Tohru Ikeguchi

The capacitated vehicle routing problem (CVRP) is one of the NP-hard combinatorial optimization problems, and efficient construction of a high-quality solution is a major challenge. In this paper, we propose a metaheuristic method based on chaotic dynamics to improve the efficiency of two local search operations: the CROSS-Exchange and the 2-opt methods. Unlike traditional methods that usually rely on randomization or fixed rules, this method dynamically controls the selection and execution of local search operations using chaotic neurodynamics. The experimental results show that this method can effectively improve the quality of the solution and algorithm performance when solving CVRP, and also provides a new solution framework for logistics optimization.

System analysis depends critically on the identification of the connections—especially the causal relationships—that exist between the components of the system. In particular, the causal relationships connecting neurons in brains, whose activities are typically observed as spike trains (a type of point process), need to be elucidated. Although various causality detection methods have been developed for time series signals, an effective causality detection method for spike trains has not been developed yet. To this end, we propose a causality detection method for spike trains based on the theory of nonlinear dynamical systems. We use the mutual prediction accuracy of the interspike intervals of spike trains for causality detection. Furthermore, we test the prediction accuracy obtained by the proposed method using the method of surrogate data from nonlinear dynamical systems theory. Numerical experiments revealed that the proposed method provides accurate causality detection for a small number of neural spike trains generated by the mathematical model.

The Izhikevich neuron model can reproduce various types of neurons, including chaotic neurons, by utilizing appropriate parameter sets. This study analyzes the responses of a periodically forced Izhikevich neuron with chaotic parameters using three measures—the diversity index, the coefficient of variation, and the local variation—to quantify interspike intervals (ISIs). The evaluation of ISIs combining these three measures clarifies the differences in neuronal activities, but evaluation using an individual measure cannot. In addition, we analyzed the change in the stability of the equilibrium points caused by a periodic input on a phase plane. The results indicate that in electrophysiologically feasible parameter sets, the stability of equilibrium points plays a crucial role in determining the critical amplitude around which irregular activities transition to regular ones. Thus, the relationship between neural behavior and the period and amplitude of the input current is contingent upon the existence and stability of equilibrium points.

Physiological experiments have described the electrophysiological properties of a single neuron, and mathematical models formulating neuronal activity have been proposed to elucidate the mechanism of information processing by the brain. In the present study, we investigated one such model, the Izhikevich neuron model, stimulated by sinusoidal inputs, with the parameter sets of four principal neuron types: regular spiking, fast spiking, intrinsically bursting, and chattering neurons. We adopted three measures: the diversity index, the coefficient of variation, and the local variation, to quantify interspike intervals from different viewpoints. The combined evaluation of these three measures clarified that the positional relationship of the nullclines, which is determined by the amplitude of sinusoidal forcing, plays a crucial role in the intrinsic properties of a periodically forced Izhikevich neuron model. Moreover, we used stroboscopic plots to clarify qualitative differences between attractors. The results also imply that such combined evaluation is applicable to the classification of neurons.

The bicycle sharing system (BSS) is one of the eco-friendly transportation systems introduced in major cities world-wide. However, BSS faces one crucial challenge: an imbalance of bicycles among the ports, because users are free to rent and return bicycles freely. It is necessary to restore the bicycles among the ports using vehicles to overcome this issue. We have already proposed search strategies for finding the tours of the vehicles in a reasonable time frame. In our previously proposed method, we used the tabu search which harnesses executing two local searches: the CROSS-exchange and the Or-opt. In the numerical experiment, we used instances with uniformly distributed ports to evaluate the performance of our previous method; however, real BSS ports are not uniformly distributed. Thus, in this paper, we use instances with real port distributions from four BSSs (Boston, Washington D.C., New York, Chicago) to investigate whether our method is effective for non-randomly distributed ports of larger-size instances (200 ports). From the numerical experiments, our proposed method is also effective for instances based on real BSS port locations.

In the brain, common inputs play an important role in eliciting synchronous firing in the assembly of neurons. However, common inputs are usually unknown to observers. If an unobserved common input can be reconstructed only from outputs, it would be beneficial to the understanding of communication in the brain. Thus, we have developed a method for reconstructing a common input only from output firing rates of uncoupled neuron models. To this end, we propose a superposed recurrence plot (SRP) comprising points determined by using a union of points at each pixel among multiple recurrence plots. The SRP method can reconstruct a common input when using various types of neurons with different firing rate baselines, even when using uncoupled neuron models that exhibit chaotic responses. The SRP method robustly reconstructs the common input applied to the neuron models when we select adequate time windows to calculate the firing rates in accordance with the width of the fluctuations. These results suggest that certain information is embedded in the firing rate. These findings could be a possible basis for analyzing whole-brain communication utilizing rate coding.

Photoplethysmography is a widely used technique to noninvasively assess heart rate, blood pressure, and oxygen saturation. This technique has considerable potential for further applications—for example, in the field of physiological and mental health monitoring. However, advanced applications of photoplethysmography have been hampered by the lack of accurate and reliable methods to analyze the characteristics of the complex nonlinear dynamics of photoplethysmograms. Methods of nonlinear time series analysis may be used to estimate the dynamical characteristics of the photoplethysmogram, but they are highly influenced by the length of the time series, which is often limited in practical photoplethysmography applications. The aim of this study was to evaluate the error in the estimation of the dynamical characteristics of the photoplethysmogram associated with the limited length of the time series. The dynamical properties were evaluated using recurrence quantification analysis, and the estimation error was computed as a function of the length of the time series. Results demonstrated that properties such as determinism and entropy can be estimated with an error lower than 1% even for short photoplethysmogram recordings. Additionally, the lower limit for the time series length to estimate the average prediction time was computed.

Photoplethysmography is a widely used technique to noninvasively assess heart rate, blood pressure, and oxygen saturation. This technique has a large potential for further applications, for example in the field of physiological and mental health monitoring. However, advanced applications of photoplethysmography have been hampered by the lack of accurate and reliable methods to analyze the characteristics of the complex nonlinear dynamics of the photoplethysmogram. Methods of nonlinear time series analysis may be used to estimate the dynamical characteristics of the photoplethysmogram but they are highly influenced by the length of the time series, which is often limited in practical photoplethysmography applications. The aim of this study was to evaluate the error in the estimation of the dynamical characteristics of the photoplethysmogram associated to the limited length of the time series. The dynamical properties were evaluated using recurrence quantification analysis, and the estimation error was computed as a function of the length of the time series. Results demonstrated that properties such as de-terminism and entropy can be estimated with an error lower than 1% even for short photople-thysmogram recordings. Additionally, the lower limit for the time series length to estimate the average prediction time was computed.