State Space Analysis of Forest Fires

This paper studies forest fires from the perspective of dynamical systems. Burnt area, precipitation and atmospheric temperatures are interpreted as state variables of a complex system and the correlations between them are investigated by means of different mathematical tools. First, we use mutual information to reveal potential relationships in the data. Second, we adopt the state space portrait to characterize the system’s behavior. Third, we compare the annual state space curves and we apply clustering and visualization tools to unveil long-range patterns. We use forest fire data for Portugal, covering the years 1980–2003. The territory is divided into two regions (North and South), characterized by different climates and vegetation. The adopted methodology represents a new viewpoint in the context of forest fires, shedding light on a complex phenomenon that needs to be better understood in order to mitigate its devastating consequences, at both economical and environmental levels.

Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

In this paper we study several natural and man-made complex phenomena in the perspective of dynamical systems. For each class of phenomena, the system outputs are time-series records obtained in identical conditions. The time-series are viewed as manifestations of the system behavior and are processed for analyzing the system dynamics. First, we use the Fourier transform to process the data and we approximate the amplitude spectra by means of power law functions. We interpret the power law parameters as a phenomenological signature of the system dynamics. Second, we adopt the techniques of non-hierarchical clustering and multidimensional scaling to visualize hidden relationships between the complex phenomena. Third, we propose a vector field based analogy to interpret the patterns unveiled by the PL parameters.

Floristic and structure of an Amazonian primary forest and a chronosequence of secondary succession

ABSTRACT The analysis of changes in species composition and vegetation structure in chronosequences improves knowledge on the regeneration patterns following land abandonment in the Amazon. Here, the objective was to perform floristic-structural analysis in mature forests (with/without timber exploitation) and secondary successions (initial, intermediate and advanced vegetation regrowth) in the Tapajós region. The regrowth age and plot locations were determined using Landsat-5/Thematic Mapper images (1984-2012). For floristic analysis, we determined the sample sufficiency and the Shannon-Weaver (H'), Pielou evenness (J), Value of Importance (VI) and Fisher's alpha (α) indices. We applied the Non-metric Multidimensional Scaling (NMDS) for similarity ordination. For structural analysis, the diameter at the breast height (DBH), total tree height (Ht), basal area (BA) and the aboveground biomass (AGB) were obtained. We inspected the differences in floristic-structural attributes using Tukey and Kolmogorov-Smirnov tests. The results showed an increase in the H', J and α indices from initial regrowth to mature forests of the order of 47%, 33% and 91%, respectively. The advanced regrowth had more species in common with the intermediate stage than with the mature forest. Statistically significant differences between initial and intermediate stages (p<0.05) were observed for DBH, BA and Ht. The recovery of carbon stocks showed an AGB variation from 14.97 t ha-1 (initial regrowth) to 321.47 t ha-1 (mature forests). In addition to AGB, Ht was also important to discriminate the typologies.

Neural mechanisms for fast recognition of auditory emotion

Emotion, audition, event-related potentials, MMN, multidimensional scaling, timbre, perception

Species richness and community structure of arboreal spider assemblages in fragments of three vegetational types at Banhado Grande wet plain, Gravataí River, Rio Grande do Sul, Brazil

The taxonomic composition, observed and estimated species richness, and patterns of community structure of arboreal spider assemblages in eleven sites surrounding the "Banhado Grande" wet plain in the state of Rio Grande do Sul, Brazil, are presented. These sites represent three different vegetational types: hillside (four sites), riparian (five sites) and flooded forests (two sites). The spiders were captured by beating on foliage and "aerial litter". A sample was defined as the result of beating on twenty bushes, tree branches or "aerial litter" clusters, which roughly corresponds to one-hour search effort per sample. Fifty five samples (five per site) were obtained, resulting in an observed richness of 212 species present as adult or identifiable juveniles. The total richness for all samples was estimated to be between 250 (Bootstrap) to 354 species (Jackknife 2). Confidence intervals of both sample and individual-based rarefaction curves for each vegetation type clearly indicated that flooded forest is the poorest vegetation type with respect to spider species richness, with hillside and riparian forests having a similar number of species. The percentage complementarity between the eleven sites indicated that all sites contain a distinct set of species, irrespective of their vegetation types. Nevertheless, the spider assemblages in riparian and hillside forests are more similar with respect to each other than when compared to flooded forest. Both cluster and nonmetric multidimensional scaling analyses showed no strong correspondence between the spider arboreal fauna and the three vegetation types. Moreover, a Mantel test revealed no significant association between species composition and geographic distance among sites.

Analyzing shapes as compositions of distances

We propose to analyze shapes as “compositions” of distances in Aitchison geometry asan alternate and complementary tool to classical shape analysis, especially when sizeis non-informative.Shapes are typically described by the location of user-chosen landmarks. Howeverthe shape – considered as invariant under scaling, translation, mirroring and rotation– does not uniquely define the location of landmarks. A simple approach is to usedistances of landmarks instead of the locations of landmarks them self. Distances arepositive numbers defined up to joint scaling, a mathematical structure quite similar tocompositions. The shape fixes only ratios of distances. Perturbations correspond torelative changes of the size of subshapes and of aspect ratios. The power transformincreases the expression of the shape by increasing distance ratios. In analogy to thesubcompositional consistency, results should not depend too much on the choice ofdistances, because different subsets of the pairwise distances of landmarks uniquelydefine the shape.Various compositional analysis tools can be applied to sets of distances directly or afterminor modifications concerning the singularity of the covariance matrix and yield resultswith direct interpretations in terms of shape changes. The remaining problem isthat not all sets of distances correspond to a valid shape. Nevertheless interpolated orpredicted shapes can be backtransformated by multidimensional scaling (when all pairwisedistances are used) or free geodetic adjustment (when sufficiently many distancesare used)

Unfolding a symmetric matrix

Graphical displays which show inter--sample distances are importantfor the interpretation and presentation of multivariate data. Except whenthe displays are two--dimensional, however, they are often difficult tovisualize as a whole. A device, based on multidimensional unfolding, isdescribed for presenting some intrinsically high--dimensional displays infewer, usually two, dimensions. This goal is achieved by representing eachsample by a pair of points, say $R_i$ and $r_i$, so that a theoreticaldistance between the $i$-th and $j$-th samples is represented twice, onceby the distance between $R_i$ and $r_j$ and once by the distance between$R_j$ and $r_i$. Self--distances between $R_i$ and $r_i$ need not be zero.The mathematical conditions for unfolding to exhibit symmetry are established.Algorithms for finding approximate fits, not constrained to be symmetric,are discussed and some examples are given.

Dynamic perceptual mapping

Perceptual maps have been used for decades by market researchers to illuminatethem about the similarity between brands in terms of a set of attributes, to position consumersrelative to brands in terms of their preferences, or to study how demographic and psychometricvariables relate to consumer choice. Invariably these maps are two-dimensional and static. Aswe enter the era of electronic publishing, the possibilities for dynamic graphics are opening up.We demonstrate the usefulness of introducing motion into perceptual maps through fourexamples. The first example shows how a perceptual map can be viewed in three dimensions,and the second one moves between two analyses of the data that were collected according todifferent protocols. In a third example we move from the best view of the data at the individuallevel to one which focuses on between-group differences in aggregated data. A final exampleconsiders the case when several demographic variables or market segments are available foreach respondent, showing an animation with increasingly detailed demographic comparisons.These examples of dynamic maps use several data sets from marketing and social scienceresearch.

Measuring subcompositional incoherence

Subcompositional coherence is a fundamental property of Aitchison s approach to compositional data analysis, and is the principal justification for using ratios of components. We maintain, however, that lack of subcompositional coherence, that is incoherence, can be measured in an attempt to evaluate whether any given technique is close enough, for all practical purposes, to being subcompositionally coherent. This opens up the field to alternative methods, which might be better suited to cope with problems such as data zeros and outliers, while being only slightly incoherent. The measure that we propose is based on the distance measure between components. We show that the two-part subcompositions, which appear to be the most sensitive to subcompositional incoherence, can be used to establish a distance matrix which can be directly compared with the pairwise distances in the full composition. The closeness of these two matrices can be quantified using a stress measure that is common in multidimensional scaling, providing a measure of subcompositional incoherence. The approach is illustrated using power-transformed correspondence analysis, which has already been shown to converge to log-ratio analysis as the power transform tends to zero.

Weighted Euclidean biplots

We construct a weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix. In contrast to regular multidimensional scaling methods for dissimilarity data, the method leads to biplots of individuals and variables while preserving all the good properties of dimension-reduction methods that are based on the singular-value decomposition. The main benefits are the decomposition of variance into components along principal axes, which provide the numerical diagnostics known as contributions, and the estimation of nonnegative weights for each variable. The idea is inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data, where the normalizations inherent in the distances can be considered as differential weighting of the variables. In weighted Euclidean biplots we allow these weights to be unknown parameters, which are estimated from the data to maximize the fit to the chosen distances or dissimilarities. These weights are estimated using a majorization algorithm. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing the matrix and displaying its rows and columns in biplots.

Dung beetle (Coleoptera, Scarabaeidae) assemblage of a highly fragmented landscape of Atlantic forest: from small to the largest fragments of northeastern Brazilian region

Human activities in tropical forests are the main causes of forest fragmentation. According to historical factor in deforestation processes, forest remnants exhibit different sizes and shapes. The aim of the present study was to evaluate the dung beetle assemblage on fragments of different degree of sizes. Sampling was performed during rainy and dry season of 2010 in six fragments of Atlantic forest, using pitfall traps baited with excrement and carrion. Also, we used two larger fragments as control. We used General Linear Models to determine whether the fragments presented distinguished dung beetle abundance and richness. Analysis of Similarities and Non-Metric Multidimensional Scaling were used to determine whether the dung beetle assemblage was grouped according to species composition. A total of 3352 individuals were collected and 19 species were identified in the six fragments sampled. Dung beetle abundance exhibited a shift according to fragment size; however, richness did not change among fragments evaluated. Also, fragments sampled and the two controls exhibited distinct species composition. The distinction on abundance of dung beetles among fragments may be related to different amount of resource available in each one. It is likely that the dung beetle richness did not distinguish among the different fragments due to the even distribution of the mammal communities in these patches, and consequent equal dung diversity. We conclude that larger fragments encompass higher abundance of dung beetle and distinct species. However, for a clearer understanding of effects of fragmentation on dung beetles in Atlantic forest, studies evaluating narrower variations of larger fragments should be conducted.

Relationships between soil class and nutritional status of coffee plantations

Farm planning requires an assessment of the soil class. Research suggest that the Diagnosis and Recommendation Integrated System (DRIS) has the capacity to evaluate the nutritional status of coffee plantations, regardless of environmental conditions. Additionally, the use of DRIS could reduce the costs for farm planning. This study evaluated the relationship between the soil class and nutritional status of coffee plants (Coffea canephora Pierre) using the Critical Level (CL) and DRIS methods, based on two multivariate statistical methods (discriminant and multidimensional scaling analyses). During three consecutive years, yield and foliar concentration of nutrients (N, P, K, Ca, Mg, S, B, Zn, Mn, Fe and Cu) were obtained from coffee plantations cultivated in Espírito Santo state. Discriminant analysis showed that the soil class was an important factor determining the nutritional status of the coffee plants. The grouping separation by the CL method was not as effective as the DRIS one. The bidimensional analysis of Euclidean distances did not show the same relationship between plant nutritional status and soil class. Multidimensional scaling analysis by the CL method indicated that 93.3 % of the crops grouped into one cluster, whereas the DRIS method split the fields more evenly into three clusters. The DRIS method thus proved to be more consistent than the CL method for grouping coffee plantations by soil class.

On the Schoenberg transformations in data analysis: theory and illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely connected to the Gaussian kernels of Machine Learning.

A comparison of rapid bioassessment protocols used in 2 regions with Mediterranean climates, the Iberian Peninsula and South Africa

Abstract. The ability of 2 Rapid Bioassessment Protocols (RBPs) to assess stream water quality was compared in 2 Mediterranean-climate regions. The most commonly used RBPs in South Africa (SAprotocol) and the Iberian Peninsula (IB-protocol) are both multihabitat, field-based methods that use macroinvertebrates. Both methods use preassigned sensitivity weightings to calculate metrics and biotic indices. The SA- and IB-protocols differ with respect to sampling equipment (mesh size: 1000 lm vs 250 300 lm, respectively), segregation of habitats (substrate vs flow-type), and sampling and sorting procedures (variable time and intensity). Sampling was undertaken at 6 sites in South Africa and 5 sites in the Iberian Peninsula. Forty-four and 51 macroinvertebrate families were recorded in South Africa and the Iberian Peninsula, respectively; 77.3% of South African families and 74.5% of Iberian Peninsula families were found using both protocols. Estimates of community similarity compared between the 2 protocols were .60% similar among sites in South Africa and .54% similar among sites in the Iberian Peninsula (BrayCurtis similarity), and no significant differences were found between protocols (Multiresponse Permutation Procedure). Ordination based on Non-metric Multidimensional Scaling grouped macroinvertebrate samples on the basis of site rather than protocol. Biotic indices generated with the 2 protocols at each site did not differ. Thus, both RBPs produced equivalent results, and both were able to distinguish between biotic communities (mountain streams vs foothills) and detect water-quality impairment, regardless of differences in sampling equipment, segregation of habitats, and sampling and sorting procedures. Our results indicate that sampling a single habitat may be sufficient for assessing water quality, but a multihabitat approach to sampling is recommended where intrinsic variability of macroinvertebrate assemblages is high (e.g., in undisturbed sites in regions with Mediterranean climates). The RBP of choice should depend on whether the objective is routine biomonitoring of water quality or autecological or faunistic studies.

Typologies textuelles et partitions musicales : dissimilarités, classification et autocorrélation

Axée dans un premier temps sur le formalisme et les méthodes, cette thèse est construite sur trois concepts formalisés: une table de contingence, une matrice de dissimilarités euclidiennes et une matrice d'échange. À partir de ces derniers, plusieurs méthodes d'Analyse des données ou d'apprentissage automatique sont exprimées et développées: l'analyse factorielle des correspondances (AFC), vue comme un cas particulier du multidimensional scaling; la classification supervisée, ou non, combinée aux transformations de Schoenberg; et les indices d'autocorrélation et d'autocorrélation croisée, adaptés à des analyses multivariées et permettant de considérer diverses familles de voisinages. Ces méthodes débouchent dans un second temps sur une pratique de l'analyse exploratoire de différentes données textuelles et musicales. Pour les données textuelles, on s'intéresse à la classification automatique en types de discours de propositions énoncées, en se basant sur les catégories morphosyntaxiques (CMS) qu'elles contiennent. Bien que le lien statistique entre les CMS et les types de discours soit confirmé, les résultats de la classification obtenus avec la méthode K- means, combinée à une transformation de Schoenberg, ainsi qu'avec une variante floue de l'algorithme K-means, sont plus difficiles à interpréter. On traite aussi de la classification supervisée multi-étiquette en actes de dialogue de tours de parole, en se basant à nouveau sur les CMS qu'ils contiennent, mais aussi sur les lemmes et le sens des verbes. Les résultats obtenus par l'intermédiaire de l'analyse discriminante combinée à une transformation de Schoenberg sont prometteurs. Finalement, on examine l'autocorrélation textuelle, sous l'angle des similarités entre diverses positions d'un texte, pensé comme une séquence d'unités. En particulier, le phénomène d'alternance de la longueur des mots dans un texte est observé pour des voisinages d'empan variable. On étudie aussi les similarités en fonction de l'apparition, ou non, de certaines parties du discours, ainsi que les similarités sémantiques des diverses positions d'un texte. Concernant les données musicales, on propose une représentation d'une partition musicale sous forme d'une table de contingence. On commence par utiliser l'AFC et l'indice d'autocorrélation pour découvrir les structures existant dans chaque partition. Ensuite, on opère le même type d'approche sur les différentes voix d'une partition, grâce à l'analyse des correspondances multiples, dans une variante floue, et à l'indice d'autocorrélation croisée. Qu'il s'agisse de la partition complète ou des différentes voix qu'elle contient, des structures répétées sont effectivement détectées, à condition qu'elles ne soient pas transposées. Finalement, on propose de classer automatiquement vingt partitions de quatre compositeurs différents, chacune représentée par une table de contingence, par l'intermédiaire d'un indice mesurant la similarité de deux configurations. Les résultats ainsi obtenus permettent de regrouper avec succès la plupart des oeuvres selon leur compositeur.