Showing papers in "Chaos in 2021"

COVID-19 second wave mortality in Europe and the United States.

Abstract: This paper introduces new methods to analyze the changing progression of COVID-19 cases to deaths in different waves of the pandemic. First, an algorithmic approach partitions each country or state's COVID-19 time series into a first wave and subsequent period. Next, offsets between case and death time series are learned for each country via a normalized inner product. Combining these with additional calculations, we can determine which countries have most substantially reduced the mortality rate of COVID-19. Finally, our paper identifies similarities in the trajectories of cases and deaths for European countries and U.S. states. Our analysis refines the popular conception that the mortality rate has greatly decreased throughout Europe during its second wave of COVID-19; instead, we demonstrate substantial heterogeneity throughout Europe and the U.S. The Netherlands exhibited the largest reduction of mortality, a factor of 16, followed by Denmark, France, Belgium, and other Western European countries, greater than both Eastern European countries and U.S. states. Some structural similarity is observed between Europe and the United States, in which Northeastern states have been the most successful in the country. Such analysis may help European countries learn from each other's experiences and differing successes to develop the best policies to combat COVID-19 as a collective unit.

Stiff neural ordinary differential equations.

Abstract: Neural Ordinary Differential Equations (ODEs) are a promising approach to learn dynamical models from time-series data in science and engineering applications. This work aims at learning neural ODEs for stiff systems, which are usually raised from chemical kinetic modeling in chemical and biological systems. We first show the challenges of learning neural ODEs in the classical stiff ODE systems of Robertson’s problem and propose techniques to mitigate the challenges associated with scale separations in stiff systems. We then present successful demonstrations in stiff systems of Robertson’s problem and an air pollution problem. The demonstrations show that the usage of deep networks with rectified activations, proper scaling of the network outputs as well as loss functions, and stabilized gradient calculations are the key techniques enabling the learning of stiff neural ODEs. The success of learning stiff neural ODEs opens up possibilities of using neural ODEs in applications with widely varying time-scales, such as chemical dynamics in energy conversion, environmental engineering, and life sciences.

Multi-scroll hidden attractor in memristive HR neuron model under electromagnetic radiation and its applications

Abstract: This paper aims to propose a novel no-equilibrium Hindmarsh-Rose (HR) neuron model with memristive electromagnetic radiation effect. Compared with other memristor-based HR neuron models, the uniqueness of this memristive HR neuron model is that it can generate multi-scroll hidden attractors with sophisticated topological structures and the parity of the scrolls can be controlled conveniently with changing the internal parameters of the memristor. In particular, the number of scrolls of the multi-scroll hidden attractors is also associated with the intensity of external electromagnetic radiation stimuli. The complex dynamics is numerically studied through phase portraits, bifurcation diagrams, Lyapunov exponents, and a two-parameter diagram. Furthermore, hardware circuit experiments are carried out to demonstrate theoretical analyses and numerical simulations. From the perspective of engineering application, a pseudo-random number generator is designed. Besides, an image encryption application and security analysis are also performed. The obtained results show that the memristive HR neuron model possesses excellent randomness and high security, which is suitable for chaos-based real-world applications.

Dynamics of a fractional epidemiological model with disease infection in both the populations.

Abstract: In order to depict a situation of possible spread of infection from prey to predator, a fractional-order model is developed and its dynamics is surveyed in terms of boundedness, uniqueness, and existence of the solutions. We introduce several threshold parameters to analyze various points of equilibrium of the projected model, and in terms of these threshold parameters, we have derived some conditions for the stability of these equilibrium points. Global stability of axial, predator-extinct, and disease-free equilibrium points are investigated. Novelty of this model is that fractional derivative is incorporated in a system where susceptible predators get the infection from preys while predating as well as from infected predators and both infected preys and predators do not reproduce. The occurrences of transcritical bifurcation for the proposed model are investigated. By finding the basic reproduction number, we have investigated whether the disease will become prevalent in the environment. We have shown that the predation of more number of diseased preys allows us to eliminate the disease from the environment, otherwise the disease would have remained endemic within the prey population. We notice that the fractional-order derivative has a balancing impact and it assists in administering the co-existence among susceptible prey, infected prey, susceptible predator, and infected predator populations. Numerical computations are conducted to strengthen the theoretical findings.

On explaining the surprising success of reservoir computing forecaster of chaos? The universal machine learning dynamical system with contrast to VAR and DMD.

Abstract: Machine learning has become a widely popular and successful paradigm, especially in data-driven science and engineering. A major application problem is data-driven forecasting of future states from a complex dynamical system. Artificial neural networks have evolved as a clear leader among many machine learning approaches, and recurrent neural networks are considered to be particularly well suited for forecasting dynamical systems. In this setting, the echo-state networks or reservoir computers (RCs) have emerged for their simplicity and computational complexity advantages. Instead of a fully trained network, an RC trains only readout weights by a simple, efficient least squares method. What is perhaps quite surprising is that nonetheless, an RC succeeds in making high quality forecasts, competitively with more intensively trained methods, even if not the leader. There remains an unanswered question as to why and how an RC works at all despite randomly selected weights. To this end, this work analyzes a further simplified RC, where the internal activation function is an identity function. Our simplification is not presented for the sake of tuning or improving an RC, but rather for the sake of analysis of what we take to be the surprise being not that it does not work better, but that such random methods work at all. We explicitly connect the RC with linear activation and linear readout to well developed time-series literature on vector autoregressive (VAR) averages that includes theorems on representability through the Wold theorem, which already performs reasonably for short-term forecasts. In the case of a linear activation and now popular quadratic readout RC, we explicitly connect to a nonlinear VAR, which performs quite well. Furthermore, we associate this paradigm to the now widely popular dynamic mode decomposition; thus, these three are in a sense different faces of the same thing. We illustrate our observations in terms of popular benchmark examples including Mackey–Glass differential delay equations and the Lorenz63 system.

Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity.

Abstract: We develop and test machine learning techniques for successfully using past state time series data and knowledge of a time-dependent system parameter to predict the evolution of the “climate” associated with the long-term behavior of a non-stationary dynamical system, where the non-stationary dynamical system is itself unknown. By the term climate, we mean the statistical properties of orbits rather than their precise trajectories in time. By the term non-stationary, we refer to systems that are, themselves, varying with time. We show that our methods perform well on test systems predicting both continuous gradual climate evolution as well as relatively sudden climate changes (which we refer to as “regime transitions”). We consider not only noiseless (i.e., deterministic) non-stationary dynamical systems, but also climate prediction for non-stationary dynamical systems subject to stochastic forcing (i.e., dynamical noise), and we develop a method for handling this latter case. The main conclusion of this paper is that machine learning has great promise as a new and highly effective approach to accomplishing data driven prediction of non-stationary systems.

Rogue waves for the fourth-order nonlinear Schrödinger equation on the periodic background.

Abstract: In this paper, we construct rogue wave solutions on the periodic background for the fourth-order nonlinear Schrodinger (NLS) equation. First, we consider two types of the Jacobi elliptic function solutions, i.e., dn- and cn-function solutions. Both dn- and cn-periodic waves are modulationally unstable with respect to the long-wave perturbations. Second, on the background of both periodic waves, we derive rogue wave solutions by combining the method of nonlinearization of spectral problem with the Darboux transformation method. Furthermore, by the study of the dynamics of rogue waves, we find that they have the analogs in the standard NLS equation, and the higher-order effects do not have effect on the magnification factor of rogue waves. In addition, when the elliptic modulus approaches 1, rogue wave solutions can reduce to multi-pole soliton solutions in which the interacting solitons form weakly bound states.

Reduced-order models for coupled dynamical systems: Data-driven methods and the Koopman operator.

Abstract: Providing efficient and accurate parameterizations for model reduction is a key goal in many areas of science and technology. Here, we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal perturbation expansions of the Koopman operator allow us to derive general stochastic parameterizations of weakly coupled dynamical systems. Such parameterizations yield a set of stochastic integrodifferential equations with explicit noise and memory kernel formulas to describe the effects of unresolved variables. We show that the perturbation expansions involved need not be truncated when the coupling is additive. The unwieldy integrodifferential equations can be recast as a simpler multilevel Markovian model, and we establish an intuitive connection with a generalized Langevin equation. This connection helps setting up a parallelism between the top-down, equation-based methodology herein and the well-established empirical model reduction (EMR) methodology that has been shown to provide efficient dynamical closures to partially observed systems. Hence, our findings, on the one hand, support the physical basis and robustness of the EMR methodology and, on the other hand, illustrate the practical relevance of the perturbative expansion used for deriving the parameterizations.

Using data assimilation to train a hybrid forecast system that combines machine-learning and knowledge-based components

Abstract: We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data are in the form of noisy partial measurements of the past and present state of the dynamical system. Recently, there have been several promising data-driven approaches to forecasting of chaotic dynamical systems using machine learning. Particularly promising among these are hybrid approaches that combine machine learning with a knowledge-based model, where a machine-learning technique is used to correct the imperfections in the knowledge-based model. Such imperfections may be due to incomplete understanding and/or limited resolution of the physical processes in the underlying dynamical system, e.g., the atmosphere or the ocean. Previously proposed data-driven forecasting approaches tend to require, for training, measurements of all the variables that are intended to be forecast. We describe a way to relax this assumption by combining data assimilation with machine learning. We demonstrate this technique using the Ensemble Transform Kalman Filter to assimilate synthetic data for the three-variable Lorenz 1963 system and for the Kuramoto–Sivashinsky system, simulating a model error in each case by a misspecified parameter value. We show that by using partial measurements of the state of the dynamical system, we can train a machine-learning model to improve predictions made by an imperfect knowledge-based model.

Many-body quantum chaos and dual-unitarity round-a-face

Abstract: We propose a new type of locally interacting quantum circuits—quantum cellular automata—that are generated by unitary interactions round-a-face (IRF). Specifically, we discuss a set (or manifold) of dual-unitary IRFs with local Hilbert space dimension d [DUIRF (d)], which generate unitary evolutions both in space and time directions of an extended 1+1 dimensional lattice. We show how arbitrary dynamical correlation functions of local observables can be evaluated in terms of finite-dimensional completely positive trace preserving unital maps in complete analogy to recently studied circuits made of dual-unitary brick gates (DUBGs). The simplest non-vanishing local correlation functions in dual-unitary IRF circuits are shown to involve observables non-trivially supported on two neighboring sites. We completely characterize the ten-dimensional manifold of DUIRF (2) for qubits ( d=2) and provide, for d=3,4,…,7, empirical estimates of its dimensionality based on numerically determined dimensions of tangent spaces at an ensemble of random instances of dual-unitary IRF gates. In parallel, we apply the same algorithm to determine dimDUBG(d) and show that they are of similar order though systematically larger than dimDUIRF(d) for d=2,3,…,7. It is remarkable that both sets have a rather complex topology for d≥3 in the sense that the dimension of the tangent space varies among different randomly generated points of the set. Finally, we provide additional data on dimensionality of the chiral extension of DUBG circuits with distinct local Hilbert spaces of dimensions d≠d′ residing at even/odd lattice sites.

Efficiency of communities and financial markets during the 2020 pandemic.

Abstract: This paper investigates the relationship between the spread of the COVID-19 pandemic, the state of community activity, and the financial index performance across 20 countries. First, we analyze which countries behaved similarly in 2020 with respect to one of three multivariate time series: daily COVID-19 cases, Apple mobility data, and national equity index price. Next, we study the trajectories of all three of these attributes in conjunction to determine which exhibited greater similarity. Finally, we investigate whether country financial indices or mobility data responded more quickly to surges in COVID-19 cases. Our results indicate that mobility data and national financial indices exhibited the most similarity in their trajectories, with financial indices responding quicker. This suggests that financial market participants may have interpreted and responded to COVID-19 data more efficiently than governments. Furthermore, results imply that efforts to study community mobility data as a leading indicator for financial market performance during the pandemic were misguided.

Effects of temperature and ion channel blocks on propagation of action potential in myelinated axons.

Abstract: Potassium ion and sodium ion channels play important roles in the propagation of action potentials along a myelinated axon. The random opening and closing of ion channels can cause the fluctuation of action potentials. In this paper, an improved Hodgkin–Huxley chain network model is proposed to study the effects of ion channel blocks, temperature, and ion channel noise on the propagation of action potentials along the myelinated axon. It is found that the chain network has minimum coupling intensity threshold and maximum tolerance temperature threshold that allow the action potentials to pass along the whole axon, and the blockage of ion channels can change these two thresholds. A striking result is that the simulated value of the optimum membrane size (inversely proportional to noise intensity) coincides with the area range of feline thalamocortical relay cells in biological experiments.

Consensus on simplicial complexes: Results on stability and synchronization

Abstract: We consider a nonlinear flow on simplicial complexes related to the simplicial Laplacian and show that it is a generalization of various consensus and synchronization models commonly studied on networks. In particular, our model allows us to formulate flows on simplices of any dimension so that it includes edge flows, triangle flows, etc. We show that the system can be represented as the gradient flow of an energy functional and use this to deduce the stability of various steady states of the model. Finally, we demonstrate that our model contains higher-dimensional analogs of structures seen in related network models.

Collective behavior in a two-layer neuronal network with time-varying chemical connections that are controlled by a Petri net.

Abstract: In this paper, we propose and study a two-layer network composed of a Petri net in the first layer and a ring of coupled Hindmarsh–Rose neurons in the second layer. Petri nets are appropriate platforms not only for describing sequential processes but also for modeling information circulation in complex systems. Networks of neurons, on the other hand, are commonly used to study synchronization and other forms of collective behavior. Thus, merging both frameworks into a single model promises fascinating new insights into neuronal collective behavior that is subject to changes in network connectivity. In our case, the Petri net in the first layer manages the existence of excitatory and inhibitory links among the neurons in the second layer, thereby making the chemical connections time-varying. We focus on the emergence of different types of collective behavior in the model, such as synchronization, chimeras, and solitary states, by considering different inhibitory and excitatory tokens in the Petri net. We find that the existence of only inhibitory or excitatory tokens disturbs the synchronization of electrically coupled neurons and leads toward chimera and solitary states.

Neuron-like spiking and bursting in Josephson junctions: A review

Abstract: The superconducting Josephson junction shows spiking and bursting behaviors, which have similarities with neuronal spiking and bursting. This phenomenon had been observed long ago by some researchers; however, they overlooked the biological similarity of this particular dynamical feature and never attempted to interpret it from the perspective of neuronal dynamics. In recent times, the origin of such a strange property of the superconducting junction has been explained and such neuronal functional behavior has also been observed in superconducting nanowires. The history of this research is briefly reviewed here with illustrations from studies of two junction models and their dynamical interpretation in the sense of biological bursting.

Fractional-calculus analysis of the transmission dynamics of the dengue infection.

Abstract: In this research paper, a novel approach in dengue modeling with the asymptomatic carrier and reinfection via the fractional derivative is suggested to deeply interrogate the comprehensive transmission phenomena of dengue infection. The proposed system of dengue infection is represented in the Liouville–Caputo fractional framework and investigated for basic properties, that is, uniqueness, positivity, and boundedness of the solution. We used the next-generation technique in order to determine the basic reproduction number R 0 for the suggested model of dengue infection; moreover, we conduct a sensitivity test of R 0 through a partial rank correlation coefficient technique to know the contribution of input factors on the output of R 0. We have shown that the infection-free equilibrium of dengue dynamics is globally asymptomatically stable for R 0 < 1 and unstable in other circumstances. The system of dengue infection is then structured in the Atangana–Baleanu framework to represent the dynamics of dengue with the non-singular and non-local kernel. The existence and uniqueness of the solution of the Atangana–Baleanu fractional system are interrogated through fixed-point theory. Finally, we present a novel numerical technique for the solution of our fractional-order system in the Atangana–Baleanu framework. We obtain numerical results for different values of fractional-order ϑ and input factors to highlight the consequences of fractional-order ϑ and input parameters on the system. On the basis of our analysis, we predict the most critical parameters in the system for the elimination of dengue infection.

Mitigating long transient time in deterministic systems by resetting.

Abstract: How long does a trajectory take to reach a stable equilibrium point in the basin of attraction of a dynamical system? This is a question of quite general interest and has stimulated a lot of activities in dynamical and stochastic systems where the metric of this estimation is often known as the transient or first passage time. In nonlinear systems, one often experiences long transients due to their underlying dynamics. We apply resetting or restart, an emerging concept in statistical physics and stochastic process, to mitigate the detrimental effects of prolonged transients in deterministic dynamical systems. We show that resetting the intrinsic dynamics intermittently to a spatial control line that passes through the equilibrium point can dramatically expedite its completion, resulting in a huge reduction in mean transient time and fluctuations around it. Moreover, our study reveals the emergence of an optimal restart time that globally minimizes the mean transient time. We corroborate the results with detailed numerical studies on two canonical setups in deterministic dynamical systems, namely, the Stuart–Landau oscillator and the Lorenz system. The key features—expedition of transient time—are found to be very generic under different resetting strategies. Our analysis opens up a door to control the mean and fluctuations in transient time by unifying the original dynamics with an external stochastic or periodic timer and poses open questions on the optimal way to harness transients in dynamical systems.

Enhanced logical chaotic resonance.

Abstract: It was demonstrated recently that logical chaotic resonance (LCR) can be observed in a bistable system. In other words, the system can operate robustly as a specific logic gate in an optimal window of chaotic signal intensity. Here, we report that the size of the optimal window of chaotic signal intensity can be remarkably extended by exploiting the constructive interaction of chaotic signal and periodic force, as well as coupling, in a coupled bistable system. In addition, medium-frequency periodic force and an increasing system size can also lead to an improvement in the response speed of logic devices. The results are corroborated by circuit experiments. Taken together, a reliable and rapid-response logic operation can be realized based on periodic force- and array-enhanced LCR.

Optimized ensemble deep learning framework for scalable forecasting of dynamics containing extreme events

Abstract: The remarkable flexibility and adaptability of both deep learning models and ensemble methods have led to the proliferation for their application in understanding many physical phenomena. Traditionally, these two techniques have largely been treated as independent methodologies in practical applications. This study develops an optimized ensemble deep learning framework wherein these two machine learning techniques are jointly used to achieve synergistic improvements in model accuracy, stability, scalability, and reproducibility, prompting a new wave of applications in the forecasting of dynamics. Unpredictability is considered one of the key features of chaotic dynamics; therefore, forecasting such dynamics of nonlinear systems is a relevant issue in the scientific community. It becomes more challenging when the prediction of extreme events is the focus issue for us. In this circumstance, the proposed optimized ensemble deep learning (OEDL) model based on a best convex combination of feed-forward neural networks, reservoir computing, and long short-term memory can play a key role in advancing predictions of dynamics consisting of extreme events. The combined framework can generate the best out-of-sample performance than the individual deep learners and standard ensemble framework for both numerically simulated and real-world data sets. We exhibit the outstanding performance of the OEDL framework for forecasting extreme events generated from a Lienard-type system, prediction of COVID-19 cases in Brazil, dengue cases in San Juan, and sea surface temperature in the Nino 3.4 region.

Transition paths of marine debris and the stability of the garbage patches.

Abstract: We used transition path theory (TPT) to infer “reactive” pathways of floating marine debris trajectories. The TPT analysis was applied on a pollution-aware time-homogeneous Markov chain model constructed from trajectories produced by satellite-tracked undrogued buoys from the National Oceanic and Atmospheric Administration's Global Drifter Program. The latter involved coping with the openness of the system in physical space, which further required an adaptation of the standard TPT setting. Directly connecting pollution sources along coastlines with garbage patches of varied strengths, the unveiled reactive pollution routes represent alternative targets for ocean cleanup efforts. Among our specific findings we highlight: constraining a highly probable pollution source for the Great Pacific garbage patch; characterizing the weakness of the Indian Ocean gyre as a trap for plastic waste; and unveiling a tendency of the subtropical gyres to export garbage toward the coastlines rather than to other gyres in the event of anomalously intense winds.

Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing.

Abstract: Reservoir computers are powerful tools for chaotic time series prediction. They can be trained to approximate phase space flows and can thus both predict future values to a high accuracy and reconstruct the general properties of a chaotic attractor without requiring a model. In this work, we show that the ability to learn the dynamics of a complex system can be extended to systems with multiple co-existing attractors, here a four-dimensional extension of the well-known Lorenz chaotic system. We demonstrate that a reservoir computer can infer entirely unexplored parts of the phase space; a properly trained reservoir computer can predict the existence of attractors that were never approached during training and, therefore, are labeled as unseen. We provide examples where attractor inference is achieved after training solely on a single noisy trajectory.

Effect of magnetic induction on the synchronizability of coupled neuron network.

Abstract: Master stability functions (MSFs) are significant tools to identify the synchronizability of nonlinear dynamical systems. For a network of coupled oscillators to be synchronized, the corresponding MSF should be negative. The study of MSF will normally be discussed considering the coupling factor as a control variable. In our study, we considered various neuron models with electromagnetic flux induction and investigated the MSF’s zero-crossing points for various values of the flux coupling coefficient. Our numerical analysis has shown that in all the neuron models we considered, flux coupling has increased the synchronization of the coupled neuron by increasing the number of zero-crossing points of MSFs or by achieving a zero-crossing point for a lesser value of a coupling parameter.

Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions

Abstract: The role of a new form of dynamic interaction is explored in a network of generic identical oscillators. The proposed design of dynamic coupling facilitates the onset of a plethora of asymptotic states including synchronous states, amplitude death states, oscillation death states, a mixed state (complete synchronized cluster and small amplitude desynchronized domain), and bistable states (coexistence of two attractors). The dynamical transitions from the oscillatory to the death state are characterized using an average temporal interaction approximation, which agrees with the numerical results in temporal interaction. A first-order phase transition behavior may change into a second-order transition in spatial dynamic interaction solely depending on the choice of initial conditions in the bistable regime. However, this possible abrupt first-order like transition is completely non-existent in the case of temporal dynamic interaction. Besides the study on periodic Stuart–Landau systems, we present results for the paradigmatic chaotic model of Rossler oscillators and the MacArthur ecological model.

A 2D hyperchaotic map with conditional symmetry and attractor growth.

Abstract: By introducing trigonometric functions, a 2D hyperchaotic map with conditional symmetric attractors is constructed, where a symmetric pair of hyperchaotic attractors and asymmetric hyperchaotic attractors is found. For the existence of periodic feedback, the newly proposed map also exhibits attractor growth under specific circumstances. The polarity balance of the discrete map can be restored from the applied sinusoidal functions, combined with an extra inversion of the constant term. To the best of our knowledge, the above properties are not found in other chaotic maps. Finally, the hardware implementation based on STM32 is conducted, and the corresponding results agree with the numerical simulation and the theoretical analysis.

Simplicial SIRS epidemic models with nonlinear incidence rates.

Abstract: Mathematical epidemiology that describes the complex dynamics on social networks has become increasingly popular. However, a few methods have tackled the problem of coupling network topology with complex incidence mechanisms. Here, we propose a simplicial susceptible-infected-recovered-susceptible (SIRS) model to investigate the epidemic spreading via combining the network higher-order structure with a nonlinear incidence rate. A network-based social system is reshaped to a simplicial complex, in which the spreading or infection occurs with nonlinear reinforcement characterized by the simplex dimensions. Compared with the previous simplicial susceptible-infected-susceptible (SIS) models, the proposed SIRS model can not only capture the discontinuous transition and the bistability of a complex system but also capture the periodic phenomenon of epidemic outbreaks. More significantly, the two thresholds associated with the bistable region and the critical value of the reinforcement factor are derived. We further analyze the stability of equilibrium points of the proposed model and obtain the condition of existence of the bistable states and limit cycles. This work expands the simplicial SIS models to SIRS models and sheds light on a novel perspective of combining the higher-order structure of complex systems with nonlinear incidence rates.

The impact of non-pharmaceutical interventions on the prevention and control of COVID-19 in New York City.

Abstract: The emergence of coronavirus disease 2019 (COVID-19) has infected more than 62 million people worldwide Control responses varied across countries with different outcomes in terms of epidemic size and social disruption This study presents an age-specific susceptible-exposed-infected-recovery-death model that considers the unique characteristics of COVID-19 to examine the effectiveness of various non-pharmaceutical interventions (NPIs) in New York City (NYC) Numerical experiments from our model show that the control policies implemented in NYC reduced the number of infections by 72% [interquartile range (IQR) 53-95] and the number of deceased cases by 76% (IQR 58-96) by the end of 2020 Among all the NPIs, social distancing for the entire population and protection for the elderly in public facilities is the most effective control measure in reducing severe infections and deceased cases School closure policy may not work as effectively as one might expect in terms of reducing the number of deceased cases Our simulation results provide novel insights into the city-specific implementation of NPIs with minimal social disruption considering the locations and population characteristics

Random-matrix theory for the Lindblad master equation.

Abstract: Open quantum systems with Markovian dynamics can be described by the Lindblad equation The quantity governing the dynamics is the Lindblad superoperator We apply random-matrix theory to this superoperator to elucidate its spectral properties The distribution of eigenvalues and the correlations of neighboring eigenvalues are obtained for the cases of purely unitary dynamics, pure dissipation, and the physically realistic combination of unitary and dissipative dynamics

Identifying influential nodes: A new method based on network efficiency of edge weight updating

Abstract: Identification of influential nodes in complex networks is an area of exciting growth since it can help us to deal with various problems. Furthermore, identifying important nodes can be used across various disciplines, such as disease, sociology, biology, engineering, just to name a few. Hence, how to identify influential nodes more accurately deserves further research. Traditional identification methods usually only focus on the local or global information of the network. However, only focusing on a part of the information in the network will lead to the loss of information, resulting in inaccurate results. In order to address this problem, an identification method based on network efficiency of edge weight updating is proposed, which can effectively incorporate both global and local information of the network. Our proposed method avoids the lack of information in the network and ensures the accuracy of the results as much as possible. Moreover, by introducing the iterative idea of weight updating, some dynamic information is also introduced into our proposed method, which is more convincing. Varieties of experiments have been carried out on 11 real-world data sets to demonstrate the effectiveness and superiority of our proposed method.

Multistability analysis and nonlinear vibration for generator set in series hybrid electric vehicle through electromechanical coupling.

Abstract: The non-linear analysis of undesired vibrations observed on hybrid electric vehicle (HEV) powertrains is hardly developed in the literature. In this paper, a mathematical modeling of the vibrations observed at the level of the electromechanical coupling between the internal combustion engine and the generator in the series architecture of HEVs, named (SHEVs), is established using the Lagrangian theory. The stability and instability motions of this SHEV are perfectly detailed using amplitude–frequency response curves. An analysis of the electromagnetic torque amplitude of the new SHEV demonstrates the presence of multistability with the coexistence of two or three different types of attractors. In addition, this new SHEV model has other dynamic regimes of chaotic and periodic oscillations. Coexisting bifurcations with parallel branches, hysteresis, and period-doubling are also discovered. A unique contribution of this work is the abundance and complicated dynamical behaviors found in such types of systems compared with some rare cases previously reported on HEV powertrain models. The simulation results obtained using non-linear analysis tools sufficiently demonstrate that the objectives of this paper are achieved.

Homological percolation transitions in growing simplicial complexes

Abstract: Simplicial complex (SC) representation is an elegant mathematical framework for representing the effect of complexes or groups with higher-order interactions in a variety of complex systems ranging from brain networks to social relationships. Here, we explore the homological percolation transitions (HPTs) of growing SCs using empirical datasets and model studies. The HPTs are determined by the first and second Betti numbers, which indicate the appearance of one- and two-dimensional macroscopic-scale homological cycles and cavities, respectively. A minimal SC model with two essential factors, namely, growth and preferential attachment, is proposed to model social coauthorship relationships. This model successfully reproduces the HPTs and determines the transition types as an infinite-order Berezinskii–Kosterlitz–Thouless type but with different critical exponents. In contrast to the Kahle localization observed in static random SCs, the first Betti number continues to increase even after the second Betti number appears. This delocalization is found to stem from the two aforementioned factors and arises when the merging rate of two-dimensional simplexes is less than the birth rate of isolated simplexes. Our results can provide a topological insight into the maturing steps of complex networks such as social and biological networks.