Publications

In this work, we present a mathematical formulation for machine learning of (1) functions on symmetric matrices that are invariant with respect to the action of permutations by conjugation, and (2) functions on point clouds that are invariant with respect to rotations, reflections, and permutations of the points. To achieve this, we provide a construction of generically separating invariant features using ideas inspired by Galois theory. We construct 𝑂⁡(𝑛2) invariant features derived from generators for the field of rational functions on 𝑛 ×𝑛 symmetric matrices that are invariant for joint permutations of rows and columns. We show that these invariant features can separate all distinct orbits of symmetric matrices, except for a measure zero set; such features can be used to universally approximate invariant functions on almost all weighted graphs. For point clouds in a fixed dimension, we prove that the number of invariant features can be reduced, generically without losing expressivity, to 𝑂⁡(𝑛), where 𝑛 is the number of points. We combine these invariant features with DeepSets to learn functions on symmetric matrices and point clouds with varying sizes. We empirically demonstrate the feasibility of our approach on molecule property regression and point cloud distance prediction.

Cosmological simulations provide a wealth of data in the form of point clouds and directed trees. A crucial goal is to extract insights from this data that shed light on the nature and composition of the Universe. In this paper we introduce CosmoBench, a benchmark dataset curated from state-of-the-art cosmological simulations whose runs required more than 41 million core-hours and generated over two petabytes of data. CosmoBench is the largest dataset of its kind: it contains 34 thousand point clouds from simulations of dark matter halos and galaxies at three different length scales, as well as 25 thousand directed trees that record the formation history of halos on two different time scales. The data in CosmoBench can be used for multiple tasks -- to predict cosmological parameters from point clouds and merger trees, to predict the velocities of individual halos and galaxies from their collective positions, and to reconstruct merger trees on finer time scales from those on coarser time scales. We provide several baselines on these tasks, some based on established approaches from cosmological modeling and others rooted in machine learning. For the latter, we study different approaches -- from simple linear models that are minimally constrained by symmetries to much larger and more computationally-demanding models in deep learning, such as graph neural networks. We find that least-squares fits with a handful of invariant features sometimes outperform deep architectures with many more parameters and far longer training time. Still there remains tremendous potential to improve these baselines by combining machine learning and cosmology to fully exploit the data. CosmoBench sets the stage for bridging cosmology and geometric deep learning at scale. We invite the community to push the frontier of scientific discovery by engaging with this dataset, available at this https URL

The formation and maintenance of the finite mammalian ovarian reserve are critical for fertility and species survival. Genetic and developmental studies have uncovered various mechanisms underlying oocyte development and maturation, revealing two curious features of the ovarian germline: (a) The establishment of the follicle reserve involves an initial massive overproduction of oocyte precursors, and (b) the total number of ovulated oocytes across an animal's fertile lifetime is a very small proportion of the initial ovarian reserve. Many have proposed that this indicates the existence of selective quality control to ensure gamete fitness. Here, we review the findings underlying the hypotheses for germline quality control during prepubertal development, homeostatic fertility, and reproductive aging. We evaluate whether the existing evidence base distinguishes the active selection of specific germ cell subsets from neutral dynamics. Throughout, we discuss strategies for applying statistical frameworks to evaluate selection in oogenesis and the implications of neutrality versus selection at various points in oocyte development.

Two-dimensional moiré materials are formed by artificially stacking atomically thin monolayers. Correlated and topological quantum phases can be engineered by precise choice of stacking geometry1--3. These designer electronic properties depend crucially on interlayer coupling and atomic registry4,5. An open question is how the atomic registry responds on ultrafast timescales to optical excitation and whether the moiré geometry can be dynamically reconfigured to tune emergent phenomena in real time. Here we show that femtosecond photoexcitation drives a coherent twist--untwist motion of the moiré superlattice in 2° and 57° twisted WSe2/MoSe2 heterobilayers, resolved directly by ultrafast electron diffraction. On above-band-gap photoexcitation, the moiré superlattice diffraction features are enhanced within 1ps and subsequently suppressed several picoseconds after, deviating markedly from typical photoinduced lattice heating. Kinetic diffraction analysis, supported by simulations of the sample dynamics, indicates a peak-to-trough local twist angle modulation of 0.6°, correlated with a sub-THz frequency moiré phonon. This motion is driven by ultrafast charge transfer that transiently increases interlayer attraction. Our results could lead to ultrafast control of moiré periodic lattice distortions and, by extension, the local moiré potential that shapes excitons, polarons and correlation-driven behaviours.

The first-order continuum partial differential equation (PDE) model proposed by Bistritzer and MacDonald [Proc. Natl. Acad. Sci. U. S. A. 108, 12233–12237 (2011)] accurately describes the single-particle electronic properties of twisted bilayer graphene at small twist angles. In this paper, we obtain higher-order corrections to the Bistritzer–MacDonald (BM) model via a systematic multiple-scales expansion. We prove that the solution of the resulting higher-order PDE model accurately approximates the corresponding tight-binding wave function under a natural choice of parameters and given initial conditions that are spectrally localized to the monolayer Dirac points. Numerical simulations of tight-binding and continuum dynamics demonstrate the validity of the higher-order continuum model. Symmetries of the higher-order models are also discussed. This work extends the analysis from Watson et al., J. Math. Phys. 64, 031502 (2023), which rigorously established the validity of the (first-order) BM model.

Viral infections can induce prolonged changes in innate immunity. Here, we use blood samples from a human influenza H3N2 challenge study (NCT03883113) to perform comprehensive multi-omics analyses. We detect remodeling of immune programs in circulating innate immune cells that persist after resolution of the infection. We find changes associated with suppressed inflammation, including decreased cytokine and AP-1 gene expression as well as decreased accessibility at AP-1 targets and interleukin-related gene promoter regions. We also find decreased histone deacetylase gene expression, increased MAP kinase gene expression, and increased accessibility at interferon-related gene promoter regions. Genes involved in inflammation and methylation remodeling show modulation of gene-chromatin site regulatory circuit activity. These results reveal a coordinated rewiring of the molecular landscape in innate immune cells induced by mild influenza virus infection.

Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to characterize these dynamics. These models use Gaussian Process (GP) priors to capture the nonlinear dependence of circuit dynamics on task and behavioral variables. Conditioned on these covariates, the data is modeled with linear dynamics. This allows for transparent interpretation and tractable Bayesian inference. We find that CLDS models can perform well even in severely data-limited regimes (e.g. one trial per condition) due to their Bayesian formulation and ability to share statistical power across nearby task conditions. In example applications, we apply CLDS to model thalamic neurons that nonlinearly encode heading direction and to model motor cortical neurons during a cued reaching task

While cryo-electron microscopy (cryo-EM) has come to prominence in the last decade due to its ability to resolve biomolecular complexes at atomic resolution, advancements in experimental and computational methods have made cryo-EM promising for investigating intracellular organization and heterogeneous molecular states. A primary challenge for these alternative applications is the development of techniques for cryo-EM data analysis, which are very computationally demanding. To this end, it is advantageous to leverage advanced scientific computing frameworks for statistical analysis. One such framework is JAX, an emerging array-oriented Python numerical computing package for automatic differentiation and vectorization with a growing ecosystem for statistical inference and machine learning. We have developed cryoJAX, a cryo-EM image simulation library for building computational data analysis applications in JAX. CryoJAX is a flexible modeling language for cryo-EM image formation and therefore can support a wide range of data analysis downstream. By integrating with the JAX ecosystem, cryoJAX enables the development and deployment of algorithms for the growing breadth of scientific applications for cryo-EM.

Machine-learning interatomic potentials have emerged as a revolutionary class of force-field models in molecular simulations, delivering quantum-mechanical accuracy at a fraction of the computational cost and enabling the simulation of large-scale systems over extended timescales. However, they often focus on modeling local environments, neglecting crucial long-range interactions. We propose a sum-of-Gaussians neural network (SOG-Net), a lightweight and versatile framework for integrating long-range interactions into a machine-learning force field. The SOG-Net employs a latent-variable learning network that seamlessly bridges short-range and long-range components, coupled with an efficient Fourier convolution layer that incorporates long-range effects. By learning sum-of-Gaussians multipliers across different convolution layers, the SOG-Net adaptively captures diverse long-range decay behaviors while maintaining close-to-linear computational complexity during training and simulation via nonuniform fast Fourier transforms. The method is demonstrated effective for a broad range of long-range systems.

Large Language Models (LLMs) are increasingly being used across applications, ranging from content generation to decision-making, raising concerns about biases embedded in them. While biases related to gender, race, and culture have been studied extensively, understanding age-bias and stereotypes of aging in LLMs remain underexplored. This study analyzes LLM-generated responses to prompts related to aging, revealing stereotypical biases about aging pertaining to technology proficiency, cognitive and physical decline, and job roles. We noted that even responses without explicit age bias also had mentions of ageist stereotypes. We discuss considerations for involving older adults’ perspectives through human-in-the-loop methodologies yet exercising caution about aspects like internalized ageism.