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Decision making in railway interlocking systems based on calculating the remainder of dividing a polynomial by a set of polynomials 基于多项式除以多项式集余数计算的铁路联锁系统决策
4区 数学 Q3 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/era.2023313
Antonio Hernando, Eugenio Roanes-Lozano, José Luis Galán-García, Gabriel Aguilera-Venegas

Decision-making in a railway station regarding the compatibility of the positions of the switches of the turnouts and the indications (proceed/stop) of the railway colour light signals is a safety-critical issue that is considered very labor-intensive. Different authors have proposed alternative solutions to automate its supervision, which is performed by the so-called railway interlocking systems. The classic railway interlocking systems are route-based and their compatibility is predetermined (usually by human experts): only some chosen routes are simultaneously allowed. Some modern railway interlocking systems are geographical and make decisions on the fly, but are unsuitable if the station is very large and the number of trains is high. In this paper, we present a completely new algebraic model for decision-making in railway interlocking systems, based on other computer algebra techniques, that bypasses the disadvantages of the approaches mentioned above (its performance does not depend on the number of trains in the railway station and can be used in large railway stations). The main goal of this work is to provide a mathematical solution to the interlocking problems. We prove that our approach solves it in linear time. Although our approach is interesting from a theoretical perspective, it has a significant limitation: it can hardly be adopted in an actual interlocking implementation, mainly due to the heavy certification requirements for this kind of safety-critical application. Nevertheless, the results may be useful for simulations that do not require certification credit.

火车站出线开关位置与铁路彩灯指示(进行/停止)的兼容性决策是一个非常劳动密集型的安全关键问题。不同的作者提出了自动化监管的替代解决方案,即所谓的铁路联锁系统。经典的铁路联锁系统是基于路线的,它们的兼容性是预先确定的(通常是由人类专家决定的):只允许一些选定的路线同时运行。一些现代铁路联锁系统是地理上的,并且可以在飞行中做出决策,但如果车站很大,火车数量很多,则不适合。在本文中,我们提出了一个全新的用于铁路联锁系统决策的代数模型,该模型基于其他计算机代数技术,绕过了上述方法的缺点(其性能不依赖于火车站的列车数量,可以用于大型火车站)。这项工作的主要目标是为联锁问题提供一个数学解决方案。我们证明了我们的方法在线性时间内解决了这个问题。尽管我们的方法从理论角度来看很有趣,但它有一个明显的限制:它很难在实际的联锁实现中采用,主要是因为这种安全关键型应用程序需要大量的认证要求。然而,结果可能对不需要认证学分的模拟有用。</ </abstract>
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引用次数: 0
Some identities of degenerate multi-poly-Changhee polynomials and numbers 退化多重多项式-长熙多项式与数的一些恒等式
4区 数学 Q3 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/era.2023367
Sang Jo Yun, Sangbeom Park, Jin-Woo Park, Jongkyum Kwon

Recently, many researchers studied the degenerate multi-special polynomials as degenerate versions of the multi-special polynomials and obtained some identities and properties of the those polynomials. The aim of this paper was to introduce the degenerate multi-poly-Changhee polynomials arising from multiple logarithms and investigate some interesting identities and properties of these polynomials that determine the relationship between multi-poly-Changhee polynomials, the Stirling numbers of the second kind, degenerate Stirling numbers of the first kind and falling factorial sequences. In addition, we investigated the phenomenon of scattering the zeros of these polynomials.

近年来,许多研究者将退化多特殊多项式作为多特殊多项式的退化形式进行了研究,并得到了这些多项式的一些性质和性质。摘要介绍了由多重对数产生的退化多重多项式,并研究了这些多项式的一些有趣的恒等式和性质,这些性质决定了多重多项式与第二类斯特林数、第一类退化斯特林数和降阶乘序列之间的关系。此外,我们还研究了这些多项式的零点散射现象。</p></abstract>
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引用次数: 0
<i>F-LSTM</i>: Federated learning-based LSTM framework for cryptocurrency price prediction &lt;i&gt;F-LSTM&lt;/i&gt;:用于加密货币价格预测的基于联邦学习的LSTM框架
4区 数学 Q3 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/era.2023330
Nihar Patel, Nakul Vasani, Nilesh Kumar Jadav, Rajesh Gupta, Sudeep Tanwar, Zdzislaw Polkowski, Fayez Alqahtani, Amr Gafar

In this paper, a distributed machine-learning strategy, i.e., federated learning (FL), is used to enable the artificial intelligence (AI) model to be trained on dispersed data sources. The paper is specifically meant to forecast cryptocurrency prices, where a long short-term memory (LSTM)-based FL network is used. The proposed framework, i.e., F-LSTM utilizes FL, due to which different devices are trained on distributed databases that protect the user privacy. Sensitive data is protected by staying private and secure by sharing only model parameters (weights) with the central server. To assess the effectiveness of F-LSTM, we ran different empirical simulations. Our findings demonstrate that F-LSTM outperforms conventional approaches and machine learning techniques by achieving a loss minimal of $ 2.3 times 10^{-4} $. Furthermore, the F-LSTM uses substantially less memory and roughly half the CPU compared to a solely centralized approach. In comparison to a centralized model, the F-LSTM requires significantly less time for training and computing. The use of both FL and LSTM networks is responsible for the higher performance of our suggested model (F-LSTM). In terms of data privacy and accuracy, F-LSTM addresses the shortcomings of conventional approaches and machine learning models, and it has the potential to transform the field of cryptocurrency price prediction.

本文采用一种分布式机器学习策略,即联邦学习(FL),使人工智能(AI)模型能够在分散的数据源上进行训练。该论文专门用于预测加密货币价格,其中使用了基于长短期记忆(LSTM)的FL网络。建议的框架,即<italic>F-LSTM</italic>利用FL,因此不同的设备在保护用户隐私的分布式数据库上进行训练。通过仅与中央服务器共享模型参数(权重)来保持敏感数据的私密性和安全性,从而保护敏感数据。为了评估<italic>F-LSTM</italic>的有效性,我们进行了不同的经验模拟。我们的研究结果表明< italital>F-LSTM</italic>通过实现2.3 乘以10^{-4}$的最小损失,优于传统方法和机器学习技术。此外,<italic>F-LSTM</italic>与完全集中的方法相比,使用的内存少得多,大约只有一半的CPU。与集中式模型相比,F-LSTM<需要更少的训练和计算时间。FL和LSTM网络的使用对我们建议的模型的更高性能负责(<italic>F-LSTM</italic>)。在数据隐私和准确性方面,< italital>F-LSTM</italic>解决了传统方法和机器学习模型的缺点,并有可能改变加密货币价格预测领域。</p></abstract>
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引用次数: 0
Advancements in AI-driven multilingual comprehension for social robot interactions: An extensive review 人工智能驱动的多语言理解在社交机器人交互中的进展:广泛回顾
4区 数学 Q3 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/era.2023334
Yanling Dong, Xiaolan Zhou

In the digital era, human-robot interaction is rapidly expanding, emphasizing the need for social robots to fluently understand and communicate in multiple languages. It is not merely about decoding words but about establishing connections and building trust. However, many current social robots are limited to popular languages, serving in fields like language teaching, healthcare and companionship. This review examines the AI-driven language abilities in social robots, providing a detailed overview of their applications and the challenges faced, from nuanced linguistic understanding to data quality and cultural adaptability. Last, we discuss the future of integrating advanced language models in robots to move beyond basic interactions and towards deeper emotional connections. Through this endeavor, we hope to provide a beacon for researchers, steering them towards a path where linguistic adeptness in robots is seamlessly melded with their capacity for genuine emotional engagement.

<abstract>< >在数字时代,人机交互正在迅速扩大,这强调了对社交机器人流利地理解和交流多种语言的需求。这不仅仅是关于解码文字,而是关于建立联系和建立信任。然而,目前许多社交机器人仅限于流行语言,服务于语言教学、医疗保健和陪伴等领域。这篇综述研究了社交机器人中人工智能驱动的语言能力,提供了它们的应用和面临的挑战的详细概述,从细微的语言理解到数据质量和文化适应性。最后,我们讨论了在机器人中集成高级语言模型的未来,以超越基本的互动,走向更深层次的情感联系。通过这一努力,我们希望为研究人员提供一个灯塔,引导他们走向一条道路,使机器人的语言熟练程度与他们真正的情感参与能力无缝融合。</p></abstract>
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引用次数: 0
Local well-posedness of perturbed Navier-Stokes system around Landau solutions 朗道解周围摄动Navier-Stokes系统的局部适定性
IF 0.8 4区 数学 Q3 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/ERA.2021010
Jingjing Zhang, Ting Zhang
In this paper, we consider the perturbed Navier–Stokes equations around the Landau solution and investigate the global well-posedness results of the perturbed system with the small initial data in the [Formula: see text] space, where [Formula: see text].
本文考虑围绕Landau解的摄动Navier-Stokes方程,在[公式:见文]空间中研究初始数据较小的摄动系统的全局适定性结果,其中[公式:见文]。
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引用次数: 3
Probabilistic invertible neural network for inverse design space exploration and reasoning 基于概率可逆神经网络的逆设计空间探索与推理
IF 0.8 4区 数学 Q3 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/era.2023043
Yiming Zhang, Zhiwei Pan, Shuyou Zhang, Na Qiu
Invertible neural network (INN) is a promising tool for inverse design optimization. While generating forward predictions from given inputs to the system response, INN enables the inverse process without much extra cost. The inverse process of INN predicts the possible input parameters for the specified system response qualitatively. For the purpose of design space exploration and reasoning for critical engineering systems, accurate predictions from the inverse process are required. Moreover, INN predictions lack effective uncertainty quantification for regression tasks, which increases the challenges of decision making. This paper proposes the probabilistic invertible neural network (P-INN): the epistemic uncertainty and aleatoric uncertainty are integrated with INN. A new loss function is formulated to guide the training process with enhancement in the inverse process accuracy. Numerical evaluations have shown that the proposed P-INN has noticeable improvement on the inverse process accuracy and the prediction uncertainty is reliable.
可逆神经网络(INN)是一种很有前途的反设计优化工具。当从给定的系统响应输入生成前向预测时,INN可以在没有太多额外成本的情况下实现反向过程。INN的逆过程定性地预测了给定系统响应的可能输入参数。为了对关键工程系统进行设计空间探索和推理,需要从逆过程中进行准确的预测。此外,INN预测缺乏对回归任务的有效不确定性量化,这增加了决策的挑战。本文提出了一种概率可逆神经网络(P-INN),它将认知不确定性和任意不确定性结合在一起。提出了一种新的损失函数来指导训练过程,提高了逆过程的精度。数值计算结果表明,所提出的P-INN方法对逆过程精度有明显提高,预测不确定性可靠。
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引用次数: 1
A modified FGL sparse canonical correlation analysis for the identification of Alzheimer's disease biomarkers 一种用于识别阿尔茨海默病生物标志物的改进FGL稀疏典型相关分析
IF 0.8 4区 数学 Q3 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/era.2023044
Shuaiqun Wang, Hui Chen, Wei Kong, Xin-gui Wu, Yafei Qian, Kai Wei
Imaging genetics mainly finds the correlation between multiple datasets, such as imaging and genomics. Sparse canonical correlation analysis (SCCA) is regarded as a useful method that can find connections between specific genes, SNPs, and diseased brain regions. Fused pairwise group lasso-SCCA (FGL-SCCA) can discover the chain relationship of genetic variables within the same modality or the graphical relationship between images. However, it can only handle genetic and imaging data from a single modality. As Alzheimer's disease is a kind of complex and comprehensive disease, a single clinical indicator cannot accurately reflect the physiological process of the disease. It is urgent to find biomarkers that can reflect AD and more synthetically reflect the physiological function of disease development. In this study, we proposed a multimodal sparse canonical correlation analysis model FGL-JSCCAGNR combined FGL-SCCA and Joint SCCA (JSCCA) method which can process multimodal data. Based on the JSCCA algorithm, it imposes a GraphNet regularization penalty term and introduces a fusion pairwise group lasso (FGL), and a graph-guided pairwise group lasso (GGL) penalty term, the algorithm in this paper can combine data between different modalities, Finally, the Annual Depression Level Total Score (GDSCALE), Clinical Dementia Rating Scale (GLOBAL CDR), Functional Activity Questionnaire (FAQ) and Neuropsychiatric Symptom Questionnaire (NPI-Q), these four clinical data are embedded in the model by linear regression as compensation information. Both simulation data and real data analysis show that when FGI-JSCCAGNR is applied to the imaging genetics study of Alzheimer's patients, the model presented here can detect more significant genetic variants and diseased brain regions. It provides a more robust theoretical basis for clinical researchers.
成像遗传学主要寻找成像和基因组学等多个数据集之间的相关性。稀疏典型相关分析(SCCA)被认为是一种有效的方法,可以发现特定基因、snp和病变脑区域之间的联系。FGL-SCCA (Fused pairwise group lasso-SCCA)可以发现同一模态内遗传变量的链关系或图像之间的图形关系。然而,它只能处理来自单一模式的遗传和成像数据。阿尔茨海默病是一种复杂的综合性疾病,单一的临床指标不能准确反映疾病的生理过程。迫切需要寻找能够反映AD的生物标志物,更综合地反映疾病发展的生理功能。本研究提出了一种结合FGL-SCCA和Joint SCCA (JSCCA)方法的多模态稀疏典型相关分析模型FGL-JSCCAGNR,可以处理多模态数据。本文算法在JSCCA算法的基础上,引入GraphNet正则化惩罚项,并引入融合两两组套索(FGL)和图导两两组套索(GGL)惩罚项,实现了不同模式间数据的组合。最后,将年度抑郁水平总分(GDSCALE)、临床痴呆评定量表(GLOBAL CDR)、功能活动问卷(FAQ)和神经精神症状问卷(NPI-Q)这四个临床数据通过线性回归作为补偿信息嵌入到模型中。仿真数据和真实数据分析均表明,将FGI-JSCCAGNR应用于阿尔茨海默病患者的成像遗传学研究时,本文模型可以检测到更显著的遗传变异和病变脑区。为临床研究者提供了更为有力的理论依据。
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引用次数: 0
Pullback dynamics and robustness for the 3D Navier-Stokes-Voigt equations with memory 三维记忆Navier-Stokes-Voigt方程的回拉动力学和鲁棒性
IF 0.8 4区 数学 Q3 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/era.2023046
Keqin Su, Rong Yang
The tempered pullback dynamics and robustness of the 3D Navier-Stokes-Voigt equations with memory and perturbed external force are considered in this paper. Based on the global well-posedness results and energy estimates involving memory, a suitable tempered universe is constructed, the robustness is finally established via the upper semi-continuity of tempered pullback attractors when the perturbation parameter epsilon tends to zero.
研究了具有记忆和摄动外力的三维Navier-Stokes-Voigt方程的回调动力学和鲁棒性。基于全局适定性结果和涉及记忆的能量估计,构造了一个合适的调质宇宙,最后在扰动参数epsilon趋于零时,通过调质回拉吸引子的上半连续性建立了鲁棒性。
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引用次数: 0
Research on en route capacity evaluation model based on aircraft trajectory data 基于飞机轨迹数据的航路容量评估模型研究
IF 0.8 4区 数学 Q3 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/era.2023087
J. Ren, Shiru Qu, Lili Wang, Yu Wang, Tingting Lu, Lijing Ma
For the sake of refined assessment of airspace operation status, improvement of the en route air traffic management performance, and alleviation of the imbalance of demand-capacity and airspace congestion, an en route accessible capacity evaluation model (based on aircraft trajectory data) is proposed in this paper. Firstly, from the perspective of flux, the en route capacity is defined and expanded from a two-dimensional concept to a three-dimensional concept. Secondly, based on the indicators of spatial flow and instantaneous density, an evaluation model of en route capacity is given. Finally, a case study is performed to validate the applicability and feasibility of the model. Results show that the en route accessible capacity, instantaneous density, and spatial flow can describe the temporal and spatial distribution of air traffic flow more precisely, as compared to the conventional indicators, such as route capacity, density, and flow. The proposed model envisages three innovations: (ⅰ) the definition of airspace accessible capacity with reference to capacity of road traffic, (ⅱ) the computation model for flux-based airspace accessible capacity and en route accessible capacity, and (ⅲ) two indicators of en route characteristics named instantaneous density and spatial flow are introduced for evaluating the micro-state of the en route. Furthermore, because of the capacity depiction of the spatial and temporal distribution of air traffic congestion within an airspace unit, this model can also help air traffic controllers balance the distribution of traffic flow density, reduce the utilization rate of horizontal airspace, and resolve flight conflicts on air routes in advance.
为了精细化空域运行状态评估,提高航路空中交通管理绩效,缓解需求容量失衡和空域拥堵,本文提出了一种基于飞机轨迹数据的航路可达容量评估模型。首先,从通量的角度对途中容量进行定义,并将其从二维概念扩展到三维概念。其次,基于空间流量和瞬时密度指标,建立了道路通行能力评价模型;最后,通过实例验证了模型的适用性和可行性。结果表明,与航线容量、密度和流量等常规指标相比,航路可达容量、瞬时密度和空间流量能更准确地描述空中交通流的时空分布。该模型提出了三个创新点:(ⅰ)参考道路交通容量定义空域通达能力;(ⅱ)基于通量的空域通达能力和航路通达能力计算模型;(ⅲ)引入瞬时密度和空间流量两个航路特征指标来评价航路微观状态。此外,由于该模型对空域单元内空中交通拥堵时空分布的容量描述,还可以帮助空中交通管制员平衡交通流密度分布,降低水平空域利用率,提前解决航线上的飞行冲突。
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引用次数: 0
The effect credit term structure of monetary policy on firms' "short-term debt for long-term investment" behavior: empirical evidence from China 货币政策信贷期限结构对企业“以短期债务换长期投资”行为的影响:来自中国的经验证据
IF 0.8 4区 数学 Q3 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/era.2023076
Liping Zheng, Jia Liao, Yuan Yu, Bin Mo, Yun Liu
This paper examines the effects and mechanism paths of monetary policy on firms' "short-term debt for long-term investment (SDFLI)" behavior using panel data of Chinese A-share listed firms from 2007-2019. The findings indicate that loose monetary policy suppresses corporate SDFLI behavior by lengthening corporate credit maturity structure through the credit maturity structure channel. In addition, heterogeneity analysis shows that loose monetary policy significantly inhibits the SDFLI behavior of state-owned enterprises(SOEs), non-high-tech firms, and firms in regions with high bank competition levels through the credit term structure channel, and the monetary policy credit term structure channel fails for non-state-owned enterprises(non-SOEs), high-tech firms, and firms in regions with low bank competition levels. The results of the heterogeneity analysis validate the plausibility that monetary policy affects firms' SDFLI behavior through the credit term structure channel.
本文利用2007-2019年中国a股上市公司面板数据,考察了货币政策对企业“短期债务换长期投资”行为的影响及其机制路径。研究发现,宽松货币政策通过信贷期限结构渠道延长企业信用期限结构,从而抑制企业SDFLI行为。此外,异质性分析表明,宽松货币政策通过信贷期限结构渠道显著抑制国有企业、非高新技术企业和银行竞争水平高的地区企业的SDFLI行为,货币政策信贷期限结构渠道对非国有企业、高新技术企业和银行竞争水平低的地区企业的SDFLI行为失效。异质性分析的结果验证了货币政策通过信贷期限结构渠道影响企业SDFLI行为的合理性。
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引用次数: 1
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