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Capturing dynamics based on data from non-autonomous, open systems

DNA in the human body stores more data than the entire world’s digital storage capacity. But more importantly, the information is continuously being produced in a dynamical way within our body, which continuously produces ATP – the energy currency of our body - an equivalent to the whole body weight in a single day. Yet, can we decipher this wealth of information in and around us in a unique way, and make sense of it? Is it deterministic, or just random?

Although Erwin Schrodinger, one of the fathers of quantum physics, argued that the living systems can be understood only within the framework of open systems, a theory of open systems is still missing. They are continuously exchanging energy and matter with the environment, and are usually complex and nonlinear. Mathematically, they are non-autonomous, and cannot be studied within the framework of an asymptotic approach. They are usually treated as stochastic, and the data they produce are analysed using probabilistic methods. Either mathematical or thermodynamic probability measures are being used to evaluate the amount of entropy they produce. In recent years, such data have been analysed with an artificial intelligence approach based on machine learning methods.

In this talk I will present an alternative framework. A finite-time approach will be introduced to study the nonautonomous dynamics of high-dimensional systems whose parameters are time-varying. Its potential for extracting the causal relationships that govern such systems will be illustrated, using examples from physical and living systems, and its difficulties and limitations will also be discussed.

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