Jun 2026· arXiv.org· Vol abs/2606.30069· 0 citations· 14 references
Computer Science
Abstract
Complex contagion models, in which adoption requires reinforcement from multiple neighbors, have been extensively studied in the monotone (no-recovery) setting, but the phase diagram of threshold models with SIS-like recovery on networks remains unmapped. We study a stochastic Watts-threshold SIS model on Erdos-Renyi and Barabasi-Albert networks and reconstruct its extinction-persistence phase boundary in the joint parameter space of transmission rate $\beta$, adoption threshold $\theta$, and infectious duration $d$. Using adaptive Delaunay-based sampling and weighted logistic regression on over 180,000 Monte Carlo trials, we find that: (i) the boundary is well described by a six-parameter interaction model whose structure is invariant across both topologies; (ii) the transition is sharp, with the 10-90\% extinction-probability band spanning only $\Delta\theta \approx 0.005$-$0.008$; and (iii) the adoption threshold is the dominant parameter governing epidemic feasibility, with transmission rate and infectious duration playing secondary and asymmetric roles. The characterization provides a quantitative reference for the complex-contagion analogue of the classical SIS epidemic threshold.
Extreme epidemic risk is controlled by the right tail of the outbreak-size distribution, but this distribution is generally unknown for non-Markovian spreading on networks. Here we determine this distribution by mapping non-Markovian SIR dynamics to an effective Markovian description. We show that arbitrary infection and recovery time statistics can be incorporated through a single edge transmissibility, yielding an effective Markovian process that reproduces the full outbreak-size statistics. For weakly heterogeneous networks, the reduction yields a universal well-mixed semiclassical theory governed by the bond-percolation reproductive number. Outbreak statistics across diverse waiting-time distributions and topologies collapse onto one predictive curve. For highly heterogeneous and empirical networks, the corresponding effective Markovian dynamics on the network captures the complete distribution. Our results provide a direct route from measured waiting-time distributions to quantitative predictions of network-level extreme-outbreak risk.
The framework supports data-informed platform governance by linking propagation thresholds, algorithmic down-ranking, reply thread moderation, intervention cost, and robustness bounds within a common threshold control language for practical settings.
The application of Monte Carlo simulation to stochastic resource-constrained project scheduling (SRCPSP) relies fundamentally on what we term the Topological Continuity Assumption [1]–the implicit hypothesis that the underlying directed acyclic graph (DAG) structure remains invariant across simulation iterations. We demonstrate that resource-leveling heuristics systematically violate this assumption. We introduce the Soft-Edge Volatility Index (SEVI), a metric quantifying the probability of precedence relation reversal during simulation. Empirical analysis across 10,000 Monte Carlo iterations reveals density-dependent bifurcation: networks exhibit SEVI values approaching unity at sufficient scale, producing multimodal duration distributions that compromise the reliability of standard percentile forecasts. This so-called "Ghost P90" – an 82-day discrepancy between baseline and simulated percentiles at N = 3000 – emerges not from input variance but from topological discontinuity. We demonstrate that applying continuous statistical metrics to discretely bifurcating state-spaces introduces significant methodological limitations in risk quantification, particularly in highly dynamic networks, with implications extending to enterprise-level schedule forecasting under resource constraints.
Venkata Mukesh Chadaram· International Conference on...· 0 citations
The simulation of rare macroscopic events in stochastic network dynamics, such as widespread epidemic outbreaks, cascading failures in communication networks, or the escape from metastable states in many-body systems, is severely hindered by methodological challenges like catastrophic rejection rates, weight degeneracy, genealogical correlations, and critical slowing down inherent to standard forward-time algorithms, splitting methods, and transition-path sampling. Conditional-path Monte Carlo (CPMC) overcomes these limitations by employing non-local Swendsen-Wang-like cluster updates that operate directly on full-system trajectories. Serving as the technical companion to [Sun, Moody, and Barthel, arXiv:2608.16171], this paper provides the rigorous mathematical foundations and algorithmic details underlying the CPMC framework. We formally define the joint path-graph probability weights and derive the transition and uniformization sum rules that guarantee detailed balance. Applying the framework to susceptible-infectious-susceptible (SIS) models, we systematically construct and optimize single-node and edge graph vertex sets specifically designed to prevent lock avalanches and maintain the structural mobility of the epidemic trunk. Furthermore, we detail a dynamic programming scheme to exactly implement complex boundary conditions - including patient-zero and macroscopic outbreak-size constraints - enabling the rejection-free generation of valid trajectories. Finally, we assess the computational complexity of the algorithm, describe parallelization strategies, and validate CPMC against exact solutions for dynamics on small networks.
Thomas Barthel, Jiazheng Sun, Jhao-Hong Peng· 1 citation
This work shows that a dual-threshold bootstrap percolation model on random hypergraphs separates a connected active backbone from large-scale endogenous activation, providing a basis for predicting cascade risk and designing targeted node- and group-level interventions in complex systems.
This work forms a correction-aware network model that tracks susceptible, exposed, infectious, and corrected agents and derive its early-invasion condition for heterogeneous communication networks, and couple this propagation model to an analytic majority-vote benchmark in which a clean-task reliability target imposes a minimum connectivity requirement.