Related papers: Domain Theory in Constructive and Predicative Univ…

A new family of solutions of the Jacobi partial differential equations for finite-dimensional Poisson systems is investigated. This family is mathematically remarkable, as the functional dependences of the solutions appear to be associated…

Motivated by the study of meromorphic vector fields, a model theory of "compact complex manifolds equipped with a generic derivation" is here proposed. This is made precise by the notion of a differential CCM-structure. A first-order…

We provide an introduction to infinite-dimensional port-Hamiltonian systems. As this research field is quite rich, we restrict ourselves to the class of infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial…

We investigate two constructive approaches to defining quasi-compact and quasi-separated schemes (qcqs-schemes), namely qcqs-schemes as locally ringed lattices and as functors from rings to sets. We work in Homotopy Type Theory and…

Deep learning models have achieved great success on various vision challenges, but a well-trained model would face drastic performance degradation when applied to unseen data. Since the model is sensitive to domain shift, unsupervised…

Recent works in domain adaptation always learn domain invariant features to mitigate the gap between the source and target domains by adversarial methods. The category information are not sufficiently used which causes the learned domain…

Although diffusion models now occupy a central place in generative modeling, introductory treatments commonly assume Euclidean data and seldom clarify their connection to discrete-state analogues. This article is a self-contained primer on…

We seek to create tools for a model-theoretic analysis of types in algebraically closed valued fields (ACVF). We give evidence to show that a notion of 'domination by stable part' plays a key role. In Part A, we develop a general theory of…

Diffusion Probabilistic Field (DPF) models the distribution of continuous functions defined over metric spaces. While DPF shows great potential for unifying data generation of various modalities including images, videos, and 3D geometry, it…

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…

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…

We present a novel general resource analysis for logic programs based on sized types.Sized types are representations that incorporate structural (shape) information and allow expressing both lower and upper bounds on the size of a set of…

This work extends the existing MACE-style finite model finding approach to multi-sorted first order logic. This existing approach iteratively assumes increasing domain sizes and encodes the related ground problem as a SAT problem. When…

Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…

We study a cost-aware programming language for higher-order recursion dubbed $\textbf{PCF}_\mathsf{cost}$ in the setting of synthetic domain theory (SDT). Our main contribution relates the denotational cost semantics of…

Recursive domain equations have natural solutions. In particular there are domains defined by strictly positive induction. The class of countably based domains gives a computability theory for possibly non-countably based topological…

The intended model of the homotopy type theories used in Univalent Foundations is the infinity-category of homotopy types, also known as infinity-groupoids. The problem of higher structures is that of constructing the homotopy types needed…

Representations of domains mean in a general way representing a domain as a suitable family endowed with set-inclusion order of some mathematical structures. In this paper, representations of domains via CF-approximation spaces are…

We prove several reflection theorems on $D$-spaces, which are Hausdorff topological spaces $X$ in which for every open neighbourhood assignment $U$ there is a closed discrete subspace $D$ such that \[ \bigcup\{U(x): x\in D\}=X. \] The…

We prove several reflection theorems on $D$-spaces, which are Hausdorff topological spaces $X$ in which for every open neighbourhood assignment $U$ there is a closed discrete subspace $D$ such that \[ \bigcup\{U(x): x\in D\}=X. \] The…