Publications

We present an efficient basis for imaginary time Green's functions based on a low rank decomposition of the spectral Lehmann representation. The basis functions are simply a set of well-chosen exponentials, so the corresponding expansion may be thought of as a discrete form of the Lehmann representation using an effective spectral density which is a sum of δ functions. The basis is determined only by an upper bound on the product βωmax, with β the inverse temperature and ωmax an energy cutoff, and a user-defined error tolerance ϵ. The number r of basis functions scales as (log(βωmax)log(1/ϵ)). The discrete Lehmann representation of a particular imaginary time Green's function can be recovered by interpolation at a set of r imaginary time nodes. Both the basis functions and the interpolation nodes can be obtained rapidly using standard numerical linear algebra routines. Due to the simple form of the basis, the discrete Lehmann representation of a Green's function can be explicitly transformed to the Matsubara frequency domain, or obtained directly by interpolation on a Matsubara frequency grid. We benchmark the efficiency of the representation on simple cases, and with a high precision solution of the Sachdev-Ye-Kitaev equation at low temperature. We compare our approach with the related intermediate representation method, and introduce an improved algorithm to build the intermediate representation basis and a corresponding sampling grid.

This case study is a reimplementation of the algorithm described in Barmherzig and Sun (2022) [1] as a Stan model. This requires the new features available in Stan 2.30

In this paper, we introduce a randomized iterative method for signal detection in uplink large-scale multiple-input multiple-output (MIMO) systems, which not only achieves a low computational complexity but also enjoys a global and exponentially fast convergence. First of all, by adopting the random sampling into the iterations, the randomized iterative detection algorithm (RIDA) is proposed for large-scale MIMO systems. We show that RIDA converges exponentially fast in terms of mean squared error (MSE). Furthermore, this global convergence always holds, and does not depend on the standard requirements such as N≫K , where N and K denote the numbers of antennas at the sides of base station and users. This broadly extends the applications of low-complexity detection in uplink large-scale MIMO systems. Then, based on a new conditional sampling, optimization and enhancements are given to further improve both the convergence and efficiency of RIDA, resulting in the modified randomized iterative detection algorithm (MRIDA). Meanwhile, with respect to MRIDA, further complexity reduction by exploiting the matrix structure is given while its implementation by deep neural networks (DNN) is also presented for a better detection performance.

Marked power spectra are two-point statistics of a marked field obtained by weighting each location with a function that depends on the local density around that point. We consider marked power spectra of the galaxy field in redshift space that up-weight low density regions, and perform a Fisher matrix analysis to assess the information content of this type of statistics using the Molino mock catalogs built upon the Quijote simulations. We identify four different ways to up-weight the galaxy field, and compare the Fisher information contained in their marked power spectra to the one of the standard galaxy power spectrum, when considering monopole and quadrupole of each statistic. Our results show that each of the four marked power spectra can tighten the standard power spectrum constraints on the cosmological parameters Om, Ob, h, ns, Mν by 15−25 and on s8 by a factor of 2. The same analysis performed by combining the standard and four marked power spectra shows a substantial improvement compared to the power spectrum constraints that is equal to a factor of 6 for σ8 and 2.5−3 for the other parameters. Our constraints may be conservative, since the galaxy number density in the Molino catalogs is much lower than the ones in future galaxy surveys, which will allow them to probe lower density regions of the large-scale structure.

We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parametrized in terms of a permutationally invariant part described by the Deep Sets neural-network architecture. The input coordinates to the Deep Sets are periodically transformed such that they are suitable to directly describe periodic bosonic systems. We show example applications to both one- and two-dimensional interacting quantum gases with Gaussian interactions, as well as to $4He$ confined in a one-dimensional geometry. For the one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.

Quaternions are important for a wide variety of rotation-related problems in computer graphics, machine vision, and robotics. We study the nontrivial geometry of the relationship between quaternions and rotation matrices by exploiting the adjugate matrix of the characteristic equation of a related eigenvalue problem to obtain the manifold of the space of a quaternion eigenvector. We argue that quaternions parameterized by their corresponding rotation matrices cannot be expressed, for example, in machine learning tasks, as single-valued functions: the quaternion solution must instead be treated as a manifold, with different algebraic solutions for each of several single-valued sectors represented by the adjugate matrix. We conclude with novel constructions exploiting the quaternion adjugate variables to revisit several classic pose estimation applications: 2D point-cloud matching, 2D point-cloud-to-projection matching, 3D point-cloud matching, 3D orthographic point-cloud-to-projection matching, and 3D perspective point-cloud-to-projection matching. We find an exact solution to the 3D orthographic least squares pose extraction problem, and apply it successfully also to the perspective pose extraction problem with results that improve on existing methods.

We propose Pathfinder, a variational method for approximately sampling from differentiable log densities. Starting from a random initialization, Pathfinder locates normal approximations to the target density along a quasi-Newton optimization path, with local covariance estimated using the inverse Hessian estimates produced by the optimizer. Pathfinder returns draws from the approximation with the lowest estimated Kullback-Leibler (KL) divergence to the true posterior. We evaluate Pathfinder on a wide range of posterior distributions, demonstrating that its approximate draws are better than those from automatic differentiation variational inference (ADVI) and comparable to those produced by short chains of dynamic Hamiltonian Monte Carlo (HMC), as measured by 1-Wasserstein distance. Compared to ADVI and short dynamic HMC runs, Pathfinder requires one to two orders of magnitude fewer log density and gradient evaluations, with greater reductions for more challenging posteriors. Importance resampling over multiple runs of Pathfinder improves the diversity of approximate draws, reducing 1-Wasserstein distance further and providing a measure of robustness to optimization failures on plateaus, saddle points, or in minor modes. The Monte Carlo KL divergence estimates are embarrassingly parallelizable in the core Pathfinder algorithm, as are multiple runs in the resampling version, further increasing Pathfinder's speed advantage with multiple cores.

We employ machine learning to decode the composition of unknown gas mixtures from the output of an array of four electrochemical sensors. The sensors use metal oxide electrodes paired with a ceramic electrolyte, yttria-stabilized zirconia (YSZ), to produce voltage responses to the presence of gases in complex mixtures. The voltages from the sensor array serve as inputs to a machine learning pipeline which first carries out multi-class classification of mixtures into types based on which gases are present at non-zero concentrations, and subsequently predicts gas concentrations given the mixture type. Thus, our model is able to take a single reading from the sensor array in response to gas mixtures involving NO, NO2, C3H8, and NH3, and output a highly accurate prediction of which gases are present in the mixture, along with the concentrations of each constituent gas. Our computational framework can be easily expanded to include additional gases and additional mixture types, allowing it to be used in numerous automotive, industrial and environmental monitoring settings.

Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Our examples can be reproduced with the code publicly available at Zenodo.

Epitopes that bind simultaneously to all human alleles of Major Histocompatibility Complex class II (MHC II) are considered one of the key factors for the development of improved vaccines and cancer immunotherapies. To engineer MHC II multiple-allele binders, we developed a protocol called PanMHC-PARCE, based on the unsupervised optimization of the epitope sequence by single-point mutations, parallel explicit-solvent molecular dynamics simulations and scoring of the MHC II-epitope complexes. The key idea is accepting mutations that not only improve the affinity but also reduce the affinity gap between the alleles. We applied this methodology to enhance a Plasmodium vivax epitope for multiple-allele binding. In vitro rate-binding assays showed that four engineered peptides were able to bind with improved affinity toward multiple human MHC II alleles. Moreover, we demonstrated that mice immunized with the peptides exhibited interferon-gamma cellular immune response. Overall, the method enables the engineering of peptides with improved binding properties that can be used for the generation of new immunotherapies.