Complex Systems Lab

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

Research Team

• Marian Gidea, PhD - Professor of Mathematics and Associate Dean for STEM Research, Yeshiva University
• Yuri Katz, PhD - Group Manager Data Science, Standard and Poor’s Global Market Intelligence  
• Arya Dutta - Doctoral Student in Mathematical Sciences, Yeshiva University 
• Ruslan Gokhman - Doctoral Student in Mathematical Sciences, Yeshiva University 
• Irit Tzemah - Doctoral Student in Mathematical Sciences, Yeshiva University
• Penghui Han - Doctoral Student in Mathematical Sciences, Yeshiva University
• Sivia H Naimer - Doctoral Student in Mathematical Sciences, Yeshiva University  
• Dachao Sun - Master's Student in Mathematical Sciences, Yeshiva University 

Recent Publications

Akingbade, S. W., Gidea, M., Manzi, M., & Nateghi, V. (2024). Why topological data analysis detects financial bubbles? Communications in Nonlinear Science and Numerical Simulation, 128, 107665.

Akingbade, S. W., Gidea, M., & M-Seara, T. (2023). Arnold diffusion in a model of dissipative system. SIAM Journal on Applied Dynamical Systems, 22(3), 1983-2023.

Aromi, L. L., Katz, Y. A., & Vives, J. (2021). Topological features of multivariate distributions: Dependency on the covariance matrix. Communications in Nonlinear Science and Numerical Simulation, 103, 105996.

Belbruno, E., Gidea, M., & Lam, W. T. (2023). Regularization of the Hill four-body problem with oblate bodies. Celestial Mechanics and Dynamical Astronomy, 135(1), 6.

Gidea, M., Goldsmith, D., Katz, Y., Roldan, P., & Shmalo, Y. (2020). Topological recognition of critical transitions in time series of cryptocurrencies. Physica A: Statistical mechanics and its applications, 548, 123843.

Gidea, M., & Katz, Y. (2018). Topological data analysis of financial time series: Landscapes of crashes. Physica A: Statistical Mechanics and its Applications, 491, 820-834.

Gluzberg, V. E., & Katz, Y. A. (2023). Topological data analysis of noise: Uniform unimodal distributions. Communications in Nonlinear Science and Numerical Simulation, 121, 107216.

Katz, Y. A., & Biem, A. (2022). Growing cumulative activity of major tropical cyclones: Detection, attribution, and projections. Communications in Nonlinear Science and Numerical Simulation, 108, 106202.

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