We give a damped proximal augmented Lagrangian method (DPALM) for solving problems with a weakly-convex objective and convex linear/non-linear constraints. Instead of taking a full stepsize, DPALM adopts a damped dual stepsize to ensure the boundedness of dual iterates. We show that DPALM can produce a (near) ε-KKT point within O(ε−2) outer itera- tions if each DPALM subproblem is solved to a proper accuracy. In addition, we establish overall iteration complexity of DPALM when the objective is ei- ther a regularized smooth function or in a regularized compositional form.

Qubit control is one of the main challenges of building a scalable Quantum computer with superconducting qubits. Current technologies are based on room temperature microwave generators. Scaling microwave control to millions of qubits is more than an engineering challenge due to the excessive heat delivered to the cryostat and the hardware cost. This talk will introduce the basics of microwave qubit control and some of its issues.

In this talk, I will present a Julia package, HypersurfaceRegions.jl, for computing all connected components in the complement of an arrangement of real algebraic hypersurfaces in $R^n$. The package is based on a modified implementation of the algorithm from the paper "Smooth Connectivity in Real Algebraic Varieties" by Cummings et al. I will outline the theory behind the algorithm and our implementation. I will demonstrate the use of the package through various examples.

As described by quantum mechanics, energy is absorbed and emitted from atoms in the form of photons with discrete energy values. When an atom absorbs or emits a photon, electrons transition up or down energy levels. The energy associated with these transition determines the frequency, i.e. color, of the absorbed or emitted light. Using Schrodinger’s equation to describe the atomic structure, and Maxwell’s equations to describe the light, a system of equations that fully describes the behavior of the light matter interaction can be derived.

A novel EigenWave algorithm is described to compute eigenvalues and eigenfunctions of elliptic boundary value problems. Based on the recently developed WaveHoltz scheme, the algorithm solves a related time-dependent wave equation as part of an iteration. At each iteration, the solution is filtered in time. After filtering, the solution mainly contains eigenmodes whose eigenvalues are near the target frequency of the filter. The iteration is embedded within a matrix-free Arnoldi algorithm, allowing the efficient computation of multiple eigenpairs near the target frequency.

Helicopter aerial refueling refers to the process of refueling a helicopter in mid-flight with the aid of a tanker aircraft. This maneuver is particularly challenging due to 1) complex aerodynamic interactions between the helicopter, the tanker, and the refueling hose-drogue system, 2) high pilot workload, 3) strict safety constraints, and 4) the contact-critical nature of the operation. To address these challenges, we propose a novel autonomous control methodology that combines model-based control with data-driven approaches such as reinforcement learning (RL).

By admixing a fraction of exact exchange (EXX), hybrid DFT provides a more accurate and reliable description of electronic structure than traditional semi-local DFT (density functional theory). However, the conventional reciprocal-space EXX evaluation is cubic scaling and computationally demanding (typically 10x–100x more expensive than semi-local DFT), which limits the applicability of hybrid DFT. To overcome this bottleneck, we have developed an accurate linear-scaling approach that exploits the sparsity of the EXX interaction using a localized representation of the occupied space.

We develop algebraic geometry for coupled cluster theory using second quantization. The high-dimensional eigenvalue problems that encode the electronic Schrödinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The truncated eigenstates parametrize well known varieties such as the Grassmannian, flag varieties and spinor varieties. We will offer a detailed study into the truncation varieties. Additionally in second quantization we work within the exterior algebra.

To function, cells must move material internally. This intracellular transport is achieved by molecular motors, which transport vesicle-bound cargo along protein filaments. In vitro experiments have uncovered the mechanochemistry of how single, isolated motors turn chemical energy into mechanical work as they "walk" along a protein filament. In cells, however, multiple motors transport cargo. Some of these motors bind to the protein filament and contribute to cargo transport; others diffuse over the surface of the cargo, and the motors transition between the two roles.

Graph convolutional networks (GCNs) are a powerful tool for graph representation learning. Due to the recursive neighborhood aggregations employed by GCNs, efficient training methods suffer from a lack of theoretical guarantees or are missing important practical elements from modern deep learning algorithms, such as adaptivity and momentum. We present several neighbor-sampling (NS) based Adam-type stochastic methods for solving a nonconvex GCN training problem.

With the surge of AI models in everyday use, examining the trustworthiness of these models remains a crucial concern. Trustworthiness is defined by several key factors: vulnerabilities inherent in the model architecture that can be exploited by adversaries, leading to faulty model use; vulnerabilities in the training data that result in unfair demographic biases, along with mechanisms to mitigate these biases; and latent representations of models that can be used to recover sensitive training information.