Publications

The electric field of an intense laser pulse can directly modify the electronic properties of materials via electromodulation up to the petahertz regime. In this regime, the energy of the quiver motion of the electron-hole pair is comparable with the photon energy, which results in complex nonadiabatic dynamics. This regime opens opportunities to probe the electronic structure of materials on the attosecond timescale. Here, we show how the quasistatic electromodulation spectroscopy based on the Franz-Keldysh effect (FKE) connects with its nonadiabatic limit, which we find to be determined by resonant transitions between Floquet-Bloch states. This insight can be applied to measure the effective mass, ponderomotive and binding energies of the electron-hole pair on a few-femtosecond timescale. We demonstrate this by experimentally investigating laser-field-driven fused silica, a prototypical material for light-wave electronics, with extreme-ultraviolet attosecond pulse trains. We reproduce the experimental transient absorption spectra with an effective band structure and a dynamical Franz-Keldysh model, offering a simple parametrization for a theoretically challenging but technologically abundant material. Ab initio calculations in α-quartz highlight the contributions of specific bands, symmetry, and crystal orientation that are hidden in the experimental data due to randomized crystallographic orientation and finite temporal and spatial coherence. We show that the dynamical FKE can be explained as a third-order nonlinear process in the weak-field regime. The delay-dependent position of the absorption maxima and minima has a minimum tilt angle, determined by transitions between the underlying Floquet-Bloch states. In our analysis, we discuss the main experimental observables and show their connection to the parameters of the solid, providing the basis for nonadiabatic electromodulation spectroscopy.

For the past half-century, structural biologists relied on the notion that similar protein sequences give rise to similar structures and functions. While this assumption has driven research to explore certain parts of the protein universe, it disregards spaces that don’t rely on this assumption. Here we explore areas of the protein universe where similar protein functions can be achieved by different sequences and different structures. We predict ~200,000 structures for diverse protein sequences from 1,003 representative genomes across the microbial tree of life and annotate them functionally on a per-residue basis. Structure prediction is accomplished using the World Community Grid, a large-scale citizen science initiative. The resulting database of structural models is complementary to the AlphaFold database, with regards to domains of life as well as sequence diversity and sequence length. We identify 148 novel folds and describe examples where we map specific functions to structural motifs. We also show that the structural space is continuous and largely saturated, highlighting the need for a shift in focus across all branches of biology, from obtaining structures to putting them into context and from sequence-based to sequence-structure-function based meta-omics analyses.

Randomized sketches of a tensor product of pvectors follow a tradeoff between statistical efficiency and computational acceleration. Commonly used approaches avoid computing the high-dimensional tensor product explicitly, resulting in a suboptimal dependence of O(3p) in the embedding dimension. We propose a simple Complex-to-Real (CtR) modification of well-known sketches that replaces real random projections by complex ones, incurring a lower O(2p)factor in the embedding dimension. The output of our sketches is real-valued, which renders
their downstream use straightforward. In particular, we apply our sketches to p-fold self-tensored inputs corresponding to the feature maps of the
polynomial kernel. We show that our method achieves state-of-the-art performance in terms of accuracy and speed compared to other randomized approximations from the literature.

This paper reviews the growing field of Bayesian prediction. Bayes point and interval prediction are defined and exemplified and situated in statistical prediction more generally. Then, four general approaches to Bayes prediction are defined and we turn to predictor selection. This can be done predictively or non-predictively and predictors can be based on single models or multiple models. We call these latter cases unitary predictors and model average predictors, respectively. Then we turn to the most recent aspect of prediction to emerge, namely prediction in the context of large observational data sets and discuss three further classes of techniques. We conclude with a summary and statement of several current open problems.

Barnard's Loop is a famous arc of Hα emission located in the Orion star-forming region. Here, we provide evidence of a possible formation mechanism for Barnard's Loop and compare our results with recent work suggesting a major feedback event occurred in the region around 6 Myr ago. We present a 3D model of the large-scale Orion region, indicating coherent, radial, 3D expansion of the OBP-Near/Briceño-1 (OBP-B1) cluster in the middle of a large dust cavity. The large-scale gas in the region also appears to be expanding from a central point, originally proposed to be Orion X. OBP-B1 appears to serve as another possible center, and we evaluate whether Orion X or OBP-B1 is more likely to be the cause of the expansion. We find that neither cluster served as the single expansion center, but rather a combination of feedback from both likely propelled the expansion. Recent 3D dust maps are used to characterize the 3D topology of the entire region, which shows Barnard's Loop's correspondence with a large dust cavity around the OPB-B1 cluster. The molecular clouds Orion A, Orion B, and Orion λ reside on the shell of this cavity. Simple estimates of gravitational effects from both stars and gas indicate that the expansion of this asymmetric cavity likely induced anisotropy in the kinematics of OBP-B1. We conclude that feedback from OBP-B1 has affected the structure of the Orion A, Orion B, and Orion λ molecular clouds and may have played a major role in the formation of Barnard's Loop.

Single-molecule force spectroscopy (smFS) is a powerful approach to studying molecular self-organization. However, the coupling of the molecule with the ever-present experimental device introduces artifacts, that complicate the interpretation of these experiments. Performing statistical inference to learn hidden molecular properties is challenging because these measurements produce non-Markovian time series, and even minimal models lead to intractable likelihoods. To overcome these challenges, we developed a computational framework built on novel statistical methods called simulation-based inference (SBI). SBI enabled us to directly estimate the Bayesian posterior, and extract reduced quantitative models from smFS, by encoding a mechanistic model into a simulator in combination with probabilistic deep learning. Using synthetic data, we could systematically disentangle the measurement of hidden molecular properties from experimental artifacts. The integration of physical models with machine-learning density estimation is general, transparent, easy to use, and broadly applicable to other types of biophysical experiments.

Single-molecule force spectroscopy (smFS) is a powerful approach to studying molecular self-organization. However, the coupling of the molecule with the ever-present experimental device introduces artifacts, that complicate the interpretation of these experiments. Performing statistical inference to learn hidden molecular properties is challenging because these measurements produce non-Markovian time series, and even minimal models lead to intractable likelihoods. To overcome these challenges, we developed a computational framework built on novel statistical methods called simulation-based inference (SBI). SBI enabled us to directly estimate the Bayesian posterior, and extract reduced quantitative models from smFS, by encoding a mechanistic model into a simulator in combination with probabilistic deep learning. Using synthetic data, we could systematically disentangle the measurement of hidden molecular properties from experimental artifacts. The integration of physical models with machine-learning density estimation is general, transparent, easy to use, and broadly applicable to other types of biophysical experiments.

Many applications in magnetic confinement fusion require the efficient calculation of surface integrals with singular integrands. The singularity subtraction approaches typically used to handle such singularities are complicated to implement and low-order accurate. In contrast, we demonstrate that the Kapur–Rokhlin quadrature scheme is well-suited for the logarithmically singular integrals encountered for a toroidally axisymmetric confinement system, is easy to implement and is high-order accurate. As an illustration, we show how to apply this quadrature scheme for the efficient and accurate calculation of the normal component of the magnetic field due to the plasma current on the plasma boundary, via the virtual-casing principle.

We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear equations for tensor cores in this tensor network. The complexity of the resulting algorithm scales linearly in the dimension of the high-dimensional density. An analysis of estimation error demonstrates the effectiveness of this method through several numerical experiments.

We develop a density-matrix renormalization group (DMRG) algorithm for the simulation of quantum circuits. This algorithm can be seen as the extension of the time-dependent DMRG from the usual situation of Hermitian Hamiltonian matrices to quantum circuits defined by unitary matrices. For small circuit depths, the technique is exact and equivalent to other matrix product state–based techniques. For larger depths, it becomes approximate in exchange for an exponential speed up in computational time. Like an actual quantum computer, the quality of the DMRG results is characterized by a finite fidelity. However, unlike a quantum computer, the fidelity depends strongly on the quantum circuit considered. For the most difficult possible circuit for this technique, the so-called "quantum supremacy" benchmark of Google LLC [Arute et al., Nature 574, 505 (2019)], we find that the DMRG algorithm can generate bit strings of the same quality as the seminal Google experiment on a single computing core. For a more structured circuit used for combinatorial optimization (quantum approximate optimization algorithm), we find a drastic improvement of the DMRG results with error rates dropping by a factor of 100 compared with random quantum circuits. Our results suggest that the current bottleneck of quantum computers is their fidelities rather than the number of qubits.