Publications

In solving hard computational problems, semidefinite program (SDP) relaxations often play an
important role because they come with a guarantee of optimality. Here, we focus on a popular
semidefinite relaxation of K-means clustering which yields the same solution as the non-convex
original formulation for well segregated datasets. We report an unexpected finding: when data
contains (greater than zero-dimensional) manifolds, the SDP solution captures such geometrical
structures. Unlike traditional manifold embedding techniques, our approach does not rely on manually defining a kernel but rather enforces locality via a nonnegativity constraint. We thus call our
approach NOnnegative MAnifold Disentangling, or NOMAD. To build an intuitive understanding
of its manifold learning capabilities, we develop a theoretical analysis of NOMAD on idealized
datasets. While NOMAD is convex and the globally optimal solution can be found by generic SDP
solvers with polynomial time complexity, they are too slow for modern datasets. To address this
problem, we analyze a non-convex heuristic and present a new, convex and yet efficient, algorithm,
based on the conditional gradient method. Our results render NOMAD a versatile, understandable,
and powerful tool for manifold learning.

We test a method to reduce unwanted sample variance when predicting Lyman-α (lyα) forest power spectra from cosmological hydrodynamical simulations. Sample variance arises due to sparse sampling of modes on large scales and propagates to small scales through non-linear gravitational evolution. To tackle this, we generate initial conditions in which the density perturbation amplitudes are {\it fixed} to the ensemble average power spectrum -- and are generated in {\it pairs} with exactly opposite phases. We run 50 such simulations (25 pairs) and compare their performance against 50 standard simulations by measuring the lyα 1D and 3D power spectra at redshifts z=2, 3, and 4. Both ensembles use periodic boxes of 40 Mpc/h containing 5123 particles each of dark matter and gas. As a typical example of improvement, for wavenumbers k=0.25 h/Mpc at z=3, we find estimates of the 1D and 3D power spectra converge 34 and 12 times faster in a paired-fixed ensemble compared with a standard ensemble. We conclude that, by reducing the computational time required to achieve fixed accuracy on predicted power spectra, the method frees up resources for exploration of varying thermal and cosmological parameters -- ultimately allowing the improved precision and accuracy of statistical inference.

Pressure plays a key role in the study of quantum materials. Its application in angle resolved photoemission (ARPES) studies, however, has so far been limited. Here, we report the evolution of the k-space electronic structure of bulk Ca2RuO4, lightly doped with Pr, under uniaxial strain. Using ultrathin plate-like crystals, we achieve uniaxial strain levels up to −4.1%, sufficient to suppress the insulating Mott phase and access the previously unexplored electronic structure of the metallic state at low temperature. ARPES experiments performed while tuning the uniaxial strain reveal that metallicity emerges from a marked redistribution of charge within the Ru t2g shell, accompanied by a sudden collapse of the spectral weight in the lower Hubbard band and the emergence of a well-defined Fermi surface which is devoid of pseudogaps. Our results highlight the profound roles of lattice energetics and of the multiorbital nature of Ca2RuO4 in this archetypal Mott transition and open new perspectives for spectroscopic measurements.

The orbital properties of stars in the disk are signatures of their formation, but they are also expected to change over time due to the dynamical evolution of the Galaxy. Stellar orbits can be quantified by three dynamical actions, J_r, L_z, and J_z, which provide measures of the orbital eccentricity, guiding radius, and non-planarity, respectively. Changes in these dynamical actions over time reflect the strength and efficiency of the evolutionary processes that drive stellar redistributions. We examine how dynamical actions of stars are correlated with their age using two samples of stars with well-determined ages: 78 solar twin stars (with ages to ~5%) and 4376 stars from the APOKASC2 sample (~20%). We compute actions using spectroscopic radial velocities from previous surveys and parallax and proper motion measurements from Gaia DR2. We find weak gradients in all actions with stellar age, of (7.51 +/- 0.52, -29.0 +/- 1.83, 1.54 +/- 0.18) kpc km/s/Gyr for J_r, L_z, and J_z, respectively. There is, however, significant scatter in the action-age relation. We caution that our results will be affected by the restricted spatial extent of our sample, particularly in the case of J_z. Nevertheless, these action-age gradients and their associated variances provide strong constraints on the efficiency of the mechanisms that drive the redistribution of stellar orbits over time and demonstrate that actions are informative as to stellar age. The shallow action-age gradients combined with the large dispersion in each action at a given age, however, renders the prospect of age inference from orbits of individual stars bleak. Using the precision measurements of [Fe/H] and [α/Fe] for our stars we investigate the abundance-action relationship and find weak correlations. Similar to our stellar age results, dynamical actions afford little discriminating power between low- and high-α stars.

In systems with detected planets, hot-Jupiters and compact systems of multiple planets are nearly mutually exclusive. We compare the relative occurrence of these two architectures as a fraction of detected planetary systems to determine the role that metallicity plays in planet formation. We show that compact multi-planet systems occur more frequently around stars of increasingly lower metallicities using spectroscopically derived abundances for more than 700 planet hosts. At higher metallicities, compact multi-planet systems comprise a nearly constant fraction of the planet hosts despite the steep rise in the fraction of hosts containing hot and cool-Jupiters. Since metal poor stars have been underrepresented in planet searches, this implies that the occurrence rate of compact multis is higher than previously reported. Due to observational limits, radial velocity planet searches have focused mainly on high-metallicity stars where they have a higher chance of finding giant planets. New extreme-precision radial velocity instruments coming online that can detect these compact multi-planet systems can target lower metallicity stars to find them.

The 3D spatiotemporal organization of the human genome inside the cell nucleus remains a major open question in cellular biology. In the time between two cell divisions, chromatin - the functional form of DNA in cells - fills the nucleus in its uncondensed polymeric form. Recent in vivo imaging experiments reveal that the chromatin moves coherently, having displacements with long-ranged correlations on the scale of microns and lasting for seconds. To elucidate the mechanism(s) behind these motions, we develop a novel coarse-grained active-polymer model where chromatin is represented as a confined flexible chain acted upon by molecular motors, which perform work by exerting dipolar forces on the system. Numerical simulations of this model account for steric and hydrodynamic interactions as well as internal chain mechanics. These demonstrate that coherent motions emerge in systems involving extensile dipoles and are accompanied by large-scale chain reconfigurations and nematic ordering. Comparisons with experiments show good qualitative agreement and support the hypothesis that self-organizing long-ranged hydrodynamic couplings between chromatin-associated active motor proteins are responsible for the observed coherent dynamics.

One of the great challenges in biology is to understand the mechanisms by which morphogenetic processes arise from molecular activities. We investigated this problem in the context of actomyosin-based cortical flow in C. elegans zygotes, where large-scale flows emerge from the collective action of actomyosin filaments and actin binding proteins (ABPs). Large-scale flow dynamics can be captured by active gel theory by considering force balances and conservation laws in the actomyosin cortex. However, which molecular activities contribute to flow dynamics and large-scale physical properties such as viscosity and active torque is largely unknown. By performing a candidate RNAi screen of ABPs and actomyosin regulators we demonstrate that perturbing distinct molecular processes can lead to similar flow phenotypes. This is indicative for a 'morphogenetic degeneracy' where multiple molecular processes contribute to the same large-scale physical property. We speculate that morphogenetic degeneracies contribute to the robustness of bulk biological matter in development.

With contemporary infrared spectroscopic surveys like APOGEE, red-giant stars can be observed to distances and extinctions at which Gaia parallaxes are not highly informative. Yet the combination of effective temperature, surface gravity, composition, and age - all accessible through spectroscopy - determines a giant's luminosity. Therefore spectroscopy plus photometry should enable precise spectrophotometric distance estimates. Here we use the APOGEE-Gaia-2MASS-WISE overlap to train a data-driven model to predict parallaxes for red-giant branch stars with 0

We measure the circular velocity curve vc(R) of the Milky Way with the highest precision to date across Galactocentric distances of 5≤R≤25 kpc. Our analysis draws on the 6-dimensional phase-space coordinates of ≳23,000 luminous red-giant stars, for which we previously determined precise parallaxes using a data-driven model that combines spectral data from APOGEE with photometric information from WISE, 2MASS, and Gaia. We derive the circular velocity curve with the Jeans equation assuming an axisymmetric gravitational potential. At the location of the Sun we determine the circular velocity with its formal uncertainty to be vc(R⊙)=(229.0±0.2)kms−1 with systematic uncertainties at the ∼5% level. We find that the velocity curve is gently but significantly declining at (−1.7±0.1)kms−1kpc−1, with a systematic uncertainty of 0.46kms−1kpc−1, beyond the inner 5 kpc. We exclude the inner 5 kpc from our analysis due to the presence of the Galactic bar, which strongly influences the kinematic structure and requires modeling in a non-axisymmetric potential. Combining our results with external measurements of the mass distribution for the baryonic components of the Milky Way from other studies, we estimate the Galaxy's dark halo mass within the virial radius to be Mvir=(7.25±0.26)⋅1011M⊙ and a local dark matter density of ρdm(R⊙)=0.30±0.03GeVcm−3.

Effective discovery of causal disease genes must overcome the statistical challenges of quantitative genetics studies and the practical limitations of human biology experiments. Here we developed diseaseQUEST, an integrative approach that combines data from human genome-wide disease studies with in silico network models of tissue- and cell-type-specific function in model organisms to prioritize candidates within functionally conserved processes and pathways. We used diseaseQUEST to predict candidate genes for 25 different diseases and traits, including cancer, longevity, and neurodegenerative diseases. Focusing on Parkinson's disease (PD), a diseaseQUEST-directed Caenhorhabditis elegans behavioral screen identified several candidate genes, which we experimentally verified and found to be associated with age-dependent motility defects mirroring PD clinical symptoms. Furthermore, knockdown of the top candidate gene, bcat-1, encoding a branched chain amino acid transferase, caused spasm-like 'curling' and neurodegeneration in C. elegans, paralleling decreased BCAT1 expression in PD patient brains. diseaseQUEST is modular and generalizable to other model organisms and human diseases of interest.