Related papers: Note on level r consensus
In this note we consider the $k$th level of the uniform random recursive tree after $n$ steps, and prove that the proportion of nodes with degree greater than $t\log n$ converges to $(1-t)^k$ almost surely, as $n\to\infty$, for every…
It is shown that a scalar field, minimally coupled to gravity may have collapsing modes even when the energy condition is violated, that is, for $(\rho+3p)<0$. This result may be useful in the investigation of the possible clustering of…
Statistical physicists have become interested in models of collective social behavior such as opinion formation, where individuals change their inherently preferred opinion if their friends disagree. Real preferences often depend on…
This work considers the problem of resilient consensus where stochastic values of trust between agents are available. Specifically, we derive a unified mathematical framework to characterize convergence, deviation of the consensus from the…
This work studies resilient leader-follower consensus with a bounded number of adversaries. Existing approaches typically require robustness conditions of the entire network to guarantee resilient consensus. However, the behavior of such…
When opinions, behaviors or ideas diffuse within a population, some are invariably stickier than others. The stickier the opinion, behavior or idea, the greater is an individual's inertia to replace it with an alternative. Here we study the…
We analyze the structure of the disagreement among a population of voters over a set of alternatives. Surveys typically ask either for pairwise comparisons, simple and intuitive for participants, or full rankings over alternatives,…
In this paper we investigate a model (based on the idea of the outflow dynamics), in which only conformity and anticonformity can lead to the opinion change. We show that for low level of aniconformity the consensus is still reachable but…
We prove a sufficient condition for a finite clique complex to collapse to a $k$-dimensional complex, and use this to exhibit thresholds for $(k+1)$-collapsibility in a sparse random clique complex. In particular, if every strongly…
Formation of consensus, in binary yes/no type of voting, is a well defined process. However, even in presence of clear incentives, the dynamics involved can be incredibly complex. Specifically, formations of large groups of similarly…
A phenomenological analysis based on the published branching fractions and $CP$ asymmetry observables of the $B\to K\pi$, $B\to\pi\pi$ and $B\to KK$ dataset is performed. The amplitude decomposition by the topological diagrams and the…
We establish a general "boundedness implies convergence" principle for a family of evolving Riemannian metrics. We then apply this principle to collapsing Calabi-Yau metrics and normalized K\"ahler-Ricci flows on torus fibered minimal…
This work extends the recent opinion dynamics model from Cheng et al., emphasizing the role of group pressure in consensus formation. We generalize the findings to incorporate social influence algorithms with general time-varying,…
In this paper, we study distributed consensus in the radio network setting. We produce new upper and lower bounds for this problem in an abstract MAC layer model that captures the key guarantees provided by most wireless MAC layers. In more…
We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically,…
Relation between problem hardness and solution space structure is an important research aspect. Model d-k-CSP generates very hard instances when $r=1$ and $r$ is near 1, where $r$ represents normalized constraint density. We find that when…
We present a user of model interaction based on the physics of kinetic exchange, and extend it to individuals placed in a grid with local interaction. We show with numerical analysis and partial analytical results that the critical symmetry…
Assuming a lower bound on the Ricci curvature of a complete Riemannian manifold, for $p< 1/2$ we show the existence of bounds on the local $L^p$ norm of the Ricci curvature that depend only on the dimension and which improve with volume…
We consider a class of models of opinion formation where the dissemination of individual opinions occurs through the spreading of local consensus and disagreement. We study the emergence of full collective consensus or maximal disagreement…
The vectorial Deffuant model is a simple stochastic process for the dynamics of opinions that also includes a confidence threshold. To understand the role of space in this type of social interactions, we study the process on the…