Related papers: BDDC and FETI-DP under Minimalist Assumptions
At the intersection of dynamical systems, control theory, and formal methods lies the construction of symbolic abstractions: these typically represent simpler, finite-state models whose behavior mimics that of an underlying concrete system…
We study dp-minimal infinite profinite groups that are equipped with a uniformly definable fundamental system of open subgroups. We show that these groups have an open subgroup $A$ such that either $A$ is a direct product of countably many…
In this work, we build on the discrete trace theory developed by Badia, Droniou, and Tushar (Foundations of Computational Mathematics, in press, 2025; \href{https://doi.org/10.1007/s10208-025-09734-6}{doi:10.1007/s10208-025-09734-6}) to…
We introduce a new class of hybrid preconditioners for solving parametric linear systems of equations. The proposed preconditioners are constructed by hybridizing the deep operator network, namely DeepONet, with standard iterative methods.…
Wedderburn's theorem on the structure of finite dimensional semisimple algebras is proved by using minimal prerequisites.
Abstract dialectical frameworks (ADFs) are a powerful generalisation of Dung's abstract argumentation frameworks. In this paper we present an answer set programming based software system, called DIAMOND (DIAlectical MOdels eNcoDing). It…
We show some basic facts about dp-minimal ordered structures. The main results are : dp-minimal groups are abelian-by-finite-exponent, in a divisible ordered dp-minimal group, any infinite set has non-empty interior, and any theory of pure…
We express the vacuum Einstein constraints in terms of differential forms - the forms include one-forms constituting an orthonormal coframe of the spatial metric. We show that if the metric is real-analytic, then the constraints can be…
We provide characterizations of continuous eigenvalues for minimal symbolic dynamical systems described by $S$-adic structures satisfying natural mild conditions, such as recognizability and primitiveness. Under the additional assumptions…
Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of…
Subatomic systems were recently introduced to identify the structural principles underpinning the normalization of proofs. "Subatomic" means that we can reformulate logical systems in accordance with two principles. Their atomic formulas…
In this note we derive the backward (automatic) differentiation (adjoint [automatic] differentiation) for an algorithm containing a conditional expectation operator. As an example we consider the backward algorithm as it is used in Bermudan…
Inhomogeneous essential boundary conditions can be appended to a well-posed PDE to lead to a combined variational formulation. The domain of the corresponding operator is a Sobolev space on the domain $\Omega$ on which the PDE is posed,…
We extend the operator preconditioning framework [R. Hiptmair, Comput. Math. with Appl. 52 (2006), pp.~699--706] to Petrov-Galerkin methods while accounting for parameter-dependent perturbations of both variational forms and their…
Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies.…
In this paper we study robust output tracking and disturbance rejection of linear partial differential equation (PDE) models. We focus on demonstrating how the abstract internal model based controller design methods developed for "regular…
Abstracting from a low level to a more explanatory high level of description, and ideally while preserving causal structure, is fundamental to scientific practice, to causal inference problems, and to robust, efficient and interpretable AI.…
We consider abstraction-based design of output-feedback controllers for dynamical systems with a finite set of inputs and outputs against specifications in linear-time temporal logic. The usual procedure for abstraction-based controller…
Inspired by rational canonical forms, we introduce and analyze two decompositions of dynamic programming (DP) problems for systems with linear dynamics. Specifically, we consider both finite and infinite horizon DP problems in which the…
There has been significant developments in the classification of boundary conditions of positive symmetric systems, also known as Friedrichs systems, after the introduction of operator theoretic framework. We take a step forward towards…