Anomalous biased diffusion in networks

We study diffusion with a bias towards a target node in networks. This problem is relevant to efficient routing strategies in emerging communication networks like optical networks. Bias is represented by a probability $p$ of the packet/particle to travel at every hop towards a site which is along the shortest path to the target node. We investigate the scaling of the mean first passage time (MFPT) with the size of the network. We find by using theoretical analysis and computer simulations that for Random Regular (RR) and Erd\H{o}s-R\'{e}nyi (ER) networks, there exists a threshold probability, $p_{th}$, such that for $p<p_{th}$ the MFPT scales anomalously as $N^\alpha$, where $N$ is the number of nodes, and $\alpha$ depends on $p$. For $p>p_{th}$ the MFPT scales logarithmically with $N$. The threshold value $p_{th}$ of the bias parameter for which the regime transition occurs is found to depend only on the mean degree of the nodes. An exact solution for every value of $p$ is given for the scaling of the MFPT in RR networks. The regime transition is also observed for the second moment of the probability distribution function, the standard deviation.Comment: 13 Pages, To appear in PR

CytoASP: a Cytoscape app for qualitative consistency reasoning, prediction and repair in biological networks

Background: Qualitative reasoning frameworks, such as the Sign Consistency Model (SCM), enable modelling regulatory networks to check whether observed behaviour can be explained or if unobserved behaviour can be predicted. The BioASP software collection offers ideal tools for such analyses. Additionally, the Cytoscape platform can offer extensive functionality and visualisation capabilities. However, specialist programming knowledge is required to use BioASP and no methods exist to integrate both of these software platforms effectively. Results: We report the implementation of CytoASP, an app that allows the use of BioASP for influence graph consistency checking, prediction and repair operations through Cytoscape. While offering inherent benefits over traditional approaches using BioASP, it provides additional advantages such as customised visualisation of predictions and repairs, as well as the ability to analyse multiple networks in parallel, exploiting multi-core architecture. We demonstrate its usage in a case study of a yeast genetic network, and highlight its capabilities in reasoning over regulatory networks. Conclusion: We have presented a user-friendly Cytoscape app for the analysis of regulatory networks using BioASP. It allows easy integration of qualitative modelling, combining the functionality of BioASP with the visualisation and processing capability in Cytoscape, and thereby greatly simplifying qualitative network modelling, promoting its use in relevant projects

Dynamic processes in complex systems using computer simulations

In this thesis I use Monte Carlo simulations to study the properties of biased and unbiased random walks on complex networks. More specifically, reaction-diffusion processes such as the trapping process A+T-> T are studied, as well as the spreading of infection in the two species reaction-diffusion process A+B->2B. These models may be relevant in communication networks where data traverses the network packets, spread of a virus in networks of routers, social networks for rumor spreading etc. In addition, a biological population model was constructed to study the evolution of the rate of biological aging based on the phenotype of the individuals. For the trapping problem we develop a simple theory to account for the behavior of the survival probability in a variety of conditions. In Erdos-Renyi (ER) networks we find that the trapping process exhibits a non-exponential behavior which depends on both the number of traps and the size of the network. In SF networks, when the trap is placed in one the network hubs, we find a new scaling with the system size. We also examine in detail the formation of a depletion zone in the trapping reaction in networks, with a single perfect trap. We show that the depletion zone is absent in regular, ER, and SF networks. The particles are homogeneously distributed in regular and ER networks, with the depletion effect appearing in very sparse networks. We also investigate the efficiency of biased random walks in complex networks. We reveal a non-universal scaling of the MFPT with the system size N with no traps present. When the hub of an SF network fails, we find that even for a small bias, fg stays relatively constant with N, while for the unbiased walk it follows a power law scaling with the system size. We also study the dynamics of the infection of a two mobile species reaction, from a single infected agent in a population of healthy agents. Find the density of healthy particles ρ(t) to be an exponential function in the long time limit in 2D, 3D lattices, ER and SF networks. We also investigate the scaling of the crossover time tc from short to long time exponential behavior, which we find to be a power law in lattices and ER networks. This crossover is shown to be absent in SF networks, where we reveal the role of the connectivity of the network in the infection process. In addition, I introduce a simple model to study how natural selection acts upon aging, which focuses on the viability of each individual. It is able to reproduce the Gompertz law of mortality and can make predictions about the relation between the level of mutation rates (beneficial/deleterious/neutral), age at reproductive maturity and the degree of biological aging. The process of aging in this simple model is revealed to be fairly complex, yielding a rich variety of results.Στην εργασία αυτή χρησιμοποίησα προσομοιώσεις Monte Carlo για τη μελέτη των ιδιοτήτων των προκατειλημμένων και τυχαίων περιπάτων σε πολύπλοκα δίκτυα. Πιο συγκεκριμένα, μελετώνται διαδικασίες διάχυσης-αντίδρασης (diffusion-reaction) όπως η παγίδευση (trapping) A+T->T, καθώς και η εξάπλωση μιας επιδημίας σε αντίδραση-διάχυση δύο ειδών A+B-> 2B. Τα μοντέλα αυτά μπορεί να αφορούν σε δίκτυα επικοινωνιών, όπου η πληροφορία μεταδίδεται σε μορφή πακέτων, την εξάπλωση ιών σε δίκτυα δρομολογητών, κοινωνικών δικτύων για φήμες που εξαπλώνονται κλπ. Επιπλέον, ένα βιολογικό μοντέλο πληθυσμού κατασκευάστηκε για τη μελέτη της εξέλιξης του ρυθμού της βιολογικής γήρανσης με βάση το φαινότυπο των ατόμων. Για το πρόβλημα της παγίδευσης έχουμε αναπτύξει μια απλή θεωρία που λαμβάνει υπόψη τη συμπεριφορά της πιθανότητας επιβίωσης σε μια ποικιλία συνθηκών. Σε Erdos-Renyi (ER) δίκτυα διαπιστώνουμε ότι η παγίδευση έχει μη εκθετική συμπεριφορά, η οποία εξαρτάται τόσο από τον αριθμό των παγίδων όσο και το μέγεθος του δικτύου. Όταν η παγίδα τοποθετείται σε ένα από τους κεντρικούς κόμβους του δικτύου στα SF δίκτυα, βρίσκουμε μια νέα κλιμάκωση με το μέγεθος του συστήματος. Έχουμε επίσης εξετάσει το σχηματισμό της ζώνης ελλείμματος (depletion zone) της αντίδρασης παγίδευσης σε δίκτυα, με μια παγίδα. Δείχνουμε ότι η ζώνη ελλείμματος είναι απούσα σε regular, ER και SF δίκτυα. Μελετήσαμε επίσης την αποτελεσματικότητα των μεροληπτικών τυχαίων περίπατων (biased random walks) σε ER και SF δίκτυα. Για δίκτυα ER όπου δεν υπάρχουν παγίδες διαπιστώσαμε μια μη καθολική κλιμάκωση του MFPT με το μέγεθος του συστήματος. Όταν ο κεντρικός κόμβος του δικτύου χαλάσει, διαπιστώνουμε ότι σε δίκτυο SF, ακόμη και μια μικρή τιμή του bias μπορεί να βελτιώσει κατά πολύ τη διαδικασία της μετάδοσης και το αποτέλεσμα είναι πιο έντονο όσο μεγαλύτερο είναι το δίκτυο. Μελετάμε επίσης τη δυναμική μιας επιδημίας σε αντιδράσεις δύο κινητών ειδών, από ένα μολυσμένο σωματίδιο σε έναν πληθυσμό υγιών σωματιδίων. Η πυκνότητα των υγιών σωματιδίων ρ(t), είναι μια εκθετική συνάρτηση σε μεγάλους χρόνους σε 2D, 3D πλέγματα, ER και SF δίκτυα. Διερευνούμε επίσης την κλιμάκωση της χρόνου crossover tc από βραχυπρόθεσμη και μακροπρόθεσμη εκθετική συμπεριφορά, που είναι νόμος δύναμης σε πλέγματα και δίκτυα ER. Αυτό το crossover φαίνεται να απουσιάζει σε SF δίκτυα, όπου αποκαλύπτεται ο ρόλος της συνδεσιμότητας του δικτύου στη διαδικασία της επιδημίας. Επιπλέον, εισάγουμε ένα απλό μοντέλο για να μελετήσουμε πώς η φυσική επιλογή δρα κατά της γήρανσης, το οποίο επικεντρώνεται στη βιωσιμότητα του κάθε ατόμου. Είναι σε θέση να αναπαράγει το νόμο Gompertz της θνησιμότητας και μπορεί να κάνει προβλέψεις για τη σχέση μεταξύ του επιπέδου των συντελεστών μετάλλαξης (επωφελείς/επιβλαβείς/ουδέτερες), την ηλικία στην αναπαραγωγική ωριμότητα και το βαθμό της βιολογικής γήρανσης. Η διαδικασία της γήρανσης σε αυτό το απλό μοντέλο αποκαλύπτεται ότι είναι αρκετά πολύπλοκη, παράγοντας μια πλούσια ποικιλία αποτελεσμάτων

DyCoNet:A Gephi Plugin for Community Detection in Dynamic Complex Networks

Community structure detection has proven to be important in revealing the underlying organisation of complex networks. While most current analyses focus on static networks, the detection of communities in dynamic data is both challenging and timely. An analysis and visualisation procedure for dynamic networks is presented here, which identifies communities and sub-communities that persist across multiple network snapshots. An existing method for community detection in dynamic networks is adapted, extended, and implemented. We demonstrate the applicability of this method to detect communities in networks where individuals tend not to change their community affiliation very frequently. When stability of communities cannot be assumed, we show that the sub-community model may be a better alternative. This is illustrated through test cases of social and biological networks. A plugin for Gephi, an open-source software program used for graph visualisation and manipulation, named "DyCoNet", was created to execute the algorithm and is freely available from https://github.com/juliemkauffman/DyCoNet

Detection of composite communities in multiplex biological networks

The detection of community structure is a widely accepted means of investigating the principles governing biological systems. Recent efforts are exploring ways in which multiple data sources can be integrated to generate a more comprehensive model of cellular interactions, leading to the detection of more biologically relevant communities. In this work, we propose a mathematical programming model to cluster multiplex biological networks, i.e. multiple network slices, each with a different interaction type, to determine a single representative partition of composite communities. Our method, known as SimMod, is evaluated through its application to yeast networks of physical, genetic and co-expression interactions. A comparative analysis involving partitions of the individual networks, partitions of aggregated networks and partitions generated by similar methods from the literature highlights the ability of SimMod to identify functionally enriched modules. It is further shown that SimMod offers enhanced results when compared to existing approaches without the need to train on known cellular interactions

Community Structure Detection for Overlapping Modules through Mathematical Programming in Protein Interaction Networks

Community structure detection has proven to be important in revealing the underlying properties of complex networks. The standard problem, where a partition of disjoint communities is sought, has been continually adapted to offer more realistic models of interactions in these systems. Here, a two-step procedure is outlined for exploring the concept of overlapping communities. First, a hard partition is detected by employing existing methodologies. We then propose a novel mixed integer non linear programming (MINLP) model, known as OverMod, which transforms disjoint communities to overlapping. The procedure is evaluated through its application to protein-protein interaction (PPI) networks of the rat, E. coli, yeast and human organisms. Connector nodes of hard partitions exhibit topological and functional properties indicative of their suitability as candidates for multiple module membership. OverMod identifies two types of connector nodes, inter and intra-connector, each with their own particular characteristics pertaining to their topological and functional role in the organisation of the network. Inter-connector proteins are shown to be highly conserved proteins participating in pathways that control essential cellular processes, such as proliferation, differentiation and apoptosis and their differences with intra-connectors is highlighted. Many of these proteins are shown to possess multiple roles of distinct nature through their participation in different network modules, setting them apart from proteins that are simply 'hubs', i.e. proteins with many interaction partners but with a more specific biochemical role

DyCoNet architecture and example analysis.

<p>a) Diagram depicting the analysis work-flow and plugin execution. b) Sub-community model applied on the TC-PIN from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101357#pone.0101357-Tang1" target="_blank">[14]</a>. Top-left: An overview of the network, consisting of 3901 nodes and 16891 edges. Top-right to bottom-right: Snapshots of the network at time points 1–5. For clarity only the k-core of the network with is shown. Node colours correspond to the community membership of each node. Layout of the network is done using the ForceAtlas2 algorithm. Parts of the network that change between time-points are indicated in circles to aid visualisation.</p