Determining species tree topologies from clade probabilities under the coalescent

One approach to estimating a species tree from a collection of gene trees is to first estimate probabilities of clades from the gene trees, and then to construct the species tree from the estimated clade probabilities. While a greedy consensus algorithm, which consecutively accepts the most probable clades compatible with previously accepted clades, can be used for this second stage, this method is known to be statistically inconsistent under the multispecies coalescent model. This raises the question of whether it is theoretically possible to reconstruct the species tree from known probabilities of clades on gene trees. We investigate clade probabilities arising from the multispecies coalescent model, with an eye toward identifying features of the species tree. Clades on gene trees with probability greater than 1/3 are shown to reflect clades on the species tree, while those with smaller probabilities may not. Linear invariants of clade probabilities are studied both computationally and theoretically, with certain linear invariants giving insight into the clade structure of the species tree. For species trees with generic edge lengths, these invariants can be used to identify the species tree topology. These theoretical results both confirm that clade probabilities contain full information on the species tree topology and suggest future directions of study for developing statistically consistent inference methods from clade frequencies on gene trees.Comment: 25 pages, 2 figure

A PDE based approach to multi-domain partitioning and quadrilateral meshing

International audienceIn this paper, we present an algorithm for partitioning any given 2d domain into regions suitable for quadrilateral meshing. It can deal with multi-domain geometries with ease, and is able to preserve the symmetry of the domain. Moreover, this method keeps the number of singularities at the junctions of the regions to a minimum. Each part of the domain, being four-sided, can then be meshed using a structured method. The partitioning stage is achieved by solving a PDE constrained problem based on the geometric properties of the domain boundaries

Saturation of the Raman amplification by self-phase modulation in silicon nanowaveguides

We experimentally show that the self-phase modulation of picosecond pump pulses, induced by both the optical Kerr effect and free-carrier refraction, has a detrimental effect on the maximum on-off Raman gain achievable in silicon on insulator nanowaveguides, causing it to saturate. A simple calculation of the Raman gain coefficient from the measured broadened output pump spectra perfectly matches the saturated behavior of the amplified Raman signal observed experimentally at different input pump powers.Comment: Accepted for publications in Applied Physics Letter

Powers of the likelihood ratio test and the correlation test using empirical bayes estimates for various shrinkages in population pharmacokinetics.

International audienceWe compared the powers of the likelihood ratio test (LRT) and the Pearson correlation test (CT) from empirical Bayes estimates (EBEs) for various designs and shrinkages in the context of nonlinear mixed-effect modeling. Clinical trial simulation was performed with a simple pharmacokinetic model with various weight (WT) effects on volume (V). Data sets were analyzed with NONMEM 7.2 using first-order conditional estimation with interaction and stochastic approximation expectation maximization algorithms. The powers of LRT and CT in detecting the link between individual WT and V or clearance were computed to explore hidden or induced correlations, respectively. Although the different designs and variabilities could be related to the large shrinkage of the EBEs, type 1 errors and powers were similar in LRT and CT in all cases. Power was mostly influenced by covariate effect size and, to a lesser extent, by the informativeness of the design. Further studies with more models are needed

Acoustic Engineering Workstation at the College of the Ozarks

The College of the Ozarks is developing the ability to provide acoustic engineering services to customers on and off-campus. The College is the only federally recognized work college with an undergraduate engineering program, which means students do not pay tuition and are assigned workstations on campus to help defray expenses and to generate income for the College. This paper addresses the purpose and administration of the workstation and how it is unique from other service-learning programs, the perceived benefits to the student workers and the engineering program, recent workstation accomplishments, lessons learned, and future plans

The Poplar-Poplar Rust Interaction: Insights from Genomics and Transcriptomics

Poplars are extensively cultivated worldwide, and their susceptibility to the leaf rust fungus Melampsora larici-populina leads to considerable damages in plantations. Despite a good knowledge of the poplar rust life cycle, and particularly the epidemics on poplar, the perennial status of the plant host and the obligate biotrophic lifestyle of the rust fungus are bottlenecks for molecular investigations. Following the completion of both M. larici-populina and Populus trichocarpa genome sequences, gene families involved in poplar resistance or in rust fungus virulence were investigated, allowing the identification of key genetic determinants likely controlling the outcome of the interaction. Specific expansions of resistance and defense-related genes in poplar indicate probable innovations in perennial species in relation with host-pathogen interactions. The genome of M. Larici-populina contains a strikingly high number of genes encoding small secreted proteins (SSPs) representing hundreds of candidate effectors. Transcriptome analyses of interacting partners in compatible and incompatible interactions revealed conserved set of genes involved in poplar defense reactions as well as timely regulated expression of SSP transcripts during host tissues colonisation. Ongoing functional studies of selected candidate effectors will be achieved mainly on the basis of recombinant protein purification and subsequent characterisation

Maths in Action in Contemporary Archaeology: numerical simulation of fire propagation in Roman buildings

This short paper explores the possibility of conducting high-performance computing simulations of complex fire propagation in buildings of archaeological interest. The simulation protocol described here involves several steps: i) the geometric modelling of the buildings, ii) the mathematical modelling of combustion and fire propagation, iii) the numerical simulation using a Large Eddy Scale approach on parallel systems and iv) the real time rendering of the simulation data. Numerical examples are provided to emphasize the e ciency of the approach and its importance in supporting research in archaeology and validating hypotheses through simulation

Prediction of Shrinkage of Individual Parameters Using the Bayesian Information Matrix in Non-Linear Mixed Effect Models with Evaluation in Pharmacokinetics

ABSTRACT: Purpose: When information is sparse, individual parameters derived from a non-linear mixed effects model analysis can shrink to the mean. The objective of this work was to predict individual parameter shrinkage from the Bayesian information matrix (M BF ). We 1) Propose and evaluate an approximation of M BF by First-Order linearization (FO), 2) Explore by simulations the relationship between shrinkage and precision of estimates and 3) Evaluate prediction of shrinkage and individual parameter precision. Methods: We approximated M BF using FO. From the shrinkage formula in linear mixed effects models, we derived the predicted shrinkage from M BF . Shrinkage values were generated for parameters of two pharmacokinetic models by varying the structure and the magnitude of the random effect and residual error models as well as the design. We then evaluated the approximation of M BF FO and compared it to Monte-Carlo (MC) simulations. We finally compared expected and observed shrinkage as well as the predicted and estimated Standard Errors (SE) of individual parameters. Results: M BF FO was similar to M BF MC. Predicted and observed shrinkages were close . Predicted and estimated SE were similar. Conclusions: M BF FO enables prediction of shrinkage and SE of individual parameters. It can be used for design optimizatio