Related papers: Interval-Valued Rank in Finite Ordered Sets
Rank and select queries on bitmaps are essential building bricks of many compressed data structures, including text indexes, membership and range supporting spatial data structures, compressed graphs, and more. Theoretically considered yet…
Many known planning tasks have inherent constraints concerning the best order in which to achieve the goals. A number of research efforts have been made to detect such constraints and to use them for guiding search, in the hope of speeding…
A characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over other characteristics. In this…
A poset $P = (X,\prec)$ is a unit OC interval order if there exists a representation that assigns an open or closed real interval $I(x)$ of unit length to each $x \in P$ so that $x \prec y$ in $P$ precisely when each point of $I(x)$ is less…
We consider sequential or active ranking of a set of n items based on noisy pairwise comparisons. Items are ranked according to the probability that a given item beats a randomly chosen item, and ranking refers to partitioning the items…
Each family $\mathcal{M}$ of means has a natural, partial order (point-wise order), that is $M \le N$ iff $M(x) \le N(x)$ for all admissible $x$. In this setting we can introduce the notion of interval-type set (a subset $\mathcal{I}…
Learning to rank is a supervised learning problem where the output space is the space of rankings but the supervision space is the space of relevance scores. We make theoretical contributions to the learning to rank problem both in the…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of sentences, given grammatical structure and the meanings of its words. This approach has…
The bootstrap is a popular and convenient method for quantifying the authority of an empirical ordering of attributes, for example of a ranking of the performance of institutions or of the influence of genes on a response variable. In the…
Selecting from or ranking a set of candidates variables in terms of their capacity for predicting an outcome of interest is an important task in many scientific fields. A variety of methods for variable selection and ranking have been…
The statistical analysis of functional data is a growing need in many research areas. In particular, a robust methodology is important to study curves, which are the output of experiments in applied statistics. In this paper we study some…
We study partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. These permutations are the linear…
Ranking populations such as institutions based on certain characteristics is often of interest, and these ranks are typically estimated using samples drawn from the populations. Due to sample randomness, it is important to quantify the…
Evaluating performance across optimization algorithms on many problems presents a complex challenge due to the diversity of numerical scales involved. Traditional data processing methods, such as hypothesis testing and Bayesian inference,…
Reasoning is a fundamentally algorithmic task. Yet current work on LLM-based reasoning relies on free-form generation whose theoretical guarantees (soundness, completeness, complexity, optimality) remain poorly understood. We argue that we…
A theoretical development is carried to establish fundamental results about rank-initial embeddings and automorphisms of countable non-standard models of set theory, with a keen eye for their sets of fixed points. These results are then…
We study the online preemptive scheduling of intervals and jobs (with restarts). Each interval or job has an arrival time, a deadline, a length and a weight. The objective is to maximize the total weight of completed intervals or jobs.…