Mathematics最新文献

{"title":"A Mathematical Perspective on the Influence of Allee Effects in Oncolytic Virotherapy.","authors":"Eymard Hernández-López, Jin Wang","doi":"10.3390/math13050744","DOIUrl":"https://doi.org/10.3390/math13050744","url":null,"abstract":"<p><p>This article is concerned with the mathematical modeling of cancer virotherapy, emphasizing the impact of Allee effects on tumor cell growth. We propose a modeling framework that describes the complex interaction between tumor cells and oncolytic viruses. The efficacy of this therapy against cancer is mathematically investigated. The analysis involves linear and logistic growth scenarios coupled with different Allee effects, including weak, strong, and hyper Allee forms. Critical points are identified, and their existence and stability are analyzed using dynamical system theories and bifurcation techniques. Also, bifurcation diagrams and numerical simulations are utilized to verify and extend analytical results. It is observed that Allee effects significantly influence the stability of the system and the conditions necessary for tumor control and eradication.</p>","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"13 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12373149/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144959713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effectiveness of PEER Intervention on Older Adults' Physical Activity Time Series Using Smoothing Spline ANOVA.","authors":"Yi Liu, Chang Liu, Liqiang Ni, Wei Zhang, Chen Chen, Janet Lopez, Hao Zheng, Ladda Thiamwong, Rui Xie","doi":"10.3390/math13030516","DOIUrl":"https://doi.org/10.3390/math13030516","url":null,"abstract":"<p><p>Falls are a major cause of injury among older adults. The Physio-fEedback Exercise pRogram (PEER) combines physio-feedback, cognitive reframing, and guided exercises to reduce fall risk. However, its impact on physical activity (PA) over time is underexplored. Functional time-series analysis offers insight into behavior patterns and sustainability. This preliminary study assessed PEER's effectiveness in improving PA levels immediately and over time. A total of 64 community-dwelling older adults were cluster-randomized into PEER <math><mo>(</mo> <mi>N</mi> <mo>=</mo> <mn>33</mn> <mo>)</mo></math> or control groups <math><mo>(</mo> <mi>N</mi> <mo>=</mo> <mn>31</mn> <mo>)</mo></math> . Participants wore Fitbit trackers, generating time-series data on activity. The PEER group completed an 8-week program, while the control group received CDC fall prevention pamphlets. PA data were analyzed using smoothing spline analysis of variance (SSANOVA), chosen for its flexibility in modeling complex, non-linear relationships in time-series data and its ability to handle skewed distributions and repeated measures. Unlike traditional parametric models, SSANOVA decomposes temporal trends into interpretable components, capturing both smooth trends and abrupt changes, such as those occurring on group workout days. This capability ensures robust and nuanced analysis of intervention effects. Results showed PEER participants significantly increased evenly and had very active minutes and reduced sedentary behavior during the intervention. No significant effect was found for light active minutes. Specifically, during the intervention period, PEER participants engaged in an average of 6.7% fewer sedentary minutes per day, 13.8% additional fairly active minutes per day, and 2.8% additional very active minutes per day compared to the control group. While the reduction in sedentary minutes and increase in fairly active minutes were not statistically significant, the increase in very active minutes was significant. However, our functional time-series analysis revealed these improvements diminished over the 15-week follow-up, indicating challenges in maintaining PA. In conclusion, PEER boosts PA and reduces sedentary behavior short-term, but strategies are needed to sustain these benefits. In conclusion, PEER boosts PA and reduces sedentary behavior short-term, but strategies are needed to sustain these benefits. Public health policies should emphasize technology-driven fall risk assessments, community-based prevention programs, and initiatives that promote physical activity, home safety, and chronic condition management.</p>","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"13 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12017781/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144024114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Persistent Topological Laplacians-A Survey.","authors":"Xiaoqi Wei, Guo-Wei Wei","doi":"10.3390/math13020208","DOIUrl":"10.3390/math13020208","url":null,"abstract":"<p><p>Persistent topological Laplacians constitute a new class of tools in topological data analysis (TDA). They are motivated by the necessity to address challenges encountered in persistent homology when handling complex data. These Laplacians combine multiscale analysis with topological techniques to characterize the topological and geometrical features of functions and data. Their kernels fully retrieve the topological invariants of corresponding persistent homology, while their non-harmonic spectra provide supplementary information. Persistent topological Laplacians have demonstrated superior performance over persistent homology in the analysis of large-scale protein engineering datasets. In this survey, we offer a pedagogical review of persistent topological Laplacians formulated in various mathematical settings, including simplicial complexes, path complexes, flag complexes, digraphs, hypergraphs, hyperdigraphs, cellular sheaves, and <math><mi>N</mi></math> -chain complexes.</p>","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"13 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12467289/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145186243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Estimating the Relative Risks of Spatial Clusters Using a Predictor-Corrector Method.","authors":"Majid Bani-Yaghoub, Kamel Rekab, Julia Pluta, Said Tabharit","doi":"10.3390/math13020180","DOIUrl":"10.3390/math13020180","url":null,"abstract":"<p><p>Spatial, temporal, and space-time scan statistics can be used for geographical surveillance, identifying temporal and spatial patterns, and detecting outliers. While statistical cluster analysis is a valuable tool for identifying patterns, optimizing resource allocation, and supporting decision-making, accurately predicting future spatial clusters remains a significant challenge. Given the known relative risks of spatial clusters over the past <math><mi>k</mi></math> time intervals, the main objective of the present study is to predict the relative risks for the subsequent interval, <math><mi>k</mi> <mo>+</mo> <mn>1</mn></math> . Building on our prior research, we propose a predictive Markov chain model with an embedded corrector component. This corrector utilizes either multiple linear regression or exponential smoothing method, selecting the one that minimizes the relative distance between observed and predicted values in the <math><mi>k</mi></math> -th interval. To test the proposed method, we first calculated the relative risks of statistically significant spatial clusters of COVID-19 mortality in the U.S. over seven time intervals from May 2020 to March 2023. Then, for each time interval, we selected the top 25 clusters with the highest relative risks and iteratively predicted the relative risks of clusters from intervals three to seven. The predictive accuracies ranged from moderate to high, indicating the potential applicability of this method for predictive disease analytics and future pandemic preparedness.</p>","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"13 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11827645/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143433472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rootlets Hierarchical Principal Component Analysis for Revealing Nested Dependencies in Hierarchical Data.","authors":"Korey P Wylie, Jason R Tregellas","doi":"10.3390/math13010072","DOIUrl":"10.3390/math13010072","url":null,"abstract":"<p><p>Hierarchical clustering analysis (HCA) is a widely used unsupervised learning method. Limitations of HCA, however, include imposing an artificial hierarchy onto non-hierarchical data and fixed two-way mergers at every level. To address this, the current work describes a novel rootlets hierarchical principal component analysis (hPCA). This method extends typical hPCA using multivariate statistics to construct adaptive multiway mergers and Riemannian geometry to visualize nested dependencies. The rootlets hPCA algorithm and its projection onto the Poincaré disk are presented as examples of this extended framework. The algorithm constructs high-dimensional mergers using a single parameter, interpreted as a <math><mi>p</mi></math> -value. It decomposes a similarity matrix from <math><mi>G</mi> <mi>L</mi> <mo>(</mo> <mi>m</mi> <mo>,</mo> <mi>R</mi> <mo>)</mo></math> using a sequence of rotations from <math><mi>S</mi> <mi>O</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo></math> , <math><mi>k</mi> <mo>≪</mo> <mi>m</mi></math> . Analysis shows that the rootlets algorithm limits the number of distinct eigenvalues for any merger. Nested clusters of arbitrary size but equal correlations are constructed and merged using their leading principal components. The visualization method then maps elements of <math><mi>S</mi> <mi>O</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo></math> onto a low-dimensional hyperbolic manifold, the Poincaré disk. Rootlets hPCA was validated using simulated datasets with known hierarchical structure, and a neuroimaging dataset with an unknown hierarchy. Experiments demonstrate that rootlets hPCA accurately reconstructs known hierarchies and, unlike HCA, does not impose a hierarchy on data.</p>","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"13 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12456745/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145138139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Principled Framework to Assess the Information-Theoretic Fitness of Brain Functional Sub-Circuits.","authors":"Duy Duong-Tran, Nghi Nguyen, Shizhuo Mu, Jiong Chen, Jingxuan Bao, Frederick H Xu, Sumita Garai, Jose Cadena-Pico, Alan David Kaplan, Tianlong Chen, Yize Zhao, Li Shen, Joaquín Goñi","doi":"10.3390/math12192967","DOIUrl":"10.3390/math12192967","url":null,"abstract":"<p><p>In systems and network neuroscience, many common practices in brain connectomic analysis are often not properly scrutinized. One such practice is mapping a predetermined set of sub-circuits, like functional networks (FNs), onto subjects' functional connectomes (FCs) without adequately assessing the information-theoretic appropriateness of the partition. Another practice that goes unchallenged is thresholding weighted FCs to remove spurious connections without justifying the chosen threshold. This paper leverages recent theoretical advances in Stochastic Block Models (SBMs) to formally define and quantify the information-theoretic fitness (e.g., prominence) of a predetermined set of FNs when mapped to individual FCs under different fMRI task conditions. Our framework allows for evaluating any combination of FC granularity, FN partition, and thresholding strategy, thereby optimizing these choices to preserve the important topological features of the human brain connectomes. By applying to the Human Connectome Project with Schaefer parcellations at multiple levels of granularity, the framework showed that the common thresholding value of 0.25 was indeed information-theoretically valid for group-average FCs, despite its previous lack of justification. Our results pave the way for the proper use of FNs and thresholding methods, and provide insights for future research in individualized parcellations.</p>","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"12 19","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12352546/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144873911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Three Weak Solutions for a Critical Non-Local Problem with Strong Singularity in High Dimension","authors":"Gabriel Neves Cunha, Francesca Faraci, Kaye Silva","doi":"10.3390/math12182910","DOIUrl":"https://doi.org/10.3390/math12182910","url":null,"abstract":"In this paper, we deal with a strongly singular problem involving a non-local operator, a critical nonlinearity, and a subcritical perturbation. We apply techniques from non-smooth analysis to the energy functional, in combination with the study of the topological properties of the sublevels of its smooth part, to prove the existence of three weak solutions: two points of local minimum and a third one as a mountain pass critical point.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"2 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249100","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":"An Attribute-Based End-to-End Policy-Controlled Signcryption Scheme for Secure Group Chat Communication","authors":"Feng Yu, Linghui Meng, Xianxian Li, Daicen Jiang, Weidong Zhu, Zhihua Zeng","doi":"10.3390/math12182906","DOIUrl":"https://doi.org/10.3390/math12182906","url":null,"abstract":"Secure instant communication is an important topic of information security. A group chat is a highly convenient mode of instant communication. Increasingly, companies are adopting group chats as a daily office communication tool. However, a large volume of messages in group chat communication can lead to message overload, causing group members to miss important information. Additionally, the communication operator’s server may engage in the unreliable behavior of stealing information from the group chat. To address these issues, this paper proposes an attribute-based end-to-end policy-controlled signcryption scheme, aimed at establishing a secure and user-friendly group chat communication mode. By using the linear secret sharing scheme (LSSS) with strong expressive power to construct the access structure in the signcryption technology, the sender can precisely control the recipients of the group chat information to avoid message overload. To minimize computational cost, a signcryption step with constant computational overhead is designed. Additionally, a message-sending mechanism combining “signcryption + encryption” is employed to prevent the operator server from maliciously stealing group chat information. Rigorous analysis shows that PCE-EtoE can resist adaptive chosen-ciphertext attacks under the standard model. Simulation results demonstrate that our theoretical derivation is correct, and that the PCE-EtoE scheme outperforms existing schemes in terms of computational cost, making it suitable for group chat communication.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"88 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249420","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":"AssocKD: An Association-Aware Knowledge Distillation Method for Document-Level Event Argument Extraction","authors":"Lijun Tan, Yanli Hu, Jianwei Cao, Zhen Tan","doi":"10.3390/math12182901","DOIUrl":"https://doi.org/10.3390/math12182901","url":null,"abstract":"Event argument extraction is a crucial subtask of event extraction, which aims at extracting arguments that correspond to argument roles when given event types. The majority of current document-level event argument extraction works focus on extracting information for only one event at a time without considering the association among events; this is known as document-level single-event extraction. However, the interrelationship among arguments can yield mutual gains in their extraction. Therefore, in this paper, we propose AssocKD, an Association-aware Knowledge Distillation Method for Document-level Event Argument Extraction, which enables the enhancement of document-level multi-event extraction with event association knowledge. Firstly, we introduce an association-aware training task to extract unknown arguments with the given privileged knowledge of relevant arguments, obtaining an association-aware model that can construct both intra-event and inter-event relationships. Secondly, we adopt multi-teacher knowledge distillation to transfer such event association knowledge from the association-aware teacher models to the event argument extraction student model. Our proposed method, AssocKD, is capable of explicitly modeling and efficiently leveraging event association to enhance the extraction of multi-event arguments at the document level. We conduct experiments on RAMS and WIKIEVENTS datasets and observe a significant improvement, thus demonstrating the effectiveness of our method.","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":"142249415","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":"Novel Classes on Generating Functions of the Products of (p,q)-Modified Pell Numbers with Several Bivariate Polynomials","authors":"Ali Boussayoud, Salah Boulaaras, Ali Allahem","doi":"10.3390/math12182902","DOIUrl":"https://doi.org/10.3390/math12182902","url":null,"abstract":"In this paper, using the symmetrizing operator δe1e22−l, we derive new generating functions of the products of p,q-modified Pell numbers with various bivariate polynomials, including Mersenne and Mersenne Lucas polynomials, Fibonacci and Lucas polynomials, bivariate Pell and bivariate Pell Lucas polynomials, bivariate Jacobsthal and bivariate Jacobsthal Lucas polynomials, bivariate Vieta–Fibonacci and bivariate Vieta–Lucas polynomials, and bivariate complex Fibonacci and bivariate complex Lucas polynomials.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"9 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249416","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}