A heuristic method for solving the Steiner tree problem in graphs using network centralities.

We propose a heuristic method of using network centralities for constructing small-weight Steiner trees in this paper. The Steiner tree problem in graphs is one of the practical NP-hard combinatorial optimization problems. Given a graph and a set of vertices called terminals in the graph, the objective of the Steiner tree problem in graphs is to find a minimum weight Steiner tree that is a tree containing all the terminals. Conventional construction methods make a Steiner tree based on the shortest paths between terminals. If these shortest paths are overlapped as much as possible, we can obtain a small-weight Steiner tree. Therefore, we proposed to use network centralities to distinguish which edges should be included to make a small-weight Steiner tree. Experimental results revealed that using the vertex or the edge betweenness centralities contributes to making small-weight Steiner trees.

Central emotions and hubs in a colexification network.

By focusing on colexification, we detected central emotions sharing semantic commonalities with many other emotions in terms of a semantic relationship of both similarity and associativity. In analysis, we created colexification networks from multiple languages by assigning a concept to a vertex and colexification to an edge. We identify concepts of emotions with a large weight in the colexification network and specify central emotions by finding hub emotions. Our resultant central emotions are four: "GOOD," "WANT," "BAD," and "LOVE."

Superposed recurrence plots for reconstructing a common input applied to 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.

Photoplethysmogram Recording Length: Defining Minimal Length Requirement from Dynamical Characteristics.

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.

Detecting prediction limit of marked point processes using constrained random shuffle surrogate data.

Marked point processes refer to time series of discrete events with additional information about the events. Seismic activities, neural activities, and price movements in financial markets are typical examples of marked point process data. In this paper, we propose a method for investigating the prediction limits of marked point process data, where random shuffle surrogate data with time window constraints are proposed and utilized to estimate the prediction limits. We applied the proposed method to the marked point process data obtained from several dynamical systems and investigated the relationship between the largest Lyapunov exponent and the prediction limit estimated by the proposed method. The results revealed a positive correlation between the reciprocal of the estimated prediction limit and the largest Lyapunov exponent of the underlying dynamical systems in marked point processes.

Threshold-varying integrate-and-fire model reproduces distributions of spontaneous blink intervals.

Spontaneous blinking is one of the most frequent human behaviours. While attentionally guided blinking may benefit human survival, the function of spontaneous frequent blinking in cognitive processes is poorly understood. To model human spontaneous blinking, we proposed a leaky integrate-and-fire model with a variable threshold which is assumed to represent physiological fluctuations during cognitive tasks. The proposed model is capable of reproducing bimodal, normal, and widespread peak-less distributions of inter-blink intervals as well as the more common popular positively skewed distributions. For bimodal distributions, the temporal positions of the two peaks depend on the baseline and the amplitude of the fluctuating threshold function. Parameters that reproduce experimentally derived bimodal distributions suggest that relatively slow oscillations (0.11-0.25 Hz) govern blink elicitations. The results also suggest that changes in blink rates would reflect fluctuations of threshold regulated by human internal states.

Reproducing Infra-Slow Oscillations with Dopaminergic Modulation.

In the human brain, billions of neurons construct a neural network via synaptic connections. Neuronal excitation and inhibition are transmitted to other neurons through synapses via neurotransmitters. Dopamine is one of these neurotransmitters that plays a number of important roles. There are a variety of rhythms in the brain, such as alpha rhythm, beta rhythm, and so on. Infra-slow oscillation, ISO, is one of the rhythms observed in the brain, and ranges below 0.1 Hz. One of the key roles of dopamine is the generation of ISO in neural networks. Although the mechanism underlying the generation of ISO remains unknown, ISO can be generated by activation of the D1-type dopamine receptor. The D1-type receptor regulates spike timing-dependent plasticity (STDP), which is a learning rule of the change in synaptic weights. In this paper, to reproduce ISO in neural networks, we show that dopaminergic modulation of STDP is essential. More specifically, we discovered a close relationship between two dopaminergic effects: modulation of the STDP function and generation of ISO. We therefore, numerically investigated the relationship in detail and proposed a possible mechanism by which ISO is generated.

Graph distance for complex networks.

Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in the theory of complex networks. Here, we propose a graph distance between networks based on a Laplacian matrix that reflects the structural and dynamical properties of networked dynamical systems. Our results indicate that the Laplacian-based graph distance effectively quantifies the structural difference between complex networks. We further show that our approach successfully elucidates the temporal properties underlying temporal networks observed in the context of face-to-face human interactions.

Oscillation, Conduction Delays, and Learning Cooperate to Establish Neural Competition in Recurrent Networks.

Specific memory might be stored in a subnetwork consisting of a small population of neurons. To select neurons involved in memory formation, neural competition might be essential. In this paper, we show that excitable neurons are competitive and organize into two assemblies in a recurrent network with spike timing-dependent synaptic plasticity (STDP) and axonal conduction delays. Neural competition is established by the cooperation of spontaneously induced neural oscillation, axonal conduction delays, and STDP. We also suggest that the competition mechanism in this paper is one of the basic functions required to organize memory-storing subnetworks into fine-scale cortical networks.

Symmetry of Lyapunov exponents in bifurcation structures of one-dimensional maps.

We observe a symmetry of Lyapunov exponents in bifurcation structures of one-dimensional maps in which there exists a pair of parameter values in a dynamical system such that two dynamical systems with these paired parameter values have the same Lyapunov exponent. We show that this is a consequence of the presence of an invariant transformation from a dynamical system with one of the two paired parameter values to that with another parameter value, which does not change natures of dynamical systems.

From networks to time series.

In this Letter, we propose a framework to transform a complex network to a time series. The transformation from complex networks to time series is realized by the classical multidimensional scaling. Applying the transformation method to a model proposed by Watts and Strogatz [Nature (London) 393, 440 (1998)], we show that ring lattices are transformed to periodic time series, small-world networks to noisy periodic time series, and random networks to random time series. We also show that these relationships are analytically held by using the circulant-matrix theory and the perturbation theory of linear operators. The results are generalized to several high-dimensional lattices.

Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise.

We analyze the time for growth of bit entropy when generating nondeterministic bits using a chaotic semiconductor laser model. The mechanism for generating nondeterministic bits is modeled as a 1-bit sampling of the intensity of light output. Microscopic noise results in an ensemble of trajectories whose bit entropy increases with time. The time for the growth of bit entropy, called the memory time, depends on both noise strength and laser dynamics. It is shown that the average memory time decreases logarithmically with increase in noise strength. It is argued that the ratio of change in average memory time with change in logarithm of noise strength can be used to estimate the intrinsic dynamical entropy rate for this method of random bit generation. It is also shown that in this model the entropy rate corresponds to the maximum Lyapunov exponent.

STDP provides the substrate for igniting synfire chains by spatiotemporal input patterns.

Spike-timing-dependent synaptic plasticity (STDP), which depends on the temporal difference between pre- and postsynaptic action potentials, is observed in the cortices and hippocampus. Although several theoretical and experimental studies have revealed its fundamental aspects, its functional role remains unclear. To examine how an input spatiotemporal spike pattern is altered by STDP, we observed the output spike patterns of a spiking neural network model with an asymmetrical STDP rule when the input spatiotemporal pattern is repeatedly applied. The spiking neural network comprises excitatory and inhibitory neurons that exhibit local interactions. Numerical experiments show that the spiking neural network generates a single global synchrony whose relative timing depends on the input spatiotemporal pattern and the neural network structure. This result implies that the spiking neural network learns the transformation from spatiotemporal to temporal information. In the literature, the origin of the synfire chain has not been sufficiently focused on. Our results indicate that spiking neural networks with STDP can ignite synfire chains in the cortices.

Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

Bootstrap nonlinear prediction.

Estimating the Jacobian matrix of a nonlinear dynamical system through observed time-series data is one of the important steps in predicting future states of the time series. The Jacobian matrix is estimated using local information about divergences of nearby trajectories. Although the basic algorithm for estimating the Jacobian matrix generally works well, it often fails for short or noisy data series. In this paper, we proposed a scheme to effectively use near-neighbor information for more accurate estimation of the Jacobian matrix using the bootstrap resampling method. Then, to confirm the validity of the proposed method, we applied it to a mathematical model and several real time series. As a result, we confirmed that the proposed method greatly improves nonlinear predictability, not only for noise-corrupted mathematical models but also for real time series.

Effects of data windows on the methods of surrogate data.

To generate surrogate data in nonlinear time series analysis, the Fourier transform is generally used. In the calculation of the Fourier transform, the time series is assumed to be periodic. Because such an assumption does not always hold true, the estimation accuracy of the Fourier transformed data and thus the power spectra is reduced. Due to such an estimation error, it is also possible that the surrogate test will lead to a false conclusion; for example, that a linear time series is nonlinear. In this paper, we experimentally evaluated the effects of data windows from the viewpoint of false rejections with several types of surrogate data. Our results indicate that if the data length becomes shorter, the false rejections by the data windows are reduced to a greater extent. However, if the data length is sufficient, the use of data windows is not a viable option. In the worst possible case wherein the linear memory of the original data is very long as in the nonstationary case, the critical length of the data for which the data windows were effective was approximately 1000.

A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems.

We construct a mixed analog/digital chaotic neuro-computer prototype system for quadratic assignment problems (QAPs). The QAP is one of the difficult NP-hard problems, and includes several real-world applications. Chaotic neural networks have been used to solve combinatorial optimization problems through chaotic search dynamics, which efficiently searches optimal or near optimal solutions. However, preliminary experiments have shown that, although it obtained good feasible solutions, the Hopfield-type chaotic neuro-computer hardware system could not obtain the optimal solution of the QAP. Therefore, in the present study, we improve the system performance by adopting a solution construction method, which constructs a feasible solution using the analog internal state values of the chaotic neurons at each iteration. In order to include the construction method into our hardware, we install a multi-channel analog-to-digital conversion system to observe the internal states of the chaotic neurons. We show experimentally that a great improvement in the system performance over the original Hopfield-type chaotic neuro-computer is obtained. That is, we obtain the optimal solution for the size-10 QAP in less than 1000 iterations. In addition, we propose a guideline for parameter tuning of the chaotic neuro-computer system according to the observation of the internal states of several chaotic neurons in the network.