Publications

We adapt recent tools developed for the analysis of Stochastic Gradient Descent (SGD) in non-convex optimization to obtain convergence and sample complexity guarantees for the vanilla policy gradient (PG). Our only assumptions are that the expected return is smooth w.r.t. the policy parameters, that its H-step truncated gradient is close to the exact gradient, and a certain ABC assumption. This assumption requires the second moment of the estimated gradient to be bounded by A ≥ 0 times the suboptimality gap, B ≥ 0 times the norm of the full batch gradient and an additive constant C ≥ 0, or any combination of aforementioned. We show that the ABC assumption is more general than the commonly used assumptions on the policy space to prove convergence to a stationary point. We provide a single convergence theorem that recovers the O(−4) sample complexity of PG. Our results also affords greater f lexibility in the choice of hyper parameters such as the step size and places no restriction on the batch size m, including the single trajectory case (i.e., m = 1). We then instantiate our theorem in different settings, where we both recover existing results and obtained improved sample complexity, e.g., for convergence to the global optimum for Fisher-nondegenerated parameterized policies.

We present a principled approach for designing stochastic Newton methods for solving f inite sum optimization problems. Our approach has two steps. First, we re-write the stationarity conditions as a system of nonlinear equations that associates each data point to a new row. Second, we apply a Subsampled Newton Raphson method to solve this system of nonlinear equations. Using our approach, we develop a new Stochastic Average Newton (SAN) method, which is incremental by design, in that it requires only a single data point per iteration. It is also cheap to implement when solving regularized generalized linear models, with a cost per iteration of the order of the number of the parameters. We show through numerical experiments that SAN requires no knowledge about the problem, neither parameter tuning, while remaining competitive as compared to classical variance reduced gradient methods (e.g. SAG and SVRG), incremental Newton and quasiNewton methods (e.g. SNM, IQN).

We present the results from a new search for candidate galaxies at z ~ 8.5-11 discovered over the 850 arcmin^2 area probed by the Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey (CANDELS). We use a photometric redshift selection including both Hubble and Spitzer Space Telescope photometry to robustly identify galaxies in this epoch at F160W 8. We calculate that the presence of seven galaxies in a single field (EGS) is an outlier at the 2-sigma significance level, implying the discovery of a significant overdensity. These scenarios will be imminently testable to high confidence within the first year of observations of the James Webb Space Telescope.

To understand the formation of the Milky Way's prominent bar it is important to know whether stars in the bar differ in the chemical element composition of their birth material as compared to disk stars. This requires stellar abundance measurements for large samples across the Milky Way's body. Such samples, e.g., luminous red giant stars observed by the Sloan Digital Sky Survey's APOGEE survey, will inevitably span a range of stellar parameters; as a consequence, both modeling imperfections and stellar evolution may preclude consistent and precise estimates of their chemical composition at a level of purported bar signatures, which has left current analyses of a chemically distinct bar inconclusive. Here, we develop a new self-calibration approach to eliminate both modeling and astrophysical abundance systematics among red giant branch (RGB) stars of different luminosities (and hence surface gravity $\mathrm{log}g$). We apply our method to 48,853 luminous APOGEE Data Release 16 RGB stars to construct spatial abundance maps of 20 chemical elements near the Milky Way's mid-plane, covering galactocentric radii of 0 kpc < RGC < 20 kpc. Our results indicate that there are no abundance variations whose geometry matches that of the bar, and that the mean abundance gradients vary smoothly and monotonically with galactocentric radius. We confirm that the high-α disk is chemically homogeneous, without spatial gradients. Furthermore, we present the most precise [Fe/H] versus RGC gradient to date with a slope of − 0.057 ±0.001 dex kpc−1 out to approximately 15 kpc.

We demonstrate the utility of the bispectrum, the Fourier three-point correlation function, for studying driving scales of magnetohydrodynamic (MHD) turbulence in the interstellar medium. We calculate the bispectrum by implementing a parallelized Monte Carlo direct measurement method, which we have made publicly available. In previous works, the bispectrum has been used to identify non-linear scaling correlations and break degeneracies in lower-order statistics like the power spectrum. We find that the bicoherence, a related statistic which measures phase coupling of Fourier modes, identifies turbulence driving scales using density and column density fields. In particular, it shows that the driving scale is phase-coupled to scales present in the turbulent cascade. We also find that the presence of an ordered magnetic field at large-scales enhances phase coupling as compared to a pure hydrodynamic case. We, therefore, suggest the bispectrum and bicoherence as tools for searching for non-locality for wave interactions in MHD turbulence.

The present-day age–metallicity relation (AMR) is a record of the star formation history of galaxies, as this traces the chemical enrichment of the gas over time. We use a zoomed-in cosmological simulation that reproduces key signatures of the Milky Way (MW), g2.79e12 from the NIHAO-UHD project, to examine how stellar migration and satellite infall shape the AMR across the disc. We find in the simulation, similar to the MW, the AMR in small spatial regions (R, z) shows turning points that connect changes in the direction of the relations. The turning points in the AMR in the simulation are a signature of late satellite infall. This satellite infall has a mass radio similar as that of the Sagittarius dwarf to the MW (∼0.001). Stars in the apex of the turning points are young and have nearly not migrated. The late satellite infall creates the turning points via depositing metal-poor gas in the disc, triggering star formation of stars in a narrow metallicity range compared to the overall AMR. The main effect of radial migration on the AMR turning points is to widen the metallicity range of the apex. This can happen when radial migration brings stars born from the infallen gas in other spatial bins, with slightly different metallicities, into the spatial bin of interest. These results indicate that it is possible that the passage of the Sagittarius dwarf galaxy played a role in creating the turning points that we see in the AMR in the Milky Way.

Astrophysical objects possessing a material surface (white dwarfs, young stars, etc.) may accrete gas from the disc through the so-called surface boundary layer (BL), in which the angular velocity of the accreting gas experiences a sharp drop. Acoustic waves excited by the supersonic shear in the BL play an important role in mediating the angular momentum and mass transport through that region. Here we examine the characteristics of the angular momentum transport produced by the different types of wave modes emerging in the inner disc, using the results of a large suite of hydrodynamic simulations of the BLs. We provide a comparative analysis of the transport properties of different modes across the range of relevant disc parameters. In particular, we identify the types of modes which are responsible for the mass accretion onto the central object. We find the correlated perturbations of surface density and radial velocity to provide an important contribution to the mass accretion rate. Although the wave-driven transport is intrinsically non-local, we do observe a clear correlation between the angular momentum flux injected into the disc by the waves and the mass accretion rate through the BL. We find the efficiency of angular momentum transport (normalized by thermal pressure) to be a weak function of the flow Mach number. We also quantify the wave-driven evolution of the inner disc, in particular the modification of the angular frequency profile in the disc. Our results pave the way for understanding wave-mediated transport in future three-dimensional, magnetohydrodynamic studies of the BLs.

Gastrulation movements in all animal embryos start with regulated deformations of patterned epithelial sheets, which are driven by cell divisions, cell shape changes, and cell intercalations. Each of these behaviors has been associated with distinct aspects of gastrulation and has been a subject of intense research using genetic, cell biological, and more recently, biophysical approaches. Most of these studies, however, focus either on cellular processes driving gastrulation or on large-scale tissue deformations. Recent advances in microscopy and image processing create a unique opportunity for integrating these complementary viewpoints. Here, we take a step toward bridging these complementary strategies and deconstruct the early stages of gastrulation in the entire Drosophila embryo. Our approach relies on an integrated computational framework for cell segmentation and tracking and on efficient algorithms for event detection. The detected events are then mapped back onto the blastoderm shell, providing an intuitive visual means to examine complex cellular activity patterns within the context of their initial anatomic domains. By analyzing these maps, we identified that the loss of nearly half of surface cells to invaginations is compensated primarily by transient mitotic rounding. In addition, by analyzing mapped cell intercalation events, we derived direct quantitative relations between intercalation frequency and the rate of axis elongation. This work is setting the stage for systems-level dissection of a pivotal step in animal development.

Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes have in-plane fluid-like dynamics and out-of-plane bending elasticity. Their open edges and micron length scale provide a tractable system to study the equilibrium energetics and dynamic pathways of membrane assembly and reconfiguration. Here, we find that doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddle-shaped surfaces with complex edge structures. The saddle-shaped membranes are well-approximated by Enneper's minimal surfaces. Theoretical modeling demonstrates that their formation is driven by increasing positive Gaussian modulus, which in turn is controlled by the fraction of short rods. Further coalescence of saddle-shaped surfaces leads to diverse topologically distinct structures, including catenoids, tri-noids, four-noids, and higher order structures. At long time scales, we observe the formation of a system-spanning, sponge-like phase. The unique features of colloidal membranes reveal the topological transformations that accompany coalescence pathways in real time. We enhance the functionality of these membranes by making their shape responsive to external stimuli. Our results demonstrate a novel pathway towards control of thin elastic sheets' shape and topology -- a pathway driven by the emergent elasticity induced by compositional heterogeneity.

We introduce a closure model for coarse-grained kinetic theories of polar active fluids. Based on a thermodynamically consistent, quasi-equilibrium approximation of the particle distribution function, the model closely captures important analytical properties of the kinetic theory, including its linear stability and the balance of entropy production and dissipation. Nonlinear simulations show the model reproduces the qualitative behavior and nonequilibrium statistics of the kinetic theory, unlike commonly used closure models. We use the closure model to simulate highly turbulent suspensions in both two and three dimensions in which we observe complex multiscale dynamics, including large concentration fluctuations and a proliferation of polar and nematic defects.