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Nakamura Laboratory (Graduate School of Information Science, University of Hyogo)
Nonlinear Data Analysis: Revealing the Underlying Nature of Phenomena from Data  (The world we see and know is not all there is)

The Nakamura Laboratory is engaged in uncovering the underlying mechanisms of phenomena that appear irregular, often hidden from direct observation, through data analysis.  Our research focuses on a wide range of time-varying phenomena, such as electrical current fluctuations, temperature changes, and foreign exchange movements.  Many phenomena cannot be examined directly.  Instead, we observe them and represent them as data.  Such data contain rich information about the phenomena; however, in themselves they are merely collections of numbers.  By identifying patterns and structures within the data and interpreting them meaningfully, we can arrive at an understanding of the phenomena.  Data analysis is a branch of applied mathematics that aims to extract underlying structures and mechanisms from large volumes of data obtained from real-world phenomena, using mathematical and statistical methods together with computational techniques.

Its applications span a wide range of fields, including biology, social systems, meteorology, economics, seismology, and space science.  In many cases, these phenomena exhibit irregular and complex behaviour.  Their dynamics are often influenced by multiple interacting factors, time delays, and nonlinearity.  In addition, non-stationarity—where the system itself or its parameters evolve over time—is another essential characteristic.  Although it is not straightforward to handle such factors appropriately, we consider them to be key to understanding the essence of the phenomena.  In the laboratory, we aim to reveal the underlying mechanisms of such complex phenomena—what may be called their “inner nature”—based on observational data.  This perspective has the potential to be applied broadly, from natural sciences to social phenomena. Our work focuses on analysing complex systems while taking into account multiple interacting factors, time delays, nonlinearity, and non-stationarity.

In my research, I aim not only to characterise data through analysis, but also to construct models that reproduce the behaviour of phenomena solely from data and enable prediction of their future evolution.  I also work on developing new data analysis methods and modelling approaches that better reflect real-world systems.  Where possible, I seek to pursue research without established models or precedents—research that involves discovering and opening doors that have not yet been recognised.  I am particularly interested in developing new ways of thinking.  Different perspectives lead to different outcomes, and new ways of thinking can give rise to new insights.  In this sense, the data analysis I pursue may be regarded as a form of intellectual exploration, grounded in mathematics, computation, and data.  Through this research, we aim to develop the ability to understand complex phenomena in a quantitative manner and to extract their essential features from data.

My main research approaches are as follows:

Research keywords: time series analysis, statistical modelling, dynamical systems, nonlinear phenomena, optimisation problems