Self-organization of heterogeneous topology and symmetry breaking in networks with adaptive thresholds and rewiring

We study an evolutionary algorithm that locally adapts thresholds and wiring in Random Threshold Networks, based on measurements of a dynamical order parameter. A control parameter $p$ determines the probability of threshold adaptations vs. link rewiring. For any $p < 1$, we find spontaneous symmetry breaking into a new class of self-organized networks, characterized by a much higher average connectivity $\bar{K}_{evo}$ than networks without threshold adaptation ($p =1$). While $\bar{K}_{evo}$ and evolved out-degree distributions are independent from $p$ for $p <1$, in-degree distributions become broader when $p \to 1$, approaching a power-law. In this limit, time scale separation between threshold adaptions and rewiring also leads to strong correlations between thresholds and in-degree. Finally, evidence is presented that networks converge to self-organized criticality for large $N$.Comment: 4 pages revtex, 6 figure

Critical Line in Random Threshold Networks with Inhomogeneous Thresholds

We calculate analytically the critical connectivity $K_c$ of Random Threshold Networks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the results by numerical simulations. We find a super-linear increase of $K_c$ with the (average) absolute threshold $|h|$, which approaches $K_c(|h|) \sim h^2/(2\ln{|h|})$ for large $|h|$, and show that this asymptotic scaling is universal for RTN with Poissonian distributed connectivity and threshold distributions with a variance that grows slower than $h^2$. Interestingly, we find that inhomogeneous distribution of thresholds leads to increased propagation of perturbations for sparsely connected networks, while for densely connected networks damage is reduced; the cross-over point yields a novel, characteristic connectivity $K_d$, that has no counterpart in Boolean networks. Last, local correlations between node thresholds and in-degree are introduced. Here, numerical simulations show that even weak (anti-)correlations can lead to a transition from ordered to chaotic dynamics, and vice versa. It is shown that the naive mean-field assumption typical for the annealed approximation leads to false predictions in this case, since correlations between thresholds and out-degree that emerge as a side-effect strongly modify damage propagation behavior.Comment: 18 figures, 17 pages revte

By hook or by crook? Morphometry, competition and cooperation in rodent sperm

Background Sperm design varies enormously across species and sperm competition is thought to be a major factor influencing this variation. However, the functional significance of many sperm traits is still poorly understood. The sperm of most murid rodents are characterised by an apical hook of the sperm head that varies markedly in extent across species. In the European woodmouse Apodemus sylvaticus (Muridae), the highly reflected apical hook of sperm is used to form sperm groups, or “trains,” which exhibited increased swimming velocity and thrusting force compared to individual sperm. Methodology/Principal Findings Here we use a comparative study of murine rodent sperm and demonstrate that the apical hook and sperm cooperation are likely to be general adaptations to sperm competition in rodents. We found that species with relatively larger testes, and therefore more intense sperm competition, have a longer, more reflected apical sperm hook. In addition, we show that sperm groups also occur in rodents other than the European woodmouse. Conclusions Our results suggest that in rodents sperm cooperation is more widespread than assumed so far and highlight the importance of diploid versus haploid selection in the evolution of sperm design and function

Leaf Morphology, Taxonomy and Geometric Morphometrics: A Simplified Protocol for Beginners

Taxonomy relies greatly on morphology to discriminate groups. Computerized geometric morphometric methods for quantitative shape analysis measure, test and visualize differences in form in a highly effective, reproducible, accurate and statistically powerful way. Plant leaves are commonly used in taxonomic analyses and are particularly suitable to landmark based geometric morphometrics. However, botanists do not yet seem to have taken advantage of this set of methods in their studies as much as zoologists have done. Using free software and an example dataset from two geographical populations of sessile oak leaves, we describe in detailed but simple terms how to: a) compute size and shape variables using Procrustes methods; b) test measurement error and the main levels of variation (population and trees) using a hierachical design; c) estimate the accuracy of group discrimination; d) repeat this estimate after controlling for the effect of size differences on shape (i.e., allometry). Measurement error was completely negligible; individual variation in leaf morphology was large and differences between trees were generally bigger than within trees; differences between the two geographic populations were small in both size and shape; despite a weak allometric trend, controlling for the effect of size on shape slighly increased discrimination accuracy. Procrustes based methods for the analysis of landmarks were highly efficient in measuring the hierarchical structure of differences in leaves and in revealing very small-scale variation. In taxonomy and many other fields of botany and biology, the application of geometric morphometrics contributes to increase scientific rigour in the description of important aspects of the phenotypic dimension of biodiversity. Easy to follow but detailed step by step example studies can promote a more extensive use of these numerical methods, as they provide an introduction to the discipline which, for many biologists, is less intimidating than the often inaccessible specialistic literature

Convergence and divergence in the evolution of cat skulls: temporal and spatial patterns of morphological diversity

Background: Studies of biological shape evolution are greatly enhanced when framed in a phylogenetic perspective. Inclusion of fossils amplifies the scope of macroevolutionary research, offers a deep-time perspective on tempo and mode of radiations, and elucidates life-trait changes. We explore the evolution of skull shape in felids (cats) through morphometric analyses of linear variables, phylogenetic comparative methods, and a new cladistic study of saber-toothed cats. Methodology/Principal Findings: A new phylogenetic analysis supports the monophyly of saber-toothed cats (Machairodontinae) exclusive of Felinae and some basal felids, but does not support the monophyly of various sabertoothed tribes and genera. We quantified skull shape variation in 34 extant and 18 extinct species using size-adjusted linear variables. These distinguish taxonomic group membership with high accuracy. Patterns of morphospace occupation are consistent with previous analyses, for example, in showing a size gradient along the primary axis of shape variation and a separation between large and small-medium cats. By combining the new phylogeny with a molecular tree of extant Felinae, we built a chronophylomorphospace (a phylogeny superimposed onto a two-dimensional morphospace through time). The evolutionary history of cats was characterized by two major episodes of morphological divergence, one marking the separation between saber-toothed and modern cats, the other marking the split between large and small-medium cats. Conclusions/Significance: Ancestors of large cats in the ‘Panthera’ lineage tend to occupy, at a much later stage, morphospace regions previously occupied by saber-toothed cats. The latter radiated out into new morphospace regions peripheral to those of extant large cats. The separation between large and small-medium cats was marked by considerable morphologically divergent trajectories early in feline evolution. A chronophylomorphospace has wider applications in reconstructing temporal transitions across two-dimensional trait spaces, can be used in ecophenotypical and functional diversity studies, and may reveal novel patterns of morphospace occupation

Surface states and Rashba-type spin polarization in antiferromagnetic MnBi2_2Te4_4

The layered van der Waals antiferromagnet MnBi$_2$Te$_4$ has been predicted to combine the band ordering of archetypical topological insulators such as Bi$_2$Te$_3$ with the magnetism of Mn, making this material a viable candidate for the realization of various magnetic topological states. We have systematically investigated the surface electronic structure of MnBi$_2$Te$_4$(0001) single crystals by use of spin- and angle-resolved photoelectron spectroscopy experiments. In line with theoretical predictions, the results reveal a surface state in the bulk band gap and they provide evidence for the influence of exchange interaction and spin-orbit coupling on the surface electronic structure.Comment: Revised versio