Reinforcement learning based adaptive control method for traffic lights in intelligent transportation

Addressing the requirements and challenges of traffic light control, a reinforcement learning based adaptive optimal control model for traffic lights in intelligent transportation systems is proposed. In the model design, we combined Markov decision process, Q-learning algorithm, and Deep Q-Learning Network (DQN) control theory to establish a comprehensive signal light Adaptive Optimal Control of Signal Lights in Intelligent Transportation Systems (AOCITL) control model. Through simulation experiments on the model and the application of actual road scene data, we have verified the superiority of the model in improving traffic system efficiency and reducing traffic pressure. The experimental results show that compared with traditional fixed cycle signal light control, the adaptive optimal control model based on reinforcement learning can significantly improve the traffic efficiency of roads, reduce the incidence of traffic accidents, and enhance the overall operational effectiveness of urban transportation systems. The proposed method is possible to further optimize the model algorithm, expand its application scope, and promote the development and practical application of intelligent transportation systems

Numerical simulations of X-rays Free Electron Lasers (XFEL)

We study a nonlinear Schr\"odinger equation which arises as an effective single particle model in X-ray Free Electron Lasers (XFEL). This equation appears as a first-principles model for the beam-matter interactions that would take place in an XFEL molecular imaging experiment in \cite{frat1}. Since XFEL is more powerful by several orders of magnitude than more conventional lasers, the systematic investigation of many of the standard assumptions and approximations has attracted increased attention. In this model the electrons move under a rapidly oscillating electromagnetic field, and the convergence of the problem to an effective time-averaged one is examined. We use an operator splitting pseudo-spectral method to investigate numerically the behaviour of the model versus its time-averaged version in complex situations, namely the energy subcritical/mass supercritical case, and in the presence of a periodic lattice. We find the time averaged model to be an effective approximation, even close to blowup, for fast enough oscillations of the external field. This work extends previous analytical results for simpler cases \cite{xfel1}.Comment: 14 page

Privacy-Preserving Polynomial Computing Over Distributed Data

In this letter, we delve into a scenario where a user aims to compute polynomial functions using their own data as well as data obtained from distributed sources. To accomplish this, the user enlists the assistance of $N$ distributed workers, thereby defining a problem we refer to as privacy-preserving polynomial computing over distributed data. To address this challenge, we propose an approach founded upon Lagrange encoding. Our method not only possesses the ability to withstand the presence of stragglers and byzantine workers but also ensures the preservation of security. Specifically, even if a coalition of $X$ workers collude, they are unable to acquire any knowledge pertaining to the data originating from the distributed sources or the user

Multiplexed Streaming Codes for Messages With Different Decoding Delays in Channel with Burst and Random Erasures

In a real-time transmission scenario, messages are transmitted through a channel that is subject to packet loss. The destination must recover the messages within the required deadline. In this paper, we consider a setup where two different types of messages with distinct decoding deadlines are transmitted through a channel that can introduce burst erasures of a length at most $B$, or $N$ random erasures. The message with a short decoding deadline $T_u$ is referred to as an urgent message, while the other one with a decoding deadline $T_v$ ($T_v > T_u$) is referred to as a less urgent message. We propose a merging method to encode two message streams of different urgency levels into a single flow. We consider the scenario where $T_v > T_u + B$. We establish that any coding strategy based on this merging approach has a closed-form upper limit on its achievable sum rate. Moreover, we present explicit constructions within a finite field that scales quadratically with the imposed delay, ensuring adherence to the upper bound. In a given parameter configuration, we rigorously demonstrate that the sum rate of our proposed streaming codes consistently surpasses that of separate encoding, which serves as a baseline for comparison

Approximation and Generalization of DeepONets for Learning Operators Arising from a Class of Singularly Perturbed Problems

Singularly perturbed problems present inherent difficulty due to the presence of a thin boundary layer in its solution. To overcome this difficulty, we propose using deep operator networks (DeepONets), a method previously shown to be effective in approximating nonlinear operators between infinite-dimensional Banach spaces. In this paper, we demonstrate for the first time the application of DeepONets to one-dimensional singularly perturbed problems, achieving promising results that suggest their potential as a robust tool for solving this class of problems. We consider the convergence rate of the approximation error incurred by the operator networks in approximating the solution operator, and examine the generalization gap and empirical risk, all of which are shown to converge uniformly with respect to the perturbation parameter. By utilizing Shishkin mesh points as locations of the loss function, we conduct several numerical experiments that provide further support for the effectiveness of operator networks in capturing the singular boundary layer behavior

Thermal vortex dynamics in thin circular ferromagnetic nanodisks

The dynamics of gyrotropic vortex motion in a thin circular nanodisk of soft ferromagnetic material is considered. The demagnetization field is calculated using two-dimensional Green's functions for the thin film problem and fast Fourier transforms. At zero temperature, the dynamics of the Landau-Lifshitz-Gilbert equation is simulated using fourth order Runge-Kutta integration. Pure vortex initial conditions at a desired position are obtained with a Lagrange multipliers constraint. These methods give accurate estimates of the vortex restoring force constant $k_F$ and gyrotropic frequency, showing that the vortex core motion is described by the Thiele equation to very high precision. At finite temperature, the second order Heun algorithm is applied to the Langevin dynamical equation with thermal noise and damping. A spontaneous gyrotropic motion takes place without the application of an external magnetic field, driven only by thermal fluctuations. The statistics of the vortex radial position and rotational velocity are described with Boltzmann distributions determined by $k_F$ and by a vortex gyrotropic mass $m_G=G^2/k_F$, respectively, where $G$ is the vortex gyrovector.Comment: 18 pages, 17 figure