The establishment of new therapeutic strategies for metabolic syndrome is urgently needed because metabolic syndrome, which is characterized by several disorders, such as hypertension, increases the risk of lifestyle-related diseases. One approach is to focus on the pre-disease state, a state with high susceptibility before the disease onset, which is considered as the best period for preventive treatment. In order to detect the pre-disease state, we recently proposed mathematical theory called the dynamical network biomarker (DNB) theory based on the critical transition paradigm. Here, we investigated time-course gene expression profiles of a mouse model of metabolic syndrome using 64 whole-genome microarrays based on the DNB theory, and showed the detection of a pre-disease state before metabolic syndrome defined by characteristic behavior of 147 DNB genes. The results of our study demonstrating the existence of a notable pre-disease state before metabolic syndrome may help to design novel and effective therapeutic strategies for preventing metabolic syndrome, enabling just-in-time preemptive interventions.

In this paper, we analyze the relation between the stability of a noisy dynamical system based on linear approximation and the covariance matrix of its stationary distribution. We reformulate the theory of dynamical network biomarkers in terms of the covariance matrix and clarify the limiting behavior of the covariance matrix when a dynamical system approaches a bifurcation point. We also discuss the relation between the Jacobian matrix and principal component analysis. An application to a simple nonlinear network model is also demonstrated.

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We review our recent work on chaos in neurons and its application to neural networks from perspective of chaos engineering. Especially, we analyze a dataset of a squid giant axon by newly combining our previous work of identifying Devaney's chaos with surrogate data analysis, and show that an axon can behave chaotically. Based on this knowledge, we use a chaotic neuron model to investigate possible information processing in the brain.