相关论文: Leaky Forcing: Extending Zero Forcing Results to a…

Several concepts that model processes of spreading (of information, disease, objects, etc.) in graphs or networks have been studied. In many contexts, we assume that some vertices of a graph $G$ are contaminated initially, before the…

Several researchers have recently explored various graph parameters that can or cannot be characterized by the spectrum of a matrix associated with a graph. In this paper we show that several NP-hard zero forcing numbers are not…

Power domination in graphs arises from the problem of monitoring an electric power system by placing as few measurement devices in the system as possible. A power dominating set of a graph is a set of vertices that observes every vertex in…

Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…

While standard flow-matching models transport noise to data uniformly, incorporating an explicit generation order - specifically, establishing coarse, low-frequency structure before fine detail - has proven highly effective for synthesizing…

Maximal leakage quantifies the leakage of information from data $X \in \mathcal{X}$ due to an observation $Y$. While fundamental properties of maximal leakage, such as data processing, sub-additivity, and its connection to mutual…

Information leakage is a class of error that can lead to severe consequences. However unlike other errors, it is rarely explicitly considered during the software testing process. LeakFuzzer advances the state of the art by using a…

In this paper we begin the study of well-failed graphs, that is, graphs in which every maximal failed zero forcing set is a maximum failed zero forcing set, or equivalently, in which every minimal fort is a minimum fort. We characterize…

We introduce a family of information leakage measures called maximal $\alpha,\beta$-leakage, parameterized by real numbers $\alpha$ and $\beta$. The measure is formalized via an operational definition involving an adversary guessing an…

In 2018, forts were defined as non-empty subsets of vertices in a graph where no vertex outside the set has exactly one neighbor in the set. Forts have since been used to characterize zero forcing sets, model zero forcing as an integer…

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…

We give short and simple proofs of the inequalities $B(G)\leq Z(L(G))$ and $Z(G)\leq Z(L(G))$ first established by Erzurumluo\u{g}lu, Meagher, and Pike, where $G$ is a graph without isolated vertices, $B(G)$ is the brushing number of $G$,…

This paper studies the problem of designing networks that are strong structurally controllable, and robust simultaneously. For given network specifications, including the number of nodes $N$, the number of leaders $N_L$, and diameter $D$,…

Let $G$ be a graph that admits a perfect matching. A {\sf forcing set} for a perfect matching $M$ of $G$ is a subset $S$ of $M$, such that $S$ is contained in no other perfect matching of $G$. This notion originally arose in chemistry in…

In elasticity, the design of a cloaking for an inclusion or a void to leave a vibrational field unperturbed by its presence, so to achieve its invisibility, is a thoroughly analyzed, but still unchallenged, mechanical problem. The 'cloaking…

We investigate the zero-forcing number for triangle-free graphs. We improve upon the trivial bound, $\delta \le Z(G)$ where $\delta$ is the minimum degree, in the triangle-free case. In particular, we show that $2 \delta - 2 \le Z(G)$ for…

A private compression design problem is studied, where an encoder observes useful data $Y$, wishes to compress it using variable length code and communicates it through an unsecured channel. Since $Y$ is correlated with private data $X$,…

A new method to extract the density of partition function zeroes (a continuous function) from their distribution for finite lattices (a discrete data set) is presented. This allows direct determination of the order and strength of phase…

This paper proposes an operational measure of non-stochastic information leakage to formalize privacy against a brute-force guessing adversary. The information is measured by non-probabilistic uncertainty of uncertain variables, the…

The two key characteristics of a normalizing flow is that it is invertible (in particular, dimension preserving) and that it monitors the amount by which it changes the likelihood of data points as samples are propagated along the network.…