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The pythagorean fuzzy set (PFS) which is developed based on intuitionistic fuzzy set, is more efficient in elaborating and disposing uncertainties in indeterminate situations, which is a very reason of that PFS is applied in various kinds of fields. How to measure the distance between two pythagorean fuzzy sets is still an open issue. Mnay kinds of methods have been proposed to present the of the question in former reaserches. However, not all of existing methods can accurately manifest differences among pythagorean fuzzy sets and satisfy the property of similarity. And some other kinds of methods neglect the relationship among three variables of pythagorean fuzzy set. To addrees the proplem, a new method of measuring distance is proposed which meets the requirements of axiom of distance measurement and is able to indicate the degree of distinction of PFSs well. Then some numerical examples are offered to to verify that the method of measuring distances can avoid the situation that some counter? intuitive and irrational results are produced and is more effective, reasonable and advanced than other similar methods. Besides, the proposed method of measuring distances between PFSs is applied in a real environment of application which is the medical diagnosis and is compared with other previous methods to demonstrate its superiority and efficiency. And the feasibility of the proposed method in handling uncertainties in practice is also proved at the same time.

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We conduct a systematic study of the approximation properties of Transformer for sequence modeling with long, sparse and complicated memory. We investigate the mechanisms through which different components of Transformer, such as the dot-product self-attention, positional encoding and feed-forward layer, affect its expressive power, and we study their combined effects through establishing explicit approximation rates. Our study reveals the roles of critical parameters in the Transformer, such as the number of layers and the number of attention heads. These theoretical insights are validated experimentally and offer natural suggestions for alternative architectures.

Crowd-sourcing deals with solving problems by assigning them to a large number of non-experts called crowd using their spare time. In these systems, the final answer to the question is determined by summing up the votes obtained from the community. The popularity of using these systems has increased by facilitation of access to community members through mobile phones and the Internet. One of the issues raised in crowd-sourcing is how to choose people and how to collect answers. Usually, the separation of users is done based on their performance in a pre-test. Designing the pre-test for performance calculation is challenging; The pre-test questions should be chosen in a way that they test the characteristics in people related to the main questions. One of the ways to increase the accuracy of crowd-sourcing systems is to pay attention to people's cognitive characteristics and decision-making model to form a crowd and improve the estimation of the accuracy of their answers to questions. People can estimate the correctness of their responses while making a decision. The accuracy of this estimate is determined by a quantity called metacognition ability. Metacoginition is referred to the case where the confidence level is considered along with the answer to increase the accuracy of the solution. In this paper, by both mathematical and experimental analysis, we would answer the following question: Is it possible to improve the performance of the crowd-sourcing system by knowing the metacognition of individuals and recording and using the users' confidence in their answers?

Legged robot locomotion is hindered by a mismatch between applications where legs can outperform wheels or treads, most of which feature deformable substrates, and existing tools for planning and control, most of which assume flat, rigid substrates. In this study we focus on the ramifications of plastic terrain deformation on the hop-to-hop energy dynamics of a spring-legged monopedal hopping robot animated by a switched-compliance energy injection controller. From this deliberately simple robot-terrain template, we derive a hop-to-hop energy return map, and we use physical experiments and simulations to validate the hop-to-hop energy map for a real robot hopping on a real deformable substrate. The dynamical properties (fixed points, eigenvalues, basins of attraction) of this map provide insights into efficient, responsive, and robust locomotion on deformable terrain. Specifically, we identify constant-fixed-point surfaces in a controller parameter space that suggest it is possible to tune control parameters for efficiency or responsiveness while targeting a desired gait energy level. We also identify conditions under which fixed points of the energy map are globally stable, and we further characterize the basins of attraction of fixed points when these conditions are not satisfied. We conclude by discussing the implications of this hop-to-hop energy map for planning, control, and estimation for efficient, agile, and robust legged locomotion on deformable terrain.

Opinion Dynamics is an interdisciplinary area of research. Psychology and Sociology have proposed models of how individuals form opinions and how social interactions influence this process. Socio-Physicists have interpreted patterns in opinion formation as arising from non-linearity in the underlying process, shaping the models. Agent-based modeling has offered a platform to study the Opinion Dynamics of large groups. This paper recasts recent models in opinion formation into a proper dynamical system, injecting the idea of clock time into evolving opinions. The time interval between successive receipts of new information (frequency of information receipts) becomes a factor to study. Social media has shrunk time intervals between information receipts, increasing their frequency. The recast models show that shorter intervals and larger networks increase an individual's propensity for polarization, defined as an inability to hold a neutral opinion. A Polarization number based on sociological parameters is proposed, with critical values beyond which individuals are prone to polarization, depending on psychological parameters. Reduced time intervals and larger interacting groups can push the Polarization number to critical values, contributing to polarization. The Extent of Polarization is defined as the width of the region around neutral within which an individual cannot hold an opinion. Results are reported for model parameters found in the literature. The findings offer an opportunity to adjust model parameters to align with empirical evidence, aiding the study of Opinion Dynamics in large social networks using Agent-Based Modeling.

Gradient aggregation has long been identified as a major bottleneck in today's large-scale distributed machine learning training systems. One promising solution to mitigate such bottlenecks is gradient compression, directly reducing communicated gradient data volume. However, in practice, many gradient compression schemes do not achieve acceleration of the training process while also preserving accuracy. In this work, we identify several common issues in previous gradient compression systems and evaluation methods. These issues include excessive computational overheads; incompatibility with all-reduce; and inappropriate evaluation metrics, such as not using an end-to-end metric or using a 32-bit baseline instead of a 16-bit baseline. We propose several general design and evaluation techniques to address these issues and provide guidelines for future work. Our preliminary evaluation shows that our techniques enhance the system's performance and provide a clearer understanding of the end-to-end utility of gradient compression methods.

This study investigates whether division on political topics is mapped with the distinctive patterns of language use. We collect a total 145,832 Reddit comments on the abortion debate and explore the languages of subreddit communities r/prolife and r/prochoice. With consideration of the Moral Foundations Theory, we examine lexical patterns in three ways. First, we compute proportional frequencies of lexical items from the Moral Foundations Dictionary in order to make inferences about each group's moral considerations when forming arguments for and against abortion. We then create n-gram models to reveal frequent collocations from each stance group and better understand how commonly used words are patterned in their linguistic context and in relation to morality values. Finally, we use Latent Dirichlet Allocation to identify underlying topical structures in the corpus data. Results show that the use of morality words is mapped with the stances on abortion.

Agent-based modeling and simulation has evolved as a powerful tool for modeling complex systems, offering insights into emergent behaviors and interactions among diverse agents. Integrating large language models into agent-based modeling and simulation presents a promising avenue for enhancing simulation capabilities. This paper surveys the landscape of utilizing large language models in agent-based modeling and simulation, examining their challenges and promising future directions. In this survey, since this is an interdisciplinary field, we first introduce the background of agent-based modeling and simulation and large language model-empowered agents. We then discuss the motivation for applying large language models to agent-based simulation and systematically analyze the challenges in environment perception, human alignment, action generation, and evaluation. Most importantly, we provide a comprehensive overview of the recent works of large language model-empowered agent-based modeling and simulation in multiple scenarios, which can be divided into four domains: cyber, physical, social, and hybrid, covering simulation of both real-world and virtual environments. Finally, since this area is new and quickly evolving, we discuss the open problems and promising future directions.

The fusion of causal models with deep learning introducing increasingly intricate data sets, such as the causal associations within images or between textual components, has surfaced as a focal research area. Nonetheless, the broadening of original causal concepts and theories to such complex, non-statistical data has been met with serious challenges. In response, our study proposes redefinitions of causal data into three distinct categories from the standpoint of causal structure and representation: definite data, semi-definite data, and indefinite data. Definite data chiefly pertains to statistical data used in conventional causal scenarios, while semi-definite data refers to a spectrum of data formats germane to deep learning, including time-series, images, text, and others. Indefinite data is an emergent research sphere inferred from the progression of data forms by us. To comprehensively present these three data paradigms, we elaborate on their formal definitions, differences manifested in datasets, resolution pathways, and development of research. We summarize key tasks and achievements pertaining to definite and semi-definite data from myriad research undertakings, present a roadmap for indefinite data, beginning with its current research conundrums. Lastly, we classify and scrutinize the key datasets presently utilized within these three paradigms.

Pre-trained Language Models (PLMs) which are trained on large text corpus via self-supervised learning method, have yielded promising performance on various tasks in Natural Language Processing (NLP). However, though PLMs with huge parameters can effectively possess rich knowledge learned from massive training text and benefit downstream tasks at the fine-tuning stage, they still have some limitations such as poor reasoning ability due to the lack of external knowledge. Research has been dedicated to incorporating knowledge into PLMs to tackle these issues. In this paper, we present a comprehensive review of Knowledge-Enhanced Pre-trained Language Models (KE-PLMs) to provide a clear insight into this thriving field. We introduce appropriate taxonomies respectively for Natural Language Understanding (NLU) and Natural Language Generation (NLG) to highlight these two main tasks of NLP. For NLU, we divide the types of knowledge into four categories: linguistic knowledge, text knowledge, knowledge graph (KG), and rule knowledge. The KE-PLMs for NLG are categorized into KG-based and retrieval-based methods. Finally, we point out some promising future directions of KE-PLMs.

The recent proliferation of knowledge graphs (KGs) coupled with incomplete or partial information, in the form of missing relations (links) between entities, has fueled a lot of research on knowledge base completion (also known as relation prediction). Several recent works suggest that convolutional neural network (CNN) based models generate richer and more expressive feature embeddings and hence also perform well on relation prediction. However, we observe that these KG embeddings treat triples independently and thus fail to cover the complex and hidden information that is inherently implicit in the local neighborhood surrounding a triple. To this effect, our paper proposes a novel attention based feature embedding that captures both entity and relation features in any given entity's neighborhood. Additionally, we also encapsulate relation clusters and multihop relations in our model. Our empirical study offers insights into the efficacy of our attention based model and we show marked performance gains in comparison to state of the art methods on all datasets.

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