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Classical spectral theory gives a complete description of a single normal operator, but it fails for noncommuting operators, where no canonical joint spectrum or simultaneous diagonalization exists. Existing approaches provide only partial…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
Machine learning models can automatically learn complex relationships, such as non-linear and interaction effects. Interpretable machine learning methods such as partial dependence plots visualize marginal feature effects but may lead to…
Many structured systems admit locally consistent descriptions that nevertheless fail to globalize when constrained by an ambient reference or feasibility condition. Diagnosing such failures is naturally an evaluative problem: given a fixed…
We consider the numerical homogenization of a class of fractal elliptic interface problems inspired by related mechanical contact problems from the geosciences. A particular feature is that the solution space depends on the actual fractal…
In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions. Specifically, we define the function spaces on which the…
In core/shell quantum dots (QDs), the interface between semiconductors of different chemical character largely determines their optoelectronic properties. In III-V/II-VI systems, this boundary involves pronounced chemical and electronic…
We introduce a framework for subspace methods which approximate the spectra of self-adjoint, unbounded operators in a local region. Using the projection-valued measure, we derive integrated spectral inequalities that also apply to unbounded…
In distributed-parameter inverse problems in computational mechanics, spatially varying fields are inferred from noisy, indirect, and heterogeneous observations. The relevant identifiability question concerns which spatial perturbation…
We investigate the steady-state organisation of active particles residing on an interface. Particle activity induces interface deformations, while the local shape of the interface guides particle movement. We consider multiple species of…
Many natural shapes have most of their characterizing features concentrated over a few regions in space. For example, humans and animals have distinctive head shapes, while inorganic objects like chairs and airplanes are made of…
We investigate a one-dimensional tight-binding lattice with asymmetrical couplings and various type of nonlinearities to study nonlinear non-Hermitian skin effect. Our focus is on the exploration of nonlinear skin modes through a…
We study various aspects of half-BPS surface defect operators in $\mathcal{N}=4$ SYM. For defects on generic points on the moduli space we use superconformal symmetry to fix the form of one-point and two-point functions of half-BPS…
The idea that structural disorder might be a novel mechanism of protein interaction is widespread in the Literature, although the number of statistically significant structural studies supporting this is surprisingly low. At variance with…
Network renormalization has traditionally relied on spatial adjacency-grouping nearby nodes together, but this approach fails to capture the dynamical correlations that govern system-wide behavior in scale-free networks. We present a…
Matrix functions extend scalar function concepts to linear operators, offering a unified framework with broad applications in mathematics, science, and engineering. Classical definitions--via power series, spectral calculus, or Jordan…
We search for new defect universality classes by considering localised interactions placed on an RG interface separating two interacting multiscalar CFTs in $4-\varepsilon$ dimensions. Studying interactions spread throughout the entire…
Hyperspectral videos (HSVs), with their inherent spatial-spectral-temporal structure, offer distinct advantages in challenging tracking scenarios such as cluttered backgrounds and small objects. However, existing methods primarily focus on…
Faceted interfaces are a key feature in self-resembling morphologies of many microstructures generated from solid state phase transformations. Interpretations, predictions and simulations of the faceted morphologies remain a challenge,…
Global feature effect methods, such as partial dependence plots, provide an intelligible visualization of the expected marginal feature effect. However, such global feature effect methods can be misleading, as they do not represent local…