Related papers: Erratum to: "Remarks on the second neighborhood pr…
Determining how close a winner of an election is to becoming a loser, or distinguishing between different possible winners of an election, are major problems in computational social choice. We tackle these problems for so-called weighted…
This submission consists of two papers: 1) an erratum that corrects an error in the proof of Proposition 4.3 in my paper "The Homogeneous Coordinate Ring of a Toric Variety", and 2) the original (unchanged) version of the paper, published…
This work studies external regret in sequential prediction games with both positive and negative payoffs. External regret measures the difference between the payoff obtained by the forecasting strategy and the payoff of the best action. In…
The Bermond-Thomassen conjecture states that, for any positive integer $r$, a digraph of minimum out-degree at least $2r-1$ contains at least $r$ vertex-disjoint directed cycles. In 2014, Bang-Jensen, Bessy and Thomass\' e proved the…
The Erd\H{o}s discrepancy problem, now a theorem by T. Tao, asks whether every sequence with values plus or minus one has unbounded discrepancy along all homogeneous arithmetic progressions. We establish weighted variants of this problem,…
R. Wang (Discrete Mathematics and Theoretical Computer Science, vol. 19(3), 2017) proposed the following problem. \textbf{Problem.} Let $D$ be a strongly connected balanced bipartite directed graph of order $2a\geq 8$. Suppose that…
We present a family of pairwise tournaments reducing $k$-class classification to binary classification. These reductions are provably robust against a constant fraction of binary errors. The results improve on the PECOC construction…
A class of acyclic digraphs $\mathscr{C}$ is linearly unavoidable if there exists a constant $c$ such that every digraph $D\in \mathscr{C}$ is contained in all tournaments of order $c\cdot |V(D)|$. The class of all acyclic digraphs is not…
This short note is an erratum to arXiv:1306.4304, correcting the proof of one of its main results. It includes some counterexamples regarding infinite-dimensional unipotent groups and affine spaces that may be of independent interest.
We extend the study of link-irregular graphs to directed graphs (digraphs), where a digraph is link-irregular if no two vertices have isomorphic directed links. We establish that link-irregular digraphs exist on $n$ vertices if and only if…
The Second Neighborhood Conjecture of Seymour asserts that every oriented graph contains a vertex~$v$ satisfying $|\Npp(v)|\ge|\Np(v)|$. We introduce \emph{Pisa graphs} -- strongly connected oriented graphs~$D$ with $\Delta(D)=\max_{v\in…
This erratum aims to correct 1) the wrong expressions, 2) some typographical errors, 3) some erroneous points made in discussion of the disparity of heat flux ratios between our full RPA model and the local conductivity model, and 4) the…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
For a fixed finite set of finite tournaments ${\mathcal F}$, the ${\mathcal F}$-free orientation problem asks whether a given finite undirected graph $G$ has an $\mathcal F$-free orientation, i.e., whether the edges of $G$ can be oriented…
Seymour's Second Neighborhood Conjecture asserts that every oriented graph has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. Combs are the graphs having no induced $C_4$, $\overline{C_4}$, $C_5$,…
Our published paper contains an incorrect statement of a result due to Artin and Zhang. This corrigendum gives the correct statement of their result and includes a new result that allows us to use their result to prove our main theorem.…
A classic problem in statistics is the estimation of the expectation of random variables from samples. This gives rise to the tightly connected problems of deriving concentration inequalities and confidence sequences, that is confidence…
This erratum corrects a number of formulae containing mistakes in the paper 'Luminosity function, sizes and FR dichotomy of radio-loud AGN', 2007, MNRAS, v. 381, p.1548. The corrections do not alter any of the conclusions in the original…
It has been pointed out by counterexamples in a 2013 paper in the IEEE Transactions on Computers [1], that there is an error in the previously ibid.\ in 2005 published paper [2] on the construction of valid digit selection tables for SRT…
Tournament ranking is a function that assigns each vertex of a tournament (i.e., a directed graph without loops, in which each pair of different vertexes is connected by exactly one arc) a number called the rank of the vertex. One of…