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Yuanzhe Xu

Publications and source records attributed to Yuanzhe Xu.

4 recordsLinked to original sources

Defects encode high-dimensional topological information

In polarization fields, Stokes skyrmions are continuous vectorial textures that encode integer-valued topological invariants across real space, enabling robust optical information encoding under complex perturbations. This topological resilience, however, fails when singular points occur where the Stokes vector has no unique limiting value, placing a fundamental constraint on skyrmion-based information manipulation. Here, we show, paradoxically, that the very defects that destroy conventional resilience can become the carriers of topological information. We introduce the resulting structures as Stokes defect skyrmions, in which singular Stokes responses constitute measurable topological degrees of freedom with theoretically minimal size. We design and realize one class of them using all-dielectric metasurfaces that combine arbitrarily controlled distinguished fast-axis singularities with customized retardance profiles. The resulting fields are then described by high-dimensional integer-valued topological tuples, providing theoretically unbounded information capacity at the nanoscale. As a proof-of-concept demonstration, selected tuple components are mapped to represent predefined alphabetic symbols, realizing controlled high-dimensional information representation within a single optical field. Our results establish Stokes defects as functional units for higher-dimensional topological encoding, expanding the role of defects from failure points to engineerable carriers of optical information.

physics.optics↗

Ising Models on Dense Regular Graphs

In this paper, we derive the limit of experiments for one parameter Ising models on dense regular graphs. In particular, we show that the limiting experiment is Gaussian in the low temperature regime, non Gaussian in the critical regime, and an infinite collection of Gaussians in the high temperature regime. We also derive the limiting distributions of the maximum likelihood and maximum pseudo-likelihood estimators, and study limiting power for tests of hypothesis against contiguous alternatives (whose scaling changes across the regimes). To the best of our knowledge, this is the first attempt at establishing the classical limits of experiments for Ising models (and more generally, Markov random fields).

math.ST↗

Signal Detection in Degree Corrected ERGMs

In this paper, we study sparse signal detection problems in Degree Corrected Exponential Random Graph Models (ERGMs). We study the performance of two tests based on the conditionally centered sum of degrees and conditionally centered maximum of degrees, for a wide class of such ERGMs. The performance of these tests match the performance of the corresponding uncentered tests in the $β$ model. Focusing on the degree corrected two star ERGM, we show that improved detection is possible at criticality using a test based on (unconditional) sum of degrees. In this setting we provide matching lower bounds in all parameter regimes, which is based on correlations estimates between degrees under the alternative, and of possible independent interest.

math.ST↗

Statistics of the two-star ERGM

In this paper, we explore the two-star Exponential Random Graph Model, which is a two parameter exponential family on the space of simple labeled graphs. We introduce auxiliary variables to express the two-star model as a mixture of the $β$ model on networks. Using this representation, we study asymptotic distribution of the number of edges, and the sampling variance of the degrees. In particular, the limiting distribution for the number of edges has similar phase transition behavior to that of the magnetization in the Curie-Weiss Ising model of Statistical Physics. Using this, we show existence of consistent estimates for both parameters in all parameter domains. Finally, we prove that the centered partial sum of degrees converges as a process to a Brownian bridge in all parameter domains, irrespective of the phase transition.

math.ST↗