A new definition of mixing and segregation: Three dimensions of a key process variable

Although a number of definitions of mixing have been proposed in the literature, no single definition accurately and clearly describes the full range of problems in the field of industrial mixing. An alternate approach is proposed which defines segregation as being composed of three separate dimensions. The first dimension is the intensity of segregation quantified by the normalized concentration variance (CoV); the second dimension is the scale of segregation or clustering; and the last dimension is the exposure or the potential to reduce segregation. The first dimension focuses on the instantaneous concentration variance; the second on the instantaneous length scales in the mixing field; and the third on the driving force for change, i.e. the mixing time scale, or the instantaneous rate of reduction in segregation. With these three dimensions in hand, it is possible to speak more clearly about what is meant by the control of segregation in industrial mixing processes. In this paper, the three dimensions of segregation are presented and defined in the context of previous definitions of mixing, and then applied to a range of industrial mixing problems to test their accuracy and robustness

Long Memory and Volatility Clustering: is the empirical evidence consistent across stock markets?

Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter alia. One advantage of these models is their ability to capture nonlinear dynamics. Another interesting manner to study the volatility phenomena is by using measures based on the concept of entropy. In this paper we investigate the long memory and volatility clustering for the SP 500, NASDAQ 100 and Stoxx 50 indexes in order to compare the US and European Markets. Additionally, we compare the results from conditionally heteroscedastic models with those from the entropy measures. In the latter, we examine Shannon entropy, Renyi entropy and Tsallis entropy. The results corroborate the previous evidence of nonlinear dynamics in the time series considered.Comment: 8 pages; 2 figures; paper presented in APFA 6 conferenc

A class of spatial econometric methods in the empirical analysis of clusters of firms in the space

In this paper we aim at identifying stylized facts in order to suggest adequate models of spatial co–agglomeration of industries. We describe a class of spatial statistical methods to be used in the empirical analysis of spatial clusters. Compared to previous contributions using point pattern methods, the main innovation of the present paper is to consider clustering for bivariate (rather than univariate) distributions, which allows uncovering co–agglomeration and repulsion phenomena between the different industrial sectors. Furthermore we present the results of an empirical application of such methods to a set of European Patent Office (EPO) data and we produce a series of empirical evidences referred to the the pair–wise intra–sectoral spatial distribution of patents in Italy in the nineties. In this analysis we are able to identify some distinctive joint patterns of location between patents of different sectors and to propose some possible economic interpretations

Ultrametric embedding: application to data fingerprinting and to fast data clustering

We begin with pervasive ultrametricity due to high dimensionality and/or spatial sparsity. How extent or degree of ultrametricity can be quantified leads us to the discussion of varied practical cases when ultrametricity can be partially or locally present in data. We show how the ultrametricity can be assessed in text or document collections, and in time series signals. An aspect of importance here is that to draw benefit from this perspective the data may need to be recoded. Such data recoding can also be powerful in proximity searching, as we will show, where the data is embedded globally and not locally in an ultrametric space.Comment: 14 pages, 1 figure. New content and modified title compared to the 19 May 2006 versio

Testing for Localisation Using Micro-Geographic Data

To study the detailed location patterns of industries, and particularly the tendency for industries to cluster relative to overallmanufacturing, we develop distance-based tests of localisation. In contrast to previous studies, our approach allows us to assess the statistical significance of departures from randomness. In addition, we treat space as continuous instead of using an arbitrary collection of geographical units. This avoids problems relating to scale and borders. We apply these tests to an exhaustive UK data set. For four-digit industries, we find that (i) only 51% of them are localised at a 5% confidence level, (ii) localisation takes place mostly at small scales below 50 kilometres, (iii) the degree of localisation is very skewed, and (iv) industries follow broad sectoral patterns with respect to localisation. Depending on the industry, smaller establishments can be the main drivers of both localisation and dispersion. Three-digit sectors show similar patterns of localisation at small scales as well as a tendency to localise at medium scales.localisation, clusters, K-density, spatial statistics