A coupled model containing two neurons and one astrocyte is constructed by integrating Hodgkin-Huxley neuronal model and Li-Rinzel calcium model. Based on this hybrid model, information transmission between neurons is studied numerically. Our results show that when the successive spikes are produced in neuron 1 (N1), the bursting-like spikes (BLSs) occur in two neurons simultaneously during the spikes being transferred to neuron 2 (N2). The existence of the astrocyte and a higher expression level of mGluRs facilitate the occurrence of BLSs, but the rate of occurrence is not sensitive to the parameters. Furthermore, time delay τ occurs during the information transmission, and τ is almost independent of the effect of the astrocyte. Additionally, we found that low coupling strength may result in the distortion of the information, and this distortion is also proven to be almost independent of the astrocyte.
Explanations of opinion bi-polarization hinge on the assumption of negative influence, individuals’ striving to amplify differences to disliked others. However, empirical evidence for negative influence is inconclusive, which motivated us to search for an alternative explanation. Here, we demonstrate that bi-polarization can be explained without negative influence, drawing on theories that emphasize the communication of arguments as central mechanism of influence. Due to homophily, actors interact mainly with others whose arguments will intensify existing tendencies for or against the issue at stake. We develop an agent-based model of this theory and compare its implications to those of existing social-influence models, deriving testable hypotheses about the conditions of bi-polarization. Hypotheses were tested with a group-discussion experiment (N = 96). Results demonstrate that argument exchange can entail bi-polarization even when there is no negative influence.
High-frequency (HF) stimulation has been shown to block conduction in excitable cells including neurons and cardiac myocytes. However, the precise mechanisms underlying conduction block are unclear. Using a multi-scale method, the influence of HF stimulation is investigated in the simplified FitzhHugh-Nagumo and biophysically-detailed Hodgkin-Huxley models. In both models, HF stimulation alters the amplitude and frequency of repetitive firing in response to a constant applied current and increases the threshold to evoke a single action potential in response to a brief applied current pulse. Further, the excitable cells cannot evoke a single action potential or fire repetitively above critical values for the HF stimulation amplitude. Analytical expressions for the critical values and thresholds are determined in the FitzHugh-Nagumo model. In the Hodgkin-Huxley model, it is shown that HF stimulation alters the dynamics of ionic current gating, shifting the steady-state activation, inactivation, and time constant curves, suggesting several possible mechanisms for conduction block. Finally, we demonstrate that HF stimulation of a network of neurons reduces the electrical activity firing rate, increases network synchronization, and for a sufficiently large HF stimulation, leads to complete electrical quiescence. In this study, we demonstrate a novel approach to investigate HF stimulation in biophysically-detailed ionic models of excitable cells, demonstrate possible mechanisms for HF stimulation conduction block in neurons, and provide insight into the influence of HF stimulation on neural networks.
Field experiments have shown that observing other people littering, stealing or lying can trigger own misconduct, leading to a decay of social order. However, a large extent of norm violations goes undetected. Hence, the direction of the dynamics crucially depends on actors’ beliefs regarding undetected transgressions. Because undetected transgressions are hardly measureable in the field, a laboratory experiment was developed, where the complete prevalence of norm violations, subjective beliefs about them, and their behavioral dynamics is measurable. In the experiment, subjects could lie about their monetary payoffs, estimate the extent of liars in their group and make subsequent lies contingent on information about other people’s lies. Results show that informed people who underestimate others’ lying increase own lying more than twice and those who overestimate, decrease it by more than half compared to people without information about others’ lies. This substantial interaction puts previous results into perspective, showing that information about others’ transgressions can trigger dynamics in both directions: the spreading of normative decay and restoring of norm adherence.
In fragmented landscape, individuals have to cope with the fragmentation level in order to aggregate in the same patch and take advantage of group-living. Aggregation results from responses to environmental heterogeneities and/or positive influence of the presence of congeners. In this context, the fragmentation of resting sites highlights how individuals make a compromise between two individual preferences: (1) being aggregated with conspecifics and (2) having access to these resting sites. As in previous studies, when the carrying capacity of available resting sites is large enough to contain the entire group, a single aggregation site is collectively selected. In this study, we have uncoupled fragmentation and habitat loss: the population size and total surface of the resting sites are maintained at a constant value, an increase in fragmentation implies a decrease in the carrying capacity of each shelter. For our model organism, Blattella germanica, our experimental and theoretical approach shows that, for low fragmentation level, a single resting site is collectively selected. However, for higher level of fragmentation, individuals are randomly distributed between fragments and the total sheltered population decreases. In the latter case, social amplification process is not activated and consequently, consensual decision making cannot emerge and the distribution of individuals among sites is only driven by their individual propensity to find a site. This intimate relation between aggregation pattern and landscape patchiness described in our theoretical model is generic for several gregarious species. We expect that any group-living species showing the same structure of interactions should present the same type of dispersion-aggregation response to fragmentation regardless of their level of social complexity.
Direct reciprocity is a mechanism for the evolution of cooperation. For the iterated prisoner’s dilemma, a new class of strategies has recently been described, the so-called zero-determinant strategies. Using such a strategy, a player can unilaterally enforce a linear relationship between his own payoff and the co-player’s payoff. In particular the player may act in such a way that it becomes optimal for the co-player to cooperate unconditionally. In this way, a player can manipulate and extort his co-player, thereby ensuring that the own payoff never falls below the co-player’s payoff. However, using a compliant strategy instead, a player can also ensure that his own payoff never exceeds the co-player’s payoff. Here, we use adaptive dynamics to study when evolution leads to extortion and when it leads to compliance. We find a remarkable cyclic dynamics: in sufficiently large populations, extortioners play a transient role, helping the population to move from selfish strategies to compliance. Compliant strategies, however, can be subverted by altruists, which in turn give rise to selfish strategies. Whether cooperative strategies are favored in the long run critically depends on the size of the population; we show that cooperation is most abundant in large populations, in which case average payoffs approach the social optimum. Our results are not restricted to the case of the prisoners dilemma, but can be extended to other social dilemmas, such as the snowdrift game. Iterated social dilemmas in large populations do not lead to the evolution of strategies that aim to dominate their co-player. Instead, generosity succeeds.
Identifying influential nodes in very large-scale directed networks is a big challenge relevant to disparate applications, such as accelerating information propagation, controlling rumors and diseases, designing search engines, and understanding hierarchical organization of social and biological networks. Known methods range from node centralities, such as degree, closeness and betweenness, to diffusion-based processes, like PageRank and LeaderRank. Some of these methods already take into account the influences of a node’s neighbors but do not directly make use of the interactions among it’s neighbors. Local clustering is known to have negative impacts on the information spreading. We further show empirically that it also plays a negative role in generating local connections. Inspired by these facts, we propose a local ranking algorithm named ClusterRank, which takes into account not only the number of neighbors and the neighbors’ influences, but also the clustering coefficient. Subject to the susceptible-infected-recovered (SIR) spreading model with constant infectivity, experimental results on two directed networks, a social network extracted from delicious.com and a large-scale short-message communication network, demonstrate that the ClusterRank outperforms some benchmark algorithms such as PageRank and LeaderRank. Furthermore, ClusterRank can also be applied to undirected networks where the superiority of ClusterRank is significant compared with degree centrality and k-core decomposition. In addition, ClusterRank, only making use of local information, is much more efficient than global methods: It takes only 191 seconds for a network with about nodes, more than 15 times faster than PageRank.
Computational modeling has emerged as an indispensable approach to resolve and predict the intricate interplay among the many ion channels underlying neuronal excitability. However, simulation results using the classic formula-based Hodgkin-Huxley (H-H) model or the superior Markov kinetic model of ion channels often deviate significantly from native cellular signals despite using carefully measured parameters. Here we found that the filters of patch-clamp amplifier not only delayed the signals, but also introduced ringing, and that the residual series resistance in experiments altered the command voltages, which had never been fully eliminated by improving the amplifier itself. To remove all the above errors, a virtual device with the parameters exactly same to that of amplifier was introduced into Markov kinetic modeling so as to establish a null-deviation model. We demonstrate that our novel null-deviation approach fully restores the native gating-kinetics of ion-channels with the data recorded at any condition, and predicts spike waveform and firing patterns clearly distinctive from those without correction.
Analysis of network dynamics became a focal point to understand and predict changes of complex systems. Here we introduce Turbine, a generic framework enabling fast simulation of any algorithmically definable dynamics on very large networks. Using a perturbation transmission model inspired by communicating vessels, we define a novel centrality measure: perturbation centrality. Hubs and inter-modular nodes proved to be highly efficient in perturbation propagation. High perturbation centrality nodes of the Met-tRNA synthetase protein structure network were identified as amino acids involved in intra-protein communication by earlier studies. Changes in perturbation centralities of yeast interactome nodes upon various stresses well recapitulated the functional changes of stressed yeast cells. The novelty and usefulness of perturbation centrality was validated in several other model, biological and social networks. The Turbine software and the perturbation centrality measure may provide a large variety of novel options to assess signaling, drug action, environmental and social interventions.
Calcium signals play a major role in the control of all key stages of neuronal development, and in particular in the growth and orientation of neuritic processes. These signals are characterized by high spatial compartmentalization, a property which has a strong relevance in the different roles of specific neuronal regions in information coding. In this context it is therefore important to understand the structural and functional basis of this spatial compartmentalization, and in particular whether the behavior at each compartment is merely a consequence of its specific geometry or the result of the spatial segregation of specific calcium influx/efflux mechanisms. Here we have developed a novel approach to separate geometrical from functional differences, regardless on the assumptions on the actual mechanisms involved in the generation of calcium signals. First, spatial indices are derived with a wavelet-theoretic approach which define a measure of the oscillations of cytosolic calcium concentration in specific regions of interests (ROIs) along a cell, in our case developing chick ciliary ganglion neurons. The resulting spatial profile demonstrates clearly that different ROIs along the neuron are characterized by specific patterns of calcium oscillations. Next we have investigated whether this inhomogeneity is due just to geometrical factors, namely the surface to volume ratio in the different subcompartments (e.g. soma vs. growth cone) or it depends on their specific biophysical properties. To this aim correlation functions are computed between the activity indices and the surface/volume ratio along the cell: the data thus obtained are validated by a statistical analysis on a dataset of different cells. This analysis shows that whereas in the soma calcium dynamics is highly correlated to the surface/volume ratio, correlations drop in the growth cone-neurite region, suggesting that in this latter case the key factor is the expression of specific mechanisms controlling calcium influx/efflux.
How different cultures evaluate a person? Is an important person in one culture is also important in the other culture? We address these questions via ranking of multilingual Wikipedia articles. With three ranking algorithms based on network structure of Wikipedia, we assign ranking to all articles in 9 multilingual editions of Wikipedia and investigate general ranking structure of PageRank, CheiRank and 2DRank. In particular, we focus on articles related to persons, identify top 30 persons for each rank among different editions and analyze distinctions of their distributions over activity fields such as politics, art, science, religion, sport for each edition. We find that local heroes are dominant but also global heroes exist and create an effective network representing entanglement of cultures. The Google matrix analysis of network of cultures shows signs of the Zipf law distribution. This approach allows to examine diversity and shared characteristics of knowledge organization between cultures. The developed computational, data driven approach highlights cultural interconnections in a new perspective.
Dated: June 26, 2013
Co-adaptation (or co-evolution), the parallel feedback process by which agents continuously adapt to the changes induced by the adaptive actions of other agents, is a ubiquitous feature of complex adaptive systems, from eco-systems to economies. We wish to understand which general features of complex systems necessarily follow from the (meta)-dynamics of co-adaptation, and which features depend on the details of particular systems. To begin this project, we present a model of co-adaptation (“The Stigmergy Game”) which is designed to be as a priori featureless as possible, in order to help isolate and understand the naked consequences of co-adaptation. In the model, heterogeneous, co-adapting agents, observe, interact with and change the state of an environment. Agents do not, ab initio, directly interact with each other. Agents adapt by choosing among a set of random “strategies,” particular to each agent. Each strategy is a complete specification of an agent's actions and payoffs. A priori, all environmental states are equally likely and all strategies have payoffs that sum to zero, so without co-adaptation agents would on average have zero “wealth”. Nevertheless, the dynamics of co-adaptation generates a structured environment in which only a subset of environmental states appear with high probability (niches) and in which agents accrue positive wealth. Furthermore, although there are no direct agent-agent interactions, there are induced non-trivial inter-agent interactions mediated by the environment. As a function of the population size and the number of possible environmental states, the system can be in one of three dynamical regions. Implications for a basic understanding of complex adaptive systems are discussed.
In the ultimatum game, two players divide a sum of money. The proposer suggests how to split and the responder can accept or reject. If the suggestion is rejected, both players get nothing. The rational solution is that the responder accepts even the smallest offer but humans prefer fair share. In this paper, we study the ultimatum game by a learning-mutation process based on quantal response equilibrium, where players are assumed boundedly rational and make mistakes when estimating the payoffs of strategies. Social learning is never stabilized at the fair outcome or the rational outcome, but leads to oscillations from offering 40 percent to 50 percent. To be precise, there is a clear tendency to increase the mean offer if it is lower than 40 percent, but will decrease when it reaches the fair offer. If mutations occur rarely, fair behavior is favored in the limit of local mutation. If mutation rate is sufficiently high, fairness can evolve for both local mutation and global mutation.
We present a dynamical systems analysis of a decision-making mechanism inspired by collective choice in house-hunting honeybee swarms, revealing the crucial role of cross-inhibitory ‘stop-signalling’ in improving the decision-making capabilities. We show that strength of cross-inhibition is a decision-parameter influencing how decisions depend both on the difference in value and on the mean value of the alternatives; this is in contrast to many previous mechanistic models of decision-making, which are typically sensitive to decision accuracy rather than the value of the option chosen. The strength of cross-inhibition determines when deadlock over similarly valued alternatives is maintained or broken, as a function of the mean value; thus, changes in cross-inhibition strength allow adaptive time-dependent decision-making strategies. Cross-inhibition also tunes the minimum difference between alternatives required for reliable discrimination, in a manner similar to Weber's law of just-noticeable difference. Finally, cross-inhibition tunes the speed-accuracy trade-off realised when differences in the values of the alternatives are sufficiently large to matter. We propose that the model, and the significant role of the values of the alternatives, may describe other decision-making systems, including intracellular regulatory circuits, and simple neural circuits, and may provide guidance in the design of decision-making algorithms for artificial systems, particularly those functioning without centralised control.
Rankings are ubiquitous around the world. Here I investigate spatial ranking patterns of English Words and Chinese Characters, and reveal a common construction pattern related to phase separation. In detail, I analyze a list of different words in the English language, and find that the frequency of the number of letters per word linearly or nonlinearly decays over its rank in the frequency table. I interpret the linearly decaying area as a linear phase that covers 96.4% words, which is in sharp contrast to a nonlinear phase (representing the nonlinearly decaying area) that covers the remaining 3.6% words. Amazingly, the phase separation phenomenon with the same two percentages of 96.4% and 3.6% holds also for the relation between strokes and characters in the Chinese language although English and Chinese are two distinctly different language systems. The common construction pattern originates from the log-normal distributions of frequencies of words or characters, which can be understood by the joint effect of both the Weber-Fechner law in psychophysics and the principle of maximum entropy in information theory.
Using a symbolic dynamics and a surrogate data approach, we show that the language exhibited by common fruit flies Drosophila (‘D.’) during courtship is as grammatically complex as the most complex human-spoken modern languages. This finding emerges from the study of fifty high-speed courtship videos (generally of several minutes duration) that were visually frame-by-frame dissected into 37 fundamental behavioral elements. From the symbolic dynamics of these elements, the courtship-generating language was determined with extreme confidence (significance level > 0.95). The languages categorization in terms of position in Chomsky’s hierarchical language classification allows to compare Drosophila’s body language not only with computer’s compiler languages, but also with human-spoken languages. Drosophila’s body language emerges to be at least as powerful as the languages spoken by humans.
We develop an efficient learning strategy of Chinese characters based on the network of the hierarchical structural relations between Chinese characters. A more efficient strategy is that of learning the same number of useful Chinese characters in less effort or time. We construct a node-weighted network of Chinese characters, where character usage frequencies are used as node weights. Using this hierarchical node-weighted network, we propose a new learning method, the distributed node weight (DNW) strategy, which is based on a new measure of nodes' importance that considers both the weight of the nodes and its location in the network hierarchical structure. Chinese character learning strategies, particularly their learning order, are analyzed as dynamical processes over the network. We compare the efficiency of three theoretical learning methods and two commonly used methods from mainstream Chinese textbooks, one for Chinese elementary school students and the other for students learning Chinese as a second language. We find that the DNW method significantly outperforms the others, implying that the efficiency of current learning methods of major textbooks can be greatly improved.
In this paper we introduce a new method to expressly use live/corporeal data in quantifying differences of time series data with an underlying limit cycle attractor; and apply it using an example of gait data. Our intention is to identify gait pattern differences between diverse situations and classify them on group and individual subject levels. First we approximated the limit cycle attractors, from which three measures were calculated: δM amounts to the difference between two attractors (a measure for the differences of two movements), δD computes the difference between the two associated deviations of the state vector away from the attractor (a measure for the change in movement variation), and δF, a combination of the previous two, is an index of the change. As an application we quantified these measures for walking on a treadmill under three different conditions: normal walking, dual task walking, and walking with additional weights at the ankle. The new method was able to successfully differentiate between the three walking conditions. Day to day repeatability, studied with repeated trials approximately one week apart, indicated excellent reliability for δM (ICCave > 0.73 with no differences across days; p > 0.05) and good reliability for δD (ICCave = 0.414 to 0.610 with no differences across days; p > 0.05). Based on the ability to detect differences in varying gait conditions and the good repeatability of the measures across days, the new method is recommended as an alternative to expensive and time consuming techniques of gait classification assessment. In particular, the new method is an easy to use diagnostic tool to quantify clinical changes in neurological patients.
As is well-known, spatial reciprocity plays an important role in facilitating the emergence of cooperative traits, and the effect of direct reciprocity is also obvious for explaining the cooperation dynamics. However, how the combination of these two scenarios influences cooperation is still unclear. In the present work, we study the evolution of cooperation in 2×2 games via considering both spatial structured populations and direct reciprocity driven by the strategy with 1-memory length. Our results show that cooperation can be significantly facilitated on the whole parameter plane. For prisoner's dilemma game, cooperation dominates the system even at strong dilemma, where maximal social payoff is still realized. In this sense, R-reciprocity forms and it is robust to the extremely strong dilemma. Interestingly, when turning to chicken game, we find that ST-reciprocity is also guaranteed, through which social average payoff and cooperation is greatly enhanced. This reciprocity mechanism is supported by mean-field analysis and different interaction topologies. Thus, our study indicates that direct reciprocity in structured populations can be regarded as a more powerful factor for the sustainability of cooperation.
We report on a quantitative analysis of relationships between the number of homicides, population size and ten other urban metrics. By using data from Brazilian cities, we show that well-defined average scaling laws with the population size emerge when investigating the relations between population and number of homicides as well as population and urban metrics. We also show that the fluctuations around the scaling laws are log-normally distributed, which enabled us to model these scaling laws by a stochastic-like equation driven by a multiplicative and log-normally distributed noise. Because of the scaling laws, we argue that it is better to employ logarithms in order to describe the number of homicides in function of the urban metrics via regression analysis. In addition to the regression analysis, we propose an approach to correlate crime and urban metrics via the evaluation of the distance between the actual value of the number of homicides (as well as the value of the urban metrics) and the value that is expected by the scaling law with the population size. This approach has proved to be robust and useful for unveiling relationships/behaviors that were not properly carried out by the regression analysis, such as the non-explanatory potential of the elderly population when the number of homicides is much above or much below the scaling law, the fact that unemployment has explanatory potential only when the number of homicides is considerably larger than the expected by the power law, and a gender difference in number of homicides, where cities with female population below the scaling law are characterized by a number of homicides above the power law.
Formation and selection of multiarmed spiral wave due to spontaneous symmetry breaking are investigated in a regular network of Hodgkin-Huxley neuron by changing the excitability and imposing spatial forcing currents on the neurons in the network. The arm number of the multiarmed spiral wave is dependent on the distribution of spatial forcing currents and excitability diversity in the network, and the selection criterion for supporting multiarmed spiral waves is discussed. A broken spiral segment is measured by a short polygonal line connected by three adjacent points (controlled nodes), and a double-spiral wave can be developed from the spiral segment. Multiarmed spiral wave is formed when a group of double-spiral waves rotate in the same direction in the network. In the numerical studies, a group of controlled nodes are selected and spatial forcing currents are imposed on these nodes, and our results show that l-arm stable spiral wave (l = 2, 3, 4,...8) can be induced to occupy the network completely. It is also confirmed that low excitability is critical to induce multiarmed spiral waves while high excitability is important to propagate the multiarmed spiral wave outside so that distinct multiarmed spiral wave can occupy the network completely. Our results confirm that symmetry breaking of target wave in the media accounts for emergence of multiarmed spiral wave, which can be developed from a group of spiral waves with single arm under appropriate condition, thus the potential formation mechanism of multiarmed spiral wave in the media is explained.
In this paper, I investigate the co-evolution of fast and slow strategy spread and game strategies in populations of spatially distributed agents engaged in a one off evolutionary dilemma game. Agents are characterized by a pair of traits, a game strategy (cooperate or defect) and a binary ‘advertising’ strategy (advertise or don’t advertise). Advertising, which comes at a cost , allows investment into faster propagation of the agents’ traits to adjacent individuals. Importantly, game strategy and advertising strategy are subject to the same evolutionary mechanism. Via analytical reasoning and numerical simulations I demonstrate that a range of advertising costs exists, such that the prevalence of cooperation is significantly enhanced through co-evolution. Linking costly replication to the success of cooperators exposes a novel co-evolutionary mechanism that might contribute towards a better understanding of the origins of cooperation-supporting heterogeneity in agent populations.
While the use of statistical physics methods to analyze large corpora has been useful to unveil many patterns in texts, no comprehensive investigation has been performed on the interdependence between syntactic and semantic factors. In this study we propose a framework for determining whether a text (e.g., written in an unknown alphabet) is compatible with a natural language and to which language it could belong. The approach is based on three types of statistical measurements, i.e. obtained from first-order statistics of word properties in a text, from the topology of complex networks representing texts, and from intermittency concepts where text is treated as a time series. Comparative experiments were performed with the New Testament in 15 different languages and with distinct books in English and Portuguese in order to quantify the dependency of the different measurements on the language and on the story being told in the book. The metrics found to be informative in distinguishing real texts from their shuffled versions include assortativity, degree and selectivity of words. As an illustration, we analyze an undeciphered medieval manuscript known as the Voynich Manuscript. We show that it is mostly compatible with natural languages and incompatible with random texts. We also obtain candidates for keywords of the Voynich Manuscript which could be helpful in the effort of deciphering it. Because we were able to identify statistical measurements that are more dependent on the syntax than on the semantics, the framework may also serve for text analysis in language-dependent applications.
Cooperation played a significant role in the self-organization and evolution of living organisms. Both network topology and the initial position of cooperators heavily affect the cooperation of social dilemma games. We developed a novel simulation program package, called ‘NetworGame’, which is able to simulate any type of social dilemma games on any model, or real world networks with any assignment of initial cooperation or defection strategies to network nodes. The ability of initially defecting single nodes to break overall cooperation was called as ‘game centrality’. The efficiency of this measure was verified on well-known social networks, and was extended to ‘protein games’, i.e. the simulation of cooperation between proteins, or their amino acids. Hubs and in particular, party hubs of yeast protein-protein interaction networks had a large influence to convert the cooperation of other nodes to defection. Simulations on methionyl-tRNA synthetase protein structure network indicated an increased influence of nodes belonging to intra-protein signaling pathways on breaking cooperation. The efficiency of single, initially defecting nodes to convert the cooperation of other nodes to defection in social dilemma games may be an important measure to predict the importance of nodes in the integration and regulation of complex systems. Game centrality may help to design more efficient interventions to cellular networks (in forms of drugs), to ecosystems and social networks.
We study a subset of the movie collaboration network, http://www.imdb.com, where only adult movies are included. We show that there are many benefits in using such a network, which can serve as a prototype for studying social interactions. We find that the strength of links, i.e., how many times two actors have collaborated with each other, is an important factor that can significantly influence the network topology. We see that when we link all actors in the same movie with each other, the network becomes small-world, lacking a proper modular structure. On the other hand, by imposing a threshold on the minimum number of links two actors should have to be in our studied subset, the network topology becomes naturally fractal. This occurs due to a large number of meaningless links, namely, links connecting actors that did not actually interact. We focus our analysis on the fractal and modular properties of this resulting network, and show that the renormalization group analysis can characterize the self-similar structure of these networks.