Complex Systems Lab Making the World Smarter, Safer and Healthier Current Projects Research Team Publications Lab News Artificial Intelligence Biotechnology Computer Science Cybersecurity Data Analytics and Visualization Digital Marketing and Media Mathematics Occupational Therapy Physician Assistant Physics Speech-Language Pathology Welcome Many real-life systems encountered in the sciences (physics, biology, climate, social sciences, economics and finance) are complex systems, in which a large number of components are subject to intricate interactions that change over time. The interactions are frequently driven by concurrent deterministic and stochastic processes. Sometimes, the systems can be modeled starting from fundamental principles that govern them. Other times, information about the systems comes from empirical observations in the form of large data sets. One challenging problem is to understand the behavior in time of such systems and forecast their future evolution. Current projects cover several areas, including: Dynamical systems and applications to celestial mechanics and astrodynamics; Topological data analysis; Financial bubbles detection; Credit risk. Researcher: Marian Gidea, PhD Professor and Associate Dean for STEM Education and Research Director, Graduate Programs in Mathematical Sciences marian.gidea@yu.edu Current Projects Stability and Instability in Hamiltonian Systems Hamiltonian systems represent mathematical models of mechanical systems that conserve total energy. In Hamiltonian dynamics, stability and instability often coexist. For some applications one is interested to ensure the stability of the system, while in others one is interested to exploit the instability. We are also studying the effect of small dissipation on Hamiltonian systems. Applications range from celestial mechanics and space mission design to optimizing the performance of piezo-electric energy harvesting devices. Topological Data Analysis (TDA) Topological Data Analysis (TDA) is a new method to analyze complex, multi-dimensional data via topological tools. TDA aims to identifies patterns and features in data not apparent through traditional statistical methods. While statistical methods rely on describing data via distribution functions, TDA is describing data in terms of the `shape’ of a point cloud. Changes of shape reflect subtle shifts in the patterns of the underlying data. We are interested in developing applications of TDA to biomedical sciences, climate, networks, and engineering. Financial Bubbles Detection We are interested in detection of market crashes and financial bubbles. In particular, we are interested in identifying early warning signals for such extreme events, which have practical applications, such as minimizing the losses from a bubble crash, or maximizing the profit from a rapid rebound. In some earlier works, we developed a TDA-based methodology for the detection of financial bubbles. Research TeamMarian Gidea, PhD - Professor of Mathematics and Associate Dean for STEM Research, Yuri Katz, PhD - Group Manager Data Science, Standard and Poor’s Global Market Intelligence Arya Dutta - Doctoral Student in Mathematical Sciences, Ruslan Gokhman - Doctoral Student in Mathematical Sciences, Irit Tzemah - Doctoral Student in Mathematical Sciences, Penghui Han - Doctoral Student in Mathematical Sciences, Sivia H Naimer - Doctoral Student in Mathematical Sciences, Dachao Sun - Master's Student in Mathematical Sciences, Recent Publications Akingbade, S. W., Gidea, M., Manzi, M., & Nateghi, V. (2024). Communications in Nonlinear Science and Numerical Simulation, 128, 107665. Akingbade, S. W., Gidea, M., & M-Seara, T. (2023). . SIAM Journal on Applied Dynamical Systems, 22(3), 1983-2023. Aromi, L. L., Katz, Y. A., & Vives, J. (2021). Communications in Nonlinear Science and Numerical Simulation, 103, 105996. Belbruno, E., Gidea, M., & Lam, W. T. (2023). . Celestial Mechanics and Dynamical Astronomy, 135(1), 6. Gidea, M., Goldsmith, D., Katz, Y., Roldan, P., & Shmalo, Y. (2020). . Physica A: Statistical mechanics and its applications, 548, 123843. Gidea, M., & Katz, Y. (2018). . Physica A: Statistical Mechanics and its Applications, 491, 820-834. Gluzberg, V. E., & Katz, Y. A. (2023). . Communications in Nonlinear Science and Numerical Simulation, 121, 107216. Katz, Y. A., & Biem, A. (2022). Communications in Nonlinear Science and Numerical Simulation, 108, 106202. Lab News Mathematical Model Anticipates Bubbles, Crashes in Bitcoin Industry Read the full story Mathematical Model Anticipates Bubbles, Crashes in Bitcoin Industry Advancing Understanding of Dynamical Systems for Sustainable Energy and Space Science Advancing Understanding of Dynamical Systems for Sustainable Energy and Space Science Math Ph.D. Candidate One of Only 30 Young Researchers Invited to Prestigious Forum Read the full story Math Ph.D. Candidate One of Only 30 Young Researchers Invited to Prestigious Forum Students Use AI to Forecast Climate Change's Local Impact for S&P Global Read the full story Students Use AI to Forecast Climate Change's Local Impact for S&P Global Mathematical Model Anticipates Bubbles, Crashes in Bitcoin Industry Read the full story Mathematical Model Anticipates Bubbles, Crashes in Bitcoin Industry Advancing Understanding of Dynamical Systems for Sustainable Energy and Space Science Advancing Understanding of Dynamical Systems for Sustainable Energy and Space Science Math Ph.D. Candidate One of Only 30 Young Researchers Invited to Prestigious Forum Read the full story Math Ph.D. Candidate One of Only 30 Young Researchers Invited to Prestigious Forum Students Use AI to Forecast Climate Change's Local Impact for S&P Global Read the full story Students Use AI to Forecast Climate Change's Local Impact for S&P Global
