Publications

Unraveling the multiphase structure of the diffuse interstellar medium as traced by neutral hydrogen (H i) is essential to understanding the lifecycle of the Milky Way. However, H i phase separation is a challenging and underconstrained problem. The neutral gas phase distribution is often inferred from the spectral line structure of H i emission. In this work, we develop a data-driven phase-separation method that extracts H i phase structure solely from the spatial morphology of H i emission intensity structures. We combine scattering spectra (SS) statistics with a Gaussian-mixture variational autoencoder model to (1) derive an interpretable statistical model of different H i phases from their multiscale morphological structures, and (2) we use this model to decompose the 2D channel maps of GALFA-H i emission in diffuse high-latitude (|b|>30) regions over narrow velocity channels (Δv=3 km/s) into cold neutral medium (CNM), warm neutral medium (WNM), and noise components. We integrate our CNM map over velocity channels to compare it to an existing map produced by a spectrum-based method. We find that the two maps are highly correlated, but ours recovers more spatially coherent structures at small scales. Our work illustrates and quantifies a clear physical connection between the H i morphology and H i phase structure, and it unlocks a new avenue for improving future phase-separation techniques by making use of both H i spectral and spatial information to decompose H i in 3D position–position–velocity space. These results are consistent with a physical picture where processes that drive H i phase transitions also shape the morphology of H i gas, imprinting a sparse, filamentary CNM that forms out of a diffuse, extended WNM.

Signaling pathways induce stereotyped transcriptional changes as stem cells progress into mature cell types during embryogenesis. Signaling perturbations are necessary to discover which genes are responsive or insensitive to pathway activity. However, gene regulation is additionally dependent on cell state-specific factors like chromatin modifications or transcription factor binding. Thus, transcriptional profiles need to be assayed in single cells to identify potentially multiple, distinct perturbation responses among heterogeneous cell states in an embryo. In perturbation studies, comparing heterogeneous transcriptional states among experimental conditions often requires samples to be collected over multiple independent experiments, which can introduce confounding batch effects. We present Design-Aware Integration of Single Cell ExpEriments (DAISEE), a new algorithm that models perturbation responses in single-cell datasets collected according to complex experimental designs. We demonstrate that DAISEE improves upon a previously available integrative nonnegative matrix factorization framework, more efficiently separating perturbation responses from confounding variation. We use DAISEE to integrate newly collected single-cell RNA sequencing datasets from 5-h-old zebrafish embryos expressing optimized photoswitchable MEK (psMEK), which globally activates the extracellular signal-regulated kinase (ERK), a signaling molecule involved in many cell specification events. psMEK drives some cells that are normally not exposed to ERK signals toward other wild type states and induces novel states expressing early-acting endothelial genes. Overactive signaling is therefore capable of producing unexpected gene expression states in developing embryos.

Sequential scientific data span many resolutions and domains, and unifying them into a common representation is a key step toward developing foundation models for the sciences. Astronomical spectra exemplify this challenge: massive surveys have collected millions of spectra across a wide range of wavelengths and resolutions, yet analyses remain fragmented across spectral domains (e.g., optical vs. infrared) and object types (e.g., stars vs. galaxies), limiting the ability to pool information across datasets. We present a deep learning model that jointly learns from heterogeneous spectra in a self-supervised manner. Our universal spectral tokenizer processes spectra from a variety of object types and resolutions directly on their native wavelength grids, producing intrinsically aligned, homogeneous, and physically meaningful representations that can be efficiently adapted to achieve competitive performance across a range of downstream tasks. For the first time, we demonstrate that a single model can unify spectral data across resolutions and domains, suggesting that our model can serve as a powerful building block for foundation models in astronomy—and potentially extend to other scientific domains with heterogeneous sequential data, such as climate and healthcare.

A numerical scheme is presented for solving the Helmholtz equation with Dirichlet or Neumann boundary conditions on piecewise smooth open curves, where the curves may have corners and multiple junctions. Existing integral equation methods for smooth open curves rely on analyzing the exact singularities of the density at endpoints for associated integral operators, explicitly extracting these singularities from the densities in the formulation, and using global quadrature to discretize the boundary integral equation. Extending these methods to handle curves with corners and multiple junctions is challenging because the singularity analysis becomes much more complex, and constructing high-order quadrature for discretizing layer potentials with singular and hypersingular kernels and singular densities is nontrivial. The proposed scheme is built upon the following two observations. First, the single-layer potential operator and the normal derivative of the double-layer potential operator serve as effective preconditioners for each other locally. Second, the recursively compressed inverse preconditioning (RCIP) method can be extended to address “implicit” second-kind integral equations. The scheme is high-order, adaptive, and capable of handling corners and multiple junctions without prior knowledge of the density singularity. It is also compatible with fast algorithms, such as the fast multipole method. The performance of the scheme is illustrated with several numerical examples.

How embryos adapt their internal cellular machinery to reductions in cell size during development remains a fundamental question in cell biology1–11. Here, we use high-resolution lattice light-sheet fluorescence microscopy and automated image analysis to quantify lineage-resolved mitotic spindle and chromosome segregation dynamics from the 2-to 64-cell stages in Caenorhabditis elegans embryos. While spindle length scales with cell size across both wild-type and size-perturbed embryos, chromosome segregation dynamics remain largely invariant, suggesting that distinct mechanisms govern these mitotic processes. Combining femtosecond laser ablation12,13 with large-scale electron tomography14, we find that central spindle microtubules mediate chromosome segregation dynamics and remain uncoupled from cell size across all stages of early development. In contrast, spindle elongation is driven by cortically anchored motor proteins and astral microtubules, rendering it sensitive to cell size12,13,15–17. Incorporating these experimental results into an extended stoichiometric model for both the spindle and chromosomes, we find that allowing only cell size and microtubule catastrophe rates to vary reproduces elongation dynamics across development. The same model also accounts for centrosome separation and pronuclear positioning in the one-cell C. elegans embryo18, spindle-length scaling across nematode species spanning ~100 million years of divergence17, and spindle rotation in human cells19. Thus, a unified stoichiometric framework provides a predictive, mechanistic account of spindle and nuclear dynamics across scales and species.

How embryos adapt their internal cellular machinery to reductions in cell size during development remains a fundamental question in cell biology1–11. Here, we use high-resolution lattice light-sheet fluorescence microscopy and automated image analysis to quantify lineage-resolved mitotic spindle and chromosome segregation dynamics from the 2- to 64-cell stages in Caenorhabditis elegans embryos. While spindle length scales with cell size across both wild-type and size-perturbed embryos, chromosome segregation dynamics remain largely invariant, suggesting that distinct mechanisms govern these mitotic processes. Combining femtosecond laser ablation12,13 with large-scale electron tomography14, we find that central spindle microtubules mediate chromosome segregation dynamics and remain uncoupled from cell size across all stages of early development. In contrast, spindle elongation is driven by cortically anchored motor proteins and astral microtubules, rendering it sensitive to cell size12,13,15–17. Incorporating these experimental results into an extended stoichiometric model for both the spindle and chromosomes, we find that allowing only cell size and microtubule catastrophe rates to vary reproduces elongation dynamics across development. The same model also accounts for centrosome separation and pronuclear positioning in the one-cell C. elegans embryo18, spindle-length scaling across nematode species spanning ~100 million years of divergence17, and spindle rotation in human cells19. Thus, a unified stoichiometric framework provides a predictive, mechanistic account of spindle and nuclear dynamics across scales and species.

Generative diffusion models learn probability densities over diverse image datasets by estimating the score with a neural network trained to remove noise. Despite their remarkable success in generating high-quality images, the internal mechanisms of the underlying score networks are not well understood. Here, we examine the image representation that arises from score estimation in a {fully-convolutional unconditional UNet}. We show that the middle block of the UNet decomposes individual images into sparse subsets of active channels, and that the vector of spatial averages of these channels can provide a nonlinear representation of the underlying clean images. Euclidean distances in this representation space are semantically meaningful, even though no conditioning information is provided during training. We develop a novel algorithm for stochastic reconstruction of images conditioned on this representation: The synthesis using the unconditional model is "self-guided" by the representation extracted from that very same model. For a given representation, the common patterns in the set of reconstructed samples reveal the features captured in the middle block of the UNet. Together, these results show, for the first time, that a measure of semantic similarity emerges, unsupervised, solely from the denoising objective.

We generalize the interpolative separable density fitting (ISDF) method, used for compressing the four-index electron repulsion integral (ERI) tensor, to incorporate adaptive real space grids for potentially highly localized single-particle basis functions. To do so, we employ a fast adaptive algorithm, the recently-introduced dual-space multilevel kernel-splitting method, to solve the Poisson equation for the ISDF auxiliary basis functions. The adaptive grids are generated using a high-order accurate, black-box procedure that satisfies a user-specified error tolerance. Our algorithm relies on the observation, which we prove, that an adaptive grid resolving the pair densities appearing in the ERI tensor can be straightforwardly constructed from one that resolves the single-particle basis functions, with the number of required grid points differing only by a constant factor. We find that the ISDF compression efficiency for the ERI tensor with highly localized basis sets is comparable to that for smoother basis sets compatible with uniform grids. To demonstrate the performance of our procedure, we consider several molecular systems with all-electron basis sets which are intractable using uniform grid-based methods. Our work establishes a pathway for scalable many-body electronic structure simulations with arbitrary smooth basis functions, making simulations of phenomena like core-level excitations feasible on a large scale.

Having an accurate reaction coordinate (RC) is essential for reliable kinetic characterization of molecular processes, but there are few quantitative metrics to evaluate RC quality. In this study, we consider the dimensionless γ metric from the Exponential Average Time-dependent Rate (EATR) method, which represents the fraction of a biasing potential along the RC that contributes to increasing the rate constant. We demonstrate that γ can be used to test whether the utility of a RC for predicting kinetics with a Metadynamics bias improves as the coordinate is iteratively updated to include new data. We evaluate RCs approximated via the iterative State Predictive Information Bottleneck (SPIB) approach, which was previously shown to be accurate across six protein–ligand dissociation systems. For these same systems, we compute γ values and mean accelerated times τ̅accel. After systematically scanning over fitting parameters, the results show that γ increases closer to 1, while τ̅accel decreases, revealing a consistent inverse correlation. These results demonstrate that γ serves as a practical criterion for RC evaluation and offers guidance for selecting SPIB–derived coordinates yielding quantitative kinetic predictions.

Having an accurate reaction coordinate (RC) is essential for reliable kinetic characterization of molecular processes, but there are few quantitative metrics to evaluate RC quality. In this study, we consider the dimensionless γ metric from the Exponential Average Time-dependent Rate (EATR) method, which represents the fraction of a biasing potential along the RC that contributes to increasing the rate constant. We demonstrate that γ can be used to test whether the utility of a RC for predicting kinetics with a Metadynamics bias improves as the coordinate is iteratively updated to include new data. We evaluate RCs approximated via the iterative State Predictive Information Bottleneck (SPIB) approach, which was previously shown to be accurate across six protein–ligand dissociation systems. For these same systems, we compute γ values and mean accelerated times τ̅accel. After systematically scanning over fitting parameters, the results show that γ increases closer to 1, while τ̅accel decreases, revealing a consistent inverse correlation. These results demonstrate that γ serves as a practical criterion for RC evaluation and offers guidance for selecting SPIB–derived coordinates yielding quantitative kinetic predictions.