Iteration Index Research Articles

Anisotropic sparse transformation for spectral CT image reconstruction

AbstractPhoton‐counting detector‐based computed tomography (PCD‐CT) is an advanced realization of spectral CT, the multi‐energy projection data is captured from the same object, hence, CT images can provide additional spectral resolution, making it possible to perform material decomposition. However, multiple projections may have a low signal‐to‐noise ratio (SNR), such that CT images suffer from noise. To handle this problem, a spectral CT image reconstruction method based on anisotropic sparse transformation (AST) is proposed. To increase the quality of reconstruction, AST through an anisotropic guided filter (AGF) and quasi norm is proposed. Then, as a new regularization, AST is introduced into an iterative reconstruction process, generating an AST‐based method. Moreover, to utilize the correlation among projection data, the average image serves as the guidance image of AGF, it varies with the iterative index, resulting in a technique of dynamic average image (DAI). The AST‐based model involves quasi norm minimization, hence an effective strategy is employed to solve the corresponding problem. A series of experiments were performed. The experiment showed that, compared to other listed methods, the result of the AST‐based method can achieve better visualization and higher quantitative indexes, hence it has application potential in the medical imaging field.

Convergence and Stability of Optimal Regulation via Generalized N-Step Value Gradient Learning.

In this article, the generalized N -step value gradient learning (GNSVGL) algorithm, which takes a long-term prediction parameter λ into account, is developed for infinite horizon discounted near-optimal control of discrete-time nonlinear systems. The proposed GNSVGL algorithm can accelerate the learning process of adaptive dynamic programming (ADP) and has a better performance by learning from more than one future reward. Compared with the traditional N -step value gradient learning (NSVGL) algorithm with zero initial functions, the proposed GNSVGL algorithm is initialized with positive definite functions. Considering different initial cost functions, the convergence analysis of the value-iteration-based algorithm is provided. The stability condition for the iterative control policy is established to determine the value of the iteration index, under which the control law can make the system asymptotically stable. Under such a condition, if the system is asymptotically stable at the current iteration, then the iterative control laws after this step are guaranteed to be stabilizing. Two critic neural networks and one action network are constructed to approximate the one-return costate function, the λ -return costate function, and the control law, respectively. It is emphasized that one-return and λ -return critic networks are combined to train the action neural network. Finally, via conducting simulation studies and comparisons, the superiority of the developed algorithm is confirmed.

Neuro-Optimal Event-Triggered Impulsive Control for Stochastic Systems via ADP.

This article presents a novel neural-network-based optimal event-triggered impulsive control method. First, a novel general-event-based impulsive transition matrix (GITM) is constructed to represent the probability distribution evolving characteristics regarding all system states across the impulsive actions, rather than the prefixed timing sequence. On the foundation of this GITM, the event-triggered impulsive adaptive dynamic programming (ETIADP) algorithm and its high-efficiency version (HEIADP) are developed to deal with the optimization problems for stochastic systems with event-triggered impulsive controls. It is shown that the obtained controller design scheme can reduce the computational and communication burden caused by updating the controller periodically. By analyzing the admissibility, monotonicity, and optimality properties of ETIADP and HEIADP, we further establish the approximation error bound of the neural networks to address the connection between the ideal and neural-network-based realizations of the present methods. It is proven that the iterative value functions of both the ETIADP and HEIADP algorithms fall in a small neighborhood of the optimum as the iteration index increases to infinity. By adopting a novel task synchronization mechanism, the proposed HEIADP algorithm fully utilizes the computing resources of multiprocessor systems (MPSs), while significantly reducing the memory requirement compared to traditional ADP approaches. Finally, we carry out a numerical study to show that the proposed methods can fulfill the desired goals.

Optimising desired gain indices to maximise selection response.

In plant breeding, we often aim to improve multiple traits at once. However, without knowing the economic value of each trait, it is hard to decide which traits to focus on. This is where "desired gain selection indices" come in handy, which can yield optimal gains in each trait based on the breeder's prioritisation of desired improvements when economic weights are not available. However, they lack the ability to maximise the selection response and determine the correlation between the index and net genetic merit. Here, we report the development of an iterative desired gain selection index method that optimises the sampling of the desired gain values to achieve a targeted or a user-specified selection response for multiple traits. This targeted selection response can be constrained or unconstrained for either a subset or all the studied traits. We tested the method using genomic estimated breeding values (GEBVs) for seven traits in a bread wheat (Triticum aestivum) reference breeding population comprising 3,331 lines and achieved prediction accuracies ranging between 0.29 and 0.47 across the seven traits. The indices were validated using 3,005 double haploid lines that were derived from crosses between parents selected from the reference population. We tested three user-specified response scenarios: a constrained equal weight (INDEX1), a constrained yield dominant weight (INDEX2), and an unconstrained weight (INDEX3). Our method achieved an equivalent response to the user-specified selection response when constraining a set of traits, and this response was much better than the response of the traditional desired gain selection indices method without iteration. Interestingly, when using unconstrained weight, our iterative method maximised the selection response and shifted the average GEBVs of the selection candidates towards the desired direction. Our results show that the method is an optimal choice not only when economic weights are unavailable, but also when constraining the selection response is an unfavourable option.

On the effect of clock offsets and quantization on learning-based adversarial games

In this work, we consider systems whose components suffer from clock offsets and quantization and study the effect of those on a reinforcement learning (RL) algorithm. Specifically, we consider an off-policy iterative RL algorithm for continuous-time systems, which uses input and state data to approximate the Nash-equilibrium of a zero-sum game. However, the data used by this algorithm are not consistent with one another, in that each of them originates from a slightly different time instant of the past, hence putting the convergence of the algorithm in question. We prove that, given that these timing inconsistencies remain below a certain threshold, the iterative off-policy RL algorithm will still converge epsilon-closely to the desired Nash policy. However, this result is conditional to a certain Lipschitz continuity and differentiability condition on the input-state data collected, which is indispensable in the presence of clock offsets. A similar result is also derived when quantization of the measured state is considered. Finally, unlike prior work, we provide a sufficiently rich data condition for the execution of the iterative RL algorithm, which can be verified a priori across all iteration indices. Simulations are performed, which verify and clarify theoretical findings.

Data-driven output consensus for a class of discrete-time multiagent systems by reinforcement learning techniques

The primary objective of this research paper is to examine the challenges associated with optimization and tracking control in discrete-time multiagent systems. This study begins by defining the optimal tracking control issue within the framework of a leader–follower multiagent system. A novel approach based on policy iteration is introduced for calculating the control law and performance index. The paper also includes an analysis of the convergence properties of this technique, ensuring its effectiveness in reaching optimal solutions. To facilitate this, an actor–critic neural network framework is utilized to approximate the control law and iterative performance index function. The proposed approach enables the real-time implementation of the policy iteration method, eliminating the requirement for prior knowledge of the system’s dynamics. The paper concludes with a series of simulation experiments that demonstrate the practicality and efficiency of the developed optimal tracking control strategies.

Design of Privacy Protection System for Target Search Based on Selection Algorithm and Sustainable Iteration Index

The data self-destruct method based on privacy cloud proposed in this paper can realize the automatic destruction of cloud data after expiration, and based on this method, a self-destruct image protection system is implemented. This project intends to combine the adaptive scale invariant Feature conversion (SIFT) extraction of ciphertext images with binary SIFT to ensure the confidentiality of the images uploaded to the server in the ciphertext space. The security protection of data is realized using Paillier homomorphic encryption technology. The feature of SIFT is extracted from the encrypted region, and it is expressed in binary form to reduce the amount of computation and memory overhead. The experimental results show that this method can effectively prevent the automatic destruction of images after expiration, so as to ensure that the user's personal information is not leaked.

Implementation of Asynchronous Distributed Gauss-Newton Optimization Algorithms for Uncertainty Quantification by Conditioning to Production Data

Summary Previous implementation of the distributed Gauss-Newton (DGN) optimization algorithm ran multiple optimization threads in parallel, employing a synchronous running mode (S-DGN). As a result, it waits for all simulations submitted in each iteration to complete, which may significantly degrade performance because a few simulations may run much longer than others, especially for time-consuming real-field cases. To overcome this limitation and thus improve the DGN optimizer’s execution, we propose two asynchronous DGN (A-DGN) optimization algorithms in this paper. The two A-DGN optimization algorithms are (1) the local-search algorithm (A-DGN-LS) to locate multiple maximum a-posteriori (MAP) estimates and (2) the integrated global-search algorithm with the randomized maximum likelihood (RML) method (A-DGN + RML) to generate hundreds of RML samples in parallel for uncertainty quantification. We propose using batch together with a checking time interval to control the optimization process. The A-DGN optimizers check the status of all running simulations after every checking time frame. The iteration index of each optimization thread is updated dynamically according to its simulation status. Thus, different optimization threads may have different iteration indices in the same batch. A new simulation case is proposed immediately once the simulation of an optimization thread is completed, without waiting for the completion of other simulations. We modified the training data set updating algorithm using each thread’s dynamically updated iteration index to implement the asynchronous running mode. We apply the modified QR decomposition method to estimate the sensitivity matrix at the best solution of each optimization thread by linear interpolation of all or a subset of the training data to avoid the issue of solving a linear system with a singular matrix because of insufficient training data points in early batches. A new simulation case (or search point) is generated by solving the Gauss-Newton (GN) trust-region subproblem (GNTRS) using the estimated sensitivity matrix. We developed a more efficient and robust GNTRS solver using eigenvalue decomposition (EVD). The proposed A-DGN optimization methods are tested and validated on a 2D analytical toy problem and a synthetic history-matching problem and then applied to a real-field deepwater reservoir model. Numerical tests confirm that the proposed A-DGN optimization methods can converge to solutions with matching quality comparable to those obtained by the S-DGN optimizers, saving on the time required for the optimizer to converge by a factor ranging from 1.3 to 2 when compared to the S-DGN optimizer depending on the problem. The new A-DGN optimization algorithms improve efficiency and robustness in solving history-matching or inversion problems, especially for uncertainty quantification of subsurface model parameters and production forecasts of real-field reservoirs by conditioning production data.

Fast multilevel iteration methods for solving nonlinear ill-posed problems

Abstract We propose a multilevel iteration method for the numerical solution of nonlinear ill-posed problems in the Hilbert space by using the Tikhonov regularization method. This leads to fast solutions of the discrete regularization methods for the nonlinear ill-posed equations. An adaptive choice of an a posteriori rule is suggested to choose the stopping index of iteration, and the rates of convergence are also derived. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.

Iterative learning tracking control for second‐order nonlinear hyperbolic impulsive partial differential systems

AbstractThis paper studies the iterative learning control (ILC) for a class of second‐order nonlinear hyperbolic impulsive partial differential systems. Firstly, to follow the discontinuous desired output, a P‐type learning law is adopted, and sufficient conditions for the convergence of the tracking error is established under identified initial state value. The rigorous analysis is also given using the impulsive Gronwall inequality. Secondly, the tracking error of output trajectory is considered in systems with state initial values shifting based on an initial learning algorithm. These results of this paper show that the tracking error on the finite time interval can uniform converge to 0 as the iteration index goes to infinity if impulse number of the systems is only a finite numbers. Finally, two numerical simulation examples are given to verify the effectiveness of the theoretical results.

Formation-Based Decentralized Iterative Learning Cooperative Impedance Control for a Team of Robot Manipulators

We present in this article a new decentralized iterative learning cooperative impedance control (ILCIC) architecture to cooperatively control the impedance for a team of robot manipulators that operate over an iteration domain. With a new definition of the neighborhood impedance error, we propose a novel formation-based cooperative control architecture, so that every manipulator can achieve the desired impedance model, even when some manipulators do not have direct access to the desired angle profiles. Besides, the desired angle profiles as well as the desired impedance model can be iteration varying, which is an important consideration when the team needs to execute different tasks in different iterations. With rigorous mathematical analysis, we show that each manipulator’s impedance error can uniformly converge to zero as the iteration index increases to infinity. A simulation study is discussed in order to further illustrate the effectiveness of the discussed algorithm.

A Travel Demand Response Model in MaaS Based on Spatiotemporal Preference Clustering

To respond to travel demand in the MaaS system, improve transport efficiency, and optimize the framework of MaaS, we propose a travel demand response model based on a spatiotemporal preference clustering algorithm that considers the impact of travel preferences and features of the MaaS system to improve travel demand response and achieve full coverage of travel demands. Specifically, in the MaaS system, the time preference hierarchical clustering algorithm is optimized with travel preference as the perception factor and preference priority order as the iteration index. Then, we cluster the departure and arrival times of reservation demand points and iteratively analyze the discrete points to obtain the set of reservation demand points with convergent time dimensions under similar preferences. Then, the spatial preference DBSCAN clustering algorithm is improved with travel preference and preference priority order as the iteration indices, and spatial clustering of the time-dense points are updated by the silhouette coefficient to obtain reservation demand points with similar spatiotemporal preference and respond to the demands. Meanwhile, traffic resources are coordinated by the MaaS system and the flexible means of transport are deployed to spatiotemporal discrete points to achieve full coverage of travel demand. Simulation shows that when the neighborhood range is 0.5 km and the least number of reservation demand sites is 3, our spatiotemporal model achieves a response rate of reservation demand points at 95%, and a demand coverage rate of 100%, which is 15% and 6.7% higher than the hierarchical clustering model and the DBSCAN clustering model, respectively. The demand response rate is also improved compared to the spatiotemporal clustering model in the customized bus model. The model and algorithm have some applicability and can be applied to areas with fixed, semifixed and flexible route transport, thereby considerably improving the travel demand response efficiency and transport service quality.

Indicators and participatory processes: a framework for assessing integrated climate vulnerability and risk as applied in Los Angeles County, California

Climate vulnerability research is enhanced by stakeholder engagement as coastal communities are increasingly vulnerable to climate-driven impacts, yet these impacts are rarely evenly distributed across space and stakeholder feedback is not always well incorporated into the process. While often used in applied management applications, integrated spatially explicit assessments of multi-faceted vulnerability and hazard less commonly appear in the scientific literature, especially those that are transferable across geographies and risk metrics. Since many geographies lack an integrated, stakeholder-driven assessment of multiple hazards and vulnerabilities within the same assessment, scientists with the National Oceanic and Atmospheric Administration’s National Centers for Coastal Ocean Science developed a transferable and integrated community vulnerability assessment framework (Framework) that relies primarily upon available secondary data and is supplemented with stakeholder-derived primary data. Using blended approaches in stakeholder engagement, we present the Framework’s six methodological steps as recently applied in Los Angeles County, California: iterative partner engagement, indicator and index development, vulnerability assessment, hazard assessment, risk assessment, and reengagement for adaptation action. We conclude that boundary-spanning organizations such as Sea Grant Extension programs can play a crucial role in participatory science and stakeholder needs assessments, and emphasize the need for continued stakeholder engagement in climate science.

Construction Cost Budget Control Based on the Dynamic Distributed Clustering Algorithm

In order to improve the effect of construction cost budget control, this paper applies the dynamic distributed clustering algorithm to the analysis of project cost budget data and proposes a two-stage strategy iterative algorithm to obtain the iterative control law and iterative performance index function. Moreover, this paper constructs an executive evaluation neural network to approximate the iterative control law and iterative performance index function, respectively. This neural network structure can implement the proposed algorithm online without the need for system dynamics. Through numerical simulation research and evaluation test research, it can be seen that the dynamic distributed clustering algorithm proposed in this paper has a good effect on the construction cost budget control system, which can effectively improve the reliability of construction project cost budget control.

Optimal group consensus control for the second‐order agents in the coopetition networks via adaptive dynamic programming and event‐triggered methods

AbstractThis article investigates the optimal group consensus control problem for the second‐order multi‐agent systems by using event‐triggered and adaptive dynamic programming methods. The proposed method only uses the interaction information among the agents. Comprehensively considering the coopetition coupling interactions among the agents, a novel tracking error function is addressed for meeting the requirement of group consensus. On this basis, we use the Bellman optimality principle to formulate the optimal group consensus problem. To implement the proposed method, the actor–critic neural networks are used to approximate the iterative performance index functions and the control policies in real time. Meanwhile, the event‐triggered condition with filter function is installed for each agent to reduce the control cost. Therefore, the weights of actor–critic networks are updated only at the event‐triggered instants. The weight estimation errors and the control policy estimation errors are proved uniformly ultimately bounded and the Zeno behavior in the system can be avoided. Finally, the comparative simulation results show that the proposed method can greatly reduce the update times of the control policy of the system.

Dynamics of Nonpolar Solutions to the Discrete Painlevé I Equation

This manuscript develops a novel understanding of non-polar solutions of the discrete Painlev\'e I equation (dP1). As the non-autonomous counterpart of an analytically completely integrable difference equation, this system is endowed with a rich dynamical structure. In addition, its non-polar solutions, which grow without bounds as the iteration index $n$ increases, are of particular relevance to other areas of mathematics. We combine theory and asymptotics with high-precision numerical simulations to arrive at the following picture: when extended to include backward iterates, known non-polar solutions of dP1 form a family of heteroclinic connections between two fixed points at infinity. One of these solutions, the Freud orbit of orthogonal polynomial theory, is a singular limit of the other solutions in the family. Near their asymptotic limits, all solutions converge to the Freud orbit, which follows invariant curves of dP1, when written as a 3-D autonomous system, and reaches the point at positive infinity along a center manifold. This description leads to two important results. First, the Freud orbit tracks sequences of period-1 and 2 points of the autonomous counterpart of dP1 for large positive and negative values of $n$, respectively. Second, we identify an elegant method to obtain an asymptotic expansion of the iterates on the Freud orbit for large positive values of $n$. The structure of invariant manifolds emerging from this picture contributes to a deeper understanding of the global analysis of an interesting class of discrete dynamical systems.

Spiking Adaptive Dynamic Programming Based on Poisson Process for Discrete-Time Nonlinear Systems.

In this article, a new iterative spiking adaptive dynamic programming (SADP) method based on the Poisson process is developed to solve optimal impulsive control problems. For a fixed time interval, combining the Poisson process and the maximum likelihood estimation (MLE), the three-tuple of state, spiking interval, and probability of Poisson distribution can be computed, and then, the iterative value functions and iterative control laws can be obtained. A property analysis method is developed to show that the value functions converge to optimal performance index function as the iterative index increases from zero to infinity. Finally, two simulation examples are given to verify the effectiveness of the developed algorithm.

Sparse Representations of Positive Functions via First- and Second-Order Pseudo-Mirror Descent

We consider expected risk minimization problems when the range of the estimator is required to be nonnegative, motivated by the settings of maximum likelihood estimation (MLE) and trajectory optimization. To facilitate nonlinear interpolation, we hypothesize that the search space is a Reproducing Kernel Hilbert Space (RKHS). We develop first and second-order variants of stochastic mirror descent employing (i) \emph{pseudo-gradients} and (ii) complexity-reducing projections. Compressive projection in the first-order scheme is executed via kernel orthogonal matching pursuit (KOMP), which overcomes the fact that the vanilla RKHS parameterization grows unbounded with the iteration index in the stochastic setting. Moreover, pseudo-gradients are needed when gradient estimates for cost are only computable up to some numerical error, which arise in, e.g., integral approximations. Under constant step-size and compression budget, we establish tradeoffs between the radius of convergence of the expected sub-optimality and the projection budget parameter, as well as non-asymptotic bounds on the model complexity. To refine the solution's precision, we develop a second-order extension which employs recursively averaged pseudo-gradient outer-products to approximate the Hessian inverse, whose convergence in mean is established under an additional eigenvalue decay condition on the Hessian of the optimal RKHS element, which is unique to this work. Experiments demonstrate favorable performance on inhomogeneous Poisson Process intensity estimation in practice.

GPN: A novel gravity model based on position and neighborhood to identify influential nodes in complex networks

The identification of influential nodes is one of the most significant and challenging research issues in network science. Many centrality indices have been established starting from topological features of networks. In this work, we propose a novel gravity model based on position and neighborhood (GPN), in which the mass of focal and neighbor nodes is redefined by the extended outspreading capability and modified k-shell iteration index, respectively. This new model comprehensively considers the position, local and path information of nodes to identify influential nodes. To test the effectiveness of GPN, a number of simulation experiments on nine real networks have been conducted with the aid of the susceptible–infected–recovered (SIR) model. The results indicate that GPN has better performance than seven popular methods. Furthermore, the proposed method has near linear time cost and thus it is suitable for large-scale networks.

Momentum extrapolation prediction-based asynchronous distributed optimization for power systems

Iterative distributed optimization algorithms usually need synchronization of subproblems at each iteration. An iteration index is defined, and subproblems are solved once at each iteration. This degrades distributed optimization scalability and computational resource under-utilization, particularly if subproblems are heterogeneous. To address these limitations for solving optimal power flow, this paper proposes a prediction-correction-based asynchronous alternating direction method of multipliers (A-ADMM). At the end of each iteration, an OPF subproblem no longer needs to wait for its neighbors’ most updated shared variable information. A momentum-based extrapolation method is developed to predict shared variable values. A correction step is designed using momentum to prevent predicted values from becoming far from the possible solution and avoid divergence. These predictions are integrated into distributed optimization to allow subproblems to be solved continuously with no need for synchronization at each iteration. The proposed A-ADMM reduces the unproductive time and computational resource under-utilization if subproblems are computationally heterogeneous. A-ADMM potentially enhances the solution speed even if subproblems are homogeneous as every iteration k is carried out using a good forecast of shared variable values in iteration k+1. Numerical results show the promising performance of the proposed algorithm.