Related papers: Metric Dimensions of March Madness Brackets
The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. There are several contexts in which studying the patterns of orthogonal matrices can be useful. One necessary condition for a matrix to be…
This work studies the following question: can plays in a Muller game be stopped after a finite number of moves and a winner be declared. A criterion to do this is sound if Player 0 wins an infinite-duration Muller game if and only if she…
In this work, we examine a generic class of simple distributed balls-into-bins algorithms. Exploiting the strong concentration bounds that apply to balls-into-bins games, we provide an iterative method to compute accurate estimates of the…
Pairwise comparison matrices often exhibit inconsistency, therefore many indices have been suggested to measure their deviation from a consistent matrix. A set of axioms has been proposed recently that is required to be satisfied by any…
Given a tournament T=(V,A), a subset X of V is an interval of T provided that for any a, b\in X and x\in V-X, (a,x) \in A if and only if (b,x)\in A. For example, \emptyset, \{x\} (x\in V) and V are intervals of T, called trivial intervals.…
We consider the covering of a ball in certain normed spaces by its congruent subsets and show that if the finite number of sets is not greater than the dimensionality of the space, then the centre of the ball either belongs to the interior…
The availability of massive data about sports activities offers nowadays the opportunity to quantify the relation between performance and success. In this study, we analyze more than 6,000 games and 10 million events in six European leagues…
In experimental applications of bounded-reasoning models, behavior is often summarized by distributions of "levels". We argue that such summaries conflate two conceptually distinct dimensions: a player's type, capturing beliefs about what…
How often can we expect a Major League Baseball team to score at least 20 runs in a single game? Considered a rare event in baseball, the outcome of scoring at least 20 runs in a game has occurred 224 times during regular season games since…
In competitive sports it is often very hard to quantify the performance. A player to score or overtake may depend on only millesimal of seconds or millimeters. In racquet sports like tennis, table tennis and squash many events will occur in…
As 3-point shooting in the NBA continues to increase, the importance of perimeter defense has never been greater. Perimeter defenders are often evaluated by their ability to tightly contest shots, but how exactly does contesting a jump shot…
Individual sports competitions provide a natural setting for examining the relative importance of talent and luck/chance in achieving success. The belief that success is primarily due to individual abilities and hard work rather than…
Multi-round competitions often double or triple the points awarded in the final round, calling it a bonus, to maximize spectators' excitement. In a two-player competition with $n$ rounds, we aim to derive the optimal bonus size to maximize…
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…
The concept of movable evidence masses that flow from supersets to subsets as specified by experts represents a suitable framework for reasoning under uncertainty. The mass flow is controlled by specialization matrices. New evidence is…
We consider the problem of counting the number of possible sets of rankings (called ranking patterns) generated by unfolding models of codimension one. We express the ranking patterns as slices of the braid arrangement and show that all…
Negative dependence of sequences of random variables is often an interesting characteristic of their distribution, as well as a useful tool for studying various asymptotic results, including central limit theorems, Poisson approximations,…
We prove that there exists a constant $c > 0$ such that the vertices of every strongly $c \cdot kt$-connected tournament can be partitioned into $t$ parts, each of which induces a strongly $k$-connected tournament. This is clearly tight up…
We introduce the concept of budget games. Players choose a set of tasks and each task has a certain demand on every resource in the game. Each resource has a budget. If the budget is not enough to satisfy the sum of all demands, it has to…
Fractional scoring has been proposed to avoid inconsistencies in the attribution of publications to percentile rank classes. Uncertainties and ambiguities in the evaluation of percentile ranks can be demonstrated most easily with small…