Non-backtracking Walk Centrality for Directed Networks

The theory of zeta functions provides an expression for the generating function of nonbacktracking walk counts on a directed network. We show how this expression can be used to produce a centrality measure that eliminates backtracking walks at no cost. We also show that the radius of convergence of the generating function is related to the spectrum of a three-by-three block matrix involving the original adjacency matrix. This gives a means to choose appropriate values of the attenuation parameter. We find that three important additional benefits arise when we use this technique to eliminate traversals around the network that are unlikely to be of relevance. First, we obtain a larger range of choices for the attenuation parameter. Second, a natural approach for determining a suitable parameter range is invariant under the removal of certain types of nodes, we can gain computational efficiencies through reducing the dimension of the resulting eigenvalue problem. Third, the dimension of the linear system defining the centrality measures may be reduced in the same manner. We show that the new centrality measure may be interpreted as standard Katz on a modified network, where self loops are added, and where nonreciprocal edges are augmented with negative weights. We also give a multilayer interpretation, where negatively weighted walks between layers compensate for backtracking walks on the only non-empty layer. Studying the limit as the attenuation parameter approaches its upper bound also allows us to propose a generalization of eigenvector-based nonbacktracking centrality measure to this directed network setting. In this context, we find that the two-by-two block matrix arising in previous studies focused on undirected networks must be extended to a new three-by-three block structure to allow for directed edges. We illustrate the centrality measure on a synthetic network, where it is shown to eliminate a localization effect present in standard Katz centrality. Finally, we give results for real networks

A multi-layer extension of the stochastic heat equation

Motivated by recent developments on solvable directed polymer models, we define a 'multi-layer' extension of the stochastic heat equation involving non-intersecting Brownian motions.Comment: v4: substantially extended and revised versio

Reaction-diffusion systems with constant diffusivities: conditional symmetries and form-preserving transformations

Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type (R. Cherniha J. Phys. A: Math. Theor., 2010. vol. 43., 405207), an exhaustive list of reaction-diffusion systems admitting such symmetry is derived. The form-preserving transformations for this class of systems are constructed and it is shown that this list contains only non-equivalent systems. The obtained symmetries permit to reduce the reaction-diffusion systems under study to two-dimensional systems of ordinary differential equations and to find exact solutions. As a non-trivial example, multiparameter families of exact solutions are explicitly constructed for two nonlinear reaction-diffusion systems. A possible interpretation to a biologically motivated model is presented

Hybridization as a threat in climate relict Nuphar pumila (Nymphaeaceae)

Field studies and conceptual work on hybridization-mediated extinction risk in climate relicts are extremely rare. Nuphar pumila (Nymphaeaceae) is one of the most emblematic climate relicts in Europe with few isolated populations in the Alpine arc. The extent of introgression with related lowland and generalist species Nupharlutea has never been studied using molecular methods. All biogeographical regions where N.pumila naturally occurs in the neighbourhood of the Alpine arc were sampled and studied using nuclear microsatellite markers. Furthermore, we used forward-in-time simulations and Approximate Bayesian Computation to check whether an introgression scenario fits with the observed admixture patterns and estimated the demographic parameters associated with this process. Our study confirms ongoing hybridization between N.pumila and N.lutea and validates it by the use of population models. More than 40 % of investigated N.pumila individuals were admixed and hybrids were found in over 60 % of studied populations. The introgression is bidirectional and is most likely a result of very recent gene flow. Our work provides strong evidence for rapid extinction risk and demographic swamping between specialized climatic relicts and closely related generalists. The remaining pure populations of N.pumila are rare in the Alpine arc and deserve high conservation priority

Microphytobenthos of Arctic Kongsfjorden (Svalbard, Norway): biomass and potential primary production along the shore line

During summer 2007, Arctic microphytobenthic potential primary production was measured at several stations around the coastline of Kongsfjorden (Svalbard, Norway) at ?5 m water depth and at two stations at five different water depths (5, 10, 15, 20, 30 m). Oxygen planar optode sensor spots were used ex situ to determine oxygen exchange in the overlying water of intact sediment cores under controlled light (ca. 100 ?mol photons m?2 s?1) and temperature (2–4°C) conditions. Patches of microalgae (mainly diatoms) covering sandy sediments at water depths down to 30 m showed high biomass of up to 317 mg chl a m?2. In spite of increasing water depth, no significant trend in “photoautotrophic active biomass” (chl a, ratio living/dead cells, cell sizes) and, thus, in primary production was measured at both stations. All sites from ?5 to 30 m water depth exhibited variable rates of net production from ?19 to +40 mg O2 m?2 h?1 (?168 to +360 mg C m?2 day?1) and gross production of about 2–62 mg O2 m?2 h?1 (17–554 mg C m?2 day?1), which is comparable to other polar as well as temperate regions. No relation between photoautotrophic biomass and gross/net production values was found. Microphytobenthos demonstrated significant rates of primary production that is comparable to pelagic production of Kongsfjorden and, hence, emphasised the importance as C source for the zoobenthos

The evolutionary significance of polyploidy

Polyploidy, or the duplication of entire genomes, has been observed in prokaryotic and eukaryotic organisms, and in somatic and germ cells. The consequences of polyploidization are complex and variable, and they differ greatly between systems (clonal or non-clonal) and species, but the process has often been considered to be an evolutionary 'dead end'. Here, we review the accumulating evidence that correlates polyploidization with environmental change or stress, and that has led to an increased recognition of its short-term adaptive potential. In addition, we discuss how, once polyploidy has been established, the unique retention profile of duplicated genes following whole-genome duplication might explain key longer-term evolutionary transitions and a general increase in biological complexity

One thousand plant transcriptomes and the phylogenomics of green plants

Abstract: Green plants (Viridiplantae) include around 450,000–500,000 species1, 2 of great diversity and have important roles in terrestrial and aquatic ecosystems. Here, as part of the One Thousand Plant Transcriptomes Initiative, we sequenced the vegetative transcriptomes of 1,124 species that span the diversity of plants in a broad sense (Archaeplastida), including green plants (Viridiplantae), glaucophytes (Glaucophyta) and red algae (Rhodophyta). Our analysis provides a robust phylogenomic framework for examining the evolution of green plants. Most inferred species relationships are well supported across multiple species tree and supermatrix analyses, but discordance among plastid and nuclear gene trees at a few important nodes highlights the complexity of plant genome evolution, including polyploidy, periods of rapid speciation, and extinction. Incomplete sorting of ancestral variation, polyploidization and massive expansions of gene families punctuate the evolutionary history of green plants. Notably, we find that large expansions of gene families preceded the origins of green plants, land plants and vascular plants, whereas whole-genome duplications are inferred to have occurred repeatedly throughout the evolution of flowering plants and ferns. The increasing availability of high-quality plant genome sequences and advances in functional genomics are enabling research on genome evolution across the green tree of life