Institut de Mathématiques de Marseille

The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a variety of complex systems has been successfully described as networks whose interacting pairs of nodes are connected by links. Yet, from human communications to chemical reactions and ecological systems, interactions can often occur in groups of three or more nodes and cannot be described simply in terms of dyads. Until recently little attention has been devoted to the higher-order architecture of real complex systems. However, a mounting body of evidence is showing that taking the higher-order structure of these systems into account can enhance our modeling capacities and help us understand and predict their dynamical behavior. Here we present a complete overview of the emerging field of networks beyond pairwise interactions. We discuss how to represent higher-order interactions and introduce the different frameworks used to describe higher-order systems, highlighting the links between the existing concepts and representations. We review the measures designed to characterize the structure of these systems and the models proposed to generate synthetic structures, such as random and growing bipartite graphs, hypergraphs and simplicial complexes. We introduce the rapidly growing research on higher-order dynamical systems and dynamical topology, discussing the relations between higher-order interactions and collective behavior. We focus in particular on new emergent phenomena characterizing dynamical processes, such as diffusion, synchronization, spreading, social dynamics and games, when extended beyond pairwise interactions. We conclude with a summary of empirical applications, and an outlook on current modeling and conceptual frontiers.

The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a variety of complex systems has been successfully described as networks whose interacting pairs of nodes are connected by links. Yet, from human communications to chemical reactions and ecological systems, interactions can often occur in groups of three or more nodes and cannot be described simply in terms of dyads. Until recently little attention has been devoted to the higher-order architecture of real complex systems. However, a mounting body of evidence is showing that taking the higher-order structure of these systems into account can enhance our modeling capacities and help us understand and predict their dynamical behavior. Here we present a complete overview of the emerging field of networks beyond pairwise interactions. We discuss how to represent higher-order interactions and introduce the different frameworks used to describe higher-order systems, highlighting the links between the existing concepts and representations. We review the measures designed to characterize the structure of these systems and the models proposed to generate synthetic structures, such as random and growing bipartite graphs, hypergraphs and simplicial complexes. We introduce the rapidly growing research on higher-order dynamical systems and dynamical topology, discussing the relations between higher-order interactions and collective behavior. We focus in particular on new emergent phenomena characterizing dynamical processes, such as diffusion, synchronization, spreading, social dynamics and games, when extended beyond pairwise interactions. We conclude with a summary of empirical applications, and an outlook on current modeling and conceptual frontiers.

We consider the Dirichlet Laplacian operator −Δ on a curved quantum guide in ℝ n(n=2,3) 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 establish basic results on existence and uniqueness for the solution of stochastic PDE's. We express the solution of a backward linear stochastic PDE in terms of the conditional law of a partially observed Markov diffusion process. It then follows that the adjoint forward stochastic PDE governs the evolution of the “unnormalized conditional density”

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

The genome of the asexual rotifer Adineta vaga lacks homologous chromosomes; instead, its allelic regions are rearranged and sometimes found on the same chromosome in a palindromic fashion, a structure reminiscent of the primate Y chromosome and of other mitotic lineages such as cancer cells. Bdelloid rotifers are thought to have persisted and diversified asexually for millions of years, which is odd because loss of sexual reproduction is widely considered to be an evolutionary dead end for metazoans. The suspicion remained that they might engage in sex on rare occasions. But here Olivier Jaillon and colleagues sequence the genome of a bdelloid rotifer, Adineta vaga, and show that its structure is incompatible with conventional meiosis, the type of cell division associated with sexual reproduction. The genome has undergone abundant gene conversion, which may limit the accumulation of deleterious mutations in the absence of meiosis. Up to 8% of the genes are of probable non-metazoan origin, probably acquired through horizontal gene transfer. These findings demonstrate positive evidence for asexual evolution, supporting the hypothesis of ancient asexuality among bdelloid rotifers. Loss of sexual reproduction is considered an evolutionary dead end for metazoans, but bdelloid rotifers challenge this view as they appear to have persisted asexually for millions of years1. Neither male sex organs nor meiosis have ever been observed in these microscopic animals: oocytes are formed through mitotic divisions, with no reduction of chromosome number and no indication of chromosome pairing2. However, current evidence does not exclude that they may engage in sex on rare, cryptic occasions. Here we report the genome of a bdelloid rotifer, Adineta vaga (Davis, 1873)3, and show that its structure is incompatible with conventional meiosis. At gene scale, the genome of A. vaga is tetraploid and comprises both anciently duplicated segments and less divergent allelic regions. However, in contrast to sexual species, the allelic regions are rearranged and sometimes even found on the same chromosome. Such structure does not allow meiotic pairing; instead, we find abundant evidence of gene conversion, which may limit the accumulation of deleterious mutations in the absence of meiosis. Gene families involved in resistance to oxidation, carbohydrate metabolism and defence against transposons are significantly expanded, which may explain why transposable elements cover only 3% of the assembled sequence. Furthermore, 8% of the genes are likely to be of non-metazoan origin and were probably acquired horizontally. This apparent convergence between bdelloids and prokaryotes sheds new light on the evolutionary significance of sex.

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: Recent years have witnessed an exponential growth in the number of identified interactions between biological molecules. These interactions are usually represented as large and complex networks, calling for the development of appropriated tools to exploit the functional information they contain. Random walk with restart (RWR) is the state-of-the-art guilt-by-association approach. It explores the network vicinity of gene/protein seeds to study their functions, based on the premise that nodes related to similar functions tend to lie close to each other in the networks. Results: In this study, we extended the RWR algorithm to multiplex and heterogeneous networks. The walk can now explore different layers of physical and functional interactions between genes and proteins, such as protein-protein interactions and co-expression associations. In addition, the walk can also jump to a network containing different sets of edges and nodes, such as phenotype similarities between diseases. We devised a leave-one-out cross-validation strategy to evaluate the algorithms abilities to predict disease-associated genes. We demonstrate the increased performances of the multiplex-heterogeneous RWR as compared to several random walks on monoplex or heterogeneous networks. Overall, our framework is able to leverage the different interaction sources to outperform current approaches. Finally, we applied the algorithm to predict candidate genes for the Wiedemann-Rautenstrauch syndrome, and to explore the network vicinity of the SHORT syndrome. Availability and implementation: The source code is available on GitHub at: https://github.com/alberto-valdeolivas/RWR-MH. In addition, an R package is freely available through Bioconductor at: http://bioconductor.org/packages/RandomWalkRestartMH/. Supplementary information: Supplementary data are available at Bioinformatics online.

THE SYNTAX OF LINEAR LOGIC The connectives of linear logic Linear logic is not an alternative logic ; it should rather be seen as an extension of usual logic. Since there is no hope to modify the extant classical or intuitionistic connectives, linear logic introduces new connectives. Exponentials : actions vs situations Classical and intuitionistic logics deal with stable truths: if A and A ⇒ B , then B, but A still holds . This is perfect in mathematics, but wrong in real life, since real implication is causal . A causal implication cannot be iterated since the conditions are modified after its use ; this process of modification of the premises (conditions) is known in physics as reaction . For instance, if A is to spend $1 on a pack of cigarettes and B is to get them, you lose $1 in this process, and you cannot do it a second time. The reaction here was that $1 went out of your pocket. The first objection to that view is that there are in mathematics, in real life, cases where reaction does not exist or can be neglected : think of a lemma which is forever true, or of a Mr. Soros, who has almost an infinite amount of dollars. Such cases are situations in the sense of stable truths. Our logical refinements should not prevent us to cope with situations, and there will be a specific kind of connectives ( exponentials , “!” and “?”) which shall express the iterability of an action, i.e. the absence of any reaction ; typically! A means to spend as many dollars as one needs.

We study degenerate complex Monge-Ampère equations of the form ( ω + d d c φ ) n = e t φ μ (\omega +dd^c\varphi )^n = e^{t \varphi }\mu where ω \omega is a big semi-positive form on a compact Kähler manifold X X of dimension n n , t ∈ R + t \in \mathbb {R}^+ , and μ = f ω n \mu =f\omega ^n is a positive measure with density f ∈ L p ( X , ω n ) f\in L^p(X,\omega ^n) , p > 1 p>1 . We prove the existence and unicity of bounded ω \omega -plurisubharmonic solutions. We also prove that the solution is continuous under a further technical condition. In case X X is projective and ω = ψ

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.

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

We study bounded ancient solutions of the Navier–Stokes equations. These are solutions with bounded velocity defined in Rn × (−1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to some scenarios of potential singularity formation for axi-symmetric solutions, and obtain extensions of results in a recent paper by Chen, Strain, Tsai and Yau [4].

An increasing number of studies demonstrate phenotypic and genetic changes in natural populations that are subject to climate change, and there is hope that some of these changes will contribute to avoiding species extinctions ('evolutionary rescue'). Here, we review theoretical models of rapid evolution in quantitative traits that can shed light on the potential for adaptation to a changing climate. Our focus is on quantitative-genetic models with selection for a moving phenotypic optimum. We point out that there is no one-to-one relationship between the rate of adaptation and population survival, because the former depends on relative fitness and the latter on absolute fitness. Nevertheless, previous estimates that sustainable rates of genetically based change usually do not exceed 0.1 haldanes (i.e., phenotypic standard deviations per generation) are probably correct. Survival can be greatly facilitated by phenotypic plasticity, and heritable variation in plasticity can further speed up genetic evolution. Multivariate selection and genetic correlations are frequently assumed to constrain adaptation, but this is not necessarily the case and depends on the geometric relationship between the fitness landscape and the structure of genetic variation. Similar conclusions hold for adaptation to shifting spatial gradients. Recent models of adaptation in multispecies communities indicate that the potential for rapid evolution is strongly influenced by interspecific competition.