Related papers: Generalizations of Leaky Forcing
The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a graph G, is used to study the maximum nullity / minimum rank of the family of symmetric matrices described by G. It is shown that for a…
Online experimentation platforms abstract away many of the details of experimental design, ensuring experimenters do not have to worry about sampling, randomisation, subject tracking, data collection, metric definition and interpretation of…
Call a graph $G$ zero-forcing for a finite abelian group $\mathcal{G}$ if for every $\ell : V(G) \to \mathcal{G}$ there is a connected $A \subseteq V(G)$ with $\sum_{a \in A} \ell(a) = 0$. The problem we pose here is to characterise the…
Let $G$ be a graph. A zero-sum flow in $G$ is an assignment of nonzero real number to the edges such that the sum of the values of all edges incident with each vertex is zero. Let $k$ be naturel number. A zero-sum $k$-flow is a flow with…
There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties…
In the first part of the article, we will outline the paradoxical picture that arises when attempting to calculate the recoil force of the water leakage from a hole at the bottom of a water tank. We will present three different options for…
Federated learning (FL) allows the collaborative training of AI models without needing to share raw data. This capability makes it especially interesting for healthcare applications where patient and data privacy is of utmost concern.…
Liquid democracy is the principle of making collective decisions by letting agents transitively delegate their votes. Despite its significant appeal, it has become apparent that a weakness of liquid democracy is that a small subset of…
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 $G$,…
A dynamic coloring of the vertices of a graph $G$ starts with an initial subset $F$ of colored vertices, with all remaining vertices being non-colored. At each time step, a colored vertex with exactly one non-colored neighbor forces this…
A $k$-weak bisection of a cubic graph $G$ is a partition of the vertex-set of $G$ into two parts $V_1$ and $V_2$ of equal size, such that each connected component of the subgraph of $G$ induced by $V_i$ ($i=1,2$) is a tree of at most $k-2$…
A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this new move one pebble is removed at vertices v and w adjacent…
Recent studies show that private training data can be leaked through the gradients sharing mechanism deployed in distributed machine learning systems, such as federated learning (FL). Increasing batch size to complicate data recovery is…
This novel work investigates the influence of the inspection system acceleration on the leakage signal in magnetic flux leakage type of non-destructive testing. The research is addressed both through designed experiments and simulations.…
Mixing effect in a stratified fluid is considered and examined. Euler equations for incompressible fluid stratified by a gravity field are applied to state a mathematical problem and describe the effect. It is found out that a system of…
BGP route leaks frequently precipitate serious disruptions to interdomain routing. These incidents have plagued the Internet for decades while deployment and usability issues cripple efforts to mitigate the problem. Peerlock, introduced in…
From network topologies to online social networks, many of today's most sensitive datasets are captured in large graphs. A significant challenge facing owners of these datasets is how to share sensitive graphs with collaborators and…
The article studies edge coverage for control flow graphs extended with explicit constraints. Achieving a given level of white-box coverage for a given code is a classic problem in software testing. We focus on designing test sets that…
Realizing flow security in a concurrent environment is extremely challenging, primarily due to non-deterministic nature of execution. The difficulty is further exacerbated from a security angle if sequential threads disclose control…
Let ${\mathcal G}$ be an infinite family of connected graphs and let $k$ be a positive integer. We say that $k$ is ${\it forcing}$ for ${\mathcal G}$ if for all $G \in {\mathcal G}$ but finitely many, the following holds. Any…