Recent years have seen increased interest in the question of whether it is possible to provide an evolutionary game-theoretic explanation for certain kinds of social norms. I sketch a proof of a general representation theorem for a large class of evolutionary game-theoretic models played on a social network, in hope that this will contribute to a greater understanding of the long-term evolutionary dynamics of such models, and hence the evolution of social norms.

At Home in the Universe. According to the modified joke, Kauffman's method is to begin any scientific investigation with the statement "Consider an NK Boolean network." Indeed, throughout At Home in the Universe just about every real-world problem gets translated into a toy-world problem involving NK Boolean networks. As with Carnap's formal languages, NK Boolean networks have the advantage of complete logical precision. But they also suffer the disadvantage of losing touch with reality. And it is (...) this disadvantage which ultimately proves the undoing of Kauffman's project. (shrink)

Antifragility is a property from which systems are able to resist stress and furthermore benefit from it. Even though antifragile dynamics is found in various real-world complex systems where multiple subsystems interact with each other, the attribute has not been quantitatively explored yet in those complex systems which can be regarded as multilayer networks. Here we study how the multilayer structure affects the antifragility of the whole system. By comparing single-layer and multilayer Boolean networks based on our recently proposed (...) antifragility measure, we found that the multilayer structure facilitated the production of antifragile systems. Our measure and findings will be useful for various applications such as exploring properties of biological systems with multilayer structures and creating more antifragile engineered systems. (shrink)

I criticize Herbert Simon 's argument for the claim that complex natural systems must constitute decomposable, mereological or functional hierarchies. The argument depends on certain assumptions about the requirements for the successful evolution of complex systems, most importantly, the existence of stable, intermediate stages in evolution. Simon offers an abstract model of any process that succeeds in meeting these requirements. This model necessarily involves construction through a decomposable hierarchy, and thus suggests that any complex, natural, i.e., evolved, system is constituted (...) by a decomposable hierarchy. I argue that Stuart Kauffman's recent models of genetic regulatory networks succeed in specifying processes that could meet Simon 's requirements for evolvability without requiring construction through a decomposable hierarchy. Since Kauffman's models are at least as plausible as Simon 's model, Simon 's argument that complex natural systems must constitute decomposable, mereological or functional hierarchies does not succeed. (shrink)

Biochemical networks are often called upon to illustrate emergent properties of living systems. In this contribution, I question such emergentist claims by means of theoretical work on genetic regulatory models and random Boolean networks. If the existence of a critical connectivity Kc of such networks has often been coined “emergent” or “irreducible”, I propose on the contrary that the existence of a critical connectivity Kc is indeed mathematically explainable in network theory. This conclusion also applies to many (...) other types of formal networks and weakens the emergentist claim attached to bio-molecular networks, and by extension to living systems. (shrink)

Models of gene regulatory networks have proven useful for understanding many aspects of the highly complex behavior of biological control networks. Randomly generated non-Boolean networks were used in experimental simulations to generate data on dynamic phenotypes as a function of several genotypic parameters. We found that predictive relationships between some phenotypes and quantitative genotypic parameters such as number of network genes, interaction density, and initial condition could be derived depending on the strength of the topological genotype on specific (...) phenotypes. We quantitated the strength of the topological genotype effect on a number of phenotypes in multi-gene networks. For phenotypes with a low influence of topological genotype, derived and empirical relationships using quantitative genotype parameters were accurate in phenotypic outcomes. We found a number of dynamic network properties, including oscillation behaviors, that were largely dependent on genotype topology, and for which no such general quantitative relationships were determinable. It remains to be determined if these results are applicable to biological gene regulatory networks. (shrink)

The area of smart power grids needs to constantly improve its efficiency and resilience, to provide high quality electrical power in a resilient grid, while managing faults and avoiding failures. Achieving this requires high component reliability, adequate maintenance, and a studied failure occurrence. Correct system operation involves those activities and novel methodologies to detect, classify, and isolate faults and failures and model and simulate processes with predictive algorithms and analytics. In this paper, we showcase the application of a complex-adaptive, self-organizing (...) modeling method, and Probabilistic Boolean Networks, as a way towards the understanding of the dynamics of smart grid devices, and to model and characterize their behavior. This work demonstrates that PBNs are equivalent to the standard Reinforcement Learning Cycle, in which the agent/model has an interaction with its environment and receives feedback from it in the form of a reward signal. Different reward structures were created to characterize preferred behavior. This information can be used to guide the PBN to avoid fault conditions and failures. (shrink)

Various threshold Boolean networks, a formalism used to model different types of biological networks, can produce similar dynamics, i.e. share same behaviors. Among them, some are complex, others not. By computing both structural and behavioral complexities, we show that most TBNs are structurally complex, even those having simple behaviors. For this purpose, we developed a new method to compute the structural complexity of a TBN based on estimates of the sizes of equivalence classes of the threshold Boolean functions (...) composing the TBN. (shrink)

Neoclassical economic theory, which still dominates the science, has proven inadequate to predict financial crises. In an increasingly globalised world, the consequences of that inadequacy are likely to become more severe. This article attributes much of the difficulty to an emphasis on equilibrium as an idealised property of economic systems. Alternatively, this article proposes that actual economies are typically out of balance, and that any equilibrium which may exist is transitory. That single changed assumption is central to complexity economics, a (...) view which is presented in detail. It is suggested that economic crises will be most effectively avoided when economists utilise methods, grounded in complexity theory, which can identify threat in an early stage. As a programmatic example, the use of Agent-Based Models (ABMs) combined with Boolean networks (BNs), is defended as a promising method for recognising vulnerability. (shrink)

Random simulation of complex dynamical systems is generally used in order to obtain information about their asymptotic behaviour (i.e., when time or size of the system tends towards infinity). A fortunate and welcome circumstance in most of the systems studied by physicists, biologists, and economists is the existence of an invariant measure in the state space allowing determination of the frequency with which observation of asymptotic states is possible. Regions found between contour lines of the surface density of this (...) invariant measure are called confiners. An example of such confiners is given for a formal neural network capable of learning. Finally, an application of this methodology is proposed in studying dependency of the network's invariant measure with regard to: 1) the mode of neurone updating (parallel or sequential), and 2) boundary conditions of the network (searching for phase transitions). (shrink)

Multi-level discrete models of genetic networks, or the more general piecewise affine differential models, provide qualitative information on the dynamics of the system, based on a small number of parameters (such as synthesis and degradation rates). Boolean models also provide qualitative information, but are based simply on the structure of interconnections. To explore the relationship between the two formalisms, a piecewise affine differential model and a Boolean model are compared, for the carbon starvation response network in E. (...) coli . The asymptotic dynamics of both models are shown to be quite similar. This study suggests new tools for analysis and reduction of biological networks. (shrink)

Explaining the behaviour of ecosystems is one of the key challenges for the biological sciences. Since 2000, new-mechanicism has been the main model to account for the nature of scientific explanation in biology. The universality of the new-mechanist view in biology has been however put into question due to the existence of explanations that account for some biological phenomena in terms of their mathematical properties (mathematical explanations). Supporters of mathematical explanation have argued that the explanation of the behaviour of ecosystems (...) is usually provided in terms of their mathematical properties, and not in mechanistic terms. They have intensively studied the explanation of the properties of ecosystems that behave following the rules of a non-random network. However, no attention has been devoted to the study of the nature of the explanation in those that form a random network. In this paper, we cover that gap by analysing the explanation of the stability behaviour of the microbiome recently elaborated by Coyte and colleagues, to determine whether it fits with the model of explanation suggested by the new-mechanist or by the defenders of mathematical explanation. Our analysis of this case study supports three theses: (1) that the explanation is not given solely in terms of mechanisms, as the new-mechanists understand the concept; (2) that the mathematical properties that describe the system play an essential explanatory role, but they do not exhaust the explanation; (3) that a non-previously identified appeal to the type of interactions that the entities in the network can exhibit, as well as their abundance, is also necessary for Coyte and colleagues’ account to be fully explanatory. From the combination of these three theses we argue for the necessity of an integrative pluralist view of the nature of behaviour explanation when this is given by appealing to the existence of a random network. (shrink)

This article delineates the notion of conjectural artworks—that is, ways of thinking and explaining formal and relational phenomena by visual means—and presents an appraisal and review of the use of such visual ways in the work of Chilean biologists and philosophers Humberto Maturana and Francisco Varela. Particularly, the article focuses on their recurrent uses of Cellular Automaton, that is, discrete, locally interacting, rule-based mathematical models, as conjectural artworks for understanding the concepts of autopoiesis, structural coupling, cognition and enaction: (i.e. Protobio (...) and Bittorio). Additionally, the article proposes a new model of conjectural artwork based on an extension of cellular automaton: random Boolean networks namely, binary systems with variable local connections. Such model, as it is argued, is useful to connect the theoretical frameworks by Maturana and Varela, especially structural coupling and enaction, with other relevant fields such as biosemiotics’ Umwelt-research and cognitive landscapes in neurodynamics, and to advance and explore the concepts of structurally coupled categorization and generalization. (shrink)

Since the outbreak of the novel coronavirus disease at the beginning of December 2019, there have been more than 28.69 million cumulative confirmed cases worldwide as of 12th September 2020, affecting over 200 countries and regions with more than 920,463 deaths. The COVID-19 pandemic has been sweeping worldwide with unexpected rapidity. In this paper, a hybrid modelling strategy based on tessellation structure- configured SEIR model is adopted to estimate the scale of the pandemic spread. Building on the data pertaining to (...) the global pandemic transmission over the last six months around the world, key impact factors in the transmission and control procedure have been analysed, including isolation rate, number of the infected cases before taking prevention measures, degree of contact scope, and medical level, so as to capture the fundamental factor influencing the pandemic. The quantitative evaluation allowed us to illustrate the magnitude of risks of pandemic and to recommend appropriate national health policy of prevention measures for effectively controlling both intra- and interregional pandemic spread. Our modelling results clearly indicate that the early-stage preventive measures are the most effective action to be taken to contain the pandemic spread of the highly contagious nature of the COVID-19. (shrink)

This article examines mixed ℋ -infinity and passivity synchronization of Markovian jumping neutral-type complex dynamical network models with randomly occurring coupling delays and actuator faults. The randomly occurring coupling delays are considered to design the complex dynamical networks in practice. These delays complied with certain Bernoulli distributed white noise sequences. The relevant data including limits of actuator faults, bounds of the nonlinear terms, and external disturbances are available for designing the controller structure. Novel Lyapunov–Krasovskii functional is constructed to verify (...) the stability of the error model and performance level. Jensen’s inequality and a new integral inequality are applied to derive the outcomes. Sufficient conditions for the synchronization error system are given in terms of linear matrix inequalities, which can be analyzed easily by utilizing general numerical programming. Numerical illustrations are given to exhibit the usefulness of the obtained results. (shrink)

The dynamical behaviour of a very general model of neural networks with random asymmetric synaptic weights is investigated in the presence of random thresholds. Using mean-field equations, the bifurcations of the fixed points and the change of regime when varying control parameters are established. Different areas with various regimes are defined in the parameter space. Chaos arises generically by a quasi-periodicity route.

Chaos in nervous system is a fascinating but controversial field of investigation. To approach the role of chaos in the real brain, we theoretically and numerically investigate the occurrence of chaos inartificial neural networks. Most of the time, recurrent networks (with feedbacks) are fully connected. This architecture being not biologically plausible, the occurrence of chaos is studied here for a randomly diluted architecture. By normalizing the variance of synaptic weights, we produce a bifurcation parameter, dependent on this variance and on (...) the slope of the transfer function, that allows a sustained activity and the occurrence of chaos when reaching a critical value. Even for weak connectivity and small size, we find numerical results in accordance with the theoretical ones previously established for fully connected infinite sized networks. The route towards chaos is numerically checked to be a quasi-periodic one, whatever the type of the first bifurcation is. Our results suggest that such high-dimensional networks behave like low-dimensional dynamical systems. (shrink)

This paper concentrates on the event-triggered H ∞ filter design for the discrete-time Markovian jump neural networks under random missing measurements and cyber attacks. Considering that the controlled system and the filtering can exchange information over a shared communication network which is vulnerable to the cyber attacks and has limited bandwidth, the event-triggered mechanism is proposed to relieve the communication burden of data transmission. A variable conforming to Bernoulli distribution is exploited to describe the stochastic phenomenon since the (...) missing measurements occur with random probability. Furthermore, seeing that the communication networks are vulnerable to external malicious attacks, the transferred information via the shared communication network may be changed by the injected false information from the attackers. Based on the above consideration, sufficient conditions for the filtering error system to maintain asymptotically stable are provided with predefined H ∞ performance. In the end, three numerical examples are given to verify the proposed theoretical results. (shrink)

This study concentrates on adaptive event-triggered control of complex dynamical networks with unpredictable coupling delays and stochastic deception attacks. The adaptive event-triggered mechanism is used to avoid the wasting of limited bandwidth. The probability of data communicated by the network is established by statistical properties and Bernoulli stochastic variables with an uncertain occurrence probability. Stability analysis based on Lyapunov–Krasovskii functional and the stability of the closed-loop system is guaranteed. Using the LMI technique, we obtain triggered parameters. To demonstrate the (...) feasibility and usefulness of the suggested methodology, two examples are shown. (shrink)

We deal with the design problem of nonfragile state estimator for discrete-time genetic regulatory networks with time-varying delays and randomly occurring uncertainties. In particular, the norm-bounded uncertainties enter into the GRNs in random ways in order to reflect the characteristic of the modelling errors, and the so-called randomly occurring uncertainties are characterized by certain mutually independent random variables obeying the Bernoulli distribution. The focus of the paper is on developing a new nonfragile state estimation method to estimate the (...) concentrations of the mRNA and the protein for considered uncertain delayed GRNs, where the randomly occurring estimator gain perturbations are allowed. By constructing a Lyapunov-Krasovskii functional, a delay-dependent criterion is obtained in terms of linear matrix inequalities by properly using the discrete-time Wirtinger-based inequality and reciprocally convex combination approach as well as the free-weighting matrix method. It is shown that the proposed method ensures that the estimation error dynamics is globally asymptotically stable and the desired estimator parameter is designed via the solutions to certain LMIs. Finally, we provide two numerical examples to illustrate the feasibility and validity of the proposed estimation results. (shrink)

Modelling contagious diseases needs to include a mechanistic knowledge about contacts between hosts and pathogens as specific as possible, e.g., by incorporating in the model information about social networks through which the disease spreads. The unknown part concerning the contact mechanism can be modelled using a stochastic approach. For that purpose, we revisit SIR models by introducing first a microscopic stochastic version of the contacts between individuals of different populations (namely Susceptible, Infective and Recovering), then by adding a random (...) perturbation in the vicinity of the endemic fixed point of the SIR model and eventually by introducing the definition of various types of random social networks. We propose as example of application to contagious diseases the HIV, and we show that a micro-simulation of individual based modelling (IBM) type can reproduce the current stable incidence of the HIV epidemic in a population of HIV-positive men having sex with men (MSM). (shrink)

Social network structure has been argued to shape the structure of languages, as well as affect the spread of innovations and the formation of conventions in the community. Specifically, theoretical and computational models of language change predict that sparsely connected communities develop more systematic languages, while tightly knit communities can maintain high levels of linguistic complexity and variability. However, the role of social network structure in the cultural evolution of languages has never been tested experimentally. Here, we present (...) results from a behavioral group communication study, in which we examined the formation of new languages created in the lab by micro‐societies that varied in their network structure. We contrasted three types of social networks: fully connected, small‐world, and scale‐free. We examined the artificial languages created by these different networks with respect to their linguistic structure, communicative success, stability, and convergence. Results did not reveal any effect of network structure for any measure, with all languages becoming similarly more systematic, more accurate, more stable, and more shared over time. At the same time, small‐world networks showed the greatest variation in their convergence, stabilization, and emerging structure patterns, indicating that network structure can influence the community's susceptibility to random linguistic changes (i.e., drift). (shrink)