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Fortschritte der Physik, Volume 74, Issue 6, June 2026.ABSTRACT We present a clear, step‐by‐step method for counting degrees of freedom and identifying constraints in general field theories. This approach, grounded in the works of Einstein, Hilbert, Cartan, Kuranishi, and, more recently, Seiler, is neither Lagrangian nor Hamiltonian in nature. Instead, it applies directly to the field equations. We offer a
Lavinia Heisenberg
wiley +1 more source
Covariance Estimation for Wide Data
WIREs Computational Statistics, Volume 18, Issue 2, June 2026.Covariance matrix estimation is fundamental to multivariate analysis, with applications spanning finance, genomics, climate science, and signal processing. This review synthesizes recent advances in high‐dimensional covariance estimation‐thresholding, linear and nonlinear shrinkage, graphical models, and random matrix theory‐under a unifying framework ...
Eran Raviv
wiley +1 more source
Studies in Applied Mathematics, Volume 156, Issue 6, June 2026.ABSTRACT We study the long‐term dynamics of followers that selectively follow one of multiple leaders on Riemannian manifolds, where the leaders interact through repulsive forces while remaining cohesively bounded. We propose a multileader–follower multiagent system defined on Riemannian manifolds. In our model, each follower chooses exactly one leader
Hyunjin Ahn
wiley +1 more source
Spatial depth for data in metric spaces
Scandinavian Journal of Statistics, Volume 53, Issue 2, Page 684-711, June 2026.Abstract We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution, allowing quantifying their centrality/outlyingness.
Joni Virta
wiley +1 more source
Bulletin of the London Mathematical Society, Volume 58, Issue 6, June 2026.Abstract Given r⩾3$r \geqslant 3$, we prove that there exists λ>0$\lambda >0$ depending only on r$r$ so that if G$G$ is a metric graph of rank r$r$ with metric entropy 1, then there exists a proper subgraph H$H$ of G$G$ with metric entropy at least λ$\lambda$. This answers a question of the second two authors together with Rieck. We interpret this as a
Tawfiq Hamed, Tarik Aougab, Matt Clay
wiley +1 more source
Martingales on manifolds and geometric Ito calculus [PDF]
This work studies properties of stochastic processes taking values in a differential manifold M with a linear connection Γ, or in a Riemannian manifold with a metric connection.
Darling, R. W. R.
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On (N(k),ξ)-semi-Riemannian 3-manifolds. [PDF]
, 2014 The object of the present paper is to study 3-dimensional (N(k), ξ)-semiRiemannian manifolds. We study (N(k), ξ)-semi-Riemannian 3-manifolds which are Ricci-semi-symmetric, locally ϕ-symmetric and have η-parallel Ricci ...
Prakasha, D.G. +2 more
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Cohomogeneity‐one solitons in Laplacian flow: Local, smoothly‐closing and steady solitons
Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.Abstract We initiate a systematic study of cohomogeneity‐one solitons in Bryant's Laplacian flow of closed G2$\text{G}_2$‐structures on a 7‐manifold, motivated by the problem of understanding finite‐time singularities of that flow. Here, we focus on solitons with symmetry groups Sp(2)${\rm Sp}(2)$ and SU(3)${\rm SU}(3)$; in both cases, we prove the ...
Mark Haskins, Johannes Nordström
wiley +1 more source
Kahler manifolds and their relatives
, 2010 Let M1 and M2 be two K¨ahler manifolds. We call M1 and M2 relatives if they share a non-trivial K¨ahler submanifold S, namely, if there exist two holomorphic and isometric immersions (K¨ahler immersions) h1 : S → M1 and h2 : S → M2. Moreover, two K¨ahler
Loi, A., Di Scala, Antonio Jose'
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On area comparison and rigidity involving the scalar curvature [PDF]
In this thesis we study the effects of lower bounds for the curvature of a Riemannian manifold M on the geometry and topology of closed, minimal hypersurfaces.
Moraru, Vlad
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