Publications

We introduce a diagrammatic multi-scale approach to the Hubbard model based on the interaction-irreducible (multi-boson) vertex of a small cluster embedded in a self-consistent medium. The vertex captures short-ranged correlations up to the length scale of the cluster, while long-ranged correlations are recovered from a set of diagrammatic equations for the Hedin three-leg vertex. By virtue of the crossing symmetry, the Fierz decoupling ambiguity of the Hubbard interaction is resolved exactly. Our benchmarks for the half-filled Hubbard model on the square lattice are in very good agreement with numerically exact diagrammatic Monte Carlo simulations.

Sampling tasks are a natural class of problems for quantum computers due to the probabilistic nature of the Born rule. Sampling from useful distributions on noisy quantum hardware remains a challenging problem. A recent paper [D. Layden et al., Nature (London) 619, 282 (2023).] proposed a quantum-enhanced Markov-chain Monte Carlo algorithm where moves are generated by a quantum device and accepted or rejected by a classical algorithm. While this procedure is robust to noise and control imperfections, its potential for quantum advantage is unclear. Here we show that there is no speedup over classical sampling on a worst-case unstructured sampling problem. We present an upper bound to the Markov gap that rules out a speedup for any unital quantum proposal.

TGF-β, essential for development and immunity, is expressed as a latent complex (L-TGF-β) non-covalently associated with its prodomain and presented on immune cell surfaces by covalent association with GARP. Binding to integrin αvβ8 activates L-TGF-β1/GARP. The dogma is that mature TGF-β must physically dissociate from L-TGF-β1 for signaling to occur. Our previous studies discovered that αvβ8-mediated TGF-β autocrine signaling can occur without TGF-β1 release from its latent form. Here, we show that mice engineered to express TGF-β1 that cannot release from L-TGF-β1 survive without early lethal tissue inflammation, unlike those with TGF-β1 deficiency. Combining cryogenic electron microscopy with cell-based assays, we reveal a dynamic allosteric mechanism of autocrine TGF-β1 signaling without release where αvβ8 binding redistributes the intrinsic flexibility of L-TGF-β1 to expose TGF-β1 to its receptors. Dynamic allostery explains the TGF-β3 latency/activation mechanism and why TGF-β3 functions distinctly from TGF-β1, suggesting that it broadly applies to other flexible cell surface receptor/ligand systems.

Temporal prediction is inherently uncertain, but representing the ambiguity in nat- ural image sequences is a challenging high-dimensional probabilistic inference problem. For natural scenes, the curse of dimensionality renders explicit den- sity estimation statistically and computationally intractable. Here, we describe an implicit regression-based framework for learning and sampling the conditional density of the next frame in a video given previous observed frames. We show that sequence-to-image deep networks trained on a simple resilience-to-noise objective function extract adaptive representations for temporal prediction. Synthetic exper- iments demonstrate that this score-based framework can handle occlusion bound- aries: unlike classical methods that average over bifurcating temporal trajectories, it chooses among likely trajectories, selecting more probable options with higher frequency. Furthermore, analysis of networks trained on natural image sequences reveals that the representation automatically weights predictive evidence by its reliability, which is a hallmark of statistical inference.

In nature, animal vocalizations can provide crucial information about identity, including kinship and hierarchy. However, lab-based vocal behavior is typically studied during brief interactions between animals with no prior social relationship, and under environmental conditions with limited ethological relevance. Here, we address this gap by establishing long-term acoustic recordings from Mongolian gerbil families, a core social group that uses an array of sonic and ultrasonic vocalizations. Three separate gerbil families were transferred to an enlarged environment and continuous 20-day audio recordings were obtained. Using a variational autoencoder (VAE) to quantify 583,237 vocalizations, we show that gerbils exhibit a more elaborate vocal repertoire than has been previously reported and that vocal repertoire usage differs significantly by family. By performing gaussian mixture model clustering on the VAE latent space, we show that families preferentially use characteristic sets of vocal clusters and that these usage preferences remain stable over weeks. Furthermore, gerbils displayed family-specific transitions between vocal clusters. Since gerbils live naturally as extended families in complex underground burrows that are adjacent to other families, these results suggest the presence of a vocal dialect which could be exploited by animals to represent kinship. These findings position the Mongolian gerbil as a compelling animal model to study the neural basis of vocal communication and demonstrates the potential for using unsupervised machine learning with uninterrupted acoustic recordings to gain insights into naturalistic animal behavior.

Analyzing the structure of sampled features from an input data distribution is challenging when constrained by limited measurements in both the number of inputs and features. Traditional approaches often rely on the eigenvalue spectrum of the sample covariance matrix derived from finite measurement matrices; however, these spectra are sensitive to the size of the measurement matrix, leading to biased insights. In this paper, we introduce a novel algorithm that provides unbiased estimates of the spectral moments of the kernel integral operator in the limit of infinite inputs and features from finitely sampled measurement matrices. Our method, based on dynamic programming, is efficient and capable of estimating the moments of the operator spectrum. We demonstrate the accuracy of our estimator on radial basis function (RBF) kernels, highlighting its consistency with the theoretical spectra. Furthermore, we showcase the practical utility and robustness of our method in understanding the geometry of learned representations in neural networks.

Single-molecule experiments are a unique tool to characterize the structural dynamics of biomolecules. However, reconstructing molecular details from noisy single-molecule data is challenging. Simulation-based inference (SBI) integrates statistical inference, physics-based simulators, and machine learning and is emerging as a powerful framework for analysing complex experimental data. Recent advances in deep learning have accelerated the development of new SBI methods, enabling the application of Bayesian inference to an ever-increasing number of scientific problems. Here, we review the nascent application of SBI to the analysis of single-molecule experiments. We introduce parametric Bayesian inference and discuss its limitations. We then overview emerging deep-learning-based SBI methods to perform Bayesian inference for complex models encoded in computer simulators. We illustrate the first applications of SBI to single-molecule force-spectroscopy and cryo-electron microscopy experiments. SBI allows us to leverage powerful computer algorithms modeling complex biomolecular phenomena to connect scientific models and experiments in a principled way.

In clinical In-Vitro Fertilization (IVF), identifying the most viable embryo for transfer is important to increasing the likelihood of a successful pregnancy. Traditionally, this process involves embryologists manually assessing embryos’ static morphological features at specific intervals using light microscopy. This manual evaluation is not only time-intensive and costly, due to the need for expert analysis, but also inherently subjective, leading to variability in the selection process. To address these challenges, we develop a multimodal model that leverages both time-lapse video data and Electronic Health Records (EHRs) to predict embryo viability. A key challenge of our research is to effectively combine time-lapse video and EHR data, given their distinct modality characteristic. We comprehensively analyze our multimodal model with various modality inputs and integration approaches. Our approach will enable fast and automated embryo viability predictions in scale for clinical IVF.

We introduce cppdlr, a C++ library implementing the discrete Lehmann representation (DLR) of functions in imaginary time and Matsubara frequency, such as Green's functions and self-energies. The DLR is based on a low-rank approximation of the analytic continuation kernel, and yields a compact and explicit basis consisting of exponentials in imaginary time and simple poles in Matsubara frequency. cppdlr constructs the DLR basis and associated interpolation grids, and implements standard operations. It provides a flexible yet high-level interface, facilitating the incorporation of the DLR into both small-scale applications and existing large-scale software projects.