Symbolic Multidimensional Scaling

__Abstract__ Multidimensional scaling (MDS) is a technique that visualizes dissimilarities between pairs of objects as distances between points in a low dimensional space. In symbolic MDS, a dissimilarity is not just a value but can represent an interval or even a histogram. Here, we present an overview of developments for symbolic MDS. We discuss how interval dissimilarities they can be represented by (concentric) circles or rectangles, how replications can be represented by a three-way MDS version, and show how nested intervals of distances can be obtained for representing histogram dissimilarities. The various models are illustrated by empirical examples

Interval linear systems as a necessary step in fuzzy linear systems

International audienceThis article clarifies what it means to solve a system of fuzzy linear equations, relying on the fact that they are a direct extension of interval linear systems of equations, already studied in a specific interval mathematics literature. We highlight four distinct definitions of a systems of linear equations where coefficients are replaced by intervals, each of which based on a generalization of scalar equality to intervals. Each of the four extensions of interval linear systems has a corresponding solution set whose calculation can be carried out by a general unified method based on a relatively new concept of constraint intervals. We also consider the smallest multidimensional intervals containing the solution sets. We propose several extensions of the interval setting to systems of linear equations where coefficients are fuzzy intervals. This unified setting clarifies many of the anomalous or inconsistent published results in various fuzzy interval linear systems studies

Low rank surrogates for polymorphic fields with application to fuzzy-stochastic partial differential equations

We consider a general form of fuzzy-stochastic PDEs depending on the interaction of probabilistic and non-probabilistic ("possibilistic") influences. Such a combined modelling of aleatoric and epistemic uncertainties for instance can be applied beneficially in an engineering context for real-world applications, where probabilistic modelling and expert knowledge has to be accounted for. We examine existence and well-definedness of polymorphic PDEs in appropriate function spaces. The fuzzy-stochastic dependence is described in a high-dimensional parameter space, thus easily leading to an exponential complexity in practical computations. To aleviate this severe obstacle in practise, a compressed low-rank approximation of the problem formulation and the solution is derived. This is based on the Hierarchical Tucker format which is constructed with solution samples by a non-intrusive tensor reconstruction algorithm. The performance of the proposed model order reduction approach is demonstrated with two examples. One of these is the ubiquitous groundwater flow model with Karhunen-Loeve coefficient field which is generalized by a fuzzy correlation length

A dissimilarity-based approach for Classification

The Nearest Neighbor classifier has shown to be a powerful tool for multiclass classification. In this note we explore both theoretical properties and empirical behavior of a variant of such method, in which the Nearest Neighbor rule is applied after selecting a set of so-called prototypes, whose cardinality is fixed in advance, by minimizing the empirical mis-classification cost. With this we alleviate the two serious drawbacks of the Nearest Neighbor method: high storage requirements and time-consuming queries. The problem is shown to be NP-Hard. Mixed Integer Programming (MIP) programs are formulated, theoretically compared and solved by a standard MIP solver for problem instances of small size. Large sized problem instances are solved by a metaheuristic yielding good classification rules in reasonable time.operations research and management science;

Network Flexibility for Recourse Considerations in Bi-Criteria Facility Location

What is the best set of facility location decisions for the establishment of a logistics network when it is uncertain how a company’s distribution strategy will evolve? What is the best configuration of a distribution network that will most likely have to be altered in the future? Today’s business environment is turbulent, and operating conditions for firms can take a turn for the worse at any moment. This fact can and often does influence companies to occasionally expand or contract their distribution networks. For most companies operating in this chaotic business environment, there is a continuous struggle between staying cost efficient and supplying adequate service. Establishing a distribution network which is flexible or easily adaptable is the key to survival under these conditions. This research begins to address the problem of locating facilities in a logistics network in the face of an evolving strategic focus through the implicit consideration of the uncertainty of parameters. The trade-off of cost and customer service is thoroughly examined in a series of multi-criteria location problems. Modeling techniques for incorporating service restrictions for facility location in strategic network design are investigated. A flexibility metric is derived for the purposes of quantifying the similarity of a set of non-dominated solutions in strategic network design. Finally, a multi-objective greedy random adaptive search (MOG) metaheuristic is applied to solve a series of bi-criteria, multi-level facility location problems

The Effect of Communicating Ambiguous Risk Information on Choice

Decision makers are frequently confronted with ambiguous risk information about activities with potential hazards. This may be a result of conflicting risk estimates from multiple sources or ambiguous risk information from a single source. The paper considers processing ambiguous risk information and its effect on the behavior of a decision maker with a-maximin expected utility preferences. The effect of imprecise risk information on behavior is related to the content of information, the decision maker’s trust in different sources of information, and his or her aversion to ambiguity.a-Maximin Expected Utility, aggregation of expert opinions, ambiguity, Knightian uncertainty, risk communication, trust in information source, Risk and Uncertainty,

Révision automatique de théories écologiques

À l’origine, ce sont des difficultés en biologie évolutive qui ont motivé cette thèse. Après des décennies à tenter de trouver une théorie basée sur la sélection capable de prédire la diversité génomique, les théoriciens n’ont pas trouvé d’alternatives pratiques à la théorie neutre. Après avoir étudié la relation entre la spéciation et la diversité (Annexes A, B, C), j’ai conclu que l’approche traditionnelle pour construire des théories serait difficile à appliquer au problème de la biodiversité. Prenons par exemple le problème de la diversité génomique, la difficulté n’est pas que l’on ignore les mécanismes impliqués, mais qu’on ne réussit pas à construire de théories capable d’intégrer ces mécanismes. Les techniques en intelligence artificielle, à l’inverse, réussissent souvent à construire des modèles prédictifs efficaces justement là où les théories traditionnelles échouent. Malheureusement, les modèles bâtis par les intelligences arti- ficielles ne sont pas clairs. Un réseau de neurones peut avoir jusqu’à un milliard de paramètres. L’objectif principal de ma thèse est d’étudier des algorithmes capable de réviser les théories écologiques. L’intégration d’idées venant de différentes branches de l’écologie est une tâche difficile. Le premier défi de ma thèse est de trouver sous quelle représentation formelle les théories écologiques doivent être encodées. Contrairement aux mathématiques, nos théories sont rarement exactes. Il y a à la fois de l’incertitude dans les données que l’on collecte, et un flou dans nos théories (on ne s’attend pas à que la théorie de niche fonctionne 100% du temps). Contrairement à la physique, où un petit nombre de forces dominent la théorie, l’écologie a un très grand nombre de théories. Le deuxième défi est de trouver comment ces théories peuvent être révisées automatiquement. Ici, le but est d’avoir la clarté des théories traditionnelles et la capacité des algorithmes en intelligence artificielle de trouver de puissants modèles prédictifs à partir de données. Les tests sont faits sur des données d’interactions d’espèces

Dissecting the assembly process of benthic communities from neotropical streams

§ La conservación y rehabilitación de la estructura y funcionamiento de los ecosistemas requiere de un conocimiento profundo de las causas y consecuencias de su biodiversidad. Sin embargo, este conocimiento es aún escaso en regiones Neotropicales. § En esta tesis, utilizo el marco conceptual de las metacomunidades para caracterizar los posibles efectos que tienen los procesos de dispersión (en tiempos ecológicos y evolutivos), selección (impulsada por factores abióticos) y deriva ecológica en la diversidad y distribución de las comunidades bentónicas fluviales. 2 § La zona de estudio, de un área de aproximadamente 40,000 km , abarcó entre 26 y 32 segmentos de ríos prístinos del Orinoco colombiano. Los puntos de muestreo abarcaron un gradiente de elevación de 300 a 3400 m.s.n.m. que incluyó un conjunto heterogéneo de ecorregiones y paisajes. § Mediante una aproximación de ligar patrones y posibles mecanismos, esta tesis proporciona evidencias de que la dispersión, la selección y la deriva están directamente involucradas en el proceso de ensamblaje de las comunidades bentónicas fluviales. § Mis hallazgos indican que uno o más eventos de limitación de la dispersión en un marco de tiempo evolutivo (eventos de aislamiento alopátrico) formaron diferentes pools de especies dentro de la cuenca del Orinoco. La extensión de estos pools coincide parcialmente con la distribución de las ecorregiones, lo que sugiere que los eventos que moldearon los paisajes fluviales y la estructura de la vegetación afectaron de manera similar la diversidad y distribución de las especies bentónicas en ecosistemas fluviales. § Adicionalmente, dentro de cada ecorregión, la dispersión, la selección y la deriva están interactuando para restringir la estructura y la dinámica de las comunidades y metacomunidades entre y dentro de los ríos. Dependiendo de la comunidad (p.e. diatomeas o insectos), el papel de cada uno de estos procesos puede prevalecer sobre el de los demás. § Estos hallazgos tienen implicaciones tanto para la investigación básica como para la aplicada (p.e. biomonitoreo) en las disciplinas de la ecología de metacomunidades y de agua dulce, así como en la conservación y la biogeografía.§ The conservation and rehabilitation of ecosystem structure and functioning requires of a deep knowledge on the causes and consequences of its biodiversity. The assembly of Neotropical communities, particularly in riverine ecosystems, remains to be dissected. § I used the metacommunity framework to dissect the relative influences of dispersal (in ecological and evolutionary timeframes), selection (driven by abiotic factors) and ecological drift on the assembly process of freshwater benthic communities. § The study was carried out at 26-32 different stream segments within an area of 2 about 40,000km , in the Colombian Orinoco. The area encompasses an elevation gradient from 3400 to 300m a.s.l. and includes a heterogeneous assembly of ecoregions and landscapes. § By using a pattern-matching approach, I provide evidences supporting that dispersal, selection and drift are directly involved in the assembly of freshwater benthic communities. § My findings indicate that one or more events of dispersal limitation (i.e. allopatric isolation) in an evolutionary timeframe shaped distinct pools of taxa in the Orinoco basin. The extent of these pools partially matches the distribution of the ecoregions, suggesting that those events molding the riverscapes and the vegetation structure similarly affect the diversity and distribution of benthic species. § Within each ecoregion, dispersal, selection and drift interact to constrain the structure and dynamics of communities and metacommunities among and within streams. Depending on the taxa belonging to each pool of species, the role of one of these processes may prevail over the others. § These findings have implications for both basic and applied research in the disciplines of metacommunity and freshwater ecology as well as of conservation and biogeography.Linking functional diversity patterns of algae and invertebrates to scale-dependent constrains of rivers from the Orinoco basinTesis con fines de doble titulación bajo el Convenio de cotutela entre la Universidad de Girona y la Universidad Nacional de Colombia.Doctorad