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We argue that existing training-free segmentation methods rely on an implicit and limiting assumption, that segmentation is a spectral graph partitioning problem over diffusion-derived affinities. Such approaches, based on global graph…
Electronic materials exhibiting phase transitions between metastable states (e.g., metal-insulator transition materials with abrupt electrical resistivity transformations) are challenging to decode. For these materials, conventional machine…
We present a new algorithm for clustering points in R^n. The key property of the algorithm is that it is affine-invariant, i.e., it produces the same partition for any affine transformation of the input. It has strong guarantees when the…
The topological phases of two-dimensional time-reversal symmetric insulators are classified by a $\mathbb{Z}_{2}$ topological invariant. Usually, the invariant is introduced and calculated by exploiting the way time-reversal symmetry acts…
In this work, we introduce a novel local pairwise descriptor and then develop a simple, effective iterative method to solve the resulting quadratic assignment through sparsity control for shape correspondence between two approximate…
We propose a robust classification algorithm for curves in 2D and 3D, under the special and full groups of affine transformations. To each plane or spatial curve we assign a plane signature curve. Curves, equivalent under an affine…
The exciting discovery of topological condensed matter systems has lately triggered a search for their photonic analogs, motivated by the possibility of robust backscattering-immune light transport. However, topological photonic phases have…
We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…
This article addresses the problem of two- and higher dimensional pattern matching, i.e. the identification of instances of a template within a larger signal space, which is a form of registration. Unlike traditional correlation, we aim at…
The performance of spectral clustering heavily relies on the quality of affinity matrix. A variety of affinity-matrix-construction (AMC) methods have been proposed but they have hyperparameters to determine beforehand, which requires strong…
Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks…
Spectral measurements of boundary localized in-gap modes are commonly used to identify topological insulators via the bulk-boundary correspondence. This can be extended to high-order topological insulators for which the most striking…
In many practical applications, signals and environments are time- varying, which makes fixed filters unreliable. Adaptive filtering, on the other hand, updates in real time to suppress noise, track nonstationary signals, and identify…
Fiber-reinforced soft biological tissues are typically modeled as hyperelastic, anisotropic, and nearly incompressible materials. To enforce incompressibility a multiplicative split of the deformation gradient into a volumetric and an…
Spatial labeling assigns labels to specific spatial locations to characterize their spatial properties and relationships, with broad applications in scientific research and practice. Measuring the similarity between two spatial labelings is…
Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, non-reciprocal chiral edge states and cavity-like confined states that have applications in both linear and…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
Time-frequency (TF) representation of non-stationary signals typically requires the effective concentration of energy distribution along the instantaneous frequency (IF) ridge, which exhibits intrinsic sparsity. Inspired by the sparse…
Crystalline symmetry can be used to predict bulk and surface properties of topological phases. For non-interacting cases, symmetry-eigenvalue analysis of Bloch states at high symmetry points in the Brillouin zone simplifies the calculation…
Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…