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We give a survey of the known connections between regularity conditions and amenability conditions in the setting of uniform algebras. For a uniform algebra $A$ we consider the set, $A_{lc}$, of functions in $A$ which are locally constant…
A parametric family of reaction-diffusion equations with nonlocal viscosity is considered. Existence of solutions and actually of pullback attractors is known from previous works. In this paper we obtain a robustness result of the…
This work is about uniform, plane, singly connected, strictly regular Hall-plates with an arbitrary number of peripheral contacts exposed to a uniform magnetic field of arbitrary strength. The strictly regular symmetry is the highest…
This note is about uniform, plane, singly connected, regular Hall-plates with an arbitrary number of contacts exposed to a uniform magnetic field of arbitrary strength. In practice, the regular symmetry is the most common one. If the…
Let $S$ be an additively idempotent semiring and $\mathbf{M}_n(S)$ be the semiring of all $n\times n$ matrices over $S$. We characterize the conditions of when the semiring $\mathbf{M}_n(S)$ is congruence-simple provided that the semiring…
This book is about solving matrix nearness problems that are related to eigenvalues or singular values or pseudospectra. These problems arise in great diversity in various fields, be they related to dynamics, as in questions of robust…
A neutral network is a subgraph of a Hamming graph, and its principal eigenvalue determines its robustness: the ability of a population evolving on it to withstand errors. Here we consider the most robust small neutral networks: the graphs…
A general closed interval matrix is a matrix whose entries are closed connected nonempty subsets of the set of the real numbers, while an interval matrix is defined to be a matrix whose entries are closed bounded nonempty intervals in the…
A vector space A of matrices is called rank-critical if any vector space that properly contains A has a strictly higher generic rank. I present a sufficient condition for A to be rank-critical, and apply this condition to prove that certain…
Polynomial minimal bases of rational vector subspaces are a classical concept that plays an important role in control theory, linear systems theory, and coding theory. It is a common practice to arrange the vectors of any minimal basis as…
The magnetic response of type-II superconductors can be irreversible due to two different reasons: vortex pinning and barriers for flux penetration. Even without bulk pinning and in absence of a microscopic Bean-Lingston surface barrier for…
In this article, we consider eigenvector centrality for the nodes of a graph and study the robustness (and stability) of this popular centrality measure. For a given weighted graph {\mathcal G} (both directed and undirected), we consider…
Let $A$ be a (not necessarily unital) separable non-elementary simple amenable C*-algebra whose tracial basis may not have finite covering dimension and may not be compact but satisfies certain condition (C). We show that $A$ is ${\cal…
In prioritization schemes, based on pairwise comparisons, such as the Analytical Hierarchy Process, it is important to extract a cardinal ranking vector from a reciprocal matrix that is unlikely to be consistent. It is natural to choose…
We first study situations where the stable AF-algebras defined by two square primitive nonsingular incidence matrices with nonnegative integer matrix elements are isomorphic even though no powers of the associated automorphisms of the…
We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the Method of Alternating Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection Algorithm…
For an $n \times n$ nonnegative matrix $P$, an isomorphism is obtained between the lattice of initial subsets (of ${1,...,n}$) for $P$ and the lattice of $P$-invariant faces of the nonnegative orthant $\IR^{n}_{+}$. Motivated by this…
A machine learning model is traditionally considered robust if its prediction remains (almost) constant under input perturbations with small norm. However, real-world tasks like molecular property prediction or point cloud segmentation have…
Associating to each pre-order on the indices 1,...,n the corresponding structural matrix ring, or incidence algebra, embeds the lattice of n-element pre-orders into the lattice of n x n matrix rings. Rings within the order-convex hull of…
The capability of a network to cope with threats and survive attacks is referred to as its robustness. This paper discusses one kind of robustness, commonly denoted structural robustness, which increases when the spectral radius of the…