相关论文: A Generalization of the {\L}o\'s-Tarski Preservati…
We propose a novel architecture for Graph Neural Networks that is inspired by the idea behind Tree Kernels of measuring similarity between trees by taking into account their common substructures, named fragments. By imposing a series of…
The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an…
The text deals with generalizations of the Markoff equation in number theory, arising from continued fractions. It gives the method for the complete resolution of such new equations, and their interpretation in algebra and algebraic…
Product structure theorems are a collection of recent results that have been used to resolve a number of longstanding open problems on planar graphs and related graph classes. One particularly useful version states that every planar graph…
Split decomposition of graphs was introduced by Cunningham (under the name join decomposition) as a generalization of the modular decomposition. This paper undertakes an investigation into the algorithmic properties of split decomposition.…
This paper initiates a discrete Hodge theory for cellular sheaves taking values in a category of lattices and Galois connections. The key development is the Tarski Laplacian, an endomorphism on the cochain complex whose fixed points yield a…
We explore new interactions between finite model theory and classical streams of universal algebra and semigroup theory. A key result is an example of finite algebras whose variety is not finitely axiomatisable in first order logic, but…
We give characterizations of the structure and degree sequences of hereditary unigraphs, those graphs for which every induced subgraph is the unique realization of its degree sequence. The class of hereditary unigraphs properly contains the…
This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general…
Large-scale graphs are widely used to represent object relationships in many real world applications. The occurrence of large-scale graphs presents significant computational challenges to process, analyze, and extract information. Graph…
A thesaurus is one, out of many, possible representations of term (or word) connectivity. The terms of a thesaurus are seen as the nodes and their relationship as the links of a directed graph. The directionality of the links retains all…
In an article dating back in 1992, Kosta Do\v{s}en initiated a project of modal translations in substructural logics, aiming at generalizing the well-known G\"{o}del-McKinsey-Tarski translation of intuitionistic logic into {\bf S4}.…
The Tarskian classical relevant logic TR arises from Tarski's work on the foundations of the calculus of relations and on first-order logic restricted to finitely many variables, presented by Tarski and Givant their book, A Formalization of…
Recent advances in deep learning have transformed many fields by introducing generic embedding spaces, capable of achieving great predictive performance with minimal labeling effort. The geology field has not yet met such success. In this…
Shapiro's notations for natural numbers, and the associated desideratum of acceptability - the property of a notation that all recursive functions are computable in it - is well-known in philosophy of computing. Computable structure theory,…
We consider general Exponential Random Graph Models (ERGMs) where the sufficient statistics are functions of homomorphism counts for a fixed collection of simple graphs $F_k$. Whereas previous work has shown a degeneracy phenomenon in dense…
The network reconfiguration problem seeks to find a rooted tree $T$ such that the energy of the (unique) feasible electrical flow over $T$ is minimized. The tree requirement on the support of the flow is motivated by operational constraints…
We introduce a notion of weak definability of first order structures, show that various classification-theoretic properties are or are not preserved under it, and that the properties which are preserved can also be characterized in terms of…
We study the geometric change of Chow cohomology classes in projective toric varieties under the Weil-McMullen dual of the intersection product with a Lefschetz element. Based on this, we introduce toric chordality, a generalization of…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…