Publications

We generalize the interpolative separable density fitting (ISDF) method, used for compressing the four-index electron repulsion integral (ERI) tensor, to incorporate adaptive real space grids for potentially highly localized single-particle basis functions. To do so, we employ a fast adaptive algorithm, the recently-introduced dual-space multilevel kernel-splitting method, to solve the Poisson equation for the ISDF auxiliary basis functions. The adaptive grids are generated using a high-order accurate, black-box procedure that satisfies a user-specified error tolerance. Our algorithm relies on the observation, which we prove, that an adaptive grid resolving the pair densities appearing in the ERI tensor can be straightforwardly constructed from one that resolves the single-particle basis functions, with the number of required grid points differing only by a constant factor. We find that the ISDF compression efficiency for the ERI tensor with highly localized basis sets is comparable to that for smoother basis sets compatible with uniform grids. To demonstrate the performance of our procedure, we consider several molecular systems with all-electron basis sets which are intractable using uniform grid-based methods. Our work establishes a pathway for scalable many-body electronic structure simulations with arbitrary smooth basis functions, making simulations of phenomena like core-level excitations feasible on a large scale.

Having an accurate reaction coordinate (RC) is essential for reliable kinetic characterization of molecular processes, but there are few quantitative metrics to evaluate RC quality. In this study, we consider the dimensionless γ metric from the Exponential Average Time-dependent Rate (EATR) method, which represents the fraction of a biasing potential along the RC that contributes to increasing the rate constant. We demonstrate that γ can be used to test whether the utility of a RC for predicting kinetics with a Metadynamics bias improves as the coordinate is iteratively updated to include new data. We evaluate RCs approximated via the iterative State Predictive Information Bottleneck (SPIB) approach, which was previously shown to be accurate across six protein–ligand dissociation systems. For these same systems, we compute γ values and mean accelerated times τ̅accel. After systematically scanning over fitting parameters, the results show that γ increases closer to 1, while τ̅accel decreases, revealing a consistent inverse correlation. These results demonstrate that γ serves as a practical criterion for RC evaluation and offers guidance for selecting SPIB–derived coordinates yielding quantitative kinetic predictions.

The method of fundamental solutions (MFS) is known to be effective for solving 3D Laplace and Stokes Dirichlet boundary value problems in the exterior of a large collection of simple smooth objects. Here, we present new scalable MFS formulations for the corresponding elastance and mobility problems. The elastance problem computes the potentials of conductors with given net charges, while the mobility problem—crucial to rheology and complex fluid applications—computes rigid body velocities given net forces and torques on the particles. The key idea is orthogonal projection of the net charge (or forces and torques) in a rectangular variant of a “completion flow.” The proposal is compatible with one-body preconditioning, resulting in well-conditioned square linear systems amenable to fast multipole accelerated iterative solution, thus a cost linear in the particle number. For large suspensions with moderate lubrication forces, MFS sources on inner proxy-surfaces give accuracy on par with a well-resolved boundary integral formulation. Our several numerical tests include a suspension of 10,000 nearby ellipsoids, using 2.6\times 10^7
total preconditioned degrees of freedom, where GMRES converges to five digits of accuracy in under two hours on one workstation

We introduce the Information-Estimation Metric (IEM), a novel form of distance function derived from an underlying continuous probability density over a domain of signals. The IEM is rooted in a fundamental relationship between information theory and estimation theory, which links the log-probability of a signal with the errors of an optimal denoiser, applied to noisy observations of the signal. In particular, the IEM between a pair of signals is obtained by comparing their denoising error vectors over a range of noise amplitudes. Geometrically, this amounts to comparing the score vector fields of the blurred density around the signals over a range of blur levels. We prove that the IEM is a valid global metric and derive a closed-form expression for its local second-order approximation, which yields a Riemannian metric. For Gaussian-distributed signals, the IEM coincides with the Mahalanobis distance. But for more complex distributions, it adapts, both locally and globally, to the geometry of the distribution. In practice, the IEM can be computed using a learned denoiser (analogous to generative diffusion models) and solving a one-dimensional integral. To demonstrate the value of our framework, we learn an IEM on the ImageNet database. Experiments show that this IEM is competitive with or outperforms state-of-the-art supervised image quality metrics in predicting human perceptual judgments.

Motivation Focused Ion Beam Scanning Electron Microscopy (FIB-SEM) is an advanced Volume Electron Microscopy technology with growing applications, featuring thinner sectioning compared to other Volume Electron Microscopes. Such axial resolution is crucial for accurate segmentation and reconstruction of fine structures in biological tissues. However, in reality, the milling thickness is not always uniform across the sample surface, resulting in the axial plane looking distorted. Existing image processing approaches often: (i) assume constant section thickness; (ii) consist of multiple separate processing steps (i.e., not in an end-to-end fashion); (iii) require ground truth images for modeling, which may entail significant labor and be unsuitable for rapid analysis.

Results We develop a deep learning method to correct non-uniform milling artifacts observed in FIB-SEM images. The proposed method is an image-to-image translation technique that can mitigate image distortions in an unsupervised manner. It conducts cross-plane learning within 3D image volumes without any ground truth annotations. We demonstrate the efficacy of our method on a real-world micro-wasp dataset, showcasing significantly improved image quality after correction with qualitative and quantitative analysis.

IgA nephropathy (IgAN), focal segmental glomerulosclerosis (FSGS), membranous nephropathy (MN), and minimal change disease (MCD) account for the majority of idiopathic glomerulopathies (GN). However, there are no powered transcriptomic datasets coupled to genetic data to investigate the genetic mechanisms underlying gene regulation in the context of GN.

The highly conserved extracellular signal–regulated kinase (ERK) regulates diverse cellular processes by phosphorylating a wide range of intracellular substrates. Its catalytic activity relies on phosphorylation by a single upstream kinase, mitogen-activated protein kinase kinase (MEK), which interacts with only a few binding partners. Here, we test whether the asymmetry in protein–protein interaction network architecture influences the coevolution of the MEK–ERK complex. Phylogenetic sequence analysis across metazoan species revealed accelerated divergence in MEK’s intrinsically disordered N-terminal docking motif (docking site [D-site]), whereas ERK remained highly conserved. Structure prediction with AlphaFold2 and extensive molecular dynamics simulations showed that five conserved D-site residues form stable hydrophobic and electrostatic contacts with ERK’s D-recruitment site. Functional assays in Drosophila melanogaster confirmed that these D-site interactions are essential for proper downstream signaling and support an allosteric role for this motif. Our results demonstrate that MEK uses a structurally simple yet evolutionarily adaptable motif to regulate MEK–ERK complex stability and binding dynamics. The D-site is strongly conserved within phylogenetic groups such as insects or terrestrial vertebrates, yet diverges across them, reflecting evolutionary pressures that balance functional conservation with signaling adaptability. The presented approach illustrates how the combined approach using sequencing data, molecular simulations, and targeted perturbations can be used to address fundamental questions about the evolution of protein–protein interaction networks.

The global dimensionality of a neural representation manifold provides rich insight into the computational process underlying both artificial and biological neural networks. However, all existing measures of global dimensionality are sensitive to the number of samples, i.e., the number of rows and columns of the sample matrix. We show that, in particular, the participation ratio of eigenvalues, a popular measure of global dimensionality, is highly biased with small sample sizes, and propose a bias-corrected estimator that is more accurate with finite samples and with noise. On synthetic data examples, we demonstrate that our estimator can recover the true known dimensionality. We apply our estimator to neural brain recordings, including calcium imaging, electrophysiological recordings, and fMRI data, and to the neural activations in a large language model and show our estimator is invariant to the sample size. Finally, our estimators can additionally be used to measure the local dimensionalities of curved neural manifolds by weighting the finite samples appropriately.

This work addresses the question of uniqueness and regularity of the minimizers of a convex but not strictly convex integral functional with linear growth in a two-dimensional setting. The integrand whose precise form derives directly from the theory of perfect plasticity behaves quadratically close to the origin and grows linearly once a speci c threshold is reached. Thus, in contrast with the only existing literature on uniqueness for functionals with linear growth, that is that which pertains to the generalized least gradient, the integrand is not a norm. We make use of hyperbolic conservation laws hidden in the structure of the problem to tackle uniqueness. Our argument strongly relies on the regularity of a vector eld the Cauchy stress in the terminology of perfect plasticity which allows us to de ne characteristic lines, and then to employ the method of characteristics. Using the detailed structure of the characteristic landscape evidenced in our preliminary study [5], we show that this vector eld is actually continuous, save for possibly two points. The di erent behaviors of the energy density at zero and at innity imply an inequality constraint on the Cauchy stress. Under a barrier type convexity assumption on the set where the inequality constraint is saturated, we show that uniqueness holds for pure Dirichlet boundary data devoid of any regularity properties, a stronger result than that of uniqueness for a given trace on the whole boundary since our minimizers can fail to attain the boundary data. We also show a partial regularity result for the minimizer.

The human auditory cortex is topographically organized. Neurons with similar response properties are spatially clustered, forming smooth maps for acoustic features such as frequency in early auditory areas, and modular regions selective for music and speech in higher-order cortex. Yet, evaluations for current computational models of auditory perception do not measure whether such topographic structure is present in a candidate model. Here, we show that cortical topography is not present in the previous best-performing models at predicting human auditory fMRI responses. To encourage the emergence of topographic organization, we adapt a cortical wiring-constraint loss originally designed for visual perception. The new class of topographic auditory models, TopoAudio, are trained to classify speech, and environmental sounds from cochleagram inputs, with an added constraint that nearby units on a 2D cortical sheet develop similar tuning. Despite these additional constraints, TopoAudio achieves high accuracy on benchmark tasks comparable to the unconstrained non-topographic baseline models. Further, TopoAudio predicts the fMRI responses in the brain as well as standard models, but unlike standard models, TopoAudio develops smooth, topographic maps for tonotopy and amplitude modulation (common properties of early auditory representation, as well as clustered response modules for music and speech (higher-order selectivity observed in the human auditory cortex). TopoAudio is the first end-to-end biologically grounded auditory model to exhibit emergent topography, and our results emphasize that a wiring-length constraint can serve as a general-purpose regularization tool to achieve biologically aligned representations.