Proceedings Series

Vol. 4 (2011), No. 2, pp. 115 – 265

Summer Solstice 2010 International Conference on Discrete Models of Complex Systems

Nancy, France; June 16–18, 2010

all authors

S. Ghosh, A. Banerjee, N. Sharma, S. Agarwal, N. Ganguly, S. Bhattacharya, A. Mukherjee

Statistical Analysis of the Indian Railway Network: A Complex Network Approach


In this paper, we study the Indian Railway Network (IRN) as a weighted complex network in which railway stations are considered as the nodes, while the weights on edges represent the number of trains directly linking two stations. Apart from the small-world characteristics and exponential distributions of node-degrees and edge-weights in the IRN, we explore the correlations of the amount of traffic with the topology of the network. The traffic in the IRN is found to be accumulated on interconnected groups of stations and is concentrated in the links between large stations. We also identify the most important stations in the IRN with respect to connectivity and traffic-flow, which help to identify some of the probable points (and regions) of congestion in the network. The study indicates several guidelines to improve the performance of the IRN.

Study Heart Rate by Tools from Complex Networks


Heart rate measured as beat-to-beat time intervals varies in time. It is believed that time intervals between subsequent normal heart contractions carry information about the regulatory system of the heart. How to quantify such signals is not clear and because of that heart rate variability is still apart from the clinic routine. In the following, we propose a method for representing a heart rate signal as a directed network. Then we study the signal properties by complex network tools. The signals to study were collected from patients recovering after the heart transplantation. The aim is to classify the progress of adapting of the new heart — graft. Moreover, it is expected that the method allows for visual classification. Our investigations are preliminary, however the obtained results are promising.

Sparsity in Model Gene Regulatory Networks


We propose a gene regulatory network model which incorporates the microscopic interactions between genes and transcription factors. In particular the gene’s expression level is determined by deterministic synchronous dynamics with contribution from excitatory interactions. We study the structure of networks that have a particular “function” and are subject to the natural selection pressure. The question of network robustness against point mutations is addressed, and we conclude that only a small part of connections defined as “essential” for cell’s existence is fragile. Additionally, the obtained networks are sparse with narrow in-degree and broad out-degree, properties well known from experimental study of biological regulatory networks. Furthermore, during sampling procedure we observe that significantly different genotypes can emerge under mutation–selection balance. All the preceding features hold for the model parameters which lay in the experimentally relevant range.

Analysis of Lattice-Gas Cellular Automaton Models for Tumor Growth by Means of Fractal Scaling


Mathematical modeling of tumor development has become a real hype within the last decade. The abundance of mathematical models has created a great need for the validation of their biological relevance. Recently, in order to characterize the tumor growth dynamics, Brú et al. have determined some statistical properties of both in vitro and in vivo solid tumor-surfaces by using fractal scaling analysis. Surprisingly, for all tumor surfaces, the statistical observables converged to a unique set of critical exponents which indicates some common features of tumor growth dynamics (linear growth rate, growth activity limited to the outer rim of the tumor mass and diffusion of newborn tumor cells on the surface from lower to higher curvature regions, typical of Molecular Beam Epitaxy (MBE) Universality). Here, we develop and analyze a lattice-gas cellular automaton (LGCA) model of solid tumor growth. Random walk dynamics are assumed for tumor cell migration and a density-dependent birth process describes the cell mitotic dynamics. Fractal scaling analysis shows that for any parameter variation the model interface dynamic follows Edward–Wilkinson (EW) Universality, which differs from experimental findings. However, the model recovers some features, i.e. linear growth rate for tumor size and proliferative activity restricted to the outer layer, observed in experiments.

GCA-w Algorithms for Traffic Simulation


The GCA-w model (Global Cellular Automata with write access) is an extension of the GCA (Global Cellular Automata) model, which is based on the cellular automata model (CA). Whereas the CA model uses static links to local neighbors, the GCA model uses dynamic links to potentially global neighbors. The GCA-w model is a further extension that allows modifying the neighbors’ states. Thereby, neighbors can dynamically be activated or deactivated. Algorithms can be described more concisely and may execute more efficiently because redundant computations can be avoided. Modeling traffic flow is a good example showing the usefulness of the GCA-w model. The Nagel–Schreckenberg algorithm for traffic simulation is first described as CA and GCA, and then transformed into the GCA-w model. This algorithm is “exclusive-write”, meaning that no write conflicts have to be resolved. Furthermore, this algorithm is extended, allowing to deactivate and to activate cars stuck in a traffic jam in order to save computation time and energy.

FLAME: A Platform for High Performance Computing of Complex Systems, Applied for Three Case Studies


FLAME allows complex models to be automatically parallelised on High Performance Computing (HPC) grids enabling large number of agents to be simulated over short periods of time. Modellers are hindered by complexities of porting models on parallel platforms and time taken to run large simulations on a single machine, which FLAME overcomes. Three case studies from different disciplines were modelled using FLAME, and are presented along with their performance results on a grid.

On Modeling Large-Scale Multi-Agent Systems with Parallel, Sequential and Genuinely Asynchronous Cellular Automata


We study certain types of Cellular Automata (CA) viewed as an abstraction of large-scale Multi-Agent Systems (MAS). We argue that the classical CA model needs to be modified in several important respects, in order to become a relevant and sufficiently general model for the large-scale MAS, and so that thus generalized model can capture many important MAS properties at the level of agent ensembles and their long-term collective behavior patterns. We specifically focus on the issue of inter-agent communication in CA, and propose sequential cellular automata (SCA) as the first step, and genuinely Asynchronous Cellular Automata (ACA) as the ultimate deterministic CA-based abstract models for large-scale MAS made of simple reactive agents. We first formulate deterministic and non-deterministic versions of sequential CA, and then summarize some interesting configuration space properties (i.e., possible behaviors) of a restricted class of sequential CA. In particular, we compare and contrast those properties of sequential CA with the corresponding properties of the classical (that is, parallel and perfectly synchronous) CA with the same restricted class of update rules. We analytically demonstrate failure of the studied sequential CA models to simulate all possible behaviors of perfectly synchronous parallel CA, even for a very restricted class of non-linear totalistic node update rules. The lesson learned is that the interleaving semantics of concurrency, when applied to sequential CA, is not refined enough to adequately capture the perfect synchrony of parallel CA updates. Last but not least, we outline what would be an appropriate CA-like abstraction for large-scale distributed computing insofar as the inter-agent communication model is concerned, and in that context we propose genuinely asynchronous CA.

Dynamics of Number of Packets in Transit in Free Flow State of Data Network


We study how the dynamics of Number of Packets in Transit (NPT) is affected by the coupling of a routing type with a volume of incoming packet traffic in a data network model of packet switching type. The NPT is a network performance indicator of an aggregate type that measures in “real time”, how many packets are in the network on their routes to their destinations. We conduct our investigation using a time-discrete simulation model that is an abstraction of the Network Layer of the ISO OSI Seven Layer Reference Model. This model focuses on packets and their routing. We consider a static routing and two different types of dynamic routings coupled with different volumes of incoming packet traffic in the network free flow state. Our study shows that the order of the values of the NPT mean value time series depends on the coupling of a routing type with a volume of incoming packet traffic and changes when the volume of incoming packet traffic increases and is closed to the critical source load values, i.e. when it is closed to the phase transition points from the network free flow state to its congested states.

Embedding Kadanoff’s Scaling Picture into the Triangular Lattice


A strictly topological aspect in renormalization theory is tackled from Kadanoff’s scaling picture which splits the square lattice into nested blocks and we study how to embed similar schemes onto the triangular lattice. From a preliminary study on the various ways of splitting the dual honeycomb into polyhexes while preserving symmetries, it is shown that only two patterns are relevant: either a 3-hexe prototile or a 4-hexe prototile. The first one has been investigated in detail by Niemeijer and van Leeuwen. The other alternative leads to an “arrowhead picture” and is the core of our proposal. As far as we know, the resulting spin lattice has never been investigated elsewhere. It should be pointed out that these scaling pictures differ from exactly solved models and in particular from the star-triangle transformation.


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