Related papers: Well-Orderedness of the Bashicu Matrix System
We present a Bounded Model Checking technique for higher-order programs. The vehicle of our study is a higher-order calculus with general references. Our technique is a symbolic state syntactical translation based on SMT solvers, adapted to…
As recommendation is essentially a comparative (or ranking) process, a good explanation should illustrate to users why an item is believed to be better than another, i.e., comparative explanations about the recommended items. Ideally, after…
We prove that every ordinal $\alpha<\omega_2$ is the order type of a certain system of uniform Borel sets in the sense of a well-ordering relation defined by Petr Novikov. This result gives a positive answer to a problem posed by Nicolas…
A scoring system is a linear classifier composed of a small number of explanatory variables, each assigned a small integer coefficient. This system is highly interpretable and allows predictions to be made with simple manual calculations…
Product formula methods, particularly the second-order Suzuki decomposition, are an important tool for simulating quantum dynamics on quantum computers due to their simplicity and unitarity preservation. While higher-order schemes have been…
Ranking is used for a wide array of problems, most notably information retrieval (search). There are a number of popular approaches to the evaluation of ranking such as Kendall's $\tau$, Average Precision, and nDCG. When dealing with…
A simple recursive scheme for parameterisation of n-by-n unitary matrices is presented.
A generate and test algorithm is described which parses a surface form into one or more lexical entries using linearly ordered phonological rules. This algorithm avoids the exponential expansion of search space which a naive parsing…
Completing a data matrix X has become an ubiquitous problem in modern data science, with applications in recommender systems, computer vision, and networks inference, to name a few. One typical assumption is that X is low-rank. A more…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
This paper is concerned with the automated complexity analysis of term rewrite systems (TRSs for short) and the ramification of these in implicit computational complexity theory (ICC for short). We introduce a novel path order with multiset…
Given some binary matrix $M$, suppose we are presented with the collection of its rows and columns in independent arbitrary orderings. From this information, are we able to recover the unique original orderings and matrix? We present an…
Fast Paxos is an algorithm for consensus that works by a succession of rounds, where each round tries to decide a value $v$ that is consistent with all past rounds. Rounds are started by a coordinator process and consistency is guaranteed…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…
An ordinal classification (OC) problem corresponds to a special type of classification characterised by the presence of a natural order relationship among the classes. This type of problem can be found in a number of real-world…
A ranking is an ordered sequence of items, in which an item with higher ranking score is more preferred than the items with lower ranking scores. In many information systems, rankings are widely used to represent the preferences over a set…
The paper "Sorting with Bialgebras and Distributive Laws" by Hinze et al. uses the framework of bialgebraic semantics to define sorting algorithms. From distributive laws between functors they construct pairs of sorting algorithms using…
We consider overdetermined systems of difference equations for a single function $u$ which are consistent, and propose a general framework for their analysis. The integrability of such systems is defined as the existence of higher order…
We consider the groups of regular circulant matrices over finite fields and integer residue class rings. In both cases we present a formula for the order of these groups. We also make a first step towards finding the algebraic structure of…
Japan is a unique country with a distinct cultural heritage, which is reflected in billions of historical documents that have been preserved. However, the change in Japanese writing system in 1900 made these documents inaccessible for the…