Random Perturbations Research Articles

Scalable synchronization cluster in networked chaotic oscillators.

Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the other oscillators remain desynchronized. Interestingly, with the increase in the coupling strength, the cluster is expanding gradually by recruiting the desynchronized oscillators one by one. This new synchronization phenomenon, which is named "scalable synchronization cluster," is explored theoretically by the method of eigenvector-based analysis, and it is revealed that the scalability of the cluster is attributed to the unique feature of the eigenvectors of the network coupling matrix. The transient dynamics of the cluster in response to random perturbations are also studied, and it is shown that in restoring to the synchronization state, oscillators inside the cluster are stabilized in sequence, illustrating again the hierarchy of the oscillators. The findings shed new light on the collective behaviors of networked chaotic oscillators and are helpful for the design of real-world networks where scalable synchronization clusters are concerned.

Measuring the substructure mass power spectrum of 23 SLACS strong galaxy–galaxy lenses with convolutional neural networks

ABSTRACT Strong gravitational lensing can be used as a tool for constraining the substructure in the mass distribution of galaxies. In this study we investigate the power spectrum of dark matter perturbations in a population of 23 Hubble Space Telescope images of strong galaxy–galaxy lenses selected from The Sloan Lens ACS (SLACS) survey. We model the dark matter substructure as a Gaussian random field perturbation on a smooth lens mass potential, characterized by power-law statistics. We expand upon the previously developed machine learning framework to predict the power-law statistics by using a convolutional neural network (CNN) that accounts for both epistemic and aleatoric uncertainties. For the training sets, we use the smooth lens mass potentials and reconstructed source galaxies that have been previously modelled through traditional fits of analytical and shapelet profiles as a starting point. We train three CNNs with different training set: the first using standard data augmentation on the best-fitting reconstructed sources, the second using different reconstructed sources spaced throughout the posterior distribution, and the third using a combination of the two data sets. We apply the trained CNNs to the SLACS data and find agreement in their predictions. Our results suggest a significant substructure perturbation favouring a high frequency power spectrum across our lens population.

Modeling the Effect of Random Environmental Perturbation on Data Precision in Niger Delta Crude Oil Production

Decision-makers most times rely on data precision to support their decision-making processes. There is also a strong belief, however, that data quality or data precision problems are widespread in practice and that reliance on poor data quality or wrong data sets can lead to devastating consequences on crude oil production and financing. This study applies the Runge-Kutta numerical method of order 45 (ordinary differential equation of order 45) to examine the effect of data precision index on the Niger Delta crude oil production due to the variation of the initial condition. The study has found out that the initial condition four (4), (IC 4) with a data precision index value of 0.0118 ranked best in the first crude oil well, the initial condition (IC) 15 with a data precision index value of 0.0021 ranked best in the second crude oil well, the initial condition (IC) 17 with a data precision index value of 0.0021 ranked best in the third crude oil well and the initial condition (IC) 20 with a data precision index value of 0.0234 ranked best in the fourth crude oil well. The study has observed that each crude oil data is associated with a best-fit-value of the data precision index.

A stochastic hormesis Ricker model and its application to multiple fields

Random noise pervades ecosystems and has the potential for having major impacts on the growth processes of pest populations. In this paper, we aim to investigate the impact of random perturbations on the hormesis Ricker model by considering control measures applied within each generation which can generate hormetic effects, where randomness is characterized by a uniform discrete distribution and white noise, respectively. The main results indicate that the addition of discrete randomness will make the model appear with blurred orbits when the intrinsic growth rate is large enough. The position of the random variable, at the end of each generation or within each generation, cause the blurred orbits to exhibit various forms. Moreover, the effects of variances and expectations of the discrete uniform random variable on the dynamics are evaluated. Further, the introduction of randomness increases the hormetic zone and the maximum response, but can increase or decrease the monotonically increasing interval under different parameter values. In contrast, the stochastic model characterized by white noise, exhibits only a small effect on the bifurcation diagrams with respect to the intrinsic growth rate and the hormesis, which may be attributed to the mean of its noise being zero. Finally, we fit the stochastic model to experimental hormetic data sets observed in multiple fields, and our results demonstrate that the stochastic hormesis Ricker model can capture the characteristics of these data accurately. These findings could provide valuable insights into the understanding of the complexities of pest population dynamics, with implications for better pest control, resource management and for other complex biological systems such as toxicology and drug development.

Robustness of reaction–diffusion PDEs predictor-feedback to stochastic delay perturbations

This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction–diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The stabilization problem under consideration involves random perturbations modeled by a finite-state Markov process that further obstruct the actuation path at the controlled boundary of the infinite-dimension plant. This scenario is useful to describe several actuation failure modes in process control. Employing the recently introduced infinite-dimensional representation of the state of an actuator subject to stochastic input delay for ODEs (Ordinary Differential Equations), we convert the stochastic input delay into r+1 unidirectional advection PDEs, where r corresponds to the number of jump states. Our stability analysis assumes full-state measurement of the spatially distributed plant’s state and relies on a hyperbolic–parabolic PDE-PDE cascade representation of the plant plus actuator dynamics. Integrating the plant and the nominal stabilizing boundary control action, all while considering probabilistic delay disturbances, we establish the proof of mean-square exponential stability as well as the well-posedness of the closed-loop system when random phenomena weaken the nominal actuator compensating effect. Our proof is based on the Lyapunov method, the theory of infinitesimal operator for stability, and C0-semigroup theory for well-posedness. Our stability result refers to the L2-norm of the plant state and the H2-norm of the actuator state. Furthermore, our study presents a qualitative analysis of the maximum deviation of the stochastic disturbance relative to the nominal delay, which is expressed as a function of the severity of the plant instability, namely, the magnitude of the reactivity coefficientand the known upper bound of the transition rate of the underlying stochastic perturbations. Extensive simulation results illustrate the viability of the robustness study.

Research on super-fitting phenomenon in sound quality prediction of silent chain transmission system

To predict the sound quality of silent chain transmission system, we propose a new data enhancement method called fuzzy generation. After enlarging the original dataset by fuzzy generation, we find that prediction model has an abnormal super-fitting phenomenon under certain conditions. In contrast to overfitting, super-fitting means that the model performs poorly on the training set but performs better on the test set. To further explore this super-fitting phenomenon, we firstly carry out a noise collection test of the silent chain transmission system. Secondly, the collected noise samples are evaluated subjectively and objectively. Based on the subjective evaluation results, we can establish the fuzzy generation interval for each sample. By selecting different membership values and different perturbation forms, the dataset is expanded three times. Training four different prediction models on the new datasets, we found that super-fitting is more likely to occur with linear perturbation. However, in the case of some membership values, the random perturbation can also lead to super-fitting. Through analyzing the prediction effect of the four models, we conclude that fuzzy generation can indeed significantly improve accuracy of model, and super-fitting is mainly caused by a special kind of data leakage. When using fuzzy generation to predict sound quality with small samples, appropriate membership value and perturbation form should be selected to avoid the occurrence of super-fitting.

Threshold-awareness in adaptive cancer therapy.

Although adaptive cancer therapy shows promise in integrating evolutionary dynamics into treatment scheduling, the stochastic nature of cancer evolution has seldom been taken into account. Various sources of random perturbations can impact the evolution of heterogeneous tumors, making performance metrics of any treatment policy random as well. In this paper, we propose an efficient method for selecting optimal adaptive treatment policies under randomly evolving tumor dynamics. The goal is to improve the cumulative "cost" of treatment, a combination of the total amount of drugs used and the total treatment time. As this cost also becomes random in any stochastic setting, we maximize the probability of reaching the treatment goals (tumor stabilization or eradication) without exceeding a pre-specified cost threshold (or a "budget"). We use a novel Stochastic Optimal Control formulation and Dynamic Programming to find such "threshold-aware" optimal treatment policies. Our approach enables an efficient algorithm to compute these policies for a range of threshold values simultaneously. Compared to treatment plans shown to be optimal in a deterministic setting, the new "threshold-aware" policies significantly improve the chances of the therapy succeeding under the budget, which is correlated with a lower general drug usage. We illustrate this method using two specific examples, but our approach is far more general and provides a new tool for optimizing adaptive therapies based on a broad range of stochastic cancer models.

DynGMA: A robust approach for learning stochastic differential equations from data

Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions, and construct likelihood-based loss by approximating the transition density to train these networks. However, these methods often rely on one-step stochastic numerical schemes, necessitating data with sufficiently high time resolution. In this paper, we introduce novel approximations to the transition density of the parameterized SDE: a Gaussian density approximation inspired by the random perturbation theory of dynamical systems, and its extension, the dynamical Gaussian mixture approximation (DynGMA). Benefiting from the robust density approximation, our method exhibits superior accuracy compared to baseline methods in learning the fully unknown drift and diffusion functions and computing the invariant distribution from trajectory data. And it is capable of handling trajectory data with low time resolution and variable, even uncontrollable, time step sizes, such as data generated from Gillespie's stochastic simulations. We then conduct several experiments across various scenarios to verify the advantages and robustness of the proposed method.

Turbulence-enhanced THz generation by multiple chaotically-distributed femtosecond filaments in air

Remote generation of electromagnetic waves in the terahertz (THz) by the volume of air medium gains increasing scientific interest due to the demand for this spectral range in solving various practical problems including those belonging to the nonlinear atmospheric optics. During self-focusing and filamentation of high-power femtosecond laser pulses in air, the source of THz radiation is the plasma of laser filaments. One of the main challenges of THz generation by a laser filament is increasing the value of optical energy conversion to the long-wavelength band. In this paper, we present the results of our studies on DC-biased THz generation during single-color filamentation in air of focused femtosecond Ti:Sapphire-laser pulses (800 nm, pulse energy up to 40 mJ). The distinctive feature of our study is that a femtosecond optical pulse propagates through a spatially-localized heated air layer containing randomly inhomogeneous refractive index perturbations, which mimics strong air turbulence. For the first time to our knowledge, we show, that the turbulent air layer formed at the beginning of the optical path allows increasing the yield of THz radiation up to 1.5 times due to the formation of multiple chaotically-arranged filaments resulting from random perturbations of the optical beam energy profile that reduces the subsequent THz (re)absorption in the filament plasma.

Higher‐Order Topological Corner States in a Specially Distorted Photonic Kagome Lattice

AbstractKagome lattices have garnered significant interest over the decades due to their rich physics and implications for exotic superconductors and topological materials. In particular, the so‐called “breathing Kagome lattice” (BKL) is often used as a prototypical model to understand higher‐order topological insulators. Here it is demonstrated that higher‐order corner states exist in a specially distorted Kagome lattice, resembling the “Inverse Hexagram” lattice distortion originally introduced in the study of charge density waves in Kagome metals. Importantly, it is found that such an Inverse Hexagram‐like Kagome lattice with C6 rotational symmetry hosts two types of in‐gap corner states, in contrast to a flat‐cutting BKL of C3 symmetry that supports only one type of corner state under the tight‐binding condition. It is shown that the nontrivial corner states exhibit a fractional corner anomaly, revealing the feature of higher‐order topology. Using laser‐written waveguide lattices as a photonic platform, these two types of corner states are experimentally observed, along with a direct comparison with the corner excitation at their trivial counterparts. Experimental observations are further corroborated by numerical simulations and stability analysis under random perturbation. These results may prove relevant and applicable to similar phenomena in other Kagome platforms beyond photonics.

Co-existence of synaptic plasticity and metastable dynamics in a spiking model of cortical circuits.

Evidence for metastable dynamics and its role in brain function is emerging at a fast pace and is changing our understanding of neural coding by putting an emphasis on hidden states of transient activity. Clustered networks of spiking neurons have enhanced synaptic connections among groups of neurons forming structures called cell assemblies; such networks are capable of producing metastable dynamics that is in agreement with many experimental results. However, it is unclear how a clustered network structure producing metastable dynamics may emerge from a fully local plasticity rule, i.e., a plasticity rule where each synapse has only access to the activity of the neurons it connects (as opposed to the activity of other neurons or other synapses). Here, we propose a local plasticity rule producing ongoing metastable dynamics in a deterministic, recurrent network of spiking neurons. The metastable dynamics co-exists with ongoing plasticity and is the consequence of a self-tuning mechanism that keeps the synaptic weights close to the instability line where memories are spontaneously reactivated. In turn, the synaptic structure is stable to ongoing dynamics and random perturbations, yet it remains sufficiently plastic to remap sensory representations to encode new sets of stimuli. Both the plasticity rule and the metastable dynamics scale well with network size, with synaptic stability increasing with the number of neurons. Overall, our results show that it is possible to generate metastable dynamics over meaningful hidden states using a simple but biologically plausible plasticity rule which co-exists with ongoing neural dynamics.

Multi-view discriminative edge heterophily contrastive learning network for attributed graph anomaly detection

Attributed graph anomaly detection aims to identify abnormal nodes that significantly differ from most nodes in terms of their attribute or structure. Recent graph contrastive learning methods, which follow an augmenting-contrasting learning scheme, have shown promising results. However, these methods still have two key limitations. Firstly, the contrastive views generated through random perturbation may not conform to abnormal patterns. Secondly, the inability to effectively discriminate heterophilic edges in anomalous networks can adversely impact the detection performance. To this end, we propose a Multi-view discriminative Edge heterophiLy cOntrastive learning Network (MELON) for attributed graph anomaly detection. Our approach addresses the aforementioned limitations by integrating human knowledge of different anomaly patterns for data augmentation and designing an edge discriminator to identify edge homophily/heterophily in an unsupervised manner. In addition, a dual-channel encoder is also designed to capture representative representations of the nodes from the discriminated homophilic/heterophilic edges. We then use a decoder to reconstruct the original network from the node representations learned by the dual-channel encoder and rank nodes according to their reconstruction error as the anomaly metric. Extensive experiments on four public benchmark datasets demonstrate that our proposed method outperforms state-of-the-art baselines.

Critical transitions on a route to chaos of natural convection on a heated horizontal circular surface

The transition route and bifurcations of the buoyant flows developing on a heated horizontal circular surface are elaborated using direct numerical simulations and direct stability analysis. A series of bifurcations, as a function of Rayleigh numbers ( $Ra$ ) ranging from $10^6$ to $6.0\times 10^7$ , are found on the route to chaos of the flows at $Pr=7$ . When $Ra<1.0\times 10^3$ , the buoyant flows above the heated horizontal surface are dominated by conduction, because of which the distinct thermal boundary layer and plume are not present. At $Ra=1.1\times 10^6$ , a Hopf bifurcation occurs, resulting in the flow transition from a steady state to a periodic puffing state. As $Ra$ increases further, the flow enters a periodic rotating state at $Ra=1.9\times 10^6$ , which is a unique state that was rarely discussed in the literature. These critical transitions, leaving from a steady state and subsequently entering a series of periodic states (puffing, rotating, flapping and period-doubling) and finally leading to chaos, are diagnosed using two-dimensional Fourier transforms. Moreover, direct stability analysis is conducted by introducing random numerical perturbations into the boundary condition of the surface heating. We find that when the state of a flow is in the vicinity of critical values (e.g. $Ra=2.0\times 10^6$ ), the flow is conditionally unstable to perturbations, and it can bifurcate from the rotating state to the flapping state in advance. However, for relatively stable flow states, such as at $Ra=1.5\times 10^6$ , the flow remains in its periodic puffing state even though it is being perturbed.

Ensemble forecasting: A foray of dynamics into the realm of statistics

AbstractUncertain quantities are often described through statistical samples. Can samples for numerical weather forecasts be generated dynamically? At a great expense, they can. With statistically constrained perturbations, a cloud of initial states is created and then integrated forward in time. By now, this technique has become ubiquitous in weather and climate research and operations. Ensembles are widely used, with demonstrated value. The atmosphere evolves in a multidimensional phase space. Does a cloud of ensemble solutions encompass the evolution of the real atmosphere? Theoretically, random perturbations in high‐dimensional spaces have negligible projection in any direction, including the error in the best estimate, therefore consistently degrading that. As the bulk of the perturbation variance lies in the null space of error, samples in multidimensional space do not contain reality. An evaluation suggests that initial and short‐range forecast error and ensemble perturbations are random draws from a high‐dimensional domain we call the subspace of possible error. Error in any initial condition is partly a result of stochastic observational and assimilation noise, while perturbations explore other, mostly independent directions from the subspace of possible error that may have resulted from other configurations of stochastic noise. What benefits may arise from the deterministic projection of such noise? Consistent with theoretical expectations, ensemble members consistently degrade the skill of the unperturbed forecast until medium range. The mean and all other products derived from ensembles suffer an 18‐hour loss in forecast Information. Since Information is a sufficient statistic, any rational user can benefit more from the unperturbed, than from an ensemble of weather forecasts. Furthermore, case‐dependent variations in the distribution or spread of ensembles have no impact on commonly used metrics. Can alternative, statistical applications provide comparable, or even higher‐quality probabilistic and other products, at the fraction of the cost of running an ensemble?

Research on uncertainties in fuel centrifugal pump based on prediction and reconstruction of internal flow field

Geometric machining errors in the blade profile and variable operating conditions in the extreme operating environment are primary factors leading to the uncertainties in pump performance. This paper presents an analysis of uncertainties of fuel centrifugal pumps by modeling the geometry uncertainty in blade machining based on the Karhunen–Loève (KL) expansion and using a polynomial chaos expansion (PCE) model. First, the geometric uncertainty in the blade machining is described by the KL expansion in three sections and a stochastic simulation of the blade geometry is performed. Then, a PCE surrogate model is trained based on the least angle regression method and validated by the bootstrap method to quantify the uncertainties of performance indices. Finally, the influence mechanism and relative importance of each input uncertainty parameter are investigated using a quasi-Monte Carlo simulation method. The results show that the KL expansion of the blade profile uses the random vector perturbation superposition of three stream surface, achieving the dimensional reduction in the blade machining error. The PCE surrogate model, trained with a dataset of 3 × 106 sample points, exhibits excellent fit, and the R-squared and adjusted R-squared for head coefficient and efficiency are both above 80%. The variance of parameter control points of the reconstructed flow field is less than 0.002. The uncertainties in both operating conditions and parameters have an influence on the distribution of the global flow field, while the influence of the uncertainty in machining error on the global flow field mainly concentrates on the power-generating positions of the blade.

An Iterated Local Search Heuristic for the Multi-Trip Vehicle Routing Problem with Multiple Time Windows

This paper studies the multi-trip vehicle routing problem with multiple time windows, which extends the multi-trip vehicle routing problem by deciding not only the sequence of customers that each vehicle serves but also the service time window of each customer. It also requires that the delivery service time is within the selected time windows and that the total demand of the customers served by the vehicle on each trip does not exceed the maximum carrying capacity. For solving the studied problem, we develop a mixed integer linear programming model with the objective of minimizing the total travel distance of vehicles and design a tailored iterative local search heuristic. Within the framework of the iterative local search, an improved Solomon greedy insertion algorithm suitable for multiple time windows and multi-trip scenarios is designed to generate the initial solution, and local search operators such as Or-opt and Relocate, as well as Random Exchange perturbation operations, are also developed. The experiment results demonstrate the effectiveness of the proposed model and algorithm and confirm that by providing customers with multiple time windows option, carriers can flexibly plan vehicle routes and select appropriate service time windows, thereby reducing the number of vehicles used and the total distance travelled and improve delivery success.

Modeling urban traffic volume incorporating driver stochasticity and traffic correlation with waveguide-based quantum walk

Urban traffic involves two stochastic factors, complicating accurate modeling: (1) Driver stochasticity, arising from driver heterogeneity and random environment perturbations, introduces unpredictable fluctuations in urban traffic volume. (2) Traffic correlation, referring to the interaction in traffic states across different regions. This paper proposes a waveguide-based quantum walk urban traffic volume model (UTVDC-QW), incorporating driver stochasticity and traffic correlation. The model uses waveguide arrays to map urban traffic networks, incorporates random environment perturbations via noise, and traffic correlation via waveguide coupling. UTVDC-QW develops measures of environment perturbations and traffic correlations. Experiments with Chengdu traffic datasets demonstrate that UTVDC-QW improves the simulation accuracy compared to reference models. In addition, the model reveals the characteristics of environment perturbations and traffic correlation in the study area. Overall, this study effectively incorporates driver stochasticity and traffic correlation by waveguide-based quantum walk, is a pioneering attempt to apply quantum computing to urban traffic modeling.

Drill tools sticking prediction based on adaptive long short-term memory

As one of the most severe disasters in deep coal mining, rockburst can be prevented through drill-hole pressure relief. However, the coal mine is characterized by high crustal stress and changeable mechanical properties of surrounding rock, which will cause drill rod deflection phenomenon, then lead to rod-deflection sticking accidents. This paper proposes a prediction method based on adaptive long short-term memory (ALSTM) for rod-deflection sticking accidents to improve drilling efficiency and reduce sticking accidents. Firstly, the sticking data is collected through the intelligent drilling condition simulation experimental platform, and then the sticking features are extracted based on the sticking data. Secondly, the sticking factor is constructed, and the sticking critical line is set. Thirdly, the good-point set and the proposed random perturbation algorithm are employed to improve the spotted hyena optimizer (SHO) to obtain the improved SHO (ISHO). Finally, we use the ISHO to optimize the hyperparameters of the long short-term memory and then establish the sticking prediction model based on ALSTM. The experimental results show that the proposed prediction model meets the demands for sticking prediction very well.

Dynamic analysis and optimal control of stochastic information cross-dissemination and variation model with random parametric perturbations.

Information dissemination has a significant impact on social development. This paper considers that there are many stochastic factors in the social system, which will result in the phenomena of information cross-dissemination and variation. The dual-system stochastic susceptible-infectious-mutant-recovered model of information cross-dissemination and variation is derived from this problem. Afterward, the existence of the global positive solution is demonstrated, sufficient conditions for the disappearance of information and its stationary distribution are calculated, and the optimal control strategy for the stochastic model is proposed. The numerical simulation supports the results of the theoretical analysis and is compared to the parameter variation of the deterministic model. The results demonstrate that cross-dissemination of information can result in information variation and diffusion. Meanwhile, white noise has a positive effect on information dissemination, which can be improved by adjusting the perturbation parameters.

Enhancement of Mine Images through Reflectance Estimation of V Channel Using Retinex Theory

The dim lighting and excessive dust in underground mines often result in uneven illumination, blurriness, and loss of detail in surveillance images, which hinders subsequent intelligent image recognition. To address the limitations of the existing image enhancement algorithms in terms of generalization and accuracy, this paper proposes an unsupervised method for enhancing mine images in the hue–saturation–value (HSV) color space. Inspired by the HSV color space, the method first converts RGB images to the HSV space and integrates Retinex theory into the brightness (V channel). Additionally, a random perturbation technique is designed for the brightness. Within the same scene, a U-Net-based reflectance estimation network is constructed by enforcing consistency between the original reflectance and the perturbed reflectance, incorporating ResNeSt blocks and a multi-scale channel pixel attention module to improve accuracy. Finally, an enhanced image is obtained by recombining the original hue (H channel), brightness, and saturation (S channel), and converting back to the RGB space. Importantly, this image enhancement algorithm does not require any normally illuminated images during training. Extensive experiments demonstrated that the proposed method outperformed most existing unsupervised low-light image enhancement methods, qualitatively and quantitatively, achieving a competitive performance comparable to many supervised methods. Specifically, our method achieved the highest PSNR value of 22.18, indicating significant improvements compared to the other methods, and surpassing the second-best WCDM method by 10.3%. In terms of SSIM, our method also performed exceptionally well, achieving a value of 0.807, surpassing all other methods, and improving upon the second-place WCDM method by 19.5%. These results demonstrate that our proposed method significantly enhanced image quality and similarity, far exceeding the performance of the other algorithms.