Publications

A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The boundaries themselves may be non-smooth. The scheme, which builds on recursively compressed inverse preconditioning (RCIP), is universal as it is independent of the nature of the singularities. Strong right-hand-side singularities, such as $1/|r|^\alpha$ with $\alpha$ close to $1$, can be treated in full machine precision. Adaptive refinement is used only in the recursive construction of the preconditioner, leading to an optimal number of discretization points and superior stability in the solve phase. The performance of the scheme is illustrated via several numerical examples, including an application to an integral equation derived from the linearized BGKW kinetic equation for the steady Couette flow.

Linear systems involving contiguous submatrices of the discrete Fourier transform (DFT)matrix arise in many applications, such as Fourier extension, superresolution, and coherent diffraction imaging. We show that the condition number of any such p\times q submatrix of the N\times NDFT matrix is at least exp\bigl( \pi 2\bigl[ min(p,q) - pqN\bigr] \bigr) , up to algebraic prefactors.That is, fixing the shape parameters (\alpha ,\beta ) := (p/N,q/N)\in (0,1)2, the growth ise\rho NasN\rightarrow \infty , the exponential rate being\rho =\pi 2[min(\alpha ,\beta ) - \alpha \beta ]. Our proof uses theKaiser--Bessel transform pair (of which we give a self-contained proof), plus estimates on sums over distorted sinc functions, to construct a localized trial vector whose DFT is also localized. We warm up with an elementary proof of the above but with half the rate, via a periodized Gaussian trial vector. Using low-rank approximation of the kerneleixt, we also prove another lower bound (4/e\pi \alpha )q, up to algebraic prefactors, which is stronger than the above for small\alpha and\beta . When combined, the bounds are within a factor of two ofthe empirical asymptotic rate, uniformly over (0,1)2, and become sharp in certain regions.However, the results are not asymptotic: they apply to essentially allN,p, andq, and with all constants explicit.

Many high-throughput sequencing data sets in biology are compositional in nature. A prominent example is microbiome profiling data, including targeted amplicon-based and metagenomic sequencing data. These profiling data comprises surveys of microbial communities in their natural habitat and sparse proportional (or compositional) read counts that represent operational taxonomic units or genes. When paired measurements of other covariates, including physicochemical properties of the habitat or phenotypic variables of the host, are available, inference of parsimonious and robust statistical relationships between the microbial abundance data and the covariate measurements is often an important first step in exploratory data analysis. To this end, we propose a sparse robust statistical regression framework that considers compositional and non-compositional measurements as predictors and identifies outliers in continuous response variables. Our model extends the seminal log-contrast model of Aitchison and Bacon-Shone (1984) by a mean shift formulation for capturing outliers, sparsity-promoting convex and non-convex penalties for parsimonious model selection, and data-driven robust initialization procedures adapted to the compositional setting. We show, in theory and simulations, the ability of our approach to jointly select a sparse set of predictive microbial features and identify outliers in the response. We illustrate the viability of our method by robustly predicting human body mass indices from American Gut Project amplicon data and non-compositional covariate data. We believe that the robust estimators introduced here and available in the R package RobRegCC can serve as a practical tool for reliable statistical regression analysis of compositional data, including microbiome survey data.

An efficient, reliable, and interpretable global solution method, the Deep learning-based algorithm for Heterogeneous Agent Models (DeepHAM), is proposed for solving high dimensional heterogeneous agent models with aggregate shocks. The state distribution is approximately represented by a set of optimal generalized moments. Deep neural networks are used to approximate the value and policy functions, and the objective is optimized over directly simulated paths. In addition to being an accurate global solver, this method has three additional features. First, it is computationally efficient in solving complex heterogeneous agent models, and it does not suffer from the curse of dimensionality. Second, it provides a general and interpretable representation of the distribution over individual states, which is crucial in addressing the classical question of whether and how heterogeneity matters in macroeconomics. Third, it solves the constrained efficiency problem as easily as it solves the competitive equilibrium, which opens up new possibilities for studying optimal monetary and fiscal policies in heterogeneous agent models with aggregate shocks.

In this paper, we consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at a collection of receivers outside the object. The data is assumed to be generated by plane waves impinging on the unknown obstacle from multiple directions and at multiple frequencies. This inverse problem can be reformulated as an optimization problem: that of finding band-limited shape and impedance functions which minimize the L2 distance between the computed value of the scattered field at the receivers and the given measurement data. The optimization problem is highly non-linear, non-convex, and ill-posed. Moreover, the objective function is computationally expensive to evaluate (since a large number of Helmholtz boundary value problems need to be solved at every iteration in the optimization loop). The recursive linearization approach (RLA) proposed by Chen has been successful in addressing these issues in the context of recovering the sound speed of an inhomogeneous object or the shape of a sound-soft obstacle. We present an extension of the RLA for the recovery of both the shape and impedance functions of the object. The RLA is, in essence, a continuation method in frequency where a sequence of single frequency inverse problems is solved. At each higher frequency, one attempts to recover incrementally higher resolution features using a step assumed to be small enough to ensure that the initial guess obtained at the preceding frequency lies in the basin of attraction for Newton’s method at the new frequency. We demonstrate the effectiveness of this approach with several numerical examples. Surprisingly, we find that one can recover the shape with high accuracy even when the measurements are generated by sound-hard or sound-soft objects, eliminating the need to know the precise boundary conditions appropriate for modeling the object under consideration. While the method is effective in obtaining high-quality reconstructions for many complicated geometries and impedance functions, a number of interesting open questions remain regarding the convergence behavior of the approach. We present numerical experiments that suggest underlying mechanisms of success and failure, pointing out areas where improvements could help lead to robust and automatic tools for the solution of inverse obstacle scattering problems.

This paper presents the results of a search for generic short-duration gravitational-wave transients in data from the third observing run of Advanced LIGO and Advanced Virgo. Transients with durations of milliseconds to a few seconds in the 24--4096 Hz frequency band are targeted by the search, with no assumptions made regarding the incoming signal direction, polarization or morphology. Gravitational waves from compact binary coalescences that have been identified by other targeted analyses are detected, but no statistically significant evidence for other gravitational wave bursts is found. Sensitivities to a variety of signals are presented. These include updated upper limits on the source rate-density as a function of the characteristic frequency of the signal, which are roughly an order of magnitude better than previous upper limits. This search is sensitive to sources radiating as little as ∼10−10M⊙c2 in gravitational waves at ∼70 Hz from a distance of 10~kpc, with 50\% detection efficiency at a false alarm rate of one per century. The sensitivity of this search to two plausible astrophysical sources is estimated: neutron star f-modes, which may be excited by pulsar glitches, as well as selected core-collapse supernova models.

The SDSS-IV Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey has obtained high-resolution spectra for thousands of red giant stars distributed among the massive satellite galaxies of the Milky Way (MW): the Large and Small Magellanic Clouds (LMC/SMC), the Sagittarius Dwarf (Sgr), Fornax (Fnx), and the now fully disrupted \emph{Gaia} Sausage/Enceladus (GSE) system. We present and analyze the APOGEE chemical abundance patterns of each galaxy to draw robust conclusions about their star formation histories, by quantifying the relative abundance trends of multiple elements (C, N, O, Mg, Al, Si, Ca, Fe, Ni, and Ce), as well as by fitting chemical evolution models to the [α/Fe]-[Fe/H] abundance plane for each galaxy. Results show that the chemical signatures of the starburst in the MCs observed by Nidever et al. in the α-element abundances extend to C+N, Al, and Ni, with the major burst in the SMC occurring some 3-4 Gyr before the burst in the LMC. We find that Sgr and Fnx also exhibit chemical abundance patterns suggestive of secondary star formation epochs, but these events were weaker and earlier (∼~5-7 Gyr ago) than those observed in the MCs. There is no chemical evidence of a second starburst in GSE, but this galaxy shows the strongest initial star formation as compared to the other four galaxies. All dwarf galaxies had greater relative contributions of AGB stars to their enrichment than the MW. Comparing and contrasting these chemical patterns highlight the importance of galaxy environment on its chemical evolution.

The competition between thermal fluctuations and potential forces governs the stability of matter in equilibrium, in particular the proliferation and annihilation of topological defects. However, driving matter out of equilibrium allows for a new class of forces that are neither attractive nor repulsive, but rather transverse. The possibility of activating transverse forces raises the question of how they affect basic principles of material self-organization and control. Here we show that transverse forces organize colloidal spinners into odd elastic crystals crisscrossed by motile dislocations. These motile topological defects organize into a polycrystal made of grains with tunable length scale and rotation rate. The self-kneading dynamics drive super-diffusive mass transport, which can be controlled over orders of magnitude by varying the spinning rate. Simulations of both a minimal model and fully resolved hydrodynamics establish the generic nature of this crystal whorl state. Using a continuum theory, we show that both odd and Hall stresses can destabilize odd elastic crystals, giving rise to a generic state of crystalline active matter. Adding rotations to a material’s constituents has far-reaching consequences for continuous control of structures and transport at all scales.

A significant fraction of Milky Way (MW) satellites exhibit phase-space properties consistent with a coherent orbital plane. Using tailored N-body simulations of a spherical MW halo that recently captured a massive (1.8 × 1011 M⊙) LMC-like satellite, we identify the physical mechanisms that may enhance the clustering of orbital poles of objects orbiting the MW. The LMC deviates the orbital poles of MW dark matter particles from the present-day random distribution. Instead, the orbital poles of particles beyond R ≈ 50 kpc cluster near the present-day orbital pole of the LMC along a sinusoidal pattern across the sky. The density of orbital poles is enhanced near the LMC by a factor $\delta {\rho }_{\max }$ = 30 percent (50 percent) with respect to underdense regions and δρiso = 15 percent (30 percent) relative to the isolated MW simulation (no LMC) between 50 and 150 kpc (150–300 kpc). The clustering appears after the LMC's pericenter (≈50 Myr ago, 49 kpc) and lasts for at least 1 Gyr. Clustering occurs because of three effects: (1) the LMC shifts the velocity and position of the central density of the MW's halo and disk; (2) the dark matter dynamical friction wake and collective response induced by the LMC change the kinematics of particles; (3) observations of particles selected within spatial planes suffer from a bias, such that measuring orbital poles in a great circle in the sky enhances the probability of their orbital poles being clustered. This scenario should be ubiquitous in hosts that recently captured a massive satellite (at least ≈1:10 mass ratio), causing the clustering of orbital poles of halo tracers.

In most animals, the oocyte is the largest cell by volume. The oocyte undergoes a period of large-scale growth during its development, prior to fertilization. At first glance, tissues that support the development of the oocyte in different organisms have diverse cellular characteristics that would seem to prohibit functional comparisons. However, these tissues often act with a common goal of establishing dynamic forms of two-way communication with the oocyte. We propose that this bidirectional communication between oocytes and support cells is a universal phenomenon that can be directly compared across species. Specifically, we highlight fruit fly and mouse oogenesis to demonstrate that similarities and differences in these systems should be used to inform and design future experiments in both models.