Publications

Since the seminal 1961 paper of Monod and Jacob, mathematical models of biomolecular circuits have guided our understanding of cell regulation. Model-based exploration of the functional capabilities of any given circuit requires systematic mapping of multidimensional spaces of model parameters. Despite significant advances in computational dynamical systems approaches, this analysis remains a nontrivial task. Here, we use a nonlinear system of ordinary differential equations to model oocyte selection in Drosophila, a robust symmetry-breaking event that relies on autoregulatory localization of oocyte-specification factors. By applying an algorithmic approach that implements symbolic computation and topological methods, we enumerate all phase portraits of stable steady states in the limit when nonlinear regulatory interactions become discrete switches. Leveraging this initial exact partitioning and further using numerical exploration, we locate parameter regions that are dense in purely asymmetric steady states when the nonlinearities are not infinitely sharp, enabling systematic identification of parameter regions that correspond to robust oocyte selection. This framework can be generalized to map the full parameter spaces in a broad class of models involving biological switches.

Since the seminal 1961 paper of Monod and Jacob, mathematical models of biomolecular circuits have guided our understanding of cell regulation. Model-based exploration of the functional capabilities of any given circuit requires systematic mapping of multidimensional spaces of model parameters. Despite significant advances in computational dynamical systems approaches, this analysis remains a nontrivial task. Here, we use a nonlinear system of ordinary differential equations to model oocyte selection in Drosophila, a robust symmetry-breaking event that relies on autoregulatory localization of oocyte-specification factors. By applying an algorithmic approach that implements symbolic computation and topological methods, we enumerate all phase portraits of stable steady states in the limit when nonlinear regulatory interactions become discrete switches. Leveraging this initial exact partitioning and further using numerical exploration, we locate parameter regions that are dense in purely asymmetric steady states when the nonlinearities are not infinitely sharp, enabling systematic identification of parameter regions that correspond to robust oocyte selection. This framework can be generalized to map the full parameter spaces in a broad class of models involving biological switches.

The competition between thermal fluctuations and potential forces is the foundation of our understanding of phase transitions and matter in equilibrium. Driving matter out of equilibrium allows for a new class of interactions which are neither attractive nor repulsive but transverse. The existence of such transverse forces immediately raises the question of how they interfere with basic principles of material self-organization. Despite a recent surge of interest, this question remains open. Here, we show that activating transverse forces by homogeneous rotation of colloidal units generically turns otherwise quiescent solids into a crystal whorl state dynamically shaped by self-propelled dislocations. Simulations of both a minimal model and a full hydrodynamics model establish the generic nature of the chaotic dynamics of these self-kneading polycrystals. Using a continuum theory, we explain how odd and Hall stresses conspire to destabilize chiral crystals from within. This chiral instability produces dislocations that are unbound by their self-propulsion. Their proliferation eventually leads to a crystalline whorl state out of reach of equilibrium matter.

The propagation of light within a material is usually well defined, with the propagation described by scattering and dispersion. In artificially designed metamaterials and in anisotropic layered materials, the dispersion can be hyperbolic, giving rise to subwavelength confinement of the light. Sternbach et al. show that the hyperbolic dispersion can be optically switched on and off on demand in the layered transition metal dichalcogenide tungsten diselenide (see the Perspective by Deng and Chen). Illuminating the material with ultrafast pulses of sub-bandgap light creates a transient waveguide, resulting in hyperbolic dispersion in the material. The ability to tune the dispersion characteristics on demand using optical pumping is an effective approach for developing ultrafast switching photonic devices and controlling the propagation of light on the nanoscale.Science, this issue p. 617; see also p. 572Collective electronic modes or lattice vibrations usually prohibit propagation of electromagnetic radiation through the bulk of common materials over a frequency range associated with these oscillations. However, this textbook tenet does not necessarily apply to layered crystals. Highly anisotropic materials often display nonintuitive optical properties and can permit propagation of subdiffractional waveguide modes, with hyperbolic dispersion, throughout their bulk. Here, we report on the observation of optically induced electronic hyperbolicity in the layered transition metal dichalcogenide tungsten diselenide (WSe2). We used photoexcitation to inject electron-hole pairs in WSe2 and then visualized, by transient nanoimaging, the hyperbolic rays that traveled along conical trajectories inside of the crystal. We establish here the signatures of programmable hyperbolic electrodynamics and assess the role of quantum transitions of excitons within the Rydberg series in the observed polaritonic response.

Asymmetric Weyl semimetals, which possess an inherently chiral structure, have different energies and dispersion relations for left- and right-handed fermions. They exhibit certain effects not found in symmetric Weyl semimetals, such as the quantized circular photogalvanic effect and the helical magnetic effect. In this work, we derive the conditions required for breaking chiral symmetry by applying an external field in symmetric Weyl semimetals. We explicitly demonstrate that in certain materials with the T

Reflected Brownian motion (RBM) in a convex polyhedral cone arises in a variety of applications ranging from the theory of stochastic networks to mathematical finance, and under general stability conditions, it has a unique stationary distribution. In such applications, to implement a stochastic optimization algorithm or quantify robustness of a model, it is useful to characterize the dependence of stationary performance measures on model parameters. In this paper, we characterize parametric sensitivities of the stationary distribution of an RBM in a simple convex polyhedral cone, that is, sensitivities to perturbations of the parameters that define the RBM—namely the covariance matrix, drift vector, and directions of reflection along the boundary of the polyhedral cone. In order to characterize these sensitivities, we study the long-time behavior of the joint process consisting of an RBM along with its so-called derivative process, which characterizes pathwise derivatives of RBMs on finite time intervals. We show that the joint process is positive recurrent and has a unique stationary distribution and that parametric sensitivities of the stationary distribution of an RBM can be expressed in terms of the stationary distribution of the joint process. This can be thought of as establishing an interchange of the differential operator and the limit in time. The analysis of ergodicity of the joint process is significantly more complicated than that of the RBM because of its degeneracy and the fact that the derivative process exhibits jumps that are modulated by the RBM. The proofs of our results rely on path properties of coupled RBMs and contraction properties related to the geometry of the polyhedral cone and directions of reflection along the boundary. Our results are potentially useful for developing efficient numerical algorithms for computing sensitivities of functionals of stationary RBMs.

Twisted van der Waals heterostructures have latterly received prominent attention for their many remarkable experimental properties, and the promise that they hold for realising elusive states of matter in the laboratory. We propose that these systems can, in fact, be used as a robust quantum simulation platform that enables the study of strongly correlated physics and topology in quantum materials. Among the features that make these materials a versatile toolbox are the tunability of their properties through readily accessible external parameters such as gating, straining, packing and twist angle; the feasibility to realize and control a large number of fundamental many-body quantum models relevant in the field of condensed-matter physics; and finally, the availability of experimental readout protocols that directly map their rich phase diagrams in and out of equilibrium. This general framework makes it possible to robustly realize and functionalize new phases of matter in a modular fashion, thus broadening the landscape of accessible physics and holding promise for future technological applications.

The energy of the lowest-lying triplet state (T1) relative to the ground and first-excited singlet states (S0, S1) plays a critical role in optical multiexcitonic processes of organic chromophores. Focusing on triplet–triplet annihilation (TTA) upconversion, the S0 to T1 energy gap, known as the triplet energy, is difficult to measure experimentally for most molecules of interest. Ab initio predictions can provide a useful alternative, however low-scaling electronic structure methods such as the Kohn–Sham and time-dependent variants of Density Functional Theory (DFT) rely heavily on the fraction of exact exchange chosen for a given functional, and tend to be unreliable when strong electronic correlation is present. Here, we use auxiliary-field quantum Monte Carlo (AFQMC), a scalable electronic structure method capable of accurately describing even strongly correlated molecules, to predict the triplet energies for a series of candidate annihilators for TTA upconversion, including 9,10 substituted anthracenes and substituted benzothiadiazole (BTD) and benzoselenodiazole (BSeD) compounds. We compare our results to predictions from a number of commonly used DFT functionals, as well as DLPNO-CCSD(T0), a localized approximation to coupled cluster with singles, doubles, and perturbative triples. Together with S1 estimates from absorption/emission spectra, which are well-reproduced by TD-DFT calculations employing the range-corrected hybrid functional CAM-B3LYP, we provide predictions regarding the thermodynamic feasibility of upconversion by requiring (a) the measured T1 of the sensitizer exceeds that of the calculated T1 of the candidate annihilator, and (b) twice the T1 of the annihilator exceeds its S1 energetic value. We demonstrate a successful example of in silico discovery of a novel annihilator, phenyl-substituted BTD, and present experimental validation via low temperature phosphorescence and the presence of upconverted blue light emission when coupled to a platinum octaethylporphyrin (PtOEP) sensitizer. The BTD framework thus represents a new class of annihilators for TTA upconversion. Its chemical functionalization, guided by the computational tools utilized herein, provides a promising route towards high energy (violet to near-UV) emission.

Early sensory areas in the brain are faced with a task analogous to the scientific process itself: given raw data, they must extract meaningful information about its underlying structure. This process is particularly difficult, because the true underlying structure of the data is never revealed, so representation learning must be largely unsupervised. Framing this process in the language of Bayesian probabilities is tempting but difficult to connect to biology, because we still lack a satisfactory account of how the machinery of Bayesian inference and learning is implemented in neural circuits. Here, we provide a theoretical account of how learning to infer latent structure can be implemented in neural networks using local synaptic plasticity. To do this, we derive a learning algorithm in which synaptic plasticity is driven by a local error signal, computed by comparing stimulus-driven responses to internal model predictions (the network's ``impression'' of the data). We associate these components with the basal and apical dendritic compartments of pyramidal neurons. Our solution builds on the Wake/Sleep algorithm (Dayan et al., 1995) by allowing learning to occur online, and capture temporal dependencies in continuous input streams. Compared to a traditional three-factor plasticity rule (Williams, 1992), it is substantially more stable and data-efficient, which allows it to be used for learning statistics of high-dimensional inputs. It is also flexible in that it is applicable to both rate-based and spiking-based neural activity, as well as different network architectures. More generally, our model provides a potential theoretical bridge from mechanistic accounts of synaptic plasticity to algorithmic descriptions of unsupervised probabilistic learning and inference.

The interplay between electron-electron correlations and disorder has been a central theme of condensed matter physics over the last several decades, with particular interest in the possibility that interactions might cause delocalization of an Anderson insulator into a metallic state, and the disrupting effects of randomness on magnetic order and the Mott phase. Here we extend this physics to explore electron-phonon interactions and show, via exact quantum Monte Carlo simulations, that the suppression of the charge density wave correlations in the half-filled Holstein model by disorder can stabilize a superconducting phase. Our simulations thus capture qualitatively the suppression of charge ordered phases and emergent superconductivity recently seen experimentally.