Random Perturbations Research Articles

A Topological Investigation of the Cosmic Web Formation

N-body simulations of the evolution of the large-scale structure of the universe (the Cosmic Web) were run while altering attractive gravity laws and initial conditions, in order to infer which properties of the universe are revealed by its current large-scale topology. The Cosmic Web was found to develop regardless of the gravitational alteration made. Significantly altering the initial conditions from Gaussian distribution ones was found to eliminate the Cosmic Web. Thus, we require small random perturbations in otherwise uniform initial conditions in the early universe, under an attractive gravitational force, for the Cosmic Web to develop.

New insights into the prediction for the potential of soil organic carbon accumulation: From the perspective of non-equilibrium statistical mechanics

The accumulation of soil organic carbon (SOC) is significant for soil health and ecosystem services. Numerous studies have assessed the dynamic changes of SOC by considering the microbial system as an equilibrium system. However, they failed to reveal the complexity of the SOC accumulation/loss process, as the microbial system is a non-equilibrium system affected by stochastic fluctuations from the external environment. This study is the first to explore the complex non-equilibrium relationship between microbial carbon use efficiency (CUE) and SOC by using potential landscape and flux in non-equilibrium statistical mechanics. Nitrogen (N) was identified as the most critical environmental factor influencing CUE on a global scale, with the transition between the carbon loss state and the carbon sequestration state observed along N gradients. Random perturbations of other environmental factors could also trigger transition. Non-equilibrium thermodynamic quantities indicated that carbon sequestration had the potential to be achieved when N = 0.5 g/kg, where active soil management measures should be taken. Furthermore, the non-equilibrium relationship between CUE and SOC was clarified through potential energy analysis, where the average deviation between predictions and actual observations of SOC is about 1.9792 g/kg. This study provides an effective framework for predicting SOC accumulation.

An enhanced competitive swarm optimizer with strongly robust sparse operator for large-scale sparse multi-objective optimization problem

In the real world, the decision variables of large-scale sparse multi-objective problems are high-dimensional, and most Pareto optimal solutions are sparse. The balance of the algorithms is difficult to control, so it is challenging to deal with such problems in general. Therefore, An Enhanced Competitive Swarm Optimizer with Strongly Robust Sparse Operator (SR-ECSO) algorithm is proposed. Firstly, the strongly robust sparse functions which accelerate particles in the population better sparsity in decision space, are used in high-dimensional decision variables. Secondly, the diversity of sparse solutions is maintained, and the convergence balance of the algorithm is enhanced by the introduction of an adaptive random perturbation operator. Finally, the state of the particles is updated using a swarm optimizer to improve population competitiveness. To verify the proposed algorithm, we tested eight large-scale sparse benchmark problems, and the decision variables were set in three groups with 100, 500, and 1000 as examples. Experimental results show that the algorithm is promising for solving large-scale sparse optimization problems.

Divided Attention Has Limited Effects on Speech Sensorimotor Control.

When vowel formants are externally perturbed, speakers change their production to oppose that perturbation both during the ongoing production (compensation) and in future productions (adaptation). To date, attempts to explain the large variability across individuals in these responses have focused on trait-based characteristics such as auditory acuity, but evidence from other motor domains suggests that attention may modulate the motor response to sensory perturbations. Here, we test the extent to which divided attention impacts sensorimotor control for supralaryngeal articulation. Neurobiologically healthy speakers were exposed to random (Experiment 1) or consistent (Experiment 2) real-time auditory perturbation of vowel formants to measure online compensation and trial-to-trial adaptation, respectively. In both experiments, participants completed two conditions: one with a simultaneous visual distractor task to divide attention and one without this secondary task. Divided visual attention slightly reduced online compensation, but only starting > 300 ms after vowel onset, well beyond the typical duration of vowels in speech. Divided attention had no effect on adaptation. The results from both experiments suggest that the use of sensory feedback in typical speech motor control is a largely automatic process unaffected by divided visual attention, suggesting that the source of cross-speaker variability in response to formant perturbations likely lies within the speech production system rather than in higher-level cognitive processes. Methodologically, these results suggest that compensation for formant perturbations should be measured prior to 300 ms after vowel onset to avoid any potential impact of attention or other higher-order cognitive factors.

Deep deterministic policy gradient caching method for privacy protection in Internet of Vehicles

To address the problem of low cache hit ratio in edge nodes for privacy-preserving in the Internet of Vehicles (IoV), a deep deterministic policy gradient caching (DDPGC) method was proposed. First, a taxi certified by a trusted authority acted as a second-level caching edge node to acquire hotspot data and store it in the local cache. It then broadcasted this information to the neighboring service requesting vehicles (SRVs). SRVs cached the broadcasted data locally and search for service requests in the order of priority of local cache, taxi, and cloud server when such requests arise. Secondly, a neural network was deployed in taxis and SRVs to maximize the caching benefit through deep reinforcement learning for decision replacement of their cached data. Finally, when SRVs were located in vehicle sparsity and could not obtain request data from neighboring vehicles, a combination of k-anonymity and random response perturbation mechanisms generated anonymity sets to send requests to cloud servers in an anonymous manner to obtain services while protecting user location privacy. Simulation experimental results show that DDPGC can effectively improve the vehicle cache hit ratio, reduce the frequency of SRV interaction with the cloud server, and effectively protect user privacy security.

Gorilla algorithm based on double random perturbation and its engineering application

Aiming at the problems of artificial gorilla troop optimization algorithm, such as easy to fall into local optimum, slow convergence speed and low optimization accuracy, an artificial gorilla troop optimization algorithm based on double random perturbation strategy is proposed. Firstly, the Halton sequence is introduced to initialize the population to increase the diversity of the population; secondly, a multi-dimensional random number strategy is used in the algorithm optimization stage and an adaptive position search mechanism is proposed in the exploration stage to improve the convergence speed of the algorithm; thirdly, a double random perturbation strategy is proposed to solve the group effect of gorillas and enhance the ability of the algorithm to jump out of the local optimum; finally, a dimension-by-dimensional update strategy is adopted to update individual positions, which improves the convergence accuracy of the algorithm. Through the comparison of the optimization results of 10 benchmark test functions and the Wilcoxon rank sum test, it can be seen that the improved algorithm has greatly improved the optimization accuracy and convergence speed. In addition, through the experimental comparative analysis of an engineering optimization problem, the superiority of the proposed algorithm in dealing with real engineering problems is further verified.

Fractional Tikhonov regularization and error estimation in inverse source problems for Biharmonic equations: a priori and a posteriori analysis under deterministic and random perturbations

Fractional Tikhonov regularization and error estimation in inverse source problems for Biharmonic equations: a priori and a posteriori analysis under deterministic and random perturbations

Zigzag instability of columnar Taylor–Green vortices in a strongly stratified fluid

We investigate the dynamics of a columnar Taylor–Green vortex array under strong stratification, focusing on Froude numbers $0.125\leq Fr \leq 1.0$ , with the aim of identifying and understanding the primary instabilities that lead to the vortices’ breakdown. Linear stability analysis reveals that the fastest-growing vertical wavenumber scales with $Fr^{-1}$ , while the dimensionless growth rate remains approximately constant. The most unstable eigenmode, identified as the mixed hyperbolic mode by Hattori et al. (J. Fluid Mech., vol. 909, 2021, A4), bears significant similarities to the zigzag instability, first discovered by Billant & Chomaz (J. Fluid Mech., vol. 418, 2000, pp. 167–188). Direct numerical simulations further confirm that the zigzag instability is crucial in amplifying initial random perturbations to finite amplitude, with the flow structure and modal growth rate consistent with the linear stability analysis. In particular, the characteristic vertical length scale of turbulence matches that of the fastest-growing linear mode. These findings underscore the broader relevance of the zigzag instability mechanism beyond its initial discovery in vortex pairs, demonstrating its role in facilitating direct energy transfer from vertically uniform vortical motions to a characteristic vertical length scale proportional to $Fr$ in strongly stratified flows.

Emergence of extreme events from randomly chirped condensate

We explore rogue wave emergence in generic wave systems governed by the nonlinear Schrödinger equation. We highlight the interplay between the stochastic focusing induced by a random chirp of a continuous wave condensate and modulation instability of the condensate to periodic and/or random perturbations. We show that regardless of its statistical properties, the random chirp of the condensate leads to a non-Gaussian, heavy-tailed probability density distribution of peak powers of the waves excited atop of the condensate, which is a statistical signature of rogue waves, or more broadly, extreme events in physics.

Stochastic Optimal Control Analysis for HBV Epidemic Model with Vaccination

In this study, we explore the concept of symmetry as it applies to the dynamics of the Hepatitis B Virus (HBV) epidemic model. By incorporating symmetric principles in the stochastic model, we ensure that the control strategies derived are not only effective but also consistent across varying conditions, and ensure the reliability of our predictions. This paper presents a stochastic optimal control analysis of an HBV epidemic model, incorporating vaccination as a pivotal control measure. We formulate a stochastic model to capture the complex dynamics of HBV transmission and its progression to acute and chronic stages. By leveraging stochastic differential equations, we examine the model’s stationary distribution and asymptotic behavior, elucidating the impact of random perturbations on disease dynamics. Optimal control theory is employed to derive control strategies aimed at minimizing the disease burden and vaccination costs. Through rigorous numerical simulations using the fourth-order Runge–Kutta method, we demonstrate the efficacy of the proposed control measures. Our findings highlight the critical role of vaccination in controlling HBV spread and provide insights into the optimization of vaccination strategies under stochastic conditions. The symmetry within the proposed model equations allows for a balanced approach to analyzing both acute and chronic stages of HBV.

An improved whale optimization algorithm for UAV swarm trajectory planning

For the problem of trajectory planning in the small-scale unmanned aerial vehicle (UAV) swarms, classical intelligent algorithms and newly emerged bio-inspired algorithms often suffer from being trapped in local optima, leading to suboptimal solutions. Moreover, these algorithms fail to ensure optimal solutions and convergence speed in high-speed dynamic UAV networking scenarios. In response to these challenges, this paper proposes an Improved Whale Optimization Algorithm (IWOA) that considers the global perspective. To address the issue of initial solution diversity, an opposition-based learning method is introduced by constructing a reverse population, enhancing the diversity of the initial population. To overcome the problem of the algorithm getting trapped in local optima, random convergence factors, and end-point random neighborhood perturbations are incorporated to accelerate the global convergence speed of the IWOA and prevent it from getting stuck in local optima. Additionally, a grid digital elevation model is employed when constructing the experimental environment model, considering various physical constraints of the UAV swarm. This ensures that the simulation validation of the IWOA algorithm is closer to real-world scenarios. Simulation results indicate that, compared to commonly used algorithms, the IWOA can generate more optimal trajectories for drone swarm planning under constraints resembling real-world scenarios. It exhibits better performance in trajectory evaluation, convergence speed, and stability, thereby meeting the requirements of trajectory planning for small-scale UAV swarms. The proposed IWOA enhances UAV swarm coordination and efficiency, significantly impacting real-world applications in various fields.

No Pulsar Timing Noise from Brownian Motion of the Sun

It was recently claimed that evidence for a stochastic gravitational wave background observed by pulsar timing arrays can be attributed instead to random perturbations of the Sun’s motion by transiting asteroids. I show that that this would lead to a large dipole component accompanying a much smaller quadrupolar perturbation of pulsar timing signals, which would not be confused with a gravitational wave signal. Such an anomalous dipole would have been detected and identified as a spurious background by the PTA collaborations, if it existed.

SIR models with vital dynamics, reinfection, and randomness to investigate the spread of infectious diseases

We investigate SIR models with vital dynamics, reinfection, and randomness at the transmission coefficient and recruitment rate. Initially, we conduct an extensive analysis of the autonomous scenario, covering aspects such as local and global well-posedness, the existence and internal structure of attractors, and the presence of gradient dynamics. Subsequently, we explore the implications of small nonautonomous random perturbations, establishing the continuity of attractors and ensuring their topological structural stability. Additionally, we study scenarios in which both the transmission coefficient and the recruitment rate exhibit time-dependent or random behavior. For each scenario, we establish the existence of attractors and delineate conditions that determine whether the disease is eradicated or reaches an endemic state. Finally, we depict numerical simulations to illustrate the theoretical results.

Stability of a Queue Fed by Scheduled Traffic at Critical Loading

Performance of a queueing system with scheduled arrivals A scheduled arrival sequence is one in which customers are scheduled to arrive at constant interarrival times, but each customer’s actual arrival time is perturbed from her scheduled arrival time by a random perturbation. In “Stability of a Queue Fed by Scheduled Traffic at Critical Loading”, V.F. Araman and P.W. Glynn consider a single server queue with deterministic service times in which customers arrive following a scheduled arrival process. Unlike a queue fed by renewal traffic, this queue is shown to be stable even when the utilization is equal to one. It is also shown that for finite mean perturbations, a necessary and sufficient condition for stability is when the positive part of the perturbation has bounded support, with no requirement on the negative part of the perturbation. Perhaps surprisingly, this criterion is not reversible, in the sense that such a queue can be stable for a scheduled traffic process in forward time, but unstable for the time-reversal of the same traffic process.

Prediction of Wind Turbine Gearbox Oil Temperature Based on Stochastic Differential Equation Modeling

Aiming at the problem of high failure rate and inconvenient maintenance of wind turbine gearboxes, this paper establishes a stochastic differential equation model that can be used to fit the change of gearbox oil temperature and adopts an iterative computational method and Markov-based modified optimization to fit the prediction sequence in order to realize the accurate prediction of gearbox oil temperature. The model divides the oil temperature change of the gearbox into two parts, internal aging and external random perturbation, adopts the approximation theorem to establish the internal aging model, and uses Brownian motion to simulate the external random perturbation. The model parameters were calculated by the Newton–Raphson iterative method based on the gearbox oil temperature monitoring data. Iterative calculations and Markov-based corrections were performed on the model prediction data. The gearbox oil temperature variations were simulated in MATLAB, and the fitting and testing errors were calculated before and after the iterations. By comparing the fitting and testing errors with the ordinary differential equations and the stochastic differential equations before iteration, the iterated model can better reflect the gear oil temperature trend and predict the oil temperature at a specific time. The accuracy of the iterated model in terms of fitting and prediction is important for the development of preventive maintenance.

Probabilistic Perturbation Bounds for Invariant, Deflating and Singular Subspaces

In this paper, we derive new probabilistic bounds on the sensitivity of invariant subspaces, deflation subspaces and singular subspaces of matrices. The analysis exploits a unified method for deriving asymptotic perturbation bounds of the subspaces under interest and utilizes probabilistic approximations of the entries of random perturbation matrices implementing the Markoff inequality. As a result of the analysis, we determine with a prescribed probability asymptotic perturbation bounds on the angles between the corresponding perturbed and unperturbed subspaces. It is shown that the probabilistic asymptotic bounds proposed are significantly less conservative than the corresponding deterministic perturbation bounds. The results obtained are illustrated by examples comparing the known deterministic perturbation bounds with the new probabilistic bounds.

Thermal convection subjected to perturbations from the bottom of a top open cavity

Perturbations are very common in the transition and heat transfer of thermal convection in nature and industry. Accordingly, thermal convection on a top-open cavity subjected to periodic and random perturbations is investigated using three-dimensional numerical simulation. A great number of numerical experiments are performed at various Rayleigh numbers and a fixed Prandtl number of 0.71 by introducing periodic and random numerical perturbations. Numerical results demonstrate that there exists the effect of periodic perturbations on the transition route over 3.5 × 103 ≤ Ra ≤ 8.5 × 104. That is, the transition route to chaos is sensitive to the amplitude of random perturbations for, e.g., 0.01 ≤ Ar ≤ 0.05, which is also characterized. Furthermore, heat transfer enhancement under periodic and random perturbations is quantified with the scaling law. This study sheds new light on the influence of periodic and random perturbations on thermal convection on the top-open cavity below heating. The possibility to control heat transfer is revealed by introducing random perturbations on the bottom of the top-open cavity.

Vector rogue waves in spin-1 Bose–Einstein condensates with spin–orbit coupling

Abstract We analytically and numerically study three-component rogue waves (RWs) in spin-1 Bose–Einstein condensates with Raman-induced spin–orbit coupling (SOC). Using the multiscale perturbative method, we obtain approximate analytical solutions for RWs with positive and negative effective masses, determined by the effective dispersion of the system. The solutions include RWs with smooth and striped shapes, as well as higher-order RWs. The analytical solutions demonstrate that the RWs in the three components of the system exhibit different velocities and their maximum peaks appear at the same spatiotemporal position, which is caused by SOC and interactions. The accuracy of the approximate analytical solutions is corroborated by comparison with direct numerical simulations of the underlying system. Additionally, we systematically explore existence domains for the RWs determined by the baseband modulational instability (BMI). Numerical simulations corroborate that, under the action of BMI, plane waves with random initial perturbations excite RWs, as predicted by the approximate analytical solutions.

COMPARACIÓN DEL RENDIMIENTO DE VARIOS ENFOQUES DE SOFT COMPUTING EN EL CONTROL DE LA FRECUENCIA DE CARGA PARA SISTEMAS ELÉCTRICOS INTERCONECTADOS QUE COMBINAN FUENTES TÉRMICAS-HIDRÁULICAS Y TÉRMICAS-DIÉSEL

Interconnected power systems offer a solution for meeting the increasing demand for reliable and efficient electricity supply. However, maintaining stability in such networks, especially in the face of frequency fluctuations, presents a significant challenge. Effective load frequency control (LFC) optimization is vital for ensuring stability by mitigating the impact of these fluctuations resulting from various disturbances. This study introduces PID LFC optimization strategies applied to a thermal-hydro and thermal-diesel interconnected power system. Six optimization methods, including ACO, PSO, GA, TLBO, DE, and CIO, are explored using four cost functions. Random step load perturbations are applied to test the response consistency of the LFCs. Initial findings indicate that recently developed CIO outperforms other algorithms in achieving desired outcomes while maintaining competitive computational expenses. Specifically, the CIO-ITAE optimized LFC demonstrates improved resilience in addressing challenges in the interconnected power system. Keywords: Load Frequency Control, LFC, Ant Colony Optimization (ACO), Differential Evolution (DE), Teaching Learning based Optimization (TLBO),Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Cohort Intelligence Optimization (CIO).

Stretched-exponential melting of a dynamically frozen state under imprinted phase noise in the ising chain in a transverse field

The concept of dynamical freezing is a phenomenon where a suitable set of local observables freezes under a strong periodic drive in a quantum many-body system. This happens because of the emergence of approximate but perpetual conservation laws when the drive is strong enough. In this work, we probe the resilience of dynamical freezing to random perturbations added to the relative phases between the interfering states (elements of a natural basis) in the time-evolving wave function after each drive cycle. We study this in an integrable Ising chain in a time-periodic transverse field. Our key finding is, that the imprinted phase noise melts the dynamically frozen state, but the decay is “slow”: a stretched-exponential decay rather than an exponential one. Stretched-exponential decays (also known as Kohlrausch relaxation) are usually expected in complex systems with time-scale hierarchies due to strong disorders or other inhomogeneities resulting in jamming, glassiness, or localization. Here we observe this in a simple translationally invariant system dynamically frozen under a periodic drive. Moreover, the melting here does not obliterate the entire memory of the initial state but leaves behind a steady remnant that depends on the initial conditions. This underscores the stability of dynamically frozen states.Graphical abstract