Publications

Under a sufficiently large load, a solid material will flow via rearrangements, where particles change neighbors. Such plasticity is most easily described in the athermal, quasistatic limit of zero temperature and infinitesimal loading rate, where rearrangements occur only when the system becomes mechanically unstable. For disordered solids, the instabilities marking the onset of rearrangements have long been believed to be fold instabilities, in which an energy barrier disappears and the frequency of a normal mode of vibration vanishes continuously. Here, we report that there exists another, anomalous, type of instability caused by the breaking of a “stabilizing bond,” whose removal creates an unstable vibrational mode. For commonly studied systems, such as those with harmonic finite-range interparticle interactions, such “discontinuous instabilities” are not only inevitable, they often dominate the modes of failure. Stabilizing bonds are a subset of all the bonds in the system and are prevalent in disordered solids generally. Although they do not trigger discontinuous instabilities in systems with vanishing stiffness at the interaction cutoff, they are, even in those cases, local indicators of incipient mechanical failure. They therefore provide an accurate structural predictor of instabilities not only of the discontinuous type but of the fold type as well.

We present efficient methods for Brillouin zone integration with a non-zero but possibly very small broadening factor η, focusing on cases in which downfolded Hamiltonians can be evaluated efficiently using Wannier interpolation. We describe robust, high-order accurate algorithms automating convergence to a user-specified error tolerance ϵ, emphasizing an efficient computational scaling with respect to η. After analyzing the standard equispaced integration method, applicable in the case of large broadening, we describe a simple iterated adaptive integration algorithm effective in the small η regime. Its computational cost scales as O(log3(η−1)) as η → 0+ in three dimensions, as opposed to O(η−3) for equispaced integration. We argue that, by contrast, tree-based adaptive integration methods scale only as O(log(η−1)/η2) for typical Brillouin zone integrals. In addition to its favorable scaling, the iterated adaptive algorithm is straightforward to implement, particularly for integration on the irreducible Brillouin zone, for which it avoids the tetrahedral meshes required for tree-based schemes. We illustrate the algorithms by calculating the spectral function of SrVO3 with broadening on the meV scale.

Mutations in signal transduction pathways lead to various diseases including cancers. MEK1 kinase, encoded by the human MAP2K1 gene, is one of the central components of the MAPK pathway and more than a hundred somatic mutations in the MAP2K1 gene were identified in various tumors. Germline mutations deregulating MEK1 also lead to congenital abnormalities, such as the cardiofaciocutaneous syndrome and arteriovenous malformation. Evaluating variants associated with a disease is a challenge, and computational genomic approaches aid in this process. Establishing evolutionary history of a gene improves computational prediction of disease-causing mutations; however, the evolutionary history of MEK1 is not well understood. Here, by revealing a precise evolutionary history of MEK1, we construct a well-defined dataset of MEK1 metazoan orthologs, which provides sufficient depth to distinguish between conserved and variable amino acid positions. We matched known and predicted disease-causing and benign mutations to evolutionary changes observed in corresponding amino acid positions and found that all known and many suspected disease-causing mutations are evolutionarily intolerable. We selected several variants that cannot be unambiguously assessed by automated prediction tools but that are confidently identified as “damaging” by our approach, for experimental validation in Drosophila. In all cases, evolutionary intolerant variants caused increased mortality and severe defects in fruit fly embryos confirming their damaging nature. We anticipate that our analysis will serve as a blueprint to help evaluate known and novel missense variants in MEK1 and that our approach will contribute to improving automated tools for disease-associated variant interpretation.

Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signalling. In this paper, a minimal, mass-conserving model of cell-polarization on a curved membrane is analyzed in the limit of slow surface diffusion. Using the tools of formal asymptotics and calculus of variations, we study the characteristic wave-pinning behavior of this system on three dynamical timescales. On the short timescale, generation of an interface separating high- and low-concentration domains is established under suitable conditions. Intermediate timescale dynamics are shown to lead to a uniform growth or shrinking of these domains to sizes that are fixed by global parameters. Finally, the long timescale dynamics reduce to area-preserving geodesic curvature flow that may lead to multi-interface steady state solutions. These results provide a foundation for studying cell polarization and related phenomena in biologically relevant geometries.

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features, such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, DP-range correction, DP long range, graphics processing unit support for customized operators, model compression, non-von Neumann molecular dynamics, and improved usability, including documentation, compiled binary packages, graphical user interfaces, and application programming interfaces. This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, this article presents a comprehensive procedure for conducting molecular dynamics as a representative application, benchmarks the accuracy and efficiency of different models, and discusses ongoing developments.

An established normative approach for understanding the algorithmic basis of neural computation is to derive online algorithms from principled computational objectives and evaluate their compatibility with anatomical and physiological observations. Similarity matching objectives have served as successful starting points for deriving online algorithms that map onto neural networks (NNs) with point neurons and Hebbian/anti-Hebbian plasticity. These NN models account for many anatomical and physiological observations; however, the objectives have limited computational power and the derived NNs do not explain multi-compartmental neuronal structures and non-Hebbian forms of plasticity that are prevalent throughout the brain. In this article, we unify and generalize recent extensions of the similarity matching approach to address more complex objectives, including a large class of unsupervised and self-supervised learning tasks that can be formulated as symmetric generalized eigenvalue problems or nonnegative matrix factorization problems. Interestingly, the online algorithms derived from these objectives naturally map onto NNs with multi-compartmental neurons and local, non-Hebbian learning rules. Therefore, this unified extension of the similarity matching approach provides a normative framework that facilitates understanding multi-compartmental neuronal structures and non-Hebbian plasticity found throughout the brain.

We consider the numerical solution of the real time equilibrium Dyson equation, which is used in calculations of the dynamical properties of quantum many-body systems. We show that this equation can be written as a system of coupled, nonlinear, convolutional Volterra integro-differential equations, for which the kernel depends self-consistently on the solution. As is typical in the numerical solution of Volterra-type equations, the computational bottleneck is the quadratic-scaling cost of history integration. However, the structure of the nonlinear Volterra integral operator precludes the use of standard fast algorithms. We propose a quasilinear-scaling FFT-based algorithm which respects the structure of the nonlinear integral operator. The resulting method can reach large propagation times, and is thus well-suited to explore quantum many-body phenomena at low energy scales. We demonstrate the solver with two standard model systems: the Bethe graph, and the Sachdev-Ye-Kitaev model.

We show that topological superconductivity may emerge upon doping of transition metal dichalcogenide heterobilayers above an integer-filling magnetic state of the topmost valence moiré band. The effective attraction between charge carriers is generated by an electric p-wave Feshbach resonance arising from interlayer excitonic physics and has a tuanble strength, which may be large. Together with the low moiré carrier densities reachable by gating, this robust attraction enables access to the long-sought p-wave BEC-BCS transition. The topological protection arises from an emergent time reversal symmetry occurring when the magnetic order and long wavelength magnetic fluctuations do not couple different valleys. The resulting topological superconductor features helical Majorana edge modes, leading to half-integer quantized spin-thermal Hall conductivity and to charge currents induced by circularly polarized light or other time-reversal symmetry-breaking fields.

We show that pressure applied to twisted WSe

We demonstrate that a single layer of graphene subject to a superlattice potential nearly commensurate to a 3 3 supercell exactly maps to the chiral model of twisted bilayer graphene, albeit with half as many degrees of freedom. We comprehensively review the properties of this