Percolation on Networks with Conditional Dependence Group

Recently, the dependence group has been proposed to study the robustness of networks with interdependent nodes. A dependence group means that a failed node in the group can lead to the failures of the whole group. Considering the situation of real networks that one failed node may not always break the functionality of a dependence group, we study a cascading failure model that a dependence group fails only when more than a fraction β of nodes of the group fail. We find that the network becomes more robust with the increasing of the parameter β. However, the type of percolation transition is always first order unless the model reduces to the classical network percolation model, which is independent of the degree distribution of the network. Furthermore, we find that a larger dependence group size does not always make the networks more fragile. We also present exact solutions to the size of the giant component and the critical point, which are in agreement with the simulations well.     

Opinion Formation by Social Influence: From Experiments to Modeling

Predicting different forms of collective behavior in human populations, as the outcome of individual attitudes and their mutual influence, is a question of major interest in social sciences. In particular, processes of opinion formation have been theoretically modeled on the basis of a formal similarity with the dynamics of certain physical systems, giving rise to an extensive collection of mathematical models amenable to numerical simulation or even to exact solution. Empirical ground for these models is however largely missing, which confine them to the level of mere metaphors of the real phenomena they aim at explaining. In this paper we present results of an experiment which quantifies the change in the opinions given by a subject on a set of specific matters under the influence of others. The setup is a variant of a recently proposed experiment, where the subject’s confidence on his or her opinion was evaluated as well. In our realization, which records the quantitative answers of 85 subjects to 20 questions before and after an influence event, the focus is put on characterizing the change in answers and confidence induced by such influence. Similarities and differences with the previous version of the experiment are highlighted. We find that confidence changes are to a large extent independent of any other recorded quantity, while opinion changes are strongly modulated by the original confidence. On the other hand, opinion changes are not influenced by the initial difference with the reference opinion. The typical time scales on which opinion varies are moreover substantially longer than those of confidence change. Experimental results are then used to estimate parameters for a dynamical agent-based model of opinion formation in a large population. In the context of the model, we study the convergence to full consensus and the effect of opinion leaders on the collective distribution of opinions.     

Social Influence and the Collective Dynamics of Opinion Formation

Social influence is the process by which individuals adapt their opinion, revise their beliefs, or change their behavior as a result of social interactions with other people. In our strongly interconnected society, social influence plays a prominent role in many self-organized phenomena such as herding in cultural markets, the spread of ideas and innovations, and the amplification of fears during epidemics. Yet, the mechanisms of opinion formation remain poorly understood, and existing physics-based models lack systematic empirical validation. Here, we report two controlled experiments showing how participants answering factual questions revise their initial judgments after being exposed to the opinion and confidence level of others. Based on the observation of 59 experimental subjects exposed to peer-opinion for 15 different items, we draw an influence map that describes the strength of peer influence during interactions. A simple process model derived from our observations demonstrates how opinions in a group of interacting people can converge or split over repeated interactions. In particular, we identify two major attractors of opinion: (i) the expert effect, induced by the presence of a highly confident individual in the group, and (ii) the majority effect, caused by the presence of a critical mass of laypeople sharing similar opinions. Additional simulations reveal the existence of a tipping point at which one attractor will dominate over the other, driving collective opinion in a given direction. These findings have implications for understanding the mechanisms of public opinion formation and managing conflicting situations in which self-confident and better informed minorities challenge the views of a large uninformed majority.     

Habitat fragmentation,percolation theory and the conservation of a keystone species

Many species survive in specialized habitats. When these habitats are destroyed or fragmented the threat of extinction looms. In this paper, we use percolation theory to consider how an environment may fragment. We then develop a stochastic, spatially explicit, individual-based model to consider the effect of habitat fragmentation on a keystone species (the army ant Eciton burchelli) in a neo tropical rainforest. The results suggest that species may become extinct even in huge reserves before their habitat is fully fragmented; this has important implications for conservation. We show that sustainable forest-harvesting strategies may not be as successful as is currently thought. We also suggest that habitat corridors, once thought of as the saviour for fragmented environments, may have a detrimental effect on population persistence.     

Modeling of the Dorsal Gradient across Species Reveals Interaction between Embryo Morphology and Toll Signaling Pathway during Evolution

Morphogenetic gradients are essential to allocate cell fates in embryos of varying sizes within and across closely related species. We previously showed that the maternal NF-κB/Dorsal (Dl) gradient has acquired different shapes in Drosophila species, which result in unequally scaled germ layers along the dorso-ventral axis and the repositioning of the neuroectodermal borders. Here we combined experimentation and mathematical modeling to investigate which factors might have contributed to the fast evolutionary changes of this gradient. To this end, we modified a previously developed model that employs differential equations of the main biochemical interactions of the Toll (Tl) signaling pathway, which regulates Dl nuclear transport. The original model simulations fit well the D. melanogaster wild type, but not mutant conditions. To broaden the applicability of this model and probe evolutionary changes in gradient distributions, we adjusted a set of 19 independent parameters to reproduce three quantified experimental conditions (i.e. Dl levels lowered, nuclear size and density increased or decreased). We next searched for the most relevant parameters that reproduce the species-specific Dl gradients. We show that adjusting parameters relative to morphological traits (i.e. embryo diameter, nuclear size and density) alone is not sufficient to reproduce the species Dl gradients. Since components of the Tl pathway simulated by the model are fast-evolving, we next asked which parameters related to Tl would most effectively reproduce these gradients and identified a particular subset. A sensitivity analysis reveals the existence of nonlinear interactions between the two fast-evolving traits tested above, namely the embryonic morphological changes and Tl pathway components. Our modeling further suggests that distinct Dl gradient shapes observed in closely related melanogaster sub-group lineages may be caused by similar sequence modifications in Tl pathway components, which are in agreement with their phylogenetic relationships.     

Read-Out of Dynamic Morphogen Gradients on Growing Domains

Quantitative data from the Drosophila wing imaginal disc reveals that the amplitude of the Decapentaplegic (Dpp) morphogen gradient increases continuously. It is an open question how cells can determine their relative position within a domain based on a continuously increasing gradient. Here we show that pre-steady state diffusion-based dispersal of morphogens results in a zone within the growing domain where the concentration remains constant over the patterning period. The position of the zone that is predicted based on quantitative data for the Dpp morphogen corresponds to where the Dpp-dependent gene expression boundaries of spalt (sal) and daughters against dpp (dad) emerge. The model also suggests that genes that are scaling and are expressed at lateral positions are either under the control of a different read-out mechanism or under the control of a different morphogen. The patterning mechanism explains the extraordinary robustness that is observed for variations in Dpp production, and offers an explanation for the dual role of Dpp in controlling patterning and growth. Pre-steady-state dynamics are pervasive in morphogen-controlled systems, thus making this a probable general mechanism for the scaled read-out of morphogen gradients in growing developmental systems.     

Operational Principles for the Dynamics of the In Vitro ParA-ParB System

In many bacteria the ParA-ParB protein system is responsible for actively segregating DNA during replication. ParB proteins move by interacting with DNA bound ParA-ATP, stimulating their unbinding by catalyzing hydrolysis, that leads to rectified motion due to the creation of a wake of depleted ParA. Recent in vitro experiments have shown that a ParB covered magnetic bead can move with constant speed over a DNA covered substrate that is bound by ParA. It has been suggested that the formation of a gradient in ParA leads to diffusion-ratchet like motion of the ParB bead but how it forms and generates a force is still a matter of exploration. Here we develop a deterministic model for the in vitro ParA-ParB system and show that a ParA gradient can spontaneously form due to any amount of initial spatial noise in bound ParA. The speed of the bead is independent of this noise but depends on the ratio of the range of ParA-ParB force on the bead to that of removal of surface bound ParA by ParB. We find that at a particular ratio the speed attains a maximal value. We also consider ParA rebinding (including cooperativity) and ParA surface diffusion independently as mechanisms for ParA recovery on the surface. Depending on whether the DNA covered surface is undersaturated or saturated with ParA, we find that the bead can accelerate persistently or potentially stall. Our model highlights key requirements of the ParA-ParB driving force that are necessary for directed motion in the in vitro system that may provide insight into the in vivo dynamics of the ParA-ParB system.     

Pruning the tree of life: k-core percolation as selection mechanism

We propose a model for evolution aiming to reproduce statistical features of fossil data, in particular the distributions of extinction events, the distribution of species per genus and the distribution of lifetimes, all of which are known to be of power-law type. The model incorporates both species-species interactions and ancestral relationships. The main novelty of this work is to show the feasibility of k-core percolation as a selection mechanism. We give theoretical predictions for the observable distributions, confirm their validity by computer simulation and compare with fossil data. A key feature of the proposed model is a co-evolving fitness landscape determined by the topology of the underlying species interactions, ecological niches emerge naturally. The predicted distributions are independent of the rate of speciation, i.e. whether one adopts an gradualist or punctuated view of evolution.     

Different Migration Patterns of Sea Urchin and Mouse Sperm Revealed by a Microfluidic Chemotaxis Device

Chemotaxis refers to a process whereby cells move up or down a chemical gradient. Sperm chemotaxis is known to be a strategy exploited by marine invertebrates such as sea urchins to reach eggs efficiently in moving water. Less is understood about how or whether chemotaxis is used by mammalian sperm to reach eggs, where fertilization takes place within the confinement of a reproductive tract. In this report, we quantitatively assessed sea urchin and mouse sperm chemotaxis using a recently developed microfluidic model and high-speed imaging. Results demonstrated that sea urchin Arbacia punctulata sperm were chemotactic toward the peptide resact with high chemotactic sensitivity, with an average velocity V_x up the chemical gradient as high as 20% of its average speed (238 μm/s), while mouse sperm displayed no statistically significant chemotactic behavior in progesterone gradients, which had been proposed to guide mammalian sperm toward eggs. This work demonstrates the validity of a microfluidic model for quantitative sperm chemotaxis studies, and reveals a biological insight that chemotaxis up a progesterone gradient may not be a universal strategy for mammalian sperm to reach eggs.     

Predicting species distributions from herbarium collections: does climate bias in collection sampling influence model outcomes?

Aim Species distribution models and geographical information system (GIS) technologies are becoming increasingly important tools in conservation planning and decision‐making. Often the rich data bases of museums and herbaria serve as the primary data for predicting species distributions. Yet key assumptions about the primary data often are untested, and violation of such assumptions may have consequences for model predictions. For example, users of primary data assume that sampling has been random with respect to geography and environmental gradients. Here we evaluate the assumption that plant voucher specimens adequately sample the climatic gradient and test whether violation of this assumption influences model predictions. Location Bolivia and Ecuador. Methods Using 323,711 georeferenced herbarium collections and nine climatic variables, we predicted the distribution of 76 plant species using maximum entropy models (MAXENT) with training points that sampled the climate environments randomly and training points that reflected the climate bias in the herbarium collections. To estimate the distribution of species, MAXENT finds the distribution of maximum entropy (i.e. closest to uniform) subject to the constraint that the expected value for each environmental variable under the estimated distribution matches its empirical average. The experimental design included species that differed in geographical range and elevation; all species were modelled with 20 and 100 training points. We examined the influence of the number of training points and climate bias in training points, elevation and range size on model performance using analysis of variance models. Results We found that significant parts of the climatic gradient were poorly represented in herbarium collections for both countries. For the most part, existing climatic bias in collections did not greatly affect distribution predictions when compared with an unbiased data set. Although the effects of climate bias on prediction accuracy were found to be greater where geographical ranges were characterized by high spatial variation in the degree of climate bias (i.e. ranges where the bias of the various climates sampled by collections deviated considerably from the mean bias), the greatest influence on model performance was the number of presence points used to train the model. Main conclusions These results demonstrate that predictions of species distributions can be quite good despite existing climatic biases in primary data found in natural history collections, if a sufficiently large number of training points is available. Because of consistent overprediction of models, these results also confirm the importance of validating models with independent data or expert opinion. Failure to include independent model validation, especially in cases where training points are limited, may potentially lead to grave errors in conservation decision‐making and planning.     

Emergence of Blind Areas in Information Spreading

Recently, contagion-based (disease, information, etc.) spreading on social networks has been extensively studied. In this paper, other than traditional full interaction, we propose a partial interaction based spreading model, considering that the informed individuals would transmit information to only a certain fraction of their neighbors due to the transmission ability in real-world social networks. Simulation results on three representative networks (BA, ER, WS) indicate that the spreading efficiency is highly correlated with the network heterogeneity. In addition, a special phenomenon, namely Information Blind Areas where the network is separated by several information-unreachable clusters, will emerge from the spreading process. Furthermore, we also find that the size distribution of such information blind areas obeys power-law-like distribution, which has very similar exponent with that of site percolation. Detailed analyses show that the critical value is decreasing along with the network heterogeneity for the spreading process, which is complete the contrary to that of random selection. Moreover, the critical value in the latter process is also larger than that of the former for the same network. Those findings might shed some lights in in-depth understanding the effect of network properties on information spreading.     

Two-Dimensional Continuum Percolation Threshold for Diffusing Particles of Nonzero Radius

Lateral diffusion in the plasma membrane is obstructed by proteins bound to the cytoskeleton. The most important parameter describing obstructed diffusion is the percolation threshold. The thresholds are well known for point tracers, but for tracers of nonzero radius, the threshold depends on the excluded area, not just the obstacle concentration. Here thresholds are obtained for circular obstacles on the continuum. Random obstacle configurations are generated by Brownian dynamics or Monte Carlo methods, the obstacles are immobilized, and the percolation threshold is obtained by solving a bond percolation problem on the Voronoi diagram of the obstacles. The percolation threshold is expressed as the diameter of the largest tracer that can cross a set of immobile obstacles at a prescribed number density. For random overlapping obstacles, the results agree with the known analytical solution quantitatively. When the obstacles are soft disks with a 1/r¹² repulsion, the percolating diameter is ∼20% lower than for overlapping obstacles. A percolation model predicts that the threshold is highly sensitive to the tracer radius. To our knowledge, such a strong dependence has so far not been reported for the plasma membrane, suggesting that percolation is not the factor controlling lateral diffusion. A definitive experiment is proposed.     

Fecundity and sexual size dimorphism of wolf spiders (Araneae: Lycosidae) along an elevational gradient in the Arctic

Fecundity and body size are central fitness-related traits, and their intra-specific responses to environmental variation are receiving increasing attention in the context of climate change. Recent results from Greenland indicate that temporal and spatial variation in body size differences between sexes (sexual size dimorphism) may be widespread among wolf spider species and could be related to climate. Here, we tested whether variation in elevation affected body size of three wolf spider (Araneae: Lycosidae) species in low-Arctic Canada, whether the sexes differed in their response to the cline, and whether changes in local density influenced this relationship. We also tested whether fecundity changed with elevation in two of the species, independent of body size variation. We found a significant sex–elevation interaction for Pardosa lapponica: female size decreased more in response to elevation than that of males. Males and females of Pardosa uintana decreased significantly in size with elevation at a similar rate. Alopecosa aculeata males increased in body size along the gradient while females did not. Pardosa lapponica females, but not P. uintana females, showed significant reduction in fecundity in response to elevation. P. uintana showed significant decreases in body size with increases in its population density. Changes in temperature and potential resource availability along the elevational gradient are probably causing these species- and sex-specific responses. Further summer warming of the region may alleviate current constraints on growth and reproduction of these species although sex-specific responses may affect their population dynamics.     

The Undecided Have the Key: Interaction-Driven Opinion Dynamics in a Three State Model

The effects of interpersonal interactions on individual’s agreements result in a social aggregation process which is reflected in the formation of collective states, as for instance, groups of individuals with a similar opinion about a given issue. This field, which has been a longstanding concern of sociologists and psychologists, has been extended into an area of experimental social psychology, and even has attracted the attention of physicists and mathematicians. In this article, we present a novel model of opinion formation in which agents may either have a strict preference for a choice, or be undecided. The opinion shift emerges, in a threshold process, as a consequence of a cumulative persuasion for either one of the two opinions in repeated interactions. There are two main ingredients which play key roles in determining the steady states: the initial fraction of undecided agents and the change in agents’ persuasion after each interaction. As a function of these two parameters, the model presents a wide range of solutions, among which there are consensus of each opinion and bi-polarization. We found that a minimum fraction of undecided agents is not crucial for reaching consensus only, but also to determine a dominant opinion in a polarized situation. In order to gain a deeper comprehension of the dynamics, we also present the theoretical framework of the model. The master equations are of special interest for their nontrivial properties and difficulties in being solved analytically.     

The optimal fraction of hydrophobic residues required to ensure protein collapse

The hydrophobic interaction is the main driving force for protein folding. Here, we address the question of what is the optimal fraction, f of hydrophobic (H) residues required to ensure protein collapse. For very small f (say f<0.1), the protein chain is expected to behave as a random coil, where the H residues are "wrapped" locally by polar (P) residues. However, for large enough f this local coverage cannot be achieved and the thermodynamic alternative to avoid contact with water is burying the H residues in the interior of a compact chain structure. The interior also contains P residues that are known to be clustered to optimize their electrostatic interactions. This means that the H residues are clustered as well, i.e. they effectively attract each other like the H-monomers in Dill's HP lattice model. Previously, we asked the question: assuming that the H monomers in the HP model are distributed randomly along the chain, what fraction of them is required to ensure a compact ground state? We claimed there that f approximately p(c), where p(c) is the site percolation threshold of the lattice (in a percolation experiment, each site of an initially empty lattice is visited and a particle is placed there with a probability p. The interest is in the critical (minimal) value, p(c), for which percolation occurs, i.e. a cluster connecting the opposite sides of the lattice is created). Due to the above correspondence between the HP model and real proteins (and assuming that the H residues are distributed at random) we suggest that the experimental f should lead to percolating clusters of H residues over the highly dense protein core, i.e. clusters of the core size. To check this theory, we treat a simplified model consisting of H and P residues represented by their alpha-carbon atoms only. The structure is defined by the C(alpha)-C(alpha) virtual bond lengths, angles and dihedral angles, and the X-ray structure is best-fitted onto a face-centered cubic lattice. Percolation experiments are carried out for 103 single-chain proteins using six different hydrophobic sets of residues. Indeed, on average, percolating clusters are generated, which supports our theory; however, some sets lead to a better core coverage than others. We also calculate the largest actual hydrophobic cluster of each protein and show that, on average, these clusters span the core, again in accord with our theory. We discuss the effect of protein size, deviations from the average picture, and implications of this study for defining reliable simplified models of proteins.     

Predicted Auxiliary Navigation Mechanism of Peritrichously Flagellated Chemotactic Bacteria

Chemotactic movement of Escherichia coli is one of the most thoroughly studied paradigms of simple behavior. Due to significant competitive advantage conferred by chemotaxis and to high evolution rates in bacteria, the chemotaxis system is expected to be strongly optimized. Bacteria follow gradients by performing temporal comparisons of chemoeffector concentrations along their runs, a strategy which is most efficient given their size and swimming speed. Concentration differences are detected by a sensory system and transmitted to modulate rotation of flagellar motors, decreasing the probability of a tumble and reorientation if the perceived concentration change during a run is positive. Such regulation of tumble probability is of itself sufficient to explain chemotactic drift of a population up the gradient, and is commonly assumed to be the only navigation mechanism of chemotactic E. coli. Here we use computer simulations to predict existence of an additional mechanism of gradient navigation in E. coli. Based on the experimentally observed dependence of cell tumbling angle on the number of switching motors, we suggest that not only the tumbling probability but also the degree of reorientation during a tumble depend on the swimming direction along the gradient. Although the difference in mean tumbling angles up and down the gradient predicted by our model is small, it results in a dramatic enhancement of the cellular drift velocity along the gradient. We thus demonstrate a new level of optimization in E. coli chemotaxis, which arises from the switching of several flagellar motors and a resulting fine tuning of tumbling angle. Similar strategy is likely to be used by other peritrichously flagellated bacteria, and indicates yet another level of evolutionary development of bacterial chemotaxis.