Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences最新文献_第4页

Unstable homotopy groups and Lie algebras. 不稳定同伦群与李代数。

IF 3.7 3区综合性期刊

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2026-08-28 DOI: 10.1098/rsta.2024.0396

Mark Behrens, Connor Malin

引用次数: 0

The Atiyah-Sutcliffe conjecture and En algebras. Atiyah-Sutcliffe猜想与代数。

IF 3.7 3区综合性期刊

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2026-08-28 DOI: 10.1098/rsta.2024.0406

Lorenzo Guerra, Paolo Salvatore

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Applications of the circle product with a right Com-module to the theory of commutative ring spectra. 带右共模的圆积在交换环谱理论中的应用。

IF 3.7 3区综合性期刊

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2026-08-28 DOI: 10.1098/rsta.2024.0404

Nicholas John Kuhn

{"title":"Applications of the circle product with a right Com-module to the theory of commutative ring spectra.","authors":"Nicholas John Kuhn","doi":"10.1098/rsta.2024.0404","DOIUrl":"https://doi.org/10.1098/rsta.2024.0404","url":null,"abstract":"If Com is the reduced commutative operad, the category of Com-algebras in spectra is the category of non-unital commutative ring spectra. The theme of this survey is that many important constructions on Com-algebras are given by taking the derived circle product with well-chosen right Com-modules. We show that examples of constructions arising this way include K⊗I, the tensor product of a based space K with such an algebra I, and TQ(I), the Topological André-Quillen homology spectrum of I. We then show how filtrations of right Com-modules can be used to filter such constructions. A natural decreasing filtration on right Com-modules is described. When specialized to the Com-bimodule Com, this defines the augmentation ideal tower of I, built out of the extended powers of TQ(I). A less studied natural increasing filtration is described. When specialized to the right Com-module used to define TQ(I), one gets a filtration on TQ(I) built out of I and the spaces in the Lie cooperad. There are two versions of this in the literature, and our setting here makes it easy to prove that these agree. Much of this applies with Com replaced by a more general reduced operad, and we make a few remarks about this. This article is part of the theme issue 'Derived Lie algebras in geometry and topology'.","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2328","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148840921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The animation of the opposite of finite sets. 有限集合的对立面的动画。

IF 3.7 3区综合性期刊

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2026-08-28 DOI: 10.1098/rsta.2024.0395

Benjamin Antieau

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Lie algebras and the (co)homology of configuration spaces. 李代数与组态空间的（co）同调。

IF 3.7 3区综合性期刊

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2026-08-28 DOI: 10.1098/rsta.2024.0402

Ben Knudsen

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Lie structures in homotopy and isotopy calculi. 同伦和同位素结石中的Lie结构。

IF 3.7 3区综合性期刊

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2026-08-28 DOI: 10.1098/rsta.2024.0403

Danica Kosanović

引用次数: 0

Higher holonomy for curved L∞-algebras 1: simplicial methods. 弯曲L∞-代数的高完整1：简单方法。

IF 3.7 3区综合性期刊

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2026-08-28 DOI: 10.1098/rsta.2024.0400

Ezra Getzler

引用次数: 0

Residual distribution predictive systems. 剩余分布预测系统。

IF 3.7 3区综合性期刊

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2026-08-27 DOI: 10.1098/rsta.2025.0080

Sam Allen, Enrico Pescara, Johanna Ziegel

{"title":"Residual distribution predictive systems.","authors":"Sam Allen, Enrico Pescara, Johanna Ziegel","doi":"10.1098/rsta.2025.0080","DOIUrl":"https://doi.org/10.1098/rsta.2025.0080","url":null,"abstract":"Conformal predictive systems are sets of predictive distributions with theoretical out-of-sample calibration guarantees. The calibration guarantees are typically that the set contains a forecast distribution whose prediction intervals exhibit the correct marginal coverage at all levels. Conformal predictive systems are constructed using conformity measures that quantify how well possible outcomes conform with historical data. However, alternative methods have been proposed to construct predictive systems with more appealing theoretical properties. We study an approach to construct predictive systems that we term residual distribution predictive systems (RDPSs). In the split conformal setting, this approach nests conformal predictive systems with a popular class of conformity measures, providing an alternative perspective on the classical approach. In the full conformal setting, the two approaches differ, and the new approach has the advantage that it does not rely on a conformity measure satisfying fairly stringent requirements to ensure that the predictive system is well-defined; it can readily be implemented alongside any point-valued regression method to yield predictive systems with out-of-sample calibration guarantees. The empirical performance of this approach is assessed using simulated data, where it is found to perform competitively with conformal predictive systems. However, the new approach offers considerable scope for implementation with alternative regression methods. This article is part of the theme issue 'Advancing uncertainty quantification in AI systems'.","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2327","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148831280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Uncertainty quantification using conformal prediction for mesh-based simulations. 基于网格模拟的保形预测的不确定性量化。

IF 3.7 3区综合性期刊

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2026-08-27 DOI: 10.1098/rsta.2025.0076

Samira Mabtoul, Izhar Ali, Shen Shyang Ho

{"title":"Uncertainty quantification using conformal prediction for mesh-based simulations.","authors":"Samira Mabtoul, Izhar Ali, Shen Shyang Ho","doi":"10.1098/rsta.2025.0076","DOIUrl":"https://doi.org/10.1098/rsta.2025.0076","url":null,"abstract":"Machine learning surrogates for computational fluid dynamics (CFD) achieve substantial speedups but lack uncertainty quantification (UQ). We develop a post hoc conformal prediction (CP) framework that wraps any trained graph neural network (GNN) surrogate to produce prediction sets with coverage near-nominal levels. Using MeshGraphNet on two benchmark datasets-CylinderFlow (2D velocity) and Flag (3D position), we compare five prediction-set geometries. Our componentwise adaptive (CW-Adaptive) method emerges as the robust universal choice, achieving 28%-55% smaller prediction sets versus ℓ2 balls across both datasets at 95% confidence while maintaining near-nominal coverage. By learning per-component scales from domain-aware features, CW-Adaptive captures both spatial heterogeneity and anisotropic error structure-outperforming Mahalanobis ellipsoids that provide only modest gains (approx. 14%) when residuals are anisotropic and inflate sets otherwise. All methods achieve coverage within 2%-3% of nominal despite distribution drift in mesh-based simulations that violates exchangeability assumption. This article is part of the theme issue 'Advancing uncertainty quantification in AI systems'.","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2327","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148831284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

CP4SBI: local conformal calibration of credible sets in simulation-based inference. CP4SBI：基于仿真的推理中可信集的局部保形校准。

IF 3.7 3区综合性期刊

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2026-08-27 DOI: 10.1098/rsta.2025.0069

Luben Miguel Cruz Cabezas, Vagner Silva Santos, Thiago Rodrigo Ramos, Pedro L C Rodrigues, Rafael Izbicki

{"title":"CP4SBI: local conformal calibration of credible sets in simulation-based inference.","authors":"Luben Miguel Cruz Cabezas, Vagner Silva Santos, Thiago Rodrigo Ramos, Pedro L C Rodrigues, Rafael Izbicki","doi":"10.1098/rsta.2025.0069","DOIUrl":"https://doi.org/10.1098/rsta.2025.0069","url":null,"abstract":"Current experimental scientists have been increasingly relying on simulation-based inference (SBI) to invert complex nonlinear models with intractable likelihoods. However, posterior approximations obtained with SBI are often miscalibrated, causing credible regions to undercover true parameters. We develop CP4SBI, a model-agnostic conformal calibration framework that constructs credible sets with local Bayesian coverage. Our two proposed variants, namely local calibration via regression trees and cumulative distribution function CDF-based calibration, enable finite-sample local coverage guarantees for any scoring function, including highest posterior density (HPD), symmetric and quantile-based regions. Experiments on widely used SBI benchmarks demonstrate that our approach improves the quality of uncertainty quantification for neural posterior estimators (NPEs) using both normalizing flows and score-diffusion modelling. This article is part of the theme issue 'Advancing uncertainty quantification in AI systems'.","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2327","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148831315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0