Related papers: Rational reductions for holonomic sequences

A set $R\subset \mathbb{N}$ is called rational if it is well-approximable by finite unions of arithmetic progressions. Examples of rational sets include many classical sets of number-theoretical origin such as the set of squarefree numbers,…

In this paper, given a simple linear recurrence sequence of algebraic numbers, which has either a dominant characteristic root or exactly two characteristic roots of maximal modulus, we give some explicit lower bounds for the index beyond…

Human-annotated textual explanations are becoming increasingly important in Explainable Natural Language Processing. Rationale extraction aims to provide faithful (i.e., reflective of the behavior of the model) and plausible (i.e.,…

In reference [8] we have considered a wide class of "well-behaved" reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degree-structures induced by good…

We identify the group of homomorphisms $\operatorname{Hom}_{\mathcal{GF}}(F,\mathbf{RU}_{\mathbb Q})$ in the category of ($\operatorname{fin}$)-global functors to the rationalization of the unitary representation ring functor and deduce…

Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…

The aim of this work is to describe the equivalence relations in $\Q/\Z$ that arise as the rational lamination of polynomials with all cycles repelling. We also describe where in parameter space one can find a polynomial with all cycles…

Consider the representation of a rational number in the form, associated with "centered" Euclidean algorithm. We prove a new formula for the limit distribution function for sequences of rationals with bounded sum of partial quotients.

In 2012 Chen and Singer introduced the notion of discrete residues for rational functions as a complete obstruction to rational summability. More explicitly, for a given rational function f(x), there exists a rational function g(x) such…

It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the…

First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…

Let the formal power series f in d variables with coefficients in an arbitrary field be a symmetric function decomposed as a series of Schur functions, and let f be a rational function whose denominator is a product of binomials of the form…

Nominal logic is a variant of first-order logic that provides support for reasoning about bound names in abstract syntax. A key feature of nominal logic is the new-quantifier, which quantifies over fresh names (names not appearing in any…

We prove that linearizing certain families of polynomial optimization problems leads to new functorial operations in real convex sets. We show that under some conditions these operations can be computed or approximated in ways amenable to…

We present a partial proof of van Hoeij-Abramov conjecture about the algorithmic possibility of computation of finite sums of rational functions. The theoretical results proved in this paper provide an algorithm for computation of a large…

We show that if $\mathcal{F}$ is any "well-behaved" subset of the Borel functions and we assume the Axiom of Determinacy then the hierarchy of degrees on $\pow(\mathbb{R})$ induced by $\mathcal{F}$ turns out to look like the Wadge hierarchy…

Let $f_{1}, \ldots, f_{k}$ be polynomials defining an algebraic set in affine $n$-space over a finite field. Suppose $k>n$. We prove that there exists a system of polynomials $g_{1}, \ldots, g_{n}$, each being a linear combination with…

We present SummaRuNNer, a Recurrent Neural Network (RNN) based sequence model for extractive summarization of documents and show that it achieves performance better than or comparable to state-of-the-art. Our model has the additional…

Let $R$ be a commutative unital ring, $a\in R$ and $t$ a positive integer. $a^{t}$-reduced $R$-modules and universally $a^{t}$-reduced $R$-modules are defined and their properties given. Known (resp. new) results about reduced $R$-modules…

We show that if a Laurent series $f\in\mathbb{C}((t))$ satisfies a particular kind of linear iterative equation, then $f$ is either a rational function or it is differentially transcendental over $\mathbb{C}(t)$. This condition is more…