identifies likely region-specific astrocyte pathways that operate in healthy brains. We leveraged our findings to compile genome-wide astrocyte-associated disease-gene predictions, employing a novel network-guided differential expression analysis (NetDIFF). We also used this data to predict a list of astrocyte-expressed genes mediating region-specific human disease, using a network-guided shortest path method (NetPATH). Both the network and our results are publicly available using an interactive web interface at http://astrocyte.princeton.edu. Our experimental and computational studies propose a strategy for disease gene and pathway prediction that may be applied to a host of human neurological disorders.

We present a data-driven method for reconstructing the galactic acceleration field from phase-space measurements of stellar streams. Our approach is based on a flexible and differentiable fit to the stream in phase-space, enabling a direct estimate of the acceleration vector along the stream. Reconstruction of the local acceleration field can be applied independently to each of several streams, allowing us to sample the acceleration field due to the underlying galactic potential across a range of scales. Our approach is methodologically different from previous works, since a model for the gravitational potential does not need to be adopted beforehand. Instead, our flexible neural-network-based model treats the stream as a collection of orbits with a locally similar mixture of energies, rather than assuming that the stream delineates a single stellar orbit. Accordingly, our approach allows for distinct regions of the stream to have different mean energies, as is the case for real stellar streams. Once the acceleration vector is sampled along the stream, standard analytic models for the galactic potential can then be rapidly constrained. We find our method recovers the correct parameters for a ground-truth triaxial logarithmic halo potential when applied to simulated stellar streams. Alternatively, we demonstrate that a flexible potential can be constrained with a neural network, though standard multipole expansions can also be constrained. Our approach is applicable to simple and complicated gravitational potentials alike, and enables potential reconstruction from a fully data-driven standpoint using measurements of slowly phase-mixing tidal debris.