Simple temporal models for ecological systems with complex spatial patterns

Spatial patterns are ubiquitous in nature. Because these patterns modify the temporal dynamics and stability properties of population densities at a range of spatial scales, their effects must be incorporated in temporal ecological models that do not represent space explicitly. We demonstrate a connection between a simple parameterization of spatial effects and the geometry of clusters in an individual-based predator–prey model that is both nonlinear and stochastic. Specifically we show that clusters exhibit a power-law scaling of perimeter to area with an exponent close to unity. In systems with a high degree of patchiness, similar power-law scalings can provide a basis for applying simple temporal models that assume well-mixed conditions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72011/1/j.1461-0248.2002.00334.x.pd

Rangs des tenseurs : bases pour la réduction de dimension et la séparation des variables

A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of the entries. The rank of a tensor extends to arrays with more than two entries the notion of rank of a matrix, bearing in mind that there are several approaches to build such an extension. When the rank is one, the variables are separated, and when it is low, the variables are weakly coupled. Many calculations are simpler on tensors of low rank. Furthermore, approximating a given tensor by a low-rank tensor makes it possible to compute some characteristics of a table, such as the partition function when it is a joint law. In this note, we present in detail an integrated and progressive approach to approximate a given tensor by a tensor of lower rank, through a systematic use of tensor algebra. The notion of tensor is rigorously defined, then elementary but useful operations on tensors are presented. After recalling several different notions for extending the rank to tensors, we show how these elementary operations can be combined to build best low rank approximation algorithms. The last chapter is devoted to applying this approach to tensors constructed as the discretisation of a multivariate function, to show that on a Cartesian grid, the rank of such tensors is expected to be low.Un tenseur est notamment un tableau à plusieurs entrées qui peut représenter, outre un jeu de données, l'expression d'une loi jointe ou d'une fonction multivariée. Il contient alors la description des interactions entre les variables correspondant à chacune des entrées. Le rang d'un tenseur étend à des tableaux à plus de deux entrées la notion de rang d'une matrice, sachant qu'il existe plusieurs approches pour construire une telle extension. Lorsque le rang vaut un, les variables sont séparées, et lorsqu'il est faible, les variables sont faiblement couplées. Bien des calculs sont plus simples sur des tenseurs de rang faible. Aussi, approcher un tenseur donné par un tenseur de rang faible permet de les rendre possibles pour calculer certaines caractéristiques d'un tableau, comme par exemple la fonction de partition quand il s'agit d'une loi jointe. Dans cette note, nous présentons en détail une approche intégrée et progressive pour approcher un tenseur donné par un tenseur de rang plus faible, par une utilisation systématique de l'algèbre tensorielle. La notion de tenseur est définie rigoureusement, puis des opérations élémentaires mais utiles sur les tenseurs sont présentées. Après avoir rappelé plusieurs notions différentes pour le rang d'un tenseur, nous montrons comment ces opérations élémentaires peuvent être combinées pour construire des algorithmes d'approximation de rang faible. Le dernier chapitre est consacré à appliquer cette approche aux tenseurs construits comme la discrétisation d'une fonction multivariée, pour montrer que sur une grille cartésienne, le rang de tels tenseurs est en général faible

Sex-biased dispersal promotes adaptive parental effects

<p>Abstract</p> <p>Background</p> <p>In heterogeneous environments, sex-biased dispersal could lead to environmental adaptive parental effects, with offspring selected to perform in the same way as the parent dispersing least, because this parent is more likely to be locally adapted. We investigate this hypothesis by simulating varying levels of sex-biased dispersal in a patchy environment. The relative advantage of a strategy involving pure maternal (or paternal) inheritance is then compared with a strategy involving classical biparental inheritance in plants and in animals.</p> <p>Results</p> <p>We find that the advantage of the uniparental strategy over the biparental strategy is maximal when dispersal is more strongly sex-biased and when dispersal distances of the least mobile sex are much lower than the size of the environmental patches. In plants, only maternal effects can be selected for, in contrast to animals where the evolution of either paternal or maternal effects can be favoured. Moreover, the conditions for environmental adaptive maternal effects to be selected for are more easily fulfilled in plants than in animals.</p> <p>Conclusions</p> <p>The study suggests that sex-biased dispersal can help predict the direction and magnitude of environmental adaptive parental effects. However, this depends on the scale of dispersal relative to that of the environment and on the existence of appropriate mechanisms of transmission of environmentally induced traits.</p

A novel approach for treatment of sacrococcygeal pilonidal sinus: less is more

Background: The surgical management of sacrococcygeal pilonidal sinus (PS) is still a matter of discussion. Therapy ranges from complete wide excision with or without closure of the wound to excochleation of the sinus with a brush. In this paper, we introduce a novel limited excision technique. The aim of this study was to assess the morbidity and recurrence rate of this technique. Materials and methods: Limited excision consisted of a selective extirpation of the sinus after tagging the tract with methylene blue. Ninety-three consecutive patients, who underwent surgery between 2001 and 2004, were analyzed. The patients' survey was performed by mail questionnaire and telephone interview inquiring recurrence, time off work, and time to wound healing. Results: Seventy-three percent of the patients were treated in an outpatient setting. With a median follow-up of 2years, the recurrence rate was 5%. The median time off work was 2weeks. The median wound healing time was 5weeks. Conclusion: Limited excision for PS can be done in an outpatient setting with a low recurrence rate and short time off wor

Géométrie sur les distances et meilleure image euclidienne avec distances pondérées

Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well established questions: Distance Geometry Problem is about finding a Euclidean realization of an incomplete set of distances in a Euclidean space, whereas Nonlinear Mapping is a weighted Least Square Scaling (LSS) method. We show how all these methods (LSS, NLM, DGP) can be assembled in a common framework, being each identified as an instance of an optimization problem with a choice of a weight matrix. We study the continuity between the solutions (which are point clouds) when the weight matrix varies, and the compactness of the set of solutions (after centering). We finally study a numerical example, showing that solving the optimization problem is far from being simple and that the numerical solution for a given procedure may be trapped in a local minimum.Les domaines de géométrie sur les distances (distance geometry) et de recherche de meilleure image euclidienne avec distances pondérées (nonlinear mapping) sont deux domaines classiques : il s’agit pour le premier de construire une isométrie d’un espace métrique discret vers un nuage de points dans un espace euclidien, ne connaissant qu’une partie des distances, et pour le second de construire un nuage avec la meilleure approximation des distances, avec pondération. Nous montrons comment ces méthodes peuvent être rassemblée en une même famille, chacune représentant un choix de pondérations dans un problème d’optimisation. On étudie la continuité entre ces solutions (qui sont des nuages de points), et la compacité des ensembles de solutions (après centrage). On étudie également un exemple numérique, montrant cependant que le prob- lème d’optimisation est loin d’être simple, et que la procédure d’optimisation peut facilement être piégée dans un minimum local

Extension de l'analyse des correspondances à des donnéees multi-dimensionnelles : un point de vue géométrique

This paper presents an extension of Correspondence Analysis (CA) to tensors through High Order Singular Value Decomposition (HOSVD) from a geometric viewpoint. Correspondence analysis is a well-known tool, developed from principal component analysis, for studying contingency tables. Different algebraic extensions of CA to multi-way tables have been proposed over the years, nevertheless neglecting its geometric meaning. Relying on the Tucker model and the HOSVD, we propose a direct way to associate with each tensor mode a point cloud. We prove that the point clouds are related to each other. Specifically using the CA metrics we show that the barycentric relation is still true in the tensor framework. Finally two data sets are used to underline the advantages and the drawbacks of our strategy with respect to the classical matrix approaches.Ce document présente une extension de l'analyse des correspondances aux tenseurs par la décomposition en valeurs singulières d'ordre élevé (HOSVD) d'un point de vue géométrique. L'analyse des correspondances est un outil bien connu, développé à partir de l'analyse en composantes principales, pour étudier les tables de contingence. Différentes extensions algébriques de l'analyse des correspondances aux tables à voies multiples ont été proposées au fil des ans. En nous appuyant sur le modèle de Tucker et la HOSVD, nous proposons d'associer à chaque mode d'un tenseur un nuage de points. Nous établissons un lien entre les cordonnées de ces différents nuages. Une telle relation est classique en Analyse Factorielle des Correspondances (AFC) pour justifier la projection simultanée des profils lignes et profils colonnes d'une table de contingence (d'où le nom de correspondance). Nous étendons une telle relation barycentrique aux liens entre les nuages de points associés aux différents modes de l'Analyse Factorielle des Correspondances Multiple d'un tenseur, construite via la HOSVD avec les métriques de l'AFC

FMR: Fast randomized algorithms for covariance matrix computations

International audienceWe present an open-source library implementing fast algorithms for covari-ance matrices computations, e.g., randomized low-rank approximations (LRA) and fast multipole matrix multiplication (FMM). The library can be used to approximate square roots of low-rank covariance matrices in O(N 2) operations in SVD form using randomized LRA, instead of the standard O(N 3) cost. Low-rank covariance matrices given as kernels, e.g., Gaussian decay, evaluated on 3D grids can be decomposed in O(N) operations using the FMM. The performance of the library is illustrated on two examples: • Generation of Gaussian Random Fields (GRF) on large spatial grids • MultiDimensional Scaling (MDS) for the classification of species

The impact of parasitism on resource allocation in a fungal host: the case of Cryphonectria parasitica and its mycovirus, Cryphonectria Hypovirus 1

International audienceParasites are known to profoundly affect resource allocation in their host. In order to investigate the effects of Cryphonectria Hypovirus 1 (CHV1) on the life-history traits of its fungal host Cryphonectria parasitica, an infection matrix was completed with the cross-infection of six fungal isolates by six different viruses. Mycelial growth, asexual sporulation, and spore size were measured in the 36 combinations, for which horizontal and vertical transmission of the viruses was also assessed. As expected by life-history theory, a significant negative correlation was found between host somatic growth and asexual reproduction in virus-free isolates. Interestingly this trade-off was found to be positive in infected isolates, illustrating the profound changes in host resource allocation induced by CHV1 infection. A significant and positive relationship was also found in infected isolates between vertical transmission and somatic growth. This last relationship suggests that in this system, high levels of virulence could be detrimental to the vertical transmission of the parasite. Those results underscore the interest of studying host–parasite interaction within the life-history theory framework, which might permit a more accurate understanding of the nature of the modifications triggered by parasite infection on host biology