Related papers: Note on level r consensus
We investigate opinion spreading by a threshold model in a situation where the influence of people is heterogeneously distributed. We focus on the response of the average opinion as a function between the trend between out-degree (number of…
Herlihy's consensus hierarchy ranks the power of various synchronization primitives for solving consensus in a model where asynchronous processes communicate through shared memory and fail by halting. This paper revisits the consensus…
We investigate a model for opinion dynamics, where individuals (modeled by vertices of a graph) hold certain abstract opinions. As time progresses, neighboring individuals interact with each other, and this interaction results in a…
Consensus on nonlinear spaces is of use in many control applications. This paper proposes a gradient descent flow algorithm for consensus on hypersurfaces. We show that if an inequality holds, then the system converges for almost all…
A ranking is an ordered sequence of items, in which an item with higher ranking score is more preferred than the items with lower ranking scores. In many information systems, rankings are widely used to represent the preferences over a set…
In this paper, we present a new classifier, which integrates significance testing results over different random subspaces to yield consensus p-values for quantifying the uncertainty of classification decision. The null hypothesis is that…
In this paper we prove that a planar set $\mathcal{X}$ of at most $mn-1$ points, where $m \le n$, is $\kappa$-dependent, if and only if there exists a number r, $1 \le r \le m-1$, and an essentially $\kappa$-dependent subset $\mathcal{Y}…
By incorporating a multilayer network and time-decaying memory into the original voter model, the coupled effects of spatial and temporal cumulation of peer pressure on consensus are investigated. Heterogeneity in peer pressure and…
This paper aims at providing rigorous theoretical analysis to investigate the consensus behavior of opinion dynamics in noisy environments. It is known that the well-known Hegselmann-Krause (HK) opinion dynamics demonstrates various…
We perform a detailed study of the Hegselmann-Krause bounded confidence opinion dynamics model with heterogeneous confidence $\varepsilon_i$ drawn from uniform distributions in different intervals $[\varepsilon_l, \varepsilon_u]$. The phase…
Often exhibiting hierarchical and overlapping structures, communities or modular groups are fundamental and complex in network science. One of the most exploited tools to detect the mesoscopic structure is synchronization. Several phenomena…
A primary goal of online deliberation platforms is to identify ideas that are broadly agreeable to a community of users through their expressed preferences. Yet, consensus elicitation should ideally extend beyond the specific statements…
In this work we present novel results to the problem of the Hegselmann-Krause dynamics in networks obtained by an extensive study of the behavior of the standard order parameter sensitive to the onset of consensus: the normalized size of…
Motivated by multi-objective optimization, we study extrema of a set of N points independently distributed inside the d-dimensional hypercube. A point in this set is k-dominated by another point when at least k of its coordinates are…
In this work we study the formation of consensus in a hierarchical population. We derive the corresponding kinetic equations, and analyze the long time behaviour of their solutions for the case of finite number of hierarchical obtaining…
We prove the inequality sum_{k=1}^infty (-1)^{k+1} r^k cos(k*phi) (k+2)^{-1} < sum_{k=1}^infty(-1)^{k+1} r^k (k+2)^{-1} for 0 < r <= 1 and 0 < phi < pi. For the case r = 1 we give two proofs. The first one is by means of a general numerical…
In this technical note, we introduce a novel approach to studying consensus of continuous-time nonlinear systems with varying topology based on Hilbert metric. We demonstrate that this metric offers significant flexibility in analyzing…
In this note we observe that the categorical structure of a flop occurs for some well-known non-commutative resolutions of a nodal curve. We describe the flop-flop spherical twists, and give a geometric interpretation in terms of…
The consensus model of Krause and Hegselmann can be naturally extended to the case in which opinions are integer instead of real numbers. Our algorithm is much faster than the original version and thus more suitable for applications. For…
Trust is a collective, self-fulfilling phenomenon that suggests analogies with phase transitions. We introduce a stylized model for the build-up and collapse of trust in networks, which generically displays a first order transition. The…