Growth series of CAT(0) cubical complexes

Let $X$ be a CAT(0) cubical complex. The growth series of $X$ at $x$ is $G_{x}(t)=\sum_{y \in Vert(X)} t^{d(x,y)}$, where $d(x,y)$ denotes $\ell_{1}$-distance between $x$ and $y$. If $X$ is cocompact, then $G_{x}$ is a rational function of $t$. In the case when $X$ is the Davis complex of a right-angled Coxeter group it is a well-known that $G_{x}(t)=1/f_{L}(-t/(1+t))$, where $f_{L}$ denotes the $f$-polynomial of the link $L$ of a vertex of $X$. We obtain a similar formula for general cocompact $X$. We also obtain a simple relation between the growth series of individual orbits and the $f$-polynomials of various links. In particular, we get a simple proof of reciprocity of these series ($G_{x}(t)=\pm G_{x}(t^{-1})$) for an Eulerian manifold $X$.Comment: 8 page

Automatic generation of large-scale paraphrases

Research on paraphrase has mostly focussed on lexical or syntactic variation within individual sentences. Our concern is with larger-scale paraphrases, from multiple sentences or paragraphs to entire documents. In this paper we address the problem of generating paraphrases of large chunks of texts. We ground our discussion through a worked example of extending an existing NLG system to accept as input a source text, and to generate a range of fluent semantically-equivalent alternatives, varying not only at the lexical and syntactic levels, but also in document structure and layout

Intuitive querying of e-Health data repositories

At the centre of the Clinical e-Science Framework (CLEF) project is a repository of well organised, detailed clinical histories, encoded as data that will be available for use in clinical care and in-silico medical experiments. An integral part of the CLEF workbench is a tool to allow biomedical researchers and clinicians to query – in an intuitive way – the repository of patient data. This paper describes the CLEF query editing interface, which makes use of natural language generation techniques in order to alleviate some of the problems generally faced by natural language and graphical query interfaces. The query interface also incorporates an answer renderer that dynamically generates responses in both natural language text and graphics

Designing a resource-efficient data structure for mobile data systems

Designing data structures for use in mobile devices requires attention on optimising data volumes with associated benefits for data transmission, storage space and battery use. For semi-structured data, tree summarisation techniques can be used to reduce the volume of structured elements while dictionary compression can efficiently deal with value-based predicates. This project seeks to investigate and evaluate an integration of the two approaches. The key strength of this technique is that both structural and value predicates could be resolved within one graph while further allowing for compression of the resulting data structure. As the current trend is towards the requirement for working with larger semi-structured data sets this work would allow for the utilisation of much larger data sets whilst reducing requirements on bandwidth and minimising the memory necessary both for the storage and querying of the data

CONTROL IN A DYNAMIC ECONOMY: MODELING THE BEHAVIOR OF THE CHINESE VILLAGE LEADER

Village leaders in the Chinese reform economy are assumed to maximize a multiple-attribute utility function; their behavior is modeled in a dynamic control framework. Using village data, structural and control equations for industrial output, grain yields, capital, non-farm employment and hybrid rice are estimated. Results confirm hypotheses that village leaders are preoccupied with rural industrialization but are also concerned about maintaining high agricultural productivity to meet grain obligations.Institutional and Behavioral Economics, Productivity Analysis,

Eulerian cube complexes and reciprocity

Let $G$ be the fundamental group of a compact nonpositively curved cube complex $Y$. With respect to a basepoint $x$, one obtains an integer-valued length function on $G$ by counting the number of edges in a minimal length edge-path representing each group element. The growth series of $G$ with respect to $x$ is then defined to be the power series $G_x(t)=\sum_g t^{|g|}$ where $|g|$ denotes the length of $g$. Using the fact that $G$ admits a suitable automatic structure, $G_x(t)$ can be shown to be a rational function. We prove that if $Y$ is a manifold of dimension $n$, then this rational function satisfies the reciprocity formula $G_x(t^{-1})=(-1)^n G_x(t)$. We prove the formula in a more general setting, replacing the group with the fundamental groupoid, replacing the growth series with the characteristic series for a suitable regular language, and only assuming $Y$ is Eulerian.Comment: Minor corrections. To appear in Algebraic and Geometric Topolog