arXiv subjects

Qiyuan Shi

Publications and source records attributed to Qiyuan Shi.

7 recordsLinked to original sources

arXiv2026

Universality of percolation at dynamic pseudocritical point

Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point. Focusing on two-dimensional percolation, we show that the size distribution of the largest cluster asymptotically approaches to a Gumbel form in the subcritical phase, a Gaussian form in the supercritical phase, and transitions within the critical finite-size scaling window. Numerical results indicate that, at consistently defined pseudocritical points, this distribution exhibits a universal form across various lattices and percolation models (bond or site), within error bars, yet differs from the distribution at the critical point. The critical polynomial, universally zero for two-dimensional percolation at the critical point, becomes nonzero at pseudocritical points. Nevertheless, numerical evidence suggests that the critical polynomial, along with other dimensionless quantities such as wrapping probabilities and Binder cumulants, assumes fixed values at the pseudocritical point that are independent of the percolation type (bond or site) but vary with lattice structures. These findings imply that while strict universality breaks down at the pseudocritical point, certain extreme-value statistics and dimensionless quantities exhibit quasi-universality, revealing a subtle connection between scaling behaviors at critical and pseudocritical points.

cond-mat.stat-mech↗

arXiv2026

Equivalent-neighbor $k$-core percolation in two dimensions

We perform large-scale numerical simulations to investigate the critical behavior of $k$-core percolation in two dimensions with an extended interaction range $r$. By systematically varying both the core index $k$ and the interaction range $r$, we construct a comprehensive phase diagram in the $(k,r)$ plane. In contrast to $k$-core percolation in infinite dimensions, no hybrid transition is observed in two dimensions: the phase diagram contains only a continuous transition regime and a strictly first-order regime, separated by a tricritical or critical-end point $(k_s,r_s)$. For $k k_s$ and finite $r>r_s$, the transition is discontinuous, with no hybrid features or critical singularities. In this first-order regime, the pseudocritical point approaches the critical point as $1/\ln L$, where $L$ is the linear system size, distinct from the $L^{-d}$ scaling typical of conventional thermodynamic first-order transitions in $d$ dimensions. This logarithmic finite-size drift is consistent with a nucleation-driven mechanism, in which rare voids trigger the collapse of the finite-range $k$-core. These results demonstrate that geometric constraints can fundamentally alter the nature of $k$-core percolation found in finite dimensions.

cond-mat.stat-mech↗

arXiv2026

Radiomics-Guided Vision Transformers for Survival Analysis

Vision Transformers (ViTs) have shown strong empirical performance on high-dimensional medical imaging data, yet their behavior under survival objectives and the interpretability of their attention mechanisms remain poorly understood. Under shallow ViTs, we design controlled experiments showing that token-level attention dynamics can recover outcome-relevant regions and that attention-based thresholding enables effective token pruning, improving both interpretability and predictive performance. We also study pretrained deep ViTs for survival analysis and propose a radiomics-guided hybrid model that integrates pixel-based embeddings with interpretable radiomic features through a multimodal Cox framework and contrastive alignment. Applied to a COVID-19 chest X-ray cohort with a composite ICU admission or mortality endpoint, the proposed approach achieves competitive discrimination while providing clinically meaningful attention maps and feature-group importance.

physics.med-ph↗

arXiv2026

Kernel-Based Learning of Chest X-ray Images for Predicting ICU Escalation among COVID-19 Patients

Kernel methods have been extensively utilized in machine learning for classification and prediction tasks due to their ability to capture complex non-linear data patterns. However, single kernel approaches are inherently limited, as they rely on a single type of kernel function (e.g., Gaussian kernel), which may be insufficient to fully represent the heterogeneity or multifaceted nature of real-world data. Multiple kernel learning (MKL) addresses these limitations by constructing composite kernels from simpler ones and integrating information from heterogeneous sources. Despite these advances, traditional MKL methods are primarily designed for continuous outcomes. We extend MKL to accommodate the outcome variable belonging to the exponential family, representing a broader variety of data types, and refer to our proposed method as generalized linear models with integrated multiple additive regression with kernels (GLIMARK). Empirically, we demonstrate that GLIMARK can effectively recover or approximate the true data-generating mechanism. We have applied it to a COVID-19 chest X-ray dataset, predicting binary outcomes of ICU escalation and extracting clinically meaningful features, underscoring the practical utility of this approach in real-world scenarios.

cs.LG↗

arXiv2026

High-precision Dynamic Monte Carlo Study of Rigidity Percolation

Rigidity percolation provides an important basis for understanding the onset of mechanical stability in disordered materials. While most studies on the triangular lattice have focused on static properties at fixed bond~(site) occupation probabilities, the dynamics of the rigidity transition remain less explored. In this work, we formulate a dynamic pebble game algorithm that monitors how rigid clusters emerge and evolve as bonds are added sequentially to an empty lattice, with computational efficiency comparable to the standard static pebble game. We uncover a previously overlooked temporal self-similarity exhibited in multiple quantities, including the cluster size changes and merged cluster sizes during bond addition, as well as the number of simultaneously merging clusters. We identify large-scale cascade events in which a single bond addition triggers the merger of an extensive number of clusters that scales with system size with inverse correlation-length exponent. Using an event-based ensemble approach, we obtain high-precision estimates of the critical point $p_c = 0.660\,277\,8(10)$, the inverse correlation-length exponent $1/ν= 0.850(3)$, and the fractal dimension $d_f = 1.850(2)$, representing substantial improvements over existing values.

cond-mat.stat-mech↗

arXiv2025

Fractal depth-first search paths in statistical physics models

We study the fractal properties of depth-first search (DFS) paths in critical configurations of statistical physics models, including the two-dimensional $O(n)$ loop model for various $n$, and bond percolation in dimensions $d = 2$ to $6$. In the $O(n)$ loop model, across both critical and tricritical Potts regimes, the fractal dimension of the DFS path consistently follows $d_{\rm DFS} = 1 + g/8$, where $g$ is the coupling constant in Coulomb gas theory, related to $n$ via $n^2 = 2 + 2 \cos(πg/2)$ with $g \in [8/3, 16/3]$. For bond percolation, the DFS path exhibits nontrivial fractal scaling across all studied dimensions. Interestingly, when DFS is applied to the full lattice without any dilution or criticality, the path is still fractal in two dimensions, with a dimension close to $7/4$, but becomes space-filling in higher dimensions. Our results demonstrate that DFS offers a robust and broadly applicable geometric probe for exploring critical phenomena beyond traditional observables.

cond-mat.stat-mech↗

arXiv2022

baker: An R package for Nested Partially-Latent Class Models

This paper describes and illustrates the functionality of the baker R package. The package estimates a suite of nested partially-latent class models (NPLCM) for multivariate binary responses that are observed under a case-control design. The baker package allows researchers to flexibly estimate population-level class prevalences and posterior probabilities of class membership for individual cases. Estimation is accomplished by calling a cross-platform automatic Bayesian inference software JAGS through a wrapper R function that parses model specifications and data inputs. The baker package provides many useful features, including data ingestion, exploratory data analyses, model diagnostics, extensive plotting and visualization options, catalyzing communications between practitioners and domain scientists. Package features and workflows are illustrated using simulated and real data sets. Package URL: https://github.com/zhenkewu/baker

stat.ME↗