Publications

We present a comprehensive investigation combining numerical simulations with experimental validation, focusing on the creeping flow behavior of a shear-banding, viscoelastic wormlike micellar (WLM) solution over concavities with various depths (D) and lengths (L). The fluid is modeled using the diffusive Giesekus model, with model parameters set to quantitatively describe the shear rheology of a 100 : 60 mM cetylpyridinium chloride:sodium salicylate aqueous WLM solution used for the experimental validation. We observe a transition from “cavity flow” to “expansion–contraction flow” as the length L exceeds the sum of depth D and channel width W. This transition is manifested by a change of vortical structures within the concavity. For L ≤ D + W, “cavity flow” is characterized by large scale recirculations spanning the concavity length. For L > D + W, the recirculations observed in “expansion–contraction flow” are confined to the salient corners downstream of the expansion plane and upstream of the contraction plane. Using the numerical dataset, we construct phase diagrams in L–D at various fixed Weissenberg numbers Wi, characterizing the transitions and describing the evolution of vortical structures influenced by viscoelastic effects.

The standard ΛCDM cosmological model predicts the presence of cold dark matter, with the current accelerated expansion of the Universe driven by dark energy. This model has recently come under scrutiny because of tensions in measurements of the expansion and growth histories of the Universe, parameterized using H0 and S8. The three-dimensional clustering of galaxies encodes key cosmological information that addresses these tensions. Here we present a set of cosmological constraints using simulation-based inference that exploits additional non-Gaussian information on nonlinear scales from galaxy clustering, inaccessible with current analyses. We analyse a subset of the Baryon Oscillation Spectroscopic Survey (BOSS) galaxy survey using SimBIG, a new framework for cosmological inference that leverages high-fidelity simulations and deep generative models. We use two clustering statistics beyond the standard power spectrum: the bispectrum and a summary of the galaxy field based on a convolutional neural network. We constrain H0 and S8 1.5 and 1.9 times more tightly than power spectrum analyses. With this increased precision, our constraints are competitive with those of other cosmological probes, even with only 10% of the full BOSS volume. Future work extending SimBIG to upcoming spectroscopic galaxy surveys (DESI, PFS, Euclid) will produce improved cosmological constraints that will develop understanding of cosmic tensions.

Unraveling the phenotypic and genetic complexity of autism is extremely challenging yet critical for understanding the biology, inheritance, trajectory, and clinical manifestations of the many forms of the condition. Here, we leveraged broad phenotypic data from a large cohort with matched genetics to characterize classes of autism and their patterns of core, associated, and co-occurring traits, ultimately demonstrating that phenotypic patterns are associated with distinct genetic and molecular programs. We used a generative mixture modeling approach to identify robust, clinically-relevant classes of autism which we validate and replicate in a large independent cohort. We link the phenotypic findings to distinct patterns of de novo and inherited variation which emerge from the deconvolution of these genetic signals, and demonstrate that class-specific common variant scores strongly align with clinical outcomes. We further provide insights into the distinct biological pathways and processes disrupted by the sets of mutations in each class. Remarkably, we discover class-specific differences in the developmental timing of genes that are dysregulated, and these temporal patterns correspond to clinical milestone and outcome differences between the classes. These analyses embrace the phenotypic complexity of children with autism, unraveling genetic and molecular programs underlying their heterogeneity and suggesting specific biological dysregulation patterns and mechanistic hypotheses.

Adapting the step size locally in the no-U-turn sampler (NUTS) is challenging because the step-size and path-length tuning parameters are interdependent. The determination of an optimal path length requires a predefined step size, while the ideal step size must account for errors along the selected path. Ensuring reversibility further complicates this tuning problem. In this paper, we present a method for locally adapting the step size in NUTS that is an instance of the Gibbs self-tuning (GIST) framework. Our approach guarantees reversibility with an acceptance probability that depends exclusively on the conditional distribution of the step size. We validate our step-size-adaptive NUTS method on Neal's funnel density and a high-dimensional normal distribution, demonstrating its effectiveness in challenging scenarios.

We study the problem of learning multi-index models in high-dimensions using a two-layer neural network trained with the mean-field Langevin algorithm. Under mild distributional assumptions on the data, we characterize the effective dimension $d_{\mathrm{eff}}$ that controls both sample and computational complexity by utilizing the adaptivity of neural networks to latent low-dimensional structures. When the data exhibit such a structure, $d_{\mathrm{eff}}$ can be significantly smaller than the ambient dimension. We prove that the sample complexity grows almost linearly with $d_{\mathrm{eff}}$, bypassing the limitations of the information and generative exponents that appeared in recent analyses of gradient-based feature learning. On the other hand, the computational complexity may inevitably grow exponentially with $d_{\mathrm{eff}}$ in the worst-case scenario. Motivated by improving computational complexity, we take the first steps towards polynomial time convergence of the mean-field Langevin algorithm by investigating a setting where the weights are constrained to be on a compact manifold with positive Ricci curvature, such as the hypersphere. There, we study assumptions under which polynomial time convergence is achievable, whereas similar assumptions in the Euclidean setting lead to exponential time complexity.

The canonical polyadic (CP) tensor decomposition decomposes a multidimensional data array into a sum of outer products of finite-dimensional vectors. Instead, we can replace some or all of the vectors with continuous functions (infinite-dimensional vectors) from a reproducing kernel Hilbert space (RKHS). We refer to tensors with some infinite-dimensional modes as quasitensors, and the approach of decomposing a tensor with some continuous RKHS modes is referred to as CP-HiFi (hybrid infinite and finite dimensional) tensor decomposition. An advantage of CP-HiFi is that it can enforce smoothness in the infinite dimensional modes. Further, CP-HiFi does not require the observed data to lie on a regular and finite rectangular grid and naturally incorporates misaligned data. We detail the methodology and illustrate it on a synthetic example.

Cryo-electron microscopy (cryo-EM) is a powerful technique for determining high-resolution 3D biomolecular structures from imaging data. As this technique can capture dynamic biomolecular complexes, 3D reconstruction methods are increasingly being developed to resolve this intrinsic structural heterogeneity. However, the absence of standardized benchmarks with ground truth structures and validation metrics limits the advancement of the field. Here, we propose CryoBench, a suite of datasets, metrics, and performance benchmarks for heterogeneous reconstruction in cryo-EM. We propose five datasets representing different sources of heterogeneity and degrees of difficulty. These include conformational heterogeneity generated from simple motions and random configurations of antibody complexes and from tens of thousands of structures sampled from a molecular dynamics simulation. We also design datasets containing compositional heterogeneity from mixtures of ribosome assembly states and 100 common complexes present in cells. We then perform a comprehensive analysis of state-of-the-art heterogeneous reconstruction tools including neural and non-neural methods and their sensitivity to noise, and propose new metrics for quantitative comparison of methods. We hope that this benchmark will be a foundational resource for analyzing existing methods and new algorithmic development in both the cryo-EM and machine learning communities.

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.

Huntington’s disease (HD) is a fatal neurodegenerative disorder resulting from an abnormal expansion of polyglutamine (polyQ) repeats in the N-terminus of the huntingtin protein. When the polyQ tract surpasses 35 repeats, the mutated protein undergoes misfolding, culminating in the formation of intracellular aggregates. Research in mouse models suggests that HD pathogenesis involves the aggregation of N-terminal fragments of the huntingtin protein (htt). These early oligomeric assemblies of htt, exhibiting diverse characteristics during aggregation, are implicated as potential toxic entities in HD. However, a consensus on their specific structures remains elusive. Understanding the heterogeneous nature of htt oligomers provides crucial insights into disease mechanisms, emphasizing the need to identify various oligomeric conformations as potential therapeutic targets. Employing coarse-grained molecular dynamics, our study aims to elucidate the mechanisms governing the aggregation process and resultant aggregate architectures of htt. The polyQ tract within htt is flanked by two regions: an N-terminal domain (N17) and a short C-terminal proline-rich segment. We conducted self-assembly simulations involving five distinct N17 + polyQ systems with polyQ lengths ranging from 7 to 45, utilizing the ProMPT force field. Prolongation of the polyQ domain correlates with an increase in β-sheet-rich structures. Longer polyQ lengths favor intramolecular β-sheets over intermolecular interactions due to the folding of the elongated polyQ domain into hairpin-rich conformations. Importantly, variations in polyQ length significantly influence resulting oligomeric structures. Shorter polyQ domains lead to N17 domain aggregation, forming a hydrophobic core, while longer polyQ lengths introduce a competition between N17 hydrophobic interactions and polyQ polar interactions, resulting in densely packed polyQ cores with outwardly distributed N17 domains. Additionally, at extended polyQ lengths, we observe distinct oligomeric conformations with varying degrees of N17 bundling. These findings can help explain the toxic gain-of-function that htt with expanded polyQ acquires.