The analysis of nonlinear dynamics is an important issue in numerous fields of science. In this study, we propose a new method to analyze the time series data using persistent homology (PH). The key idea is the application of PH to the distance matrix. Using this method, we can obtain the topological features embedded in the trajectories. We apply this method to the logistic map, Rössler system, and electrocardiogram data. The results reveal that our method can effectively identify nonlocal characteristics of the attractor and can classify data based on the amount of noise.

Mapper, a topological data analysis method for high-dimensional data, represents a topological structure as a simplicial complex or graph based on the nerve of clusters. We propose V-Mapper (velocity Mapper), an extension of Mapper, for high-dimensional data with velocity. V-Mapper simultaneously describes a topological structure and flow as a weighted directed graph (V-Mapper graph) by embedding velocity in the edges of the Mapper graph. We apply V-Mapper to single-cell gene expression data using a method for inferring the velocity of gene expression. Moreover, the application of the Hodge decomposition on graph enhances the interpretation of the flow within V-Mapper graph.

We propose and demonstrate a topological test for spatial dependence based on the framework of persistent homology. We compare our method to Moran's I, a classical measure of spatial auto-correlation, on synthetic datasets as well as on election and COVID data. We find about 65-75% agreement between the main variant of our method and Moran's I on real datasets. While the Moran's I test is more sensitive overall on these datasets, there are instructive instances (synthetic and real) where our method detects a spatial pattern that the Moran's I test does not.

Cystic fibrosis (CF) is a progressive genetic disease that causes persistent lung infections and limits the ability to breathe over time. The defective gene, Cystic Fibrosis Transmembrane Conductance Regulator (CFTR), changes a protein that creates thick mucus. The mucus clogs the airways and traps bacteria leading to infections, extensive lung damage, and failure. The objective of the proposed research is to develop and utilize novel Focused Ultrasound (FU) systems to investigate muco-modulation (the ability to alter the properties of mucus) for CF. The immediate goals of the research are as follows: 1) to utilize unfocused/focused ultrasound system to observe muco-modulation in a simulation study and 2) to design and develop customized FU system to target multiple sites to modulate mucus structure/function in a targeted area, without disrupting gross tissue function. The long-term goal of this study is to produce a wearable therapeutic device for human beings that provides non-invasive therapy and to create a complete system model that spans across electrical, acoustical, and biological domains. Thus, the research aims will extend the development of disease-specific and patient-specific treatment for CF using non-invasive ultrasound vibrations. The results presented here comprise as the first step towards that realization.

Much research on secure and safe AI analysis methods for users has been conducted. They are 1) secure multiparty computation (SMC), 2) quasi-homomorphic encryption, 3) federated learning (FL), and so on. It is known that both utility and confidentiality are essential for machine learning using confidential data. However, there is a trade-off between them. In the previous paper, we proposed a learning method for secure distributed processing using decomposition data and parameters. The characteristic feature of this method is to achieve high confidentiality through distributed processing with decomposed data and parameters. On the other hand, the realization of machine learning through the distribution and integration of decomposition data leads to an increase in computational complexity and a deterioration of computational accuracy. In particular, while increasing the number of servers improves confidentiality, this problem becomes more pronounced. In this paper, we propose scalability improvement of simplified, secure distributed processing methods of BP and NG methods to suppress the computational complexity associated with an increase in the number of servers and demonstrate its effectiveness through a numerical simulation.

The path-integral quantum Monte Carlo (PIQMC) method is widely used as a classical simulation algorithm for quantum annealing. Replicas represent different points in imaginary time. We propose and demonstrate a swarm-like ground-state searching algorithm based on the PIQMC method for automatically fluctuation-controlled simulated annealing. Replicas help one another to search for the ground state of an Ising system as if forming a swarm and working cooperatively. Their interactions are local, simple and fluctuate to a certain degree. Such fluctuations are necessary to escape local minima, but the fluctuations do not need to be explicitly controlled. The size of fluctuations is automatically adjusted as annealing proceeds. We solve max-cut problems for algorithm evaluation, each of which corresponds to a graph of 100 vertices. We also solve the same problems using a conventional method based on the Metropolis algorithm for comparison.

We have developed a nonlinear method of time series analysis that allows us to obtain multiple nonlinear trends without harmonics from a given set of numerical data. We propose to apply the method to recognize the ongoing status of COVID-19 infection with an analytical equation for nonlinear trends. We found that there is only a single nonlinear trend, and this result justifies the use of a week-based infection growth rate. In addition, the fit with the obtained analytical equation for the nonlinear trend holds for a duration of more than three months for the Delta variant infection time series. The fitting also visualizes the transition to the Omicron variant.

In this paper, we propose a complex-valued neural network based on the widely linear estimation taking advantage of its geometric structure, and show that it can learn geometric transformations that the conventional neural networks cannot. First we formulate a fully augmented complex-valued neuron model based on the widely linear estimation. It is a generalized complex-valued neuron model that includes a usual complex-valued neuron and a degenerated case called a degenerated fully augmented complex-valued neuron. A fully augmented complex-valued neural network consists of such fully augmented complex-valued neurons. Secondly, we derive the back-propagation learning algorithms for the multi-layered fully augmented complex-valued neural networks. Finally, we find out via experiments that the multi-layered fully augmented complex-valued neural network has the different ability to learn 2D affine transformation from that of the usual complex-valued neural network.

This paper proposed a packet drop probability function with an adjustable nonlinearity parameter in random early detection (RED) for active queue management of a router to control network congestion. We investigated the effect of nonlinearity on the average queue size, average throughput, average retransmission rate, average round-trip time, and fairness index for two widely used loss-based congestion control algorithms: Reno and CUBIC. Simulations were performed with Tail-Drop and the original RED to clarify the effect of nonlinearity under different traffic loads. The results showed that the RED with a nonlinear function did not aggravate the network performance statistics because achieved high throughput while maintaining a low-queuing delay, such as the original RED with a linear function under the extremely heavy traffic condition. Under the light and the heavy traffic conditions, increasing the bending degree of the nonlinear function accomplished high throughput by preventing excessive discarding of packets.

Discriminative restricted Boltzmann machine (DRBM) is a probabilistic three-layered neural network, consisting of the input, hidden, and output layers, that helps to solve classification problems. This study attempts to improve the generalization property of the DRBM. Regularization methods such as L₁ or L₂ regularizations can be used to control the representation power of a learning model and suppress over-fitting to a dataset. To control the representation power of the DRBM, an alternative regularization approach is proposed, in which sparse regularization is imposed on the values of the hidden variables of the DRBM. In the resultant model, the sparse regularization controls the effective size of the hidden layer of the DRBM. Unlike standard regularization methods, in the proposed model, parameters that control the sparsity strength are trainable. The method is validated through numerical experiments based on benchmark datasets.

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.

Restricted Boltzmann machines (RBMs) are a type of statistical machine learning model used in various applications. However, training RBM models is computationally difficult owing to the requirement of calculating expectations that have a combinatorial explosion. We provide a new and effective learning algorithm based on spatial Monte Carlo integration, which is an extension of the standard Monte Carlo integration and can approximate such intractable expectations with high accuracy. The proposed method exhibited superior performance compared to the standard learning method, i.e., contrastive divergence, in terms of accuracy and learning speed. However, there were cases in which the proposed learning method exhibited reduced performances. Thus, we further demonstrate that a heuristic initialization of the learning parameters can suppress this degradation.

Critical transitions and early warning signals are gaining attention in various fields such as ecology, climatology, and economics. However, quantitative estimation of the critical transition probability remains difficult. In this study, I propose a method to estimate the critical transition probability. It is based on a previous method using quadratic polynomial approximation, and skewness filtering is added as a reject option. The proposed method is applied to May model, a mathematical model of an ecosystem, as an example case. The results of numerical simulations show that the proposed method has much better precision than the previous method without skewness filtering, achieving a relative error of approximately ±50% for the mean escape time.

In this paper, an image sequence decomposition by the sigma-delta cellular neural network (SD-CNN) with coupled cells and its composition framework is proposed. The SD-CNN, having coupled cells inspired by the second-order sigma-delta modulator, is employed for image sequence decomposition, and it enables effective image decomposition by the effects of complex dynamics. In our method, pixel luminance is described by the number of spikes within a discrete time window that corresponds to the number of SD-CNN iterations. For efficient image decomposition, a high luminance which requires a long time window, should be compensated. To solve this problem, we introduce the cumulated luminance integrator enables compensating a high luminance even with a short time window. Experimental results on various test images in the Kodak dataset and the Waterloo dataset support that all the test images can be mathematically lossless reconstructed from an image sequence decomposed via our method. It is also confirmed that the proposed method improves transmission efficiency for the Kodak dataset by approximately 80%, which is an issue with our previous method.

This paper relates to study on a new deterministic particle swarm optimization (D-PSO) called Optimizer based on Spiking Neural-oscillator Networks (OSNNs). OSNNs have a swarm consisting of plural particles which search a solution space interacting with each other. A single particle consists of plural spiking neural oscillators (`spiking oscillators') modeled by integrate-and-fire neurons. The spiking oscillators are coupled by a network topology and interact with each other by exchanging their own spike signals. Such interaction results in that coupling spiking oscillators can take synchronous or asynchronous dynamics and affects search performances of OSNNs. Herein we propose the basic algorithm of OSNNs and applied Ring 1-way network topology to coupling spiking oscillators. We theoretically analyzed parameter conditions for OSNNs, demonstrated the analytic results, and verified search performances of OSNNs through numerical simulations. We also herein discuss search performances of OSNNs and the relationship between the search performances and analytic results, and clarify prospective parameter regions which lead to good search performances in solving optimization problems.

A global stabilization method for the conversion characteristics of a bidirectional DC/DC converter and its application in peer-to-peer energy transfer systems is described. Peer-to-peer energy transfer is a control strategy in which the supply and load cooperate to transmit power, and it requires the global operation of the converter. According to the power relation, the bidirectional DC/DC converter has two equilibrium points. To realize global stability, a unique equilibrium point is achieved by eliminating the untargeted equilibrium point using the power relationship between the ports. Global stability is realized by setting feedback gains to converge globally to this equilibrium point. The experimental results demonstrate the global stability of the proposed method when applied to a stand-alone system and a peer-to-peer energy transfer system.

This paper reports on the development of straightforward software for bifurcation point detection in discrete-time dynamical systems with a fast and versatile algorithm. Nested-layer particle swarm optimization (NLPSO) is an effective general-purpose bifurcation point detection strategy. In contrast to traditional gradient-based methods, the NLPSO method does not require derivatives of the objective functions. Note that NLPSO can incur high time costs, and parallel computation is practical. The software reported in this study employs modified NLPSO that is optimized for parallel computing. The proposed algorithm is fast and easy to use with limited knowledge of bifurcation point detection, algorithms, or parallel computing techniques.

Neuromorphic engineering, wherein the structure of a neural system is reconstructed and its applications are exploited on CMOS integrated circuits, presents various developments. This study focuses on interface technology that can adapt CMOS integrated circuits to a neural system. Existing neural stimulators are designed to accurately transmit signals and accurately stimulate the nerves; however, embedding them into the brain is challenging owing to their size and power [1]. One solution is to reduce the circuit area and power consumption at the expense of certain precision. This study successfully induces nerve activity using a designed circuit that is connected to the brain of rat; the proposed circuit demonstrates a good effect of charge balance. Moreover, this paper proposes CMOS neural stimulating circuits with low power consumption and a small area.

Detecting unstable periodic orbits in chaotic systems based on the time series is a fundamental problem in nonlinear dynamics, but it often becomes extremely challenging one. In this study, we propose a new approach for detecting unstable periodic points using reservoir computing and stability transformation method. We connects reservoir computing, which is a well-known machine learning technique, and stability transformation method, which can detect unstable periodic points in chaotic dynamical systems, to perform unstable periodic points detection in a data-driven and model-free process. In this paper, we use an example of the Hénon map to demonstrate detecting unstable fixed point and unstable 2-periodic points.

In the cerebral cortex, excitatory postsynaptic potentials (EPSPs) exhibit a long-tailed distribution. Although EPSPs induce rich neural activity, their contributions to brain function remain unclear. Therefore, this study evaluated the effect of the dynamics induced by long-tailed synaptic weights by constructing a reservoir computing (RC) model and comparing the memory capacity and predictive accuracy for nonlinear time-series between RCs, with and without strong weights. The results revealed that strong weights significantly enhance the RC performance through gamma-band dynamic neural activity. This mechanism may support the cognitive processes in the actual brain network.

This study estimates a parameter space from only two time-series data sets in order to predict when a critical transition occurs caused by a saddle-node bifurcation. By estimating the parameter space, we can plot a bifurcation diagram corresponding to the original bifurcation diagram. In addition, the Lyapunov exponent can also be approximated in the estimated parameter space and corresponds to the bifurcation diagram. Thereby, we expect that the parameter value at which the critical transition occurs is predicted. In numerical experiments, we estimate the parameter space for the coupled dynamics of water and vegetation, and we compare the bifurcation diagrams in the original and estimated parameter spaces. For predicting when the critical transition occurs, we confirm that the Lyapunov exponent reaches zero when the critical transition occurs. In addition, we compare the prediction results between the proposed method and early warning signals.

We investigate bifurcations of periodic solutions observed in the forced Wilson-Cowan neuron pair by both the brute-force computation and the shooting method. By superimposing the results given by both methods, a detailed topological classification of periodic solutions is achieved that includes tori and chaos attractors in the parameter space is achieved. We thoroughly explore the parameter space composed of threshold values, amplitude, and angular velocity of an external forcing term. Many bifurcation curves that are invisible when using brute-force method are solved by the shooting method. We find out a typical bifurcation structure including Arnold tongue in the angular velocity and the amplitude of the external force parameter plane, and confirm its fractal structure. In addition, the emergence of periodic bursting responses depending on these patterns is explained.

In regions with heavy snowfall, there has long been a serious problem of great inconvenience and danger to people's lives caused by the snowfall. To tackle this problem, a novel framework for efficient snowmelting should be proposed, which can be useful in the control systems design for the considered road healing systems. In this paper, we propose a road heating system using underground power distribution lines. As a main result, we derive a mathematical model of the system. The nonlinear ordinary differential equation (ODE) model is introduced to describe the spatial and temporal variation of the voltage of the distribution line. The validity of the model is verified by numerical simulations using actual data of solar radiation and PV power generation of Toyama Prefecture, Japan in winter.

Non-terrestrial networks, composed of ground, air, and satellite communications, are considered one of the key components for the Beyond 5G/6G, and optical satellite communication is a fundamental technology to enable high-capacity communications. It is affected by interruptions of optical communications due to clouds on the communication link. A satellite can mitigate the interruption by switching its destination ground station to the other communication available station, though it brings additional delays in establishing optical links. In this study, we propose a ground station selection method using reinforcement learning algorithms to realize a fast and stable satellite-terrestrial optical communication system. We introduce two multi-armed bandit algorithms, Q-learning and Deep Q-learning, for the proposed method. We evaluate them using actual data of the optical satellite communication availability. Our simulation results show that the proposed method with deep Q-learning has the best average throughput. The proposed scheme efficiently follows changes in the state of communication links, and it becomes even better than fixed to ideal best link.

Traffic congestion is closely associated with various social issues that must be solved urgently. With the recent advancement of machine learning technologies, diverse methods for predicting traffic congestion have been developed. Specifically, traffic prediction using deep learning can provide highly accurate performance. Nevertheless, several difficulties remain because of the complexity of deep learning models: particularly, they require large amounts of data and computational power. For this study, we strive to achieve traffic prediction precision using a simple linear model. Instead of improving complex models, we select training data appropriately with a linear model and then verify the feasibility of prediction by exploring “data complexity”. The prediction results imply that the linear model is as precise as deep learning even with fewer number of data and parameters. We use actual data from expressways collected using detectors.

Word vectors are applied various tasks in natural language processing. However, the potentiality of the word vectors of Japanese has not been discussed as much as those of English. Therefore, the purpose of this paper is to classify the genre of modern Japanese literary works using characteristic features evaluated by the word vectors. The accuracy of the classification between novels and poetic works was 95%, and the one between novels and essays was 90%. The word vectors are applicable in the genre classification problem in modern Japanese literary works.

Finding the shortest paths for packets in communication networks is one of the vital engineering challenges. Recently, a routing strategy using gravitational centrality has been proposed to find efficient transmitting routes for packets to their destinations. This routing strategy successfully mitigates the congestion of packets in the networks and effectively transmits many packets to their destinations by using gravitational centrality. However, this routing strategy is difficult to transmit the packets to their destinations if large volumes of packets flow in the communication networks because fixed costs are used to determine the shortest paths for every source-destination pair. To overcome these problems, we have already proposed a routing strategy using congestion signals. This routing strategy further mitigates the congestion of packets compared to conventional routing strategies such as the routing strategy with gravitational centrality. In this study, we comprehensively evaluate the routing strategy with the congestion signals if different types of centralities are incorporated into the costs of links and various topologies are applied to the communication network models. Numerical experiments illustrate that our routing strategy using the congestion signals mitigates the congestion of packets even if other types of centralities are incorporated. In addition, our proposed routing strategy shows effective transmitting performance for the various topologies of networks.

In this paper, we present the effectiveness of a frequency domain-based loss function using the discrete cosine transform (DCT) for the bit-depth enhancement (BDE) problem that recovers high-bit-depth images from low-bit-depth images. By minimizing the loss between the DCT coefficients, it is expected to recover smooth luminance changes by suppressing extra frequency components caused by the weak gradients contained in the false contour artifacts. Moreover, we proposed a frequency domain-based multi-level BDE method to deal with different bit-depth degradation. The proposed multi-level BDE method identifies the bit-depth of the input image by embedding the bit-depth information in the frequency domain, and it recovered the missing lower bits appropriately. Experimental results show that the model optimized with frequency-based loss outperforms the model optimized with other losses in the comparison considering the objective and subjective results. Furthermore, we show that the proposed multi-level BDE method is effective for more severe bit-depth degradation on a specific benchmark dataset.

In the present paper, we investigate the dynamical features of the rule sequence at each time step which realize the description of digital sound data. From previous research, we have performed the description with the limited number of 256 rules of three-rules sets of one dimensional cellular automata with two states and three neighbors referred as to 1-2-3 CA hereafter for various digital sounds and Huffman coding, and have successfully achieved a fully compressed description of the target sound data without reproducing the error. In order to investigate the dynamical features of the rule sequences at each time step, we perform numerical Wolfram's classification method. From computer experiments, in Pronounced word data, all the rule sequences are composed with Wolfram's class1, 2 and 4, whereas in musical data, all the rule sequences are composed with Wolfram's class2 and 4. Thus, we have succeed to classify the rule sequences among the genres of data.

Various natural disasters occur in Japan, including avalanches, earthquakes, and volcanic eruptions. Thus, a novel rescue system that can quickly search for survivors after a disaster is necessary. Although wireless systems are suitable for this purpose, the optimal frequency for achieving low-attenuation communication must be determined. In this study, the transmission characteristics of sub-THz waves in Sakurajima and Shinmoedake volcanic ashes were measured. The results showed that the optimum frequency was different for each volcanic ash sample. The specific transmittance in the case of Sakurajima and Shinmoedake is 90.3% at 47.6 GHz and 85.9% at 93.4 GHz, respectively.

We construct a nonlinear lattice model to investigate the dynamics of nonlinear behavior in phononic crystals (PnCs). Two types of mass points and springs are introduced in the model to reproduce the difference in material properties between the scatterers and background in PnCs. The nonlinearity is introduced to the model by changing the mass of each mass point depending on the displacement gradient at the mass point. We numerically confirm that both the 1D and 2D models have the bandgap in the linear dispersion relation. Moreover, in both model, switching behavior of wave propagation is found.

Few-shot classification is a classification made on the basis of very few samples, and meta-learning methods (also called “learning to learn”) are often employed to accomplish it. Research on poisoning attacks against meta-learning-based few-shot classifier has recently started to be investigated. While poisoning attacks aimed at disrupting the availability of the classifier during meta-testing have been studied in Xu et al. [1] and Oldewage et al. [2], backdoor poisoning in meta-testing has only been briefly explored by Oldewage et al. [2] under limited conditions. We formulate a backdoor poisoning attack on meta-learning-based few-shot classification in this study. We show that the proposed backdoor poisoning attack is effective against the few-shot classification using model-agnostic meta-learning (MAML) [3] through experiments.

In this study, we attempt to learn the parameters of a multilayer perceptron (MLP) using the particle swarm optimization (PSO) method, which is an approximate solution method for optimization problems without requiring the derivative information of the evaluation function. We used the gradient method and PSO to learn to classify a linearly inseparable dataset with an MLP in the middle layer with a few neurons. We experimentally confirmed that PSO outperformed gradient-based learning.

In this study, using k-means and UMAP, we verified that the sentence vectors generated by Sentence-BERT as distributed representations of sentences capture the meaning of sentences well. To this end, we visualized the sentence vectors by generating images matching the meaning of the sentence from the sentence vectors generated by Sentence-BERT. The results confirm that although there were differences in the information represented by each dimension as distributional features of the sentence vector, this information overlapped substantially.

This contribution introduces the design of multivalued multiband frequency response filters exploiting nonlinear feedback design techniques. The interest in this topic is related to the possibility of analysing in real-time sinusoidal signals unveiling whether their main frequency components increase or decrease along different complex paths and in fixed sets of windows. This can be done by using the effects of frequency hysteresis, peculiar characteristic of the proposed devices.

We investigate the influence of a local bridge on a social network of 25 coupled chaotic circuits. From synchronization phenomena of coupled chaotic circuits, we show that coupled chaotic circuits connected at both ends of a local bridge easily break down. Through computer simulations, the network is predicted to switch between global synchronization and partial synchronization. To analyze synchronization behavior, we define the asynchronous probability for a given time interval. Moreover, we demonstrate in experiments using real physical circuits the same synchronization behavior.

We designed an analog single-electron (SE) information-processing circuit that mimics the behavior of a fish shoal. Although SE circuits are functional, there is not yet an optimum information-processing method established for them. To tackle this issue, we take inspiration from the behavior of fish shoals, where each fish determines its behavior by interacting with other fish, as in a multi-agent system. We demonstrated our SE circuit to effectively mimic one of the three rules of the Boids algorithm regarding fish shoal behavior through computer simulation. We believe our approach is a strong candidate for SE circuits having optimum information processing.

Recently, an importance of estimating driver's experiences has been recognized in advanced driver assistant systems. Furthermore, neuro-imaging studies showed that the characteristics of functional whole-brain networks, typified as functional connectivity, strongly reflect driving performance. In this study, we estimated functional connectivity through electroencephalogram (EEG) signals while watching a driving scene by phase lag index (PLI) with high spatio-temporal resolution and compared the functional connectivity between beginner and expert groups for driving. The results showed significantly enhanced gamma-band functional connectivity in the expert groups. Therefore, the PLI approach could be utilized for estimating driving performance in the advanced driver assistant systems.