Mathematics最新文献

{"title":"Toward Real-Time Scalable Rigid-Body Simulation Using GPU-Optimized Collision Detection and Response","authors":"Nak-Jun Sung, Min Hong","doi":"10.3390/math13193230","DOIUrl":"https://doi.org/10.3390/math13193230","url":null,"abstract":"We propose a GPU-parallelized collision-detection and response framework for rigid-body dynamics, designed to efficiently handle densely populated 3D simulations in real time. The method combines explicit Euler time integration with a hierarchical Octree–AABB collision-detection scheme, enabling early pruning and localized refinement of contact checks. To resolve collisions, we employ a two-step response algorithm that integrates non-penetration correction and impulse-based velocity updates, stabilized through smoothing, clamping, and bias mechanisms. The framework is fully implemented within Unity3D using compute shaders and optimized GPU kernels. Experiments across multiple mesh models and increasing object counts demonstrate that the proposed hierarchical configuration significantly improves scalability and frame stability compared to conventional flat AABB methods. In particular, a two-level hierarchy achieves the best trade-off between spatial resolution and computational cost, maintaining interactive frame rates (≥30 fps) under high-density scenarios. These results suggest the practical applicability of our method to real-time simulation systems involving complex collision dynamics.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"13 19","pages":"3230-3230"},"PeriodicalIF":0.0,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147899471","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":"Analysis and Mean-Field Limit of a Hybrid PDE-ABM Modeling Angiogenesis-Regulated Resistance Evolution","authors":"Louis Shuo Wang, Jiguang Yu, Shijia Li, Zonghao Liu","doi":"10.3390/math13172898","DOIUrl":"https://doi.org/10.3390/math13172898","url":null,"abstract":"Mathematical modeling is indispensable in oncology for unraveling the interplay between tumor growth, vascular remodeling, and therapeutic resistance. We present a hybrid modeling framework (continuum-discrete) and present its hybrid mathematical formulation as a coupled partial differential equation–agent-based (PDE-ABM) system. It couples reaction–diffusion fields for oxygen, drug, and tumor angiogenic factor (TAF) with discrete vessel agents and stochastic phenotype transitions in tumor cells. Stochastic phenotype switching is handled with an exact Gillespie algorithm (a Monte Carlo method that simulates random phenotype flips and their timing), while moment-closure methods (techniques that approximate higher-order statistical moments to obtain a closed, tractable PDE description) are used to derive mean-field PDE limits that connect microscale randomness to macroscopic dynamics. We provide existence/uniqueness results for the coupled PDE-ABM system, perform numerical analysis of discretization schemes, and derive analytically tractable continuum limits. By linking stochastic microdynamics and deterministic macrodynamics, this hybrid mathematical formulation—i.e., the coupled PDE-ABM system—captures bidirectional feedback between hypoxia-driven angiogenesis and resistance evolution and provides a rigorous foundation for predictive, multiscale oncology models.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"13 17","pages":"2898-2898"},"PeriodicalIF":0.0,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.mdpi.com/2227-7390/13/17/2898/pdf?version=1757503068","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147919068","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":"Computational Simulation of Aneurysms Using Smoothed Particle Hydrodynamics","authors":"Yong Wu, Fei Wang, Xianhong Sun, Zibo Liu, Zhi Xiong, Mingzhi Zhang, Baoquan Zhao, Teng Zhou","doi":"10.3390/math13152439","DOIUrl":"https://doi.org/10.3390/math13152439","url":null,"abstract":"Modeling and simulation of aneurysm formation, growth, and rupture plays an essential role in a wide spectrum of application scenarios, ranging from risk stratification to stability prediction, and from clinical decision-making to treatment innovation. Unfortunately, it remains a non-trivial task due to the difficulties imposed by the complex and under-researched pathophysiological mechanisms behind the different development stages of various aneurysms. In this paper, we present a novel computational method for aneurysm simulation using smoothed particle hydrodynamics (SPH). Firstly, we consider blood in a vessel as a kind of incompressible fluid and model its flow dynamics using the SPH method; and then, to simulate aneurysm growth and rupture, the relationship between the aneurysm development and the properties of fluid particles is established by solving the motion control equation. In view of the prevalence of aneurysms in bifurcation vessels, we further enhance the capability of the model by introducing a solution for bifurcation aneurysms simulation according to Murray’s law. In addition, a CUDA parallel computing scheme is also designed to speed up the simulation process. To evaluate the performance of the proposed method, we conduct extensive experiments with different physical parameters associated with morphological characteristics of an aneurysm. The experimental results demonstrate the effectiveness and efficiency of proposed method in modeling and simulating aneurysm formation, growth, and rupture.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"13 15","pages":"2439-2439"},"PeriodicalIF":0.0,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.mdpi.com/2227-7390/13/15/2439/pdf?version=1753784295","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147897698","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":"Accelerated Numerical Simulations of a Reaction-Diffusion- Advection Model Using Julia-CUDA","authors":"Angelo Ciaramella, Davide De De Angelis, Pasquale De Luca, Livia Marcellino","doi":"10.3390/math13091488","DOIUrl":"https://doi.org/10.3390/math13091488","url":null,"abstract":"The emergence of exascale computing systems presents both opportunities and challenges in scientific computing, particularly for complex mathematical models requiring high-performance implementations. This paper addresses these challenges in the context of biomedical applications, specifically focusing on tumor angiogenesis modeling. We present a parallel implementation for solving a system of partial differential equations that describe the dynamics of tumor-induced blood vessel formation. Our approach leverages the Julia programming language and its CUDA capabilities, combining a high-level paradigm with efficient GPU acceleration. The implementation incorporates advanced optimization strategies for memory management and kernel organization, demonstrating significant performance improvements for large-scale simulations while maintaining numerical accuracy. Experimental results confirm the performance gains and reliability of the proposed parallel implementation.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"13 9","pages":"1488-1488"},"PeriodicalIF":0.0,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.mdpi.com/2227-7390/13/9/1488/pdf?version=1746020812","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147382066","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":"Decoding Colon Cancer Heterogeneity Through Integrated miRNA–Gene Network Analysis","authors":"Qingcai He, Zhilong Mi, T. Liu, Taihang Huang, Mao Li, Binghui Guo, Zhiming Zheng","doi":"10.3390/math13061020","DOIUrl":"https://doi.org/10.3390/math13061020","url":null,"abstract":"Colon adenocarcinoma (COAD) demonstrates significant clinical heterogeneity across disease stages, gender, and age groups, posing challenges for unified therapeutic strategies. This study establishes a multi-dimensional stratification framework through integrative analysis of miRNA–gene co-expression networks, employing the MRNETB algorithm coupled with Markov flow entropy (MFE) centrality quantification. Analysis of TCGA-COAD cohorts revealed stage-dependent regulatory patterns centered on CDX2-hsa-miR-22-3p-MUC13 interactions, with progressive dysregulation mirroring tumor progression. Gender-specific molecular landscapes have emerged, characterized by predominant SLC26A3 expression in males and GPA33 enrichment in females, suggesting divergent pathogenic mechanisms between genders. Striking age-related disparities were observed, where early-onset cases exhibited molecular signatures distinct from conventional COAD, highlighted by marked XIST expression variations. Drug-target network analysis identified actionable candidates including CEACAM5-directed therapies and differentiation-modulating agents. Our findings underscore the critical need for heterogeneity-aware clinical decision-making, providing a roadmap for stratified intervention paradigms in precision oncology.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"13 6","pages":"1020-1020"},"PeriodicalIF":0.0,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.mdpi.com/2227-7390/13/6/1020/pdf?version=1742542848","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147906018","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 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":"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":"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":2.2,"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}