Institut de Mathématiques de Marseille

We consider the Dirichlet Laplacian operator<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mo>−</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow></mml:math>on a curved quantum guide in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msup><mml:mi>ℝ </mml:mi><mml:mi>n</mml:mi></mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>with an asymptotically straight reference curve. We give uniqueness results for the inverse problem associated to the reconstruction of the curvature by using either observations of spectral data or a boot-strapping method.

We consider a backward stochastic differential equation, whose data (the final condition and the coefficient) are given functions of a jump-diffusion process. We prove that under mild conditions the solution of the BSDE provides a viscosity solution of a system of parabolic integral-partial differential equations. Under an additional assumption, that system of equations is proved to have a unique solution, in a given class of continuous functions

We prove that the recently introduced Yang–Baxter σ-model can be considered as an integrable deformation of the principal chiral model. We find also an explicit one-to-one map transforming every solution of the principal chiral model into a solution of the deformed model. With the help of this map, the standard procedure of the dressing of the principal chiral solutions can be directly transferred into the deformed Yang–Baxter context.

With more than 30,000 species, ray-finned fish represent approximately half of vertebrates. The evolution of ray-finned fish was impacted by several whole genome duplication (WGD) events including a teleost-specific WGD event (TGD) that occurred at the root of the teleost lineage about 350 million years ago (Mya) and more recent WGD events in salmonids, carps, suckers and others. In plants and animals, WGD events are associated with adaptive radiations and evolutionary innovations. WGD-spurred innovation may be especially relevant in the case of teleost fish, which colonized a wide diversity of habitats on earth, including many extreme environments. Fish biodiversity, the use of fish models for human medicine and ecological studies, and the importance of fish in human nutrition, fuel an important need for the characterization of gene expression repertoires and corresponding evolutionary histories of ray-finned fish genes. To this aim, we performed transcriptome analyses and developed the PhyloFish database to provide (i) de novo assembled gene repertoires in 23 different ray-finned fish species including two holosteans (i.e. a group that diverged from teleosts before TGD) and 21 teleosts (including six salmonids), and (ii) gene expression levels in ten different tissues and organs (and embryos for many) in the same species. This resource was generated using a common deep RNA sequencing protocol to obtain the most exhaustive gene repertoire possible in each species that allows between-species comparisons to study the evolution of gene expression in different lineages. The PhyloFish database described here can be accessed and searched using RNAbrowse, a simple and efficient solution to give access to RNA-seq de novo assembled transcripts.

We have developed methods and tools based on the Gene Ontology (GO) resource allowing the identification of statistically over- or under-represented terms in a gene dataset; the clustering of functionally related genes within a set; and the retrieval of genes sharing annotations with a query gene. GO annotations can also be constrained to a slim hierarchy or a given level of the ontology. The source codes are available upon request, and distributed under the GPL license.

Plastid Origins The glaucophytes, represented by the alga Cyanophora paradoxa , are the putative sister group of red and green algae and plants, which together comprise the founding group of photosynthetic eukaryotes, the Plantae. In their analysis of the genome of C. paradoxa , Price et al. (p. 843 ; see the Perspective by Spiegel ) demonstrate a unique origin for the plastid in the ancestor of this supergroup, which retains much of the ancestral diversity in genes involved in carbohydrate metabolism and fermentation, as well as in the gene content of the mitochondrial genome. Moreover, about 3.3% of nuclear genes in C. paradoxa seem to carry a signal of cyanobacterial ancestry, and key genes involved in starch biosynthesis are derived from energy parasites such as Chlamydiae. Rapid radiation, reticulate evolution via horizontal gene transfer, high rates of gene divergence, loss, and replacement, may have diffused the evolutionary signals within this supergroup, which perhaps explains previous difficulties in resolving its evolutionary history.

BACKGROUND: In general, the construction of trees is based on sequence alignments. This procedure, however, leads to loss of informationwhen parts of sequence alignments (for instance ambiguous regions) are deleted before tree building. To overcome this difficulty, one of us previously introduced a new and rapid algorithm that calculates dissimilarity matrices between sequences without preliminary alignment. RESULTS: In this paper, HIV (Human Immunodeficiency Virus) and SIV (Simian Immunodeficiency Virus) sequence data are used to evaluate this method. The program produces tree topologies that are identical to those obtained by a combination of standard methods detailed in the HIV Sequence Compendium. Manual alignment editing is not necessary at any stage. Furthermore, only one user-specified parameter is needed for constructing trees. CONCLUSION: The extensive tests on HIV/SIV subtyping showed that the virus classifications produced by our method are in good agreement with our best taxonomic knowledge, even in non-coding LTR (Long Terminal Repeat) regions that are not tractable by regular alignment methods due to frequent duplications/insertions/deletions. Our method, however, is not limited to the HIV/SIV subtyping. It provides an alternative tree construction without a time-consuming aligning procedure.

MOTIVATION: Assessing functional associations between an experimentally derived gene or protein set of interest and a database of known gene/protein sets is a common task in the analysis of large-scale functional genomics data. For this purpose, a frequently used approach is to apply an over-representation-based enrichment analysis. However, this approach has four drawbacks: (i) it can only score functional associations of overlapping gene/proteins sets; (ii) it disregards genes with missing annotations; (iii) it does not take into account the network structure of physical interactions between the gene/protein sets of interest and (iv) tissue-specific gene/protein set associations cannot be recognized. RESULTS: To address these limitations, we introduce an integrative analysis approach and web-application called EnrichNet. It combines a novel graph-based statistic with an interactive sub-network visualization to accomplish two complementary goals: improving the prioritization of putative functional gene/protein set associations by exploiting information from molecular interaction networks and tissue-specific gene expression data and enabling a direct biological interpretation of the results. By using the approach to analyse sets of genes with known involvement in human diseases, new pathway associations are identified, reflecting a dense sub-network of interactions between their corresponding proteins. AVAILABILITY: EnrichNet is freely available at http://www.enrichnet.org. CONTACT: Natalio.Krasnogor@nottingham.ac.uk, reinhard.schneider@uni.lu or avalencia@cnio.es SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics Online.

Graphene–gold metasurface architectures that can provide significant gains in plasmonic detection sensitivity for trace-amount target analytes are reported. Benefiting from extreme phase singularities of reflected light induced by strong plasmon-mediated energy confinements, the metasurface demonstrates a much-improved sensitivity to molecular bindings nearby and achieves an ultralow detection limit of 1 × 10−18 m for 7.3 kDa 24-mer single-stranded DNA. As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re-organized for online delivery, but are not copy-edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

We here describe PRODISTIN, a new computational method allowing the functional clustering of proteins on the basis of protein-protein interaction data. This method, assessed biologically and statistically, enabled us to classify 11% of the Saccharomyces cerevisiae proteome into several groups, the majority of which contained proteins involved in the same biological process(es), and to predict a cellular function for many otherwise uncharacterized proteins.

We interpret the following fully nonlinear second-order partial differential equation as the value function of a certain optimal controlled diffusion problem, where is a second order elliptic partial differential operator parametrized by the control variable αϵA: with Here σ,b, and c are functions defined on with values respectively in and is a real function defined on . A particular case of this equation is when . In this case, the equation is the well-known Hamilton-Jacobi-Bellman equation. The problem is formulated as follows: The state equation of the control problem is a classical one. The cost function is described by an adapted solution of a certain backward stochastic differential equation. The paper discusses Bellman's dynamic programming principle for this problem The value function is proved to be a viscosity solution of the above possibly degenerate fully nonlinear equation

Go back to An-fang, the Peace Square at An-Fang, the Beginning Place at An-Fang, where all things start (…) An-Fang was near a city, the only living city with a pre-atomic name (…) The headquarters of the People Programmer was at An-Fang, and there the mistake happened: A ruby trembled. Two tourmaline nets failed to rectify the laser beam. A diamond noted the error. Both the error and the correction went into the general computer. Cordwainer Smith The Dead Lady of Clown Town , 1964.

Soit F, le corps fini q lments. On montre (thorme 1) que la srie formelle / (X )= ^ o /" X" F, [[X]] est algbrique sur F, (X ) si et seulement si la suite des coefficients (/") est engendre par un automate fini. On en dduit que sif{X) est algbrique sur F,(X) et sur ^q'(X} alors/(JO est rationnelle pourvu que log ql\o% q'^Q.

High-dimensional multi-omics data are now standard in biology. They can greatly enhance our understanding of biological systems when effectively integrated. To achieve proper integration, joint Dimensionality Reduction (jDR) methods are among the most efficient approaches. However, several jDR methods are available, urging the need for a comprehensive benchmark with practical guidelines. We perform a systematic evaluation of nine representative jDR methods using three complementary benchmarks. First, we evaluate their performances in retrieving ground-truth sample clustering from simulated multi-omics datasets. Second, we use TCGA cancer data to assess their strengths in predicting survival, clinical annotations and known pathways/biological processes. Finally, we assess their classification of multi-omics single-cell data. From these in-depth comparisons, we observe that intNMF performs best in clustering, while MCIA offers an effective behavior across many contexts. The code developed for this benchmark study is implemented in a Jupyter notebook-multi-omics mix (momix)-to foster reproducibility, and support users and future developers.

This Letter presents a wavelet technique for extracting coherent vortices from three-dimensional turbulent flows, which is applied to a homogeneous isotropic turbulent flow at resolution N = 256(3). The coherent flow is reconstructed from only 3%N wavelet coefficients that retain the vortex tubes, and 98.9% of the energy with the same k(-5/3) spectrum as the total flow. In contrast, the remaining 97%N wavelet coefficients correspond to the incoherent flow which is structureless, decorrelated, and whose effect can therefore be modeled statistically.

There is epidemiological evidence that patients with certain Central Nervous System (CNS) disorders have a lower than expected probability of developing some types of Cancer. We tested here the hypothesis that this inverse comorbidity is driven by molecular processes common to CNS disorders and Cancers, and that are deregulated in opposite directions. We conducted transcriptomic meta-analyses of three CNS disorders (Alzheimer's disease, Parkinson's disease and Schizophrenia) and three Cancer types (Lung, Prostate, Colorectal) previously described with inverse comorbidities. A significant overlap was observed between the genes upregulated in CNS disorders and downregulated in Cancers, as well as between the genes downregulated in CNS disorders and upregulated in Cancers. We also observed expression deregulations in opposite directions at the level of pathways. Our analysis points to specific genes and pathways, the upregulation of which could increase the incidence of CNS disorders and simultaneously lower the risk of developing Cancer, while the downregulation of another set of genes and pathways could contribute to a decrease in the incidence of CNS disorders while increasing the Cancer risk. These results reinforce the previously proposed involvement of the PIN1 gene, Wnt and P53 pathways, and reveal potential new candidates, in particular related with protein degradation processes.

While Caenorhabditis elegans specifically responds to infection by the up-regulation of certain genes, distinct pathogens trigger the expression of a common set of genes. We applied new methods to conduct a comprehensive and comparative study of the transcriptional response of C. elegans to bacterial and fungal infection. Using tiling arrays and/or RNA-sequencing, we have characterized the genome-wide transcriptional changes that underlie the host's response to infection by three bacterial (Serratia marcescens, Enterococcus faecalis and otorhabdus luminescens) and two fungal pathogens (Drechmeria coniospora and Harposporium sp.). We developed a flexible tool, the WormBase Converter (available at http://wormbasemanager.sourceforge.net/), to allow cross-study comparisons. The new data sets provided more extensive lists of differentially regulated genes than previous studies. Annotation analysis confirmed that genes commonly up-regulated by bacterial infections are related to stress responses. We found substantial overlaps between the genes regulated upon intestinal infection by the bacterial pathogens and Harposporium, and between those regulated by Harposporium and D. coniospora, which infects the epidermis. Among the fungus-regulated genes, there was a significant bias towards genes that are evolving rapidly and potentially encode small proteins. The results obtained using new methods reveal that the response to infection in C. elegans is determined by the nature of the pathogen, the site of infection and the physiological imbalance provoked by infection. They form the basis for future functional dissection of innate immune signaling. Finally, we also propose alternative methods to identify differentially regulated genes that take into account the greater variability in lowly expressed genes.

BACKGROUND: Qualitative frameworks, especially those based on the logical discrete formalism, are increasingly used to model regulatory and signalling networks. A major advantage of these frameworks is that they do not require precise quantitative data, and that they are well-suited for studies of large networks. While numerous groups have developed specific computational tools that provide original methods to analyse qualitative models, a standard format to exchange qualitative models has been missing. RESULTS: We present the Systems Biology Markup Language (SBML) Qualitative Models Package ("qual"), an extension of the SBML Level 3 standard designed for computer representation of qualitative models of biological networks. We demonstrate the interoperability of models via SBML qual through the analysis of a specific signalling network by three independent software tools. Furthermore, the collective effort to define the SBML qual format paved the way for the development of LogicalModel, an open-source model library, which will facilitate the adoption of the format as well as the collaborative development of algorithms to analyse qualitative models. CONCLUSIONS: SBML qual allows the exchange of qualitative models among a number of complementary software tools. SBML qual has the potential to promote collaborative work on the development of novel computational approaches, as well as on the specification and the analysis of comprehensive qualitative models of regulatory and signalling networks.

We consider nonlinear diffusive evolution equations posed on bounded space\ndomains, governed by fractional Laplace-type operators, and involving porous\nmedium type nonlinearities. We establish existence and uniqueness results in a\nsuitable class of solutions using the theory of maximal monotone operators on\ndual spaces. Then we describe the long-time asymptotics in terms of\nseparate-variables solutions of the friendly giant type. As a by-product, we\nobtain an existence and uniqueness result for semilinear elliptic non local\nequations with sub-linear nonlinearities. The Appendix contains a review of the\ntheory of fractional Sobolev spaces and of the interpolation theory that are\nused in the rest of the paper.\n

Deciphering invasion routes from molecular data is crucial to understanding biological invasions, including identifying bottlenecks in population size and admixture among distinct populations. Here, we unravel the invasion routes of the invasive pest Drosophila suzukii using a multi-locus microsatellite dataset (25 loci on 23 worldwide sampling locations). To do this, we use approximate Bayesian computation (ABC), which has improved the reconstruction of invasion routes, but can be computationally expensive. We use our study to illustrate the use of a new, more efficient, ABC method, ABC random forest (ABC-RF) and compare it to a standard ABC method (ABC-LDA). We find that Japan emerges as the most probable source of the earliest recorded invasion into Hawaii. Southeast China and Hawaii together are the most probable sources of populations in western North America, which then in turn served as sources for those in eastern North America. European populations are genetically more homogeneous than North American populations, and their most probable source is northeast China, with evidence of limited gene flow from the eastern US as well. All introduced populations passed through bottlenecks, and analyses reveal five distinct admixture events. These findings can inform hypotheses concerning how this species evolved between different and independent source and invasive populations. Methodological comparisons indicate that ABC-RF and ABC-LDA show concordant results if ABC-LDA is based on a large number of simulated datasets but that ABC-RF out-performs ABC-LDA when using a comparable and more manageable number of simulated datasets, especially when analyzing complex introduction scenarios.