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Topological edge states in electromagnetic systems feature a set of attracting fundamental properties and unveil prospective applications based on disorder robustness and tailored localization. Despite active efforts in implementing…
Topology is an important degree of freedom in characterizing electronic systems. Recently, it also brings new theoretical frontiers and many potential applications in photonics. However, the verification of the topological nature is highly…
Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high energy theories, quantum information, and condensed matter physics. In condensed matter systems, a wide range of…
Accurately restoring topology is both challenging and crucial in tubular structure extraction tasks, such as blood vessel segmentation and road network extraction. Diverging from traditional approaches based on pixel-level classification,…
Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…
Graphene features topological edge bands that connect the pair of Dirac points through either sectors of the 1D Brillouin zone depending on edge configurations (zigzag or bearded). Because of their flat dispersion, spontaneous edge…
Topological photonics holds the promise for enhanced robustness of light localization and propagation enabled by the global symmetries of the system. While traditional designs of topological structures rely on lattice symmetries, there is…
This paper presents a new approach, so-called boundary variation diminishing (BVD), for reconstructions that minimize the discontinuities (jumps) at cell interfaces in Godunov type schemes. It is motivated by the observation that…
This paper presents a proper generalized decomposition (PGD) based reduced-order model of hierarchical deep-learning neural networks (HiDeNN). The proposed HiDeNN-PGD method keeps both advantages of HiDeNN and PGD methods. The automatic…
We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on…
Calculations of propagating quantum trajectories associated to a wave function provide new insight into quantum processes such as particle scattering and diffraction. Here, hydrodynamic calculations of electron beam imaging under conditions…
Iterative algorithms have many advantages for linear tomographic image reconstruction when compared to back-projection based methods. However, iterative methods tend to have significantly higher computational complexity. To overcome this,…
Conventional methods of wavefront reconstruction from the raw data of the Shack-Hartmann sensor use the focal spot shifts and discard the high-frequency information about the wavefront. Phase-retrieval-based methods treat the Hartmann…
In the Network Inference problem, one seeks to recover the edges of an unknown graph from the observations of cascades propagating over this graph. In this paper, we approach this problem from the sparse recovery perspective. We introduce a…
Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central…
Edge detection is an important field in image processing. Edges characterize object boundaries and are therefore useful for segmentation, registration, feature extraction, and identification of objects in a scene. In this paper, an approach…
Diffusion-based graph generative models have recently obtained promising results for graph generation. However, existing diffusion-based graph generative models are mostly one-shot generative models that apply Gaussian diffusion in the…
This paper presents reconstructions of homogeneous targets from the 2D and 3D Fresnel databases by one-step imaging methods based on the computation of topological derivative and topological energy fields. The electromagnetic inverse…
We propose interpretable graph neural networks for sampling and recovery of graph signals, respectively. To take informative measurements, we propose a new graph neural sampling module, which aims to select those vertices that maximally…
Ptychography is a popular microscopic imaging modality for many scientific discoveries and sets the record for highest image resolution. Unfortunately, the high image resolution for ptychographic reconstruction requires significant amount…