The EHTA for Two Shallow Water Wave Equations

Abstract In this paper, two shallow water wave equations are studied by using the extended homoclinic test approach (EHTA). The new exact solutions for the shallow water wave equations are obtained. Their dynamic properties of some exact solutions are discussed and their profiles of these solutions are given by using of software Maple. Mathematics Subject Classification: 35B05, 35B10, 35B1

Analysis about Optimal Portfolio under G-Expectation

AbstractIn this paper, an optimal portfolio selection rule under G-expectation is established and explicit optimal portfolio for a particular class of utility functions is investigated

The EHTA for the Modified Nizhnik-Novikov-Vesselov Equation

AbstractIn this paper, by using the extended homoclinic test approach, a new type of two-wave solutions are constructed for the Modified Nizhnik-Novikov-Vesselov equation. Their dynamic properties of some exact solutions are discussed and their profiles of these solutions are given by Maple

Estimation of covariance matrix with ARMA structure through quadratic loss function

In this paper we propose a novel method to estimate the high-dimensional covariance matrix with an order-1 autoregressive moving average process, i.e. ARMA(1,1), through quadratic loss function. The ARMA(1,1) structure is a commonly used covariance structures in time series and multivariate analysis but involves unknown parameters including the variance and two correlation coefficients. We propose to use the quadratic loss function to measure the discrepancy between a given covariance matrix, such as the sample covariance matrix, and the underlying covariance matrix with ARMA(1,1) structure, so that the parameter estimates can be obtained by minimizing the discrepancy.Simulation studies and real data analysis show that the proposed method works well in estimating the covariance matrix with ARMA(1,1) structure even if the dimension is very high

Illegal Intrusion Detection for In-Vehicle CAN Bus Based on Immunology Principle

The controller area network (CAN) bus has become one of the most commonly used protocols in automotive networks. Some potential attackers inject malicious data packets into the CAN bus through external interfaces for implementing illegal operations (intrusion). Anomaly detection is a technique for network intrusion detection which can detect malicious data packs by comparing the normal data packets with incoming data packets obtained from the network traffic. The data of a normal network is in a symmetric and stable state, which will become asymmetric when compromised. Considering the in-vehicle network, the CAN bus is symmetrically similar to the immune system in terms of internal network structure and external invasion threats. In this work, we use an intrusion detection method based on the dendritic cell algorithm (DCA). However, existing studies suggest the use of optimization methods to improve the accuracy of classification algorithms, and the current optimization of the parameters of the detection method mostly relies on the manual tuning of the parameters, which is a large workload. In view of the above challenges, this paper proposes a new detection algorithm based on the particle swarm optimization algorithm (PSO) and gravitational search algorithm (GSA) to improve the dendritic cell algorithm (PSO-GSA-DCA). PSO-GSA-DCA achieves adaptive parameter tuning and improves detection accuracy by mixing optimization algorithms and using them to optimize the dendritic cell algorithm classifier. Additionally, DCA-based CAN message attribute matching rules (measured by information gain and standard deviation of CAN data) are proposed for matching the three input signals (PAMP, DS, SS) of the DCA. The experimental results show that our proposed scheme has a significant improvement in accuracy, which can reach 91.64%, and lower time loss compared with other correlation anomaly detection schemes. Our proposed method also enables adaptive tuning, which solves the problem that most models now rely on manual tuning