Related papers: The monoids of the patience sorting algorithm
We analyze the set of increasingly enumerable additive submonoids of R, for instance, the set of logarithms of the positive integers with respect to a given base. We call them $\omega$-monoids. The $\omega$-monoids for which consecutive…
We study a class of polynomial optimization problems with a robust polynomial matrix inequality (PMI) constraint where the uncertainty set itself is defined also by a PMI. These can be viewed as matrix generalizations of semi-infinite…
We generalize the Robinson-Schensted-Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to new enumerative results that have representation theoretic interpretations as decompositions of centralizer…
Monoids generated by elements of order two appear in numerous places in the literature. For example, Coxeter reflection groups in geometry, Kuratowski monoids in topology, various monoids generated by regular operations in language theory…
Sentence embedding is essential for many NLP tasks, with contrastive learning methods achieving strong performance using annotated datasets like NLI. Yet, the reliance on manual labels limits scalability. Recent studies leverage large…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
Combining the representations of the words that make up a sentence into a cohesive whole is difficult, since it needs to account for the order of words, and to establish how the words present relate to each other. The solution we propose…
Natural language is hierarchically structured: smaller units (e.g., phrases) are nested within larger units (e.g., clauses). When a larger constituent ends, all of the smaller constituents that are nested within it must also be closed.…
Conventional multi-label recognition methods often focus on label confidence, frequently overlooking the pivotal role of partial order relations consistent with human preference. To resolve these issues, we introduce a novel method for…
This paper introduces a new comparison base stable sorting algorithm, named RS sort. RS Sort involves only the comparison of pair of elements in an array which ultimately sorts the array and does not involve the comparison of each element…
Preference learning has become the foundation of aligning Large Language Models (LLMs) with human intent. Popular methods, such as Direct Preference Optimization (DPO), minimize surrogate losses as proxies for the intractable pairwise…
Multinomial processing tree (MPT) models are tools for disentangling the contributions of latent cognitive processes in a given experimental paradigm. The present note analyzes MPT models subject to order constraints on subsets of its…
We introduce a new approach for designing Random-order Contention Resolution Schemes (RCRS) via exact solution in continuous time. Given a function $c(y):[0,1] \rightarrow [0,1]$, we show how to select each element which arrives at time $y…
Learning to Rank has traditionally considered settings where given the relevance information of objects, the desired order in which to rank the objects is clear. However, with today's large variety of users and layouts this is not always…
This paper presents a deterministic, strongly polynomial time algorithm for computing the matrix rank for a class of symbolic matrices (whose entries are polynomials over a field). This class was introduced, in a different language, by…
An algorithm is presented for unranking permutations in transposition order: Given a seed s\in N, the algorithm produces a permutation P(s) that differs from the permutation P(s+1) by the transposition of two elements.
We study the class of monoids that arise as the submonoid of right units of finitely presented special inverse monoids (SIMs). Gray and Ru\v{s}kuc (2024) gave the first example of a finitely presented SIM whose submonoid of right units does…
The compressed word problem for a finitely generated monoid M asks whether two given compressed words over the generators of M represent the same element of M. For string compression, straight-line programs, i.e., context-free grammars that…
Polynomial closure is a standard operator which is applied to a class of regular languages. In the paper, we investigate three restrictions called left (LPol), right (RPol) and mixed polynomial closure (MPol). The first two were known while…
In recent years, saliency ranking has emerged as a challenging task focusing on assessing the degree of saliency at instance-level. Being subjective, even humans struggle to identify the precise order of all salient instances. Previous…