René Thomas’ discrete modelling of gene regulatory networks (GRN) is a well-known approach to study the dynamics resulting from a set of interacting genes. It deals with some parameters which reflect the possible targets of trajectories. Those parameters are a priori unknown, but they may generally be deduced from a well-chosen set of biologically observed trajectories. Besides, it neglects the time delays for a gene to pass from one level of expression to another one. The purpose of this paper is to show that we can account for time delays of increasing or decreasing expression levels of genes in a GRN, while preserving powerful enough computer-aided reasoning capabilities. We designed a more accurate abstraction of GRN where delays are now supposed to be non-null unknown new parameters. We show that such models, together with hybrid model-checking algorithms, make it possible to obtain some results about the behaviour of a network of interacting genes, since dynamics depend on the respective values of the parameters. The characteristic of our approach is that, among possible execution trajectories in the model, we can automatically find out both viability cycles and absorption in capture basins. As a running example, we show that we are able to discriminate between various possible dynamics of mucus production in the bacterium Pseudomonas aeruginosa.
We study traffic dynamics in growing scale-free networks. Both the scale-free structure of the network and the adaptive nature of the dynamics which controls traffic in the network are considered in the model. The model is investigated with computer simulations and analytically for the case of a scale-free tree. For the scale-free tree, an exact formula and its power law approximation of the complementary cumulative distribution function of link load (edge betweenness) is presented. We examine whether the scaling properties of the network affect the performance of the transport mechanism and estimate the average number of competing transport mechanisms at bottlenecks. We find that bottlenecks tend to appear on the periphery of the network as the performance increases. Various bandwidth allocation strategies are compared. We show that the best performance is achieved when capacity is distributed proportionally to the expected load of links. We demonstrate that it is necessary to study both the topology and the dynamics of the transport mechanism to understand the whole system.
Emergence, a concept that first appeared in philosophy, has been widely explored in the domain of complex systems and is sometimes considered to be the key ingredient that makes ‘complex systems’ ‘complex’. Our goal in this paper is to give a broad survey of emergence definitions, to extract a shared definition structure and to discuss some of the remaining issues. We do not know of any comparable surveys about the emergence concept. For this presentation, we start from a broadly applicable approach and finish with more specific propositions. We first present five selected works with a short analysis of each. We then propose a merged analysis in which we isolate a common structure through all definitions but also what we think needs further research. Finally, we briefly describe some perspectives about the emergence engine idea also referred to as emergent engineering.
The evolution of the immune system of jawed vertebrates with its vast array of clonally expressed lymphocyte receptors is usually viewed as optimized for the defense of the organism. There is a clear association between neo-Darwinism, the dominant view in current biology, and the usual description of immunological activity as adaptive immunity. Herein, using the concepts of spandrels and exaptation created by Gould and coworkers, we review data from comparative immunology and claim that the immune system was not formed as a system optimized for the defense of the organism, but rather may be viewed as a spandrel, a consequence of processes not originally linked to interactions with foreign materials.
A non-linear theory proposed different models of perception of ambiguous patterns, describing different aspects of multistable behaviour of the brain. This paper aims to review the phenomenon of ambiguity in art and to show that the mathematical models of the perception of ambiguous patterns should be regarded as one of the basic models of artistic perception. The following type of ambiguity in art will be considered. Visual ambiguity in painting, semantic (meaning) ambiguity in literature (for instance, ambiguity which V. Shklovsky called ‘the man who is out of his proper place’), ambiguity in puns, jokes and anecdotes, and mixed (visual and semantic) ambiguity in acting and sculpture. The complexity theory of the brain revealed that the human brain as a complex system operates close to the point of instability and ambiguity in art must be regarded as an important tool for supporting the brain near this critical point that gives human beings possibilities for better adaptation.
We apply our previously developed method of ‘topographic’ analysis of networks to the problem of epidemic spreading. We consider the simplest form of epidemic spreading, namely the ‘SI’ model. We argue that the eigenvector centrality of a node is a good indicator of that node’s spreading power. From this we develop seven specific predictions. In particular, we predict that each region (as defined by our approach) will have its own S curve for cumulative adoption over time, and we describe the various phases of the S curve in terms of motion of the infection over the region. Our predictions are well supported by simulations. In particular, the significance of regions to epidemic spreading is clear. Finally, we develop a mathematical theory, giving partial support to our picture. The theory includes a precise quantitative definition of the spreading power of a node, and some approximate analytical results for epidemic spreading.
One of the major obstacles found when trying to construct artefacts derived from principles observed in living beings is the lack of actual dynamic hardware with autonomous capabilities. Even if programmable devices offer the possibility of modifying the functionality implemented in the device, they rely on external hardware and software elements to provide its physical configuration. In this paper we present a new family of electronic devices, called POEtic, whose architecture has been derived from the basic properties that can be extracted from the three major organization principles present in living beings: phylogenesis, ontogenesis and epigenesis. We will demonstrate that the capabilities present in these new programmable devices make them an ideal candidate for the real-time emulation of large-scale biologically inspired spiking neural network models.
The problem of network worms is worsening despite increasing efforts and expenditure on cyber-security. Worm propagation is a random process that creates a complex system of interacting agents (worm copies) over the propagation medium – a scale-free graph, representing real-world networks. Understanding the propagation of network worms on scale-free graphs is the first step towards devising effective techniques for worm quarantining. After presenting the drawbacks of existing mean-field models, we develop a pair-approximation (correlation) model of worm propagation that employs the salient network characteristics – order, size, degree distribution, and transitivity. Inclusion of the transitivity shows significant improvement over existing pair-approximation models. The validity of the model is confirmed by comparing the numeric solution of the model to results from our individual-based simulation. Our model demonstrates that the network structure has considerable impact on the propagation dynamics when the worm uses local propagation strategies.
In this paper we study deliberate attacks on the infrastructure of large scale-free networks. These attacks are based on the importance of individual vertices in the network in order to be successful, and the concept of centrality (originating from social science) has already been utilized in their study with success. Some measures of centrality however, as betweenness, have disadvantages that do not facilitate the research in this area. We show that with the aid of scale-free network characteristics such as the clustering coefficient we can get results that balance the current centrality measures, but also gain insight into the workings of these networks.
There is a growing awareness for the need to understand the basic design principles of living systems. In May of 2005, a diverse group of researchers from the fields of biomedicine, physics, mathematics, engineering, and computer science were brought together in Mizpe Hayamim, Israel to contemplate the current and future trends in computational modeling of biology. In the following work we provide an overview of the discussions that took place and describe some of the research projects that were presented. We also discuss how these seemingly disparate efforts may be integrated and directed at the development of meaningful computational models of biological systems. The wide range of techniques presented in Mizpe Hayamim served to demonstrate not only the breadth of scale found in biology but also the diversity in criteria for the development and application of numerical models in the field. One of the key issues remains the reconciliation of different model types and their effective use as a single composite representation. By attempting to formulate a unifying theme that transcends traditional boundaries between disciplines, it is hoped that this workshop provided a first rallying point that will promote a new level of interaction and synergy in the field.
In biological systems, emergent properties may develop due to numerous individual molecular elements in a population being strongly coupled in a non-linear manner. Under suitable conditions, the formation in vitroof a population of microtubules, a major component of the cellular skeleton (cytoskeleton), behaves as a complex system and develops a number of emergent phenomena. These preparations, which initially contain just two molecular species, a nucleotide and a protein, self-organize by reaction and diffusion and the morphology that develops is determined at a critical moment early in the process by weak external factors, such as gravity and magnetic fields. The process also results in other emergent phenomena, namely replication of form, generation of positional information, and collective transport and organization of colloidal-sized particles. Microtubules are responsible both for cellular organization and the transport of subcellular particles from one part of the cell to another. Frequently, this behaviour is triggered by some weak internal or external factor. The in vitroobservations outlined thus illustrate how in a simple biological system, a complex behaviour may give rise to emergent phenomena that outwardly resemble major biological functions.
This work focuses on the application of on-line programmable microfluidic bioprocessing as a complementation vehicle towards the design of artificial cells. The electronically controlled collection, separation and channel transfer of the biomolecules are monitored by a sensitive fluorescence setup. Two different physical effects, electrophoresis and electroosmotic flow, are used to allow for a detailed micro-control of fluids in micro-reaction environments. A combination of these two basic electronically controlled input reaction chambers makes combinatorial fluidic networks and indefinitely sustained biochemical or chemical reaction networks feasible. Experimental data showing the power of this approach is presented. Not only does this processing power pave the way towards the development of artificial cells (using a technology to complement not yet established autonomous metabolic or replication capabilities) but it also opens up new processes for applications of combinatorial chemistry and lab-on-a-chip biotechnology to drug discovery and diagnosis.
In this paper we show how to go beyond the study of the topological properties of the Internet, by measuring its dynamical state using special active probing techniques and the methods of network tomography. We demonstrate this approach by measuring the key state parameters of Internet paths, the characteristics of queuing delay, in a part of the European Internet. In the paper we describe in detail the ETOMIC measurement platform that was used to conduct the experiments, and the applied method of queuing delay tomography. The main results of the paper are maps showing various spatial structure in the characteristics of queuing delay corresponding to the resolved part of the European Internet. These maps reveal that the average queuing delay of network segments spans more than two orders of magnitude, and that the distribution of this quantity is very well fitted by the log-normal distribution.
A three-variable discrete delay model is proposed for the circadian rhythm of the mammals with BMAL1, PER-CRY complex and REV-ERBαprotein concentrations as the dynamical variables. The delay model is phenomenological in nature rather than the precise description of all the underlying complex processes. The goal of this paper is to study the effects of delay in the circadian rhythms of mammals that appears in both the positive and negative feedback loops of the model. The delay model exhibits 24-hour limit cycle oscillations, entrainment to light-dark (LD) cycles and phase response curves. The model is also found to exhibit quasiperiodic and chaotic oscillations under LD cycles when delay is varied. These are linked to non-24-hour sleep-wake syndrome and cancer incidence. The mutations in Bmal1–/– , PerBrdm1, Rev-Erbα–/–are explained in terms of delay, whereas the double mutations PerBrdm1/Cry2–/–and Cry1–/–/ Cry2–/–are explained in terms of the strength of delayed positive and negative regulations. The delay model in essence captures the core mechanism of the mammalian circadian rhythms with a smaller number of variables and parameters.
The use of parity-check gates in information theory has proved to be very efficient. In particular, error correcting codes based on parity checks over low-density graphs show excellent performances. Another basic issue of information theory, namely data compression, can be addressed in a similar way by a kind of dual approach. The theoretical performance of such a Parity Source Coder can attain the optimal limit predicted by the general rate-distortion theory. However, in order to turn this approach into an efficient compression code (with fast encoding/decoding algorithms) one must depart from parity checks and use some general random gates. By taking advantage of analytical approaches from the statistical physics of disordered systems and SP-like message passing algorithms, we construct a compressor based on low-density non-linear gates with a very good theoretical and practical performance.
Many peer-to-peer (P2P) applications benefit from node specialization: for example, the use of supernodes, the semantic clustering of media files or the distribution of different computing tasks among nodes. We describe simulation experiments with a simple selfish re-wiring protocol (SLAC) that can spontaneously self-organize networks into internally specialized groups (or ‘tribes’). Peers within the tribes pool their specialisms, sharing tasks and working altruistically as a team – or ‘tribe’ – even though their individual behaviour is selfish. This approach is scalable, robust and self-organizing. These results have implications and applications in many disciplines and areas beyond P2P systems.
Th is conference followed the one organized in Torino (Italy) in December 2004 with support from the coordination actions EXYSTENCE and ONCE-CS, funded by the Future and Emerging Technologies Unit of the European Commission. ECCS’05 benefi ted from the same support and was the fi rst conference in an annual series organized by the new European Complex System Society (ECSS) and its Conference Steering Committee.
