Hung D. Nguyen

Krishnamurthy Dvijotham, Hung Nguyen, Konstantin Turitsyn

Quadratic systems of equations appear in several applications. The results in this paper are motivated by quadratic systems of equations that describe equilibrium behavior of physical infrastructure networks like the power and gas grids. The quadratic systems in infrastructure networks are parameterized- the parameters can represent uncertainty (estimation error in resistance/inductance of a power transmission line, for example)or controllable decision variables (power outputs of generators,for example). It is then of interest to understand conditions on the parameters under which the quadratic system is guaranteed to have a solution within a specified set (for example, bounds on voltages and flows in a power grid). Given nominal values of the parameters at which the quadratic system has a solution and the Jacobian of the quadratic system at the solution i snon-singular, we develop a general framework to construct convex regions around the nominal value such that the system is guaranteed to have a solution within a given distance of the nominal solution. We show that several results from recen tliterature can be recovered as special cases of our framework,and demonstrate our approach on several benchmark power systems.

An Le, Nehal Mehta, William Freeman et al.

In this study, we developed deep learning-based method to classify the type of surgery performed for epiretinal membrane (ERM) removal, either internal limiting membrane (ILM) removal or ERM-alone removal. Our model, based on the ResNet18 convolutional neural network (CNN) architecture, utilizes postoperative optical coherence tomography (OCT) center scans as inputs. We evaluated the model using both original scans and scans preprocessed with energy crop and wavelet denoising, achieving 72% accuracy on preprocessed inputs, outperforming the 66% accuracy achieved on original scans. To further improve accuracy, we integrated tunable wavelet units with two key adaptations: Orthogonal Lattice-based Wavelet Units (OrthLatt-UwU) and Perfect Reconstruction Relaxation-based Wavelet Units (PR-Relax-UwU). These units allowed the model to automatically adjust filter coefficients during training and were incorporated into downsampling, stride-two convolution, and pooling layers, enhancing its ability to distinguish between ERM-ILM removal and ERM-alone removal, with OrthLattUwU boosting accuracy to 76% and PR-Relax-UwU increasing performance to 78%. Performance comparisons showed that our AI model outperformed a trained human grader, who achieved only 50% accuracy in classifying the removal surgery types from postoperative OCT scans. These findings highlight the potential of CNN based models to improve clinical decision-making by providing more accurate and reliable classifications. To the best of our knowledge, this is the first work to employ tunable wavelets for classifying different types of ERM removal surgery.

An D. Le, Hung Nguyen, Melanie Tran et al.

This paper presents the first study to apply tunable wavelet units (UwUs) for 3D retinal layer segmentation from Optical Coherence Tomography (OCT) volumes. To overcome the limitations of conventional max-pooling, we integrate three wavelet-based downsampling modules, OrthLattUwU, BiorthLattUwU, and LS-BiorthLattUwU, into a motion-corrected MGU-Net architecture. These modules use learnable lattice filter banks to preserve both low- and high-frequency features, enhancing spatial detail and structural consistency. Evaluated on the Jacobs Retina Center (JRC) OCT dataset, our framework shows significant improvement in accuracy and Dice score, particularly with LS-BiorthLattUwU, highlighting the benefits of tunable wavelet filters in volumetric medical image segmentation.

Hung D. Nguyen, Konstantin Turitsyn

Dynamic response of loads has a significant effect on system stability and directly determines the stability margin of the operating point. Inherent uncertainty and natural variability of load models make the stability assessment especially difficult and may compromise the security of the system. We propose a novel mathematical "robust stability" criterion for the assessment of small-signal stability of operating points. Whenever the criterion is satisfied for a given operating point, it provides mathematical guarantees that the operating point will be stable with respect to small disturbances for any dynamic response of the loads. The criterion can be naturally used for identification of operating regions secure from the occurrence of Hopf bifurcation. Several possible applications of the criterion are discussed, most importantly the concept of Robust Stability Assessment (RSA) that could be integrated in dynamic security assessment packages and used in contingency screening and other planning and operational studies.