Fast Fourier Transforms for the Rook Monoid

We define the notion of the Fourier transform for the rook monoid (also called the symmetric inverse semigroup) and provide two efficient divide-and-conquer algorithms (fast Fourier transforms, or FFTs) for computing it. This paper marks the first extension of group FFTs to non-group semigroups

Moving up and moving down: a new way of examining country growth dynamics

"Do the countries which grow share the same features as those which decline? How can some countries achieve such long-term sustainable growth while others fail so badly? This paper builds on the emerging literature on growth asymmetries by examining movement across income categories in the World Development Reports over a significant period of time. The results confirm the existence of asymmetries and find that the factors which are correlated with movement upwards or downwards are markedly different. Evidence is presented which suggests that growth episodes share some common features while economic collapse may occur for a broader range of reasons." Authors' Abstracteconomic growth, income growth, Growth dynamics, Growth asymmetries, trade, Economic policy, Conflict, Institutions, Geography,

Evaluating prose style transfer with the Bible

In the prose style transfer task a system, provided with text input and a target prose style, produces output which preserves the meaning of the input text but alters the style. These systems require parallel data for evaluation of results and usually make use of parallel data for training. Currently, there are few publicly available corpora for this task. In this work, we identify a high-quality source of aligned, stylistically distinct text in different versions of the Bible. We provide a standardized split, into training, development and testing data, of the public domain versions in our corpus. This corpus is highly parallel since many Bible versions are included. Sentences are aligned due to the presence of chapter and verse numbers within all versions of the text. In addition to the corpus, we present the results, as measured by the BLEU and PINC metrics, of several models trained on our data which can serve as baselines for future research. While we present these data as a style transfer corpus, we believe that it is of unmatched quality and may be useful for other natural language tasks as well

Separation of Variables and the Computation of Fourier Transforms on Finite Groups, II

We present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite group. By extending work which connects Bratteli diagrams to the construction of Fast Fourier Transform algorithms %\cite{sovi}, we make explicit use of the path algebra connection to the construction of Gel'fand-Tsetlin bases and work in the setting of quivers. We relate this framework to the construction of a {\em configuration space} derived from a Bratteli diagram. In this setting the complexity of an algorithm for computing a Fourier transform reduces to the calculation of the dimension of the associated configuration space. Our methods give improved upper bounds for computing the Fourier transform for the general linear groups over finite fields, the classical Weyl groups, and homogeneous spaces of finite groups, while also recovering the best known algorithms for the symmetric group and compact Lie groups.Comment: 53 pages, 5 appendices, 34 figure