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An intersection digraph is a digraph where every vertex $v$ is represented by an ordered pair $(S_v, T_v)$ of sets such that there is an edge from $v$ to $w$ if and only if $S_v$ and $T_w$ intersect. An intersection digraph is reflexive if…
A test set for a formal language (set of strings) L is a subset T of L such that for any two string homomorphisms f and g defined on L, if the restrictions of f and g on T are identical functions, then f and g are identical on the entire L.…
String diagrams are a powerful tool for reasoning about composite structures in symmetric monoidal categories. By representing string diagrams as graphs, equational reasoning can be done automatically by double-pushout rewriting. !-graphs…
Given a graph $G$, viewed as a loop-less symmetric digraph, we study the maximum number of fixed points in a conjunctive boolean network with $G$ as interaction graph. We prove that if $G$ has no induced $C_4$, then this quantity equals…
We study obstacle problems governed by two distinct types of diffusion operators involving interacting free boundaries. We obtain a somewhat surprising coupling property, leading to a comprehensive analysis of the free boundary. More…
The interplay of topological constraints, excluded volume interactions, persistence length and dynamical entanglement length in solutions and melts of linear chains and ring polymers is investigated by means of kinetic Monte Carlo…
Dialogue topic segmentation supports summarization, retrieval, memory management, and conversational continuity. Despite decades of work, evaluation practice remains dominated by strict boundary matching and F1-based metrics. Modern large…
Finding a set of empirical criteria fulfilled by any theory satisfying the generalized notion of noncontextuality is a challenging task of both operational and foundational importance. This work presents a methodology for constructing the…
Large Language Models (LLMs) have demonstrated remarkable abilities, one of the most important being in-context learning (ICL). With ICL, LLMs can derive the underlying rule from a few demonstrations and provide answers that comply with the…
A path in an(a) edge(vertex)-colored graph is called a conflict-free path if there exists a color used on only one of its edges(vertices). An(A) edge(vertex)-colored graph is called conflict-free (vertex-)connected if for each pair of…
For a tree decomposition $\mathcal{T}$ of a graph $G$, let $\mu(\mathcal{T})$ denote the maximum size of an induced matching in $G$ with the property that some bag of $\mathcal{T}$ contains at least one endpoint of every edge of the…
In the 1970s, Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is no. Specifically, for each positive integer $k$, we construct…
Humans effortlessly identify objects by leveraging a rich understanding of the surrounding scene, including spatial relationships, material properties, and the co-occurrence of other objects. In contrast, most computational object…
We study the problem of deciding whether a given language is directed. A language $L$ is \emph{directed} if every pair of words in $L$ have a common (scattered) superword in $L$. Deciding directedness is a fundamental problem in connection…
We study a question arising in inverse scattering theory: given a penetrable obstacle, does there exist an incident wave that does not scatter? We show that every penetrable obstacle with real-analytic boundary admits such an incident wave.…
Finding a maximum independent set (MIS) of a given fam- ily of axis-parallel rectangles is a basic problem in computational geom- etry and combinatorics. This problem has attracted significant atten- tion since the sixties, when Wegner…
Intersecting codes are a classical object in coding theory whose rank-metric analogue has recently been introduced. Although the definition formally parallels the Hamming-metric case, the structure and parameter constraints of rank-metric…
We introduce the notion of delineation. A graph class $\mathcal C$ is said delineated if for every hereditary closure $\mathcal D$ of a subclass of $\mathcal C$, it holds that $\mathcal D$ has bounded twin-width if and only if $\mathcal D$…
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…
Let $C(X)$ be the ring of all continuous real valued functions defined on a completely regular Hausdorff topological space $X$. The zero-set intersection graph $\Gamma (C(X))$ of $C(X)$ is a simple graph with vertex set all non units of…