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Polynomial crisp-minimization algorithm for fuzzy deterministic automata ☆

FUZZY SETS AND SYSTEMS 2024年 495卷

作者： de Mendivil Grau, Aitor Gonzalez Farina, Federico Stanimirovic, Stefan Micic, Ivana Gonzalez de Mendivil, Jose Ramon Univ Publ Navarra Dept Estadist Informat & Matemat Arrosadia S-N Pamplona 31006 Spain Univ Nis Fac Sci & Math Visegradska 33 Nish 18000 Serbia

Designing automata minimization algorithms is a significant topic in Automata Theory and Languages with practical applications. In this paper, we develop an efficient minimization algorithm for deterministic fuzzy finite automata over locally finite lattices. More precisely, the algorithm outputs an equivalent minimal crisp-deterministic fuzzy finite automaton for an input fuzzy deterministic finite automaton (FDfA). The running time of the proposed algorithm is polynomial for particular types of locally finite lattices, specifically for max-min-based complete residuated lattices. The intuition behind the proposed algorithm relies on the polynomial minimization algorithm's intuition for ordinary deterministic automata developed by Vazquez de Parga, Garcia, and Lopez (2013) [35]. The motivation for this study comes from the fact that the original algorithm's notions and meanings are lost in the context of fuzzy automata. Thus, we establish a new theoretical foundation that provides the correctness and the polynomial-time nature of this new crisp-minimization algorithm for FDfAs.

关键词： Deterministic fuzzy automaton minimization algorithm Fuzzy & aacute tomaton Brzozowski's algorithm Locally finite lattices

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Multicast Power minimization algorithm Based on PSO for Multicast algorithm

Multicast Power Minimization Algorithm Based on PSO for Mult...

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2019 International Conference on Applied Mathematics, Modeling, Simulation and Optimization(AMMSO 2019)

作者： Xiao-ling WU School of Information Technology and Engineering Guangzhou College of Commerce

MPM problem has been mathematically formulated to a constrained optimization problem by using Hybrid PSO. Considering that the centralized algorithm requiring a global knowledge of the networks is impractical in large wireless networks, the distributed version of the centralized algorithm is employed, which requires multihop neighborhood information under the assumption that limited frequency band is available. A variety of simulations have been conducted to examine the performance of the proposed approach and the results show that our algorithm consistently outperforms existing techniques.

关键词： MPM minimization algorithm PSO

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Accurate simulation of the anisotropic dendrite crystal growth by the 3DVar data assimilation

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COMPUTER PHYSICS COMMUNICATIONS 2025年 311卷

作者： Zheng, Fenglian Xiao, Xufeng Xinjiang Univ Coll Math & Syst Sci Urumqi 830046 Peoples R China

The growth phenomenon of dendritic crystals is a common occurrence in nature, forming a structure similar to tree branches during its evolution. However, in practical computations, model parameters and initial conditions may have observational errors, which cause large errors in numerical simulation results. To improve the accuracy and efficiency of numerical simulation, this study uses a three-dimensional variational (3DVar) data assimilation algorithm. We consider using the phase-field dendritic crystal growth (PF-DCG) model as the governing equation for numerical simulation. Through the optimization problem of 3DVar, we will incorporate the observed solutions from experimental data into the process of solving numerical solutions to modify them, thereby achieving the goal of data assimilation. This study mainly evaluates two different categories of problems: initial observational errors and model parameter errors. In the numerical experiment section, we obtain the numerical solution by using the operator splitting method (OSM) and explore the effectiveness of this method and investigate the influence of various factors such as adjustment factors, spatio-temporal sampling rates, and parameter perturbation ratios on the effectiveness of data assimilation. The experimental results show that this method can effectively assimilate the observation data, thus accurately simulating the growth process of dendritic crystals.

关键词： Phase-field crystal model Three-dimensional variational data assimilation minimization algorithm

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Decidability of the minimization of fuzzy tree automata with membership values in complete lattices

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2022年第1期68卷 461-478页

作者： Ghorani, Maryam Moghari, Somaye Shahrood Univ Technol Fac Math Sci Shahrood Iran

The objective of this paper is to introduce a method for constructing a minimal lattice-valued tree automaton with membership values in a totally ordered lattice (in short LT A), based on the solvability of a system of fuzzy polynomial equations. Since the minimization problem strongly depends on the equivalence problem, at first, the equivalence problem is examined. For this purpose, the notion of h-equivalence is defined, and a necessary and sufficient condition for the equivalence between two LT As is provided. It is shown that the equivalence problem of LT As is decidable. In the minimization problem, the following question is replied: given an LT A A and a positive integer k, is there an LT A with k states equivalent to A? Decidability of the minimization problem is demonstrated, and an approach to return a minimal LT A equivalent to the original one is presented. Also, the time complexity of the proposed algorithm is analyzed. Finally, some examples are presented to clarify the minimization problem.

关键词： Lattice-valued tree automata minimization algorithm Equivalence problem Complete lattice

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A new nonmonotone line search method for nonsmooth nonconvex optimization

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OPTIMIZATION 2024年第2期73卷 429-441页

作者： Akbari, Z. Univ Mazandaran Dept Math Sci Babolsar Iran

In this paper, we develop a nonmonotone line search strategy for minimization of the locally Lipschitz functions. First, the descent direction (DD) is defined based on partial derivative(epsilon)f(.) where epsilon > 0. Next, we introduce a minimization algorithm to find a step length along the DD satisfying the nonsmooth nonmonotone Armijo condition. Choosing an adequate step length is the main purpose of the classic nonmonotone line search methods for a given DD, while in this paper both a search direction and step length are simultaneously computed. The global convergence of the minimization algorithm is proved by some assumptions on the DD. Finally, the proposed algorithm is implemented in the MATLAB environment and compared with another existing nonsmooth algorithm on some nonconvex nonsmooth optimization test problems. The efficiency of the proposed algorithm is shown by numerical results in solving some small-scale and large-scale nonsmooth optimization test problems.

关键词： Lipschitz functions nonmonotone line search method NN Armijo condition minimization algorithm global convergence

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Modified wave dispersion properties in 1D and 2D state-based peridynamic media

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2023年 151卷 21-35页

作者： Alebrahim, Reza Univ RomaTre Dept Civil Comp Sci & Aeronaut Technol Engn Rome Italy

This study introduces a modification of wave propagation in state-based peridynamics (PD). Comprehensive investigations have been conducted to analyze wave dispersion in both 1-D and 2-D domains. We employ weighted residual techniques, specifically point collocation and the Galerkin method, to mitigate the wave dispersion phenomenon by introducing a set of scaling coefficients. The square-frequencies of the bond-and state-based PD models are correlated defining a new formulation. Utilizing these scaling coefficients, we demonstrate that the solution of the original PD converges towards that of the non-dispersive classical continuum method. is shown that the proposed method alleviates wave dispersion in all PD models accurately.

关键词： State-based peridynamics Dispersion behavior Wave propagation minimization algorithm

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Wave propagation improvement in two-dimensional bond-based peridynamics model

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE 2021年第14期235卷 2542-2553页

作者： Alebrahim, Reza Packo, Pawel Zaccariotto, Mirco Galvanetto, Ugo Univ Padua Ind Engn Dept V Venezia 1 I-35131 Padua Italy AGH Univ Sci & Technol Dept Robot & Mechatron Krakow Poland

In this study, methods to mitigate anomalous wave propagation in 2-D Bond-Based Peridynamics (PD) are presented. Similarly to what happens in classical non-local models, an irregular wave transmission phenomenon occurs at high frequencies. This feature of the dynamic performance of PD, limits its potential applications. A minimization method based on the weighted residual point collocation is introduced to substantially extend the frequency range of wave motion modeling. The optimization problem, developed through inverse analysis, is set up by comparing exact and numerical dispersion curves and minimizing the error in the frequency-wavenumber domain. A significant improvement in the wave propagation simulation using Bond-Based PD is observed.

关键词： Peridynamics wave propagation minimization algorithm optimization numerical analysis

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Learning from non-irreducible Markov chains

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2023年第2期523卷

作者： Sandric, Nikola Sebek, Stjepan Univ Zagreb Dept Math Zagreb Croatia Univ Zagreb Fac Elect Engn & Comp Dept Appl Math Zagreb Croatia

Most of the existing literature on supervised machine learning problems focuses on the case when the training data set is drawn from an i.i.d. sample. However, many practical problems are characterized by temporal dependence and strong correlation between the marginals of the data-generating process, suggesting that the i.i.d. assumption is not always justified. This problem has been already considered in the context of Markov chains satisfying the Doeblin condition. This condition, among other things, implies that the chain is not singular in its behavior, i.e. it is irreducible. In this article, we focus on the case when the training data set is drawn from a not necessarily irreducible Markov chain. Under the assumption that the chain is uniformly ergodic with respect to the L1-Wasserstein distance, and certain regularity assumptions on the hypothesis class and the state space of the chain, we first obtain a uniform convergence result for the corresponding sample error, and then we conclude learnability of the approximate sample error minimization algorithm and find its generalization bounds. At the end, a relative uniform convergence result for the sample error is also discussed.(c) 2023 Elsevier Inc. All rights reserved.

关键词： Approximate sample error minimization algorithm Generalization bounds Markov chain Wasserstein distance

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IMPROVED RATIONAL APPROXIMATION FOR SPATIALLY-DEPENDENT RESONANCE SELF-SHIELDING IN CASMO5

IMPROVED RATIONAL APPROXIMATION FOR SPATIALLY-DEPENDENT RESO...

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2021 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021

作者： Ferrer, Rodolfo Hykes, Joshua Studsvik Scandpower 1070 Riverwalk Dr. Suite 150 Idaho FallsID83402 United States

ISBN: (纸本)9781713886310

Recently, a new Spatially-Dependent resonance Self-Shielding (SDSS) method was developed and implemented into CASMO5 within the framework of Equivalence Theory. An Optimal Two-Term Rational (OTTR) approximation for the Stoker-Weiss treatment of concentric annular fuel regions yielded an adequate approximation for fuel-to-fuel collision probabilities for a subdivided cylindrical fuel region. Reference fuel-to-fuel probabilities, obtained by performing a series of fixed-source, two-dimensional transport calculations, are used in searching for optimal coefficients to the rational approximation. Three search algorithms are evaluated in this work with the goal of obtaining the best practical accuracy at minimal computational cost. An improved formulation of SDSS is proposed and tested to further reduce the error of the rational approximation, especially for the outer rings of the fuel pellet. Numerical results are presented which provide a comparison of various choices for search algorithms and confirm the improved accuracy obtained by using the new proposed formulation for the rational approximation. The Levenberg-Marquardt and Nelder-Mead methods both perform well, with a small advantage to Nelder-Mead for its slightly shorter runtimes. The 6-degrees-of-freedom (dof) rational approximation achieves significantly better accuracy (up to an 8x error reduction at the pellet rim) than the previous 3-dof model. Copyright © 2021 AMERICAN NUCLEAR SOCIETY, INCORPORATED, LA GRANGE PARK, ILLINOIS *** rights reserved.

关键词： CASMO5 minimization algorithm rational approximation resonance self-shielding

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Automatic Estimation System of Building Frames with Integrated Structural Design Information (AutoES)

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IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY-TRANSACTIONS OF CIVIL ENGINEERING 2020年第4期44卷 1145-1157页

作者： Kim, Doyeong Lim, Chaeyeon Liu, Yue Kim, Sunkuk Kyung Hee Univ Dept Architectural Engn 1732 Deogyeong Daero Yongin 17104 Gyeonggi Do South Korea Korea Inst Civil Engn & Bldg Technol 283 Goyang Daero Goyang Si 10223 Gyeonggi Do South Korea

Construction project participants seek to accurately determine construction costs as soon as a design is completed. However, it may take a minimum of several weeks for cost estimation after the structural design and drawings are completed. Manual quantity surveying is time-consuming and requires significant experience and time. Even if computerized software is used, it is time-consuming to enter structural design information into the estimation software. In addition, the estimated quantity may result in inaccurate cost owing to drawing errors or quantity surveyors' mistake, and it is not the exact quantity to be put into actual construction, which can cause numerous problems in the construction phase. If the information can be automatically received for estimation, the exact quantity for construction can be estimated without omission or errors. To estimate the exact quantity after structural analysis and design of building projects, this study proposes an automatic estimation system of building frames with integrated structural design information (AutoES). Using the algorithms of AutoES, the task of estimation can be accomplished with an exact bill of quantities including a bar bending schedule within 1 week.

关键词： Automatic estimation Special order Structural design minimization algorithm Integrated project delivery

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