Publications

Non-negative Matrix Factorization (NMF) methods offer an appealing unsupervised learning method for real-time analysis of streaming spectral data in time-sensitive data collection, such as in situ characterization of materials. However, canonical NMF methods are optimized to reconstruct a full dataset as closely as possible, with no underlying requirement that the reconstruction produces components or weights representative of the true physical processes. In this work, we demonstrate how constraining NMF weights or components, provided as known or assumed priors, can provide significant improvement in revealing true underlying phenomena. We present a PyTorch based method for efficiently applying constrained NMF and demonstrate this on several synthetic examples. When applied to streaming experimentally measured spectral data, an expert researcher-in-the-loop can provide and dynamically adjust the constraints. This set of interactive priors to the NMF model can, for example, contain known or identified independent components, as well as functional expectations about the mixing of components. We demonstrate this application on measured X-ray diffraction and pair distribution function data from in situ beamline experiments. Details of the method are described, and general guidance provided to employ constrained NMF in extraction of critical information and insights during in situ and high-throughput experiments.

We present an efficient implementation of periodic Gaussian density fitting (GDF) using the Coulomb metric. The three-center integrals are divided into two parts by range-separating the Coulomb kernel, with the short-range part evaluated in real space and the long-range part in reciprocal space. With a few algorithmic optimizations, we show that this new method -- which we call range-separated GDF (RSGDF) -- scales sublinearly to linearly with the number of k-points for small to medium-sized k-point meshes that are commonly used in periodic calculations with electron correlation. Numerical results on a few three-dimensional solids show about 10-fold speedups over the previously developed GDF with little precision loss. The error introduced by RSGDF is about 10

The performance of objective image quality assessment (IQA) models has been evaluated primarily by comparing model predictions to human quality judgments. Perceptual datasets gathered for this purpose have provided useful benchmarks for improving IQA methods, but their heavy use creates a risk of overfitting. Here, we perform a large-scale comparison of IQA models in terms of their use as objectives for the optimization of image processing algorithms. Specifically, we use eleven full-reference IQA models to train deep neural networks for four low-level vision tasks: denoising, deblurring, super-resolution, and compression. Subjective testing on the optimized images allows us to rank the competing models in terms of their perceptual performance, elucidate their relative advantages and disadvantages in these tasks, and propose a set of desirable properties for incorporation into future IQA models.

We describe a new algorithm to solve the time dependent, frequency integrated radiation transport (RT) equation implicitly, which is coupled to an explicit solver for equations of magnetohydrodynamics (MHD) using {\sf Athena++}. The radiation filed is represented by specific intensities along discrete rays, which are evolved using a conservative finite volume approach for both cartesian and curvilinear coordinate systems. All the terms for spatial transport of photons and interactions between gas and radiation are calculated implicitly together. An efficient Jacobi-like iteration scheme is used to solve the implicit equations. This removes any time step constrain due to the speed of light in RT. We evolve the specific intensities in the lab frame to simplify the transport step. The lab-frame specific intensities are transformed to the co-moving frame via Lorentz transformation when the source term is calculated. Therefore, the scheme does not need any expansion in terms of v/c. The radiation energy and momentum source terms for the gas are calculated via direct quadrature in the angular space. The time step for the whole scheme is determined by the normal Courant -- Friedrichs -- Lewy condition in the MHD module. We provide a variety of test problems for this algorithm including both optically thick and thin regimes, and for both gas and radiation pressure dominated flows to demonstrate its accuracy and efficiency.

Active galactic nuclei (AGNs) are powered by geometrically thin accretion disks surrounding a central supermassive black hole. Here we explore the evolution of stars embedded in these extreme astrophysical environments (AGN stars). Because AGN disks are much hotter and denser than most components of the interstellar medium, AGN stars are subject to very different boundary conditions than normal stars. They are also strongly affected by both mass accretion, which can run away given the vast mass of the disk, and mass loss due to super-Eddington winds. Moreover, chemical mixing plays a critical role in the evolution of these stars by allowing fresh hydrogen accreted from the disk to mix into their cores. We find that, depending on the local AGN density and sound speed and the duration of the AGN phase, AGN stars can rapidly become very massive (M > 100 M⊙). These stars undergo core collapse, leave behind compact remnants, and contribute to polluting the disk with heavy elements. We show that the evolution of AGN stars can have a profound impact on the evolution of AGN metallicities, as well as the production of gravitational wave sources observed by LIGO-Virgo. We point to our Galactic Center as a region well suited to testing some of our predictions for this exotic stellar evolutionary channel.

Latent Gaussian copula models provide a powerful means to perform multi-view data integration since these models can seamlessly express dependencies between mixed variable types (binary, continuous, zero-inflated) via latent Gaussian correlations. The estimation of these latent correlations, however, comes at considerable computational cost, having prevented the routine use of these models on high-dimensional data. Here, we propose a new computational approach for estimating latent correlations via a hybrid multi-linear interpolation and optimization scheme. Our approach speeds up the current state of the art computation by several orders of magnitude, thus allowing fast computation of latent Gaussian copula models even when the number of variables p is large. We provide theoretical guarantees for the approximation error of our numerical scheme and support its excellent performance on simulated and real-world data. We illustrate the practical advantages of our method on high-dimensional sparse quantitative and relative abundance microbiome data as well as multi-view data from The Cancer Genome Atlas Project. Our method is implemented in the R package mixedCCA, available at https://github.com/irinagain/mixedCCA this https URL.

Cortical pyramidal neurons receive inputs from multiple distinct neural populations and integrate these inputs in separate dendritic compartments. We explore the possibility that cortical microcircuits implement Canonical Correlation Analysis (CCA), an unsupervised learning method that projects the inputs onto a common subspace so as to maximize the correlations between the projections. To this end, we seek a multi-channel CCA algorithm that can be implemented in a biologically plausible neural network. For biological plausibility, we require that the network operates in the online setting and its synaptic update rules are local. Starting from a novel CCA objective function, we derive an online optimization algorithm whose optimization steps can be implemented in a single-layer neural network with multi-compartmental neurons and local non-Hebbian learning rules. We also derive an extension of our online CCA algorithm with adaptive output rank and output whitening. Interestingly, the extension maps onto a neural network whose neural architecture and synaptic updates resemble neural circuitry and synaptic plasticity observed experimentally in cortical pyramidal neurons.

In cells, cytoskeletal filament networks are responsible for cell movement, growth, and division. Filaments in the cytoskeleton are driven and organized by crosslinking molecular motors. In reconstituted cytoskeletal systems, motor activity is responsible for far-from-equilibrium phenomena such as active stress, self-organized flow, and spontaneous nematic defect generation. How microscopic interactions between motors and filaments lead to larger-scale dynamics remains incompletely understood. To build from motor–filament interactions to predict bulk behavior of cytoskeletal systems, more computationally efficient techniques for modeling motor–filament interactions are needed. Here, we derive a coarse-graining hierarchy of explicit and continuum models for crosslinking motors that bind to and walk on filament pairs. We compare the steady-state motor distribution and motor-induced filament motion for the different models and analyze their computational cost. All three models agree well in the limit of fast motor binding kinetics. Evolving a truncated moment expansion of motor density speeds the computation by 103–106 compared to the explicit or continuous-density simulations, suggesting an approach for more efficient simulation of large networks. These tools facilitate further study of motor–filament networks on micrometer to millimeter length scales.

Active fluids consume fuel at the microscopic scale, converting this energy into forces that can drive macroscopic motions over scales far larger than their microscopic constituents. In some cases, the mechanisms that give rise to this phenomenon have been well characterized, and can explain experimentally observed behaviors in both bulk fluids and those confined in simple stationary geometries. More recently, active fluids have been encapsulated in viscous drops or elastic shells so as to interact with an outer environment or a deformable boundary. Such systems are not as well understood. In this work, we examine the behavior of droplets of an active nematic fluid. We study their linear stability about the isotropic equilibrium over a wide range of parameters, identifying regions in which different modes of instability dominate. Simulations of their full dynamics are used to identify their nonlinear behavior within each region. When a single mode dominates, the droplets behave simply: as rotors, swimmers, or extensors. When parameters are tuned so that multiple modes have nearly the same growth rate, a pantheon of modes appears, including zigzaggers, washing machines, wanderers, and pulsators.

The Hubbard model represents the fundamental model for interacting quantum systems and electronic correlations. Using the two-dimensional half-filled Hubbard model at weak coupling as testing grounds, we perform a comparative study of a comprehensive set of state of the art quantum many-body methods. Upon cooling into its insulating antiferromagnetic ground-state, the model hosts a rich sequence of distinct physical regimes with crossovers between a high-temperature incoherent regime, an intermediate temperature metallic regime and a low-temperature insulating regime with a pseudogap created by antiferromagnetic fluctuations. We assess the ability of each method to properly address these physical regimes and crossovers through the computation of several observables probing both quasiparticle properties and magnetic correlations, with two numerically exact methods (diagrammatic and determinantal quantum Monte Carlo) serving as a benchmark. By combining computational results and analytical insights, we elucidate the nature and role of spin fluctuations in each of these regimes and explain, in particular, how quasiparticles can coexist with increasingly long-range antiferromagnetic correlations in the metallic regime. We also critically discuss whether imaginary time methods are able to capture the non-Fermi liquid singularities of this fully nested system.