Network Automata: Coupling structure and function in real-world networks

We introduce Network Automata, a framework which couples the topological evolution of a network to its structure. It is useful for dealing with networks in which the topology evolves according to some specified microscopic rules and, simultaneously, there is a dynamic process taking place on the network that both depends on its structure but is also capable of modifying it. It is a generic framework for modeling systems in which network structure, dynamics, and function are interrelated. At the practical level, this framework allows for easy implementation of the microscopic rules involved in such systems. To demonstrate the approach, we develop a class of simple biologically inspired models of fungal growth.Comment: 7 pages, 5 figures, 1 tables. Revised content - surplus text and figures remove

Structurally dynamic spin market networks

The agent-based model of stock price dynamics on a directed evolving complex network is suggested and studied by direct simulation. The stationary regime is maintained as a result of the balance between the extremal dynamics, adaptivity of strategic variables and reconnection rules. The inherent structure of node agent "brain" is modeled by a recursive neural network with local and global inputs and feedback connections. For specific parametric combination the complex network displays small-world phenomenon combined with scale-free behavior. The identification of a local leader (network hub, agent whose strategies are frequently adapted by its neighbors) is carried out by repeated random walk process through network. The simulations show empirically relevant dynamics of price returns and volatility clustering. The additional emerging aspects of stylized market statistics are Zipfian distributions of fitness.Comment: 13 pages, 5 figures, accepted in IJMPC, references added, minor changes in model, new results and modified figure

On computational irreducibility and the predictability of complex physical systems

Using elementary cellular automata (CA) as an example, we show how to coarse-grain CA in all classes of Wolfram's classification. We find that computationally irreducible (CIR) physical processes can be predictable and even computationally reducible at a coarse-grained level of description. The resulting coarse-grained CA which we construct emulate the large-scale behavior of the original systems without accounting for small-scale details. At least one of the CA that can be coarse-grained is irreducible and known to be a universal Turing machine.Comment: 4 pages, 2 figures, to be published in PR

Coarse-graining of cellular automata, emergence, and the predictability of complex systems

We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's classification. The resulting coarse-grained CA that we construct are capable of emulating the large-scale behavior of the original systems without accounting for small-scale details. Several CA that can be coarse-grained by this construction are known to be universal Turing machines; they can emulate any CA or other computing devices and are therefore undecidable. We thus show that because in practice one only seeks coarse-grained information, complex physical systems can be predictable and even decidable at some level of description. The renormalization group flows that we construct induce a hierarchy of CA rules. This hierarchy agrees well with apparent rule complexity and is therefore a good candidate for a complexity measure and a classification method. Finally we argue that the large scale dynamics of CA can be very simple, at least when measured by the Kolmogorov complexity of the large scale update rule, and moreover exhibits a novel scaling law. We show that because of this large-scale simplicity, the probability of finding a coarse-grained description of CA approaches unity as one goes to increasingly coarser scales. We interpret this large scale simplicity as a pattern formation mechanism in which large scale patterns are forced upon the system by the simplicity of the rules that govern the large scale dynamics.Comment: 18 pages, 9 figure

Emerging properties of financial time series in the “Game of Life”

We explore the spatial complexity of Conway’s “Game of Life,” a prototypical cellular automaton by means of a geometrical procedure generating a two-dimensional random walk from a bidimensional lattice with periodical boundaries. The one-dimensional projection of this process is analyzed and it turns out that some of its statistical properties resemble the so-called stylized facts observed in financial time series. The scope and meaning of this result are discussed from the viewpoint of complex systems. In particular, we stress how the supposed peculiarities of financial time series are, often, overrated in their importance

Towards generalized measures grasping CA dynamics

In this paper we conceive Lyapunov exponents, measuring the rate of separation between two initially close configurations, and Jacobians, expressing the sensitivity of a CA's transition function to its inputs, for cellular automata (CA) based upon irregular tessellations of the n-dimensional Euclidean space. Further, we establish a relationship between both that enables us to derive a mean-field approximation of the upper bound of an irregular CA's maximum Lyapunov exponent. The soundness and usability of these measures is illustrated for a family of 2-state irregular totalistic CA

Astrobiological Complexity with Probabilistic Cellular Automata

Search for extraterrestrial life and intelligence constitutes one of the major endeavors in science, but has yet been quantitatively modeled only rarely and in a cursory and superficial fashion. We argue that probabilistic cellular automata (PCA) represent the best quantitative framework for modeling astrobiological history of the Milky Way and its Galactic Habitable Zone. The relevant astrobiological parameters are to be modeled as the elements of the input probability matrix for the PCA kernel. With the underlying simplicity of the cellular automata constructs, this approach enables a quick analysis of large and ambiguous input parameters' space. We perform a simple clustering analysis of typical astrobiological histories and discuss the relevant boundary conditions of practical importance for planning and guiding actual empirical astrobiological and SETI projects. In addition to showing how the present framework is adaptable to more complex situations and updated observational databases from current and near-future space missions, we demonstrate how numerical results could offer a cautious rationale for continuation of practical SETI searches.Comment: 37 pages, 11 figures, 2 tables; added journal reference belo

Maintaining Vaccine Delivery Following the Introduction of the Rotavirus and Pneumococcal Vaccines in Thailand

Although the substantial burdens of rotavirus and pneumococcal disease have motivated many countries to consider introducing the rotavirus vaccine (RV) and heptavalent pneumococcal conjugate vaccine (PCV-7) to their National Immunization Programs (EPIs), these new vaccines could affect the countries' vaccine supply chains (i.e., the series of steps required to get a vaccine from their manufacturers to patients). We developed detailed computational models of the Trang Province, Thailand, vaccine supply chain to simulate introducing various RV and PCV-7 vaccine presentations and their combinations. Our results showed that the volumes of these new vaccines in addition to current routine vaccines could meet and even exceed (1) the refrigerator space at the provincial district and sub-district levels and (2) the transport cold space at district and sub-district levels preventing other vaccines from being available to patients who arrive to be immunized. Besides the smallest RV presentation (17.1 cm3/dose), all other vaccine introduction scenarios required added storage capacity at the provincial level (range: 20 L–1151 L per month) for the three largest formulations, and district level (range: 1 L–124 L per month) across all introduction scenarios. Similarly, with the exception of the two smallest RV presentation (17.1 cm3/dose), added transport capacity was required at both district and sub-district levels. Added transport capacity required across introduction scenarios from the provincial to district levels ranged from 1 L–187 L, and district to sub-district levels ranged from 1 L–13 L per shipment. Finally, only the smallest RV vaccine presentation (17.1 cm3/dose) had no appreciable effect on vaccine availability at sub-districts. All other RV and PCV-7 vaccines were too large for the current supply chain to handle without modifications such as increasing storage or transport capacity. Introducing these new vaccines to Thailand could have dynamic effects on the availability of all vaccines that may not be initially apparent to decision-makers

Animal Interactions and the Emergence of Territoriality

Inferring the role of interactions in territorial animals relies upon accurate recordings of the behaviour of neighbouring individuals. Such accurate recordings are rarely available from field studies. As a result, quantification of the interaction mechanisms has often relied upon theoretical approaches, which hitherto have been limited to comparisons of macroscopic population-level predictions from un-tested interaction models. Here we present a quantitative framework that possesses a microscopic testable hypothesis on the mechanism of conspecific avoidance mediated by olfactory signals in the form of scent marks. We find that the key parameters controlling territoriality are two: the average territory size, i.e. the inverse of the population density, and the time span during which animal scent marks remain active. Since permanent monitoring of a territorial border is not possible, scent marks need to function in the temporary absence of the resident. As chemical signals carried by the scent only last a finite amount of time, each animal needs to revisit territorial boundaries frequently and refresh its own scent marks in order to deter possible intruders. The size of the territory an animal can maintain is thus proportional to the time necessary for an animal to move between its own territorial boundaries. By using an agent-based model to take into account the possible spatio-temporal movement trajectories of individual animals, we show that the emerging territories are the result of a form of collective animal movement where, different to shoaling, flocking or herding, interactions are highly heterogeneous in space and time. The applicability of our hypothesis has been tested with a prototypical territorial animal, the red fox (Vulpes vulpes)