Random Environment Research Articles

A new self-adaptive mission aborting policy for systems operating in uncertain random shock environment

A new self-adaptive mission aborting policy for systems operating in uncertain random shock environment

First-passage time for many-particle diffusion in space-time random environments

First-passage time for many-particle diffusion in space-time random environments

The effects of additional food and environmental stochasticity on the asymptotic properties of a nutrient–phytoplankton model

In this paper, we investigate the deterministic and stochastic features of an additional food provided nutrient–phytoplankton model, and discuss the effects of additional food and environmental stochasticity (noise) on its asymptotic properties. A detailed global dynamics analysis of the deterministic model is firstly provided, and then the critical conditions for persistence and extinction of phytoplankton is found. For the stochastic model, we establish some sufficient conditions for the exponential extinction of phytoplankton and the existence of stationary distribution. By solving the Fokker–Planck equation, the explicit expression of local probability density of the stochastic model is further derived. With the help of probability density, we obtain the mean, variance, skewness and kurtosis of the biomass of phytoplankton, and numerically find the additional food and stochasticity have complex effects on these statistical properties. Both theoretical and numerical findings indicate that the additional food source is favorable for the growth of phytoplankton, whereas the stochasticity is adverse to its growth. Moreover, the additional food source and stochasticity play important roles in the formation of phytoplankton bloom.

Shortage Policies for a Jump Process with Positive and Negative Batch Arrivals in a Random Environment

We study a continuous-review stock management of a retailer for a single item in a limited storage (buffer) in a random environment. The stock level fluctuates according to two independent compound Poisson processes with discrete amounts of items (batches) that enter and leave the storage facility. The storage facility is controlled by a three-parameter base-stock replenishment policy. All items exceeding the storage capacity are transferred to an unlimited foreign facility. In addition, a restricted backlogging possibility is permitted; additional demands for items are lost sales. We further assume a random shelf life, the possibility of total inventory collapse, and a random lead time. Applying Markov theory, we derive the optimal control parameters minimizing the long-run expected total cost. A sensitivity analysis is conducted focusing on the comparison between the pure lost-sales policy and a partial backordering policy. Accordingly, we identify cases where one policy is cost effective compared to the other, particularly with respect to the batch patterns (sign, rate, average, and variability), and the associated costs.

Wolbachia invasion dynamics of a random mosquito population model with imperfect maternal transmission and incomplete CI.

In this work, we formulate a random Wolbachia invasion model incorporating the effects of imperfect maternal transmission and incomplete cytoplasmic incompatibility (CI). Under constant environments, we obtain the following results: Firstly, the complete invasion equilibrium of Wolbachia does not exist, and thus the population replacement is not achievable in the case of imperfect maternal transmission; Secondly, imperfect maternal transmission or incomplete CI may obliterate bistability and backward bifurcation, which leads to the failure of Wolbachia invasion, no matter how many infected mosquitoes would be released; Thirdly, the threshold number of the infected mosquitoes to be released would increase with the decrease of the maternal transmission rate or the intensity of CI effect. In random environments, we investigate in detail the Wolbachia invasion dynamics of the random mosquito population model and establish the initial release threshold of infected mosquitoes for successful invasion of Wolbachia into the wild mosquito population. In particular, the existence and stability of invariant probability measures for the establishment and extinction of Wolbachia are determined.

Uniform Cramér moderate deviations and Berry–Esseen bounds for superadditive bisexual branching processes in random environments

Uniform Cramér moderate deviations and Berry–Esseen bounds for superadditive bisexual branching processes in random environments

Long-term, landscape-level assessment of aquatic pesticide exposure to identify amphibian ontological traits affecting vulnerability.

Amphibians worldwide are threatened by habitat loss, some of which is driven by a changing climate, as well as exposure to pesticides, among other causes. The timing and duration of the larval development phase vary between species, thereby influencing the relative impacts of stochastic hydroregime conditions as well as potential aquatic pesticide exposure. We describe the stages of breeding through metamorphosis for eight amphibian species, based on optimal hydroregime conditions, and use a model of pesticide fate and exposure representative of central Florida citrus groves to simulate hydrodynamics based on observed weather data over a 54-year period. Using the Pesticide in Water Calculator and Plant Assessment Tool, we estimated daily wetland depth and pyraclostrobin exposure, with label-recommended application quantities. Species' timing and duration of larval development determined the number of years of suitable hydroregime for breeding and the likelihood of exposure to peak aquatic concentrations of pyraclostrobin. Although the timing of pesticide application determined the number of surviving larvae, density-dependent constraints of wetland hydroregime also affected larval survival across species and seasons. Further defining categorical amphibian life history types and habitat requirements supports the development of screening-level assessments by incorporating environmental stochasticity at the appropriate temporal resolution. Subsequent refinement of these screening-level risk assessment strategies to include spatially explicit landscape data along with terrestrial exposure estimates would offer additional insights into species vulnerability to pesticide exposure throughout the life cycle. Computational simulation of ecologically relevant exposure scenarios, such as these, offers a more realistic interpretation of differential agrichemical risk among species based on their phenology and habits and provides a more situation-specific risk assessment perspective for threatened species. Integr Environ Assess Manag 2024;00:1-10. Published 2024. This article is a U.S. Government work and is in the public domain in the USA.

Study of the Extremely Low-Frequency Noise Characteristics of a Micro-Thrust Measurement Platform.

The critical structural parameters are optimized and studied using the numerical simulation method to improve the resolution and stability of the Micro-Thrust Measurement Platform (MTMP). Under two different ground random vibration environments, the parameters, such as pivot thickness, pendulum rod length, and pivot structure, are focused on analyzing the influence of the system's resolution and stability. The results show that when the thickness of the pivot is 0.04 mm or 0.2 mm, and the pendulum rod length is 2 m, the effect of ground random vibration on the MTMP is minimized. At 0.1 mHz, it can reach 0.0057 μN/Hz. In the series double-pivot structure, an appropriate increase in the distance between the sheets can further optimize the above conclusions. The results and analysis within this study can provide support for the engineering design of the MTMP.

Identity Based Authentication Scheme (IAS) for Securing WSN Based Internet of Things

The growing number of connected devices in IoT networks has raised security concerns. These networks face unique challenges, including limited resources, lack of standardized security protocols, and diverse devices and applications. Identity-based authentication is needed to address these threats and limitations. Implementing a multi-factor authentication system can enhance security and protect sensitive information from unauthorized access. The proposed Identity Based Authentication (IAS) scheme is implemented using the NS-2 simulator to address security challenges in IoT networks. Each node is assigned a unique identity for authentication, ensuring only authorized access and preventing security breaches. The IAS scheme enhances IoT network security by verifying node identities. Two scenarios are considered to evaluate the scalability and interoperability of the IAS scheme. The first scenario involves a random environment, assessing performance in real-world settings with varying device densities and network conditions. The second scenario involves a cluster-based environment, providing insights into the scheme's functionality and efficiency. By examining both scenarios, this research aims to provide a comprehensive understanding of how the authentication scheme performs in different deployment scenarios. The findings highlight the importance of selecting the appropriate authentication scheme based on the specific network environment and requirements. The superiority of the IAS authentication scheme suggests its potential for widespread adoption and implementation in various network scenarios over other authentication schemes.

Effect of lead-free solder thermal interface material thickness on the reliability of electronic components in a random vibration environment

The reliability of electronic components has persistently posed challenges for engineers. This study addresses the critical need of understanding the impact of random vibration on the reliability of lead-free solder as thermal interface materials (TIM) within electronic components. ANSYS software was deployed to design, develop, and simulate the electronic model, with a focus on the TIM. SAC405 lead-free solder served as the TIM, its thickness was varied between 0.01 to 0.06 mm (at 0.01 mm intervals). The results from this investigation reveal relevant correlations. As the TIM thickness increases, there's a noticeable reduction in stress and strain while the deformation increases. Remarkably, a direct relationship emerges between TIM thickness and fatigue life; thicker TIM correlates with increased fatigue life. In addition, at a TIM thickness of 0.01 mm, the fatigue life measurements were 2.76 x 104, 1.63 x 104, and 0.792 x 104 for Equations 1, 2, and 3, respectively. These findings carry profound implications for engineers, serving as a guiding framework to aid in the selection of optimal TIM thickness for electronic components if lead-free solders are used as TIM. Understanding these trade-offs between stress, strain, deformation, and fatigue life is pivotal, empowering engineers to make informed decisions during electronic system design and development, ultimately enhancing overall reliability. Using lead-free solders as TIM in electronic applications is proposed by this study due to the thermal and reliability benefits presented.

A.s. convergence rate for Mandelbrot’s cascade in a random environment

. For Mandelbrot’s cascade (Y n ) in an independent and identically distributed (i.i.d.) random environment ξ, we are interested in the a.s. convergence rate of the Mandelbrot’s martingale (W n ) to its limit W, where W n = Y n / E ξ Y n is the normalized partition function. We obtain sufficient conditions under which W−W n has an exponential convergence rate: W − W n = o ( e − n a ) a.s. for some a > 0 explicitly calculated; we also find conditions under which W−W n has a polynomial convergence rate: W − W n = o ( n − α ) a.s. for some α > 0. Similar conclusions hold for Mandelbrot’s cascade in a varying environment.

ACT: Empowering Decision Transformer with Dynamic Programming via Advantage Conditioning

Decision Transformer (DT), which employs expressive sequence modeling techniques to perform action generation, has emerged as a promising approach to offline policy optimization. However, DT generates actions conditioned on a desired future return, which is known to bear some weaknesses such as the susceptibility to environmental stochasticity. To overcome DT's weaknesses, we propose to empower DT with dynamic programming. Our method comprises three steps. First, we employ in-sample value iteration to obtain approximated value functions, which involves dynamic programming over the MDP structure. Second, we evaluate action quality in context with estimated advantages. We introduce two types of advantage estimators, IAE and GAE, which are suitable for different tasks. Third, we train an Advantage-Conditioned Transformer (ACT) to generate actions conditioned on the estimated advantages. Finally, during testing, ACT generates actions conditioned on a desired advantage. Our evaluation results validate that, by leveraging the power of dynamic programming, ACT demonstrates effective trajectory stitching and robust action generation in spite of the environmental stochasticity, outperforming baseline methods across various benchmarks. Additionally, we conduct an in-depth analysis of ACT's various design choices through ablation studies. Our code is available at https://github.com/LAMDA-RL/ACT.

Learning Discrete-Time Major-Minor Mean Field Games

Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and cannot model major players that strongly influence other players, severely limiting the class of problems that can be handled. We propose a novel discrete time version of major-minor MFGs (M3FGs), along with a learning algorithm based on fictitious play and partitioning the probability simplex. Importantly, M3FGs generalize MFGs with common noise and can handle not only random exogeneous environment states but also major players. A key challenge is that the mean field is stochastic and not deterministic as in standard MFGs. Our theoretical investigation verifies both the M3FG model and its algorithmic solution, showing firstly the well-posedness of the M3FG model starting from a finite game of interest, and secondly convergence and approximation guarantees of the fictitious play algorithm. Then, we empirically verify the obtained theoretical results, ablating some of the theoretical assumptions made, and show successful equilibrium learning in three example problems. Overall, we establish a learning framework for a novel and broad class of tractable games.

OVD-Explorer: Optimism Should Not Be the Sole Pursuit of Exploration in Noisy Environments

In reinforcement learning, the optimism in the face of uncertainty (OFU) is a mainstream principle for directing exploration towards less explored areas, characterized by higher uncertainty. However, in the presence of environmental stochasticity (noise), purely optimistic exploration may lead to excessive probing of high-noise areas, consequently impeding exploration efficiency. Hence, in exploring noisy environments, while optimism-driven exploration serves as a foundation, prudent attention to alleviating unnecessary over-exploration in high-noise areas becomes beneficial. In this work, we propose Optimistic Value Distribution Explorer (OVD-Explorer) to achieve a noise-aware optimistic exploration for continuous control. OVD-Explorer proposes a new measurement of the policy's exploration ability considering noise in optimistic perspectives, and leverages gradient ascent to drive exploration. Practically, OVD-Explorer can be easily integrated with continuous control RL algorithms. Extensive evaluations on the MuJoCo and GridChaos tasks demonstrate the superiority of OVD-Explorer in achieving noise-aware optimistic exploration.

Improved Double Deep Q-Network Algorithm Applied to Multi-Dimensional Environment Path Planning of Hexapod Robots.

Detecting transportation pipeline leakage points within chemical plants is difficult due to complex pathways, multi-dimensional survey points, and highly dynamic scenarios. However, hexapod robots' maneuverability and adaptability make it an ideal candidate for conducting surveys across different planes. The path-planning problem of hexapod robots in multi-dimensional environments is a significant challenge, especially when identifying suitable transition points and planning shorter paths to reach survey points while traversing multi-level environments. This study proposes a Particle Swarm Optimization (PSO)-guided Double Deep Q-Network (DDQN) approach, namely, the PSO-guided DDQN (PG-DDQN) algorithm, for solving this problem. The proposed algorithm incorporates the PSO algorithm to supplant the traditional random selection strategy, and the data obtained from this guided approach are subsequently employed to train the DDQN neural network. The multi-dimensional random environment is abstracted into localized maps comprising current and next level planes. Comparative experiments were performed with PG-DDQN, standard DQN, and standard DDQN to evaluate the algorithm's performance by using multiple randomly generated localized maps. After testing each iteration, each algorithm obtained the total reward values and completion times. The results demonstrate that PG-DDQN exhibited faster convergence under an equivalent iteration count. Compared with standard DQN and standard DDQN, reductions in path-planning time of at least 33.94% and 42.60%, respectively, were observed, significantly improving the robot's mobility. Finally, the PG-DDQN algorithm was integrated with sensors onto a hexapod robot, and validation was performed through Gazebo simulations and Experiment. The results show that controlling hexapod robots by applying PG-DDQN provides valuable insights for path planning to reach transportation pipeline leakage points within chemical plants.

Unraveling the forces shaping foraging dynamics in harvester ant colonies: Recruitment efficiency and environmental variability

The collective foraging behavior of ant colonies is a central focus in behavioral ecology. This paper enhances the classical model of foraging dynamics in harvester ant colonies by introducing a nonlinear recruitment rate and considering environmental variability. Initially, we analyze the existence and stability of steady states in the deterministic model. The results suggest that an increase in mean recruitment time can reduce the foraging threshold, leading to both forward and backward bifurcations. Furthermore, both average recruitment time and the interference intensity of recruiters impact the number of workers in each subgroup. Subsequently, we conduct an analysis of the long-term and transient dynamics of collective foraging in random environments, providing sufficient conditions for the colony to sustain foraging activity. The findings emphasize the scene-dependent impact of environmental stochasticity on foraging dynamics. When ant colonies deterministically cease foraging, environmental stochasticity may unexpectedly prolong the foraging state. Conversely, when colonies deterministically persist in foraging, environmental stochasticity may disrupt this continuity. Additionally, the effect of environmental stochasticity on foraging status varies with the initial worker size. Sizes near the boundary of the basin of attraction between non-foraging and foraging states exhibit greater sensitivity to environmental stochasticity, and sufficiently large stochasticity can impact foraging dynamics across a broader range of initial worker sizes. These findings underscore the intricate interplay between intrinsic factors (e.g., recruitment efficiency and interference intensity) and extrinsic factors (e.g., environmental stochasticity) in shaping the collective foraging dynamics of ant colonies.

A multivariate extension of the Erdős–Taylor theorem

AbstractThe Erdős–Taylor theorem (Acta Math Acad Sci Hungar, 1960) states that if $$\textsf{L}_N$$ L N is the local time at zero, up to time 2N, of a two-dimensional simple, symmetric random walk, then $$\tfrac{\pi }{\log N} \,\textsf{L}_N$$ π log N L N converges in distribution to an exponential random variable with parameter one. This can be equivalently stated in terms of the total collision time of two independent simple random walks on the plane. More precisely, if $$\textsf{L}_N^{(1,2)}=\sum _{n=1}^N \mathbb {1}_{\{S_n^{(1)}= S_n^{(2)}\}}$$ L N ( 1 , 2 ) = ∑ n = 1 N 1 { S n ( 1 ) = S n ( 2 ) } , then $$\tfrac{\pi }{\log N}\, \textsf{L}^{(1,2)}_N$$ π log N L N ( 1 , 2 ) converges in distribution to an exponential random variable of parameter one. We prove that for every $$h \geqslant 3$$ h ⩾ 3 , the family $$ \big \{ \frac{\pi }{\log N} \,\textsf{L}_N^{(i,j)} \big \}_{1\leqslant i<j\leqslant h}$$ { π log N L N ( i , j ) } 1 ⩽ i < j ⩽ h , of logarithmically rescaled, two-body collision local times between h independent simple, symmetric random walks on the plane converges jointly to a vector of independent exponential random variables with parameter one, thus providing a multivariate version of the Erdős–Taylor theorem. We also discuss connections to directed polymers in random environments.

Modified time domain randomization technique for multi-shaker non-stationary non-Gaussian random vibration control

Traditional random vibration environmental tests simulate stationary Gaussian random vibration environments. In this work, the generation and closed-loop control of multi-shaker non-stationary non-Gaussian random vibration signals with the modified time domain randomization technique are studied. The amplitude modulation function is introduced to control the non-stationary and non-Gaussian characteristics that the root mean square value of the generated signal changes with time. The kurtosis relationship between the one frame pseudo-random signal and consecutive true random signal is derived theoretically. It is found that the kurtosis of the consecutive non-stationary random signal is determined by the amplitude modulation function and kurtosis of the pseudo-random signal. The standard deviation of the time-varying root mean square reflects the non-stationary characteristics of the generated signal. A control strategy for multi-shaker non-stationary non-Gaussian random vibration environmental test is proposed. The non-stationary and non-Gaussian characteristics are extracted from the measured response signals so that the power spectral densities, kurtoses and non-stationary characteristics can be controlled simultaneously. The results from the simulation examples and multi-shaker vibration experiments prove the feasibility and practicability of the proposed non-stationary non-Gaussian random signal generation method and control strategy.

Limit Theorems for a Supercritical Branching Process with Immigration at Zero in a Random Environment

Let Z be a supercritical branching process with immigration at zero in a random environment, where the immigration is allowed entering a generation iff the previous generation is empty. The limit theorems for the naturally normalized population size Wn shall be investigated, under both the annealed law and quenched law. In addition, in the linear fractional case, the harmonic moments of W and the convergence rate of the transition probabilities p(n) l;j of Z are studied.

Heat kernel fluctuations and quantitative homogenization for the one-dimensional Bouchaud trap model

We present on-diagonal heat kernel estimates and quantitative homogenization statements for the one-dimensional Bouchaud trap model. The heat kernel estimates are obtained using standard techniques, with key inputs coming from a careful analysis of the volume growth of the invariant measure of the process under study. As for the quantitative homogenization results, these include both quenched and annealed Berry–Esseen-type theorems, as well as a quantitative quenched local limit theorem. Whilst the model we study here is a particularly simple example of a random walk in a random environment, we believe the roadmap we provide for establishing the latter result in particular will be useful for deriving quantitative local limit theorems in other, more challenging, settings.