相关论文: Unit interval parking functions and the $r$-Fubini…

We provide a simple proof of a result, due to G. Alberti, concerning a rank-one property for the singular part of the derivative of vector-valued functions of bounded variation.

Associated with the $r$-Shi arrangement and $r$-Catalan arrangement in $\Bbb{R}^n$, we introduce a cubic matrix for each region to establish two bijections in a uniform way. Firstly, the positions of minimal positive entries in column…

Instead of testing for unanimous agreement, I propose learning how broad of a consensus favors one distribution over another (of earnings, productivity, asset returns, test scores, etc.). Specifically, given a sample from each of two…

For \alpha in the interval [0,1], we consider the one-parameter family of \alpha-continued fraction maps, which include the Gauss map (\alpha=1) and the nearest integer (\alpha=1/2) and by-excess (\alpha=0) continued fraction maps. To each…

The interior polynomial of a directed graph is defined as the $h^*$-polynomial of the graph's (extended) root polytope, and it displays several attractive properties. Here we express its degree in terms of the minimum cardinality of a…

We prove a Fubini rule for $\infty$-co/ends of $\infty$-functors $F : \mathcal C^\text{op}\times\mathcal C\to \mathcal D$. This allows to lay down "integration rules", similar to those in classical co/end calculus, also in the setting of…

Consider the stochastic heat equation $\dot{u}=\frac12 u"+\sigma(u)\xi$ on $(0\,,\infty)\times\mathbb{R}$ subject to $u(0)\equiv1$, where $\sigma:\mathbb{R}\to\mathbb{R}$ is a Lipschitz (local) function that does not vanish at $1$, and…

For $f$ convex and increasing, we prove the inequality $ \int f(|U'|) \geq \int f(nT')$, every time that $U$ is a Sobolev function of one variable and $T$ is the non-decreasing map defined on the same interval with the same image measure as…

A broad range of on-line behaviors are mediated by interfaces in which people make choices among sets of options. A rich and growing line of work in the behavioral sciences indicate that human choices follow not only from the utility of…

Motivated by an influential result of Bourgain and Tzafriri, we consider continuous matrix functions $A:\mathbb{R}\to M_{n\times n}$ and lower $\ell_2$-norm bounds associated with their restriction to certain subspaces. We prove that for…

We consider the space of matrices, with given number of rows and of columns, equipped with the classic trace scalar product. With any matrix (source) norm, we associate a coupling, called Capra, between the space of matrices and itself.…

We study functions that produce a ranking of $n$ individuals from $n$ such rankings and are impartial in the sense that the position of an individual in the output ranking does not depend on the input ranking submitted by that individual.…

This paper considers the problem of inference after ranking. In our setting, we are interested in any population whose rank according to some random quantity, such as an estimated treatment effect, a measure of value-added, or benefit (net…

Rank functors on a quiver $Q$ are certain additive functors from the category of representations of $Q$ to the category of finite-dimensional vector spaces. Composing with the dimension function on vector spaces gives a rank function on…

We propose a generalized car parking problem where either a car of size $\sigma$ or of size $m\sigma$ ($m>1$) is sequentially parked on a line with probability $q$ and $(1-q)$, respectively. The free parameter $q$ interpolates between the…

We demonstrate a method for proving precise concentration inequalities in uniformly random trees on $n$ vertices, where $n\geq1$ is a fixed positive integer. The method uses a bijection between mappings…

Formula One race weekends are structured around multiple sessions: practices, qualifying, and the Grand Prix itself, each contributing to final race performance. This study analyzes nearly two decades of races, encompassing 7,800…

We want to select the best systems out of a given set of systems (or rank them) with respect to their expected performance. The systems allow random observations only and we assume that the joint observation of the systems has a…

Suppose that a target function is monotonic, namely, weakly increasing, and an available original estimate of this target function is not weakly increasing. Rearrangements, univariate and multivariate, transform the original estimate to a…

We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem…