Publications

The method of Helsing and co-workers evaluates Laplace and related layer potentials generated by a panel (composite) quadrature on a curve, efficiently and with high-order accuracy for arbitrarily close targets. Since it exploits complex analysis, its use has been restricted to two dimensions (2D). We first explain its loss of accuracy as panels become curved, using a classical complex approximation result of Walsh that can be interpreted as "electrostatic shielding" of a Schwarz singularity. We then introduce a variant that swaps the target singularity for one at its complexified parameter preimage; in the latter space the panel is flat, hence the convergence rate can be much higher. The preimage is found robustly by Newton iteration. This idea also enables, for the first time, a near-singular quadrature for potentials generated by smooth curves in 3D, building on recurrences of Tornberg-Gustavsson. We apply this to accurate evaluation of the Stokes flow near to a curved filament in the slender body approximation. Our 3D method is several times more efficient (both in terms of kernel evaluations, and in speed in a C implementation) than the only existing alternative, namely, adaptive integration.

Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete optimization techniques, to this ordering problem. We benchmark their performance as well as that of the commonly-used greedy search on physically relevant tensor networks. Where computationally feasible, we also compare them with the optimal contraction sequence obtained by an exhaustive search. We find that the algorithms we consider consistently outperform a greedy search given equal computational resources, with an advantage that scales with tensor network size. We compare the obtained contraction sequences and identify signs of highly non-local optimization, with the more sophisticated algorithms sacrificing run-time early in the contraction for better overall performance.

Van-der Waals (vdW) atomically layered crystals can act as optical waveguides over a broad range of the electromagnetic spectrum ranging from Terahertz to visible. Unlike common Si-based waveguides, vdW semiconductors host strong excitonic resonances that may be controlled using non-thermal stimuli including electrostatic gating and photoexcitation. Here, we utilize waveguide modes to examine photo-induced changes of excitons in the prototypical vdW semiconductor, WSe

Normative models of neural computation offer simplified yet lucid mathematical descriptions of murky biological phenomena. Previously, online Principal Component Analysis (PCA) was used to model a network of single-compartment neurons accounting for weighted summation of upstream neural activity in the soma and Hebbian/anti-Hebbian synaptic learning rules. However, synaptic plasticity in biological neurons often depends on the integration of synaptic currents over a dendritic compartment rather than total current in the soma. Motivated by this observation, we model a pyramidal neuronal network using online Canonical Correlation Analysis (CCA). Given two related datasets represented by distal and proximal dendritic inputs, CCA projects them onto the subspace which maximizes the correlation between their projections. First, adopting a normative approach and starting from a single-channel CCA objective function, we derive an online gradient-based optimization algorithm whose steps can be interpreted as the operation of a pyramidal neuron. To model networks of pyramidal neurons, we introduce a novel multi-channel CCA objective function, and derive from it an online gradient-based optimization algorithm whose steps can beinterpreted as the operation of a pyramidal neuron network including its architecture, dynamics, and synaptic learning rules. Next, we model a neuron with more than two dendritic compartments by deriving its operation from a known objective function for multi-view CCA. Finally, we confirm the functionality of our networks via numerical simulations. Overall, our work presents a simplified but informative abstraction of learning in a pyramidal neuron network, and demonstrates how such networks can integrate multiple sources of inputs.

We demonstrate that an achiral stretching force transforms disk-shaped colloidal membranes composed of chiral rods into twisted ribbons with handedness opposite the preferred twist of the rods. Using an experimental technique that enforces torque-free boundary conditions we simultaneously measure the force-extension curve and the ribbon shape. An effective theory that accounts for the membrane bending energy and uses geometric properties of the edge to model the internal liquid crystalline degrees of freedom explains both the measured force-extension curve and the force-induced twisted shape.

Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projected Entangled Pair States (PEPS). Guided by extensive exact diagonalization and density matrix renormalization group calculations, we construct an optimized symmetric PEPS for a SU(3)1 chiral spin liquid on the square lattice. Characteristic features are revealed by the entanglement spectrum (ES) on an infinitely long cylinder. In all three ℤ3 sectors, the level counting of the linear dispersing modes is in full agreement with SU(3)1 Wess-Zumino-Witten conformal field theory prediction. Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence. Possible universal properties of topological SU(N)k chiral PEPS are discussed.

A genetic etiology is identified for one-third of patients with congenital heart disease (CHD), with 8% of cases attributable to coding de novo variants (DNVs). To assess the contribution of noncoding DNVs to CHD, we compared genome sequences from 749 CHD probands and their parents with those from 1,611 unaffected trios. Neural network prediction of noncoding DNV transcriptional impact identified a burden of DNVs in individuals with CHD (n = 2,238 DNVs) compared to controls (n = 4,177; P = 8.7 × 10−4). Independent analyses of enhancers showed an excess of DNVs in associated genes (27 genes versus 3.7 expected, P = 1 × 10−5). We observed significant overlap between these transcription-based approaches (odds ratio (OR) = 2.5, 95% confidence interval (CI) 1.1–5.0, P = 5.4 × 10−3). CHD DNVs altered transcription levels in 5 of 31 enhancers assayed. Finally, we observed a DNV burden in RNA-binding-protein regulatory sites (OR = 1.13, 95% CI 1.1–1.2, P = 8.8 × 10−5). Our findings demonstrate an enrichment of potentially disruptive regulatory noncoding DNVs in a fraction of CHD at least as high as that observed for damaging coding DNVs.

A novel optimization formulation is provided for holographic phase retrieval with data subjected to Poisson shot noise in the low-photon regime. This formulation, based on regularized maximum likelihood estimation, consistently provides improved image reconstruction.

AU Microscopii (AU Mic) is the second closest pre main sequence star, at a distance of 9.79 parsecs and with an age of 22 million years. AU Mic possesses a relatively rare and spatially resolved3 edge-on debris disk extending from about 35 to 210 astronomical units from the star, and with clumps exhibiting non-Keplerian motion. Detection of newly formed planets around such a star is challenged by the presence of spots, plage, flares and other manifestations of magnetic activity on the star. Here we report observations of a planet transiting AU Mic. The transiting planet, AU Mic b, has an orbital period of 8.46 days, an orbital distance of 0.07 astronomical units, a radius of 0.4 Jupiter radii, and a mass of less than 0.18 Jupiter masses at 3 sigma confidence. Our observations of a planet co-existing with a debris disk offer the opportunity to test the predictions of current models of planet formation and evolution.

Microbial diversity in the cystic fibrosis (CF) lung decreases over decades as pathogenic bacteria such as Pseudomonas aeruginosa take over. The dynamics of the CF microbiome and metabolome over shorter time frames, however, remain poorly studied. Here, we analyze paired microbiome and metabolome data from 594 sputum samples collected over 401 days from six adult CF subjects (subject mean = 179 days) through periods of clinical stability and 11 CF pulmonary exacerbations (CFPE). While microbiome profiles were personalized (permutational multivariate analysis of variance [PERMANOVA] r2 = 0.79, P < 0.001), we observed significant intraindividual temporal variation that was highest during clinical stability (linear mixed-effects [LME] model, P = 0.002). This included periods where the microbiomes of different subjects became highly similar (UniFrac distance, <0.05). There was a linear increase in the microbiome alpha-diversity and in the log ratio of anaerobes to pathogens with time (n = 14 days) during the development of a CFPE (LME P = 0.0045 and P = 0.029, respectively). Collectively, comparing samples across disease states showed there was a reduction of these two measures during antibiotic treatment (LME P = 0.0096 and P = 0.014, respectively), but the stability data and CFPE data were not significantly different from each other. Metabolome alpha-diversity was higher during CFPE than during stability (LME P = 0.0085), but no consistent metabolite signatures of CFPE across subjects were identified. Virulence-associated metabolites from P. aeruginosa were temporally dynamic but were not associated with any disease state. One subject died during the collection period, enabling a detailed look at changes in the 194 days prior to death. This subject had over 90% Pseudomonas in the microbiome at the beginning of sampling, and that level gradually increased to over 99% prior to death. This study revealed that the CF microbiome and metabolome of some subjects are dynamic through time. Future work is needed to understand what drives these temporal dynamics and if reduction of anaerobes correlate to clinical response to CFPE therapy.