Search Results (19)

The extensive deployment of quadrotors in complex environmental missions has revealed a critical challenge: degradation of trajectory tracking accuracy due to time-varying wind disturbances. Conventional model-based controllers struggle to adapt to nonlinear wind field dynamics, while data-driven approaches often suffer from catastrophic forgetting that compromises environmental adaptability. This paper proposes a reinforcement learning framework with continual adaptation capabilities to enhance robust tracking performance for quadrotors operating in dynamic wind fields. We develop a continual reinforcement learning framework integrating continual backpropagation algorithms with reinforcement learning. Initially, a foundation model is trained in wind-free conditions. When wind disturbance intensity undergoes gradual variations, a neuron utility assessment mechanism dynamically resets inefficient neurons to maintain network plasticity. Concurrently, a multi-objective reward function is designed to improve both training precision and efficiency. The Gazebo/PX4 simulation platform was utilized to validate the wind disturbance stepwise growth and stochastic variations. This approach demonstrated a reduction in the root mean square error of trajectory tracking when compared to the standard PPO algorithm. The proposed framework resolves the plasticity loss problem in deep reinforcement learning through structured neuron resetting, significantly enhancing the continual adaptation capabilities of quadrotors in dynamic wind fields. Full article

We examine the dynamics of a system influenced by a backbone structure, incorporating linear non-local terms that account for both irreversible and reversible processes, such as absorption and adsorption–desorption. Additionally, we introduce stochastic resetting to analyze its effects on the system’s behavior from both analytical and numerical perspectives. Our findings reveal a rich spectrum of dynamics, emphasizing connections to anomalous diffusion and providing new insights into transport phenomena in complex environments. Full article

In this study, we explore the impact of stochastic resetting on the dynamics of random walks on a T-fractal network. By employing the generating function technique, we establish a recursive relation between the generating function of the first passage time (FPT) and derive the relationship between the mean first passage time (MFPT) with resetting and the generating function of the FPT without resetting. Our analysis covers various scenarios for a random walker reaching a target site from the starting position; for each case, we determine the optimal resetting probability ${\gamma }^{*}$ that minimizes the MFPT. We compare the results with the MFPT without resetting and find that the inclusion of resetting significantly enhances the search efficiency, particularly as the size of the network increases. Our findings highlight the potential of stochastic resetting as an effective strategy for the optimization of search processes in complex networks, offering valuable insights for applications in various fields in which efficient search strategies are crucial. Full article

The time irreversibility of a dynamical process refers to the phenomenon where its behaviour or statistical properties change when it is observed under a time-reversal operation, i.e., backwards in time and indicates the presence of an “arrow of time”. It is an important feature of both synthetic and real-world systems, as it represents a macroscopic property that describes the mechanisms driving the dynamics at a microscale level and that stems from non-linearities and the presence of non-conservative forces within them. While many alternatives have been proposed in recent decades to assess this feature in experimental time series, the evaluation of their performance is hindered by the lack of benchmark time series of known reversibility. To solve this problem, we here propose and evaluate the use of a geometric Brownian motion model with stochastic resetting. We specifically use synthetic time series generated with this model to evaluate eight irreversibility tests in terms of sensitivity with respect to several characteristics, including their degree of irreversibility and length. We show how tests yield at times contradictory results, including the false detection of irreversible dynamics in time-reversible systems with a frequency higher than expected by chance and how most of them detect a multi-scale irreversibility structure that is not present in the underlying data. Full article

We consider two different time fractional telegrapher’s equations under stochastic resetting. Using the integral decomposition method, we found the probability density functions and the mean squared displacements. In the long-time limit, the system approaches non-equilibrium stationary states, while the mean squared displacement saturates due to the resetting mechanism. We also obtain the fractional telegraph process as a subordinated telegraph process by introducing operational time such that the physical time is considered as a Lévy stable process whose characteristic function is the Lévy stable distribution. We also analyzed the survival probability for the first-passage time problem and found the optimal resetting rate for which the corresponding mean first-passage time is minimal. Full article

In this study, we investigate a nonlinear diffusion process in which particles stochastically reset to their initial positions at a constant rate. The nonlinear diffusion process is modeled using the porous media equation and its extensions, which are nonlinear diffusion equations. We use analytical and numerical calculations to obtain and interpret the probability distribution of the position of the particles and the mean square displacement. These results are further compared and shown to agree with the results of numerical simulations. Our findings show that a system of this kind exhibits non-Gaussian distributions, transient anomalous diffusion (subdiffusion and superdiffusion), and stationary states that simultaneously depend on the nonlinearity and resetting rate. Full article

We study the long-time dynamics of the mean squared displacement of a random walker moving on a comb structure under the effect of stochastic resetting. We consider that the walker’s motion along the backbone is diffusive and it performs short jumps separated by random resting periods along fingers. We take into account two different types of resetting acting separately: global resetting from any point in the comb to the initial position and resetting from a finger to the corresponding backbone. We analyze the interplay between the waiting process and Markovian and non-Markovian resetting processes on the overall mean squared displacement. The Markovian resetting from the fingers is found to induce normal diffusion, thereby minimizing the trapping effect of fingers. In contrast, for non-Markovian local resetting, an interesting crossover with three different regimes emerges, with two of them subdiffusive and one of them diffusive. Thus, an interesting interplay between the exponents characterizing the waiting time distributions of the subdiffusive random walk and resetting takes place. As for global resetting, its effect is even more drastic as it precludes normal diffusion. Specifically, such a resetting can induce a constant asymptotic mean squared displacement in the Markovian case or two distinct regimes of subdiffusive motion in the non-Markovian case. Full article

The Ornstein–Uhlenbeck (O-U) process with resetting is considered as the anomalous transport taking place on a three-dimensional comb. The three-dimensional comb is a comb inside a comb structure, consisting of backbones and fingers in the following geometrical correspondence x–backbone →y–fingers–backbone →z–fingers. Realisation of the O-U process on the three-dimensional comb leads to anomalous (non-Markovian) diffusion. This specific anomalous transport in the presence of resets results in non-equilibrium stationary states. Explicit analytical expressions for the mean values and the mean squared displacements along all three directions of the comb are obtained and verified numerically. The marginal probability density functions for each direction are obtained numerically by Monte Carlo simulation of a random transport described by a system of coupled Langevin equations for the comb geometry. Full article

In this work, the SET and RESET processes of bipolar resistive switching memories with silicon nanocrystals (Si-NCs) embedded in an oxide matrix is simulated by a stochastic model. This model is based on the estimation of two-dimensional oxygen vacancy configurations and their relationship with the resistive state. The simulation data are compared with the experimental current-voltage data of Si-NCs/Si${\mathrm{O}}_2$ multilayer-based memristor devices. Devices with 1 and 3 Si-NCs/Si${\mathrm{O}}_2$ bilayers were analyzed. The Si-NCs are assumed as agglomerates of fixed oxygen vacancies, which promote the formation of conductive filaments (CFs) through the multilayer according to the simulations. In fact, an intermediate resistive state was observed in the forming process (experimental and simulated) of the 3-BL device, which is explained by the preferential generation of oxygen vacancies in the sites that form the complete CFs, through Si-NCs. Full article

We introduce a refined way to diffusely explore complex networks with stochastic resetting where the resetting site is derived from node centrality measures. This approach differs from previous ones, since it not only allows the random walker with a certain probability to jump from the current node to a deliberately chosen resetting node, rather it enables the walker to jump to the node that can reach all other nodes faster. Following this strategy, we consider the resetting site to be the geometric center, the node that minimizes the average travel time to all the other nodes. Using the established Markov chain theory, we calculate the Global Mean First Passage Time (GMFPT) to determine the search performance of the random walk with resetting for different resetting node candidates individually. Furthermore, we compare which nodes are better resetting node sites by comparing the GMFPT for each node. We study this approach for different topologies of generic and real-life networks. We show that, for directed networks extracted for real-life relationships, this centrality focused resetting can improve the search to a greater extent than for the generated undirected networks. This resetting to the center advocated here can minimize the average travel time to all other nodes in real networks as well. We also present a relationship between the longest shortest path (the diameter), the average node degree and the GMFPT when the starting node is the center. We show that, for undirected scale-free networks, stochastic resetting is effective only for networks that are extremely sparse with tree-like structures as they have larger diameters and smaller average node degrees. For directed networks, the resetting is beneficial even for networks that have loops. The numerical results are confirmed by analytic solutions. Our study demonstrates that the proposed random walk approach with resetting based on centrality measures reduces the memoryless search time for targets in the examined network topologies. Full article

We propose a two-dimensional model of biochemical activation process, whereby self-propelling particles of finite correlation times are injected at the center of a circular cavity with constant rate equal to the inverse of their lifetime; activation is triggered when one such particle hits a receptor on the cavity boundary, modeled as a narrow pore. We numerically investigated this process by computing the particle mean-first exit times through the cavity pore as a function of the correlation and injection time constants. Due to the breach of the circular symmetry associated with the positioning of the receptor, the exit times may depend on the orientation of the self-propelling velocity at injection. Stochastic resetting appears to favor activation for large particle correlation times, where most of the underlying diffusion process occurs at the cavity boundary. Full article

As a model for economic and ecological systems, replicator dynamics represent a basic form of agent competition for finite resources. Here, we investigate the effects of stochastic resetting in this kind of processes. Random reset events abruptly lead individual resources to a small value from which dynamics must start anew. Numerical results show that resource distribution over the population of competing agents develops highly nonuniform profiles, exhibiting clustering and fluctuations with anomalous dependence on the population size. This non-standard statistical behavior jeopardizes an analytical treatment based on mean-field assumptions. We propose alternative simplified analytical approaches which provide a stylized description of entropy evolution for the clustered distribution of resources and explain the unusually slow decrease of fluctuations. Full article

Distributed machine learning is primarily motivated by the promise of increased computation power for accelerating training and mitigating privacy concerns. Unlike machine learning on a single device, distributed machine learning requires collaboration and communication among the devices. This creates several new challenges: (1) the heavy communication overhead can be a bottleneck that slows down the training, and (2) the unreliable communication and weaker control over the remote entities make the distributed system vulnerable to systematic failures and malicious attacks. This paper presents a variant of stochastic gradient descent (SGD) with improved communication efficiency and security in distributed environments. Our contributions include (1) a new technique called error reset to adapt both infrequent synchronization and message compression for communication reduction in both synchronous and asynchronous training, (2) new score-based approaches for validating the updates, and (3) integration with both error reset and score-based validation. The proposed system provides communication reduction, both synchronous and asynchronous training, Byzantine tolerance, and local privacy preservation. We evaluate our techniques both theoretically and empirically. Full article

The application of the fractional calculus in the mathematical modelling of relaxation processes in complex heterogeneous media has attracted a considerable amount of interest lately. The reason for this is the successful implementation of fractional stochastic and kinetic equations in the studies of non-Debye relaxation. In this work, we consider the rotational diffusion equation with a generalised memory kernel in the context of dielectric relaxation processes in a medium composed of polar molecules. We give an overview of existing models on non-exponential relaxation and introduce an exponential resetting dynamic in the corresponding process. The autocorrelation function and complex susceptibility are analysed in detail. We show that stochastic resetting leads to a saturation of the autocorrelation function to a constant value, in contrast to the case without resetting, for which it decays to zero. The behaviour of the autocorrelation function, as well as the complex susceptibility in the presence of resetting, confirms that the dielectric relaxation dynamics can be tuned by an appropriate choice of the resetting rate. The presented results are general and flexible, and they will be of interest for the theoretical description of non-trivial relaxation dynamics in heterogeneous systems composed of polar molecules. Full article

This review addresses issues of various drift–diffusion and inhomogeneous advection problems with and without resetting on comblike structures. Both a Brownian diffusion search with drift and an inhomogeneous advection search on the comb structures are analyzed. The analytical results are verified by numerical simulations in terms of coupled Langevin equations for the comb structure. The subordination approach is one of the main technical methods used here, and we demonstrated how it can be effective in the study of various random search problems with and without resetting. Full article