Mathematics最新文献

{"title":"Incorporating Digital Footprints into Credit-Scoring Models through Model Averaging","authors":"Linhui Wang, Jianping Zhu, Chenlu Zheng, Zhiyuan Zhang","doi":"10.3390/math12182907","DOIUrl":"https://doi.org/10.3390/math12182907","url":null,"abstract":"Digital footprints provide crucial insights into individuals’ behaviors and preferences. Their role in credit scoring is becoming increasingly significant. Therefore, it is crucial to combine digital footprint data with traditional data for personal credit scoring. This paper proposes a novel credit-scoring model. First, lasso-logistic regression is used to select key variables that significantly impact the prediction results. Then, digital footprint variables are categorized based on business understanding, and candidate models are constructed from various combinations of these groups. Finally, the optimal weight is selected by minimizing the Kullback–Leibler loss. Subsequently, the final prediction model is constructed. Empirical analysis validates the advantages and feasibility of the proposed method in variable selection, coefficient estimation, and predictive accuracy. Furthermore, the model-averaging method provides the weights for each candidate model, providing managerial implications to identify beneficial variable combinations for credit scoring.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"LMKCDEY Revisited: Speeding Up Blind Rotation with Signed Evaluation Keys","authors":"Yongwoo Lee","doi":"10.3390/math12182909","DOIUrl":"https://doi.org/10.3390/math12182909","url":null,"abstract":"Recently, Lee et al. introduced a novel blind rotation technique utilizing ring automorphisms also known as LMKCDEY. Among known prominent blind rotation methods, LMKCDEY stands out because of its minimal key size and efficient runtime for arbitrary secret keys, although Chillotti et al.’s approach, commonly referred to as CGGI, offers faster runtime when using binary or ternary secrets. In this paper, we propose an enhancement to LMKCDEY’s runtime by incorporating auxiliary keys that encrypt the negated values of secret key elements. Our method not only achieves faster execution than LMKCDEY but also maintains a smaller key size compared to the ternary version of CGGI. Moreover, the proposed technique is compatible with LMKCDEY with only minimal adjustments. Experimental results with OpenFHE demonstrate that our approach can improve bootstrapping runtime by 5–28%, depending on the chosen parameters.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"12 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A New Instance Segmentation Model for High-Resolution Remote Sensing Images Based on Edge Processing","authors":"Xiaoying Zhang, Jie Shen, Huaijin Hu, Houqun Yang","doi":"10.3390/math12182905","DOIUrl":"https://doi.org/10.3390/math12182905","url":null,"abstract":"With the goal of addressing the challenges of small, densely packed targets in remote sensing images, we propose a high-resolution instance segmentation model named QuadTransPointRend Net (QTPR-Net). This model significantly enhances instance segmentation performance in remote sensing images. The model consists of two main modules: preliminary edge feature extraction (PEFE) and edge point feature refinement (EPFR). We also created a specific approach and strategy named TransQTA for edge uncertainty point selection and feature processing in high-resolution remote sensing images. Multi-scale feature fusion and transformer technologies are used in QTPR-Net to refine rough masks and fine-grained features for selected edge uncertainty points while balancing model size and accuracy. Based on experiments performed on three public datasets: NWPU VHR-10, SSDD, and iSAID, we demonstrate the superiority of QTPR-Net over existing approaches.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"116 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantitative Portfolio Management: Review and Outlook","authors":"Michael Senescall, Rand Kwong Yew Low","doi":"10.3390/math12182897","DOIUrl":"https://doi.org/10.3390/math12182897","url":null,"abstract":"This survey aims to provide insightful and objective perspectives on the research history of quantitative portfolio management strategies with suggestions for the future of research. The relevant literature can be clustered into four broad themes: portfolio optimization, risk-parity, style integration, and machine learning. Portfolio optimization attempts to find the optimal trade-off of future returns per unit of risk. Risk-parity attempts to match the exposure of various asset classes such that no single asset class dominates portfolio risk. Style integration combines risk factors on a security level such that rebalancing differences cancel out. Finally, machine learning utilizes large arrays of tunable parameters to predict future asset behavior and solve non-convex optimization problems. We conclude that machine learning will likely be the focus of future research.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"20 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Case-Based Deduction for Entailment Tree Generation","authors":"Jihao Shi, Xiao Ding, Ting Liu","doi":"10.3390/math12182893","DOIUrl":"https://doi.org/10.3390/math12182893","url":null,"abstract":"Maintaining logical consistency in structured explanations is critical for understanding and troubleshooting the reasoning behind a system’s decisions. However, existing methods for entailment tree generation often struggle with logical consistency, resulting in erroneous intermediate conclusions and reducing the overall accuracy of the explanations. To address this issue, we propose case-based deduction (CBD), a novel approach that retrieves cases with similar logical structures from a case base and uses them as demonstrations for logical deduction. This method guides the model toward logically sound conclusions without the need for manually constructing logical rule bases. By leveraging a prototypical network for case retrieval and reranking them using information entropy, CBD introduces diversity to improve in-context learning. Our experimental results on the EntailmentBank dataset show that CBD significantly improves entailment tree generation, achieving performance improvements of 1.7% in Task 1, 0.6% in Task 2, and 0.8% in Task 3 under the strictest Overall AllCorrect metric. These findings confirm that CBD enhances the logical consistency and overall accuracy of AI systems in structured explanation tasks.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"2 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Univariate Vector-Valued Rational Interpolation and Recovery Problems","authors":"Lixia Xiao, Peng Xia, Shugong Zhang","doi":"10.3390/math12182896","DOIUrl":"https://doi.org/10.3390/math12182896","url":null,"abstract":"In this paper, we consider a novel vector-valued rational interpolation algorithm and its application. Compared to the classic vector-valued rational interpolation algorithm, the proposed algorithm relaxes the constraint that the denominators of components of the interpolation function must be identical. Furthermore, this algorithm can be applied to construct the vector-valued interpolation function component-wise, with the help of the common divisors among the denominators of components. Through experimental comparisons with the classic vector-valued rational interpolation algorithm, it is found that the proposed algorithm exhibits low construction cost, low degree of the interpolation function, and high approximation accuracy.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"15 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Study on Linguistic Z-Graph and Its Application in Social Networks","authors":"Rupkumar Mahapatra, Sovan Samanta, Madhumangal Pal, Tofigh Allahviranloo, Antonios Kalampakas","doi":"10.3390/math12182898","DOIUrl":"https://doi.org/10.3390/math12182898","url":null,"abstract":"This paper presents a comprehensive study of the linguistic Z-graph, which is a novel framework designed to analyze linguistic structures within social networks. By integrating concepts from graph theory and linguistics, the linguistic Z-graph provides a detailed understanding of language dynamics in online communities. This study highlights the practical applications of linguistic Z-graphs in identifying central nodes within social networks, which are crucial for online businesses in market capture and information dissemination. Traditional methods for identifying central nodes rely on direct connections, but social network connections often exhibit uncertainty. This paper focuses on using fuzzy theory, particularly linguistic Z-graphs, to address this uncertainty, offering more detailed insights compared to fuzzy graphs. Our study introduces a new centrality measure using linguistic Z-graphs, enhancing our understanding of social network structures.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"144 3 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tightness of Harary Graphs","authors":"Abolfazl Javan, Ali Moeini, Mohammad Shekaramiz","doi":"10.3390/math12182894","DOIUrl":"https://doi.org/10.3390/math12182894","url":null,"abstract":"In the design of real-world networks, researchers evaluate various structural parameters to assess vulnerability, including connectivity, toughness, and tenacity. Recently, the tightness metric has emerged as a potentially superior vulnerability measure, although many related theorems remain unknown due to its novelty. Harary graphs, known for their maximum connectivity, are an important class of graph models for network design. Prior work has evaluated the vulnerability of three types of Harary graphs using different parameters, but the tightness metric has not been thoroughly explored. This article aims to calculate the tightness values for all three types of Harary graphs. First, it will attempt to calculate the lower bound for the value of the tightness parameter in Harary graphs using existing lemmas and theorems. Then, by presenting new lemmas and theorems, we will try to find the exact value or upper bound for this parameter in Harary graphs. For the first type of Harary graph, the tightness is precisely determined, while for the second and third types, upper bounds are provided due to structural complexity. The lemmas, theorems, and proof methods presented in this research may be used to calculate other graph and network parameters. However, the newness of the tightness parameter means that further research is needed to fully characterize its properties.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"20 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Second Critical Exponent for a Time-Fractional Reaction-Diffusion Equation","authors":"Takefumi Igarashi","doi":"10.3390/math12182895","DOIUrl":"https://doi.org/10.3390/math12182895","url":null,"abstract":"In this paper, we consider the Cauchy problem of a time-fractional nonlinear diffusion equation. According to Kaplan’s first eigenvalue method, we first prove the blow-up of the solutions in finite time under some sufficient conditions. We next provide sufficient conditions for the existence of global solutions by using the results of Zhang and Sun. In conclusion, we find the second critical exponent for the existence of global and non-global solutions via the decay rates of the initial data at spatial infinity.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"14 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear Perception Characteristics Analysis of Ocean White Noise Based on Deep Learning Algorithms","authors":"Tao Qian, Ying Li, Jun Chen","doi":"10.3390/math12182892","DOIUrl":"https://doi.org/10.3390/math12182892","url":null,"abstract":"Caused by nonlinear vibration, ocean white noise exhibits complex dynamic characteristics and nonlinear perception characteristics. To explore the potential application of ocean white noise in engineering and health fields, novel methods based on deep learning algorithms are proposed to generate ocean white noise, contributing to marine environment simulation in ocean engineering. A comparative study, including spectrum analysis and auditory testing, proved the superiority of the generation method using deep learning networks over general mathematical or physical methods. To further study the nonlinear perception characteristics of ocean white noise, novel experimental research based on multi-modal perception research methods was carried out within a constructed multi-modal perception system environment, including the following two experiments. The first audiovisual comparative experiment thoroughly explores the system’s user multi-modal perception experience and influence factors, explicitly focusing on the impact of ocean white noise on human perception. The second sound intensity testing experiment is conducted to further explore human multi-sensory interaction and change patterns under white noise stimulation. The experimental results indicate that user visual perception ability and state reach a relatively high level when the sound intensity is close to 50 dB. Further numerical analysis based on the experimental results reveals the internal influence relationship between user perception of multiple senses, showing a fluctuating influence law to user visual concentration and a curvilinear influence law to user visual psychology from the sound intensity of ocean white noise. This study underscores ocean white noise’s positive effect on human perception enhancement and concentration improvement, providing a research basis for multiple field applications such as spiritual healing, perceptual learning, and artistic creation for human beings. Importantly, it provides valuable references and practical insights for professionals in related fields, contributing to the development and utilization of the marine environment.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"51 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}