Related papers: Note on level r consensus
We study a multistage epidemic model which generalizes the SIR model and where infected individuals go through K>0 stages of the epidemic before being removed. An infected individual in stage k=1,...,K may infect a susceptible individual,…
Ryser's Conjecture states that for any $r$-partite $r$-uniform hypergraph, the vertex cover number is at most $r{-}1$ times the matching number. This conjecture is only known to be true for $r\leq 3$ in general and for $r\leq 5$ if the…
In the Sznajd consensus model on the square lattice, two people who agree in their opinions convince their neighbours of this opinion. We generalize it to many layers representing many age levels, and check if still a consensus among all…
In this paper we address the consensus problem in the context of networked agents whose communication graph can be split into a certain number of clusters in such a way that interactions between agents in the same clusters are cooperative,…
Certain consensus seeking multi-agent systems can be formulated as gradient descent flows of a disagreement function. We study how known pathologies of gradient descent flows in Euclidean spaces carry over to consensus seeking systems that…
Let $K[\mathcal{O}(P)]$ denote the toric ring of the order polytope $\mathcal{O}(P)$ of a finite partially ordered set $P$ and $K[\mathcal{C}(P)]$ that of the chain polytope $\mathcal{C}(P)$. It will be shown that $\beta_{p,…
This paper considers trial-offer markets where consumer preferences are modeled by a multinomial logit with social influence and position bias. The social signal for a product is given by its current market share raised to power r (or…
The essential subtoposes of a fixed topos form a complete lattice, which gives rise to the notion of a level in a topos. In the familiar example of simplicial sets, levels coincide with dimensions and give rise to the usual notions of…
The celebrated union-closed conjecture is concerned with the cardinalities of various subsets of the Boolean $d$-cube. The cardinality of such a set is equivalent, up to a constant, to its measure under the uniform distribution, so we can…
A gap in the proof prevents us to show that surfaces with constant mean curvature closed to 1/2 in H2 X R and having boundary with curvature greater than one, contained in a horizontal section P of H2 X R are topological disks, provided…
This paper investigates the application of consensus clustering and meta-clustering to the set of all possible partitions of a data set. We show that when using a "complement" of Rand Index as a measure of cluster similarity, the…
Hierarchy significantly shapes interactions in social structures by organizing individuals or groups based on status, power, or privilege. This study investigates how hierarchy affects structural balance as temperature variations, which…
Geometric realization of opinion is considered as a simplex and the opinion space of a group of individuals is a simplicial complex whose topological features are monitored in the process of opinion formation. The agents are physically…
Many organizations describe their processes as consensus-driven, but there is no consensus on the definition of consensus. Qualitative definitions of consensus prioritize social phenomena like "unity" that are not necessarily measurable.…
Operating System (OS) fingerprinting is critical for network security, but conventional methods do not provide formal uncertainty quantification mechanisms. Conformal Prediction (CP) could be directly wrapped around existing methods to…
We study the Hegselmann-Krause model of opinion dynamics on sparse, unbiased networks generated via Wilson's algorithm, unveiling how network connectivity and confidence bounds jointly determine collective behavior. By systematically…
At present, there are discrepancies between the measurements of several observables in B-->pi K decays and the predictions of the standard model (the ``B-->pi K puzzle''). Although the effect is not yet statistically significant -- it is at…
This paper considers the consensus problem of a novel opinion dynamics model with group pressure and self-confidence. Different with the most existing paper, the influence of friends of friends in a social network is taken into account,…
Convergence analysis of consensus algorithms is revisited in the light of the Hilbert distance. Tsitsiklis Lyapunov function is shown to be the Hilbert distance to consensus in log coordinates. Birkhoff theorem, which proves contraction of…
We introduce the problem of asymptotic subspace consensus, which requires the outputs of processes to converge onto a common subspace while remaining inside the convex hull of initial vectors.This is a relaxation of asymptotic consensus in…