数学最新文献

{"title":"Towards the development of an efficient nonlinear controller for ART and cART against HIV infection.","authors":"Muhammad Arsalan, Muhammad Tariq Sadiq, Abubakar Rafique, Ahmad Almogren, Xiaojun Yu","doi":"10.1007/s00285-026-02471-6","DOIUrl":"https://doi.org/10.1007/s00285-026-02471-6","url":null,"abstract":"<p><p>The Human Immuno-deficiency Virus (HIV) is responsible for attacking the CD4+ T cells present in human blood and causes the human immune system to become vulnerable for numerous contagious and opportunistic diseases. It is hence pertinent to curb the spread of HIV infection using anti-HIV drugs. This study integrates sigmoid function with conventional sliding mode control and incorporate it within the framework of multi-objective optimal model predictive controller to reduce the impact of HIV infection through anti-retro-viral therapy. The proposed algorithm is designed using a deterministic HIV-human immune system model that also includes the dynamics of cytotoxic T-lymphocytes precursor and effector cells. The research work provides the detailed design of nonlinear sigmoid based SMC controller and its Lyapunov theory based stability analysis. This designed controller is then integrated within the framework of MPC. Simulation level dosage bounds derived from the considered reference values for anti-HIV drug dosage has been realized to explicate and understand the relationship between administered dosage and control inputs. To validate the superior performance of the proposed controller, the results are compared to that of recently proposed nonlinear backstepping, state-feedback and synergetic controllers. Lastly, the proposed control algorithm is also evaluated using a three-state, three-input HIV model to examine its applicability to combination anti-retro-viral therapy (cART). The simulations demonstrate that the proposed sigmoid SMC-MPC framework can regulate the modeled drug inputs while simultaneously improving the simulated CD4+ T-cell response and suppressing viral load. The results are intended to demonstrate the algorithmic performance of the proposed nonlinear control framework within the considered mathematical models. Importantly, this study is simulation-based and does not constitute a clinical treatment strategy or a recommendation for automated administration of anti-retro-viral drugs. The simulations are performed using MATLAB/Simulink. The observations and results presented in this study are also analyzed to substantiate the need of nonlinear feedback controllers to limit the amount of administered treatment burden to effectively and efficiently curb HIV advancement. Results showed that the proposed hybrid sigmoid SMC-MPC approach effectively lowered the initial drug dosage requirements by 30%. Whereas, the reduction in final steady state dosage has been reduced by upto 70% while reducing the convergence time of viral load by 14%. Similarly, the convergence time of healthy CD4+ T cell count, to the desired reference level, has been reduced by 26.8%. These results indicate favorable algorithmic performance within the considered simulation framework.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149197353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Anisotropic variable exponent Sobolev spaces and applications to elliptic equations with critical growth","authors":"Nabil Chems Eddine,Maria Alessandra Ragusa","doi":"10.1007/s13540-026-00591-w","DOIUrl":"https://doi.org/10.1007/s13540-026-00591-w","url":null,"abstract":"Abstract We establish critical embeddings for anisotropic Sobolev spaces with variable exponents, resolving, under log-Hölder continuity supplemented by finite Sobolev regularity and a quantitative integrability-gap condition, an open problem raised by Fan. We derive a Poincaré-type inequality at the harmonic-mean critical scale, give compactness criteria when the critical exponent is attained on a nontrivial set, and prove a corresponding concentration–compactness principle. These results are then applied to anisotropic Leray–Lions equations with critical growth. Under a global quantitative superlinearity condition, the problem possesses a nontrivial weak solution for a sufficiently large reaction parameter. Under the additional oddness assumptions, for every prescribed integer m , it possesses at least m distinct pairs of nontrivial weak solutions once the parameter exceeds a sufficient threshold depending on m .","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"2 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149210373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrigendum to “A D3Q27 multiple-relaxation-time lattice Boltzmann method for turbulent flows” [Computers & Mathematics with Applications 69(6) (2015) 518-529]","authors":"K. Suga,&nbsp;Y. Kuwata,&nbsp;K. Takashima,&nbsp;R. Chikasue","doi":"10.1016/j.camwa.2026.09.022","DOIUrl":"10.1016/j.camwa.2026.09.022","url":null,"abstract":"","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"220 ","pages":"Page 552"},"PeriodicalIF":2.7,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149084848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"SURVEY BEHAVIOR AND COGNITION ACROSS THE LIFE COURSE: EVIDENCE FROM THE PANEL STUDY OF INCOME DYNAMICS.","authors":"Malak B Kalasho, Esther M Friedman, Thomas F Crossley","doi":"10.1093/jssam/smag010","DOIUrl":"10.1093/jssam/smag010","url":null,"abstract":"<p><p>Cognitive abilities across adulthood are important pre-cursors to dementia. The primary way to capture cognitive abilities is via expensive and time-consuming standardized cognitive tests. We explore the extent to which cognition can be inferred from indicators of survey response behavior (SRB), such as the time to complete a questionnaire and the incidence of contradictory responses. We use nationally representative data from a mixed-mode supplement to the Panel Study of Income Dynamics collected in 2016. This Wellbeing and Daily Life supplement includes rich cognitive data capturing both verbal and quantitative reasoning, and paradata from the supplement (e.g., time to complete). We assess the ability of survey response behavior to improve prediction of cognitive ability after accounting for standard sociodemographic variables typically available in surveys. We explore this from age 30 and across the life course. We find that SRB measures provide modest but consistent explanatory power across a wide range of ages. The explanatory power of SRB measures in our data is less than that of education, except at the oldest ages. SRB measures contain useful additional information, but models that include basic demographics, education and SRB measures leave much of the variation in cognitive ability unexplained. Which SRB measures best predict cognitive ability is consistent across cognitive measure but differs by age. Errors (i.e., contradictory responses) and response times are the best predictors at working ages but skips and backups are more predictive at older ages.</p>","PeriodicalId":17146,"journal":{"name":"Journal of Survey Statistics and Methodology","volume":" ","pages":"smag010"},"PeriodicalIF":1.9,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13675063/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149216431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A functional inequality related to Domar’s uniform boundedness theorem","authors":"Thomas Ransford","doi":"10.1007/s00010-026-01334-1","DOIUrl":"10.1007/s00010-026-01334-1","url":null,"abstract":"<div><p>We study the functional inequality </p><div><div><span>$$ f(r+s)le g(r)+alpha f(s) quad (r,s&gt;0). $$</span></div></div><p>Here <span>(g:(0,infty )rightarrow [0,infty ))</span> is a given decreasing function, <span>(alpha )</span> is a constant such that <span>(0&lt;alpha &lt;1)</span>, and the problem is to determine whether the family of decreasing functions <span>(f:(0,infty )rightarrow [0,infty ))</span> that satisfy this inequality is bounded above by some finite function on <span>((0,infty ))</span> and, if so, to find bounds for this function. We present a solution to this problem, and use it to give a new proof of a theorem of Domar on the uniform boundedness of certain families of subharmonic functions, while also obtaining explicit bounds.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"100 6","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189765","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":"Gradient boosting machine for survival prediction in studies with general failure-time outcome-dependent sampling design.","authors":"Haolin Li, Haibo Zhou, Jianwen Cai","doi":"10.1007/s10985-026-09732-y","DOIUrl":"10.1007/s10985-026-09732-y","url":null,"abstract":"<p><p>Outcome-dependent sampling (ODS) designs are widely used in epidemiological and biomedical research as cost-effective alternatives to full cohort studies. While existing research has focused on parameter estimation and inference under specific models, survival prediction in ODS settings remains underexplored. In this paper, we propose a gradient boosting machine tailored for survival prediction in studies conducted using general failure-time ODS designs. Our approach integrates a weighting scheme to correct for sampling bias and improves predictive accuracy. We introduce a weighted empirical risk based on the integrated Brier score for hyperparameter tuning and establish its convergence to the corresponding integrated Brier-score risk. The proposed method is evaluated through extensive simulations and applied to the Cancer Incidence and Mortality of Uranium Miners Study, and is shown to have improved effectiveness in survival prediction. This work advances machine learning methods for ODS studies, offering valuable insights for personalized medicine and clinical decision-making in failure-time ODS settings.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":"32 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13668957/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149185620","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":"Dynamic Modeling and Control of Brucellosis in a Metapopulation Network Considering Animal Transportation: A Case Study of Xinjiang, China.","authors":"Xin Pei, Erjia Cui, Mingtao Li, Chaojian Shen, Yurong Wei, Jie Wei, Xiaoyun Mi, Wenjun Jing, Juan Zhang, Zhen Jin","doi":"10.1007/s11538-026-01776-3","DOIUrl":"https://doi.org/10.1007/s11538-026-01776-3","url":null,"abstract":"<p><p>Cross-regional animal transportation is a crucial factor in the spatial transmission of brucellosis, and infections occurring during transportation cannot be overlooked. Clarifying the spatiotemporal transmission patterns of brucellosis under animal transportation mechanisms is of great significance for enabling targeted prevention and control of the disease. Based on data from the Xinjiang Animal Husbandry and Veterinary Big Data Platform, we constructed a directed and weighted sheep transportation network. We established a coupled human-sheep metapopulation model for brucellosis that incorporates infection during animal transportation, thereby providing a more accurate description of brucellosis spread across the metapopulation network. The epidemic threshold was derived theoretically. For the application, a brucellosis transmission model was simulated based on the constructed sheep transportation network in Xinjiang. It was observed that with an increase in transportation rate, epidemic threshold first decreases then increases, indicating that excessively high or low transportation rates should be avoided. Notably, epidemic threshold also increases as the infection rate during transportation rises, which exacerbates brucellosis epidemics in practice, so its potential risks cannot be ignored. For brucellosis control, we first identified key regions and key transportation routes using network centrality, then simulated the control effect with practical control measures. The results demonstrated that strengthening quarantine at checkpoints and reducing sheep transportation between key areas and other regions are more effective than implementing the same measures on critical transportation routes. Specifically, node degree centrality can effectively identify key regions. In early control stage, prioritize reducing internal infection rates through regular quarantine, purification and standardized breeding management; in the middle and late stages, the most effective control is increase culling rate. Our study clarifies the impact of animal transportation and infections occurring during transportation, and analyzes the effectiveness of different control measures from network structure perspective, providing a theoretical basis for brucellosis control in Xinjiang and other regions.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 11","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149191171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Haagerup property is not invariant under quasi-isometry","authors":"Mathieu Carette,&nbsp;Kevin Whyte,&nbsp;Sylvain Arnt,&nbsp;Thibault Pillon,&nbsp;Alain Valette","doi":"10.1112/blms.70516","DOIUrl":"https://doi.org/10.1112/blms.70516","url":null,"abstract":"<p>Using the work of Cornulier–Valette and Whyte (see Appendix A for the latter), we show that neither the Haagerup property nor weak amenability is invariant under quasi-isometry of finitely generated groups. Appendix B shows, using the same examples, that the same holds for vanishing of the equivariant <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$L^p$</annotation>\u0000 </semantics></math>-compression.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 11","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70516","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177119","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":"Popularity Regression-Based Latent Space Model for Large-Scale Sparse Network Analysis","authors":"Zhan Gao,Danyang Huang,Rui Pan,Hansheng Wang","doi":"10.1080/01621459.2026.2744404","DOIUrl":"https://doi.org/10.1080/01621459.2026.2744404","url":null,"abstract":"","PeriodicalId":17227,"journal":{"name":"Journal of the American Statistical Association","volume":"10 1","pages":"1-101"},"PeriodicalIF":3.7,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamic Bayesian Networks with Conditional Dynamics in Edge Additions and Deletions","authors":"Lupe S. H. Chan,&nbsp;Amanda M. Y. Chu,&nbsp;Mike K. P. So","doi":"10.1002/asmb.70135","DOIUrl":"https://doi.org/10.1002/asmb.70135","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This study presents a dynamic Bayesian network framework that facilitates intuitive, gradual edge changes. We use two conditional dynamics to model the edge additions and deletions, as well as edge selections, separately. In contrast to previous research that employed a mixture network approach—which limits the number of edge changes—or relied on structural priors to induce gradual changes—often leading to ambiguous network evolution—our model fosters more frequent and intuitive edge change dynamics. Moreover, when the maximum number of parents for the nodes in the network is &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;≪&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ dll n $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, the correlation matrix can be represented by at most &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ nd=O(n) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; correlations. In contrast, conventional dynamic correlation models necessitate &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ nleft(n-1right)/2=Oleft({n}^2right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; correlations. Consequently, the structure specified by the Bayesian network facilitates dimensionality reduction of the correlation matrix from &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ Oleft({n}^2right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"42 6","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}