Lewis Carroll's Doublets Net of English Words: Network Heterogeneity in a Complex System

Lewis Carroll''s English word game Doublets is represented as a system of networks with each node being an English word and each connectivity edge confirming that its two ending words are equal in letter length, but different by exactly one letter. We show that this system, which we call the Doublets net, constitutes a complex body of linguistic knowledge concerning English word structure that has computable multiscale features. Distributed morphological, phonological and orthographic constraints and the language''s local redundancy are seen at the node level. Phonological communities are seen at the network level. And a balancing act between the language''s global efficiency and redundancy is seen at the system level. We develop a new measure of intrinsic node-to-node distance and a computational algorithm, called community geometry, which reveal the implicit multiscale structure within binary networks. Because the Doublets net is a modular complex cognitive system, the community geometry and computable multi-scale structural information may provide a foundation for understanding computational learning in many systems whose network structure has yet to be fully analyzed.     

Discovering biogeographic and ecological clusters with a graph theoretic spin on factor analysis

Factor analysis (FA) has the advantage of highlighting each semi‐distinct cluster of samples in a data set with one axis at a time, as opposed to simply arranging samples across axes to represent gradients. However, in the case of presence–absence data it is confounded by absences when gradients are long. No statistical model can cope with this problem because the raw data simply do not present underlying information about the length of such gradients. Here I propose an easy way to tease out this information. It is a simple emendation of FA called stepping down, which involves giving an absence a negative value when the missing species nowhere co‐occurs with the species found in the relevant sample. Specifically, a binary co‐occurrence graph is created, and the magnitude of negative values is made a function of how far the graph must be traversed in order to link the missing species with each species that is present. Simulations show that standard FA yields inferior results to FA based on stepped‐down matrices in terms of mapping clusters into axes one‐by‐one. Standard FA is also uninformative when applied to a global bat inventory data set. Step‐down FA (SDFA) easily flags the main biogeographic groupings. Methods like correspondence analysis, non‐metric multidimensional scaling, and Bayesian latent variable modelling are not commensurate with SDFA because they do not seek to find a one‐to‐one mapping of axes and clusters. Stepping down seems promising as a means of illustrating clusters of samples, especially when there are subtle or complex discontinuities in gradients.     

A Model of Filiform Hair Distribution on the Cricket Cercus

Crickets and other orthopteran insects sense air currents with a pair of abdominal appendages resembling antennae, called cerci. Each cercus in the common house cricket Acheta domesticus is covered with between 500 to 750 filiform mechanosensory hairs. The distribution of the hairs on the cerci, as well as the global patterns of their movement axes, are very stereotypical across different animals in this species, and the development of this system has been studied extensively. Although hypotheses regarding the mechanisms underlying pattern development of the hair array have been proposed in previous studies, no quantitative modeling studies have been published that test these hypotheses. We demonstrate that several aspects of the global pattern of mechanosensory hairs can be predicted with considerable accuracy using a simple model based on two independent morphogen systems. One system constrains inter-hair spacing, and the second system determines the directional movement axes of the hairs.     

Tree-based networks: characterisations,metrics, and support trees

Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer. One way to obtain such a network is by starting with a (rooted) phylogenetic tree T, called a base tree, and adding arcs between arcs of T. The class of phylogenetic networks that can be obtained in this way is called tree-based networks and includes the prominent classes of tree-child and reticulation-visible networks. Initially defined for binary phylogenetic networks, tree-based networks naturally extend to arbitrary phylogenetic networks. In this paper, we generalise recent tree-based characterisations and associated proximity measures for binary phylogenetic networks to arbitrary phylogenetic networks. These characterisations are in terms of matchings in bipartite graphs, path partitions, and antichains. Some of the generalisations are straightforward to establish using the original approach, while others require a very different approach. Furthermore, for an arbitrary tree-based network N, we characterise the support trees of N, that is, the tree-based embeddings of N. We use this characterisation to give an explicit formula for the number of support trees of N when N is binary. This formula is written in terms of the components of a bipartite graph.

     

Cytogeometrical determination of ciliary pattern formation in the hypotrich ciliate Stylonychia mytilus: II. Stability and field regulation

The first regeneration sequence after folding of right fragments of Stylonychia mytilus results in formation of mirror-imaged incomplete doublets illustrating independent determination of polar and lateral axes. Analysis of the second morphogenetic sequence illustrates that the independent determination of polar and lateral axes is stable through a subsequent cellular reorganization and confirms that cytogeometry participates in determination of ciliary pattern. The morphogenetic inversion of cirral row primordia in this type of fragment is reflected in the structure of the individual cirri. These data not only extend and confirm our earlier study on this type of fragment, but also are consistent with the conclusion derived from data on a different type of mirror-imaged doublet, that global patterning and assembly of ciliature are independently determined.     

The architecture of weighted mutualistic networks

Several ecosystem services directly depend on mutualistic interactions. In species rich communities, these interactions can be studied using network theory. Current knowledge of mutualistic networks is based mainly on binary links; however, little is known about the role played by the weights of the interactions between species. What new information can be extracted by analyzing weighted mutualistic networks? In performing an exhaustive analysis of the topological properties of 29 weighted mutualistic networks, our results show that the generalist species, defined as those with a larger number of interactions in a network, also have the strongest interactions. Though most interactions of generalists are with specialists, the strongest interactions occur between generalists. As a result and by defining binary and weighted clustering coefficients for bipartite networks, we demonstrate that generalists form strongly‐interconnected groups of species. The existence of these strong clusters reinforces the idea that generalist species govern the coevolution of the whole community.     

Typical trajectories of coupled degrade-and-fire oscillators: from dispersed populations to massive clustering

We consider the dynamics of a piecewise affine system of degrade-and-fire oscillators with global repressive interaction, inspired by experiments on synchronization in colonies of bacteria-embedded genetic circuits. Due to global coupling, if any two oscillators happen to be in the same state at some time, they remain in sync at all subsequent times; thus clusters of synchronized oscillators cannot shrink as a result of the dynamics. Assuming that the system is initiated from random initial configurations of fully dispersed populations (no clusters), we estimate asymptotic cluster sizes as a function of the coupling strength. A sharp transition is proved to exist that separates a weak coupling regime of unclustered populations from a strong coupling phase where clusters of extensive size are formed. Each phenomena occurs with full probability in the thermodynamics limit. Moreover, the maximum number of asymptotic clusters is known to diverge linearly in this limit. In contrast, we show that with positive probability, the number of asymptotic clusters remains bounded, provided that the coupling strength is sufficiently large.     

Capturing the Dynamics of a Hybrid Multiscale Cancer Model with a Continuum Model

Cancer is a complex disease involving processes at spatial scales from subcellular, like cell signalling, to tissue scale, such as vascular network formation. A number of multiscale models have been developed to study the dynamics that emerge from the coupling between the intracellular, cellular and tissue scales. Here, we develop a continuum partial differential equation model to capture the dynamics of a particular multiscale model (a hybrid cellular automaton with discrete cells, diffusible factors and an explicit vascular network). The purpose is to test under which circumstances such a continuum model gives equivalent predictions to the original multiscale model, in the knowledge that the system details are known, and differences in model results can be explained in terms of model features (rather than unknown experimental confounding factors). The continuum model qualitatively replicates the dynamics from the multiscale model, with certain discrepancies observed owing to the differences in the modelling of certain processes. The continuum model admits travelling wave solutions for normal tissue growth and tumour invasion, with similar behaviour observed in the multiscale model. However, the continuum model enables us to analyse the spatially homogeneous steady states of the system, and hence to analyse these waves in more detail. We show that the tumour microenvironmental effects from the multiscale model mean that tumour invasion exhibits a so-called pushed wave when the carrying capacity for tumour cell proliferation is less than the total cell density at the tumour wave front. These pushed waves of tumour invasion propagate by triggering apoptosis of normal cells at the wave front. Otherwise, numerical evidence suggests that the wave speed can be predicted from linear analysis about the normal tissue steady state.     

Ecological,historical and evolutionary determinants of modularity in weighted seed‐dispersal networks

Modularity is a recurrent and important property of bipartite ecological networks. Although well‐resolved ecological networks describe interaction frequencies between species pairs, modularity of bipartite networks has been analysed only on the basis of binary presence–absence data. We employ a new algorithm to detect modularity in weighted bipartite networks in a global analysis of avian seed‐dispersal networks. We define roles of species, such as connector values, for weighted and binary networks and associate them with avian species traits and phylogeny. The weighted, but not binary, analysis identified a positive relationship between climatic seasonality and modularity, whereas past climate stability and phylogenetic signal were only weakly related to modularity. Connector values were associated with foraging behaviour and were phylogenetically conserved. The weighted modularity analysis demonstrates the dominating impact of ecological factors on the structure of seed‐dispersal networks, but also underscores the relevance of evolutionary history in shaping species roles in ecological communities.     

Mirror-image configuration of the cortical pattern causes modifications in propagation of microtubular structures in the hypotrich ciliateParaurostyla weissei

Analysis or the development of microtubular structures in the mirror-image doublet cell lines of a hypotrich ciliate,Paraurostyla weissei, revealed several modifications in standard morphogenesis. Ciliary primordia can be formed without prior disaggregation of the preformed marginal cirri, on the left instead of the right hand side of an old row. Two or more overlapping streak segments may originate from disaggregating old marginal cirri, giving rise to two or three cirral rows. Inverted marginal cirri occasionally develop de novo and can be propagated clonally. Thus the modifications in developmental processes concern the positioning of primordia, the number of forming structures and the polarity of these structures. The microtubular triplets in the basal bodies of normal and inverted cirri do not differ, indicating that the large-scale reversal of the overall pattern has no effect on the assembly of microtubular triplets. The study indicates that the control of cytotactic propagation of compound microtubular structures is either modified or partially suppressed in a morphogenetic field where the positional values along one of the main cellular axes (lateral) have been reversed.     

Two New Diophrys‐Like Genera and Their Type Species,Apodiophrys ovalis n. g., n. sp. and Heterodiophrys zhui n. g., n. sp. (Ciliophora: Euplotida), with Notes on Their Molecular Phylogeny

ABSTRACT. Based on both morphological and molecular information, two new euplotid genera Apodiophrys n. g. and Heterodiophrys n. g. are described in the present paper. Apodiophrys n. g. is defined as sculptured Diophryinae with bipartite adoral zone; frontoventral cirri arranged in Diophrys‐pattern; marginal cirri located in two clearly separated groups. Heterodiophrys n. g. is recognizable by the combination of Diophrys‐like frontoventral cirri and the unique structure of several marginal cirri that are arranged in a long row. The type species for both new genera, Apodiophrys ovalis n. sp. and Heterodiophrys zhui n. sp., collected from southern China sea, are described. The small subunit rRNA (SSU rRNA) gene sequences for both new taxa are determined. Phylogenetic analyses based on these data indicate that Apodiophrys is most closely related to Paradiophrys, which then clusters with Uronychia species. Thus, Apodiophrys–Paradiophrys is separated from other typical Diophrys‐like genera in the SSU rRNA gene trees. The new genus Heterodiophrys is basal to the sister group of Diophrys–Diophryopsis, hence belongs to the “core”Diophrys‐complex.     

Reorienting in Virtual 3D Environments: Do Adult Humans Use Principal Axes,Medial Axes or Local Geometry?

Studies have shown that animals, including humans, use the geometric properties of environments to orient. It has been proposed that orientation is accomplished primarily by encoding the principal axes (i.e., global geometry) of an environment. However, recent research has shown that animals use local information such as wall length and corner angles as well as local shape parameters (i.e., medial axes) to orient. The goal of the current study was to determine whether adult humans reorient according to global geometry based on principal axes or whether reliance is on local geometry such as wall length and sense information or medial axes. Using a virtual environment task, participants were trained to select a response box located at one of two geometrically identical corners within a featureless rectangular-shaped environment. Participants were subsequently tested in a transformed L-shaped environment that allowed for a dissociation of strategies based on principal axes, medial axes and local geometry. Results showed that participants relied primarily on a medial axes strategy to reorient in the L-shaped test environment. Importantly, the search behaviour of participants could not be explained by a principal axes-based strategy.     

Cluster Analysis of Weighted Bipartite Networks: A New Copula-Based Approach

In this work we are interested in identifying clusters of “positional equivalent” actors, i.e. actors who play a similar role in a system. In particular, we analyze weighted bipartite networks that describes the relationships between actors on one side and features or traits on the other, together with the intensity level to which actors show their features. We develop a methodological approach that takes into account the underlying multivariate dependence among groups of actors. The idea is that positions in a network could be defined on the basis of the similar intensity levels that the actors exhibit in expressing some features, instead of just considering relationships that actors hold with each others. Moreover, we propose a new clustering procedure that exploits the potentiality of copula functions, a mathematical instrument for the modelization of the stochastic dependence structure. Our clustering algorithm can be applied both to binary and real-valued matrices. We validate it with simulations and applications to real-world data.     

Emergence of Complex Haplotypes from Microevolutionary Variation in Sequence and Structure of <Emphasis Type="Italic">Colias</Emphasis> Phosphoglucose Isomerase

A molecular evolutionary explanation of natural genetic variation requires analysis of specific variants’ evolutionary dynamics. To pursue this for phosphoglucose isomerase (PGI) of Colias butterflies, whose polymorphism is maintained by strong natural selection, we assembled a large data set of wild haplotypes, highly variable at the amino acid and DNA levels. The most common electrophoretic, i.e., charge macrostate, allele class, 3, is conserved in its pattern of charged amino acid residues. The next most common macrostate, 4, has multiple patterns of charge, i.e., microstates, while less common (1, 2, 5, 6) macrostates are very diverse. Macrostate 4 shows significant linkage disequilibrium (LD) among its variants, especially for two groups of five haplotypes each. We find extensive intragenic recombination among all haplotypes except the two high-LD groups of macrostate 4, which display none. Phyletic relations among haplotypes are largely reticulate, again except for the high-LD groups of macrostate 4, which form clades with strong bootstrap support. Charge-changing and linked charge-neutral amino acid variants occur in diverse parts of PGI’s sequence. Homology-based modeling of PGI’s structure shows that these regions are related spatially in ways suggesting functional interaction. The high-LD groups of macrostate 4 display parallel amino acid variation in these regions. This pattern of haplotype clades with high LD among multiple varying sites, emerging from chaotically recombining variation, may be a “signature” of refinement of complex adaptive sequences by recombination and selection. It should be tested further in this study system and others as a possibly general feature of the evolution of living complexity.     

Sparse gamma rhythms arising through clustering in adapting neuronal networks

Gamma rhythms (30-100 Hz) are an extensively studied synchronous brain state responsible for a number of sensory, memory, and motor processes. Experimental evidence suggests that fast-spiking interneurons are responsible for carrying the high frequency components of the rhythm, while regular-spiking pyramidal neurons fire sparsely. We propose that a combination of spike frequency adaptation and global inhibition may be responsible for this behavior. Excitatory neurons form several clusters that fire every few cycles of the fast oscillation. This is first shown in a detailed biophysical network model and then analyzed thoroughly in an idealized model. We exploit the fact that the timescale of adaptation is much slower than that of the other variables. Singular perturbation theory is used to derive an approximate periodic solution for a single spiking unit. This is then used to predict the relationship between the number of clusters arising spontaneously in the network as it relates to the adaptation time constant. We compare this to a complementary analysis that employs a weak coupling assumption to predict the first Fourier mode to destabilize from the incoherent state of an associated phase model as the external noise is reduced. Both approaches predict the same scaling of cluster number with respect to the adaptation time constant, which is corroborated in numerical simulations of the full system. Thus, we develop several testable predictions regarding the formation and characteristics of gamma rhythms with sparsely firing excitatory neurons.     

Multiscale modelling as a tool to prescribe realistic boundary conditions for the study of surgical procedures

This work was motivated by the problems of analysing detailed 3D models of vascular districts with complex anatomy. It suggests an approach to prescribing realistic boundary conditions to use in order to obtain information on local as well as global haemodynamics. A method was developed which simultaneously solves Navier-Stokes equations for local information and a non-linear system of ordinary differential equations for global information. This is based on the principle that an anatomically detailed 3D model of a cardiovascular district can be achieved by using the finite element method. In turn the finite element method requires a specific boundary condition set. The approach outlined in this work is to include the system of ordinary differential equations in the boundary condition set. Such a multiscale approach was first applied to two controls: (i) a 3D model of a straight tube in a simple hydraulic network and (ii) a 3D model of a straight coronary vessel in a lumped-parameter model of the cardiovascular system. The results obtained are very close to the solutions available for the pipe geometry. This paper also presents preliminary results from the application of the methodology to a particular haemodynamic problem: namely the fluid dynamics of a systemic-to-pulmonary shunt in paediatric cardiac surgery.     

Dental homologies in lamniform sharks (Chondrichthyes: Elasmobranchii).

The dentitions of lamniform sharks are said to exhibit a unique heterodonty called the "lamnoid tooth pattern." The presence of an inflated hollow "dental bulla" on each jaw cartilage allows the recognition of homologous teeth across most modern macrophagous lamniforms based on topographic correspondence through the "similarity test." In most macrophagous lamniforms, three tooth rows are supported by the upper dental bulla: two rows of large anterior teeth followed by a row of small intermediate teeth. The lower tooth row occluding between the two rows of upper anterior teeth is the first lower anterior tooth row. Like the first and second lower anterior tooth rows, the third lower tooth row is supported by the dental bulla and may be called the first lower intermediate tooth row. The lower intermediate tooth row occludes between the first and second upper lateral tooth rows situated distal to the upper dental bulla, and the rest of the upper and lower tooth rows, all called lateral tooth rows, occlude alternately. Tooth symmetry cannot be used to identify their dental homology. The presence of dental bullae can be regarded as a synapomorphy of Lamniformes and this character is more definable than the "lamnoid tooth pattern." The formation of the tooth pattern appears to be related to the evolution of dental bullae. This study constitutes the first demonstration of supraspecific tooth-to-tooth dental homologies in nonmammalian vertebrates.     

Drug-target network

The global set of relationships between protein targets of all drugs and all disease-gene products in the human protein-protein interaction or 'interactome' network remains uncharacterized. We built a bipartite graph composed of US Food and Drug Administration-approved drugs and proteins linked by drug-target binary associations. The resulting network connects most drugs into a highly interlinked giant component, with strong local clustering of drugs of similar types according to Anatomical Therapeutic Chemical classification. Topological analyses of this network quantitatively showed an overabundance of 'follow-on' drugs, that is, drugs that target already targeted proteins. By including drugs currently under investigation, we identified a trend toward more functionally diverse targets improving polypharmacology. To analyze the relationships between drug targets and disease-gene products, we measured the shortest distance between both sets of proteins in current models of the human interactome network. Significant differences in distance were found between etiological and palliative drugs. A recent trend toward more rational drug design was observed.     

Exploring the evolutionary dynamics of Rhizobium plasmids through bipartite network analysis

The genus Rhizobium usually has a multipartite genome architecture with a chromosome and several plasmids, making these bacteria a perfect candidate for plasmid biology studies. As there are no universally shared genes among typical plasmids, network analyses can complement traditional phylogenetics in a broad-scale study of plasmid evolution. Here, we present an exhaustive analysis of 216 plasmids from 49 complete genomes of Rhizobium by constructing a bipartite network that consists of two classes of nodes, the plasmids and homologous protein families that connect them. Dissection of the network using a hierarchical clustering strategy reveals extensive variety, with 34 homologous plasmid clusters. Four large clusters including one cluster of symbiotic plasmids and two clusters of chromids carrying some truly essential genes are widely distributed among Rhizobium. In contrast, the other clusters are quite small and rare. Symbiotic clusters and rare accessory clusters are exogenetic and do not appear to have co-evolved with the common accessory clusters; the latter ones have a large coding potential and functional complementarity for different lifestyles in Rhizobium. The bipartite network also provides preliminary evidence of Rhizobium plasmid variation and formation including genetic exchange, plasmid fusion and fission, exogenetic plasmid transfer, host plant selection, and environmental adaptation.