This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations extending our findings in Dahlke and Schneider (Anal Appl 17(2):235-291, 2019, Thms. 4.5, 4.9, 4.12, 4.14) to domain...
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This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations extending our findings in Dahlke and Schneider (Anal Appl 17(2):235-291, 2019, Thms. 4.5, 4.9, 4.12, 4.14) to domains of polyhedral type. In particular, we study the smoothness in the specific scale B-tau,tau(r), 1/tau = r/d + 1/p of Besov spaces. The regularity in these spaces determines the approximation order that can be achieved by adaptive and other nonlinear approximation schemes. We show that for all cases under consideration the Besov regularity is high enough to justify the use of adaptive algorithms.
作者：
Ji, XiaojunWang, RuWang, HaoLiu, WenjianShandong Univ
Res Ctr Math & Interdisciplinary Sci Qingdao 266237 Shandong Peoples R China Shandong Univ
Frontiers Sci Ctr Nonlinear Expectat Minist Educ Qingdao 266237 Shandong Peoples R China Shandong Univ
Qingdao Inst Theoret & Computat Sci Inst Frontier & Interdisciplinary Sci Qingdao 266237 Shandong Peoples R China
As an optimal one-dimensional reaction coordinate, the committor function not only describes the probability of a trajectory initiated at a phase space point first reaching the product state before reaching the reacta...
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As an optimal one-dimensional reaction coordinate, the committor function not only describes the probability of a trajectory initiated at a phase space point first reaching the product state before reaching the reactant state but also preserves the kinetics when utilized to run a reduced dynamics model. However, calculating the committor function in high-dimensional systems poses significant challenges. In this paper, within the framework of milestoning, exact expressions for committor functions at two levels of coarse graining are given, including committor functions of phase space point to point (CFPP) and milestone to milestone (CFMM). When combined with transition kernels obtained from trajectory analysis, these expressions can be utilized to accurately and efficiently compute the committor functions. Furthermore, based on the calculated committor functions, an adaptive algorithm is developed to gradually refine the transition state region. Finally, two model examples are employed to assess the accuracy of these different formulations of committor functions.
In long haul communication environments, speech data transmission is severely affected by echoes. This phenomenon results in high bit errors as well as in degraded and annoying performance. Traditionally these problem...
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In long haul communication environments, speech data transmission is severely affected by echoes. This phenomenon results in high bit errors as well as in degraded and annoying performance. Traditionally these problems, including hybrid and acoustic echoes, have been controlled through the use of echo suppressors. These suppressors were subsequently replaced by line echo cancellers using adaptive Finite Impulse Response filters. Fractional calculus has been applied successfully for fixed filtering with constant coefficients and in discrete time adaptive filtering that adjusts the weights according to the environment. This paper presents the Fractional Least Mean Square (FLMS) and Fractional Normalized LMS (FNLMS) algorithms for application in echo cancellation. Moreover, the performances of the FLMS and FNLMS are compared with those provided by the standard LMS, NLMS and Block Discrete Fourier Transform solutions. The mean square error criterion is used as the performance comparison criterion for two types of voice signals namely real and synthetic. The simulation results show a performance improvement of about 50% over the traditional counterparts.
This paper investigates a distributed control strategy for the safety configuration of spacecraft systems subject to parameter uncertainty. The main feature lies in that the proposed control strategy is designed by di...
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Over recent years, many advancements in networks have taken place with now the advent of 6G. With these growing advancements, challenges in managing networks also emerge. Network Digital Twins (NDTs) is one of the pot...
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ISBN:
(数字)9798350368369
ISBN:
(纸本)9798350368376
Over recent years, many advancements in networks have taken place with now the advent of 6G. With these growing advancements, challenges in managing networks also emerge. Network Digital Twins (NDTs) is one of the potential technology in solving many of these challenges because of the capability to virtually replicate the physical network elements. One of the key challenges is predicting network traffic especially with the exponentially growing number of devices in the network. In this paper, we study and show how varying the “look-back period” and “forecast horizon” significantly affects traffic predictions. Look-back period or window size is how much of the historical data is used by a prediction algorithm to make predictions. Forecast horizon is how far in the future we can predict. These highly impact how accurately traffic is predicted in networks and as well significantly determine how well Digital Twins (DTs) for networks accurately reflect traffic of the physical network.
In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal app...
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In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques, solving problems with nonlinearities elegantly. In this paper, we present data-selective adaptive kernel normalized least-mean square (KNLMS) algorithms that can increase their learning rate and reduce their computational complexity. In fact, these methods deal with kernel expansions, creating a growing structure also known as the dictionary, whose size depends on the number of observations and their innovation. The algorithms described herein use an adaptive step-size to accelerate the learning and can offer an excellent tradeoff between convergence speed and steady state, which allows them to solve nonlinear filtering and estimation problems with a large number of parameters without requiring a large computational cost. The data-selective update scheme also limits the number of operations performed and the size of the dictionary created by the kernel expansion, saving computational resources and dealing with one of the major problems of kernel adaptive algorithms. A statistical analysis is carried out along with a computational complexity analysis of the proposed algorithms. Simulations show that the proposed KNLMS algorithms outperform existing algorithms in examples of nonlinear system identification and prediction of a time series originating from a nonlinear difference equation. (C) 2018 Elsevier B.V. All rights reserved.
Abstract: The theory of vertical fall in the atmosphere was investigated as applied to an unmanned return spacecraft for various cases of ratio of the initial and quasi-steady-state velocities of fall. The modeling of...
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The choice of relaxation parameter in the projected successive overrelaxation (PSOR) method for nonnegative quadratic programming problems is problem-dependent. We present novel adaptive PSOR algorithms that adaptivel...
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The power systems of offshore jack-up drilling rigs consist of diesel generators running in parallel load-sharing mode, controlled by an automatic Power Management System (PMS). In this paper, the operational performa...
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The Influence Maximization problem is a classic and well-studied problem in the area of Social Networks Analysis. In this problem you have a social network, a given information diffusion model, and a budget B, and you...
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ISBN:
(纸本)9798400714269
The Influence Maximization problem is a classic and well-studied problem in the area of Social Networks Analysis. In this problem you have a social network, a given information diffusion model, and a budget B, and you have to select a set of at most B nodes (seeds) to activate in order to start an information diffusion campaign that is able to reach the (expected) largest number of nodes in the network. Recently, to better model viral marketing scenarios where advertisers conduct multiple rounds of viral marketing to promote one product, attention has been given to the adaptive and the multi-round versions of the problem. Here the campaign is orchestrated on a horizon of T rounds and at the beginning of each round a different set of seeds is activated that can be adaptively selected given the results of the previous rounds. In this paper we generalize this setting to the case where the diffusion probabilities of the links in the network are not known in advance and they have to be learned while the campaign is *** study the problem under the lens of online bandit algorithms, and we propose an online learning algorithm that is able to achieve a constant approximation of the optimal solution with only constant regret with respect to T. We also propose an alternative approach and we give preliminary experimental evidence that this outperforms our online learning algorithm in terms of computational complexity, keeping the regret sublinear.
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