Publications

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We present a classical approximation algorithm for the MAX-2-Local Hamiltonian problem. This is a maximization version of the QMA-complete 2-Local Hamiltonian problem in quantum computing, with the additional assumption that each local term is positive semidefinite. The MAX-2-Local Hamiltonian problem generalizes NP-hard constraint satisfaction problems, and our results may be viewed as generalizations of approximation approaches for the MAX-2-CSP problem. We work in the product state space and extend the framework of Goemans and Williamson for approximating MAX-2-CSPs. The key difference is that in the product state setting, a solution consists of a set of normalized 3-dimensional vectors rather than boolean numbers, and we leverage approximation results for rank-constrained Grothendieck inequalities. For MAX-2-Local Hamiltonian we achieve an approximation ratio of 0.328. This is the first example of an approximation algorithm beating the random quantum assignment ratio of 0.25 by a constant factor.

Determining a process–structure–property relationship is the holy grail of materials science, where both computational prediction in the forward direction and materials design in the inverse direction are essential. Problems in materials design are often considered in the context of process–property linkage by bypassing the materials structure, or in the context of structure–property linkage as in microstructure-sensitive design problems. However, there is a lack of research effort in studying materials design problems in the context of process–structure linkage, which has a great implication in reverse engineering. In this work, given a target microstructure, we propose an active learning high-throughput microstructure calibration framework to derive a set of processing parameters, which can produce an optimal microstructure that is statistically equivalent to the target microstructure. The proposed framework is formulated as a noisy multi-objective optimization problem, where each objective function measures a deterministic or statistical difference of the same microstructure descriptor between a candidate microstructure and a target microstructure. Furthermore, to significantly reduce the physical waiting wall-time, we enable the high-throughput feature of the microstructure calibration framework by adopting an asynchronously parallel Bayesian optimization by exploiting high-performance computing resources. Case studies in additive manufacturing and grain growth are used to demonstrate the applicability of the proposed framework, where kinetic Monte Carlo (kMC) simulation is used as a forward predictive model, such that for a given target microstructure, the target processing parameters that produced this microstructure are successfully recovered.

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While dragonflies are well-known for their high success rates when hunting prey, how the underlying neural circuitry generates the prey-interception trajectories used by dragonflies to hunt remains an open question. I present a model of dragonfly prey interception that uses a neural network to calculate motor commands for prey-interception. The model uses the motor outputs of the neural network to internally generate a forward model of prey-image translation resulting from the dragonfly's own turning that can then serve as a feedback guidance signal, resulting in trajectories with final approaches very similar to proportional navigation. The neural network is biologically-plausible and can therefore can be compared against in vivo neural responses in the biological dragonfly, yet parsimonious enough that the algorithm can be implemented without requiring specialized hardware.

The widely parallel, spiking neural networks of neuromorphic processors can enable computationally powerful formulations. While recent interest has focused on primarily machine learning tasks, the space of appropriate applications is wide and continually expanding. Here, we leverage the parallel and event-driven structure to solve a steady state heat equation using a random walk method. The random walk can be executed fully within a spiking neural network using stochastic neuron behavior, and we provide results from both IBM TrueNorth and Intel Loihi implementations. Additionally, we position this algorithm as a potential scalable benchmark for neuromorphic systems.

Deep learning networks have become a vital tool for image and data processing tasks for deployed and edge applications. Resource constraints, particularly low power budgets, have motivated methods and devices for efficient on-edge inference. Two promising methods are reduced precision communication networks (e.g. binary activation spiking neural networks) and weight pruning. In this paper, we provide a preliminary exploration for combining these two methods, specifically in-training weight pruning of whetstone networks, to achieve deep networks with both sparse weights and binary activations.

Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity molecules. Here we study the distribution of the polarity protein Cdc42 in a mass-conserved membrane-bulk model, and explore the effects of diffusion and spatial dimensionality on spatio-temporal pattern formation. We first analyze a one-dimensional (1-D) model for Cdc42 oscillations in fission yeast, consisting of two diffusion equations in the bulk domain coupled to nonlinear ODEs for binding kinetics at each end of the cell. In 1-D, our analysis reveals the existence of symmetric and asymmetric steady states, as well as anti-phase relaxation oscillations typical of slow-fast systems. We then extend our analysis to a two-dimensional (2-D) model with circular bulk geometry, for which species can either diffuse inside the cell or become bound to the membrane and undergo a nonlinear reaction-diffusion process. We also consider a nonlocal system of PDEs approximating the dynamics of the 2-D membrane-bulk model in the limit of fast bulk diffusion. In all three model variants we find that mass conservation selects perturbations of spatial modes that simply redistribute mass. In 1-D, only anti-phase oscillations between the two ends of the cell can occur, and in-phase oscillations are excluded. In higher dimensions, no radially symmetric oscillations are observed. Instead, the only instabilities are symmetry-breaking, either corresponding to stationary Turing instabilities, leading to the formation of stationary patterns, or to oscillatory Turing instabilities, leading to traveling and standing waves. Codimension-two Bogdanov–Takens bifurcations occur when the two distinct instabilities coincide, causing traveling waves to slow down and to eventually become stationary patterns. Our work clarifies the effect of geometry and dimensionality on behaviors observed in mass-conserved cell polarity models.

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Atomic precision advanced manufacturing (APAM) offers creation of donor devices in an atomically thin layer doped beyond the solid solubility limit, enabling unique device physics. This presents an opportunity to use APAM as a pathfinding platform to investigate digital electronics at the atomic limit. Scaling to smaller transistors is increasingly difficult and expensive, necessitating the investigation of alternative fabrication paths that extend to the atomic scale. APAM donor devices can be created using a scanning tunneling microscope (STM). However, these devices are not currently compatible with industry standard fabrication processes. There exists a tradeoff between low thermal budget (LT) processes to limit dopant diffusion and high thermal budget (HT) processes to grow defect-free layers of epitaxial Si and gate oxide. To this end, we have developed an LT epitaxial Si cap and LT deposited Al2O3 gate oxide integrated with an atomically precise single-electron transistor (SET) that we use as an electrometer to characterize the quality of the gate stack. The surface-gated SET exhibits the expected Coulomb blockade behavior. However, the gate’s leverage over the SET is limited by defects in the layers above the SET, including interfaces between the Si and oxide, and structural and chemical defects in the Si cap. We propose a more sophisticated gate stack and process flow that is predicted to improve performance in future atomic precision devices.

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