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DIP-MOEA:a double-grid interactive preference based multi-ob jective evolutionary algorithm for formalizing preferences of decision makers 被引量:1
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作者 Luda ZHAO Bin WANG +2 位作者 Xiaoping JIANG Yicheng LU Yihua HU 《Frontiers of Information Technology & Electronic Engineering》 SCIE EI CSCD 2022年第11期1714-1732,共19页
The final solution set given by almost all existing preference-based multi-objective evolutionary algorithms(MOEAs)lies a certain distance away from the decision makers’preference information region.Therefore,we prop... The final solution set given by almost all existing preference-based multi-objective evolutionary algorithms(MOEAs)lies a certain distance away from the decision makers’preference information region.Therefore,we propose a multi-ob jective optimization algorithm,referred to as the double-grid interactive preference based MOEA(DIPMOEA),which explicitly takes the preferences of decision makers(DMs)into account.First,according to the optimization ob jective of the practical multi-ob jective optimization problems and the preferences of DMs,the membership functions are mapped to generate a decision preference grid and a preference error grid.Then,we put forward two dominant modes of population,preference degree dominance and preference error dominance,and use this advantageous scheme to update the population in these two grids.Finally,the populations in these two grids are combined with the DMs’preference interaction information,and the preference multi-ob jective optimization interaction is performed.To verify the performance of DIP-MOEA,we test it on two kinds of problems,i.e.,the basic DTLZ series functions and the multi-ob jective knapsack problems,and compare it with several different popular preference-based MOEAs.Experimental results show that DIP-MOEA expresses the preference information of DMs well and provides a solution set that meets the preferences of DMs,quickly provides the test results,and has better performance in the distribution of the Pareto front solution set. 展开更多
关键词 Multi-objective evolutionary algorithm(MOEA) formalizing preference of decision makers Population renewal strategy Preference interaction
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Individual Software Expertise Formalization and Assessment from Project Management Tool Databases
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作者 Traian-Radu Plosca Alexandru-Mihai Pescaru +1 位作者 Bianca-Valeria Rus Daniel-Ioan Curiac 《Computers, Materials & Continua》 2026年第1期389-411,共23页
Objective expertise evaluation of individuals,as a prerequisite stage for team formation,has been a long-term desideratum in large software development companies.With the rapid advancements in machine learning methods... Objective expertise evaluation of individuals,as a prerequisite stage for team formation,has been a long-term desideratum in large software development companies.With the rapid advancements in machine learning methods,based on reliable existing data stored in project management tools’datasets,automating this evaluation process becomes a natural step forward.In this context,our approach focuses on quantifying software developer expertise by using metadata from the task-tracking systems.For this,we mathematically formalize two categories of expertise:technology-specific expertise,which denotes the skills required for a particular technology,and general expertise,which encapsulates overall knowledge in the software industry.Afterward,we automatically classify the zones of expertise associated with each task a developer has worked on using Bidirectional Encoder Representations from Transformers(BERT)-like transformers to handle the unique characteristics of project tool datasets effectively.Finally,our method evaluates the proficiency of each software specialist across already completed projects from both technology-specific and general perspectives.The method was experimentally validated,yielding promising results. 展开更多
关键词 Expertise formalization transformer-based models natural language processing augmented data project management tool skill classification
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Steady‑state microbunching based on transverse‑longitudinal coupling
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作者 Xiu‑Jie Deng Alexander Wu Chao +3 位作者 Wen‑Hui Huang Zi‑Zheng Li Zhi‑Long Pan Chuan‑Xiang Tang 《Nuclear Science and Techniques》 2026年第1期1-49,共49页
In this study,three specific scenarios of a novel accelerator light source mechanism called steady-state microbunching(SSMB)were studied:longitudinal weak focusing,longitudinal strong focusing,and generalized longitud... In this study,three specific scenarios of a novel accelerator light source mechanism called steady-state microbunching(SSMB)were studied:longitudinal weak focusing,longitudinal strong focusing,and generalized longitudinal strong focusing(GLSF).At present,GLSF is the most promising method for realizing high-power short-wavelength coherent radiation with mild requirements on modulation laser power.Its essence is to exploit the ultrasmall natural vertical emittance of an electron beam in a planar storage ring for efficient microbunching formation,like a partial transverse-longitudinal emittance exchange in the optical laser wavelength range.Based on an in-depth investigation of related beam physics,a solution for a GLSF SSMB storage ring that can deliver 1 kW average-power EUV light is presented.The work in this paper,such as the generalized Courant–Snyder formalism,analysis of theoretical minimum emittances,transverse-longitudinal coupling dynamics,and derivation of the bunching factor and modulation strengths for laser-induced microbunching schemes,is expected to be useful not only for the development of SSMB but also for future accelerator light sources in general that demand increasingly precise electron beam phase space manipulations. 展开更多
关键词 Steady-state microbunching Extreme ultraviolet ARPES Generalized Courant-Snyder formalism Theoretical minimum emittances Longitudinal weak focusing Longitudinal strong focusing Generalized longitudinal strong focusing Transverse-longitudinal coupling Damping wiggler
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A case for formalizing subseries(subepochs)of the Cenozoic Era^((a)) 被引量:2
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作者 Martin J.Head Marie-Pierre Aubry +2 位作者 Mike Walker Kenneth G.Miller Brian R.Pratt 《Episodes》 2017年第1期22-27,共6页
Subseries/subepochs(e.g.,Lower/Early Eocene,Upper/Late Pleistocene)have yet to be formally defined despite their wide use in the Cenozoic literature.This has led to concerns about the stability of their definition and... Subseries/subepochs(e.g.,Lower/Early Eocene,Upper/Late Pleistocene)have yet to be formally defined despite their wide use in the Cenozoic literature.This has led to concerns about the stability of their definition and uncertainty over their status that has led to inconsistencies in capitalization.To address these issues,we propose for the Cenozoic that subseries/subepochs be defined formally by reference to Global Boundary Stratotype Sections and Points and ratified in the same way as for other formal chronostratigraphic units.Formalization of subseries/subepochs for the Cenozoic will respect their deep historical roots,recognise their chronostratigraphic nature,stabilize their definition,ensure consistency in application,embrace their de-facto use as formal terms within the Paleogene,Neogene and especially Quaternary communities,and resolve the question of capitalization:an upper-case initial letter without exception. 展开更多
关键词 global boundary stratotype sections PALEOGENE QUATERNARY chronostratigraphic units FORMALIZATION SUBSERIES subepochs cenozoic era
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A General Scheme for Formalizing Defaults Using the Predicate ab(I,S)
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作者 沈一栋 《Journal of Computer Science & Technology》 SCIE EI CSCD 1999年第2期159-164,共6页
In common sense reasoning two typical types of defaults are encoun- tered. One is of the form 'All birds can fly except b1, b2,…, and bm(m>1)' , and the other 'All birds can fly, but there exist except... In common sense reasoning two typical types of defaults are encoun- tered. One is of the form 'All birds can fly except b1, b2,…, and bm(m>1)' , and the other 'All birds can fly, but there exist exceptiona' . The first type of defaults is readily formalized but the other, as some researchers have noticed, is difficult to deal witb. This paper establisbes a geaeral scheme for formalising defaults of the two typea, the key to which is the introduction of a two-argument predicate ab(I,S) to represent exceptional objects. 展开更多
关键词 common sense reasoning DEFAULT FORMALIZATION
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Deformations and extensions of modified λ-differential Lie-Yamaguti algebras
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作者 TENG Wen PAN Yuewei 《中山大学学报(自然科学版)(中英文)》 北大核心 2025年第4期115-127,共13页
The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce t... The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group. 展开更多
关键词 Lie-Yamaguti algebra modifiedλ-differential operator representation and cohomology one-parameter formal deformation Abelian extension
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基于自由基介导Formal Diels-Alder反应的复杂天然产物全合成
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作者 黄俊 尹蓉 曹婷婷 《化学学报》 北大核心 2025年第11期1424-1434,共11页
经过近一个世纪的研究发展,官能团化的双烯体和亲双烯体参与的Diels-Alder反应以其良好的反应性和立体选择性控制,已广泛应用于复杂天然产物、药物分子和各种功能分子的合成中.最新研究表明,在温和条件下进行的自由基介导亲双烯体和双... 经过近一个世纪的研究发展,官能团化的双烯体和亲双烯体参与的Diels-Alder反应以其良好的反应性和立体选择性控制,已广泛应用于复杂天然产物、药物分子和各种功能分子的合成中.最新研究表明,在温和条件下进行的自由基介导亲双烯体和双烯体参与的formal Diels-Alder反应为立体选择性构建六元环体系提供了全新的合成策略.本综述针对自由基介导formal Diels-Alder反应在活性复杂天然产物全合成的应用展开简单概述,主要包括经自由基正离子介导formal Diels-Alder反应、单电子转移引发formal Diels-Alder反应和双自由基参与的formal Diels-Alder反应三种环化反应途径,并对其在目标环系精准构建中的应用进行深入探讨. 展开更多
关键词 自由基正离子 双自由基 formal Diels-Alder反应 [4+2]-环加成反应 天然产物全合成
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Extensions and Deformations of 3-Lie Algebras with Higher Derivations
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作者 Shuangjian GUO 《Journal of Mathematical Research with Applications》 2025年第1期20-32,共13页
In this paper,we call a tuple consisting of 3-Lie algebra and a higher derivation on it a 3-LieHDer pair.We introduce a cohomology theory of 3-LieHDer pairs.Next,we interpret the second cohomology group as the space o... In this paper,we call a tuple consisting of 3-Lie algebra and a higher derivation on it a 3-LieHDer pair.We introduce a cohomology theory of 3-LieHDer pairs.Next,we interpret the second cohomology group as the space of all isomorphism classes of abelian extensions.Finally,we consider formal deformations of 3-LieHDer pairs that are governed by the cohomology with self-coefficient. 展开更多
关键词 higher derivations 3-LieHDer pairs COHOMOLOGY EXTENSIONS formal deformations
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Semantic Knowledge Based Reinforcement Learning Formalism for Smart Learning Environments
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作者 Taimoor Hassan Ibrar Hussain +3 位作者 Hafiz Mahfooz Ul Haque Hamid Turab Mirza Muhammad Nadeem Ali Byung-Seo Kim 《Computers, Materials & Continua》 2025年第10期2071-2094,共24页
Smart learning environments have been considered as vital sources and essential needs in modern digital education systems.With the rapid proliferation of smart and assistive technologies,smart learning processes have ... Smart learning environments have been considered as vital sources and essential needs in modern digital education systems.With the rapid proliferation of smart and assistive technologies,smart learning processes have become quite convenient,comfortable,and financially affordable.This shift has led to the emergence of pervasive computing environments,where user’s intelligent behavior is supported by smart gadgets;however,it is becoming more challenging due to inconsistent behavior of Artificial intelligence(AI)assistive technologies in terms of networking issues,slow user responses to technologies and limited computational resources.This paper presents a context-aware predictive reasoning based formalism for smart learning environments that facilitates students in managing their academic as well as extra-curricular activities autonomously with limited human intervention.This system consists of a three-tier architecture including the acquisition of the contextualized information from the environment autonomously,modeling the system using Web Ontology Rule Language(OWL 2 RL)and Semantic Web Rule Language(SWRL),and perform reasoning to infer the desired goals whenever and wherever needed.For contextual reasoning,we develop a non-monotonic reasoning based formalism to reason with contextual information using rule-based reasoning.The focus is on distributed problem solving,where context-aware agents exchange information using rule-based reasoning and specify constraints to accomplish desired goals.To formally model-check and simulate the system behavior,we model the case study of a smart learning environment in the UPPAAL model checker and verify the desired properties in the model,such as safety,liveness and robust properties to reflect the overall correctness behavior of the system with achieving the minimum analysis time of 0.002 s and 34,712 KB memory utilization. 展开更多
关键词 CONTEXT-AWARENESS reinforcement learning multi-agent systems non-monotonic reasoning formal verification
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Occupational Trajectories of Immigrant Workers in Brazil:Unequal Pathways
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作者 Lilian Suzuki 《Journalism and Mass Communication》 2025年第3期142-156,共15页
This study sought to analyze the occupational habits of immigrant workers in the formal Brazilian labor market from a sociological perspective.It was understood that a study on occupation should observe professional a... This study sought to analyze the occupational habits of immigrant workers in the formal Brazilian labor market from a sociological perspective.It was understood that a study on occupation should observe professional and employment history,which may include an analysis over time of workers in the same profession or in periods of professional mobility.In order to understand occupational trajectories and related aspects,this study used data that were collected through semi-structured interviews and surveys with immigrant workers who were employed in the Brazilian formal labor market.The interviews and surveys revealed a strong polarization among the immigrant workers present in Brazil-while a small part holds highly skilled occupations,the majority participate at the base of the productivity hierarchy. 展开更多
关键词 occupational trajectories IMMIGRANTS formal labor market mobility MIGRATION
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Platforms for Prosperity China’s platform giants are poised to drive the next wave of economic growth
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作者 ZHANG SHASHA 《ChinAfrica》 2025年第1期49-51,共3页
On 20 April 1994,China made its first o!cial full-function connection to the World Wide Web through a 64-kilobyte international leased line,marking the country’s formal entry into the global digital age.The year 2024... On 20 April 1994,China made its first o!cial full-function connection to the World Wide Web through a 64-kilobyte international leased line,marking the country’s formal entry into the global digital age.The year 2024 marked the 30th anniversary of the country’s entry into the internet era. 展开更多
关键词 PLATFORM internet FORMAL
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BUILDING BRIDGES THROUGH CULTURE Cambodia and China deepen ties with people-to-people exchanges
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作者 Kin Phea 《China Report ASEAN》 2025年第1期32-33,共2页
Cambodia and China have long enjoyed a close relationship grounded in centuries of historical,cultural,and political ties.From their early connections in the 13th Century to today’s multifaceted partnership,the bond ... Cambodia and China have long enjoyed a close relationship grounded in centuries of historical,cultural,and political ties.From their early connections in the 13th Century to today’s multifaceted partnership,the bond between these two nations has been built on mutual respect and cooperation,fortified by economic collaboration and a profound connection between their peoples.Since the formal establishment of diplomatic ties in 1958,Cambodia and China have fostered an enduring“ironclad”friendship that weathered challenges and adapted to the everchanging global dynamics. 展开更多
关键词 mutual FORMAL EXCHANGES
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Envisioning the blueprint:Aeronautics in large models era
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作者 Weiwei ZHANG Shule ZHAO 《Chinese Journal of Aeronautics》 2025年第8期139-141,共3页
Following the groundbreaking introduction of the Transformer architecture in 2017,the development of Large Language Models(LLMs)formally commenced.In May 2020,Chat GPT-3,with over one hundred billion parameters,entere... Following the groundbreaking introduction of the Transformer architecture in 2017,the development of Large Language Models(LLMs)formally commenced.In May 2020,Chat GPT-3,with over one hundred billion parameters,entered the public eye,marking a significant milestone in LLM advancement. 展开更多
关键词 AERONAUTICS large languagemodels transformer architecture transformerarchitecture llms chatgpt large language models llms formally
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Echoes across Cultures A youthful take on China-Singapore friendship from a Chinese student in Singapore
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作者 Antony Hardi 《China Report ASEAN》 2025年第8期48-49,共2页
When China and Singapore exchanged formal handshakes in 1990,few could have imagined that 35 years later,a Data Science undergraduate named Hu Yunxin would be happily counting hawker-centre noodles while memorizing re... When China and Singapore exchanged formal handshakes in 1990,few could have imagined that 35 years later,a Data Science undergraduate named Hu Yunxin would be happily counting hawker-centre noodles while memorizing regression formulas along Clementi Road.Yet it is precisely these small,personal stories that breathe life into grand diplomatic milestones.In celebration of the anniversary,I spoke with Yunxin—freshly returned from her first year at the National University of Singapore(NUS)—to discover how the Lion City looks through Chinese eyes. 展开更多
关键词 SINGAPORE Clementi Road data science FRIENDSHIP China memorizing regression formulas hawker centre exchanged formal handshakes
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Improving Machine Translation Formality with Large Language Models
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作者 Murun Yang Fuxue Li 《Computers, Materials & Continua》 2025年第2期2061-2075,共15页
Preserving formal style in neural machine translation (NMT) is essential, yet often overlooked as an optimization objective of the training processes. This oversight can lead to translations that, though accurate, lac... Preserving formal style in neural machine translation (NMT) is essential, yet often overlooked as an optimization objective of the training processes. This oversight can lead to translations that, though accurate, lack formality. In this paper, we propose how to improve NMT formality with large language models (LLMs), which combines the style transfer and evaluation capabilities of an LLM and the high-quality translation generation ability of NMT models to improve NMT formality. The proposed method (namely INMTF) encompasses two approaches. The first involves a revision approach using an LLM to revise the NMT-generated translation, ensuring a formal translation style. The second approach employs an LLM as a reward model for scoring translation formality, and then uses reinforcement learning algorithms to fine-tune the NMT model to maximize the reward score, thereby enhancing the formality of the generated translations. Considering the substantial parameter size of LLMs, we also explore methods to reduce the computational cost of INMTF. Experimental results demonstrate that INMTF significantly outperforms baselines in terms of translation formality and translation quality, with an improvement of +9.19 style accuracy points in the German-to-English task and +2.16 COMET score in the Russian-to-English task. Furthermore, our work demonstrates the potential of integrating LLMs within NMT frameworks to bridge the gap between NMT outputs and the formality required in various real-world translation scenarios. 展开更多
关键词 Neural machine translation FORMALITY large language model text style transfer style evaluation reinforcement learning
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Coupled Solutions for Two-Dimensional Decagonal Piezoelectric Quasicrystals with Cracks
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作者 Xiang Mu Zhaowei Zhu +1 位作者 Liangliang Zhang Yang Gao 《Acta Mechanica Solida Sinica》 2025年第1期115-124,共10页
With the assistance of Stroh formalism,the general solutions satisfying the basic laws of linear elastic theory are written in complex variable forms.To analyze the fracture behavior of two-dimensional decagonal piezo... With the assistance of Stroh formalism,the general solutions satisfying the basic laws of linear elastic theory are written in complex variable forms.To analyze the fracture behavior of two-dimensional decagonal piezoelectric quasicrystals,an elliptical hole model under different boundary conditions is established.The analytical expressions of generalized stress intensity factors(GSIFs)are obtained,respectively,for four general cases:a Griffith crack with generalized remote uniform loading,arbitrary loading on the crack surface,concentrated loading at any position of the crack surface,and multiple collinear periodic cracks under uniform loading at infinity.Numerical examples are given,and the effects of crack length,loading position,loading condition,and crack period on GSIFs are discussed.The derived analytical solutions of cracks play a significant role in understanding the phonon-phason and electromechanical coupled behavior in quasicrystals,and they also serve as criteria for fracture analysis. 展开更多
关键词 Piezoelectric quasicrystals Stroh formalism Straight crack Generalized stress intensity factors
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Exact multi-field coupling modeling and analysis of piezoelectric semiconductor plates
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作者 Lele ZHANG Zheng ZHAO +2 位作者 Xiaofan HU Guoquan NIE Jinxi LIU 《Applied Mathematics and Mechanics(English Edition)》 2025年第7期1331-1346,共16页
This study aims to present exact multi-field coupling modeling and analysis of a simply-supported rectangular piezoelectric semiconductor(PSC)plate.Under the linear assumption of drift-diffusion current for a small el... This study aims to present exact multi-field coupling modeling and analysis of a simply-supported rectangular piezoelectric semiconductor(PSC)plate.Under the linear assumption of drift-diffusion current for a small electron concentration perturbation,the governing equations are solved by extending the classical Stroh formalism to involve all the physical fields of PSCs.The general solutions are obtained and then utilized to analyze three-dimensional(3D)problems of static deformation and free vibration of the PSC plate.To investigate the multi-physics interactions along the plate thickness,the distribution forms of electromechanical fields and electron concentration perturbation are given exactly,which are helpful for the development of the PSC plate theory.The differences between the PSC and purely piezoelectric as well as purely elastic counterparts are emphasized,in the context of evaluating the material performances with changing initial electron concentration.The results demonstrate that the PSC coupling exists only within a specific range of the initial electron concentration,where it exhibits a transition from the piezoelectric characteristics to the elastic ones.In addition,the dependence of coupling behaviors on the plate thickness is clarified.These results can not only be benchmarks in the development of PSC plate theories or other numerical methods,but also be guidance for the design of plate-based PSC devices. 展开更多
关键词 piezoelectric semiconductor(PSC)plate Stroh formalism static deformation free vibration exact solution
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Reinforcement learning with soft temporal logic constraints using limit-deterministic generalized Büchi automaton
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作者 Mingyu Cai Zhangli Zhou +2 位作者 Lin Li Shaoping Xiao Zhen Kan 《Journal of Automation and Intelligence》 2025年第1期39-51,共13页
This paper investigates control synthesis for motion planning under conditions of uncertainty,specifically in robot motion and environmental properties,which are modeled using a probabilistic labeled Markov decision p... This paper investigates control synthesis for motion planning under conditions of uncertainty,specifically in robot motion and environmental properties,which are modeled using a probabilistic labeled Markov decision process(PL-MDP).To address this,a model-free reinforcement learning(RL)approach is designed to produce a finite-memory control policy that meets complex tasks specified by linear temporal logic(LTL)formulas.Recognizing the presence of uncertainties and potentially conflicting objectives,this study centers on addressing infeasible LTL specifications.A relaxed LTL constraint enables the agent to adapt its motion plan,allowing for partial satisfaction by accounting for necessary task violations.Additionally,a new automaton structure is introduced to increase the density of accepting rewards,facilitating deterministic policy outcomes.The proposed RL framework is rigorously analyzed and prioritizes two key objectives:(1)satisfying the acceptance condition of the relaxed product MDP,and(2)minimizing long-term violation costs.Simulation and experimental results are presented to demonstrate the framework’s effectiveness and robustness. 展开更多
关键词 Formal methods in robotics and automation Linear temporal logic Motion planning Optimal control
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Anharmonic Phonon Dynamics and the Origin of Ultralow Lattice Thermal Conductivity in CuBiI_(4):Implications for Thermoelectric Applications
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作者 Feng Xiao Qing-Yu Xie +2 位作者 Ru Yu Junrong Zhang Bao-Tian Wang 《Chinese Physics Letters》 2025年第12期201-219,共19页
Phonon quasiparticles and their anharmonic interactions govern heat transport in insulators.Accurate characterization of phonon frequencies and linewidths,especially beyond the quasiparticle approximation,is essential... Phonon quasiparticles and their anharmonic interactions govern heat transport in insulators.Accurate characterization of phonon frequencies and linewidths,especially beyond the quasiparticle approximation,is essential for understanding anharmonic effects and lattice thermal conductivity.Here,we investigate the anharmonic lattice dynamics and phonon transport in crystalline copper halides CuBiI_(4) using the self-consistent phonon theory,combined with the Wigner transport formalism and the quasi-harmonic Green–Kubo method.Results show that the three-phonon bubble self-energy substantially renormalizes the phonon dispersion,inducing strong modedependent broadening.Depending on the strength of the anharmonic scattering,phonons exhibit particle-like,wave-like,or overdamped transport characteristics,with broadened states contributing additional coherent thermal transport channels.We establish a consistent description of the overdamped phonon self-energy and advance the microscopic understanding of the strongly anharmonic phonon thermal transport in CuBiI_(4).Overdamped phonon modes significantly hinder the lattice thermal transport by reducing phonon lifetimes.However,the still well-defined phonon dispersions mitigate carrier scattering induced by the local structural disorder.Anisotropic electrical transport properties are obtained by considering polar and non-polar electroacoustic coupling and ionized impurity scattering mechanisms.Upon electron doping,the thermoelectric figure of merit of n-type CuBiI_(4) reaches 2.25 at 800 K. 展开更多
关键词 phonon frequencies lattice thermal conductivityherewe anharmonic effects wigner transport formalism heat transport phonon quasiparticles anharmonic lattice dynamics crystalline copper halides cubii
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Tensor Network Algorithm to Solve Polaron Impurity Problems
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作者 Ruofan Chen Lei Gu Chu Guo 《Chinese Physics Letters》 2025年第12期183-200,共18页
The polaron problem is a very old problem in condensed matter physics that dates back to the thirties,but still remains largely unsolved today,especially when electron–electron interaction is taken into consideration... The polaron problem is a very old problem in condensed matter physics that dates back to the thirties,but still remains largely unsolved today,especially when electron–electron interaction is taken into consideration.The presence of both electron–electron and electron–phonon interactions in the problem invalidates most existing numerical methods,which are either computationally too expensive or simply intractable.The continuous-time quantum Monte Carlo(CTQMC)methods could tackle this problem,but they are only effective on the imaginarytime axis.In this work,we present a method based on tensor networks and the path integral formalism to solve polaron impurity problems.As both the electron and phonon baths can be integrated out via the Feynman–Vernon influence functional in the path integral formalism,our method is free of bath discretization error.It can also flexibly work on imaginary time,Keldysh contour,and L-shaped Kadanoff contour.In addition,our method can naturally resolve several long-existing challenges:(i)non-diagonal hybridization function;(ii)measuring multi-time correlations beyond single-particle Green’s functions.We demonstrate the effectiveness and accuracy of our method with extensive numerical examples against analytic solutions,exact diagonalization,and CTQMC.We also perform full-fledged real-time calculations that have never been done before to our knowledge,which could serve as a benchmarking baseline for future method developments. 展开更多
关键词 tensor networks electron phonon interactions Feynman Vernon influence functional polaron problem condensed matter physics continuous time quantum Monte Carlo path integral formalism electron electron interaction
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