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In this paper, an exploratory hierarchical method to classify variables is introduced as an alternative to principal component analysis when dealing with stock-exchange price time-series. The method is based on a particular principal component analysis applied to pairs of variables, each one associated to a group to be merged. Applied to time-series, this method reveals advantageous, since it helps in defining the number of groups and their composition, while providing a factorial structure of both the hierarchy’s nodes and the partition groups. Moreover, all the issued factors, which are weighted sums of the original variables forming the groups, result in easily interpretable representative variables of them. As a case study, the method is applied to a set of Brazilian financial stock price time-series, providing representative series for each of the five groups of the proposed partition. This result complements the information on the data set provided by principal component analysis, limited to the usual orthogonal factors, each one representing an independent source of variation. It is likely that the use of such classification method may help both in deepening the knowledge of a market structure and the modelling of the different time-series, based on the modelling of their representative one.

Aim: To identify functional traits that best predict community assembly without knowing the underlying environmental drivers. Methods: We propose a new method based on the correlation r(XY) between two matrices of potential community composition: the matrix X is fuzzy-weighted by trait similarities of species, and the matrix Y is derived by Beals smoothing using the probabilities of species co-occurrences. Since X is based on one or more traits, r(XY) measures how well the traits used for fuzzy-weighting reflect the species co-occurrence patterns in Y. We developed an optimisation algorithm to identify the traits maximising this correlation, together with an appropriate permutational test for significance. Using metacommunity data generated by a stochastic, individual-based, spatially explicit model, we assessed the type I error and the power of our method across different simulation scenarios, varying environmental filtering parameters, number of traits and trait correlation structures. Then, we applied the method to real-world community and trait data of dry calcareous grassland communities across Germany to identify, out of 49 traits, the combination of traits that maximised r(XY). Results: The method correctly identified the relevant traits involved in the assembly mechanisms of simulated communities, showing high power and accurate type I error. It proved to be robust against confounding aspects related to interactions between environmental factors, strength of limiting factors, and trait collinearity. In the grassland dataset, the method identified five traits that best explained community assembly. These traits reflect the size and the leaf economics spectrum, which are related to succession and resource supply, factors that may not be always measured in real-world situations. Conclusions: Our method successfully identified the relevant traits mediating community assembly, therefore providing insights on the underlying environmental and biotic factors, even if these are hidden, unmeasured or not accessible at the spatial or temporal scale of the study.

AimTo identify functional traits that best predict community assembly without knowing the driving environmental factors.MethodsWe propose a new method that is based on the correlation r(XY) between two matrices of potential community composition: matrix X is fuzzy-weighted by trait similarities of species, and matrix Y is derived by Beals smoothing using the probabilities of species co-occurrences. Since matrix X is based on one or more traits, r(XY) measures how well the traits used for fuzzy-weighting reflect the observed co-occurrence patterns. We developed an optimization algorithm that identifies those traits that maximize this correlation, together with an appropriate permutational test for significance. Using metacommunity data generated by a stochastic, individual-based, spatially explicit model, we assessed the type I error and the power of our method across different simulation scenarios, varying environmental filtering parameters, number of traits and trait correlation structures. We then applied the method to real-world community and trait data of dry calcareous grassland communities across Germany to identify, out of 49 traits, the combination of traits that maximizes r(XY).ResultsThe method correctly identified the relevant traits involved in the community assembly mechanisms specified in simulations. It had high power and accurate type I error and was robust against confounding aspects related to interactions between environmental factors, strength of limiting factors, and correlation among traits. In the grassland dataset, the method identified five traits that best explained community assembly. These traits reflected the size and the leaf economics spectrum, which are related to succession and resource supply, factors that may not be always measured in real-world situations.ConclusionsOur method successfully identified the relevant traits mediating community assembly driven by environmental factors which may be hidden for not being measured or accessible at the spatial or temporal scale of the study.

RESUMO A Política Nacional de Resíduos Sólidos (pnrs) brasileira assigna aos municípios brasileiros a responsabilidade pela prestação dos serviços de limpeza urbana e a gestão de resíduos, no entanto, as pesquisas destacam as dificuldades, por parte dos próprios municípios, em adotar uma política que cumpra as obrigações da lei antes mencionada. O presente artigo explora o problema de partir das correspondências entre o próprio ambiente institucional municipal (os principais fatores socioeconômicos, políticos e culturais) e a gestão municipal dos resíduos (especificamente, a presença de um Plano de Gestão Integrada de Resíduos Sólidos). Depois de uma breve introdução ao tema, o texto apresenta uma análise descritiva da difusão dos Planos nas microrregiões do Rio Grande do Sul, a continuação, o artigo apresenta uma análise de correspondências múltiplas que proporciona de forma exploratória um quadro geral da gestão municipal de resíduos em seu ambiente institucional. ABSTRACT The National Solid Waste Policy (Política Nacional de Resíduos Sólidos, pnrs) assigns Brazilian municipalities the responsibility of providing urban cleaning and waste management services; however, scholars report the difficulty of municipalities in adopting a policy that meets the obligations of the aforementioned law. This article explores the correspondences between the municipal institutional environment itself (the main socioeconomic, political and cultural factors) and municipal waste management (specifically, the presence of an Integrated Solid Waste Management Plan). After a brief introduction to the issue, this paper shows a descriptive analysis of the presence of these plans in the mesoregions of Rio Grande do Sul. The article then presents a multiple correspondence analysis that provides an exploratory overview of municipal waste management in its institutional environment.

In this paper we propose an exploratory methodology, devoted to classify the pixels of a Digital Elevation Model (DEM), to be used as a morphometric basis for studies in other frameworks. The aim is to classify the terrain units according to eight topographical local gradients, computed as differences between each pixel and the eight surrounding ones. A partition of the pixels into homogeneous classes is carried out, emphasizing different details of the terrain units characteristics. Each class is described by a complete set of statistics of terrain attributes, including elevation, slope, and aspect, and graphical tools are used to ease the understanding of the partition. In addition, appropriate colours are attributed to each class, in order to build a thematic map that may simulate a three-dimensional effect. They are defined by computing their hue and saturation according to each class mean slope and aspect, respectively. Applications to Mount Soratte (Italy) and Cephalonia island (Greece) show how the results may be successfully used to describe in different ways the morphometric structure of the terrain under study and provide appropriate graphical representations.

The geomorphometric classifications of three groups of volcanoes situated in the Andes Cordillera, Central America, and Mexico are performed and compared. Input data are eight local topographic gradients (i.e. elevation differences) obtained by processing each volcano raster ASTER-GDEM data. The pixels of each volcano DEM have been classified into 17 classes through a K-means clustering procedure following principal component analysis of the gradients. The spatial distribution of the classes, representing homogeneous terrain units, is shown on thematic colour maps, where colours are assigned according to mean slope and aspect class values. The interpretation of the geomorphometric classification of the volcanoes is based on the statistics of both gradients and morphometric parameters (slope, aspect and elevation). The latter were used for a comparison of the volcanoes, performed through classes' slope/aspect scatterplots and multidimensional methods. In this paper, we apply the mentioned methodology on 21 volcanoes, randomly chosen from Mexico to Patagonia, to show how it may contribute to detect geomorphological similarities and differences among them. As such, both its descriptive and graphical abilities may be a useful complement to future volcanological studies.

The authors introduce colleagues and friends from Africa and South America who collaborate with them in programs of international cooperation for teaching and research. They then chat with them about the problems and the perspectives of mathematics in developing countries. The discussion centers on the main obstacles to improving mathematics in such countries: the need to train local students at the PhD level, as well as the necessity to motivate them to come back if they are trained abroad, and to allow them to continue to profit from ongoing international relations.

The identification of a reduced dimensional representation of the data is among the main issues of exploratory multidimensional data analysis and several solutions had been proposed in the literature according to the method. Principal Component Analysis (PCA) is the method that has received the largest attention thus far and several identification methods—the so-called stopping rules—have been proposed, giving very different results in practice, and some comparative study has been carried out. Some inconsistencies in the previous studies led us to try to fix the distinction between signal from noise in PCA—and its limits—and propose a new testing method. This consists in the production of simulated data according to a predefined eigenvalues structure, including zero-eigenvalues. From random populations built according to several such structures, reduced-size samples were extracted and to them different levels of random normal noise were added. This controlled introduction of noise allows a clear distinction between expected signal and noise, the latter relegated to the non-zero eigenvalues in the samples corresponding to zero ones in the population. With this new method, we tested the performance of ten different stopping rules. Of every method, for every structure and every noise, both power (the ability to correctly identify the expected dimension) and type-I error (the detection of a dimension composed only by noise) have been measured, by counting the relative frequencies in which the smallest non-zero eigenvalue in the population was recognized as signal in the samples and that in which the largest zero-eigenvalue was recognized as noise, respectively. This way, the behaviour of the examined methods is clear and their comparison/evaluation is possible. The reported results show that both the generalization of the Bartlett’s test by Rencher and the Bootstrap method by Pillar result much better than all others: both are accounted for reasonable power, decreasing with noise, and very good type-I error. Thus, more than the others, these methods deserve being adopted.

In this work, the reconstruction of the Burt's table, Greenacre (1988)'s Joint Correspondence Analysis (JCA), and Gower & Hand (1996)'s Extended Matching Coefficient (EMC) are compared to Multiple Correspondence Analysis (MCA) in order to check the quality of the methods. In particular, for the whole table, the ability is considered separately the diagonal, and the off-diagonal tables, that is the ability to describe either each character's distribution or the interaction between pairs of characters, or both. The theoretical aspects are discussed first, and finally the results obtained in an application are shown and discussed.

Aphasia is called the loss of some abilities related to language production and/or comprehension. In the framework of aphasia studies, the ability of the patient to recognize and correctly verbalize a set of images is verified through suitable tests. Since the images are supposed to be easily and unequivocally recognized and named by every person, tailoring images taken from the Snodgrass and Vanderwarts (1980) original test to the Brazilian reality is necessary. We faced the following two issues: the selection of images that are easily recognizable, and the estimate of an index measuring the primitivity of the corresponding word, that is how early in life a person heard the word. To this aim, two surveys have been carried out, where the images were proposed to non-aphasic judges. We report in this paper the results of the exploratory multidimensional analyses carried out to select both images and judges and to define the primitivity index.

For the study of El Nino phenomenon, winds data collected from the Equator belt of Pacific ocean would be analyzed through PCA. In this paper, the 2-dimensional nature of winds is discussed in respect to the possible ways in which PCA may be implemented. Among others, complex PCA is proposed and compared on a small example to other methods based on real PCA. Then, the first results on a larger data table are illustrated.

The article presents the main results of a survey on voting behavior at the State Participatory Budgeting of Rio Grande do Sul (also known as Consulta popular). The research is based on a sample of 389 respondents, all residents in San Borja, city in the western border of Rio Grande do Sul (Brazil). The article aims to address participation and vote in Consulta popular, considered its role of social inclusion and promotion of political participation. After a brief descriptive analysis, in order to get a better synthetic overview of the data, we submitted the considered characters to two different multidimensional analyses, in search of possible relations among them. The analyses performed were an exploratory one (a Multiple Correspondence Analysis, MCA) and a Generalized Linear Model by hypothesizing a Binomial distribution for the nominal data.

In order to assess the response of the radial growth of Pinus pinea L. to climatic variability in Central Italy, dendrochronological and dendroclimatological analyses were carried out on five different populations scattered along the Tyrrhenian coasts of the peninsula. The aim of this study is to contribute to the understanding of the ecological demands of this species, particularly in the study area. For each site total ring, early-, and late-wood width chronologies were developed. Multidimensional analyses were performed for the three tree-ring datasets in order to analyze the relations between sites chronologies. Both Principal Component Analyses and hierarchical classifications highlighted an important difference of one site in respect to the other, probably due to site characteristics. Correlation functions were performed to infer the main climatic factors controlling the radial growth of the species. For a comparative study, we limited our attention to the common interval 1926-2003 (78 years) in which the response of the tree-ring chronologies to climate at both local and regional scale was investigated. Positive moisture balance in the late spring-summer period of the year of growth is the climatic driver of P. pinea radial growth in the study area. Moreover, this study shows how low summer temperatures strongly favor the radial growth of the species. Fil: Piraino, Sergio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Mendoza. Instituto Argentino de Investigaciones de Zonas Aridas; Argentina Fil: Camiz, Sergio. Universita degli studi di Roma "Sapienza". Dipartimento di Matematica; Italia Fil: Di Filippo, Alfredo. Universita Degli Studi Della Tuscia. DendrologyLab; Italia Fil: Piovesan, Gianluca. Universita Degli Studi Della Tuscia. DendrologyLab; Italia Fil: Spada, Francesco. Universita degli studi di Roma "Sapienza". Dipartimento de biología ambientale; Italia

In this paper a three-step procedure is proposed to deal with ecological data, usually very complex in their treatment. The three steps – exploratory, confirmatory, and modelling phases – reflect the different methodological approaches necessary in each phase of the study. To illustrate the methodology, a case study is proposed, concerning the suitability of plants as pollution bioindicators. Samples of differently aged Pinus pinea L. needles were collected throughout 1 year in three different locations, whose human disturbance was known to be different. In the samples some morphological and functional parameters were measured, whose relation with the stress was already known. The exploratory analysis suggested pollution with human origin, the needle’s age, and the environmental conditions as the main factors of influence of damage. The confirmatory analysis confirmed both site and age as main factors and occasionally the sampling date. On this basis, some models were estimated separately for each site: models that best described the damage as function of age resulted non-linear and some of them with seasonal fluctuations. As a result, whereas the models described well enough the pollution temporal variation, the difference of pollution in the sites was best described by the different values of the models parameters in the different sites. In short, different pollution conditions are described better by the damage trend than by the individual measures. The three-step procedure resulted of high utility in outlining the most interesting relations to investigate through the modelling, the opportunity to model the indicators variation along time separately for each site, and to introduce the seasonal variation in some models.

The problem of the proper dimension of the solution of a Multiple Correspondence Analysis (MCA) is discussed, based on both the re-evaluation of the explained inertia sensu Benzecri (Les Cahiers de l’Analyse des Donnees 4:377–379, 1979) and Greenacre (Multiple correspondence analysis and related methods, Chapman and Hall (Kluwer), Dordrecht, 2006) and a test proposed by Ben Ammou and Saporta (Revue de Statistique Appliquee 46:21–35, 1998). This leads to the consideration of a better reconstruction of the off-diagonal sub-tables of the Burt’s table crossing the nominal characters taken into account. Thus, Greenacre (Biometrika 75:457–467, 1988) Joint Correspondence Analysis (JCA) is introduced, the results obtained on an application are shown, and the quality of reconstruction of both MCA and JCA solutions are compared to that of a series of Simple Correspondence Analyses run on the whole set of two-way tables. It results that JCA’s reduced-dimensional reconstruction is much better than the MCA’s one, that reveals highly biased and non-monotone, but also than the MCA’s re-evaluation, as suggested by Greenacre (Multiple correspondence analysis and related methods, Chapman and Hall (Kluwer), Dordrecht, 2006).

Grassland communities with Brachypodium cespitosum, B. genuense, or B. rupestre, distributed along Alps and Apennines were analysed, considering soil edaphic measures. Submitted to both principal components and cluster analysis six groups of relevés resulted, whose edaphic structure was compared to nominal characters. As a confirmation of results, stepwise discriminant analysis showed the edaphic characters responsible of the different species presence in the grasslands. As results, Brachypodium rupestre seems to be present on more basic soils, rich of clay, whereas B. genuense grows on more acid soils, rich in nourishment, and B. cespitosum seems to be in an intermediate position. The type of growth then, seems to depend strongly on the edaphic soil conditions., Des pâturages à Brachypodium cespitosum, B. rupestre ou B. genuense, répartis dans les Alpes et les Apennins, ont été étudiés du point de vue des caractères édaphiques. Une analyse en composantes principales suivie d’une classification a permis de déterminer six groupes de relevés dont la composition a été mise en rapport avec les mesures édaphiques. Une analyse discriminante pas à pas a montré les caractères édaphiques les plus corrélés avec la croissance des différentes espèces de Brachypodium de ces pâturages. En résumé, Brachypodium rupestre semble s’installer sur des sols plus basiques et plus riches en argile, tandis que B. genuense croît sur des sols plus acides et plus riches en éléments nutritifs, B. cespitosum se situant dans une position intermédiaire. Il semble donc que le type de croissance dépende fortement des conditions édaphiques., Camiz Sergio, Dowgiallo Giuseppina, Lucchese Fernando. Edaphic characters of Brachypodium communities on the Alps and the Apennines. In: Ecologia mediterranea, tome 17,1991. pp. 33-49.

For the analysis of a corpus of Mesopotamian seals, aiming at studying them on the image structure point of view, the problem of a suitable coding is discussed. For the analysis of the image syntactical composition a special coding was developed, based on hierarchical sequences of symbols, whose differences are measured through a particular Levenshtein distance. The results of principal coordinates analysis on these distances are discussed.

For the analysis of a corpus of Mesopotamian seals, aiming at studying them on the image structure point of view, the problem of a suitable coding is discussed. For the analysis of the image composition a textual coding was developed. In this way, both the iconographical elements and attitudes and the subpattern composing the image, can be treated, through textual exploratory techniques. The results of a textual correspondence analysis are discussed.

Given a set of 16 points on a grid, a set of randomly biased distances matrices is built and ten methods for their Euclidean approximantion are compared to identify which minimize the stress. The Principal Coordinates Analysis of Torgerson’s (1958) matrix of biased distances, limited to positive eigenvalues proved to be more effective than methods based on monotonous transformations’ aiming at getting the corresponding Torgerson’s (1958) matrix positive semidefinite prior to PCoA. Its behaviour resulted close to Kruskal Non-Metric Multidimensional Scaling and Bennani Dosse (1998) Optimal Scaling, with the advantage of the identification a posteriori of the suitable dimension.

The different techniques used for Euclidean approximation of distances are discussed. In the special case of points in a Euclidean space, whose distances are biased due to measure errors, accepting negative eigenvalues may help in the interpretation of results that are less biased than those obtained through an additive constant solution. Numerical examples are given.

For the interpretation of a two-way contingency table cross-classification, based on two hierarchies, new indexes are developed, able at evaluating relative contribution of either hierarchy nodes to the other’s nodes or partitions. Indexes are based on groups’ inertia projection onto the orthogonal basis, associated to the explanatory hierarchy, in a vector space with χ2 metrics. An application based on Lombardy municipalities 1991 Census data is given.