Publications

Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs should map to similar pairs of outputs. However, the operation of these networks (and of similar networks) requires a fixed-point iteration to determine the output corresponding to a given input, which means that dynamics must operate on a faster time scale than the variation of the input. Further, during these fast dynamics such networks typically "disable" learning, updating synaptic weights only once the fixed-point iteration has been resolved. Here, we derive a network for PCA-based dimensionality reduction that avoids this fast fixed-point iteration. The key novelty of our approach is a modification of the similarity matching objective to encourage near-diagonality of a synaptic weight matrix. We then approximately invert this matrix using a Taylor series approximation, replacing the previous fast iterations. In the offline setting, our algorithm corresponds to a dynamical system, the stability of which we rigorously analyze. In the online setting (i.e., with stochastic gradients), we map our algorithm to a familiar neural network architecture and give numerical results showing that our method converges at a competitive rate. The computational complexity per iteration of our online algorithm is linear in the total degrees of freedom, which is in some sense optimal.

Pulsar timing arrays (PTAs) can be used to detect and study gravitational waves in the nanohertz band (i.e., wavelengths of order light-years). This requires high-precision, decades-long data sets from sensitive, instrumentally stable telescopes. NANOGrav and its collaborators in the International Pulsar Timing Array consortium are on the verge of the first detection of the stochastic background produced by supermassive binary black holes, which form via the mergers of massive galaxies. By providing Northern hemisphere sky coverage with exquisite sensitivity and higher frequency coverage compared to the SKA, a Next-Generation Very Large Array (ngVLA) will be a fundamental component in the next phase of nanohertz GW astrophysics, enabling detailed characterization of the stochastic background and the detection of individual sources contributing to the background, as well as detections of (or stringent constraints on) cosmic strings and other exotica. Here we summarize the scientific goals of PTAs and the technical requirements for the ngVLA to play a significant role in the characterization of the nanohertz gravitational wave universe.

We derive analytic, closed form, numerically stable solutions for the total flux received from a spherical planet, moon or star during an occultation if the specific intensity map of the body is expressed as a sum of spherical harmonics. Our expressions are valid to arbitrary degree and may be computed recursively for speed. The formalism we develop here applies to the computation of stellar transit light curves, planetary secondary eclipse light curves, and planet-planet/planet-moon occultation light curves, as well as thermal (rotational) phase curves. In this paper we also introduce STARRY, an open-source package written in C++ and wrapped in Python that computes these light curves. The algorithm in STARRY is six orders of magnitude faster than direct numerical integration and several orders of magnitude more precise. STARRY also computes analytic derivatives of the light curves with respect to all input parameters for use in gradient-based optimization and inference, such as Hamiltonian Monte Carlo (HMC), allowing users to quickly and efficiently fit observed light curves to infer properties of a celestial body's surface map.

It has been demonstrated that the time variability of a star's brightness at different frequencies can be used to infer its surface gravity, radius, mass, and age. With large samples of light curves now available from Kepler and K2, and upcoming surveys like TESS, we wish to quantify the overall information content of this data and identify where the information resides. As a first look into this question, we ask which stellar parameters we can predict from the brightness variations in red-giant stars data and to what precision, using a data-driven, nonparametric model. We demonstrate that the long-cadence (30 minute) Kepler light curves for 2000 red-giant stars can be used to predict their ${T}_{\mathrm{eff}}$ and $\mathrm{log}g$. Our inference makes use of a data-driven model of a part of the autocorrelation function (ACF) of the light curve, where we posit a polynomial relationship between stellar parameters and the ACF pixel values. We find that this model, trained using 1000 stars, can be used to recover the temperature ${T}_{\mathrm{eff}}$ to <100 K, the surface gravity to <0.1 dex, and the asteroseismic power-spectrum parameters ${\nu }_{\max }$ and ${\rm{\Delta }}\nu $ to <11 μHz and <0.9 μHz (lesssim15%). We recover ${T}_{\mathrm{eff}}$ from range of time lags 0.045 < ${T}_{\mathrm{lag}}$ < 370 days and the $\mathrm{log}g$, ${\nu }_{\max }$, and ${\rm{\Delta }}\nu $ from the range 0.045 < ${T}_{\mathrm{lag}}$ < 35 days. We do not discover any information about stellar metallicity in this model of the ACF. The information content of the data about each parameter is empirically quantified using this method, enabling comparisons to theoretical expectations about convective granulation.

We have recently proposed a nonequilibrium Green’s function (NEGF) approach to include Auger decay processes in the ultrafast charge dynamics of photoionized molecules. Within the so-called generalized Kadanoff–Baym ansatz the fundamental unknowns of the NEGF equations are the reduced one-particle density matrix of bound electrons and the occupations of the continuum states. Both unknowns are one-time functions like the density in time-dependent functional theory (TDDFT). In this work, we assess the accuracy of the approach against configuration interaction (CI) calculations in one-dimensional model systems. Our results show that NEGF correctly captures qualitative and quantitative features of the relaxation dynamics provided that the energy of the Auger electron is much larger than the Coulomb repulsion between two holes in the valence shells. For the accuracy of the results dynamical electron-electron correlations or, equivalently, memory effects play a pivotal role. The combination of our NEGF approach with the Sham–Schlüter equation may provide useful insights for the development of TDDFT exchange-correlation potentials with a history dependence.

We extend the first-principles analysis of attosecond transient absorption spectroscopy to two-dimensional materials. As an example of two-dimensional materials, we apply the analysis to monolayer hexagonal boron nitride (h-BN) and compute its transient optical properties under intense few-cycle infrared laser pulses. Nonadiabatic features are observed in the computed transient absorption spectra. To elucidate the microscopic origin of these features, we analyze the electronic structure of h-BN with density functional theory and investigate the dynamics of specific energy bands with a simple two-band model. Finally, we find that laser-induced intraband transitions play a significant role in the transient absorption even for the two-dimensional material and that the nonadiabatic features are induced by the dynamical Franz-Keldysh effect with an anomalous band dispersion.

ulsar-timing analyses are sensitive to errors in the solar-system ephemerides (SSEs) that timing models utilise to estimate the location of the solar-system barycentre, the quasi-inertial reference frame to which all recorded pulse times-of-arrival are referred. Any error in the SSE will affect all pulsars, therefore pulsar timing arrays (PTAs) are a suitable tool to search for such errors and impose independent constraints on relevant physical parameters. We employ the first data release of the International Pulsar Timing Array to constrain the masses of the planet-moons systems and to search for possible unmodelled objects (UMOs) in the solar system. We employ ten SSEs from two independent research groups, derive and compare mass constraints of planetary systems, and derive the first PTA mass constraints on asteroid-belt objects. Constraints on planetary-system masses have been improved by factors of up to 20 from the previous relevant study using the same assumptions, with the mass of the Jovian system measured at 9.5479189(3)×10−4 M⊙. The mass of the dwarf planet Ceres is measured at 4.7(4)×10−10 M⊙. We also present the first sensitivity curves using real data that place generic limits on the masses of UMOs, which can also be used as upper limits on the mass of putative exotic objects. For example, upper limits on dark-matter clumps are comparable to published limits using independent methods. While the constraints on planetary masses derived with all employed SSEs are consistent, we note and discuss differences in the associated timing residuals and UMO sensitivity curves.

We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced wavelet-like smooth orthogonal functions. We adapt the gausslets to particular systems using one dimensional coordinate transformations, putting more basis functions near nuclei, while maintaining orthogonality. Three dimensional basis functions are composed out of products of the 1D functions in an efficient way called multislicing. We demonstrate the new bases with both Hartree Fock and density matrix renormalization group (DMRG) calculations on hydrogen chain systems. With both methods, we can go to higher accuracy in the complete basis set limit than is practical for conventional Gaussian basis sets, with errors near 0.1 mH per atom.

To understand superconductivity in Chevrel phase compounds and guide the search for interesting properties in materials created with Chevrel phase molecules as building blocks, we use ab-initio methods to study the properties of single Mo6X8 molecules with X=S, Se, Te as well as the bulk solid PbMo6S8. In bulk PbMo6S8, the different energy scales from strong to weak are: the band kinetic energy, the intra-molecular Coulomb interaction, the on-molecule Jahn-Teller energy and the Hund's exchange coupling. The metallic state is stable with respect to Mott and polaronic insulating states. The bulk compound is characterized by a strong electron-phonon interaction with the largest coupling involving phonon modes with energies in the range from 11 meV to 17 meV and with a strong inter-molecule (Peierls) character. A two-band Eliashberg equation analysis shows that the superconductivity is strong-coupling, with different gaps on the two Fermi surface sheets. A Bergman-Rainer analysis of the functioanl derivative of the transition temperature with respect to the electron-phonon coupling reveals that the Peierls modes provide the most important contribution to the superconductivity. This work illustrates the importance of inter-molecular coupling for collective phenomena in molecular solids.