arXiv subjects

Zengru Di

Publications and source records attributed to Zengru Di.

At least 19 recordsLinked to original sources

arXiv2026

Response Morphologies of a Canonical Fluctuation Diagnostic Across Ehrenfest Phase Transitions

Microcanonical inflection-point analysis identifies MIPA-type higher-order transition structures from derivatives of the microcanonical entropy. Until recently, however, there was no canonical formulation for probing the corresponding fluctuation-level behavior directly from measurable energy fluctuations without reconstructing the density of states. Previous work addressed this limitation by introducing a canonical fluctuation diagnostic that quantifies energy-fluctuation asymmetry. Here, we investigate how this diagnostic behaves across representative first-, second-, and third-order phase transitions in the Ehrenfest classification. We consider the eight-state Potts model, the two-dimensional Ising model, and ideal three-dimensional Bose--Einstein condensation. The Potts and Ising systems exhibit a robust paired-extremum structure of the diagnostic near their respective transition regions, whereas ideal Bose--Einstein condensation exhibits a discontinuous response at the condensation temperature in the thermodynamic limit. These results show that a single fluctuation-based observable can display qualitatively distinct response morphologies across thermodynamic regimes, reflecting sensitivity to the nature of the underlying phase transition rather than serving as a direct classifier of Ehrenfest order.

cond-mat.stat-mech↗

arXiv2026

Text Distance from Nested and Hierarchical Repetitions: A Compression-Based Perspective

We present a new method for structural sequence analysis grounded in Algorithmic Information Theory (AIT). At its core is the Ladderpath approach, which extracts nested and hierarchical relationships among repeated substructures in linguistic sequences -- an instantiation of AIT's principle of describing data through minimal generative programs. These structures are then used to define three distance measures: a normalized compression distance (NCD), and two alternative distances derived directly from the Ladderpath representation. Integrated with a $k$-nearest neighbor classifier, these distances achieve strong and consistent performance across in-distribution, out-of-distribution (OOD), and few-shot text classification tasks. In particular, all three methods outperform both gzip-based NCD and BERT under OOD and low-resource settings. These results demonstrate that the structured representations captured by Ladderpath preserve intrinsic properties of sequences and provide a lightweight, interpretable, and training-free alternative for text modeling. This work highlights the potential of AIT-based approaches for structural and domain-agnostic sequence understanding.

cs.CL↗

arXiv2026

Threshold-Controlled Geometric Reorganization in 2D Bootstrap Percolation

Two-dimensional bootstrap percolation is usually characterized by bulk observables, but whether increasing the activation threshold qualitatively reorganizes the geometry of the absorbing state has remained unclear. Here we show that the response undergoes a threshold-controlled geometric crossover. At low thresholds, the extrema of bulk and boundary-sensitive observables remain confined to a single collective low-$p$ window. At high thresholds, they split into distinct branches, revealing multiple geometric response scales. Over the accessible system sizes, the dominant finite-size signatures shift from fluctuations of the final active density to non-singleton boundary observables, while the fluctuation peak itself decreases. Time-resolved mechanism traces show that this crossover is accompanied by a progression from extended collective propagation to frontier exhaustion and, at the highest threshold, to quasi-one-step stabilization. Our results identify boundary organization as the dominant structural signature of high-threshold bootstrap percolation and show that conventional bulk observables alone do not capture the full reorganization of the absorbing state.

cond-mat.stat-mech↗

arXiv2026

Spectral Signatures of Third-Order Pseudo-Transitions in Finite Systems: An Eigen-Microstate Approach

Third-order pseudo-transitions in finite systems reflect reorganization beyond conventional criticality, yet their identification usually relies on microcanonical entropy, which is often inaccessible in practice. Here we introduce a spectral generalized response within the eigen-microstate framework. From the distribution of normalized spectral weights, we construct the third-order ratio $R_3=K_3/(K_2)^3$, which probes asymmetric redistribution among fluctuation modes beyond leading-mode condensation. Across Ising and Potts models on regular lattices and random regular networks, extrema of $R_3$ consistently track higher-order anomalies. Combined with spectral projection, the method further distinguishes dependent and independent branches: the former remain tied to the dominant ordering channel, whereas the latter arise from redistribution within the subleading fluctuation subspace. The effective spectral dimension $R_{\mathrm{eff}}$ provides the participation background in which these anomalies develop. These results establish a geometric characterization of third-order pseudo-transitions as reorganizations of statistical weight in configuration space and provide an order-parameter-free route to finite-size structural criticality.

cond-mat.stat-mech↗

arXiv2026

Third-order transitions in Ising and Potts models on Watts--Strogatz small-world networks

We study third-order transitions in the two-dimensional Ising and Potts model on regular lattices and Watts--Strogatz small-world networks. Cluster observables are used to track post-critical boundary reorganization and pre-critical cluster breakup. For the Ising model, the critical temperature $T_c$ is calibrated independently from Binder-cumulant crossings and susceptibility peaks, whereas for the Potts model on small-world networks it is identified operationally from the dominant critical peak of $\mathrm d\langle P\rangle/\mathrm dT$. The independent and dependent third-order transitions are identified from the isolated-spin peak and the post-critical structural extremum, respectively. For both lattice and small-world topologies, we find the robust ordering $T_{\mathrm{ind}}<T_c<T_{\mathrm{dep}}$. Increasing the rewiring probability shifts all three characteristic temperatures upward and enhances the visibility of the post-critical transition. The effect is especially clear in the Potts model, where perimeter-based observables are more sensitive to multistate boundary fluctuations. The systematic persistence of the characteristic temperature hierarchy across topologies and finite sizes argues against interpreting these features as incidental finite-size irregularities. Instead, our results support their interpretation as genuine third-order transitions whose structural detectability can be amplified by network topology.

cond-mat.stat-mech↗

arXiv2026

Canonical Criterion for Third-Order Transitions

Microcanonical inflection-point analysis (MIPA) identifies third-order transitions from derivatives of the microcanonical entropy, but whether such transitions admit a direct canonical formulation has remained unclear. Here we establish a fluctuation-based canonical framework for third-order transitions through a cumulant-ratio criterion whose signed extrema define their canonical counterparts and, in the single-saddle regime, are asymptotically linked to microcanonical classification. Because the criterion depends only on energy cumulants, it avoids explicit density-of-states reconstruction and remains operational in nonequilibrium steady states. Physically, it reveals dependent and independent third-order transitions as fluctuation reorganizations around low-order transitions, namely disordered-side precursors and ordered-side restructuring. Benchmarks on Onsager's two-dimensional Ising solution, finite size Potts models, and a driven nonreciprocal Ising model show that the framework is theoretically grounded and broadly applicable.

cond-mat.stat-mech↗

arXiv2026

The mechanistic origin of branching-driven nucleation in abrupt phase transitions

Phase transitions are the macroscopic manifestation of microscopic processes that drive a system towards a new state. The detailed evolution of these processes, particularly in abrupt phase transitions, are currently not fully understood. Here, we introduce a theoretical framework based on internal node dependencies within a single-layer lattice. Crucially, we demonstrate that the fundamental mechanism underlying abrupt transitions is nucleation propagation preceded by a slow cascading process which scales with the range of dependencies. Our findings show that the synergy between these two distinct stages is essential for the occurrence of an abrupt transition. The first stage of a slow cascading mechanism was recently observed experimentally in superconducting layered materials, where heat acts as the dependency links, for the limit of infinite dependency range. Our model thus generalizes the framework to include finite dependency ranges, revealing previously unobserved mechanisms that could be experimentally verified through controlling the range of thermal diffusion in the material. As a universal mechanism, our model provides a robust method to test nucleation-controlled phase transitions in multiple systems, providing a path to discover and understand microscopic mechanisms in phase transitions.

physics.soc-ph↗

arXiv2025

Network localization governs social contagion dynamics with macro-level reinforcement

The spread of ideas, behaviors, and technologies generally depends on feedback mechanisms operating across multiple scales. Previous studies have extensively examined pairwise transmission and local reinforcement. However, the role of macro-level social influence -- where widespread adoption enhances further adoption -- remains understudied. Here, we focus on a contagion process that incorporates both pairwise interactions and macro-level reinforcement. We show that the contagion undergoes a shift from continuous to mixed-order transition as macro-level influence exceeds a reinforcement threshold. Simulations on various real-world networks indicate that network localization governs the contagion outcomes by determining the critical point and the reinforcement threshold. Building on this insight, we develop a structural metric linking network localization to contagion dynamics, revealing a key trade-off: networks that facilitate weak contagion tend to experience slower diffusion and lower adoption rates, while networks that suppress weak contagions enable faster and more widespread adoption. These findings challenge the conventional belief that stronger local connectivity uniformly promotes contagion.

physics.soc-ph↗

arXiv2025

Analyzing Cascade Sizes of Stopped Projects in SourceForge: Is SOC Theory Applicable to OSSOCs?

Based on three rounds of data extraction, we first construct complex network models to identify the cascade sizes of stopped projects and their distributions in SourceForge (March 2000 to February 2013). We then analyze and discover characteristics of these cascade sizes and their distributions: most cascade sizes are 1; two extreme sizes coexist; and the cascade sizes in each Period of SourceForge's peak phase exhibit a power-law distribution while lacking scale-free properties. Finally, we discuss the limitations of this study and their implications for Self-Organized Criticality theory.

physics.soc-ph↗

arXiv2024

Iterative structural coarse-graining for contagion dynamics in complex networks

Contagion dynamics in complex networks drive critical phenomena such as epidemic spread and information diffusion,but their analysis remains computationally prohibitive in large-scale, high-complexity systems. Here, we introduce the Iterative Structural Coarse-Graining (ISCG) framework, a scalable methodology that reduces network complexity while preserving key contagion dynamics with high fidelity. Importantly, we derive theoretical conditions ensuring the precise preservation of both macroscopic outbreak sizes and microscopic node-level infection probabilities during network reduction. Under these conditions, extensive experiments on diverse empirical networks demonstrate that ISCG achieves significant complexity reduction without sacrificing prediction accuracy. Beyond simplification, ISCG reveals multiscale structural patterns that govern contagion processes, enabling practical solutions to longstanding challenges in contagion dynamics. Specifically, ISCG outperforms traditional adaptive centrality-based approaches in identifying influential spreaders, immunizing critical edges, and optimizing sentinel placement for early outbreak detection, offering superior accuracy and computational efficiency. By bridging computational efficiency with dynamical fidelity, ISCG provides a transformative framework for analyzing large-scale contagion processes, with broad applications for epidemiology, information dissemination, and network resilience.

physics.soc-ph↗

arXiv2024

Pseudo Transitions in the Finite-Size Blume-Capel Model

This article investigates the pseudo transitions of the Blume-Capel model on two-dimensional finite-size lattices. By employing the Wang-Landau sampling method and microcanonical inflection point analysis, we identified the positions of phase transitions as well as higher-order phase transitions. Through Metropolis sampling and canonical ensemble analysis, we determined the geometric characteristics of the system at these transition points. When the crystal field parameter $D$ exceeds 1.965, crossing the tricritical point, no third-order dependent phase transition is observed. However, a fourth-order independent transition was identified in the high-temperature region, and through Metropolis sampling analysis, a phase transition from the ordered paramagnetic phase to the disordered paramagnetic phase was confirmed, enhancing the phase diagram. Furthermore, the positions of the third-order phase transition obtained from both microcanonical and canonical analyses are consistent and mutually corroborative. We speculate that third-order dependent transitions vanish in the presence of strong first-order phase transitions.

cond-mat.stat-mech↗

arXiv2024

Geometric properties of the additional third-order transitions in the two-dimensional Potts model

Within the canonical ensemble framework, this paper investigates the presence of higher-order transition signals in the $q$-state Potts model (for $q \geq 3$), using two geometric order parameters: isolated spins number and the average perimeter of clusters. Our results confirm that higher-order transitions exist in the Potts model, where the number of isolated spins reliably indicates third-order independent transitions. This signal persists regardless of the system's phase transition order, even at higher values of $q$. In contrast, the average perimeter of clusters, used as an order parameter for detecting third-order dependent transitions, shows that for $q = 6$ and $q = 8$, the signal for third-order dependent transitions disappears, indicating its absence in systems undergoing first-order transitions. These findings are consistent with results from microcanonical inflection-point analysis, further validating the robustness of this approach.

cond-mat.stat-mech↗

arXiv2024

An Artificial Neural Network for Image Classification Inspired by Aversive Olfactory Learning Circuits in Caenorhabditis Elegans

This study introduces an artificial neural network (ANN) for image classification task, inspired by the aversive olfactory learning circuits of the nematode Caenorhabditis elegans (C. elegans). Despite the remarkable performance of ANNs in a variety of tasks, they face challenges such as excessive parameterization, high training costs and limited generalization capabilities. C. elegans, with its simple nervous system comprising only 302 neurons, serves as a paradigm in neurobiological research and is capable of complex behaviors including learning. This research identifies key neural circuits associated with aversive olfactory learning in C. elegans through behavioral experiments and high-throughput gene sequencing, translating them into an image classification ANN architecture. Additionally, two other image classification ANNs with distinct architectures were constructed for comparative performance analysis to highlight the advantages of bio-inspired design. The results indicate that the ANN inspired by the aversive olfactory learning circuits of C. elegans achieves higher accuracy, better consistency and faster convergence rates in image classification task, especially when tackling more complex classification challenges. This study not only showcases the potential of bio-inspired design in enhancing ANN capabilities but also provides a novel perspective and methodology for future ANN design.

cs.NE↗

arXiv2024

Uncovering multi-order Popularity and Similarity Mechanisms in Link Prediction by graphlet predictors

Link prediction has become a critical problem in network science and has thus attracted increasing research interest. Popularity and similarity are two primary mechanisms in the formation of real networks. However, the roles of popularity and similarity mechanisms in link prediction across various domain networks remain poorly understood. Accordingly, this study used orbit degrees of graphlets to construct multi-order popularity- and similarity-based network link predictors, demonstrating that traditional popularity- and similarity-based indices can be efficiently represented in terms of orbit degrees. Moreover, we designed a supervised learning model that fuses multiple orbit-degree-based features and validated its link prediction performance. We also evaluated the mean absolute Shapley additive explanations of each feature within this model across 550 real-world networks from six domains. We observed that the homophily mechanism, which is a similarity-based feature, dominated social networks, with its win rate being 91\%. Moreover, a different similarity-based feature was prominent in economic, technological, and information networks. Finally, no single feature dominated the biological and transportation networks. The proposed approach improves the accuracy and interpretability of link prediction, thus facilitating the analysis of complex networks.

cs.SI↗

arXiv2023

Nucleation phenomena and extreme vulnerability of spatial k-core systems

K-core percolation is a fundamental dynamical process in complex networks with applications that span numerous real-world systems. Earlier studies focus primarily on random networks without spatial constraints and reveal intriguing mixed-order transitions. However, real-world systems, ranging from transportation and communication networks to complex brain networks, are not random but are spatially embedded. Here, we study k-core percolation on two-dimensional spatially embedded networks and show that, in contrast to regular percolation, the length of connections can control the transition type, leading to four different types of phase transitions associated with novel phenomena and a rich phase diagram. A key finding is the existence of a metastable phase in which microscopic localized damage, independent of system size, can cause a macroscopic phase transition, a result which cannot be achieved in traditional percolation. In this case, local failures can spontaneously propagate the damage radially until the system entirely collapses, a phenomenon analogous to the nucleation process. These findings suggest novel features and extreme vulnerabilities of spatially embedded k-core network systems, and highlight the necessity to take into account the characteristic length of links when designing robust spatial networks. Furthermore, our insight about the microscopic processes and their origin during the mixed order and first order abrupt transitions in k-core networks could shed light on the mechanisms of many systems where such transitions occur.

physics.soc-ph↗

arXiv2023

Learning noise-induced transitions by multi-scaling reservoir computing

Noise is usually regarded as adversarial to extract the effective dynamics from time series, such that the conventional data-driven approaches usually aim at learning the dynamics by mitigating the noisy effect. However, noise can have a functional role of driving transitions between stable states underlying many natural and engineered stochastic dynamics. To capture such stochastic transitions from data, we find that leveraging a machine learning model, reservoir computing as a type of recurrent neural network, can learn noise-induced transitions. We develop a concise training protocol for tuning hyperparameters, with a focus on a pivotal hyperparameter controlling the time scale of the reservoir dynamics. The trained model generates accurate statistics of transition time and the number of transitions. The approach is applicable to a wide class of systems, including a bistable system under a double-well potential, with either white noise or colored noise. It is also aware of the asymmetry of the double-well potential, the rotational dynamics caused by non-detailed balance, and transitions in multi-stable systems. For the experimental data of protein folding, it learns the transition time between folded states, providing a possibility of predicting transition statistics from a small dataset. The results demonstrate the capability of machine-learning methods in capturing noise-induced phenomena.

nlin.AO↗

arXiv2023

The precursor of the critical transitions in majority vote model with the noise feedback from the vote layer

In this paper, we investigate phase transitions in the Majority-Vote model coupled with noise layers of different structures. We examine the Square lattice and Random-regular networks, as well as their combinations, for both vote layers and noise layers. Our findings reveal the presence of independent third-order transitions in all cases and dependent third-order transitions when critical transitions occur. This suggests that dependent third-order transitions may serve as precursors to critical transitions in non-equilibrium systems. Furthermore, we observe that when the structure of vote layers is local, the coupling between the vote layer and the noise layer leads to the absence of critical phenomena.

physics.soc-ph↗

arXiv2023

Disruptive papers in science are losing impact

The impact and originality are two critical dimensions for evaluating scientific publications, measured by citation and disruption metrics respectively. Despite the extensive effort made to understand the statistical properties and evolution of each of these metrics, the relations between the two remain unclear. In this paper, we study the evolution during last 70 years of the correlation between scientific papers' citation and disruption, finding surprisingly a decreasing trend from positive to negative correlations over the years. Consequently, during the years, there are fewer and fewer disruptive works among the highly cited papers. These results suggest that highly disruptive studies nowadays attract less attention from the scientific community. The analysis on papers' references supports this trend, showing that papers citing older references, less popular references and diverse references become to have less citations. Possible explanations for the less attention phenomenon could be due to the increasing information overload in science, and citations become more and more prominent for impact. This is supported by the evidence that research fields with more papers have a more negative correlation between citation and disruption. Finally, we show the generality of our findings by analyzing and comparing six disciplines.

cs.DL↗