Related papers: Note on level r consensus
A famous conjecture of Ryser is that in an $r$-partite hypergraph the covering number is at most $r-1$ times the matching number. If true, this is known to be sharp for $r$ for which there exists a projective plane of order $r-1$. We show…
We consider finite Bernoulli convolutions with a parameter $1/2 < r < 1$ supported on a discrete point set, generically of size $2^N$. These sequences are uniformly distributed with respect to the infinite Bernoulli convolution measure…
In approval voting, individuals vote for all platforms that they find acceptable. In this situation it is natural to ask: When is agreement possible? What conditions guarantee that some fraction of the voters agree on even a single…
A popular approach to unveiling the black box of neural NLP models is to leverage saliency methods, which assign scalar importance scores to each input component. A common practice for evaluating whether an interpretability method is…
Predictions based on the chirally normalized vector meson dominance model for decay rates and distributions of $\tau$ decays into $K\pi\pi\nu_\tau$ final states are discussed. Disagreements with experimental results can be traced back to…
Let $\pi:\mathbb{P}(\mathcal{O}(0)\oplus \mathcal{O}(k))\to \mathbb{P}^{n-1}$ be a projective bundle over $\mathbb{P}^{n-1}$ with $1\leq k \leq n-1$. In this paper, we show that lens space $L(k\, ;1)(r)$ with radius $r$ embedded in…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
The measurements of B -> pi K decays have been in disagreement with the predictions of the Standard Model (SM) for some time. In this paper, we perform an update of this puzzle using the latest (2008) data. We find that the situation has…
For a Riemannian covering $\pi\colon M_1\to M_0$, the bottoms of the spectra of $M_0$ and $M_1$ coincide if the covering is amenable. The converse implication does not always hold. Assuming completeness and a lower bound on the Ricci…
While the very first consensus protocols for the synchronous model were designed to match the worst-case lower bound, deciding in exactly t+1 rounds in all runs, it was soon realized that they could be strictly improved upon by early…
This paper presents a simple generalization of the basic atomic read/write register object, whose genericity parameter spans the whole set of integers and is such that its k-parameterized instance has exactly consensus number k. This…
We study consensus processes on the complete graph of $n$ nodes. Initially, each node supports one from up to n opinions. Nodes randomly and in parallel sample the opinions of constant many nodes. Based on these samples, they use an update…
In 2014, Keevash famously proved the existence of $(n,q,r)$-Steiner systems as part of settling the Existence Conjecture of Combinatorial Designs (dating from the mid-1800s). In 2020, Glock, K\"uhn, and Osthus conjectured a minimum degree…
Ryser's conjecture says that for every $r$-partite hypergraph $H$ with matching number $\nu(H)$, the vertex cover number is at most $(r-1)\nu(H)$. This far reaching generalization of K\"onig's theorem is only known to be true for $r\leq 3$,…
We study the critical behavior of a continuous opinion model, driven by kinetic exchanges in a fully-connected population. Opinions range in the real interval $[-1,1]$, representing the different shades of opinions against and for an issue…
This paper deals with interactions between committee members as they rank a large list of applicants for a given position and eventually reach consensus. We will see that for a natural deterministic model the ranking can be described by…
A striking discovery in the field of network science is that the majority of real networked systems have some universal structural properties. In generally, they are simultaneously sparse, scale-free, small-world, and loopy. In this paper,…
The central conjecture of parameterized complexity states that FPT is not equal to W[1], and is generally regarded as the parameterized counterpart to P != NP. We revisit the issue of the plausibility of FPT != W[1], focusing on two…
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In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.