Scalable Modeling of Memory and Diversity in Stochastic Networks
Publication Title: Unifying non-Markovian dynamics and agent heterogeneity in scalable stochastic networks
Summary
- Question
- This study introduces MOSAIC (Modeling of Stochastic Agents with Individual Complexity), a computational framework designed to simulate stochastic processes while incorporating agent-specific heterogeneity and memory effects. The researchers aimed to unify Markovian and non-Markovian dynamics within a scalable system that retains computational efficiency comparable to traditional methods.
- Why it Matters
- Understanding stochastic processes is critical across disciplines, from biology to epidemiology and finance. Traditional methods often overlook key real-world complexities, such as individual variability and temporal memory. MOSAIC bridges this gap, enabling researchers to model systems more accurately and efficiently, with applications ranging from immune responses to social network dynamics. Its ability to simulate diverse systems at scale could improve insights into phenomena like disease spread, transcriptional regulation, and behavioral patterns.
- Methods
- The researchers developed MOSAIC by extending the Gillespie algorithm, a widely used stochastic simulation method. MOSAIC introduces agent-specific dynamics and memory effects, allowing for non-Markovian waiting times and heterogeneous interaction rates. The framework uses rejection sampling to maintain efficiency, even for systems with millions of interacting agents. Applications were tested in immune cell competition, RNA transcription with feedback, and social network simulations.
- Key Findings
- MOSAIC successfully captured features that traditional methods often miss or model inefficiently. For example, it accurately simulated clonal B-cell competition, demonstrating realistic dominance patterns among high-affinity clones. It also modeled RNA transcription with state-dependent delays, reproducing oscillatory dynamics in gene expression. In social networks, MOSAIC-TN extended the framework to capture bursty human activity and history-dependent interactions, aligning closely with empirical data from scientific conferences.
- Implications
- The findings suggest MOSAIC can advance stochastic modeling by accurately representing systems with complex heterogeneity and memory effects. Its scalability makes it a practical tool for studying large-scale biological, social, and physical systems. Researchers and practitioners can use MOSAIC to gain deeper insights into processes like immune system dynamics, gene regulation, and social behaviors, potentially informing public health strategies and technological innovation.
- Next Steps
Future work will extend MOSAIC to hybrid deterministic–stochastic systems and sparse network topologies. Additional directions include applications in personalized medicine, adaptive synthetic biology, and epidemic modeling. Optimizing the framework for larger distributed simulations could further enhance its usability across diverse fields.
- Funding Information
- This research was supported by the COSMIC European Training Network funded by the European Union’s Horizon 2020 research and innovation program under grant agreement No 765158, and the Swiss National Science Foundation (Sinergia grant CRSII5 193832). Yale University also provided funding and support for this research.
Full Citation
Pélissier A, Phan M, Le Bail D, Beerenwinkel N, Rodríguez Martínez M. Unifying non-Markovian dynamics and agent heterogeneity in scalable stochastic networks. Nature Communications 2026, 17: 3345. PMID: 41771859, PMCID: PMC13066373, DOI: 10.1038/s41467-026-69817-y.
This AI-assisted summary has been reviewed and approved by at least one of the study's authors to ensure it accurately reflects the research.
Authors
Aurélien Pélissier
First AuthorMaría Rodríguez Martínez, PhD, MSc
Last AuthorAssociate Professor of Biomedical Informatics and Data Science