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We introduce the concept of maximal directions of increasingness (resp. decreasingness) of an aggregation function. In the bivariate case, we derive these maximal directions with respect to points on the main diagonal of the unit square for a symmetric aggregation function that has either piecewise convex or piecewise concave level curves and is differentiable up to second order. With any bivariate aggregation function of the latter type we associate another bivariate aggregation function that has the same maximal directions of increasingness (resp. decreasingness) while having straight lines as level curves. We explore under which conditions the latter aggregation function is a semi-copula, a quasi-copula or a copula. As a by-product we establish a new construction method for aggregation functions with given diagonal section.

We present a fuzzy version of the notion of relational Galois connection between fuzzy transitive directed graphs (fuzzy T-digraphs) on the specific setting in which the underlying algebra of truth values is a complete Heyting algebra. The components of such fuzzy Galois connection are fuzzy relations satisfying certain reasonable properties expressed in terms of the so-called full powering. Moreover, we provide a necessary and sufficient condition under which it is possible to construct a right adjoint for given fuzzy relation between a fuzzy T-digraph and an unstructured set.

First, we recall the properties of the curved section of a copula that is specified by an automorphism of the unit interval. Then, inspired by the operation of diagonal splicing of two copulas, we develop the curved splicing operation, which essentially glues together different restrictions of two copulas that share the same curved section. In order to exploit this operation in practice, we propose two new classes of semilinear copulas. Applying the curved splicing operation to members of these two classes leads to two other classes of semilinear copulas.

This paper presents a review of the concept of an n-quasi-copula, starting from the characterization of functions that can be derived from operations on random variables. We recall several other characterizations and properties that have been proven in the literature, highlighting the differences between the bivariate case and the higher-dimensional case. Additionally, we recall several applications of n-quasi-copulas such as their role in the study of bounds on sets of n-copulas. We also recall various classes of n-quasi-copulas that have been studied in the literature. Finally, we present some questions that have not yet been answered in the literature.

Made available in DSpace on 2022-04-28T19:30:19Z (GMT). No. of bitstreams: 0 Previous issue date: 2022-05-15 Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) This paper shows that the Hukuhara difference and generalized gH-difference, as well as the gH-division, are not inclusion-isotonic interval extensions of the difference and division of real numbers, respectively, and discusses how this fact may affect the reliability of some results in specific epistemic mathematical models with respect to the semantics being considered. Departamento de Matemática e Matemática Aplicada Universidade Federal de Lavras, MG Departamento de Matemática Aplicada Universidade Estadual Paulista, SP Department of Mathematical and Statistical Science University of Colorado Instituto de Ciência e Tecnologia Universidade Federal de São Paulo, SP KERMIT Department of Data Analysis and Mathematical Modelling, Coupure links 653 Departamento de Matemática Aplicada Universidade Estadual Paulista, SP CAPES: 001

Context Diel use of forest and open habitats by large herbivores is linked to species-specific needs of multiple and heterogeneous resources. However, forest cover layers might deviate considerably for a given landscape, potentially affecting evaluations of animals’ habitat use. Objectives We assessed inconsistency in the estimates of diel forest use by red and roe deer at GPS location and home range (HR) levels, using two geographic layers: Tree Cover Density (TCD) and Corine Land Cover (CLC). Methods We first measured the classification mismatch of red and roe deer GPS locations between TCD and CLC, also with respect to habitat units’ size. Then, we used Generalised Least Squares models to assess the proportional use of forest at day and night at the GPS location and HR levels, both with TCD and CLC. Results About 20% of the GPS locations were inconsistently classified as forest or open habitat by the two layers, particularly within smaller habitat units. Overall proportion of forest and open habitat, though, was very similar for both layers. In all populations, both deer species used forest more at day than at night and this pattern was more evident with TCD than with CLC. However, at the HR level, forest use estimates were only marginally different between the two layers. Conclusions When estimating animal habitat use, geographic layer choice requires careful evaluation with respect to ecological questions and target species. Habitat use analyses based on GPS locations are more sensitive to layer choice than those based on home ranges.

We consider the winning probability relation associated with a set of (real-valued) random variables. Its computation requires knowledge of the marginal cumulative distribution functions of the random variables and of the bivariate cumulative distribution function of any couple of these random variables. Here, the copulas underlying these bivariate cumulative distribution functions are assumed to be identical and to belong to the parametric family of Frank copulas, although this most likely does not represent the real dependence and might even not be feasible at all; the Frank copula parameter should thus be regarded as a parameter of the method presented. This winning probability relation is then exploited to establish a strict partial order on the set of random variables. This is realized by computing an appropriate α-cut that yields a cycle-free crisp relation, resulting in a strict partial order upon computing its transitive closure. For any given Frank copula, we focus on finding the lowest possible value of α, called (minimal) cutting level, such that cutting the winning probability relation strictly above that value results in a crisp relation that is free from cycles of length m, with m ∈ { 3 , 4 , … } , irrespective of the marginal cumulative distribution functions of the random variables. We are able to give closed-form expressions for these cutting levels: (1) for all m when the copula is either the independence copula or one of the two Frechet-Hoeffding bounds; (2) for any Frank copula when m = 4 or when m tends to infinity. The relationship between the cutting level, the cycle length and the Frank copula parameter is discussed.

The development of quality monitoring systems for perishable food products like seafood requires extensive data collection under specified packaging and storage conditions, followed by advanced data analysis and interpretation. Even though the benefits of using volatile organic compounds as food quality indices have been recognized, few studies have focused on real-time quantification of the seafood volatilome and subsequent systematic identification of the most important spoilage indicators. In this study, spoilage of Atlantic salmon (Salmo salar) stored under modified atmospheres (% CO2/O2/N2) and air was characterized by performing multivariate statistical analysis and augmented ordinal regression modelling for data collected by microbiological, chemical and sensory analyses. Out of 25 compounds quantified by selected-ion flow-tube mass spectrometry, ethanol, dimethyl sulfide and hydrogen sulfide were found characteristic under anaerobic conditions (0/0/100 and 60/0/40), whereas spoilage under air was primarily associated with the production of alcohols and ketones. Under high-O2 MAP (60/40/0), only 3-methylbutanal fulfilled the identification criteria. Overall, this manuscript presents a systematic and widely applicable methodology for the identification of most potential seafood spoilage indicators within the context of intelligent packaging technology development. In particular, parallel application of statistics and modelling was found highly beneficial for the performance of the quality characterization process and for the practical applicability of the obtained results in food quality monitoring.

Probabilistic topic modelling is frequently used in machine learning and statistical analysis for extracting latent information from complex datasets. Despite being closely associated with natural language processing and text mining, these methods possess several properties that make them particularly attractive in metabolomics applications where the applicability of traditional multivariate statistics tends to be limited. The aim of the study was thus to introduce probabilistic topic modelling – more specifically, Latent Dirichlet Allocation (LDA) – in a novel experimental context: volatilome-based (sea) food spoilage characterization. This was realized as a case study, focusing on modelling the spoilage of Atlantic salmon (Salmo salar) at 4 °C under different gaseous atmospheres (% CO2/O2/N2): 0/0/100 (A), air (B), 60/0/40 (C) or 60/40/0 (D). First, an exploratory analysis was performed to optimize the model tunings and to consequently model salmon spoilage under 100% N2 (A). Based on the obtained results, a systematic spoilage characterization protocol was established and used for identifying potential volatile spoilage indicators under all tested storage conditions. In conclusion, LDA could be used for extracting sets of underlying VOC profiles and identifying those signifying salmon spoilage, giving rise to an extensive discussion regarding the key points associated with model tuning and/or spoilage analysis. The identified compounds were well in accordance with a previously established approach based on partial least squares regression analysis (PLS). Overall, the outcomes of the study not only reflect the promising potential of LDA in spoilage characterization, but also provide several new insights into the development of data-driven methods for food quality analysis.

[EN] Most of the strategies for boundary image evaluation involve the comparison of computer-generated images with ground truth solutions. While this can be done in different manners, recent years have seen a dominance of techniques based on the use of confusion matrices. That is, techniques that, at the evaluation stage, interpret boundary detection as a classification problem. These techniques require a correspondence between the boundary pixels in the candidate image and those in the ground truth; that correspondence is further used to create the confusion matrix, from which evaluation statistics can be computed. The correspondence between boundary images faces different challenges, mainly related to the matching of potentially displaced boundaries. Interestingly, boundary image comparison relates to many other fields of study in literature, from object tracking to biometrical identification. In this work, we survey all existing strategies for boundary matching, we propose a taxonomy to embrace them all, and perform a usability-driven quantitative analysis of their behaviour., The authors gratefully acknowledge the financial support of the Spanish Ministry of Science (PID2019-108392GB-I00, AEI/10.13039/50110 0 011033), ass well as that of the Research Foundation Flanders (FWO project 3G.0838.12.N)

Comparison and similarity measurement have been a key topic in computer vision for a long time. There is, indeed, an extensive list of algorithms and measures for image or subimage comparison. The superiority or inferiority of different measures is hard to scrutinize, especially considering the dimensionality of their parameter space and their many different configurations. In this work, we focus on the comparison of binary images, and study different variations of Baddeley's Delta Metric, a popular metric for such images. We study the possible parameterizations of the metric, stressing the numerical and behavioural impact of different settings. Specifically, we consider the parameter settings proposed by the original author, as well as the substitution of distance transformations by regularized distance transformations, as recently presented by Brunet and Sills. We take a qualitative perspective on the effects of the settings, and also perform quantitative experiments on separability of datasets for boundary evaluation. The authors gratefully acknowledge the financial support by the Spanish Ministry of Science (project PID2019-108392GB-I00 AEI/FEDER, UE), as well as that by Navarra Servicios y Tecnologías S.A. (NASERTIC).

The geometrical interpretation of symmetry of a function on the unit square is that it takes the same value in mirror images w.r.t. the main diagonal. Here, this concept is generalized by considering the reflection w.r.t. a curve representing the graph of an automorphism of the unit interval. A function on the unit square that takes the same value in mirror images w.r.t. such a curve is called symmetric w.r.t. that curve. Moreover, a measure is proposed for quantifying to what extent a (quasi-)copula can be regarded as being asymmetric w.r.t. a given curve. The major part of the paper is concerned with establishing lower and upper bounds on this degree of asymmetry. Finally, it is shown that these bounds are sharp within the class of copulas.

We study the relationship between the poset of supermodular n-quasi-copulas and the posets of n-quasi-copulas and n-copulas. It is known that, for n ⩾ 3 , the poset of n-quasi-copulas is not order-isomorphic to the Dedekind–MacNeille completion of the poset of n-copulas. We complement the latter result by showing that, for n ⩾ 3 , the structure of the poset of n-quasi-copulas is more closely related to that of the poset of supermodular n-quasi-copulas than that of the poset of n-copulas.

In this paper we study the smallest and the greatest M-Lipschitz continuous n-ary aggregation functions with a given diagonal section. We show that several properties that were studied for the smallest and the greatest 1-Lipschitz continuous binary aggregation functions with a given diagonal section extend naturally to higher dimensions while considering different Lipschitz constants. Just as in the binary case, we show that the smallest n-quasi-copula with a given diagonal section coincides with the smallest 1-Lipschitz n-ary aggregation function with that diagonal section. Additionally, we show that the smallest n-quasi-copula with a given diagonal section, called the Bertino n-quasi-copula, is supermodular for any n ⩾ 2 .

We investigate a functional inequality for copulas that has emerged from our study of the comparison of a set of random variables pairwisely coupled by a same copula. Any copula satisfying this inequality is necessarily symmetric and radially symmetric. Moreover, any associative copula satisfying this inequality is a solution to the well-known Frank equation. For this reason, the inequality is coined the Frank inequality. We fully characterize the associative copulas that satisfy the Frank inequality: they turn out to be either Frank copulas or ordinal sums of a same Frank copula with equidistant idempotent elements. As a by-product, we observe that Frank copulas are super-additive on the unit square.

We prove a representation theorem for copulas that are (simultaneously) symmetric and radially symmetric. We use this representation theorem to propose a method to construct an n-ary symmetric function that is radially symmetric, starting from an ( n − 1 ) -dimensional copula and an n-ary auxiliary function. We study the necessary and sufficient conditions on this auxiliary function that guarantee our construction method to result in a symmetric and radially symmetric n-dimensional copula. We examine several options for defining the auxiliary function in the trivariate case, inspired by the nesting of copulas, the lifting of copulas and product-like extensions. For each choice of auxiliary function, we provide several examples for different families of copulas.

In this work, we focus on adjunctions, also called isotone Galois connections, in the framework of fuzzy preordered sets (hereafter, fuzzy preposets). Specifically, we present necessary and sufficient conditions so that, given a mapping f:A→B from a fuzzy preposet A into an unstructured set B, it is possible to construct a suitable fuzzy preorder relation on B for which there exists a mapping g:B→A such that the pair (f,g) constitutes an adjunction.

We study the class of supermodular n-quasi-copulas.We show that some properties of 2-copulas extend to supermodular n-quasi-copulas.We introduce the class of k-dimensionally-increasing n-quasi-copulas.We solve an open problem regarding a characterization of n-quasi-copulas. We show that as the dimensionality increases, more and more interesting classes of operations can be identified between the class of n-quasi-copulas and the class of n-copulas. One such class is the class of supermodular n-quasi-copulas. We observe that some properties of 2-copulas that cannot be generalized to higher-dimensional copulas, hold true for supermodular n-quasi-copulas. Additionally, we show that trying to generalize a volume-based characterization of bivariate copulas to higher dimensions, results in a restrictive class of n-quasi-copulas.

Early blight and brown spot, caused by respectively Alternaria solani and Alternaria alternata, can lead to severe yield losses in potato-growing areas. To date, fungicide application is the most effective measure to control the disease. However, in recent years, a reduced sensitivity towards several active ingredients has been reported. To shed light on this issue, Alternaria isolates were collected from different potato fields in Belgium during two growing seasons. Subsequently, the sensitivity of these isolates was assessed using four widely used fungicides with different modes of action. Demethylation inhibitors, quinone outside inhibitors, a dithiocarbamate and a carboxylic acid amide were included in this study. Although all fungicides reduced spore germination and vegetative growth of Alternaria species to some extent, the interspecies sensitivity was very variable. In general, A. solani was more suppressed by the fungicides compared to A. alternata. The effectiveness of the dithiocarbamate mancozeb was high, whereas the quinone outside inhibitor azoxystrobin showed a limited activity, especially towards A. alternata. Therefore, a subset of the A. alternata and A. solani isolates was tested for the presence of, respectively, the G143A substitution and the F129L substitution in the cytochrome b. The frequency of A. alternata isolates bearing the resistant G143A allele (approximately 65%) was comparable in both sampling years, although sensitivity of isolates decreased during the growing season. This finding points to a shift of the population towards resistant isolates. Both the European genotype I and American genotype II were present in the A. solani population, with genotype I being the most prevalent. None of the genotype I isolates carried the F129L substitution, whereas in 83% of the genotype II isolates this substitution was present. Our results demonstrate for the first time that the Belgian Alternaria population on potato comprises a considerable broad spectrum of isolates with different sensitivity to fungicides.

In the problem setting of constructing an n-copula given its diagonal section and all of its ( n - 1 ) -dimensional marginals, we introduce a new class of symmetric n-copulas, which generalizes the well-known class of bivariate upper semilinear copulas. These new upper semilinear n-copulas are constructed by linear interpolation on segments connecting the main diagonal of the unit hypercube 0, 1n to one of its upper faces. We focus on the case where the ( n - 1 ) -dimensional marginals are upper semilinear ( n - 1 ) -copulas themselves, in which case the n-copula is actually constructed given its diagonal section and the diagonal sections of its k-marginals ( k ź { 2 , 3 , ź , n - 1 } ). We provide necessary and sufficient conditions on these diagonal sections that guarantee that the upper semilinear construction method yields an n-copula. Several examples are provided.

In the evaluation of boundary detection methods it is common to use as ground truth a set of boundary images that are hand-made by human experts. This work proposes a novel representation of this ground truth. More specifically, we propose to combine the hand-made boundary images into a set-based consensus, which is constructed from the concordances and discordances among the images. We study the theoretical and visual properties of this consensus and present an application to boundary image quality evaluation.

Implication and aggregation functions play important complementary roles in the field of fuzzy logic. Both have been intensively investigated since the early 1980s, revealing a tight relationship between them. However, the main results regarding this relationship, published by Fodor and Demirli DeBaets in the 1990s, have been poorly disseminated and are nowadays somewhat obsolete due to the subsequent advances in the field. The present paper deals with the translation of the classical logical equivalence p ? q ? ?p?q, often called material implication, to the fuzzy framework, which establishes a one-to-one correspondence between implication functions and disjunctors (the class of aggregation functions that extend the Boolean disjunction to the unit interval). The construction of implication functions from disjunctors via negation functions, and vice versa, is reviewed, stressing the properties of disjunctors (respectively, implication functions) that ensure certain properties of implication functions (disjunctors).

This paper provides a partial answer to an open problem recently posed by R. Mesiar and J. Kalicka regarding the existence of an n-dimensional Bertino copula with a given diagonal section for any n ⩾ 2 . It is known that for any 2-diagonal function, there exists a 2-dimensional Bertino copula that has the given 2-diagonal function as diagonal section. In the present paper, we introduce the notion of a regular n-diagonal function and we characterise for any n ⩾ 3 the sets D n of regular n-diagonal functions for which there exists an n-dimensional Bertino copula whose diagonal section coincides with the given n-diagonal function. We prove that D n + 1 is strictly included in D n , for all n ⩾ 2 , and that D n is the set of all increasing n / ( n − 1 ) -Lipschitz continuous n-diagonal functions. As a by-product, we show that all marginal copulas of an n-dimensional Bertino copula are Bertino copulas themselves. Examples are given to illustrate the construction of an n-dimensional Bertino copula with a given diagonal section and the characterisation of the sets D n .

[EN] In this paper, we propose the concepts of the composition of possibilistic variables and state functions. While in conventional compositional data analysis, the interdependent components of a deterministic vector must add up to a specific quantity, we consider such components as possibilistic variables. The concept of state function is intended to describe the state of a dynamic variable over time. If a state function is used to model decay in time, it is called the ageing function. We present a practical implementation of our concepts through the development of a model for a supply chain planning problem, specifically the order promising process for perishables. We use the composition of possibilistic variables to model the existence of different non-homogeneous products in a lot (sub-lots with lack of homogeneity in the product), and the ageing function to establish a shelf life-based pricing policy. To maintain a reasonable complexity and computational efficiency, we propose the procedure to obtain an equivalent interval representation based on alpha -cuts, allowing to include both concepts by means of linear mathematical programming. Practical experiments were conducted based on data of a Spanish supply chain dedicated to pack and distribute oranges and tangerines. The results validated the functionality of both, the compositions of possibilistic variables and ageing functions, showing also a very good performance in terms of the interpretation of a real problem with a good computational performance., We would also thank Dr. José De Jesús Arias García for useful discussions during the development of this work. This research has been supported by the Ministry of Science, Technology and Telecommunications, government of Costa Rica (MICITT), through the Program of Innovation and Human Capital for Competitiveness (PINN) (contract number PED-019-2015-1). We acknowledge the partial support of the project 691249, RUCAPS: Enhancing and implementing knowledge based ICT solutions within high risk and uncertain conditions for agriculture production systems , funded by the European Union s research and innovation programme under the H2020 Marie Skłodowska-Curie Actions.

Background The multidisciplinary nature of nutrition research is one of its main strengths. At the same time, however, it presents a major obstacle to integrate data analysis, especially for the terminological and semantic interpretations that specific research fields or communities are used to. To date, a proper ontology to structure and formalize the concepts used for the description of nutritional studies is still lacking. Results We have developed the Ontology for Nutritional Studies (ONS) by harmonizing selected pre-existing de facto ontologies with novel health and nutritional terminology classifications. The ONS is the result of a scholarly consensus of 51 research centers in nine European countries. The ontology classes and relations are commonly encountered while conducting, storing, harmonizing, integrating, describing, and searching nutritional studies. The ONS facilitates the description and specification of complex nutritional studies as demonstrated with two application scenarios. Conclusions The ONS is the first systematic effort to provide a solid and extensible formal ontology framework for nutritional studies. Integration of new information can be easily achieved by the addition of extra modules (i.e., nutrigenomics, metabolomics, nutrikinetics, and quality appraisal). The ONS provides a unified and standardized terminology for nutritional studies as a resource for nutrition researchers who might not necessarily be familiar with ontologies and standardization concepts. Electronic supplementary material The online version of this article (10.1186/s12263-018-0601-y) contains supplementary material, which is available to authorized users.

SUMMARYRelationships between milk fatty acids (MFA) and methane (CH4) emissions from dairy cattle were explored. Data from a total of 12 studies including 39 treatments were gathered in the database. Methane was expressed as daily emissions (g/d), relative to dry matter intake (g/kg), milk production (g/kg milk) and body weight (g/kg). The univariate correlations between MFA and CH4 were based on absolute means and on relative changes of each treatment compared with its corresponding control. Saturated fatty acids, odd- and branched-chain FA and long-chain poly-unsaturated FA were positively related to CH4, while cis- and trans-isomers of mono-unsaturated FA were negatively related to CH4. However, most of the coefficients of determination (R2) of these univariate regressions ranged from 0·2 to 0·7, indicating that individual MFA only explain a limited part of the variation in CH4. Significant relationships between MFA and CH4 varied depending on the unit in which emissions were expressed. Similarly, some MFA seemed more suited to predict relative changes in CH4 emissions rather than absolute amounts. The present findings contribute to the exploration of the potential of MFA as biomarkers for CH4 emissions from dairy cattle, although differences between studies in the detail of MFA analysis and hence the number of MFA reported in the current study, complicates this kind of literature survey.

Due to their ability to grow in complex environments, fungi play an important role in most ecosystems and have for that reason been the subject of numerous studies. Some of the main obstacles to the study of fungal growth are the heterogeneity of growth environments and the limited scope of laboratory experiments. Given the increasing availability of image capturing techniques, a new approach lies in image analysis. Most previous image analysis studies involve manual labelling of the fungal network, tracking of individual hyphae, or invasive techniques that do not allow for tracking the evolution of the entire fungal network. In response, this work presents a highly versatile tool combining image analysis and graph theory to monitor fungal growth through time and space for different fungal species and image resolutions. In addition, a new experimental set-up is presented that allows for a functional description of fungal growth dynamics and a quantitative mutual comparison of different growth behaviors. The presented method is completely automated and facilitates the extraction of the most studied fungal growth features such as the total length of the mycelium, the area of the mycelium and the fractal dimension. The compactness of the fungal network can also be monitored over time by computing measures such as the number of tips, the node degree and the number of nodes. Finally, the average growth angle and the internodal length can be extracted to study the morphology of the fungi. In summary, the introduced method offers an updated and broader alternative to classical and narrowly focused approaches, thus opening new avenues of investigation in the field of mycology.

The aim of this study was to assess the potential of milk fatty acids as diagnostic tool for hyperketonemia of 93 dairy cows in a 3×2 factorial arrangement. Cows were fed a glucogenic or lipogenic diet and originally were intended to be subjected to a 0-, 30-, or 60-d dry period. Nevertheless, some of the cows, which were intended for inclusion in the 0-d dry period group, dried off spontaneously. Milk was collected in wk 2, 3, 4, and 8 of lactation for milk fat analysis. Blood was sampled from wk 2 to 8 after parturition for β-hydroxybutyrate (BHBA) analysis. Cases were classified into 2 groups: hyperketonemia (BHBA ≥1.2mmol/L) and nonhyperketonemia (BHBA

Synopsis Objective A new protocol is described for assessing the efficacy of the dispenser of some packaging systems (PSs) of preservative-free cosmetic products in protecting both their contained formula and their delivered doses. Methods Practically, aiming at mimicking contacts with a non-sterile skin or fingers, the dispensing system is put into contact with a pre-contaminated fabric by a standardized colonization of P. aeruginosa. Results When applied to three different types of packaging, results show clear differences in both criteria between these conditioning articles, that is variable efficacies in protecting the contained product and the delivered doses, knowing that the first aspect is of paramount importance. Conclusion The proposed protocol is proved being able to discriminate between different PSs and provides information on strong and weak features of certain types dispensing technologies prone to efficiently decrease either the dose contamination or to prevent contamination in reaching the contained product. Therefore, the proposed protocol can contribute to an objective selection of a PS for protecting a cosmetic care product with a low content of preservative or preservative free. Resume Objectif Un nouveau protocole est decrit pour evaluer l'efficacite du distributeur de certains systemes d'emballage (PS) des produits cosmetiques sans conservateurs pour proteger a la fois leur formule contenue et leurs doses delivrees. Methodes Pratiquement, visant a mimer les contacts avec les doigts ou une peau non sterile, le systeme de distribution est mis en contact avec un tissu pre-contamine par une colonisation normalisee de P. aeruginosa. Resultats Lorsqu'il est applique a trois types d'emballages differents, les resultats montrent des differences claires dans les deux criteres entre ces articles de conditionnement, ce est a dire des efficacites variables dans la protection du produit contenu et les doses delivrees, sachant que le premier aspect est d'une importance primordiale. Conclusion Le protocole propose est montre capable de discriminer entre les differents systemes d'emballage et fournit des informations sur les caracteristiques forts et faibles de certains types de technologies de distribution prevues a diminuer de facon efficace soit la contamination de la dose ou a prevenir la contamination qui pourrait atteindre le produit contenu. Par consequent, le protocole propose peut contribuer a une selection objective d'un PS pour proteger un produit de soin cosmetique avec une faible teneur d'agent de conservation ou exempt d'agent de conservation.

Copulas are nothing else but supermodular functions with absorbing element 0 and neutral element 1. Although a copula C cannot be modular on the unit square itself, it is effectively so on every rectangle with zero C-volume. In this paper, we show that an appropriate modular function on the unit square can be transformed into a copula by performing a simple truncation operation (either from below or above to ensure the compatibility with the Frechet-Hoeffding bounds). Modular functions on the unit square admit an additive representation in terms of two univariate functions. We specifically focus on cases where these univariate functions are sections (horizontal, vertical, diagonal) of a given copula. Ample illustrations are provided.