Results 141 to 150 of about 8,616 (247)
Lifts of continuous and Hölder alpha curves in the configuration space MN/SN$M^N/S_N$
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract In this paper, we study the quotient space X=MN/SN$X = M^N / S_N$ of equivalence classes of N$N$‐tuples in a metric space (M,dM)$(M, d_M)$, equipped with the metric induced by the minimal total pairing distance. Given a continuous path F:(0,1)→X$F: (0,1) \rightarrow X$, we prove that there exist continuous functions f1,⋯,fN:(0,1)→M$f_1, \dots,
Charles L. Fefferman +3 more
wiley +1 more source
Cross‐Method Explanation Stability Under Prediction‐Preserving Perturbations in Explainable AI
Applied AI Letters, Volume 7, Issue 2, June 2026.The cross‐method analysis showed common vulnerability patterns across gradient‐based and perturbation‐based explainers, whereas Grad‐CAM demonstrated a specific ability to be resilient. Further discussion revealed that, before prediction changes with increasing ε, explanation divergence could already have commenced, indicating that further explanation ...
Muhammad Hasnain +4 more
wiley +1 more source
Fourier Mass Lower Bounds for Batchelor‐Regime Passive Scalars
Communications on Pure and Applied Mathematics, Volume 79, Issue 6, Page 1449-1466, June 2026.ABSTRACT Batchelor predicted that a passive scalar ψν$\psi ^\nu$ with diffusivity ν$\nu$, advected by a smooth fluid velocity, should typically have Fourier mass distributed as |ψ̂ν|2(k)≈|k|−d$|\widehat{\psi }^\nu |^2(k) \approx |k|^{-d}$ for |k|≪ν−1/2$|k| \ll \nu ^{-1/2}$.
William Cooperman, Keefer Rowan
wiley +1 more source
On MAP Estimates and Source Conditions for Drift Identification in SDEs
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT We consider the inverse problem of identifying the drift in an stochastic differential equation (SDE) from n$n$ observations of its solution at M+1$M+1$ distinct time points. We derive a corresponding maximum a posteriori (MAP) estimate, we prove differentiability properties as well as a so‐called tangential cone condition for the forward ...
Daniel Tenbrinck +3 more
wiley +1 more source
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT In this work, we present an anisotropic multi‐goal error control based on the dual weighted residual (DWR) method for time‐dependent convection–diffusion–reaction (CDR) equations. Motivated by former work, we combine multiple goals to single error functionals with weights chosen as algorithmic parameters.
Markus Bause +5 more
wiley +1 more source
Some convergently three-term trust region conjugate gradient algorithms under gradient function non-Lipschitz continuity. [PDF]
Sci RepHu W, Wu J, Yuan G.
europepmc +1 more source
International Journal of Robust and Nonlinear Control, Volume 36, Issue 9, Page 4957-4970, June 2026.ABSTRACT Data‐based learning of system dynamics allows model‐based control approaches to be applied to systems with partially unknown dynamics. Gaussian process regression is a preferred approach that outputs not only the learned system model but also the variance of the model, which can be seen as a measure of uncertainty.
Daniel Landgraf +2 more
wiley +1 more source
Parabolic PDEs with Dynamic Data under a Bounded Slope Condition. [PDF]
Arch Ration Mech AnalBögelein V, Duzaar F, Treu G.
europepmc +1 more source
Piecewise polynomial approximation on non-Lipschitz domains
We prove best approximation error estimates for discontinuous piecewise polynomial approximation in fractional Sobolev spaces on non-Lipschitz meshes of non-Lipschitz domains. In particular, the boundary of the domain, and the boundaries of the mesh elements, can be fractal.
openaire +2 more sources
Coulomb branch algebras via symplectic cohomology
Journal of Topology, Volume 19, Issue 2, June 2026.Abstract Let (M¯,ω)$(\bar{M}, \omega)$ be a compact symplectic manifold with convex boundary and c1(TM¯)=0$c_1(T\bar{M})=0$. Suppose that (M¯,ω)$(\bar{M}, \omega)$ is equipped with a convex Hamiltonian G$G$‐action for some connected, compact Lie group G$G$.
Eduardo González +2 more
wiley +1 more source