My main research topics

I am a mathematician by training and my research interest concern the theory of stochastic processes. I am particularly interested in the theory of stochastic reaction networks, which are a family of continuous time Markov chains typically used as models in biochemistry. My research focuses on

  • the study of possible connections between dynamical features of the model and structural properties of the associate reaction graph;

  • the study of long-term dynamics of the model (absorptions, stationary distributions, etc.);

  • model approximations and complexity reduction;

  • general applications of stochastic reaction network theory.

Publications
Elena Sabbioni, Rebeka Szabó, Paola Siri, Daniele Cappelletti, Gábor Lente, Enrico Bibbona (2024). Final nanoparticle size distribution under unusual parameter regimes. THE JOURNAL OF CHEMICAL PHYSICS.
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D Cappelletti, Ga Rempala (2023). Individual Molecules Dynamics in Reaction Network Models. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS.
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Daniele Cappelletti, Badal Joshi (2022). Transition graph decomposition for complex balanced reaction networks with non-mass-action kinetics. MATHEMATICAL BIOSCIENCES AND ENGINEERING.
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Sarah Azouvi, Daniele Cappelletti (2021). Private Attacks in Longest Chain Proof-of-stake Protocols with Single Secret Leader Elections. AFT ‘21: Proceedings of the 3rd ACM Conference on Advances in Financial Technologies.
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D. Cappelletti, A. Pal Majumder, C. Wiuf (2021). The dynamics of stochastic mono-molecular reaction systems in stochastic environments. STOCHASTIC PROCESSES AND THEIR APPLICATIONS.
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D. F. Anderson, D. Cappelletti, J. Kim, T. D. Nguyen (2020). Tier structure of strongly endotactic reaction networks. STOCHASTIC PROCESSES AND THEIR APPLICATIONS.
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D. Cappelletti, A. Gupta, M. Khammash (2020). A hidden integral structure endows absolute concentration robust systems with resilience to dynamical concentration disturbances: A hidden integral structure endows absolute concentration robust systems with resilience to dynamical concentration disturbances. JOURNAL OF THE ROYAL SOCIETY INTERFACE.
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D. F. Anderson, D. Cappelletti, J. Kim (2020). Stochastically modeled weakly reversible reaction networks with a single linkage class. JOURNAL OF APPLIED PROBABILITY.
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D. Cappelletti, E. Feliu, C. Wiuf (2020). Addition of flow reactions preserving multistationarity and bistability. MATHEMATICAL BIOSCIENCES.
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D. Cappelletti, A. Ortiz-Munoz, D. F. Anderson, E. Winfree (2020). Stochastic chemical reaction networks for robustly approximating arbitrary probability distributions. THEORETICAL COMPUTER SCIENCE.
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D Cappelletti, A Gupta, M Khammash (2019). A linear constrained integral feedback for a class of reaction systems with absolute concentration robustness. 2019 IEEE 58th Conference on Decision and Control (CDC).
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D. F. Anderson, D. Cappelletti (2019). Discrepancies between extinction events and boundary equilibria in reaction networks. JOURNAL OF MATHEMATICAL BIOLOGY.
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D.F. Anderson, D. Cappelletti, M. Koyama, T.G. Kurtz (2018). Non-explosivity of Stochastically Modeled Reaction Networks that are Complex Balanced. Bulletin of Mathematical Biology.
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Elisenda Feliu, Daniele Cappelletti, Carsten Wiuf (2018). Node balanced steady states: Unifying and generalizing complex and detailed balanced steady states. Mathematical Biosciences.
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D. Cappelletti, C. Wiuf (2017). Uniform approximation of solutions by elimination of intermediate species in deterministic reaction networks. SIAM Journal on Applied Dynamical Systems.
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D.F. Anderson, D. Cappelletti, T.G. Kurtz (2017). Finite time distributions of stochastically modeled chemical systems with absolute concentration robustness. SIAM Journal on Applied Dynamical Systems.
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D. Cappelletti, C. Wiuf (2016). Elimination of intermediate species in multiscale stochastic reaction networks. Annals of Applied Probability.
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D. Cappelletti, C. Wiuf (2016). Product-form poisson-like distributions and complex balanced reaction systems. SIAM Journal on Applied Mathematics.
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Giovanni Brancaccio, Renzo Lombardi, Teseo Stefanini, Pia Torri, David Russo, Nader Gorji, Daniele Cappelletti, Giovanni Maria Celoria (2012). Comparison of Embolic Load in Femoropopliteal Interventions: Percutaneous Transluminal Angioplasty Versus Stenting. Vascular and Endovascular Surgery.
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