Publications

Pattern-forming networks have diverse roles in cell biology. Rod-shaped fission yeast cells use pattern formation to control the localization of mitotic signaling proteins and the cytokinetic ring. During interphase, the kinase Cdr2 forms membrane-bound multiprotein complexes termed nodes, which are positioned in the cell middle due in part to the node inhibitor Pom1 enriched at cell tips. Node positioning is important for timely cell cycle pro-gression and positioning of the cytokinetic ring. Here, we combined experimental and mod-eling approaches to investigate pattern formation by the Pom1-Cdr2 system. We found that Cdr2 nodes accumulate near the nucleus, and Cdr2 undergoes nucleocytoplasmic shuttling when cortical anchoring is reduced. We generated particle-based simulations based on tip inhibition, nuclear positioning, and cortical anchoring. We tested model predictions by inves-tigating Pom1-Cdr2 localization patterns after perturbing each positioning mechanism, in-cluding in both anucleate and multinucleated cells. Experiments show that tip inhibition and cortical anchoring alone are sufficient for the assembly and positioning of nodes in the ab-sence of the nucleus, but that the nucleus and Pom1 facilitate the formation of unexpected node patterns in multinucleated cells. These findings have implications for spatial control of cytokinesis by nodes and for spatial patterning in other biological systems.

This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is free of the curse of dimensionality (CoD). Such a feature is critical for high-dimensional analysis and stands in contrast to classical metrics (e.g., the Wasserstein metric). The proposed metrics fall into the category of integral probability metrics, for which we specify criteria of test function spaces to guarantee the property of being free of CoD. Examples of the selected test function spaces include the reproducing kernel Hilbert spaces, Barron space, and flow-induced function spaces. Three applications of the proposed metrics are presented: 1. The convergence of empirical measure in the case of random variables; 2. The convergence of n-particle system to the solution to McKean–Vlasov stochastic differential equation; 3. The construction of an ɛ-Nash equilibrium for a homogeneous n-player game by its mean-field limit. As a byproduct, we prove that, given a distribution close to the target distribution measured by our metric and a certain representation of the target distribution, we can generate a distribution close to the target one in terms of the Wasserstein metric and relative entropy. Overall, we show that the proposed class of metrics is a powerful tool to analyze the convergence of empirical measures in high dimensions without CoD.

In this paper, we consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the object. One of the standard approaches for solving this problem is to reformulate it as an optimization problem: finding the boundary of the domain that minimizes the L2 distance between computed values of the scattered field and the given measurement data. The optimization problem is computationally challenging since the local set of convexity shrinks with increasing frequency and results in an increasing number of local minima in the vicinity of the true solution. In many practical experimental settings, low frequency measurements are unavailable due to limitations of the experimental setup or the sensors used for measurement. Thus, obtaining a good initial guess for the optimization problem plays a vital role in this environment. We present a neural network warm-start approach for solving the inverse scattering problem, where an initial guess for the optimization problem is obtained using a trained neural network. We demonstrate the effectiveness of our method with several numerical examples. For high frequency problems, this approach outperforms traditional iterative methods such as Gauss-Newton initialized without any prior (i.e., initialized using a unit circle), or initialized using the solution of a direct method such as the linear sampling method. The algorithm remains robust to noise in the scattered field measurements and also converges to the true solution for limited aperture data. However, the number of training samples required to train the neural network scales exponentially in frequency and the complexity of the obstacles considered. We conclude with a discussion of this phenomenon and potential directions for future research.

Harnessing the enhanced light-matter coupling and quantum vacuum fluctuations resulting from mode volume compression in optical cavities is a promising route towards functionalizing quantum materials and realizing exotic states of matter. Here, we extend cavity quantum electrodynamical materials engineering to correlated magnetic systems, by demonstrating that a Fabry-Pérot cavity can be used to control the magnetic state of the proximate quantum spin liquid α-RuCl

The Su-Schrieffer-Heeger (SSH) model, with bond phonons modulating electron tunneling, is a paradigmatic electron-phonon model that hosts an antiferromagnetic order to bond order transition at half-filling. In the presence of repulsive Hubbard interaction, the antiferromagnetic phase is enhanced, but the phase transition remains first-order. Here we explore the physics of the SSH model with attractive Hubbard interaction, which hosts an interesting interplay among charge order, s-wave pairing, and bond order. Using the numerically exact determinant quantum Monte Carlo method, we show that both charge order, present at weak electron-phonon coupling, and bond order, at large coupling, give way to s-wave pairing when the system is doped. Furthermore, we demonstrate that the SSH electron-phonon interaction competes with the attractive Hubbard interaction and reduces the s-wave pairing correlation.

The transverse field Ising model (TFIM) on the half-infinite chain possesses an edge zero mode. This work considers an impurity model -- TFIM perturbed by a boundary integrability breaking interaction. For sufficiently large transverse field, but in the ordered phase of the TFIM, the zero mode is observed to decay. The decay is qualitatively different from zero modes where the integrability breaking interactions are non-zero all along the chain. It is shown that for the impurity model, the zero mode decays by relaxing to a non-local quasi-conserved operator, the latter being exactly conserved when the opposite edge of the chain has no non-commuting perturbations so as to ensure perfect degeneracy of the spectrum. In the thermodynamic limit, the quasi-conserved operator vanishes, and a regime is identified where the decay of the zero mode obeys Fermi's Golden Rule. A toy model for the decay is constructed in Krylov space and it is highlighted how Fermi's Golden Rule may be recovered from this toy model.

Understanding the emergent electronic structure in twisted atomically thin layers has led to the exciting field of twistronics. However, practical applications of such systems are challenging since the specific angular correlations between the layers must be precisely controlled and the layers have to be single crystalline with uniform atomic ordering. Here, we suggest an alternative, simple and scalable approach where nanocrystalline two-dimensional (2D) film on three-dimensional (3D) substrates yield twisted-interface-dependent properties. Ultrawide-bandgap hexagonal boron nitride (h-BN) thin films are directly grown on high in-plane lattice mismatched wide-bandgap silicon carbide (4H-SiC) substrates to explore the twist-dependent structure-property correlations. Concurrently, nanocrystalline h-BN thin film shows strong non-linear second-harmonic generation and ultra-low cross-plane thermal conductivity at room temperature, which are attributed to the twisted domain edges between van der Waals stacked nanocrystals with random in-plane orientations. First-principles calculations based on time-dependent density functional theory manifest strong even-order optical nonlinearity in twisted h-BN layers. Our work unveils that directly deposited 2D nanocrystalline thin film on 3D substrates could provide easily accessible twist-interfaces, therefore enabling a simple and scalable approach to utilize the 2D-twistronics integrated in 3D material devices for next-generation nanotechnology.

Quasiparticles consisting of correlated electron(s) and hole(s), such as excitons and trions, play important roles in the optical phenomena of van der Waals semiconductors and serve as unique platforms for studies of many-body physics. Herein, we report a gate-tunable exciton-to-trion transition in pressurized monolayer MoSe2, in which the electronic band structures are modulated continuously within a diamond anvil cell. The emission energies of both the exciton and trion undergo large blueshifts over 90 meV with increasing pressure. Surprisingly, the trion binding energy remains constant at 30 meV, regardless of the applied pressure. Combining ab initio density functional theory calculations and quantum Monte Carlo simulations, we find that the remarkable robustness of the trion binding energy originates from the spatially diffused nature of the trion wave function and the weak correlation between its constituent electron--hole pairs. Our findings shed light on the optical properties of correlated excitonic quasiparticles in low-dimensional materials.

Human biology is rooted in highly specialized cell types programmed by a common genome, 98% of which is outside of genes. Genetic variation in the enormous noncoding space is linked to the majority of disease risk. To address the problem of linking these variants to expression changes in primary human cells, we introduce ExPectoSC, an atlas of modular deep-learning-based models for predicting cell-type-specific gene expression directly from sequence. We provide models for 105 primary human cell types covering 7 organ systems, demonstrate their accuracy, and then apply them to prioritize relevant cell types for complex human diseases. The resulting atlas of sequence-based gene expression and variant effects is publicly available in a user-friendly interface and readily extensible to any primary cell types. We demonstrate the accuracy of our approach through systematic evaluations and apply the models to prioritize ClinVar clinical variants of uncertain significance, verifying our top predictions experimentally.

Variational inference (VI) is a method to approximate the computationally intractable posterior distributions that arise in Bayesian statistics. Typically, VI fits a simple parametric distribution to be close to the target posterior, optimizing an appropriate objective such as the evidence lower bound (ELBO). In this work, we present a new approach to VI. Our method is based on the principle of score matching---namely, that if two distributions are equal then their score functions (i.e., gradients of the log density) are equal at every point on their support. With this principle, we develop score-matching VI, an iterative algorithm that seeks to match the scores between the variational approximation and the exact posterior. At each iteration, score-matching VI solves an inner optimization, one that minimally adjusts the current variational estimate to match the scores at a newly sampled value of the latent variables. We show that when the variational family is a Gaussian, this inner optimization enjoys a closed-form solution, which we call Gaussian score matching VI (GSM-VI). GSM-VI is a ``black box'' variational algorithm in that it only requires a differentiable joint distribution, and as such it can be applied to a wide class of models. We compare GSM-VI to black box variational inference (BBVI), which has similar requirements but instead optimizes the ELBO. We first study how GSM-VI behaves as a function of the problem dimensionality, the condition number of the target covariance matrix (when the target is Gaussian), and the degree of mismatch between the approximating and exact posterior distribution. We then study GSM-VI on a collection of real-world Bayesian inference problems from the posteriorDB database of datasets and models. We find that GSM-VI is faster than BBVI and equally or more accurate. Specifically, over a wide range of target posteriors, GSM-VI requires 10-100x fewer gradient evaluations than BBVI to obtain a comparable quality of approximation.