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Electroencephalography-based Brain Computer Interfaces (BCIs) invariably have a degenerate performance due to the considerable individual variability. To address this problem, we develop a novel domain adaptation method with optimal transport and frequency mixup for cross-subject transfer learning in motor imagery BCIs. Specifically, the preprocessed EEG signals from source and target domain are mapped into latent space with an embedding module, where the representation distributions and label distributions across domains have a large discrepancy. We assume that there exists a non-linear coupling matrix between both domains, which can be utilized to estimate the distance of joint distributions for different domains. Depending on the optimal transport, the Wasserstein distance between source and target domains is minimized, yielding the alignment of joint distributions. Moreover, a new mixup strategy is also introduced to generalize the model, where the inputs trials are mixed in frequency domain rather than in raw space. The extensive experiments on three evaluation benchmarks are conducted to validate the proposed framework. All the results demonstrate that our method achieves a superior performance than previous state-of-the-art domain adaptation approaches.

Abstract It was reported recently that chaos properties could be used to relieve inter‐symbol interference caused by multipath propagation in chaos‐based wireless communication system. Although there exists the optimal decoding threshold to theoretically eliminate the inter‐symbol interference, its practical implementation is still a challenge due to the strong requirement to know the future symbols to be transmitted. To tackle this almost ‘impossible’ task, convolutional neural network with deep learning structure is proposed to predict future symbols based on the received signal, to further reduce inter‐symbol interference and to obtain a better bit error rate performance. Due to the short time predictability of chaotic signal, the proposed method is able to predict short‐term future symbols and get a better threshold suitable for the time‐variant channel. The analytical bit error rate of the proposed method is derived. The contributions of the paper are as follows: firstly, a convolutional neural network with deep learning structure is proposed for the first time to predict the future symbols in the chaos baseband wireless communication system, which does not require much training in this important application; secondly, the future bits predicted by the trained convolutional neural network are used together with the past decoded bits to calculate more accurate decoding threshold compared with the existing methods, yielding a better bit error rate performance. Numerical simulations and experimental results validate the effectiveness of our theory and the superiority of the proposed method.

In the field of quantum chaos, spectral statistics is one of the most extensively investigated characteristics. Despite a large body of existing literature, the effects of many-body interactions on the spectral statistics of relativistic quantum systems remain poorly understood. Treating electron-electron interactions through the one-orbital mean-field Hubbard model, we address this fundamental issue using graphene billiards with the geometric shape of a circular sector as prototypical systems. Our approach is to consider the two characteristically different cases where the statistics are Poisson and Gaussian orthogonal ensemble (GOE) so the corresponding classical dynamics are typically integrable and chaotic, respectively, and to systematically investigate how the statistics change as the Hubbard interaction strength increases from zero. We find that, for energies near the Dirac point, the Hubbard interactions have a significant effect on the spectral statistics. Regardless of the type of spectral statistics to begin with, increasing the Hubbard interaction strength up to a critical value causes the statistics to approach GOE, rendering more applicable the random matrix theory. As the interaction strength increases beyond the critical value, the statistics evolve toward Poisson, due to the emergence of an energy gap rendering the quasiparticles massive. We also find that the energy levels above and below the Dirac point can exhibit different statistics, and the many-body interactions have little effect on the statistics for levels far from the Dirac point. These results reveal the intriguing interplay between many-body interactions and the spectral statistics, which we develop a physical picture to understand.

Chaotic signals require very wide bandwidth to be transmitted in a practical channel, which is difficult for the practical transducer or antenna to convert such a broadband signal. To address this problem, in this work, Chaotic Shape-forming Filter (CSF) is used to obtain the baseband signal, and the corresponding matched filter is used at the receiver to maximize the signal-to-noise ratio. At the same time, the symbol judgment threshold determined by the chaos properties is used to reduce the Inter-Symbol Interference (ISI) effect. Simulations and virtual channel experiments show that the radio-wave communication system using chaos is inferior to the conventional radio-wave communication system using Square Root Raised Cosine (SRRC) shape-forming filter in a single path channel. This is because SRRC eliminates ISI in single path, but CSF does not. However, the chaos-based communication with anti-multipath decoding algorithm shows significantly better Bit Error Rate (BER) performance than the traditional communication system using SRRC and a minimum mean square error (MMSE) channel equalization in a multipath channel. This work shows the potential application prospect of chaos-based communication in future 5G or 6G engineering communication systems.

Modern telecommunication networks represent a large-scale construction and deployment effort, with renovations occurring almost continuously over the course of decades. The resulting networks consist of numerous dimensions, each following its own trajectory of development, commingled into a complex ecosystem. Typical attributes used to characterize networks (e.g., interference, coverage, throughput, robustness, and cost) fail to fully capture a key feature of future wireless networks, namely the degree of organization. This is increasingly important when we consider the trajectory of the evolution of 5G and beyond networks with respect to densification, heterogeneity, and distributed and self-organizing decision-making.

New findings have been identified recently for chaos application in communication systems, including the simplest matched filter to maximize the signal-to-noise ratio (SNR) and the ability to resist multi-path propagation. However, chaos has a broad band frequency spectrum, which impedes its application in the conventional wireless communication systems due to the antenna and transducer bandwidth. To deal with such problem, the chaos generated by a second order hybrid system (SOHS) with a fixed basis function is used for Differential Chaos Shift Keying (DCSK) communication. A sinusoidal and its orthogonal signal are used to separate the reference signal and the information bearing signal, which are transmitted in the wireless channel. In such a way, the obstacle to broadband signal transmission in a wireless channel is overcome. A matched filter, using the convolution of the received signal and the time reverse of the basis function, maximizes the SNR at the receiver. Moreover, the proposed SOHS-DCSK provides an additional bitstream due to the chaotic signal generated by the SOHS, being capable to encode information as well. The two information sub-streams can be transmitted simultaneously in the proposed method, which possesses different bit transmission rates and reliability. In this way, the High Priority (HP) information bits are transmitted at a low transmission rate, while the Low Priority (LP) information bits are transmitted at a higher transmission rate. Hence, the proposed SOHS-DCSK method not only provides a higher data transmission rate as compared to the conventional DCSK but also makes the transmitted signal to be compatible with the conventional transducer and antenna. Due to the matched filter used, the proposed method achieves a lower bit error rate of the HP information as compared to the other existing enhanced DCSK variants for both additive white Gaussian noise channel and wireless communication channel. The numerical simulations and experiments based on the wireless open-access research platform show the validity and superiority of the proposed method.

We develop a framework based on the deep convolutional neural network (DCNN) for model-free prediction of the occurrence of extreme events both in time (“when”) and in space (“where”) in nonlinear physical systems of spatial dimension two. The measurements or data are a set of two-dimensional snapshots or images. For a desired time horizon of prediction, a proper labeling scheme can be designated to enable successful training of the DCNN and subsequent prediction of extreme events in time. Given that an extreme event has been predicted to occur within the time horizon, a space-based labeling scheme can be applied to predict, within certain resolution, the location at which the event will occur. We use synthetic data from the two-dimensional complex Ginzburg-Landau equation and empirical wind speed data from the North Atlantic Ocean to demonstrate and validate our machine-learning-based prediction framework. The trade-offs among the prediction horizon, spatial resolution, and accuracy are illustrated, and the detrimental effect of spatially biased occurrence of extreme events on prediction accuracy is discussed. The deep learning framework is viable for predicting extreme events in the real world.

Complex networks, including physical, biological and social systems are ubiquitous, but understanding of how to control them is elusive. Here Wang et al. develop a framework based on the concept of attractor networks to facilitate the study of controllability of nonlinear dynamics in complex systems.

To predict a critical transition due to parameter drift without relying on a model is an outstanding problem in nonlinear dynamics and applied fields. A closely related problem is to predict whether the system is already in or if the system will be in a transient state preceding its collapse. We develop a model-free, machine-learning-based solution to both problems by exploiting reservoir computing to incorporate a parameter input channel. We demonstrate that, when the machine is trained in the normal functioning regime with a chaotic attractor (i.e., before the critical transition), the transition point can be predicted accurately. Remarkably, for a parameter drift through the critical point, the machine with the input parameter channel is able to predict not only that the system will be in a transient state, but also the distribution of the transient lifetimes and their average before the final collapse, revealing an important physical property of transient chaos.

In this work, an enhanced differential chaos shift keying (DCSK), based on a first order hybrid chaotic system, is being proposed for a high reliability underwater acoustic communication system. It can be integrated into systems that use standard existing transducers. We show that a coherent operation between the received signal and the time reversal of the basis function in a first order hybrid chaotic system maximizes the signal to noise ratio at the receiver. Concurrently, DCSK configuration is used to resist the distortion caused by the complex underwater acoustic channel. Our simulation results show that the proposed method has lower bit error rate (BER). In addition, it shows higher communication reliability over underwater acoustic channel as compared to the conventional DCSK using logistic map and its variant forms such as Correlation Delay Shift Keying (CDSK), Phase-Separate DCSK (PS-DCSK), High Efficiency DCSK (HE-DCSK), and Reference Modulated DCSK (RM-DCSK).

The phenomenon of Fano resonance is ubiquitous in a large variety of wave scattering systems, where the resonance profile is typically asymmetric. Whether the parameter characterizing the asymmetry should be complex or real is an issue of great experimental interest. Using coherent quantum transport as a paradigm and taking into account of the collective contribution from all available scattering channels, we derive a universal formula for the Fano-resonance profile. We show that our formula bridges naturally the traditional Fano formulas with complex and real asymmetry parameters, indicating that the two types of formulas are fundamentally equivalent (except for an offset). The connection also reveals a clear footprint for the conductance resonance during a dephasing process. Therefore, the emergence of complex asymmetric parameter when fitting with experimental data needs to be properly interpreted. Furthermore, we have provided a theory for the width of the resonance, which relates explicitly the width to the degree of localization of the close-by eigenstates and the corresponding coupling matrices or the self-energies caused by the leads. Our work not only resolves the issue about the nature of the asymmetry parameter, but also provides deeper physical insights into the origin of Fano resonance. Since the only assumption in our treatment is that the transport can be described by the Green’s function formalism, our results are also valid for broad disciplines including scattering problems of electromagnetic waves, acoustics, and seismology.

The major fungal pathogen of humans, Candida albicans, mounts robust responses to oxidative stress that are critical for its virulence. These responses counteract the reactive oxygen species (ROS) that are generated by host immune cells in an attempt to kill the invading fungus. Knowledge of the dynamical processes that instigate C. albicans oxidative stress responses is required for a proper understanding of fungus-host interactions. Therefore, we have adopted an interdisciplinary approach to explore the dynamical responses of C. albicans to hydrogen peroxide (H2O2). Our deterministic mathematical model integrates two major oxidative stress signalling pathways (Cap1 and Hog1 pathways) with the three major antioxidant systems (catalase, glutathione and thioredoxin systems) and the pentose phosphate pathway, which provides reducing equivalents required for oxidative stress adaptation. The model encapsulates existing knowledge of these systems with new genomic, proteomic, transcriptomic, molecular and cellular datasets. Our integrative approach predicts the existence of alternative states for the key regulators Cap1 and Hog1, thereby suggesting novel regulatory behaviours during oxidative stress. The model reproduces both existing and new experimental observations under a variety of scenarios. Time- and dose-dependent predictions of the oxidative stress responses for both wild type and mutant cells have highlighted the different temporal contributions of the various antioxidant systems during oxidative stress adaptation, indicating that catalase plays a critical role immediately following stress imposition. This is the first model to encapsulate the dynamics of the transcriptional response alongside the redox kinetics of the major antioxidant systems during H2O2 stress in C. albicans.

ABSTRACT Immune cells exploit reactive oxygen species (ROS) and cationic fluxes to kill microbial pathogens, such as the fungus Candida albicans. Yet, C. albicans is resistant to these stresses in vitro. Therefore, what accounts for the potent antifungal activity of neutrophils? We show that simultaneous exposure to oxidative and cationic stresses is much more potent than the individual stresses themselves and that this combinatorial stress kills C. albicans synergistically in vitro. We also show that the high fungicidal activity of human neutrophils is dependent on the combinatorial effects of the oxidative burst and cationic fluxes, as their pharmacological attenuation with apocynin or glibenclamide reduced phagocytic potency to a similar extent. The mechanistic basis for the extreme potency of combinatorial cationic plus oxidative stress—a phenomenon we term stress pathway interference—lies with the inhibition of hydrogen peroxide detoxification by the cations. In C. albicans this causes the intracellular accumulation of ROS, the inhibition of Cap1 (a transcriptional activator that normally drives the transcriptional response to oxidative stress), and altered readouts of the stress-activated protein kinase Hog1. This leads to a loss of oxidative and cationic stress transcriptional outputs, a precipitous collapse in stress adaptation, and cell death. This stress pathway interference can be suppressed by ectopic catalase (Cat1) expression, which inhibits the intracellular accumulation of ROS and the synergistic killing of C. albicans cells by combinatorial cationic plus oxidative stress. Stress pathway interference represents a powerful fungicidal mechanism employed by the host that suggests novel approaches to potentiate antifungal therapy. IMPORTANCE The immune system combats infection via phagocytic cells that recognize and kill pathogenic microbes. Human neutrophils combat Candida infections by killing this fungus with a potent mix of chemicals that includes reactive oxygen species (ROS) and cations. Yet, Candida albicans is relatively resistant to these stresses in vitro. We show that it is the combination of oxidative plus cationic stresses that kills yeasts so effectively, and we define the molecular mechanisms that underlie this potency. Cations inhibit catalase. This leads to the accumulation of intracellular ROS and inhibits the transcription factor Cap1, which is critical for the oxidative stress response in C. albicans. This triggers a dramatic collapse in fungal stress adaptation and cell death. Blocking either the oxidative burst or cationic fluxes in human neutrophils significantly reduces their ability to kill this fungal pathogen, indicating that combinatorial stress is pivotal to immune surveillance.

Chaotic saddles are nonattracting dynamical invariant sets that can lead to a variety of physical phenomena. We describe the blowout bifurcation of chaotic saddles located in the symmetric invariant manifold of coupled systems and discuss dynamical phenomena associated with this bifurcation.

The cell cycle is a sequence of biochemical events that are controlled by complex but robust molecular machinery. This enables cells to achieve accurate self-reproduction under a broad range of different conditions. Environmental changes are transmitted by molecular signalling networks, which coordinate their action with the cell cycle. The cell cycle process and its responses to environmental stresses arise from intertwined nonlinear interactions among large numbers of simpler components. Yet, understanding of how these pieces fit together into a coherent whole requires a systems biology approach. Here, we present a novel mathematical model that describes the influence of osmotic stress on the entire cell cycle of S. cerevisiae for the first time. Our model incorporates all recently known and several proposed interactions between the osmotic stress response pathway and the cell cycle. This model unveils the mechanisms that emerge as a consequence of the interaction between the cell cycle and stress response networks. Furthermore, it characterises the role of individual components. Moreover, it predicts different phenotypical responses for cells depending on the phase of cells at the onset of the stress. The key predictions of the model are: (i) exposure of cells to osmotic stress during the late S and the early G2/M phase can induce DNA re-replication before cell division occurs, (ii) cells stressed at the late G2/M phase display accelerated exit from mitosis and arrest in the next cell cycle, (iii) osmotic stress delays the G1-to-S and G2-to-M transitions in a dose dependent manner, whereas it accelerates the M-to-G1 transition independently of the stress dose and (iv) the Hog MAPK network compensates the role of the MEN network during cell division of MEN mutant cells. These model predictions are supported by independent experiments in S. cerevisiae and, moreover, have recently been observed in other eukaryotes.

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

The inference of an underlying network topology from local observations of a complex system composed of interacting units is usually attempted by using statistical similarity measures, such as cross-correlation (CC) and mutual information (MI). The possible existence of a direct link between different units is, however, hindered within the time-series measurements. Here we show that, for the class of systems studied, when an abrupt change in the ordered set of CC or MI values exists, it is possible to infer, without errors, the underlying network topology from the time-series measurements, even in the presence of observational noise, non-identical units, and coupling heterogeneity. We find that a necessary condition for the discontinuity to occur is that the dynamics of the coupled units is partially coherent, i.e., neither complete disorder nor globally synchronous patterns are present. We critically compare the inference methods based on CC and MI, in terms of how effective, robust, and reliable they are, and conclude that, in general, MI outperforms CC in robustness and reliability. Our findings could be relevant for the construction and interpretation of functional networks, such as those constructed from brain or climate data.

Evolutionary games model a common type of interactions in a variety of complex, networked, natural systems and social systems. Given such a system, uncovering the interacting structure of the underlying network is key to understanding its collective dynamics. Based on compressive sensing, we develop an efficient approach to reconstructing complex networks under game-based interactions from small amounts of data. The method is validated by using a variety of model networks and by conducting an actual experiment to reconstruct a social network. While most existing methods in this area assume oscillator networks that generate continuous-time data, our work successfully demonstrates that the extremely challenging problem of reverse engineering of complex networks can also be addressed even when the underlying dynamical processes are governed by realistic, evolutionary-game type of interactions in discrete time.