Publications

Active nematics exhibit spontaneous flows through a well-known linear instability of the uniformly aligned quiescent state. Here, we show that even a linearly stable uniform state can experience a nonlinear instability, resulting in a discontinuous transition to spontaneous flows. In this case, quiescent and flowing states may coexist. Through a weakly nonlinear analysis and a numerical study, we trace the bifurcation diagram of striped patterns and show that the underlying pitchfork bifurcation switches from supercritical (continuous) to subcritical (discontinuous) by varying the flow-alignment parameter. We predict that the discontinuous spontaneous flow transition occurs for a wide range of parameters, including systems of contractile flow-aligning rods. Our predictions are relevant to active nematic turbulence and can potentially be tested in experiments on either cell layers or active cytoskeletal suspensions.

Learning probability models from data is at the heart of many machine learning endeavors, but is notoriously difficult due to the curse of dimensionality. We introduce a new framework for learning normalized energy (log probability) models that is inspired from diffusion generative models, which rely on networks optimized to estimate the score. We modify a score network architecture to compute an energy while preserving its inductive biases. The gradient of this energy network with respect to its input image is the score of the learned density, which can be optimized using a denoising objective. Importantly, the gradient with respect to the noise level provides an additional score that can be optimized with a novel secondary objective, ensuring consistent and normalized energies across noise levels. We train an energy network with this dual score matching objective on the ImageNet64 dataset, and obtain a cross-entropy (negative log likelihood) value comparable to the state of the art. We further validate our approach by showing that our energy model strongly generalizes: estimated log probabilities are nearly independent of the specific images in the training set. Finally, we demonstrate that both image probability and dimensionality of local neighborhoods vary significantly with image content, in contrast with traditional assumptions such as concentration of measure or support on a low-dimensional manifold.

Studies of fate patterning during development typically emphasize cell-cell communication via diffusible chemical signals. Recent experiments on stem cell colonies, however, suggest that in some cases mechanical stresses, rather than secreted chemicals, enable long-ranged cell-cell interactions that specify positional information and pattern cell fates. These findings inspire a model of mechanical patterning: fate affects cell contractility, and pressure in the cell layer biases fate. Cells at the colony edge, more contractile than cells at the center, seed a pattern that propagates via force transmission. Strikingly, our model implies that the width of the outer fate domain varies nonmonotonically with substrate stiffness, a prediction that we confirm experimentally; we argue that a similar dependence on substrate stiffness can be achieved by a chemical morphogen only if strong constraints on the signaling pathway's mechanobiology are met. Our findings thus support the idea that mechanical stress can mediate patterning in the complete absence of chemical morphogens, even in nonmotile cell layers, thus expanding the repertoire of possible roles for mechanical signals in development and morphogenesis. Future tests of additional model predictions, like the effect of anisotropic substrate rigidity, will further broaden the range of achievable fate patterns.

Characterizing the conformational ensemble of biomolecular systems is key to understand their functions. Cryoelectron microscopy (cryo-EM) captures two-dimensional snapshots of biomolecular ensembles, giving in principle access to thermodynamics. However, these images are very noisy and show projections of the molecule in unknown orientations, making it very difficult to identify the biomolecule’s conformation in each individual image. Here, we introduce cryo-EM simulation-based inference (cryoSBI) to infer the conformations of biomolecules and the uncertainties associated with the inference from individual cryo-EM images. CryoSBI builds on simulation-based inference, a merger of physics-based simulations and probabilistic deep learning, allowing us to use Bayesian inference even when likelihoods are too expensive to calculate. We begin with an ensemble of conformations, templates from experiments, and molecular modeling, serving as structural hypotheses. We train a neural network approximating the Bayesian posterior using simulated images from these templates and then use it to accurately infer the conformation of the biomolecule from each experimental image. Training is only done once on simulations, and after that, it takes just a few milliseconds to make inference on an image, making cryoSBI suitable for arbitrarily large datasets and direct analysis on micrographs. CryoSBI eliminates the need to estimate particle pose and imaging parameters, significantly enhancing the computational speed compared to explicit likelihood methods. Importantly, we obtain interpretable machine learning models by integrating physics-based approaches with deep neural networks, ensuring that our results are transparent and reliable. We illustrate and benchmark cryoSBI on synthetic data and showcase its promise on experimental single-particle cryo-EM data.

Computational psychiatry studies suggest that individuals with autism spectrum disorder (ASD) inflexibly update their expectations. Here we leveraged high-yield rodent psychophysics, extensive behavioral modeling and brain-wide single-cell extracellular recordings to assess whether mice with different genetic perturbations associated with ASD show this same computational anomaly, and if so, what neurophysiological features are shared across genotypes. Mice harboring mutations in Fmr1, Cntnap2 or Shank3B show a blunted update of priors during decision-making. Compared with mice that flexibly updated their priors, inflexible updating of priors was associated with a shift in the weighting of prior encoding from sensory to frontal cortices. Furthermore, frontal areas in mouse models of ASD showed more units encoding deviations from the animals’ long-run prior, and sensory responses did not differentiate between expected and unexpected observations. These findings suggest that distinct genetic instantiations of ASD may yield common neurophysiological and behavioral phenotypes.

The remarkable cohesion and coordination observed in moving animal groups and their collective responsiveness to threats are thought to be mediated by scale-free correlations, where changes in the behavior of one animal influence others in the group, regardless of the distance between them. But are these features independent of group size? Here, we investigate group cohesiveness and collective responsiveness in computational models of massive schools of fish of up to 50,000 individuals. We show that as the number of swimmers increases, flow interactions destabilize the school, creating clusters that constantly fragment, disperse, and regroup, similar to their biological counterparts. We calculate the spatial correlation and speed of information propagation in these dynamic clusters. Spatial correlations in cohesive and polarized clusters are indeed scale free, much like in natural animal groups, but fragmentation events are preceded by a decrease in correlation length, thus diminishing the group's collective responsiveness, leaving it more vulnerable to predation events. Importantly, in groups undergoing collective turns, the information about the change in direction propagates linearly in time among group members, thanks to the non-reciprocal nature of the visual interactions between individuals. Merging speeds up the transfer of information within each cluster by several fold, while fragmentation slows it down. Our findings suggest that flow interactions may have played an important role in group size regulation, behavioral adaptations, and dispersion in living animal groups.

This article shows that it is, in principle, possible to make a dielectric rod completely invisible to an incident electromagnetic plane wave of a given frequency. Students can derive the conditions that make the rod invisible if they understand the concept of plane waves, the boundary conditions for electric and magnetic fields, and the complex representation of electromagnetic fields. With access to appropriate software, students can determine the bandwidth of the invisibility and investigate whether it is possible to make an invisible rod out of real-world materials. A more advanced project proposed is to use electromagnetic software to find perfectly conducting hollow structures that are invisible to an incident plane wave.

Time-dependent Wannier functions were initially proposed as a means for calculating the polarization current in crystals driven by external fields. In this work, we present a simple gauge where Wannier states are defined based on the maximally localized functions at the initial time, and are propagated using the time-dependent Bloch states obtained from established first-principles calculations, avoiding the costly Wannierization at ech time step. We show that this basis efficiently describes the time-dependent polarization of the laser driven system through the analysis of the motion of Wannier centers. We use this technique to analyze highly nonlinear and non-perturbative responses such as high harmonic generation in solids, using the hexagonal boron nitride as an illustrative example, and we show how it provides an intuitive picture for the physical mechanisms.

Embedding materials in optical cavities has emerged as an intriguing perspective for controlling quantum materials, but a key challenge lies in measuring properties of the embedded matter. Here, we propose a framework for probing strongly correlated cavity-embedded materials through direct measurements of cavity photons. We derive general relations between photon and matter observables inside the cavity, and show how these can be measured via the emitted photons. As an example, we demonstrate how the entanglement phase transition of an embedded H

The optical conductivity provides a comprehensive view of the electronic response of materials to electromagnetic fields, offering insights into transport phenomena, optoelectronic properties, and other fundamental aspects of condensed matter physics. We present an automatic, high-order accurate, and adaptive Brillouin zone integration algorithm for the calculation of the optical conductivity using the Kubo formula, with a nonzero but small broadening factor 𝜂, focusing on the case in which a Hamiltonian in a downfolded model can be evaluated efficiently using Wannier interpolation. The algorithm uses iterated adaptive integration to exploit the localization of the transport distribution near energy and energy-difference isosurfaces, yielding polylogarithmic computational complexity with respect to 𝜂, rather than the algebraic complexity of uniform integration rules. To demonstrate the method, we compute the AC optical conductivity of a three-band tight-binding model, and are able to resolve the Drude and interband peaks with broadening in the sub-meV regime to several digits of accuracy. Our algorithm automates convergence testing to a user-specified error tolerance, providing an important tool in black-box first-principles calculations of electrical transport phenomena and other response functions.