Periodic Reporting for period 4 - NoMaMemo (Non-Markovian Memory-Based Modelling of Near- and Far-From-Equilibrium Dynamical Systems)
Okres sprawozdawczy: 2024-06-01 do 2025-08-31
Our modern world is awash with data, and among its many forms, time series data is one of the most pervasive. Experiments, simulations, meteorological records, and economic observations all generate vast amounts of time series data. Yet extracting useful information from these data is daunting. One may aim to identify governing equations or instead classify entire systems by comparing data sets. Concrete examples in chemistry and physics include proton transfer in water, reactions along a reaction coordinate, protein folding and unfolding, and particle motion in liquids. These are governed by classical or quantum-mechanical equations of motion, such as the Hamilton or Schrödinger equations. In biology, attention often shifts to non-equilibrium systems—for example, the motility patterns of cells or multicellular organisms—where time series data are used to classify cancer cells as benign or malignant. Beyond the natural sciences, time series also underpin economics and meteorology, such as stock prices, currency exchange rates, and daily temperatures. Despite their diversity, time series data across these domains share common traits. Historically, different fields have developed their own analysis tools: physicists and chemists often employ differential equations with noise, biologists use random walk models, and computational economists apply algorithmic models. Central to the present ERC project, NoMaMemo, is the proposal that all these systems can be described within a unified framework of stochastic, coupled, nonlinear integro-differential equations.
To achieve these goals, we developed a suite of numerical techniques capable of extracting key information from diverse data sets, independent of their source. These methods build on our earlier work in “memory extraction” techniques within a common framework provided by the generalized Langevin equation (GLE). The GLE is a standard theoretical model for systems with memory effects. It consists of differential equations that incorporate environmental noise, an energy landscape from force interactions, and a memory-dependent friction term that couples to the system’s full history, introducing a dynamic environment into the model. Memory extraction refers to determining the functional form of this friction term directly from time-series data, providing a complete system characterization within our general NoMaMemo framework.
Overall, we made significant advances in the projection methodology, the primary theoretical framework for constructing GLEs and defining the role of friction. Our techniques for handling complex dependencies beyond simple linear friction are now widely adopted, and our group is at the forefront of developing non-equilibrium projection methods. These are essential for understanding the stochastic nature of living systems and for analyzing other complex phenomena, including meteorological patterns and economic dynamics.
We have achieved a broad range of applications. In the area of protein folding, we demonstrated that accurately predicting long-timescale folding kinetics requires the full multi-timescale friction profile. More fundamentally, we showed that basic units of molecular conformation, such as rotating dihedral bonds, deviate strongly from expected diffusion laws because of the complex nature of solvent coupling at the molecular level. In ultrafast molecular vibrational spectroscopy, we extracted time-dependent friction acting on chemical bonds, allowing us to predict infrared spectra in excellent agreement with experiment. Our models also reproduce the dynamics of complex biological systems, such as active cytoskeletal networks and red blood cell flickering. Finally, we showed that the swimming behavior of single-cell organisms can be classified by features of non-Markovian dynamics. By analyzing the stochastic search strategies seen in many foraging animals, we found that memory in the search path improves efficiency when target locations are correlated.
As part of dissemination, we organized the international conference “Memory of Rare and Non-Equilibrium Events” in Tashkent, Uzbekistan, and published an invited review, Memory and Friction: From the Nanoscale to the Macroscale, in Annual Review of Physical Chemistry.
Overall, we made significant advances in the projection methodology, the primary theoretical framework for constructing GLEs and defining the role of friction. Our techniques for handling complex dependencies beyond simple linear friction are now widely adopted, and our group is at the forefront of developing non-equilibrium projection methods. These are essential for understanding the stochastic nature of living systems and for analyzing other complex phenomena, including meteorological patterns and economic dynamics.
We have achieved a broad range of applications. In the area of protein folding, we demonstrated that accurately predicting long-timescale folding kinetics requires the full multi-timescale friction profile. More fundamentally, we showed that basic units of molecular conformation, such as rotating dihedral bonds, deviate strongly from expected diffusion laws because of the complex nature of solvent coupling at the molecular level. In ultrafast molecular vibrational spectroscopy, we extracted time-dependent friction acting on chemical bonds, allowing us to predict infrared spectra in excellent agreement with experiment. Our models also reproduce the dynamics of complex biological systems, such as active cytoskeletal networks and red blood cell flickering. Finally, we showed that the swimming behavior of single-cell organisms can be classified by features of non-Markovian dynamics. By analyzing the stochastic search strategies seen in many foraging animals, we found that memory in the search path improves efficiency when target locations are correlated.
As part of dissemination, we organized the international conference “Memory of Rare and Non-Equilibrium Events” in Tashkent, Uzbekistan, and published an invited review, Memory and Friction: From the Nanoscale to the Macroscale, in Annual Review of Physical Chemistry.
The importance of our results cannot be overstated. We present a numerical-analytical toolbox that enables physicists, chemists, biologists, computer scientists, economists, and others to build well-defined models for their data. The breadth of this reach is already evident from the diverse applications achieved by our group. Because our protocol is based on the GLE framework, it rests on a solid foundation in theoretical physics. What distinguishes NoMaMemo are its advanced memory extraction techniques and its proven success across many fields. Our tools are readily applicable to time series data of any kind, therefore offering unbounded potential. We plan to continue developing and applying these methods beyond the active lifespan of NoMaMemo. Many of the researchers we have trained are now in related positions, carrying this knowledge into new domains. The development of theoretical frameworks and advanced tools for non-equilibrium systems remains one of the greatest challenges in non-Markovian stochastic physics. Understanding non-equilibrium physical, chemical, and biological systems offers a wealth of unanswered questions, which we will continue to pursue. Following the completion of the consolidated NoMaMemo investigation, we will extend our non-Markovian framework broadly, generating insight from the molecular level to the organism level, and up to the terrestrial scale.