Exotic swarming dynamics of high-dimensional swarmalators.

Swarmalators are oscillators that can swarm as well as sync via a dynamic balance between their spatial proximity and phase similarity. Swarmalator models employed so far in the literature comprise only one-dimensional phase variables to represent the intrinsic dynamics of the natural collectives. Nevertheless, the latter can indeed be represented more realistically by high-dimensional phase variables. For instance, the alignment of velocity vectors in a school of fish or a flock of birds can be more realistically set up in three-dimensional space, while the alignment of opinion formation in population dynamics could be multidimensional, in general. We present a generalized D-dimensional swarmalator model, which more accurately captures self-organizing behaviors of a plethora of real-world collectives by self-adaptation of high-dimensional spatial and phase variables. For a more sensible visualization and interpretation of the results, we restrict our simulations to three-dimensional spatial and phase variables. Our model provides a framework for modeling complicated processes such as flocking, schooling of fish, cell sorting during embryonic development, residential segregation, and opinion dynamics in social groups. We demonstrate its versatility by capturing the maneuvers of a school of fish, qualitatively and quantitatively, by a suitable extension of the original model to incorporate appropriate features besides a gallery of its intrinsic self-organizations for various interactions. We expect the proposed high-dimensional swarmalator model to be potentially useful in describing swarming systems and programmable and reconfigurable collectives in a wide range of disciplines, including the physics of active matter, developmental biology, sociology, and engineering.

Predicting multiple observations in complex systems through low-dimensional embeddings.

Forecasting all components in complex systems is an open and challenging task, possibly due to high dimensionality and undesirable predictors. We bridge this gap by proposing a data-driven and model-free framework, namely, feature-and-reconstructed manifold mapping (FRMM), which is a combination of feature embedding and delay embedding. For a high-dimensional dynamical system, FRMM finds its topologically equivalent manifolds with low dimensions from feature embedding and delay embedding and then sets the low-dimensional feature manifold as a generalized predictor to achieve predictions of all components. The substantial potential of FRMM is shown for both representative models and real-world data involving Indian monsoon, electroencephalogram (EEG) signals, foreign exchange market, and traffic speed in Los Angeles Country. FRMM overcomes the curse of dimensionality and finds a generalized predictor, and thus has potential for applications in many other real-world systems.

Deep learning-based state prediction of the Lorenz system with control parameters.

Nonlinear dynamical systems with control parameters may not be well modeled by shallow neural networks. In this paper, the stable fixed-point solutions, periodic and chaotic solutions of the parameter-dependent Lorenz system are learned simultaneously via a very deep neural network. The proposed deep learning model consists of a large number of identical linear layers, which provide excellent nonlinear mapping capability. Residual connections are applied to ease the flow of information and a large training dataset is further utilized. Extensive numerical results show that the chaotic solutions can be accurately forecasted for several Lyapunov times and long-term predictions are achieved for periodic solutions. Additionally, the dynamical characteristics such as bifurcation diagrams and largest Lyapunov exponents can be well recovered from the learned solutions. Finally, the principal factors contributing to the high prediction accuracy are discussed.

Distributed Partial Quantum Consensus of Qubit Networks With Connected Topologies.

In this article, we consider the partial quantum consensus problem of a qubit network in a distributed view. The local quantum operation is designed based on the Hamiltonian by using the local information of each quantum system in a network of qubits. We construct the unitary transformation for each quantum system to achieve the partial quantum consensus, that is, the directions of the quantum states in the Bloch ball will reach an agreement. A simple case of two-qubit quantum systems is considered first, and a minimum completing time of reaching partial consensus is obtained based on the geometric configuration of each qubit. Furthermore, we extend the approaches to deal with the more general N -qubit networks. Two partial quantum consensus protocols, based on the Lyapunov method for chain graphs and the geometry method for connected graphs, are proposed. The geometry method can be utilized to deal with more general connected graphs, while for the Lyapunov method, the global consensus can be obtained. The numerical simulation over a qubit network is demonstrated to verify the validity and the effectiveness of the theoretical results.

Synchronization enhancement subjected to adaptive blinking coupling.

Synchronization holds a significant role, notably within chaotic systems, in various contexts where the coordinated behavior of systems plays a pivotal and indispensable role. Hence, many studies have been dedicated to investigating the underlying mechanism of synchronization of chaotic systems. Networks with time-varying coupling, particularly those with blinking coupling, have been proven essential. The reason is that such coupling schemes introduce dynamic variations that enhance adaptability and robustness, making them applicable in various real-world scenarios. This paper introduces a novel adaptive blinking coupling, wherein the coupling adapts dynamically based on the most influential variable exhibiting the most significant average disparity. To ensure an equitable selection of the most effective coupling at each time instance, the average difference of each variable is normalized to the synchronous solution's range. Due to this adaptive coupling selection, synchronization enhancement is expected to be observed. This hypothesis is assessed within networks of identical systems, encompassing Lorenz, Rössler, Chen, Hindmarsh-Rose, forced Duffing, and forced van der Pol systems. The results demonstrated a substantial improvement in synchronization when employing adaptive blinking coupling, particularly when applying the normalization process.

Co-evolution of heterogeneous cognition in spatial snowdrift game with asymmetric cost.

The emergence of the evolutionary game on complex networks provides a fresh framework for studying cooperation behavior between complex populations. Numerous recent progress has been achieved in studying asymmetric games. However, there is still a substantial need to address how to flexibly express the individual asymmetric nature. In this paper, we employ mutual cognition among individuals to elucidate the asymmetry inherent in their interactions. Cognition arises from individuals' subjective assessments and significantly influences their decision-making processes. In social networks, mutual cognition among individuals is a persistent phenomenon and frequently displays heterogeneity as the influence of their interactions. This unequal cognitive dynamic will, in turn, influence the interactions, culminating in asymmetric outcomes. To better illustrate the inter-individual cognition in asymmetric snowdrift games, the concept of favor value is introduced here. On this basis, the evolution of cognition and its relationship with asymmetry degree are defined. In our simulation, we investigate how game cost and the intensity of individual cognitive changes impact the cooperation frequency. Furthermore, the temporal evolution of individual cognition and its variation under different parameters was also examined. The simulation results reveal that the emergence of heterogeneous cognition effectively addresses social dilemmas, with asymmetric interactions among individuals enhancing the propensity for cooperative choices. It is noteworthy that distinctions exist in the rules governing cooperation and cognitive evolution between regular networks and Watts-Strogatz small-world networks. In light of this, we deduce the relationship between cognition evolution and cooperative behavior in co-evolution and explore potential factors influencing cooperation within the system.

Technology of the photobiostimulation of the brain's drainage system during sleep for improvement of learning and memory in male mice.

In this study on healthy male mice using confocal imaging of dye spreading in the brain and its further accumulation in the peripheral lymphatics, we demonstrate stronger effects of photobiomodulation (PBM) on the brain's drainage system in sleeping vs. awake animals. Using the Pavlovian instrumental transfer probe and the 2-objects-location test, we found that the 10-day course of PBM during sleep vs. wakefulness promotes improved learning and spatial memory in mice. For the first time, we present the technology for PBM under electroencephalographic (EEG) control that incorporates modern state of the art facilities of optoelectronics and biopotential detection and that can be built of relatively cheap and commercially available components. These findings open a new niche in the development of smart technologies for phototherapy of brain diseases during sleep.

Impact of periodic vaccination in SEIRS seasonal model.

We study three different strategies of vaccination in an SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) seasonal forced model, which are (i) continuous vaccination; (ii) periodic short-time localized vaccination, and (iii) periodic pulsed width campaign. Considering the first strategy, we obtain an expression for the basic reproduction number and infer a minimum vaccination rate necessary to ensure the stability of the disease-free equilibrium (DFE) solution. In the second strategy, short duration pulses are added to a constant baseline vaccination rate. The pulse is applied according to the seasonal forcing phases. The best outcome is obtained by locating intensive immunization at inflection of the transmissivity curve. Therefore, a vaccination rate of 44.4% of susceptible individuals is enough to ensure DFE. For the third vaccination proposal, additionally to the amplitude, the pulses have a prolonged time width. We obtain a non-linear relationship between vaccination rates and the duration of the campaign. Our simulations show that the baseline rates, as well as the pulse duration, can substantially improve the vaccination campaign effectiveness. These findings are in agreement with our analytical expression. We show a relationship between the vaccination parameters and the accumulated number of infected individuals, over the years, and show the relevance of the immunization campaign annual reaching for controlling the infection spreading. Regarding the dynamical behavior of the model, our simulations show that chaotic and periodic solutions as well as bi-stable regions depend on the vaccination parameters range.

Bursting multistability induced by double-Hopf bifurcation.

We study the slow-fast dynamics of a system with a double-Hopf bifurcation and a slowly varying parameter. The model consists of coupled Bonhöffer-van der Pol oscillators excited by a periodic slow-varying AC source. We consider two cases where the slowly varying parameter passes by or crosses the double-Hopf bifurcation, respectively. Due to the system's multistability, two bursting solutions are observed in each case: single-mode bursting and two-mode bursting. Further investigation reveals that the double-Hopf bifurcation causes a stable coexistence of these two bursting solutions. The mechanism of such coexistence is explained using the slowly changing phase portraits of the fast subsystem. We also show the robustness of the observed effect in the vicinity of the double-Hopf bifurcation.

Extreme multistability in symmetrically coupled clocks.

Extreme multistability (EM) is characterized by the emergence of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. EM implies complex and hardly predictable asymptotic dynamical behavior. We analyze a model for pendulum clocks coupled by springs and suspended on an oscillating base and show how EM can be induced in this system by specifically designed coupling. First, we uncover that symmetric coupling can increase the dynamical complexity. In particular, the coexistence of multiple isolated attractors and continuous families of stable periodic states is generated in a symmetric cross-coupling scheme of four pendulums. These coexisting infinitely many states are characterized by different levels of phase synchronization between the pendulums, including anti-phase and in-phase states. Some of the states are characterized by splitting of the pendulums into groups with silent sub-threshold and oscillating behavior, respectively. The analysis of the basins of attraction further reveals the complex dependence of EM on initial conditions.

Mechanisms of Activation of Brain's Drainage during Sleep: The Nightlife of Astrocytes.

The study of functions, mechanisms of generation, and pathways of movement of cerebral fluids has a long history, but the last decade has been especially productive. The proposed glymphatic hypothesis, which suggests a mechanism of the brain waste removal system (BWRS), caused an active discussion on both the criticism of some of the perspectives and our intensive study of new experimental facts. It was especially found that the intensity of the metabolite clearance changes significantly during the transition between sleep and wakefulness. Interestingly, at the cellular level, a number of aspects of this problem have been focused on, such as astrocytes-glial cells, which, over the past two decades, have been recognized as equal partners of neurons and perform many important functions. In particular, an important role was assigned to astrocytes within the framework of the glymphatic hypothesis. In this review, we return to the "astrocytocentric" view of the BWRS function and the explanation of its activation during sleep from the viewpoint of new findings over the last decade. Our main conclusion is that the BWRS's action may be analyzed both at the systemic (whole-brain) and at the local (cellular) level. The local level means here that the neuro-glial-vascular unit can also be regarded as the smallest functional unit of sleep, and therefore, the smallest functional unit of the BWRS.

Machine discovery of partial differential equations from spatiotemporal data: A sparse Bayesian learning framework.

This study presents a general framework, namely, Sparse Spatiotemporal System Discovery (S3d), for discovering dynamical models given by Partial Differential Equations (PDEs) from spatiotemporal data. S3d is built on the recent development of sparse Bayesian learning, which enforces sparsity in the estimated PDEs. This approach enables a balance between model complexity and fitting error with theoretical guarantees. The proposed framework integrates Bayesian inference and a sparse priori distribution with the sparse regression method. It also introduces a principled iterative re-weighted algorithm to select dominant features in PDEs and solve for the sparse coefficients. We have demonstrated the discovery of the complex Ginzburg-Landau equation from a traveling-wave convection experiment, as well as several other PDEs, including the important cases of Navier-Stokes and sine-Gordon equations, from simulated data.

Machine Learning Technology for EEG-Forecast of the Blood-Brain Barrier Leakage and the Activation of the Brain's Drainage System during Isoflurane Anesthesia.

Anesthesia enables the painless performance of complex surgical procedures. However, the effects of anesthesia on the brain may not be limited only by its duration. Also, anesthetic agents may cause long-lasting changes in the brain. There is growing evidence that anesthesia can disrupt the integrity of the blood-brain barrier (BBB), leading to neuroinflammation and neurotoxicity. However, there are no widely used methods for real-time BBB monitoring during surgery. The development of technologies for an express diagnosis of the opening of the BBB (OBBB) is a challenge for reducing post-surgical/anesthesia consequences. In this study on male rats, we demonstrate a successful application of machine learning technology, such as artificial neural networks (ANNs), to recognize the OBBB induced by isoflurane, which is widely used in surgery. The ANNs were trained on our previously presented data obtained on the sound-induced OBBB with an 85% testing accuracy. Using an optical and nonlinear analysis of the OBBB, we found that 1% isoflurane does not induce any changes in the BBB, while 4% isoflurane caused significant BBB leakage in all tested rats. Both 1% and 4% isoflurane stimulate the brain's drainage system (BDS) in a dose-related manner. We show that ANNs can recognize the OBBB induced by 4% isoflurane in 57% of rats and BDS activation induced by 1% isoflurane in 81% of rats. These results open new perspectives for the development of clinically significant bedside technologies for EEG-monitoring of OBBB and BDS.

The ocean carbon sinks and climate change.

The oceans act as major carbon dioxide sinks, greatly influencing global climate. Knowing how these sinks evolve would advance our understanding of climate dynamics. We construct a conceptual box model for the oceans to predict the temporal and spatial evolution of CO2 of each ocean, and the time-evolution of their salinities. Surface currents, deep water flows, freshwater influx, and major fluvial contributions are considered, as also the effect of changing temperature with time. We uncover the strongest carbon uptake to be from the Southern Ocean, followed by the Atlantic. The North Atlantic evolves into the most saline ocean with time and increasing temperatures. The Amazon River is found to have significant effects on CO2 sequestration trends. An alternative flow scenario of the Amazon is investigated, giving interesting insights into the global climate in the Miocene epoch.

Adaptive resonance and control of chaos in a new memristive generalized FitzHugh-Nagumo bursting model.

In a new memristive generalized FitzHugh-Nagumo bursting model, adaptive resonance (AR), in which the neuron system's response to a varied stimulus can be improved by the ideal intensity of adaptation currents, is examined. We discovered that, in the absence of electromagnetic induction, there is signal detection at the greatest resonance peak of AR using the harmonic balance approach. For electromagnetic induction's minor impacts, this peak of the AR is optimized, whereas for its larger effects, it disappears. We demonstrate dependency on adaption strength as a bifurcation parameter, the presence of period-doubling, and chaotic motion regulated and even annihilated by the increase in electromagnetic induction using bifurcation diagrams and Lyapunov exponents at specific resonance frequencies. The suggested system shows the propagation of localized excitations as chaotic or periodic modulated wave packets that resemble breathing structures. By using a quantitative recurrence-based analysis, it is possible to examine these plausible dynamics in the structures of the recurrence plot beyond the time series and phase portraits. Analytical and numerical analyses are qualitatively consistent.

Diffusion Source Inference for Large-Scale Complex Networks Based on Network Percolation.

This article studies the diffusion-source-inference (DSI) problem, whose solution plays an important role in real-world scenarios such as combating misinformation and controlling diffusions of information or disease. The main task of the DSI problem is to optimize an estimator, such that the real source can be more precisely targeted. In this article, we assume that the state of a number of nodes, called observer set, in a network could be investigated if necessary, and study what configuration of those nodes could facilitate a better solution for the DSI problem. In particular, we find that the conventional error distance metric cannot precisely evaluate the effectiveness of varied DSI approaches in heterogeneous networks, and thus propose a novel and more general measurement, the candidate set, that is formulated to contain the diffusion source for sure. We propose the percolation-based evolutionary framework (PrEF) to optimize the observer set such that the candidate set can be minimized. Hence, one could further conduct more intensive investigation or search on only a few nodes to target the source. To achieve that, we first theoretically show that the size of the candidate set is bounded by the size of the largest component cover, and demonstrate that there are some similarities between the DSI problem and the network immunization problem. We find that, given the associated direction information of the diffusion is known on observers, the minimization of the candidate set is equivalent to the minimization of the order parameter if we view the observer set as the removal node set. Hence, PrEF is developed based on the network percolation and evolutionary algorithm. The effectiveness of the proposed method is validated on both synthetic and empirical networks in regard to varied circumstances. Our results show that the developed approach could achieve much smaller candidate sets compared to the state of the art in almost all cases, e.g., it is better in 26 out of 27 empirical networks and 155 out of 162 cases regarding the critical threshold. Meanwhile, our approach is also more stable, i.e., it works well irrespective of varied infection probabilities, diffusion models, and underlying networks. More importantly, we provide a framework for the analysis of the DSI problem in large-scale networks.

Arctic weather variability and connectivity.

The Arctic's rapid sea ice decline may influence global weather patterns, making the understanding of Arctic weather variability (WV) vital for accurate weather forecasting and analyzing extreme weather events. Quantifying this WV and its impacts under human-induced climate change remains a challenge. Here we develop a complexity-based approach and discover a strong statistical correlation between intraseasonal WV in the Arctic and the Arctic Oscillation. Our findings highlight an increased variability in daily Arctic sea ice, attributed to its decline accelerated by global warming. This weather instability can influence broader regional patterns via atmospheric teleconnections, elevating risks to human activities and weather forecast predictability. Our analyses reveal these teleconnections and a positive feedback loop between Arctic and global weather instabilities, offering insights into how Arctic changes affect global weather. This framework bridges complexity science, Arctic WV, and its widespread implications.

Mechanisms of Photostimulation of Brain's Waste Disposal System: The Role of Singlet Oxygen.

There is strong evidence that augmentation of the brain's waste disposal system via stimulation of the meningeal lymphatics might be a promising therapeutic target for preventing neurological diseases. In our previous studies, we demonstrated activation of the brain's waste disposal system using transcranial photostimulation (PS) with a laser 1267 nm, which stimulates the direct generation of singlet oxygen in the brain tissues. Here we investigate the mechanisms underlying this phenomenon. Our results clearly demonstrate that PS-mediated stimulation of the brain's waste disposal system is accompanied by activation of lymphatic contractility associated with subsequent intracellular production of the reactive oxygen species and the nitric oxide underlying lymphatic relaxation. Thus, PS stimulates the brain's waste disposal system by influencing the mechanisms of regulation of lymphatic pumping.