Publications

A chasm exists between mathematical software libraries written for MPI-based applications and those written for OpenMP applications. Recently, however, PETSc enables the simple use of its MPI-based linear solvers from OpenMP applications. Separately, the MPICH MPI development team has started a new project to allow almost seamless MPI use in OpenMP applications. Both proposed approaches would result in a similar user experience. We discuss the reasons for these projects and their potential for providing more numerical library choices for OpenMP applications, including the unlimited assortment of linear solvers available in PETSc. In addition, we present the performance of an application using the first approach, demonstrating its efficacy.

Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at a given time represents only a small fraction of what is needed to predict future states, either due to measurement uncertainty or because only a small fraction of the state can be observed. This is true for example in solar physics, where we can observe the Sun’s surface and atmosphere, but its evolution is driven by internal processes for which we lack direct measurements. In this paper, we tackle the probabilistic prediction of partially observable, long-memory dynamical systems, with applications to solar dynamics and the evolution of active regions. We show that standard inference schemes, such as autoregressive rollouts, fail to capture long-range dependencies in the data, largely because they do not integrate past information effectively. To overcome this, we propose a multiscale inference scheme for diffusion models, tailored to physical processes. Our method generates trajectories that are temporally fine-grained near the present and coarser as we move farther away, which enables capturing long-range temporal dependencies without increasing computational cost. When integrated into a diffusion model, we show that our inference scheme significantly reduces the bias of the predicted distributions and improves rollout stability.

While foundation models have shown promise across a variety of fields, astronomy lacks a unified framework for joint modeling across its highly diverse data modalities. In this paper, we present AION-1, the first large-scale multimodal foundation family of models for astronomy. AION-1 enables arbitrary transformations between heterogeneous data types using a two-stage architecture: modality-specific tokenization followed by transformer-based masked modeling of cross-modal token sequences. Trained on over 200M astronomical objects, AION-1 demonstrates strong performance across regression, classification, generation, and object retrieval tasks. Beyond astronomy, AION-1 provides a scalable blueprint for multimodal scientific foundation models that can seamlessly integrate heterogeneous combinations of real-world observations. Our model release is entirely open source, including the dataset, training script, and weights.

nferring dynamic cellular processes from static single-cell measurements remains a central challenge in genomics. Here we introduce ArchVelo, a new method for modeling gene regulation and inferring cell trajectories using single-cell simultaneous chromatin accessibility (scATAC-seq) and transcriptomic (scRNA-seq) profiling. ArchVelo represents chromatin accessibility as a set of archetypes—shared regulatory programs—and models their dynamic influence on transcription. Compared to previous methods, ArchVelo improves inference accuracy and gene-level latent time alignment, and enables identification of the underlying transcription factor activity. We benchmark ArchVelo on developing mouse brain and human hematopoiesis datasets and apply it to CD8 T cells responding to viral infection, revealing distinct trajectories of differentiation and proliferation. Focusing on the progenitor CD8 T cell population with key roles in sustaining immune responses and translationally linked to immunotherapy outcomes, we identify a previously uncharacterized differentiation trajectory from Ccr6− to Ccr6+ progenitors, shared between acute and chronic infection. In sum, ArchVelo provides a principled framework for modeling dynamic gene regulation in multi-omic single-cell data across biological systems.

In a step toward developing a model of human primary visual cortex, a recent study introduced a model of spatial frequency tuning in V1 (Broderick, Simoncelli, & Winawer, 2022). The model is compact, using just 9 parameters to predict BOLD response amplitude for locations across all of V1 as a function of stimulus orientation and spatial frequency. Here we replicated this analysis in a new dataset, the ‘nsdsynthetic’ supplement to the Natural Scenes Dataset (Allen et al., 2022), to assess generalization of model parameters. Furthermore, we extended the analyses to extrastriate maps V2 and V3. For each retinotopic map in the 8 NSD subjects, we fit the 9-parameter model. Despite many experimental differences between NSD and the original study, including stimulus size, experimental design, and MR field strength, there was good agreement in most model parameters. The dependence of preferred spatial frequency on eccentricity in V1 was similar between NSD and Broderick et al. Moreover, the effect of absolute stimulus orientation on spatial frequency maps was similar: higher preferred spatial frequency for horizontal and cardinal orientations compared to vertical and oblique orientations in both studies. The extension to extrastriate maps revealed that the biggest change in tuning between maps was in bandwidth: the bandwidth in spatial frequency tuning increased by 70% from V1 to V2 and 100% from V1 to V3, paralleling known increases in receptive field size. Together, the results show robust reproducibility and bring us closer to a systematic characterization of spatial encoding in the human visual system.

The segregation of the epiblast (EPI) and primitive endoderm (PE) cell types in the preimplantation mouse embryo is not only a crucial decision that sets aside the precursors of the embryo proper from extraembryonic cells, respectively, but also has served as a central model to study a key concept in mammalian development: how much of developmental patterning is predetermined vs. stochastically emergent. Here, we address this question by quantitative live imaging of multiple endogenously tagged transcription factors key to this fate decision and trace their dynamics at a single-cell resolution through the formation of EPI and PE cell fates. Strikingly, we reveal an initial symmetry breaking event, the formation of a primary EPI cell lineage, and show that this is linked to the dynamics of the prior inner cell mass/trophectoderm fate decision through the expression of SOX2. This primary EPI lineage, through fibroblast growth factor (FGF) signaling, induces an increase in the transcription factor GATA6 in other inner cell mass cells, setting them on the course toward PE differentiation. Interestingly, this trajectory can switch during a defined developmental window, leading to the emergence of secondary EPI cells. Finally, we show that early expression levels of NANOG, which are seemingly stochastic, can bias whether a cell’s trajectory switches to secondary EPI or continues as PE. Our data give unique insight into how fate patterning is initiated and propagated during unperturbed embryonic development through the interplay of lineage-history-biased and stochastic cell-intrinsic molecular features, unifying previous models of EPI/PE segregation.

We present a randomized algorithm for producing a quasi-optimal hierarchically semi-
separable (HSS) approximation to an N ×N matrix A using only matrix-vector products with A and
AT. We prove that, using O(k log(N/k)) matrix-vector products and O(N k2 log(N/k)) additional
runtime, the algorithm returns an HSS matrix B with rank-k blocks whose expected Frobenius norm
error E[∥A − B∥2
F] is at most O(log(N/k)) times worse than the best possible approximation error by
an HSS rank-k matrix. In fact, the algorithm we analyze in a simple modification of an empirically
effective method proposed by [Levitt & Martinsson, SISC 2024]. As a stepping stone towards our
main result, we prove two results that are of independent interest: a similar guarantee for a variant of
the algorithm which accesses A’s entries directly, and explicit error bounds for near-optimal subspace
approximation using projection-cost-preserving sketches. To the best of our knowledge, our analysis
constitutes the first polynomial-time quasi-optimality result for HSS matrix approximation, both in
the explicit access model and the matrix-vector product query model.

The first cell fate bifurcation in mammalian development directs cells toward either the trophectoderm (TE) or inner cell mass (ICM) compartments in pre-implantation embryos. This decision is regulated by the subcellular localization of a transcriptional co-activator YAP and takes place over several progressively asynchronous cleavage divisions. As a result of this asynchrony and variable arrangement of blastomeres, reconstructing the dynamics of the TE/ICM cell specification from fixed embryos is extremely challenging. To address this, we developed a live-imaging approach and applied it to measure pairwise dynamics of nuclear YAP and its direct target genes, CDX2 and SOX2, which are key transcription factors of the TE and ICM, respectively. Using these datasets, we constructed a generative model of the first cell fate bifurcation, which reveals the time-dependent statistics of the TE and ICM cell allocation. In addition to making testable predictions for the joint dynamics of the full YAP/CDX2/SOX2 motif, the model revealed the stochastic nature of the induction timing of the key cell fate determinants and identified the features of YAP dynamics that are necessary or sufficient for this induction. Notably, temporal heterogeneity was particularly prominent for SOX2 expression among ICM cells. As heterogeneities within the ICM have been linked to the initiation of the second cell fate decision in the embryo, understanding the origins of this variability is of key significance. The presented approach reveals the dynamics of the first cell fate choice and lays the groundwork for dissecting the next cell fate decisions in mouse development.

The quasi-2D electrostatic systems, characterized by periodicity in two dimensions with a free third dimension, have garnered significant interest in many fields. We apply the sum-of-Gaussians (SOG) approximation to the Laplace kernel, dividing the interactions into near-field, mid-range, and long-range components. The near-field component, singular but compactly supported in a local domain, is directly calculated. The mid-range component is managed using a procedure similar to nonuniform fast Fourier transforms in three dimensions. The long-range component, which includes Gaussians of large variance, is treated with polynomial interpolation/anterpolation in the free dimension and Fourier spectral solver in the other two dimensions on proxy points. Unlike the fast Ewald summation, which requires extensive zero padding in the case of high aspect ratios, the separability of Gaussians allows us to handle such case without any zero padding in the free direction. Furthermore, while NUFFTs typically rely on certain upsampling in each dimension, and the truncated kernel method introduces an additional factor of upsampling due to kernel oscillation, our scheme eliminates the need for upsampling in any direction due to the smoothness of Gaussians, significantly reducing computational cost for large-scale problems. Finally, whereas all periodic fast multipole methods require dividing the periodic tiling into a smooth far part and a near part containing its nearest neighboring cells, our scheme operates directly on the fundamental cell, resulting in better performance with simpler implementation. We provide a rigorous error analysis showing that upsampling is not required in NUFFT-like steps, achieving O(N N) complexity with a small prefactor. The performance of the scheme is demonstrated via extensive numerical experiments.

Structuring the photon density of states and light-matter coupling in optical cavities has emerged as a promising approach to modifying the equilibrium properties of materials through strong light-matter interactions. In this article, we employ state-of-the-art quantum electrodynamical density functional theory (QEDFT) to study the modifications of the electronic and structural properties of two-dimensional (2D) van der Waals (vdW) layered materials by the cavity vacuum field fluctuations. We find that cavity photons modify the electronic density through localization along the photon polarization directions, a universal effect observed for all the 2D materials studied here. This modification of the electronic structure tunes the material properties, such as the shifting of energy valleys in monolayer h-BN and 2H-MoS2, enabling tunable band gaps. Also, it tunes the interlayer spacing in bilayer 2H-MoS2 and Td-MoTe2, allowing for adjustable ferroelectric, nonlinear Hall effect, and optical properties, as a function of light-matter coupling strength. Our findings open an avenue for engineering a broad range of 2D layered quantum materials by tuning vdW interactions through fluctuating cavity photon fields.