Related papers: Transduction of Automatic Sequences and Applicatio…
I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a…
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…
Tensor networks (TNs) have been gaining interest as multiway data analysis tools owing to their ability to tackle the curse of dimensionality and to represent tensors as smaller-scale interconnections of their intrinsic features. However,…
In this case study in ``fully automated enumeration'', we illustrate how to take full advantage of symbolic computation by developing (what we call) `symbolic-dynamical-programming' algorithms for computing many terms of `hard to compute…
We introduce generalizations of powers and factor complexity via orbits of group actions. These generalizations include concepts like abelian powers and abelian complexity. It is shown that this notion of factor complexity cannot be used to…
This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…
Existence of long arithmetic progression in sumsets and subset sums has been studied extensively in the field of additive combinatorics. These additive combinatorics results play a central role in the recent progress of fundamental problems…
Optimizing over the cone of nonnegative polynomials, and its dual counterpart, optimizing over the space of moments that admit a representing measure, are fundamental problems that appear in many different applications from engineering and…
We consider finite iterated generalized harmonic sums weighted by the binomial $\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator…
For a fixed integer N, and fixed numbers b_1,...,b_N, we consider sequences, the nth term (a_n) of which is the sum of the squares of the terms in the expansion of (b_1 + ... + b_N)^n. In the case all b_i=1, we give a formula for a…
For a hypergeometric series $\sum_k f(k,a, b, ...,c)$ with parameters $a, b, >...,c$, Paule has found a variation of Zeilberger's algorithm to establish recurrence relations involving shifts on the parameters. We consider a more general…
Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…
Source code summarizing is a task of writing short, natural language descriptions of source code behavior during run time. Such summaries are extremely useful for software development and maintenance but are expensive to manually…
Pre-trained language model representations have been successful in a wide range of language understanding tasks. In this paper, we examine different strategies to integrate pre-trained representations into sequence to sequence models and…
In recent years, Z.-W. Sun proposed several sophisticated conjectures on congruences for finite sums with terms involving combinatorial sequences such as central trinomial coefficients, Domb numbers and Franel numbers. These sums are double…
The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful…
We present a new approach to enhancing Answer Set Programming (ASP) with Constraint Processing techniques which allows for solving interesting Constraint Satisfaction Problems in ASP. We show how constraints on finite domains can be…
We introduce Trans-gram, a simple and computationally-efficient method to simultaneously learn and align wordembeddings for a variety of languages, using only monolingual data and a smaller set of sentence-aligned data. We use our new…
Sequence-to-sequence (s2s) models are the basis for extensive work in natural language processing. However, some applications, such as multi-document summarization, multi-modal machine translation, and the automatic post-editing of machine…
A lot of the recent success in natural language processing (NLP) has been driven by distributed vector representations of words trained on large amounts of text in an unsupervised manner. These representations are typically used as general…