Cellwise
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Related Articles from SNS
Log-Ratio Propagation on the Simplex: A Theory of Cellwise Contamination for Compositional Data
Announce Type: cross Abstract: Compositional data must be analysed through log-ratios: scale invariance, the defining axiom of the field, leaves no alternative. The centred log-ratio divides by the geometric mean of every part, so a single contaminated component shifts every centred-log-ratio coordinate at once, displacing the log-ratio vector by a fixed amount that no choice of coordinates can reduce. We develop a theory of cellwise contamination on the simplex around this observation.
Cellwise and Casewise Robust Covariance in High Dimensions
Announce Type: replace-cross Abstract: The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers. These can be casewise outliers, such as cases belonging to a different population, or cellwise outliers, which are deviating cells (entries) of the data matrix. Recently some robust covariance estimators have been developed that can handle both types of outliers, but their computation is only feasible up to at most 20 dimensions.
A Parallel and Adaptive Mesh-Free Method for Discontinuous Coefficient Fields in Heterogeneous Porous Media
arXiv:2605.16564v2 Announce Type: replace Abstract: Discontinuous coefficient fields arise in many computational physics problems and are often represented as cellwise constant data tied to a given spatial discretization. Such representations are inherently mesh-dependent, requiring interpolation or projection whenever they are transferred to a different discretization. In this work, we develop \emph{Parallel and Adaptive Mesh-Free Approximation (PAM)}, a mesh-independent framework that...
Physics-Informed Residuals for Adaptive Mesh Refinement in Finite-Difference PDE Solvers
Announce Type: new Abstract: Classical finite-difference solvers remain reliable tools for partial differential equations, but their efficiency depends on where mesh resolution is placed. Uniform refinement can waste degrees of freedom when solution difficulty is localised near sharp gradients, fronts, oscillations, or constraint-sensitive regions. This paper studies a hybrid strategy in which a physics-informed neural network (PINN) is used not as the final solver, but as an off-grid...
Physics-Informed Residuals for Adaptive Mesh Refinement in Finite-Difference PDE Solvers
arXiv:2606.02475v2 Announce Type: replace Abstract: Classical finite-difference solvers remain reliable tools for partial differential equations, but their efficiency depends on where mesh resolution is placed. Uniform refinement can waste degrees of freedom when solution difficulty is localised near sharp gradients, fronts, oscillations, or constraint-sensitive regions. This paper studies a hybrid strategy in which a physics-informed neural network (PINN) is used not as the final solver,...