Effective atomic orbitals for fuzzy atoms

The method of extracting effective atomic orbitals and effective minimal basis sets from molecular wave function characterizing the state of an atom in a molecule is developed in the framework of the "fuzzy" atoms. In all cases studied, there were as many effective orbitals that have considerable occupation numbers as orbitals in the classical minimal basis. That is considered to be of high conceptual importance

Energy partitioning for "fuzzy" atoms

The total energy of molecule in terms of 'fuzzy atoms' presented as sum of one- and two-atomic energy components is described. The divisions of three-dimensional physical space into atomic regions exhibit continuous transition from one to another. The energy components are on chemical energy scale according to proper definitions. The Becke's integration scheme and weight function determines realization of method which permits effective numerical integrations

Prox1 interacts with Atoh1 and Gfi1, and regulates cellular differentiation in the inner ear sensory epithelia.

Inner ear hair cells and supporting cells arise from common precursors and, in mammals, do not show phenotypic conversion. Here, we studied the role of the homeodomain transcription factor Prox1 in the inner ear sensory epithelia. Adenoviral-mediated Prox1 transduction into hair cells in explant cultures led to strong repression of Atoh1 and Gfi1, two transcription factors critical for hair cell differentiation and survival. Luciferase assays showed that Prox1 can repress transcriptional activity of Gfi1 independently of Atoh1. Prox1 transduction into cochlear outer hair cells resulted in degeneration of these cells, consistent with the known phenotype of Gfi1-deficient mice. These results together with the widespread expression of endogenous Prox1 within the population of inner ear supporting cells point to the role for Prox1 in antagonizing the hair cell phenotype in these non-sensory cells. Further, in vivo analyses of hair cells from Gfi1-deficient mice suggest that the cyclin-dependent kinase inhibitor p57(Kip2) mediates the differentiation- and survival-promoting functions of Gfi1. These data reveal novel gene interactions and show that these interactions regulate cellular differentiation within the inner ear sensory epithelia. The data point to the tight regulation of phenotypic characteristics of hair cells and supporting cells.

Ressuscitação cardiopulmonar com a utilização do desfibrilador externo semi-automático: avaliação do processo ensino-aprendizagem

Estudos demonstram que a sobrevida após uma parada cardíaca diminui 10% para cada minuto de atraso na desfibrilação, e que a taxa de sobrevivência é de 98% quando ela é conseguida em 30 segundos. No atendimento de uma parada cardíaca, é primordial que seja incluído no treinamento a utilização dos desfibriladores externos semi-automáticos (DEA). O objetivo deste estudo foi comparar a Habilidade Psicomotora e o Conhecimento Teórico de leigos na técnica da ressuscitação cardiopulmonar (RCP) utilizando o DEA, antes e após treinamento. A amostra constituiu-se de 40 funcionários administrativos de uma instituição pública que receberam treinamento da técnica da RCP, utilizando o DEA, em laboratório. O aumento significativo de acertos nos itens do instrumento de avaliação da Habilidade Psicomotora e do Conhecimento Teórico, após o treinamento, indica que houve melhora no desempenho dos participantes.

Labeling Regulations and Segregation of First- and, Second-Generation Genetically Modified Products: Innovation Incentives and Welfare Effects, April 2005

We review some of the most significant issues and results on the economic effects of genetically modified (GM) product innovation, with emphasis on the question of GM labeling and the need for costly segregation and identity preservation activities. The analysis is organized around an explicit model that can accommodate the features of both first-generation and second-generation GM products. The model accounts for the proprietary nature of GM innovations and for the critical role of consumer preferences vis-à-vis GM products, as well as for the impacts of segregation and identity preservation and the effects of a mandatory GM labeling regulation. We also investigate briefly a novel question in this setting, the choice of “research direction”when both cost-reducing and quality-enhancing GM innovations are feasible.

Student modeling based on fuzzy inference mechanisms

The paper presents a competence-based instructional design system and a way to provide a personalization of navigation in the course content. The navigation aid tool builds on the competence graph and the student model, which includes the elements of uncertainty in the assessment of students. An individualized navigation graph is constructed for each student, suggesting the competences the student is more prepared to study. We use fuzzy set theory for dealing with uncertainty. The marks of the assessment tests are transformed into linguistic terms and used for assigning values to linguistic variables. For each competence, the level of difficulty and the level of knowing its prerequisites are calculated based on the assessment marks. Using these linguistic variables and approximate reasoning (fuzzy IF-THEN rules), a crisp category is assigned to each competence regarding its level of recommendation.

On the Segregation of Genetically Modified, Conventional, and Organic Products in European Agriculture: A Multi-market Equilibrium Analysis, October 2005

Evaluating the possible benefits of the introduction of genetically modified (GM) crops must address the issue of consumer resistance as well as the complex regulation that has ensued. In the European Union (EU) this regulation envisions the “co-existence” of GM food with conventional and quality-enhanced products, mandates the labelling and traceability of GM products, and allows only a stringent adventitious presence of GM content in other products. All these elements are brought together within a partial equilibrium model of the EU agricultural food sector. The model comprises conventional, GM and organic food. Demand is modelled in a novel fashion, whereby organic and conventional products are treated as horizontally differentiated but GM products are vertically differentiated (weakly inferior) relative to conventional ones. Supply accounts explicitly for the land constraint at the sector level and for the need for additional resources to produce organic food. Model calibration and simulation allow insights into the qualitative and quantitative effects of the large-scale introduction of GM products in the EU market. We find that the introduction of GM food reduces overall EU welfare, mostly because of the associated need for costly segregation of non-GM products, but the producers of quality-enhanced products actually benefit.

Collective Marketing Arrangements for Geographically Differentiated Agricultural Products: Welfare Impacts and Policy Implications, May 2006

This paper examines the incentive of atomistic agricultural producers within a specific geographical region to differentiate and collectively market products. We develop a model that allows us to analyze the market and welfare effects of the main types of real-world producer organizations, using it to derive economic insights regarding the circumstances under which these organizations will evolve, and describing implications of the results obtained in the context of an ongoing debate between the European Union and United States. As the anticipated fixed costs of development and marketing increase and the anticipated size of the market falls, it becomes essential to increase the ability of the producer organization to control supply in order to ensure the coverage of fixed costs. Whenever a collective organization allows a market (with a new product) to exist that otherwise would not have existed there is an increase in societal welfare. Counterintuitively, stronger property right protection for producer organizations may be welfare enhancing even after a differentiated product has been developed. The reason for this somewhat paradoxical result is that legislation aimed at curtailing the market power of producer organizations may induce large technological distortions.

The Exotic Palaeo-Thethys Terrane in Central Iran: New geological data from Anarak, Jandaq and Posht-e-Badam areas

Résumé Le « terrane » d'Anarak-Jandak occupe une position géologique clé au nord-ouest du Microcontinent Centre-East Iranien (CE1M), connecté avec le Bloc du Grand Kavir et la ceinture métamorphique de Sanandaj-Sirjan. Nous discutons ici l'origine de ces différentes unités, reliées jusqu'à présent à des épisodes orogéniques d'âge Précambrien à Paléozoïque inférieur, pour conclure finalement de leur affinité paléotéthysienne. Leur histoire commence par un épisode de rifting d'âge Ordovicien supérieur-Dévonien inférieur, pour se terminer au Trias par la collision des blocs Cimmériens dérivé du Gondwana avec le Bloc du Turan d'affinité asiatique (événement Eocimmérien). La plus importante unité métamorphique affleurant au sud-ouest de la région de Jandak-Anarak-Kaboudan est une épaisse séquence silicoclastique à grains fins contenant des blocs ophiolitiques (marginal-sea-type), et des associations basalte-gabbro à signatures géochimiques de type supra-subduction. Dans la région de Nakhlak, nous avons daté ces gabbros par la méthode U-Pb à 387f0.11 Ma ; les roches métamorphiques pélitiques ont donné des âges de refroidissement Ar-Ar pour la muscovite de 320 à 333 Ma. Ce complexe d'accrétion "varisque" a été métamorphisé dans le faciès schiste vert-amphibolite au cours de l'accrétion de la ceinture granitique d'Airekan, d'âge Cambrien inférieur (549±15 Ma par la méthode U/Pb), qui affleure aujourd'hui à l'extrémité nord-ouest du terrane d'Anarak-Jandak . La subduction vers le nord de l'océan Paléotéthys depuis le Paléazoïque supérieur jusqu'au Trias, a permis l'accumulation de grandes quantités de matériel océanique dans la zone de subduction. Par exemple, une succession de guyots (Anarak, Kaboudan, et Meraji Seamounts) et de hauts sous-marins, entrés en collision oblique avec le prisme d'accrétion, est à l'origine d'un léger métamorphisme de type HP qui affecte ces séries {âges Ar-Ar de 280 à 230 Ma). De plus, le magmatisme bimodal de Chah Gorbeh est caractérisé d'une part par des roches de type trondjémite-gabbros (262 Ma), d'autre part par des laves en coussin de type basaltes alcalins-rhyolites; ces roches magmatiques ont recoupé l'ophiolite d'Anarak lors de la mise en place de cette dernière dans la fosse interne de subduction. Quant au prisme d'accrétion de Doshakh, d'âge essentiellement Permien supérieur, i1 a été accrété le long de la marge continentale et métamorphisé dans le faciès schiste vert. La fermeture de la Paléotéthys s'enregistre finalement par la sédimentation dans le bassin d'avant pays du flysch de Bayazeh, d'âge probable Triasique. Le matériel issu de l'arc magmatique de la Paléotéthys est très bien préservé dans les dépôts infra-arc Dévonien supérieur-Carbonifère de Godar-e-Siah, ainsi que dans la succession d'avant-arc de Nakhlak. Pendant l'intervalle Paléozoïque supérieur-Trias, la région de Jandak a été soumise à un régime extensif de type bassin d'arrière-arc, dont un témoin pourrait être la ceinture ophiolitique d'Arusan, elle-même comparable aux écailles ophiolitiques d'Aghdarband au nord-est de l'Iran. Cet ensemble métamorphique est recoupé par des granites d'arc à collisionnel datés à 215±15 Ma. Dans la région de Yazd, témoin de la marge passive Cimmérienne, la sédimentation syn-rift Silurienne à Dévonienne inférieure a été interrompue pendant l'intervalle Trias moyen-Trias supérieur; il en a été de même pour les dépôts de plate-forme Paléozoïque supérieur. L'érosion, qui dans ce dernier cas a atteint le Permien, pourrait être liée au bombement flexural de la marge passive. La collision finale n'a pas induit de déformations trop importantes, et se caractérise par la mise en place de nappes sur la marge passive. Cet événement est scellé par des dépôts molassique du Lias. D'un point de vue régional, la zone s'étendant actuellement de la Mer Noire au Pamir a été soumise à six épisodes d'extension-compression du Jurassique inférieur (début du l'ouverture en position arrière-arc de la Néotéthys) à l'Eocène moyen. Par exemple, le terrane d'AnarakJandak, probablement situé entre le Kopeh Dagh et la plate-forme nord Afghane, s'est complètement détaché de sa patrie d'origine au début du Crétacé supérieur. Des preuves de cet événement se retrouvent dans les séries de plate-forme de Khur (préservation de séries syn-rift puis de marge passive). Les ophiolites de Nain et de Sabzevar sont de plus interprétée comme un témoin de l'existence de ce bassin d'arrière-arc. Dans l'intervalle Eocène-Oligocène, l'indentation par la plaque indienne de l'Eurasie a été contemporaine de la rotation horaire de fragments de l'ancien microcontinent Iranien et de la formation du CEIM. Cette rotation est responsable du transport du terrane d'Anarak-Jandak vers sa position actuelle en Iran Central, et de la dislocation de Terranes de moindre importance, comme le bloc de Posht-e Badam. Depuis le Miocène supérieur, et à la suite de la collision entre l'Arabie et l'Iran, le ternane d'Anarak-Jandak a subi des déformations liées à l'activité d'une zone de cisaillement dextre parallèle à la suture du Zagros, à l'arrière de l'arc magmatique d'Uromieh-Dokhtar. Résumé large public Le Microcontinent Centre-Est Iranien occupe une position géologique clé au centre de l'Iran. Les différentes unités qui le composent, reliées jusqu'à présent à des épisodes orogéniques d'âge Précambrien à Paléozoïque inférieur, sont maintenant rajeunies et liés à la fermeture de l'océean Paléotéthys. Leur histoire commence par un épisode de rifting d'âge Ordovicien supérieur à Dévonien inférieur, pour se terminer au Trias par la collision des- blocs Cimmériens, dérivés du Gondwana, avec le Bloc du Turan d'affinité asiatique. Dans la marge active asiatique de la Paléotéthys, nous avons daté les restes d'un océan marginal à 387±0.11 Ma. Ce complexe d'accrétion a été métamorphisé au cours de la réaccrétion de la ceinture granitique d'Airekan, d'âge Cambrien inférieur (549±15 Ma), qui affleure aujourd'hui à l'extrémité nord-ouest du « terrane » d'Anarak-Jandak correspondant à la plus grande partie de la région étudiée. Le matériel issu de l'arc magmatique de la Paléotéthys est très bien préservé et daté du Dévonien supérieur-Carbonifère. Pendant l'intervalle Paléozoïque supérieur-Trias, la région a été soumise à un régime extensif de type bassin d'arrière-arc, dont un témoin pourrait être la ceinture ophiolitique d'Arusan, comparable aux écailles ophiolitiques d'Aghdarband au nord-est de l'Iran. Cet ensemble métamorphique est recoupé par des granites datés à 215±15 Ma. La subduction vers le nord de l'océan Paléotéthys depuis le Paléozoïque supérieur jusqu'au Trias, a permis l'accumulation de grandes quantités de matériel océanique dans la zone de subduction. Par exemple, une succession de volcans sous-marins, entrés en collision avec le prisme d'accrétion, est à l'origine d'un léger métamorphisme de type HP qui affecte ces séries (280 à 230 Ma). Quant au prisme d'accrétion de Doshakh, d'âge essentiellement Permien supérieur, il a été mis en place le long de la marge continentale et métamorphisé dans le faciès schiste vert. La fermeture de la Paléotéthys s'enregistre finalement par la sédimentation dans le bassin d'avant pays du flysch de Bayazeh, d'âge Triasique. Dans la région de Yazd, on trouve les témoins de la marge passive Cimmérienne, la sédimentation syn-rift Silurienne à Dévonienne inférieure a été interrompue pendant l'intervalle Trias moyen-Trias supérieur, marqué par la flexuration de la marge passive lorsqu'elle rentra en collision avec la marge active asiatique. Cet événement est scellé par des dépôts molassique à charbon du Lias. Le «terrane» d'Anarak-Jandak, probablement situé à l'origine entre le Kopeh Dagh et la plate-forme nord Afghane, s'est complètement détaché de cette région au début du Crétacé supérieur lors de l'ouverture d'un bassin d'arrière-arc, engendré, cette fois, par la subduction de l'océan Néotéthys situé au sud des blocs cimmériens. Des preuves de cet événement se retrouvent dans les séries syn-rift, puis de marge passive de Khour. Les ophiolites de Nain et de Sabzevar sont interprétées comme un témoin de l'existence de ce bassin d'arrière-arc. Dans l'intervalle Eocène-Oligocène, l'indentation de l'Eurasie par la plaque indienne a été contemporaine de la rotation horaire de fragments de l'ancien microcontinent centre-Iranien. Cette rotation de près de 90° est responsable du transport du « terrane » d'Anarak-Jandak vers sa position actuelle. Abstract The Anarak-Jandaq terrane occupies a strategic geological situation at the north-western part of the Central-East Iranian Microcontinent (CEIM) and in connection with the Great Kavir Block and Sanandaj-Sirjan metamorphic belt. Our recent findings redefine the origin of these mentioned areas so far attributed to the Precambrian-Early Palaeozoic orogenic episodes, to be now directly related to the tectonic evolution of the Palaeo-Tethys Ocean, commenced by Late Ordovician-Early Devonian rifting events and terminated in the Triassic by the Eocimmerian tectonic event due to the collision of the Cimmerian blocks with the Asiatic Turan block. The most distributed metamorphic unit that is exposed from the south-west of Jandaq to the Anarak and Kaboudan areas is a thick and fine grain siliciclastic sequence accompanied by marginal-sea-basin ophiolitic blocks including basalt-gabbro association with supra-subduction-geochemical signature. These gabbros in the Nakhlak area were dated by U/Pb method at 387.6 ± 0.11 Ma and the metamorphic pelitic rocks yielded a range of 320 to 333 Ma muscovite-cooling ages based on 40Ar/39 Ar method. This "Variscan" accretionary complex was metamorphosed in greenschist-amphibolite facies during accretion to the Lower Cambrian Airekan granitic belt (549 ± 15 Ma by U/Pb method) that crops out at the northwestern edge of the Anarak-Jandaq terrane. Continued northward subduction of the Palaeo-Tethys Ocean during the entire Late Palaeozoic-Middle Triassic brought huge amount of oceanic material to the subduction zone. One chain of Carboniferous-Triassic oceanic rises and seamounts (the Anarak, Kaboudan, and Meraji Seamounts) obliquely collided with the accretionary wedge and created a mild HP metamorphic event (280-230 Ma based on 40Ar/39Ar results). Bimodal magmatism of the Chah Gorbeh area is characterized by a 262 Ma trondjemite-gabbro as well as pillow alkalibasalts-rhyolites which intruded the Anarak ophiolite when it was being emplaced within the inner-wall trench. The mainly Late Permian-Triassic Doshakh wedge was accreted along the continent and metamorphosed under lower greenschist facies and the probable Triassic Bayazeh flysch filled the foreland basin during the final closure. The Palaeo-Tethys magmatic arc products have been well preserved in the Late Devonian-Carboniferous Godar-e-Siah intra-arc deposits and the Triassic Nakhlak fore-arc succession. During the Late Palaeozoic-Triassic times, the Jandaq area has been affected by back-arc extension and probably the Arusan ophiolitic belt is the remnant of this narrow basin comparable to the Aqdarband ophiolitic remnant in north-east Iran. This metamorphic belt was intruded by 215 ± 15 Ma arc to collisional granites. In the passive margin of the Cimmerian block, on the Yazd region, the Silurian-Early Devonian syn-rift succession as well as the nearly continuous Upper Palaeozoic platform-type deposition was interrupted during the Middle to Late Triassic time, local erosion down to Devonian levels may be related to flexural bulge erosion. The collision event was not so strong to generate intensive deformation but was accompanied by some nappe thrusting onto the passive margin. It is finally unconformably covered by Liassic continental molassic deposits. Related to the onset of Neo-Tethyan back-arc opening in Early Jurassic to Mid-Eocene times, six periods of extensional-compressional events have differently influenced an elongated area, extending from the West Black Sea to Pamir. The Anarak-Jandaq terrane which was situated somewhere in this affected area, probably between the Kopeh Dagh and North Afghan platform, was completely detached from its source at the beginning of the Late Cretaceous

Proposta de reconhecimento de padrão de conforto em clientes com pênfigo vulgar utilizando a Lógica Fuzzy

Propuesta de reconocimiento del estándar de comodidad en clientes con pénfigo vulgar utilizando la Lógica FuzzyO objetivo é propor a Lógica Fuzzy para reconhecimento de padrões de conforto de pessoas submetidas a uma tecnologia de cuidar em Enfermagem por apresentarem pênfigo vulgar, uma doença cutâneo-mucosa rara que acomete principalmente adultos. A proposta aplicável em métodos experimentais com sujeitos submetidos à comparação quali-quantitativa (taxonomia/pertinência) do padrão de conforto antes e depois da intervenção. Requer o registro em escala cromática correspondente à intensidade de cada atributo: dor; mobilidade e comprometimento da autoimagem. As regras Fuzzy estabelecidas pela máquina de inferência definem o padrão de conforto em desconforto máximo, mediano e mínimo, traduzindo a eficácia dos cuidados de Enfermagem. Apesar de pouco utilizada na área de Enfermagem, essa lógica viabiliza pesquisas sem dimensionamento a priori do número de sujeitos em função da estimação de parâmetros populacionais. Espera-se avaliação do padrão de conforto do cliente com pênfigo diante da tecnologia aplicada de forma personalizada, conduzindo a avaliação global.

Measures of fit in multiple correspondence analysis of crisp and fuzzy coded data

When continuous data are coded to categorical variables, two types of coding are possible: crisp coding in the form of indicator, or dummy, variables with values either 0 or 1; or fuzzy coding where each observation is transformed to a set of "degrees of membership" between 0 and 1, using co-called membership functions. It is well known that the correspondence analysis of crisp coded data, namely multiple correspondence analysis, yields principal inertias (eigenvalues) that considerably underestimate the quality of the solution in a low-dimensional space. Since the crisp data only code the categories to which each individual case belongs, an alternative measure of fit is simply to count how well these categories are predicted by the solution. Another approach is to consider multiple correspondence analysis equivalently as the analysis of the Burt matrix (i.e., the matrix of all two-way cross-tabulations of the categorical variables), and then perform a joint correspondence analysis to fit just the off-diagonal tables of the Burt matrix - the measure of fit is then computed as the quality of explaining these tables only. The correspondence analysis of fuzzy coded data, called "fuzzy multiple correspondence analysis", suffers from the same problem, albeit attenuated. Again, one can count how many correct predictions are made of the categories which have highest degree of membership. But here one can also defuzzify the results of the analysis to obtain estimated values of the original data, and then calculate a measure of fit in the familiar percentage form, thanks to the resultant orthogonal decomposition of variance. Furthermore, if one thinks of fuzzy multiple correspondence analysis as explaining the two-way associations between variables, a fuzzy Burt matrix can be computed and the same strategy as in the crisp case can be applied to analyse the off-diagonal part of this matrix. In this paper these alternative measures of fit are defined and applied to a data set of continuous meteorological variables, which are coded crisply and fuzzily into three categories. Measuring the fit is further discussed when the data set consists of a mixture of discrete and continuous variables.

Nursing workload in specialized Semi-intensive Therapy unit: workforce size criteria

Abstract OBJECTIVE To assess the nursing workload (NW) in Semi-intensive Therapy Unit, specialized in the care of children with Craniofacial anomalies and associated syndromes; to compare the amount of workforce required according to the Nursing Activities Score (NAS) and the COFEN Resolution 293/04. METHOD Cross-sectional study, whose sample was composed of 72 patients. Nursing workload was assessed through retrospective application of the NAS. RESULTS the NAS mean was 49.5%. Nursing workload for the last day of hospitalization was lower in patients being discharged to home (p<0.001) and higher on the first compared to last day of hospitalization (p< 0.001). The number of professionals required according to NAS was superior to the COFEN Resolution 293/04, being 17 and 14, respectively. CONCLUSION the nursing workload corresponded to approximately 50% of the working time of nursing professional and was influenced by day and outcome of hospitalization. The amount of professionals was greater than that determined by the existing legislation.

An Automatic Approach for Learning and Tuning Gaussian Interval Type-2 Fuzzy Membership Functions Applied to Lung CAD Classification System

The potential of type-2 fuzzy sets for managing high levels of uncertainty in the subjective knowledge of experts or of numerical information has focused on control and pattern classification systems in recent years. One of the main challenges in designing a type-2 fuzzy logic system is how to estimate the parameters of type-2 fuzzy membership function (T2MF) and the Footprint of Uncertainty (FOU) from imperfect and noisy datasets. This paper presents an automatic approach for learning and tuning Gaussian interval type-2 membership functions (IT2MFs) with application to multi-dimensional pattern classification problems. T2MFs and their FOUs are tuned according to the uncertainties in the training dataset by a combination of genetic algorithm (GA) and crossvalidation techniques. In our GA-based approach, the structure of the chromosome has fewer genes than other GA methods and chromosome initialization is more precise. The proposed approach addresses the application of the interval type-2 fuzzy logic system (IT2FLS) for the problem of nodule classification in a lung Computer Aided Detection (CAD) system. The designed IT2FLS is compared with its type-1 fuzzy logic system (T1FLS) counterpart. The results demonstrate that the IT2FLS outperforms the T1FLS by more than 30% in terms of classification accuracy.

The economic effects of a Spanish trade boycott against Catalan products

We study the potential consequences of a hypothetical trade boycott against Catalan products organized by some sectors of the Spanish society mainly for political reasons. A symmetric trade boycott would have two effects: a reduction of Catalan exports to Spain and a partial process of import substitution in Catalonia. In order to quantify the economic impact of the boycott, we compare the "actual" Catalan economy, as described in the input-output table for 2005, with a "simulated" Catalan economy that takes into account the effects of a boycott on the trade exchanges between Catalonia and Spain.

Fuzzy coding in constrained ordinations

Canonical correspondence analysis and redundancy analysis are two methods of constrained ordination regularly used in the analysis of ecological data when several response variables (for example, species abundances) are related linearly to several explanatory variables (for example, environmental variables, spatial positions of samples). In this report I demonstrate the advantages of the fuzzy coding of explanatory variables: first, nonlinear relationships can be diagnosed; second, more variance in the responses can be explained; and third, in the presence of categorical explanatory variables (for example, years, regions) the interpretation of the resulting triplot ordination is unified because all explanatory variables are measured at a categorical level.