The recent developments in measurement techniques have allowed us to observe multidimensional time series data in various fields. Thus, detecting causal relations between elements from multidimensional time series data is useful for prediction, model generation, and system control. In addition, causal relations between elements can be detected to estimate network connections. In other words, the network structure can be estimated from multidimensional time series data by using causality detection methods. Among the several methods for detecting causality, Granger causality is a well-known method that is widely used for causal estimation between time series. On the other hand, a method called convergent cross mapping (CCM) has been proposed, which can distinguish causality from pseudo-correlation. It is important to investigate whether CCM will be effective with increased number of elements, even though the evaluation of its performance with a few elements has been reported in the literature. Moreover, it is important to evaluate the performance with changing dynamics of the elements. In this study, to estimate the connectivity between elements in complex networks, we apply CCM to mathematical models of complex networks, or the Watts-Strogatz model. In particular, we investigate how complex network structures affect causal estimation, by applying CCM to multidimensional time series data produced from complex networks. According to the results, we find the connectivity estimation accuracies in the regular ring-lattice network to be slightly higher than those in random networks. Furthermore, we reveal that it is easier to perform connectivity estimation for a network with a community structure than a random structure.

We have already proposed a multiple-vehicle bike sharing system routing problem (mBSSRP) to adjust the number of bicycles at each port using multiple vehicles in short time. However, there are many strict constraints in the mBSSRP, thus it is difficult to obtain feasible solutions of the mBSSRP for some instances. To obtain feasible solutions of the mBSSRP, we have proposed a mBSSRP with soft constraints (mBSSRP-S) that removes some constraints from mBSSRP and appends violations to an objective function as penalties, and a searching strategy that explores both the feasible and infeasible solution spaces. Numerical experiments indicated that solving mBSSRP-S to obtain feasible solutions of mBSSRP results in better performance than solving mBSSRP directly. However, mBSSRP-S includes infeasible solutions of mBSSRP, thus the neighborhood solutions and computational costs increase. In this study, we propose search strategies with low computational costs while maintaining performance. In particular, we propose two search strategies: the first one is to reduce neighborhood solutions to obtain a feasible solution in a short time before finding a feasible solution of the mBSSRP, and the second one is to change the problem to be solved (mBSSRP or mBSSRP-S) after a feasible solution is obtained and to search good near-optimal solutions in a short time. As the first search strategy, we propose two search methods for reducing the number of neighborhood solutions in the Or-opt and the CROSS-exchange and compare their performance with our previous results. From numerical experiments, we confirmed that a feasible solution can be obtained within a short time by exploring only the normal order insertion of the Or-opt and the normal order exchange of the CROSS-exchange as the neighborhood solutions. Next, as the second search strategy after a feasible solution of mBSSRP is obtained, we propose four search methods and compare their performance with our previous results. Numerical experiments show that the search method that only searches for the normal order insertion of the Or-opt and the normal order exchange of the CROSS-exchange with hard constraints after obtaining a feasible solution can obtain short tours within a short time.

One of the engineering applications of chaotic nonlinear dynamical systems is a pseudorandom number generator. Pseudorandom numbers generated from chaotic dynamical systems are called chaotic random numbers. A logistic map which exhibits a chaotic response can be used as such a chaotic random number. However, an important issue exists when we use such dynamical systems as a pseudorandom number generator by a digital computer: when the chaotic response of a logistic map is reproduced numerically, the number of iterations that the chaotic response is sustained depends on the precision of the numerical calculation, because the precision of the numerical calculation affects the size of the numerical error. In this paper, we extended the logistic map to an integer logistic map to reduce such numerical errors. We investigated the performance of chaotic random numbers obtained from the integer logistic map with varying numerical precisions and transforming them into binary random numbers. We then used NIST SP 800-22 to evaluate the performance of the random numbers. The results show that a numerical precision of 20 orders of magnitude or more is desirable to the generation of a well-performing chaotic random numbers from the response of the integer logistic map.

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.

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.