Mathematics最新文献

{"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":"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":null,"pages":null},"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":"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":null,"pages":null},"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":"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":null,"pages":null},"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}

{"title":"High-Resolution Spatiotemporal Forecasting with Missing Observations Including an Application to Daily Particulate Matter 2.5 Concentrations in Jakarta Province, Indonesia","authors":"I Gede Nyoman Mindra Jaya, Henk Folmer","doi":"10.3390/math12182899","DOIUrl":"https://doi.org/10.3390/math12182899","url":null,"abstract":"Accurate forecasting of high-resolution particulate matter 2.5 (PM2.5) levels is essential for the development of public health policy. However, datasets used for this purpose often contain missing observations. This study presents a two-stage approach to handle this problem. The first stage is a multivariate spatial time series (MSTS) model, used to generate forecasts for the sampled spatial units and to impute missing observations. The MSTS model utilizes the similarities between the temporal patterns of the time series of the spatial units to impute the missing data across space. The second stage is the high-resolution prediction model, which generates predictions that cover the entire study domain. The second stage faces the big N problem giving rise to complex memory and computational problems. As a solution to the big N problem, we propose a Gaussian Markov random field (GMRF) for innovations with the Matérn covariance matrix obtained from the corresponding Gaussian field (GF) matrix by means of the stochastic partial differential equation (SPDE) method and the finite element method (FEM). For inference, we propose Bayesian statistics and integrated nested Laplace approximation (INLA) in the R-INLA package. The above approach is demonstrated using daily data collected from 13 PM2.5 monitoring stations in Jakarta Province, Indonesia, for 1 January–31 December 2022. The first stage of the model generates PM2.5 forecasts for the 13 monitoring stations for the period 1–31 January 2023, imputing missing data by means of the MSTS model. To capture temporal trends in the PM2.5 concentrations, the model applies a first-order autoregressive process and a seasonal process. The second stage involves creating a high-resolution map for the period 1–31 January 2023, for sampled and non-sampled spatiotemporal units. It uses the MSTS-generated PM2.5 predictions for the sampled spatiotemporal units and observations of the covariate’s altitude, population density, and rainfall for sampled and non-samples spatiotemporal units. For the spatially correlated random effects, we apply a first-order random walk process. The validation of out-of-sample forecasts indicates a strong model fit with low mean squared error (0.001), mean absolute error (0.037), and mean absolute percentage error (0.041), and a high R² value (0.855). The analysis reveals that altitude and precipitation negatively impact PM2.5 concentrations, while population density has a positive effect. Specifically, a one-meter increase in altitude is linked to a 7.8% decrease in PM2.5, while a one-person increase in population density leads to a 7.0% rise in PM2.5. Additionally, a one-millimeter increase in rainfall corresponds to a 3.9% decrease in PM2.5. The paper makes a valuable contribution to the field of forecasting high-resolution PM2.5 levels, which is essential for providing detailed, accurate information for public health policy. The approach presents a new and innovative method for addressi","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249110","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":"Enhancing Autism Spectrum Disorder Classification with Lightweight Quantized CNNs and Federated Learning on ABIDE-1 Dataset","authors":"Simran Gupta, Md. Rahad Islam Bhuiyan, Sadia Sultana Chowa, Sidratul Montaha, Rashik Rahman, Sk. Tanzir Mehedi, Ziaur Rahman","doi":"10.3390/math12182886","DOIUrl":"https://doi.org/10.3390/math12182886","url":null,"abstract":"Autism spectrum disorder (ASD) is a complex neurodevelopmental condition that presents significant diagnostic challenges due to its varied symptoms and nature. This study aims to improve ASD classification using advanced deep learning techniques applied to neuroimaging data. We developed an automated system leveraging the ABIDE-1 dataset and a novel lightweight quantized one-dimensional (1D) Convolutional Neural Network (Q-CNN) model to analyze fMRI data. Our approach employs the NIAK pipeline with multiple brain atlases and filtering methods. Initially, the Regions of Interest (ROIs) are converted into feature vectors using tangent space embedding to feed into the Q-CNN model. The proposed 1D-CNN is quantized through Quantize Aware Training (QAT). As the quantization method, int8 quantization is utilized, which makes it both robust and lightweight. We propose a federated learning (FL) framework to ensure data privacy, which allows decentralized training across different data centers without compromising local data security. Our findings indicate that the CC200 brain atlas, within the NIAK pipeline’s filt-global filtering methods, provides the best results for ASD classification. Notably, the ASD classification outcomes have achieved a significant test accuracy of 98% using the CC200 and filt-global filtering techniques. To the best of our knowledge, this performance surpasses previous studies in the field, highlighting a notable enhancement in ASD detection from fMRI data. Furthermore, the FL-based Q-CNN model demonstrated robust performance and high efficiency on a Raspberry Pi 4, underscoring its potential for real-world applications. We exhibit the efficacy of the Q-CNN model by comparing its inference time, power consumption, and storage requirements with those of the 1D-CNN, quantized CNN, and the proposed int8 Q-CNN models. This research has made several key contributions, including the development of a lightweight int8 Q-CNN model, the application of FL for data privacy, and the evaluation of the proposed model in real-world settings. By identifying optimal brain atlases and filtering methods, this study provides valuable insights for future research in the field of neurodevelopmental disorders.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249112","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}