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In multiple-testing problems, where a large number of hypotheses are tested simultaneously, false discovery rate (FDR) control can be achieved with the well-known Benjamini–Hochberg procedure, which adapts to the amount of signal in the data, under certain distributional assumptions. Many modifications of this procedure have been proposed to improve power in scenarios where the hypotheses are organized into groups or into a hierarchy, as well as other structured settings. Here we introduce the ‘structure-adaptive Benjamini–Hochberg algorithm’ (SABHA) as a generalization of these adaptive testing methods. The SABHA method incorporates prior information about any predetermined type of structure in the pattern of locations of the signals and nulls within the list of hypotheses, to reweight the p-values in a data-adaptive way. This raises the power by making more discoveries in regions where signals appear to be more common. Our main theoretical result proves that the SABHA method controls the FDR at a level that is at most slightly higher than the target FDR level, as long as the adaptive weights are constrained sufficiently so as not to overfit too much to the data—interestingly, the excess FDR can be related to the Rademacher complexity or Gaussian width of the class from which we choose our data-adaptive weights. We apply this general framework to various structured settings, including ordered, grouped and low total variation structures, and obtain the bounds on the FDR for each specific setting. We also examine the empirical performance of the SABHA method on functional magnetic resonance imaging activity data and on gene–drug response data, as well as on simulated data.

The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It is shown that the Rabinovich system can exhibit a hidden attractor in the case of multistability as well as a classical self-excited attractor. The hidden attractor in this system can be localized by analytical/numerical methods based on the continuation and perpetual points. The concept of finite-time Lyapunov dimension is developed for numerical study of the dimension of attractors. A conjecture on the Lyapunov dimension of self-excited attractors and the notion of exact Lyapunov dimension are discussed. A comparative survey on the computation of the finite-time Lyapunov exponents and dimension by different algorithms is presented. An adaptive algorithm for studying the dynamics of the finite-time Lyapunov dimension is suggested. Various estimates of the finite-time Lyapunov dimension for the hidden attractor and hidden transient chaotic set in the case of multistability are given.

The public transportation system is now dealing with a number of problems brought on by the sharp increase in automobile ownership in cities as well as the buildup of vehicles as a result of events and accidents. However, the city’s limited road network capacity cannot keep up with the increasing traffic demand, which further worsens travel conditions and results in a waste of time and money. Given that it is challenging to enhance the capacity of the road network in practice, efficient vehicle travel and evacuation using algorithms has emerged as a recent study focus. It is crucial to learn how to manage urban traffic issues during emergencies and maintain smooth and safe traffic flow. The existing studies only consider the optimized route selection for individual vehicles, signal cycle of traffic lights and deploy historical data to disperse the vehicles on alternative routes. However, such works do not consider the conflict of routes between vehicles, the customized traffic demand of each vehicle and uncertain traffic conditions. Therefore, this paper proposes a novel approach to facilitate the user to select the optimal route with real-time traffic scenario. Furthermore, the Nash equilibrium is established by mutual information swapping and self-adaptive learning method. Simulation results show that the proposed algorithm has better route selection capability in real-time personalized road traffic as compared with existing algorithms.

To solve the split common null point problem with multiple output sets in Hilbert spaces, we introduce two new self-adaptive algorithms and prove strong convergence theorems for both of them.

In this paper, an efficient face recognition method using AGA and ANFIS-ABC has been proposed. At first stage, the face images gathered from the database are preprocessed. At Second stage, an interest point which is used to improve the detection rate consequently. The parameters used in the interest point determination are optimized using the Adaptive Genetic Algorithm. Finally using ANFIS, face images are classified by using extracted features. During the training process, the parameters of ANFIS are optimized using Artificial Bee Colony Algorithm (ABC) in order to improve the accuracy. The performance of the proposed ANFIS-ABC technique is evaluated using an ORL database with 400 images of 40 individuals, YALE-B database with 165 images of 15 individuals and finally with real time video the detection rate and false alarm rate is compared with proposed and existing methods to prove the system efficiency.

In vehicle GNSS/INS integrated navigation, robust and adaptive algorithms have become one of the key technologies for achieving a comprehensive PNT due to their ability to control the gross errors of the observation model and dynamic model. The Sage–Husa algorithm is widely used in optimizing the Kalman filter due to its ability to estimate the observation or state covariance without prior information. However, the quality of observations in complex environments is prone to large fluctuations, so the averaging method is not suitable for dynamic navigation. To solve this problem, this article designs a double window structure and introduces a time-dependent fading weighted factor. At the same time, a logarithmic form factor constructor is proposed in order to avoid anomalies in the robust and adaptive factor. The traditional innovation adaptive filter is improved and turned into a multi-factor adaptive filter. In this paper, an improved fault detection algorithm is used to combine a robust algorithm with an adaptive algorithm to adapt to different gross errors in different scenarios. The experimental results of complex scenarios show that the position RMSE of the improved algorithm in the east, north, and height directions is 0.68 m, 0.71 m, and 1.05 m, respectively, which are reduced by 39.3%, 39.3%, and 70.3% compared to the EKF.

In order to automatically recognize different kinds of objects from their backgrounds, a self-adaptive segmentation algorithm that can effectively extract the targets from various surroundings is of great importance. Image thresholding is widely adopted in this field because of its simplicity and high efficiency. The entropy-based and variance-based algorithms are two main kinds of image thresholding methods, and have been independently developed for different kinds of images over the years. In this paper, their advantages are combined and a new algorithm is proposed to deal with a more general scope of images, including the long-range correlations among the pixels that can be determined by a nonextensive parameter. In comparison with the other famous entropy-based and variance-based image thresholding algorithms, the new algorithm performs better in terms of correctness and robustness, as quantitatively demonstrated by four quality indices, ME, RAE, MHD, and PSNR. Furthermore, the whole process of the new algorithm has potential application in self-adaptive object recognition.

This paper reviews the past and the recent research on Adaptive Filter algorithms based on adaptive noise cancellation systems. In many applications of noise cancellation, the change in signal characteristics could be quite fast which requires the utilization of adaptive algorithms that converge rapidly. Algorithms such as LMS and RLS proves to be vital in the noise cancellation are reviewed including principle and recent modifications to increase the convergence rate and reduce the computational complexity for future implementation. The purpose of this paper is not only to discuss various noise cancellation LMS algorithms but also to provide the reader with an overview of the research conducted.

In this paper, for two different forms of non-smooth convex optimization problems, we investigate the self-adaptive algorithms with inertia acceleration. Firstly, we propose a self-adaptive proximal gradient algorithm with an inertial step. Under reasonable parameters, the strong convergence theorem is established. Secondly, we propose a self-adaptive split proximal algorithm with inertial acceleration. We prove that our algorithm converges strongly under suitable conditions. Notably, both inertial algorithms are extended to multi-step inertial version to accelerate the convergence of the algorithms. Finally, numerical results illustrate the performances of our algorithms.

In this study, a novel adaptive strategy is designed based on fractional least mean square (LMS) algorithm for parameter estimation of Hammerstein nonlinear autoregressive moving average system with exogenous noise (HN-ARMAX). The design scheme consists of parameterization of HN-ARMAX systems to obtain linear-in-parameter models and to use fractional LMS algorithm for adapting unknown parameter vectors. The performance analysis of the proposed method is carried out based on convergence to the desired values of HN-ARMAX systems, and comparison is made with state-of-the-art kernel LMS and Volterra LMS algorithms. The consistency in terms of accuracy and convergence is established through the results of statistical analysis based on sufficient large number of independent runs rather than single successful run of the algorithm. The performance of proposed scheme is superior due to its strong mathematical foundations, nonlinear weight updating mechanism and more convergence controlling variables but at the cost of bit more computational requirements.