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We estimate fair graphs from graph-stationary nodal observations such that connections are not biased with respect to sensitive attributes. Edges in real-world graphs often exhibit preferences for connecting certain pairs of groups. Biased…
The aim of this work is to establish a linear instability criterium of stationary solutions for the Korteweg-de Vries model on a star graph with a structure represented by a finite collections of semi-infinite edges. By considering a…
Let $(M, g)$, $(N, h)$ be compact Riemannian manifolds without boundary, and let $f$ be a smooth map from $M$ into $N$. We consider a covariant symmetric tensor $T_f$ $=$ ${\displaystyle f^*h - \frac{1}{m} |df|^2 g}$, where $f^*h$ denotes…
Spatial processes with nonstationary and anisotropic covariance structure are often used when modelling, analysing and predicting complex environmental phenomena. Such processes may often be expressed as ones that have stationary and…
We study how the "full hierarchy" of invariant manifolds for nonautonomous integrodifference equations on the Banach spaces of $p$-integrable functions behaves under spatial discretization of Galerkin type. These manifolds include the…
We introduce the novel concept of a non-stationary iterated function system by considering a countable sequence of distinct set-valued maps $\{\mathcal{F}_k\}_{k\in \mathbb{N}}$ where each $\mathcal{F}_k$ maps $\mathcal{H}(X)\to…
The purpose of this paper is to introduce and study the following graph theoretic paradigm. Let $$T_Kf(x)=\int K(x,y) f(y) d\mu(y),$$ where $f: X \to {\Bbb R}$, $X$ a set, finite or infinite, and $K$ and $\mu$ denote a suitable kernel and a…
We study the structure and compute the stable rank of C*-algebras of finite higher-rank graphs. We completely determine the stable rank of the C*-algebra when the k-graph either contains no cycle with an entrance, or is cofinal. We also…
We generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs. We show that under certain conditions, any feature generated by such a network is approximately invariant to permutations…
Graph neural networks have emerged as a powerful tool for learning spatiotemporal interactions. However, conventional approaches often rely on predefined graphs, which may obscure the precise relationships being modeled. Additionally,…
We introduce topological invariants for gapless systems and study the associated boundary phenomena. More generally, the symmetry properties of the low-energy conformal field theory (CFT) provide discrete invariants, establishing the notion…
In this note we explore a fully unsupervised deep-learning framework for simulating non-linear structural equation models from observational training data. The main contribution of this note is an architecture for applying moment-matching…
We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…
A new method to calculate spectroscopic properties of deformed nuclei is proposed: configuration interaction on top of projected density functional theory (CI-PDFT). The general concept of this approach is discussed in the framework of…
Graph Neural Networks (GNNs) have established themselves as a key component in addressing diverse graph-based tasks. Despite their notable successes, GNNs remain susceptible to input perturbations in the form of adversarial attacks. This…
A full theory for hinged beams and degenerate plates with multiple intermediate piers is developed. The analysis starts with the variational setting and the study of the linear stationary problem in one dimension. Well-posedness results are…
Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane…
Suspended graphene samples are observed to be gently rippled rather than being flat. In [M. Friedrich, U. Stefanelli. Graphene ground states, arXiv:1802.05049], we have checked that this nonplanarity can be rigorously described within the…
Motivated by recent studies on the dynamics of colloidal solutions in narrow channels, we consider the steady state properties of an assembly of non interacting particles subject to the action of a traveling potential moving at a constant…
We demonstrate the emergence of a robust tetrahedral magnetic ground state in monolayer graphene doped to the van Hove singularity (vHS). This noncoplanar, gapped spin configuration - featuring four equally inclined moments - has been…