Growth of positive words and lower bounds of the growth rate for Thompson's group (F)p

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Computational explorations in Thompson's group F

Here we describe the results of some computational explorations in Thompson's group F. We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult question whether or not Thompson's group is amenable. We also describe experiments to estimate the exponential growth rate of F and the rate of escape of symmetric random walks with respect to the standard generating set.

Combinatorial and metric properties of Thompson's group T

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T.

External sources of innovation and industry-university interaction:evidence from Spanish firms

This paper is about the firm innovation process and the cooperation of the innovative firms with other firms and public institutions. A special attention is paid to the cooperation with universities. We use the Technological Innovation Survey (TIS) from the Instituto Nacional de Estadística (Spain) in order to obtain data for 4,159 innovative firms. Our results show that firm's cooperation activities are closely linked to the characteristics of the industry and the firm as well as to the origin of public funds for R&D activities. Key words: Innovation, universities, Spanish economy. JEL code: O31, I20, L60

A note on Spatial Autocorrelation at a Local Level

In this paper we analyze the existence of spatial autocorrelation at a local level in Catalonia using variables such as urbanisation economies, population density, human capital and firm entries. From a static approach, our results show that spatial autocorrelation is weak and diminishes as the distance between municipalities increases. From a dynamic approach, however, spatial autocorrelation increased over the period we analysed. These results are important from a policy point of view, since it is essential to know how economic activities are spatially concentrated or disseminated. Key words: spatial autocorrelation, municipalities. JEL classification: R110, R120

Entradas y salidas de empresas: un contraste de las hipótesis de independencia, simetría y simultaneidad

En este trabajo se analiza una vía alternativa en el debate de la convergencia regional en España: el estudio de la dinámica industrial de sus Comunidades Autónomas. Para ello se analizan los flujos de entrada y salida de establecimientos industriales en las manufacturas delas regiones españolas y se abordan los factores de carácter sectorial o regional que inciden sobre la movilidad industrial. Las specificaciones econométricas adoptan la estructura de un sistema de ecuaciones y cubren las tres hipótesis fundamentales que se han abordado en laliteratura (independencia, simetría y simultaneidad) a partir de un panel de datos construido con informaciones procedentes del Registro de Establecimientos Industriales y la Encuesta Industrial. Palabras clave: demografía industrial, sistemas de ecuaciones, datos de panel

Firm Size and Geographical Aggregation: An Empirical Appraisal in Industrial Location

This paper assesses empirically the importance of size discrimination and disaggregate data for deciding where to locate a start-up concern. We compare three econometric specifications using Catalan data: a multinomial logit with 4 and 41 alternatives (provinces and comarques, respectively) in which firm size is the main covariate; a conditional logit with 4 and 41 alternatives including attributes of the sites as well as size-site interactions; and a Poisson model on the comarques and the full spatial choice set (942 municipalities) with site-specific variables. Our results suggest that if these two issues are ignored, conclusions may be misleading. We provide evidence that large and small firms behave differently and conclude that Catalan firms tend to choose between comarques rather than between municipalities. Moreover, labour-intensive firms seem more likely to be located in the city of Barcelona. Keywords: Catalonia, industrial location, multinomial response model. JEL: C250, E30, R00, R12

The Determinants of Entry are not Independent of Start-up Size: Some evidence from Spanish manufacturing

In this paper we explore the determinants of firm start-up size of Spanish manufacturing industries. The industries' barriers to entry affect the ability of potential entrants to enter the markets and the size range at which they decide to enter. In order to examine the relationships between barriers to entry and size we applied the quantile regression techniques. Our results indicate that the variables that characterize the structure of the market, the variables that are related to the behaviour of the incumbent firms and the rate of growth of the industries generate different barriers depending on the initial size of the entrants. Keywords: Entry, regression quantiles, start-up size. JEL classification: L110, L600

A territorial approach to firm entry: The effect of city size

This paper concerns the effects of territorial factors on the processes involved in the creation of manufacturing firms in Spanish cities. Most contributions have focused on regional factors rather than urban ones. Here we assume that it is possible to identify certain urban factors that attract new firms. We use data for the entry of firms in Spanish manufacturing industries between 1994 and 2002. This paper contributes to the existing literature on market entry. Key words: cities, regions, firm entry and Spanish economy. JEL: R0, R12, L60

Pure braid subgroups of braided Thompson's groups

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Absolute type shaft encoding using LFSR

Maximal-length binary sequences have been known for a long time. They have many interesting properties, one of them is that when taken in blocks of n consecutive positions they form 2ⁿ-1 different codes in a closed circular sequence. This property can be used for measuring absolute angular positions as the circle can be divided in as many parts as different codes can be retrieved. This paper describes how can a closed binary sequence with arbitrary length be effectively designed with the minimal possible block-length, using linear feedback shift registers (LFSR). Such sequences can be used for measuring a specified exact number of angular positions, using the minimal possible number of sensors that linear methods allow.