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Topological crystalline phases in electronic structures can be generally classified using the spatial symmetry characters of the valence bands and mapping them onto appropriate symmetry indicators. These mappings have been recently applied…
Statistical quality control in semiconductor manufacturing hinges on effective diagnostics of wafer bin maps, wherein a key challenge is to detect how defective chips tend to spatially cluster on a wafer--a problem known as spatial pattern…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realise and investigate topological quantum spin liquid phases. This new and exciting direction brings about important research…
Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can…
This paper presents a novel approach for the identification of linear time-periodic (LTP) systems in continuous time. This method is based on harmonic modeling and consists in converting any LTP system into an equivalent LTI system with…
We consider gapped Z2 spin liquids, where spinon quasiparticles may carry fractional quantum numbers of space group symmetry. In particular, spinons can carry fractional crystal momentum. We show that such quantum number fractionalization…
There are a variety of industrial products that possess periodic textures or surfaces, such as carbon fiber textiles and display panels. Traditional image-based quality inspection methods for these products require identifying the periodic…
Successful scientific applications of large-scale molecular dynamics often rely on automated methods for identifying the local crystalline structure of condensed phases. Many existing methods for structural identification, such as Common…
We propose a robust approach for performing automatic species-level recognition of fossil pollen grains in microscopy images that exploits both global shape and local texture characteristics in a patch-based matching methodology. We…
The classifications approaches for the crystallographic symmetries of patterns that are more or less periodic in two dimensions are critically reviewed and their relative performance qualitatively evaluated. The information theory based…
Designing topological materials with specific topological indices is a complex inverse problem, traditionally tackled through manual, intuition-driven methods that are neither scalable nor efficient for exploring the vast space of possible…
We propose a fast collocation method based on Krylov subspace iterative solver on general nonuniform grids for the fractional Laplacian problem, in which the fractional operator is presented in a singular integral formulation. The method is…
Fermionic Gaussian operators are foundational tools in quantum many-body theory, numerical simulation of fermionic dynamics, and fermionic linear optics. While their structure is fully determined by two-point correlations, evaluating their…
We introduce a framework for subspace methods which approximate the spectra of self-adjoint, unbounded operators in a local region. Using the projection-valued measure, we derive integrated spectral inequalities that also apply to unbounded…
In this paper, we propose a new framework for segmenting feature-based moving objects under affine subspace model. Since the feature trajectories in practice are high-dimensional and contain a lot of noise, we firstly apply the sparse PCA…
The statistical analysis of marked point processes requires disentangling complex spatial arrangements from attribute-dependent interactions. While classical summary statistics are effective for second-order dependencies, they frequently…
Sparse system identification of nonlinear dynamic systems is still challenging, especially for stiff and high-order differential equations for noisy measurement data. The use of highly correlated functions makes distinguishing between true…
Hyperspectral images provide abundant spatial and spectral information that is very valuable for material detection in diverse areas of practical science. The high-dimensions of data lead to many processing challenges that can be addressed…
We show that Bayesian inference, like that used in statistical mechanics, can guide the systematic construction of Fourier dark-field methods for localizing periodicity in near-field (e.g. scanning-tunneling and electron-phase-contrast)…