Related papers: Generalizations of Leaky Forcing
Leaky waves are an important class of waves, particularly for guiding waves along structures embedded within another medium; a mismatch in wavespeeds often leads to leakage of energy from the waveguide, or interface, into the medium, which…
Exchanging gradients is a widely used method in modern multi-node machine learning system (e.g., distributed training, collaborative learning). For a long time, people believed that gradients are safe to share: i.e., the training data will…
A pebbling move on a weighted graph removes some pebbles at a vertex and adds one pebble at an adjacent vertex. The number of pebbles removed is the weight of the edge connecting the vertices. A vertex is reachable from a pebble…
The probability leakage of model M with respect to evidence E is defined. Probability leakage is a kind of model error. It occurs when M implies that events $y$, which are impossible given E, have positive probability. Leakage does not…
A mathematical model is identifiable if its parameters can be recovered from data. Here, we focus on a particular class of model, linear compartmental models, which are used to represent the transfer of substances in a system. We analyze…
The 1-2-3 Conjecture asks whether almost all graphs can be (edge-)labelled with $1,2,3$ so that no two adjacent vertices are incident to the same sum of labels. In the last decades, several aspects of this problem have been studied in…
The core vertex set of a graph is an invariant of the graph. It consists of those vertices associated with the non-zero entries of the nullspace vectors of a $\{0,1\}$-adjacency matrix. The remaining vertices of the graph form the…
The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a…
In this paper we consider a simple model of random graph process with {\it hard} copying as follows: At each time step $t$, with probability $0<\alpha\leq 1$ a new vertex $v_t$ is added and $m$ edges incident with $v_t$ are added in the…
Let G be a graph with a perfect matching. A complete forcing set of G is a subset of edges of G to which the restriction of every perfect matching is a forcing set of it. The complete forcing number of G is the minimum cardinality of…
Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a…
In this paper we present a new kind of boundary layer flow produced by an electromagnetic Lorentz force which acts parallel to the plate in an electrically conductive fluid. The plate is motionless and the ambient fluid stagnant. This flow…
Agentic large language model systems increasingly automate tasks by retrieving URLs and calling external tools. We show that this workflow gives rise to implicit prompt injection: adversarial instructions embedded in automatically generated…
Large Language Models (LLMs) enable a new ecosystem with many downstream applications, called LLM applications, with different natural language processing tasks. The functionality and performance of an LLM application highly depend on its…
A signed graph is a graph with a positive or negative sign on each edge. Regarding each edge as two half edges, an orientation of a signed graph is an assignment of a direction to each of its half edges such that the two half edges of a…
A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…
Let $k$ and $\ell$ be positive integers. We prove that if $1 \leq \ell \leq o_k(k^{6/5})$, then in every large enough graph $G$, the fraction of $k$-vertex subsets that induce exactly $\ell$ edges is at most $1/e + o_k(1)$. Together with a…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
This paper studies the problem of reasoning about flow security properties in virtualised computing networks with mobility from perspective of formal language. We propose a distributed process algebra CSP_{4v} with security labelled…
Graph burning is a round-based game or process that discretely models the spread of influence throughout a network. We introduce a generalization of graph burning which applies to hypergraphs, as well as a variant called ''lazy'' hypergraph…