Related papers: Note on level r consensus
A famous conjecture of Ryser states that any $r$-partite set system has transversal number at most $r-1$ times their matching number. This conjecture is only known to be true for $r\leq3$ in general, for $r\leq5$ if the set system is…
It is examined whether the number ($J$) of (joint) publications of a "main scientist" with her/his coauthors ranked according to rank ($r$) importance, i.e. $ J \propto 1/r $, as found by Ausloos [1] still holds for subfields, i.e. when the…
We present a model of set theory, in which, for a given $n\ge2$, there exists a non-ROD-uniformizable planar lightface $\varPi^1_n$ set in $\mathbb R\times\mathbb R$, whose all vertical cross-sections are countable sets (and in fact Vitali…
In this paper, we propose an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets. Instead of assuming the exact convex projection proposed in the literature, we allow each node to…
In previous work of this author it was conjectured that the sum of power sums $p_\lambda,$ for partitions $\lambda$ ranging over an interval $[(1^n), \mu]$ in reverse lexicographic order, is Schur-positive. Here we investigate this…
We explore the impact of social noise, characterized by nonconformist behavior, on the phase transition within the framework of the majority rule model. The order-disorder transition can reflect the consensus-polarization state in a social…
In this paper, we propose a two-layer adoption-opinion model to study the diffusion of two competing technologies within a population whose opinions evolve under social influence and adoption-driven feedback. After adopting one technology,…
A well-known conjecture, often attributed to Ryser, states that the cover number of an $r$-partite $r$-uniform hypergraph is at most $r - 1$ times larger than its matching number. Despite considerable effort, particularly in the…
During the past decade, nine papers have obtained increasingly strong consequences from the assumption that boolean or bounded-query hierarchies collapse. The final four papers of this nine-paper progression actually achieve downward…
The CP asymmetry in $B^0\to K^+\pi^-$ is expected to be similar to that in $B^+\to K^+\pi^0$. The experimental data however show $\sim 5\sigma$ difference between the two, leading to the so called $\Delta {A}_{K\pi}$ puzzle. Employing sum…
We study a one-dimensional version of the Hopfield model with long, but finite range interactions below the critical temperature. In the thermodynamic limit we obtain large deviation estimates for the distribution of the ``local'' overlaps,…
We study the convergence rate of a hierarchy of upper bounds for polynomial minimization problems, proposed by Lasserre [SIAM J. Optim. 21(3) (2011), pp. 864-885], for the special case when the feasible set is the unit (hyper)sphere. The…
We define the quantile set of order $\alpha \in \left[ 1/2,1\right) $ associated to a law $P$ on $\mathbb{R}^{d}$ to be the collection of its directional quantiles seen from an observer $O\in \mathbb{R}^{d}$. Under minimal assumptions these…
We consider a general class of three--state models where individuals hold one of two opposite opinions, or are neutral, and exchange opinions in generic pairwise interactions. We show that when opinions spread in a population where a…
We show that the hyperplane conjecture holds for the classes of $k$-intersection bodies with arbitrary measures in place of volume.
A Ranking r-Constraint Satisfaction Problem (ranking r-CSP) consists of a ground set of vertices V, an arity r >= 2, a parameter k and a constraint system c, where c is a function which maps rankings of r-sized subsets of V to {0,1}. The…
This paper proposes an analysis of the effects of consensus and preference aggregation on the consistency of pairwise comparisons. We define some boundary properties for the inconsistency of group preferences and investigate their relation…
Collapse, or a gravitational-like phase transition is studied in a microcanonical ensemble of particles with an attractive $1/r^{\alpha}$ potential. A mean field continuous integral equation is used to determine a saddle-point density…
We introduce the confident voter model, in which each voter can be in one of two opinions and can additionally have two levels of commitment to an opinion --- confident and unsure. Upon interacting with an agent of a different opinion, a…
In the compromise model of Deffuant et al., opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter \epsilon. The opinions of a randomly…