Publications

We study how to estimate a nearly low-rank Toeplitz covariance matrix T from compressed measurements. Recent work of Qiao and Pal addresses this problem by combining sparse rulers (sparse linear arrays) with frequency finding (sparse Fourier transform) algorithms applied to the Vandermonde decomposition of T. Analytical bounds on the sample complexity are shown, under the assumption of sufficiently large gaps between the frequencies in this decomposition. In this work, we introduce random ultra-sparse rulers and propose an improved approach based on these objects. Our random rulers effectively apply a random permutation to the frequencies in T's Vandermonde decomposition, letting us avoid frequency gap assumptions and leading to improved sample complexity bounds. In the special case when T is circulant, we theoretically analyze the performance of our method when combined with sparse Fourier transform algorithms based on random hashing. We also show experimentally that our ultra-sparse rulers give significantly more robust and sample efficient estimation then baseline methods.

The female meiotic spindles of most animals are acentrosomal and undergo drastic morphological changes while transitioning from metaphase to anaphase. The ultra-structure of acentrosomal spindles, and how this enables such dramatic rearrangements remains largely unknown. To address this, we applied light microscopy, large-scale electron tomography and mathematical modeling of female meiotic C. elegans spindles undergoing the transition from metaphase to anaphase. Combining these approaches, we find that meiotic spindles are dynamic arrays of short microtubules that turn over on second time scales. The results show that the transition from metaphase to anaphase correlates with an increase in the number of microtubules and a decrease of their average length. To understand the mechanisms that drive this transition, we developed a mathematical model for the microtubule length distribution that considers microtubule growth, catastrophe, and severing. Using Bayesian inference to compare model predictions and data, we find that microtubule turn-over is the major driver of the observed large-scale reorganizations. Our data suggest that cutting of microtubules occurs, but that most microtubules are not severed before undergoing catastrophe.

Binary black holes (BBHs) detected by gravitational wave (GW) observations could be broadly divided into two formation channels: those formed through field binary evolution and those assembled dynamically in dense stellar systems. Each of these formation channels, and their sub-channels, populate a distinct region in the effective spin-mass (χeff−M) plane. Depending on the branching ratio of different channels, an ensemble of BBHs could show a trend in this plane. Here we fit a mass-dependent distribution for χeff to the GWTC-1 BBHs from the first and second observing runs of Advanced LIGO and Advanced Virgo. We find a negative correlation between mass and the mean effective spin (χ¯eff), and positive correlation with its dispersion (σχeff) at 75\% and 80\% confidence. This trend is robust against the choice of mass variable, but most pronounced when the mass variable is taken to be the chirp mass of the binary. The result is consistent with significant contributions from both dynamically assembled and field binaries in the GWTC-1 catalog. The upcoming LIGO O3a data release will critically test this interpretation.

Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from a theoretical point of view. The mathematical description of learning problems involves very large collections of interacting random variables, difficult to handle analytically as well as numerically. This complexity is precisely the object of study of statistical physics. Its mission, originally pointed toward natural systems, is to understand how macroscopic behaviors arise from microscopic laws. Mean-field methods are one type of approximation strategy developed in this view. We review a selection of classical mean-field methods and recent progress relevant for inference in neural networks. In particular, we remind the principles of derivations of high-temperature expansions, the replica method and message passing algorithms, highlighting their equivalences and complementarities. We also provide references for past and current directions of research on neural networks relying on mean-field methods.

Ta
2
NiSe
5
is one of the most promising materials for hosting an excitonic insulator ground state. While a number of experimental observations have been interpreted in this way, the precise nature of the symmetry breaking occurring in
Ta
2
NiSe
5
, the electronic order parameter, and a realistic microscopic description of the transition mechanism are, however, missing. By a symmetry analysis based on first-principles calculations, we uncover the discrete lattice symmetries which are broken at the transition. We identify a purely electronic order parameter of excitonic nature that breaks these discrete crystal symmetries and contributes to the experimentally observed lattice distortion from an orthorombic to a monoclinic phase. Our results provide a theoretical framework to understand and analyze the excitonic transition in Ta_2NiSe_5 and settle the fundamental questions about symmetry breaking governing the spontaneous formation of excitonic insulating phases in solid-state materials.

We show how a large family of interacting nonequilibrium phases of matter can arise from the presence of multiple time-translation symmetries, which occur by quasiperiodically driving an isolated, quantum many-body system with two or more incommensurate frequencies. These phases are fundamentally different from those realizable in time-independent or periodically driven (Floquet) settings. Focusing on high-frequency drives with smooth time dependence, we rigorously establish general conditions for which these phases are stable in a parametrically long-lived “preheating” regime. We develop a formalism to analyze the effect of the multiple time-translation symmetries on the dynamics of the system, which we use to classify and construct explicit examples of the emergent phases. In particular, we discuss time quasicrystals which spontaneously break the time-translation symmetries, as well as time-translation symmetry-protected topological phases.

A notion of quantum natural evolution strategies is introduced, which provides a geometric synthesis of a number of known quantum/classical algorithms for performing classical black-box optimization. Recent work of Gomes et al. [2019] on combinatorial optimization using neural quantum states is pedagogically reviewed in this context, emphasizing the connection with natural evolution strategies. The algorithmic framework is illustrated for approximate combinatorial optimization problems, and a systematic strategy is found for improving the approximation ratios. In particular it is found that natural evolution strategies can achieve state-of-art approximation ratios for Max-Cut, at the expense of increased computation time.

We present an extensive ALMA spectroscopic follow-up programme of the z=4.3 structure SPT2349−56, one of the most actively star-forming proto-cluster cores known, to identify additional members using their [C{\sc ii}] 158\,μm and \mbox{CO(4--3)} lines. In addition to robustly detecting the 14 previously published galaxies in this structure, we identify a further 15 associated galaxies at z=4.3, resolving 55±5\,per cent of the 870-μm flux density at 0.5\,arcsec resolution compared to 21\,arcsec single-dish data. These galaxies are distributed into a central core containing 23 galaxies extending out to 300\,kpc in diameter, and a northern extension, offset from the core by 400\,kpc, containing three galaxies. We discovered three additional galaxies in a red {\it Herschel\/}-SPIRE source 1.5\,Mpc from the main structure, suggesting the existence of many other sources at the same redshift as SPT2349−56 that are not yet detected in the limited coverage of our data. An analysis of the velocity distribution of the central galaxies indicates that this region may be virialized with a mass of (9±5)×1012\,M⊙, while the two offset galaxy groups are about 30 and 60\,per cent less massive and show significant velocity offsets from the central group. We calculate the [C{\sc ii}] and far-infrared number counts, and find evidence for a break in the [C{\sc ii}] luminosity function. We estimate the average SFR density within the region of SPT2349−56 containing single-dish emission (a proper diametre of 720\,kpc), assuming spherical symmetry, to be roughly 4×104\,M⊙\,yr−1\,Mpc−3; this may be an order of magnitude greater than the most extreme examples seen in simulations.

The Galactic bulge is a tumultuous dense region of space, packed with stars separated by far smaller distances than those in the Solar neighborhood. A quantification of the frequency and proximity of close stellar encounters in this environment dictates the exchange of material, disruption of planetary orbits, and threat of sterilizing energetic events. We present estimated encounter rates for stars in the Milky Way bulge found using a combination of numerical and analytical methods. By integrating the orbits of bulge stars with varying orbital energy and angular momentum to find their positions over time, we were able to estimate how many close stellar encounters the stars should experience as a function of orbit shape. We determined that ~80% of bulge stars have encounters within 1000 AU and that half of bulge stars will have >35 such encounters, both over a gigayear. Our work has interesting implications for the long-term survivability of planets in the Galactic bulge.

Many scientific disciplines rely on computational methods for data analysis, model generation, and prediction. Implementing these methods is often accomplished by researchers with domain expertise but without formal training in software engineering or computer science. This arrangement has led to underappreciation of sustainability and maintainability of scientific software tools developed in academic environments. Some software tools have avoided this fate, including the scientific library Rosetta. We use this software and its community as a case study to show how modern software development can be accomplished successfully, irrespective of subject area. Rosetta is one of the largest software suites for macromolecular modeling, with 3.1 million lines of code and many state-of-the-art applications. Since the mid 1990s, the software has been developed collaboratively by the RosettaCommons, a community of academics from over 60 institutions worldwide with diverse backgrounds including chemistry, biology, physiology, physics, engineering, mathematics, and computer science. Developing this software suite has provided us with more than two decades of experience in how to effectively develop advanced scientific software in a global community with hundreds of contributors. Here we illustrate the functioning of this development community by addressing technical aspects (like version control, testing, and maintenance), community-building strategies, diversity efforts, software dissemination, and user support. We demonstrate how modern computational research can thrive in a distributed collaborative community. The practices described here are independent of subject area and can be readily adopted by other software development communities.