Publications

In recent years, semidefinite programs (SDP) have been the subject of interesting research in the field of clustering. In many cases, these convex programs deliver the same answers as non-convex alternatives and come with a guarantee of optimality. Unexpectedly, we find that a popular semidefinite relaxation of K-means (SDP-KM), learns manifolds present in the data, something not possible with the original K-means formulation. To build an intuitive understanding of its manifold learning capabilities, we develop a theoretical analysis of SDP-KM on idealized datasets. Additionally, we show that SDP-KM even segregates linearly non-separable manifolds. SDP-KM is convex and the globally optimal solution can be found by generic SDP solvers with polynomial time complexity. To overcome poor performance of these solvers on large datasets, we explore efficient algorithms based on the explicit Gramian representation of the problem. These features render SDP-KM a versatile and interesting tool for manifold learning while remaining amenable to theoretical analysis.

We study the dynamics of screening in photodoped Mott insulators with long-ranged interactions using a nonequilibrium implementation of the GW plus extended dynamical mean-field theory formalism. Our study demonstrates that the complex interplay of the injected carriers with bosonic degrees of freedom (charge fluctuations) can result in long-lived transient states with properties that are distinctly different from those of thermal equilibrium states. Systems with strong nonlocal interactions are found to exhibit a self-sustained population inversion of the doublons and holes. This population inversion leads to low-energy antiscreening which can be detected in time-resolved electron-energy-loss spectra.

We determine the radio size distribution of a large sample of 152 SMGs in COSMOS that were detected with ALMA at 1.3 mm. For this purpose, we used the observations taken by the VLA-COSMOS 3 GHz Large Project. One hundred and fifteen of the 152 target SMGs were found to have a 3 GHz counterpart. The median value of the major axis FWHM at 3 GHz is derived to be 4.6±0.4 kpc. The radio sizes show no evolutionary trend with redshift, or difference between different galaxy morphologies. We also derived the spectral indices between 1.4 and 3 GHz, and 3 GHz brightness temperatures for the sources, and the median values were found to be α=−0.67 and TB=12.6±2 K. Three of the target SMGs, which are also detected with the VLBA, show clearly higher brightness temperatures than the typical values. Although the observed radio emission appears to be predominantly powered by star formation and supernova activity, our results provide a strong indication of the presence of an AGN in the VLBA and X-ray-detected SMG AzTEC/C61. The median radio-emitting size we have derived is 1.5-3 times larger than the typical FIR dust-emitting sizes of SMGs, but similar to that of the SMGs' molecular gas component traced through mid-J line emission of CO. The physical conditions of SMGs probably render the diffusion of cosmic-ray electrons inefficient, and hence an unlikely process to lead to the observed extended radio sizes. Instead, our results point towards a scenario where SMGs are driven by galaxy interactions and mergers. Besides triggering vigorous starbursts, galaxy collisions can also pull out the magnetised fluids from the interacting disks, and give rise to a taffy-like synchrotron-emitting bridge. This provides an explanation for the spatially extended radio emission of SMGs, and can also cause a deviation from the well-known IR-radio correlation.

We explore theoretically the aerodynamics of a recently fabricated jellyfish-like flying machine (Ristroph & Childress, J. R. Soc. Interface, vol. 11 (92), 2014, 20130992). This experimental device achieves flight and hovering by opening and closing opposing sets of wings. It displays orientational or postural flight stability without additional control surfaces or feedback control. Our model ‘machine’ consists of two mirror-symmetric massless flapping wings connected to a volumeless body with mass and moment of inertia. A vortex sheet shedding and wake model is used for the flow simulation. Use of the fast multipole method allows us to simulate for long times and resolve complex wakes. We use our model to explore the design parameters that maintain body hovering and ascent, and investigate the performance of steady ascent states. We find that ascent speed and efficiency increase as the wings are brought closer, due to a mirror-image ‘ground-effect’ between the wings. Steady ascent is approached exponentially in time, which suggests a linear relationship between the aerodynamic force and ascent speed. We investigate the orientational stability of hovering and ascent states by examining the flyer’s free response to perturbation from a transitory external torque. Our results show that bottom-heavy flyers (centre of mass below the geometric centre) are capable of recovering from large tilts, whereas the orientation of the top-heavy flyers diverges. These results are consistent with the experimental observations in Ristroph & Childress (J. R. Soc. Interface, vol. 11 (92), 2014, 20130992), and shed light upon future designs of flapping-wing micro aerial vehicles that use jet-based mechanisms.

Distances to individual stars in our own Galaxy are critical in order to piece together the nature of its velocity and spatial structure. Core helium burning red clump (RC) stars have similar luminosities, are abundant throughout the Galaxy, and thus constitute good standard candles. We build a hierarchical probabilistic model to quantify the quality of RC stars as standard candles using parallax measurements from the first Gaia data release. A unique aspect of our methodology is to fully account for (and marginalize over) parallax, photometry, and dust corrections uncertainties, which leads to more robust results than standard approaches. We determine the absolute magnitude and intrinsic dispersion of the RC in 2MASS bands J, H, Ks, Gaia G band, and WISE bands W1, W2, W3, and W4. We find that the absolute magnitude of the RC is −1.61± 0.01 (in Ks), +0.44± 0.01 (in G) , −0.93± 0.01 (in J), −1.46± 0.01 (in H), −1.68± 0.02 (in W1), −1.69± 0.02 (in W2), −1.67± 0.02 (in W3), 1.76± 0.01 mag (in W4). The mean intrinsic dispersion is ∼0.17± 0.03 mag across all bands (yielding a typical distance precision of ∼ 8%). Thus RC stars are reliable and precise standard candles. In addition, we have also re-calibrated the zero point of the absolute magnitude of the RC in each band, which provide a benchmark for future studies to estimate distances to RC stars. Finally, the parallax error shrinkage in the hierarchical model outlined in this work can be used to obtain more precise parallaxes than Gaia for the most distant RC stars across the Galaxy.

The absolute number and the density profiles of different types of stars in the solar neighborhood are a fundamental anchor for studies of the initial mass function, stellar evolution, and galactic structure. Using data from the Gaia DR1 Tycho-Gaia Astrometric Solution, we reconstruct Gaia's selection function and we determine Gaia's volume completeness, the local number density, and the vertical profiles of different spectral types along the main sequence from early A stars to late K stars as well as along the giant branch. We clearly detect the expected flattening of the stellar density profile near the mid-plane for all stellar types: All vertical profiles are well represented by sech^2 profiles, with scale heights ranging from ~50 pc for A stars to ~150 pc for G and K dwarfs and giants. We determine the luminosity function along the main sequence for M_V < 7 (M >~ 0.72M⊙) and along the giant branch for M_J >~ -2.5. Converting this to a mass function, we find that the high-mass (M > 1M⊙) present-day mass function along the main sequence is d n / d M = 0.016 (M/M⊙)−4.7 stars/pc^3/M⊙. Extrapolating below M = 0.72M⊙, we find a total mid-plane stellar density of 0.040+/-0.002 M⊙/pc^3. Giants contribute 0.00039+/-0.00001 stars/pc^3 or about 0.00046+/-0.00005 M⊙/pc^3. The star-formation rate surface density is \Sigma(t) = 7+/-1 exp(-t/[7+/-1 Gyr]) M⊙/pc^2/Gyr. Overall, we find that Gaia DR1's selection biases are manageable and allow a detailed new inventory of the solar neighborhood to be made that agrees with and extends previous studies. This bodes well for mapping the Milky Way with the full Gaia data set.

The primary sample of the {\it Gaia} Data Release 1 is the Tycho-Gaia Astrometric Solution (TGAS): ≈ 2 million Tycho-2 sources with improved parallaxes and proper motions relative to the initial catalog. This increased astrometric precision presents an opportunity to find new binary stars and moving groups. We search for high-confidence comoving pairs of stars in TGAS by identifying pairs of stars consistent with having the same 3D velocity using a marginalized likelihood ratio test to discriminate candidate comoving pairs from the field population. Although we perform some visualizations using (bias- corrected) inverse parallax as a point estimate of distance, the likelihood ratio is computed with a probabilistic model that includes the covariances of parallax and proper motions and marginalizes the (unknown) true distances and 3D velocities of the stars. We find 13,085 comoving star pairs among 10,606 unique stars with separations as large as 10 pc (our search limit). Some of these pairs form larger groups through mutual comoving neighbors: many of these pair networks correspond to known open clusters and OB associations, but we also report the discovery of several new comoving groups. Most surprisingly, we find a large number of very wide (>1 pc) separation comoving star pairs, the number of which increases with increasing separation and cannot be explained purely by false-positive contamination. Our key result is a catalog of high-confidence comoving pairs of stars in TGAS. We discuss the utility of this catalog for making dynamical inferences about the Galaxy, testing stellar atmosphere models, and validating chemical abundance measurements.

Resource-efficiency is important for biological function of neurons. Using the perceptron as a model of a neuron, we show that resource-efficient learning implies sparse neural connectivity. The perceptron associates inputs to outputs by adjusting its synaptic weights. The learned synaptic weights are proposed to be the most resource-efficient by minimizing a biological resource cost given by the total absolute synaptic weight (l1-norm). Analytical methods from statistical physics and numerical simulations demonstrate that a resource-efficient perceptron has sparse connectivity. Sparseness decreases and resource usage increases with the number of associations to be learned. Our results have implications for synaptic connectivity in the cerebellum, where supervised learning is believed to happen.

The mitotic spindle ensures the faithful segregation of chromosomes. Here we combine the first large-scale serial electron tomography of whole mitotic spindles in early C. elegans embryos with live-cell imaging to reconstruct all microtubules in 3D and identify their plus- and minus-ends. We classify them as kinetochore (KMTs), spindle (SMTs) or astral microtubules (AMTs) according to their positions, and quantify distinct properties of each class. While our light microscopy and mutant studies show that microtubules are nucleated from the centrosomes, we find only a few KMTs directly connected to the centrosomes. Indeed, by quantitatively analysing several models of microtubule growth, we conclude that minus-ends of KMTs have selectively detached and depolymerized from the centrosome. In toto, our results show that the connection between centrosomes and chromosomes is mediated by an anchoring into the entire spindle network and that any direct connections through KMTs are few and likely very transient.

We describe a fast, stable algorithm for the solution of the inverse acoustic scattering problem in two dimensions. Given full aperture far field measurements of the scattered field for multiple angles of incidence, we use Chen's method of recursive linearization to reconstruct an unknown sound speed at resolutions of thousands of square wavelengths in a fully nonlinear regime. Despite the fact that the underlying optimization problem is formally ill-posed and non-convex, recursive linearization requires only the solution of a sequence of linear least squares problems at successively higher frequencies. By seeking a suitably band-limited approximation of the sound speed profile, each least squares calculation is well-conditioned and involves the solution of a large number of forward scattering problems, for which we employ a recently developed, spectrally accurate, fast direct solver. For the largest problems considered, involving 19,600 unknowns, approximately one million partial differential equations were solved, requiring approximately two days to compute using a parallel MATLAB implementation on a multi-core workstation.