Publications

We study dynamical (quasi)-condensation in the Fermi-Hubbard model starting from a completely uncorrelated initial state of adjacent doubly occupied sites. We show that upon expansion of the system in one dimension, dynamical (quasi)-condensation occurs not only for large interactions via the condensation of doublons, but also for small interactions. The behavior of the system is distinctly different in the two parameter regimes, underlining a different mechanism at work. We address the question whether the dynamical (quasi-)condensation effect persists in the thermodynamic limit. For this purpose, we use the two-particle reduced density matrix method, which allows the extension to large system sizes, long propagation times, and two-dimensional (2D) systems. Our results indicate that the effect vanishes in the thermodynamic limit. However, especially in 2D, further investigation beyond numerically tractable system sizes calls for the use of quantum simulators, for which we show that the described effect can be investigated by probing density fluctuations.

A significant hurdle in developing high-performance semiconductor quantum technologies utilizing deep defects is related to charge dynamics. Unfortunately, progress in modeling their charge dynamics has been hindered over recent decades due to the absence of appropriate multiscale models capable of accurately representing the atomic properties of these defects and their impact on device performance. Here, we present a semi-ab initio method for modeling the bound states of deep defects in semiconductor quantum technologies, applied to the negatively charged nitrogen vacancy (NV−) center in diamond. We employ density functional theory calculations to construct accurate potentials for an effective mass model, which allow us to unveil the structure of the bound hole states. We develop a model to calculate the nonradiative capture cross sections, which agrees with experiment within one order of magnitude. Finally, we present our attempt at constructing the photoionization spectrum of NV0→NV− + bound hole, showing that the electronic transitions of the bound holes can be distinguished from phonon sidebands. This paper offers a practical and efficient solution to a long-standing challenge in understanding the charge dynamics of deep defects.

A primary cilium, made of nine microtubule doublets enclosed in a cilium membrane, is a mechanosensing organelle that bends under an external mechanical load and sends an intracellular signal through transmembrane proteins activated by cilium bending. The nine microtubule doublets are the main load-bearing structural component, while the transmembrane proteins on the cilium membrane are the main sensing component. No distinction was made between these two components in all existing models, where the stress calculated from the structural component (nine microtubule doublets) was used to explain the sensing location, which may be totally misleading. For the first time, we developed a microstructure-based primary cilium model by considering these two components separately. First, we refined the analytical solution of bending an orthotropic cylindrical shell for individual microtubule, and obtained excellent agreement between finite element simulations and the theoretical predictions of a microtubule bending as a validation of the structural component in the model. Second, by integrating the cilium membrane with nine microtubule doublets and simulating the tip-anchored optical tweezer experiment on our computational model, we found that the microtubule doublets may twist significantly as the whole cilium bends. Third, besides being cilium-length-dependent, we found the mechanical properties of the cilium are also highly deformation-dependent. More important, we found that the cilium membrane near the base is not under pure in-plane tension or compression as previously thought, but has significant local bending stress. This challenges the traditional model of cilium mechanosensing, indicating that transmembrane proteins may be activated more by membrane curvature than membrane stretching. Finally, we incorporated imaging data of primary cilia into our microstructure-based cilium model, and found that comparing to the ideal model with uniform microtubule length, the imaging-informed model shows the nine microtubule doublets interact more evenly with the cilium membrane, and their contact locations can cause even higher bending curvature in the cilium membrane than near the base.

The perception of sensory attributes is often quantified through measurements of sensitivity (the ability to detect small stimulus changes), as well as through direct judgements of appearance or intensity. Despite their ubiquity, the relationship between these two measurements remains controversial and unresolved. Here, we propose a framework in which they arise from different aspects of a common representation. Specifically, we assume that judgements of stimulus intensity (e.g., as measured through rating scales) reflect the mean value of an internal representation, and sensitivity reflects a combination of mean value and noise properties, as quantified by the statistical measure of Fisher Information. Unique identification of these internal representation properties can be achieved by combining measurements of sensitivity and judgments of intensity. As a central example, we show that Weber{\textquoteright}s law of perceptual sensitivity can co-exist with Stevens{\textquoteright} power-law scaling of intensity ratings (for all exponents), when the noise amplitude increases in proportion to the representational mean. We then extend this result beyond the Weber{\textquoteright}s law range by incorporating a more general and physiology-inspired form of noise, and show that the combination of noise properties and sensitivity measurements accurately predicts intensity ratings across a variety of sensory modalities and attributes. Our framework unifies two primary perceptual measurements {\textendash} thresholds for sensitivity and rating scales for intensity {\textendash} and provides a neural interpretation for the underlying representation.Significance Statement Perceptual measurements of sensitivity to stimulus changes and stimulus appearance (intensity) are ubiquitous in the study of perception. However, the relationship between these two seemingly disparate measurements remains unclear. Proposals for unification have been made for over 60 years, but they generally lack support from perceptual or physiological measurements. Here, we provide a framework that offers a unified interpretation of perceptual sensitivity and intensity measurements, and we demonstrate its consistency with experimental measurements across multiple perceptual domains.Competing Interest StatementThe authors have declared no competing interest.

We introduce a novel and flexible framework for constructing locally adaptive Hamiltonian Monte Carlo (HMC) samplers by Gibbs sampling the algorithm's tuning parameters conditionally based on the position and momentum at each step. For adaptively sampling path lengths, this framework -- which we call Gibbs self-tuning (GIST) -- encompasses randomized HMC, multinomial HMC, the No-U-Turn Sampler (NUTS), and the Apogee-to-Apogee Path Sampler as special cases. The GIST framework is illustrated with a novel alternative to NUTS for locally adapting path lengths, evaluated with an exact Hamiltonian for a high-dimensional, ill-conditioned Gaussian measure and with the leapfrog integrator for a suite of diverse models.

Recent works have shown that neural networks optimized by gradient-based methods can adapt to sparse or low-dimensional target functions through feature learning; an often studied target is the sparse parity function on the unit hypercube. However, such isotropic data setting does not capture the anisotropy and low intrinsic dimensionality exhibited in realistic datasets. In this work, we address this shortcoming by studying how gradient-based feature learning interacts with structured (anisotropic) input data: we consider the classification of -sparse parity on high-dimensional orthotope where the feature coordinates have varying magnitudes, and analyze the learning complexity of the mean-field Langevin dynamics (MFLD), which describes the noisy gradient descent update on two-layer neural network. We show that the statistical complexity (i.e. sample size) and computational complexity (i.e. network width) of MFLD can both be improved when prominent directions of the anisotropic input data align with the support of the target function. Moreover, by employing a coordinate transform determined by the gradient covariance, the width can be made independent of the target degree. Lastly, we demonstrate the benefit of feature learning by establishing a kernel lower bound on the classification error, which applies to neural networks in the lazy regime.

We study emergent dynamics in a viscous drop subject to interfacial nematic activity. Using hydrodynamic simulations, we show how the interplay of nematodynamics, activity-driven flows and surface deformations gives rise to a sequence of self-organized behaviors of increasing complexity, from periodic braiding motions of topological defects to chaotic defect dynamics and active turbulence, along with spontaneous shape changes and translation. Our findings recapitulate qualitative features of experiments and shed light on the mechanisms underpinning morphological dynamics in active interfaces.

Biomolecular recruitment by phase separated condensates has emerged as a key organising principle of biological processes. One such process is the RNA silencing pathway, which regulates gene expression and genomic defense against foreign nucleic acids. In C. elegans, this pathway involves siRNA amplification at perinuclear germ granules named Mutator foci. The formation of Mutator foci depends on the phase separation of MUT-16, acting as a scaffolding protein to recruit other components of the Mutator complex. Earlier studies have indicated a crucial role for an exoribonuclease, MUT-7, in RNA silencing. The recruitment of MUT-7 to Mutator foci is facilitated by a bridging protein, MUT-8. However, how MUT-8 binds to MUT-16 remains elusive. We resolved the molecular drivers of MUT-16 phase separation and the recruitment of MUT-8 using multi-scale molecular dynamics simulations and in vitro experiments. Residue-level coarse-grained simulations predicted the relative phase separation propensities of MUT-16 disordered regions, which we validated by experiments.

Coarse-grained simulations at residue-level and near atomic-resolution also indicated the essential role of aromatic amino acids (Tyr and Phe) in MUT-16 phase separation. Furthermore, coarse-grained and atomistic simulations of MUT-8 N-terminal prion-like domain with phase separated MUT-16 condensate revealed the importance of cation-π interaction between Tyr residues of MUT-8 and Arg/Lys residues of MUT-16. By re-introducing atomistic detail to condensates from coarse-grained and 350 µs all-atom simulations in explicit solvent on Folding@Home, we demonstrate Arg-Tyr interaction surpasses the strength of Lys-Tyr interactions in the recruitment of MUT-8. The atomistic simulations show that the planar guanidinium group of Arg also engages in sp2-π interaction, and hydrogen bonds with the Tyr residues and these additional favorable contacts are missing in the Lys-Tyr interactions. In agreement with simulations, the mutation of seven Arg residues in MUT-16 to Lys and Ala weakens MUT-8 binding in vitro.

The interaction of fibers in a viscous (Stokes) fluid plays a crucial role in industrial and biological processes, such as sedimentation, rheology, transport, cell division, and locomotion. Numerical simulations generally rely on slender body theory (SBT), an asymptotic, nonconvergent approximation whose error blows up as fibers approach each other. Yet convergent boundary integral equation (BIE) methods which completely resolve the fiber surface have so far been impractical due to the prohibitive cost of layer-potential quadratures in such high aspect-ratio 3D geometries. We present a high-order Nyström quadrature scheme with aspect-ratio independent cost, making such BIEs practical. It combines centerline panels (each with a small number of poloidal Fourier modes), toroidal Green's functions, generalized Chebyshev quadratures, HPC parallel implementation, and FMM acceleration. We also present new BIE formulations for slender bodies that lead to well conditioned linear systems upon discretization. We test Laplace and Stokes Dirichlet problems, and Stokes mobility problems, for slender rigid closed fibers with (possibly varying) circular cross-section, at separations down to 1/20 of the slender radius, reporting convergence typically to at least 10 digits. We use this to quantify the breakdown of numerical SBT for close-to-touching rigid fibers. We also apply the methods to time-step the sedimentation of 512 loops with up to 1.65 million unknowns at around 7 digits of accuracy.

Coiled-coil protein motifs have become widely employed in the design of biomaterials. Some of these designs have been studied for use in drug delivery due to the unique ability of coiled-coils to impart stability, oligomerization, and supramolecular assembly. To leverage these properties and improve drug delivery, release, and targeting, a variety of nano- to mesoscale architectures have been adopted. Coiled-coil drug delivery and therapeutics have been developed by using the coiled-coil alone, designing for higher-order assemblies such as fibers and hydrogels, and combining coiled-coil proteins with other biocompatible structures such as lipids and polymers. We review the recent development of these structures and the design criteria used to generate functional proteins of varying sizes and morphologies.