相关论文: Let's reinvent subtraction

On a manifold or a closed subset of a Euclidean vector space, a retraction enables to move in the direction of a tangent vector while staying on the set. Retractions are a versatile tool to perform computational tasks such as optimization,…

We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…

In this paper, we use a new method to prove cut-elimination of weak intuitionistic tense logic. This method focuses on splitting the contraction rule and cut rules. Further general theories and applications of this method shall be developed…

We survey current term-wise techniques for quadratizing high-degree pseudo-Boolean functions and introduce a new one, which allows multiple splits of terms. We also introduce the first aggregative approach, which splits a collection of…

Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…

In this paper we present a general method for information extraction that exploits the features of data compression techniques. We first define and focus our attention on the so-called "dictionary" of a sequence. Dictionaries are…

An important task in NLP applications such as sentence simplification is the ability to take a long, complex sentence and split it into shorter sentences, rephrasing as necessary. We introduce a novel dataset and a new model for this `split…

Subtraction games is a class of combinatorial games. It was solved since the Sprague-Grundy Theory was put forward. This paper described a new algorithm for subtraction games. The new algorithm can find win or lost positions in subtraction…

Methods for generating new distributions from old can be thought of as techniques for simplifying integrals used in reverse. Hence integrating a probability density function (pdf) by parts provides a new way of modifying distributions; the…

A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…

Colimits are a fundamental construction in category theory. They provide a way to construct new objects by gluing together existing objects that are related in some way. We introduce a complementary notion of anticolimits, which provide a…

We present a new and powerful algebraic framework for graph rewriting, based on drags, a class of graphs enjoying a novel composition operator. Graphs are embellished with roots and sprouts, which can be wired together to form edges. Drags…

We describe a novel technique and implemented system for constructing a subcategorization dictionary from textual corpora. Each dictionary entry encodes the relative frequency of occurrence of a comprehensive set of subcategorization…

Amongst the best means to summarize is highlighting. In this paper, we aim to generate summary highlights to be overlaid on the original documents to make it easier for readers to sift through a large amount of text. The method allows…

A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.

We unify and extend previous bijections on plane quadrangulations to bipartite and quasibipartite plane maps. Starting from a bipartite plane map with a distinguished edge and two distinguished corners (in the same face or in two different…

Deduction systems and graph rewriting systems are compared within a common categorical framework. This leads to an improved deduction method in diagrammatic logics.

The use of terms from natural and social scientific titles and abstracts is studied from the perspective of sublanguages and their specialized dictionaries. Different notions of sublanguage distinctiveness are explored. Objective methods…

In this paper we provide insight into the classes of strongly subadditive/superadditive functions by highlighting numerous new examples and new results.

Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…