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Complex Systems Lab

Making the World Smarter, Safer and Healthier

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

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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.

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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.

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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 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  
  • Samuel Akingbade Doctoral Student in Mathematical Sciences, Yeshiva University 
  • Atreish Ramlakhan - Doctoral Student in Mathematical Sciences, Yeshiva University 
  • Semyon Lomasov Undergraduate Student, Yeshiva University 
  • Yedidya Moise  Undergraduate Student, 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 Simulation128, 107665.

Akingbade, S. W., Gidea, M., & M-Seara, T. (2023). Arnold diffusion in a model of dissipative systemSIAM Journal on Applied Dynamical Systems22(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 Simulation103, 105996.

Belbruno, E., Gidea, M., & Lam, W. T. (2023). Regularization of the Hill four-body problem with oblate bodiesCelestial Mechanics and Dynamical Astronomy135(1), 6.

Gidea, M., Goldsmith, D., Katz, Y., Roldan, P., & Shmalo, Y. (2020). Topological recognition of critical transitions in time series of cryptocurrenciesPhysica A: Statistical mechanics and its applications548, 123843.

Gidea, M., & Katz, Y. (2018). Topological data analysis of financial time series: Landscapes of crashesPhysica A: Statistical Mechanics and its Applications491, 820-834.

Gluzberg, V. E., & Katz, Y. A. (2023). Topological data analysis of noise: Uniform unimodal distributionsCommunications in Nonlinear Science and Numerical Simulation121, 107216.

Katz, Y. A., & Biem, A. (2022). Growing cumulative activity of major tropical cyclones: Detection, attribution, and projections. Communications in Nonlinear Science and Numerical Simulation108, 106202.

Lab News

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Mathematical Model Anticipates Bubbles, Crashes in Bitcoin Industry

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

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Math Ph.D. Candidate One of Only 30 Young Researchers Invited to Prestigious Forum

Math Ph.D. Candidate One of Only 30 Young Researchers Invited to Prestigious Forum

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Students Use AI to Forecast Climate Change's Local Impact for S&P Global

Students Use AI to Forecast Climate Change's Local Impact for S&P Global

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Mathematical Model Anticipates Bubbles, Crashes in Bitcoin Industry

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

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Math Ph.D. Candidate One of Only 30 Young Researchers Invited to Prestigious Forum

Math Ph.D. Candidate One of Only 30 Young Researchers Invited to Prestigious Forum

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Students Use AI to Forecast Climate Change's Local Impact for S&P Global

Students Use AI to Forecast Climate Change's Local Impact for S&P Global

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