Generic separating sets for 3D elasticity tensors

We define what is a generic separating set of invariant functions (a.k.a. a weak functional basis) for tensors. We produce then two generic separating sets of polynomial invariants for 3D elasticity tensors, one made of 19 polynomials and one made of 21 polynomials (but easier to compute) and a generic separating set of 18 rational invariants. As a byproduct, a new integrity basis for the fourth-order harmonic tensor is provided

Evaluation of the models handling heterotachy in phylogenetic inference

International audienceBACKGROUND: The evolutionary rate at a given homologous position varies across time. When sufficiently pronounced, this phenomenon-also called heterotachy, may produce artefactual phylogenetic reconstructions under the commonly used models of sequence evolution. These observations have motivated the development of models that explicitly recognize heterotachy, with research directions proposed along two main axes: 1) the covarion approach, where sites switch from variable to invariable states; and 2) the mixture of branch lengths (MBL) approach, where alignment patterns are assumed to arise from one of several sets of branch lengths, under a given phylogeny. RESULTS: Here, we report the first statistical comparisons contrasting the performance of covarion and MBL modeling strategies. Using simulations under heterotachous conditions, we explore the properties of three model comparison methods: the Akaike information criterion, the Bayesian information criterion, and cross validation. Although more time consuming, cross validation is the most reliable of the three methods as it directly measures the predictive power of a model on 'future' data. We also analyze three large datasets (nuclear proteins of animals, mitochondrial proteins of mammals, and plastid proteins of plants), and find the optimal number of components of the MBL model to be two for all datasets, indicating that this model is preferred over the standard homogeneous model. However, the covarion model is always favored over the optimal MBL model. CONCLUSION: We demonstrated, using three large datasets, that the covarion model is more efficient at handling heterotachy than the MBL model. This is probably due to the fact that the MBL model requires a drastic increase in the number of parameters, as compared to two supplementary parameters of the covarion approach. Further improvements of the both the mixture and the covarion approaches might be obtained by modeling heterogeneous behavior both along time and across sites

Fast optimization of statistical potentials for structurally constrained phylogenetic models

<p>Abstract</p> <p>Background</p> <p>Statistical approaches for <it>protein design </it>are relevant in the field of molecular evolutionary studies. In recent years, new, so-called structurally constrained (<it>SC</it>) models of protein-coding sequence evolution have been proposed, which use statistical potentials to assess sequence-structure compatibility. In a previous work, we defined a statistical framework for optimizing knowledge-based potentials especially suited to SC models. Our method used the maximum likelihood principle and provided what we call the <it>joint </it>potentials. However, the method required numerical estimations by the use of computationally heavy <it>Markov Chain Monte Carlo </it>sampling algorithms.</p> <p>Results</p> <p>Here, we develop an alternative optimization procedure, based on a <it>leave-one-out </it>argument coupled to fast gradient descent algorithms. We assess that the leave-one-out potential yields very similar results to the joint approach developed previously, both in terms of the resulting potential parameters, and by Bayes factor evaluation in a phylogenetic context. On the other hand, the leave-one-out approach results in a considerable computational benefit (up to a 1,000 fold decrease in computational time for the optimization procedure).</p> <p>Conclusion</p> <p>Due to its computational speed, the optimization method we propose offers an attractive alternative for the design and empirical evaluation of alternative forms of potentials, using large data sets and high-dimensional parameterizations.</p

Phylogenetic structural modeling of molecular evolution

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal

A maximum likelihood framework for protein design

BACKGROUND: The aim of protein design is to predict amino-acid sequences compatible with a given target structure. Traditionally envisioned as a purely thermodynamic question, this problem can also be understood in a wider context, where additional constraints are captured by learning the sequence patterns displayed by natural proteins of known conformation. In this latter perspective, however, we still need a theoretical formalization of the question, leading to general and efficient learning methods, and allowing for the selection of fast and accurate objective functions quantifying sequence/structure compatibility. RESULTS: We propose a formulation of the protein design problem in terms of model-based statistical inference. Our framework uses the maximum likelihood principle to optimize the unknown parameters of a statistical potential, which we call an inverse potential to contrast with classical potentials used for structure prediction. We propose an implementation based on Markov chain Monte Carlo, in which the likelihood is maximized by gradient descent and is numerically estimated by thermodynamic integration. The fit of the models is evaluated by cross-validation. We apply this to a simple pairwise contact potential, supplemented with a solvent-accessibility term, and show that the resulting models have a better predictive power than currently available pairwise potentials. Furthermore, the model comparison method presented here allows one to measure the relative contribution of each component of the potential, and to choose the optimal number of accessibility classes, which turns out to be much higher than classically considered. CONCLUSION: Altogether, this reformulation makes it possible to test a wide diversity of models, using different forms of potentials, or accounting for other factors than just the constraint of thermodynamic stability. Ultimately, such model-based statistical analyses may help to understand the forces shaping protein sequences, and driving their evolution

Heterotachy and long-branch attraction in phylogenetics

BACKGROUND: Probabilistic methods have progressively supplanted the Maximum Parsimony (MP) method for inferring phylogenetic trees. One of the major reasons for this shift was that MP is much more sensitive to the Long Branch Attraction (LBA) artefact than is Maximum Likelihood (ML). However, recent work by Kolaczkowski and Thornton suggested, on the basis of simulations, that MP is less sensitive than ML to tree reconstruction artefacts generated by heterotachy, a phenomenon that corresponds to shifts in site-specific evolutionary rates over time. These results led these authors to recommend that the results of ML and MP analyses should be both reported and interpreted with the same caution. This specific conclusion revived the debate on the choice of the most accurate phylogenetic method for analysing real data in which various types of heterogeneities occur. However, variation of evolutionary rates across species was not explicitly incorporated in the original study of Kolaczkowski and Thornton, and in most of the subsequent heterotachous simulations published to date, where all terminal branch lengths were kept equal, an assumption that is biologically unrealistic. RESULTS: In this report, we performed more realistic simulations to evaluate the relative performance of MP and ML methods when two kinds of heterogeneities are considered: (i) within-site rate variation (heterotachy), and (ii) rate variation across lineages. Using a similar protocol as Kolaczkowski and Thornton to generate heterotachous datasets, we found that heterotachy, which constitutes a serious violation of existing models, decreases the accuracy of ML whatever the level of rate variation across lineages. In contrast, the accuracy of MP can either increase or decrease when the level of heterotachy increases, depending on the relative branch lengths. This result demonstrates that MP is not insensitive to heterotachy, contrary to the report of Kolaczkowski and Thornton. Finally, in the case of LBA (i.e. when two non-sister lineages evolved faster than the others), ML outperforms MP over a wide range of conditions, except for unrealistic levels of heterotachy. CONCLUSION: For realistic combinations of both heterotachy and variation of evolutionary rates across lineages, ML is always more accurate than MP. Therefore, ML should be preferred over MP for analysing real data, all the more so since parametric methods also allow one to handle other types of biological heterogeneities much better, such as among sites rate variation. The confounding effects of heterotachy on tree reconstruction methods do exist, but can be eschewed by the development of mixture models in a probabilistic framework, as proposed by Kolaczkowski and Thornton themselves

Computation of minimal covariants bases for 2D coupled constitutive laws

We produce minimal integrity bases for both isotropic and hemitropic invariant algebras (and more generally covariant algebras) of most common bidimensional constitutive tensors and -- possibly coupled -- laws, including piezoelectricity law, photoelasticity, Eshelby and elasticity tensors, complex viscoelasticity tensor, Hill elasto-plasticity, and (totally symmetric) fabric tensors up to twelfth-order. The concept of covariant, which extends that of invariant is explained and motivated. It appears to be much more useful for applications. All the tools required to obtain these results are explained in detail and a cleaning algorithm is formulated to achieve minimality in the isotropic case. The invariants and covariants are first expressed in complex forms and then in tensorial forms, thanks to explicit translation formulas which are provided. The proposed approach also applies to any $n$-uplet of bidimensional constitutive tensors

Making sense of methods – a conversation about qualitative research in library and information studies

Currently there is an embarrassment of riches with regards to the range of research methods appropriate for library and information studies [LIS]; including qualitative and quantitative methods as well as ‘mixed methods’. All of this provides a rich body of resources for researchers, but this abundance also has a downside since it can also result in confusion and perplexity amongst researchers as they plan their investigative studies. Contributions such as this special issue are welcome opportunities to resolve and ameliorate this situation, and so in our contribution we seek to address some of these issues in the form of an interchange between two researchers with interests that include, but are not limited to, research in LIS. Between us we have a wide range of publications, as well as 80 plus PhD completions, many of which fall under the heading of LIS – broadly conceived. In particular we would claim specific expertise in Grounded Theory [Bryant] and Action Research [Abbott-Halpin]. Our aim is to seek clarification of some of the key methodological issues; although we realize that this is unlikely to provide any definitive outcome, it may assist those seeking guidance on these matters

A model to predict image formation in the three-dimensional field ion microscope

This article presents a numerical model dedicated to the simulation of field ion microscopy (FIM). FIM was the first technique to image individual atoms on the surface of a material. By a careful control of the field evaporation of the atoms from the surface, the bulk of the material exposed, and, through a digitally processing a sequence of micrographs, a three-dimensional reconstruction can be achieved. 3DFIM is particularly suited to the direct observation of crystalline defects such as vacancies, interstitials, vacancy clusters, dislocations, and any combinations of theses defects that underpin the physical properties of materials. This makes 3DFIM extremely valuable for many material science and engineering applications, and further developing this technique is becoming crucial. The proposed model enables the simulation of imaging artefacts that are induced by non-regular field evaporation and by the impact of the perturbation of the electric field distribution of the distorted distribution of atoms close to defects. The model combines the meshless algorithm for field evaporation proposed by Rolland et al. (Robin-Rolland Model, or RRM) with fundamental aspects of the field ionization process of the gas image involved in FIM

The CC-Bio Project: Studying the Effects of Climate Change on Quebec Biodiversity

Anticipating the effects of climate change on biodiversity is now critical for managing wild species and ecosystems. Climate change is a global driver and thus affects biodiversity globally. However, land-use planners and natural resource managers need regional or even local predictions. This provides scientists with formidable challenges given the poor documentation of biodiversity and its complex relationships with climate. We are approaching this problem in Quebec, Canada, through the CC-Bio Project (http://cc‑bio.uqar.ca/), using a boundary organization as a catalyst for team work involving climate modelers, biologists, naturalists, and biodiversity managers. In this paper we present the CC-Bio Project and its general approach, some preliminary results, the emerging hypothesis of the northern biodiversity paradox (a potential increase of biodiversity in northern ecosystems due to climate change), and an early assessment of the conservation implications generated by our team work