Julien Clement

Exact p-value calculation for heterotypic clusters of regulatory motifs and its application in computational annotation of cis-regulatory modules

Backgroundcis-Regulatory modules (CRMs) of eukaryotic genes often contain multiple binding sites for transcription factors. The phenomenon that binding sites form clusters in CRMs is exploited in many algorithms to locate CRMs in a genome. This gives rise to the problem of calculating the statistical significance of the event that multiple sites, recognized by different factors, would be found simultaneously in a text of a fixed length. The main difficulty comes from overlapping occurrences of motifs. So far, no tools have been developed allowing the computation of p-values for simultaneous occurrences of different motifs which can overlap.ResultsWe developed and implemented an algorithm computing the p-value that s different motifs occur respectively k1, ..., ksor more times, possibly overlapping, in a random text. Motifs can be represented with a majority of popular motif models, but in all cases, without indels. Zero or first order Markov chains can be adopted as a model for the random text. The computational tool was tested on the set of cis-regulatory modules involved in D. melanogaster early development, for which there exists an annotation of binding sites for transcription factors. Our test allowed us to correctly identify transcription factors cooperatively/competitively binding to DNA.MethodThe algorithm that precisely computes the probability of simultaneous motif occurrences is inspired by the Aho-Corasick automaton and employs a prefix tree together with a transition function. The algorithm runs with the O(n|Σ|(m|ℋMathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaat0uy0HwzTfgDPnwy1egaryqtHrhAL1wy0L2yHvdaiqaacqWFlecsaaa@3762@| + K|σ|K) ∏iki) time complexity, where n is the length of the text, |Σ| is the alphabet size, m is the maximal motif length, |ℋMathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaat0uy0HwzTfgDPnwy1egaryqtHrhAL1wy0L2yHvdaiqaacqWFlecsaaa@3762@| is the total number of words in motifs, K is the order of Markov model, and kiis the number of occurrences of the i th motif.ConclusionThe primary objective of the program is to assess the likelihood that a given DNA segment is CRM regulated with a known set of regulatory factors. In addition, the program can also be used to select the appropriate threshold for PWM scanning. Another application is assessing similarity of different motifs.AvailabilityProject web page, stand-alone version and documentation can be found at http://bioinform.genetika.ru/AhoPro/

Self-stabilizing counting in mobile sensor networks

Distributed computing has to adapt its techniques to mobile sensor networks and cope with constraints like small memory size or lack of computation power. In this paper we extend the results of Angluin et al (see [1,2,3,4]) by finding self-stabilizing algorithms to count the number of agents in the network. We focus on two different models of communication, with a fixed antenna or with pairwise interactions. In both models we decide if there exist algorithms (probabilistic, deterministic, with k-fair adversary) to solve the self-stabilizing counting problem.

Self-stabilizing counting in mobile sensor networks with a base station

Distributed computing must adapt its techniques to networks of mobile agents. Indeed, we are facing new problems like the small size of memory and the lack of computational power. In this paper, we extend the results of Angluin et al (see [4,3,2,1]) by finding self-stabilizing algorithms to count the number of agents in the network. We focus on two different models of communication, with a fixed base station or with pairwise interactions. In both models we decide if there exist algorithms (probabilistic, deterministic, with k-fair adversary) to solve the self-stabilizing counting problem.

The cost of probabilistic agreement in oblivious robot networks

In this paper, we look at the time complexity of two agreement problems in networks of oblivious mobile robots, namely, at the gathering and scattering problems. Given a set of robots with arbitrary initial locations and no initial agreement on a global coordinate system, gathering requires that all robots reach the exact same but not predetermined location. In contrast, scattering requires that no two robots share the same location. These two abstractions are fundamental coordination problems in cooperative mobile robotics. Oblivious solutions are appealing for self-stabilization since they are self-stabilizing at no extra cost. As neither gathering nor scattering can be solved deterministically under arbitrary schedulers, probabilistic solutions have been proposed recently. The contribution of this paper is twofold. First, we propose a detailed time complexity analysis of a modified probabilistic gathering algorithm. Using Markov chains tools and additional assumptions on the environment, we prove that the convergence time of gathering can be reduced from O(n^2) (the best known bound) to O(1) or O([emailxa0protected]?log(logn)), depending on the model of multiplicity detection. Second, using the same technique, we prove that scattering can also be achieved in fault-free systems with the same bounds.

Guidelines for the Verification of Population Protocols

We address the problem of verification by model checking of the basic population protocol (PP) model of Angluin et al. [1]. This problem has received special attention in the last two years and new tools have been proposed to deal with it. We show that the problem can be solved by using the existing model-checking tools, e.g., Spin and Prism. In order to do so, we apply the counter abstraction to get an abstraction of the PP model which can be efficiently verified by the existing model-checking tools. Moreover, this abstraction preserves the correct stabilization property of PP models. To deal with the fairness assumed by the PP models, we provide two new recipes. The first one gives sufficient conditions under which the PP model fairness can be replaced by the weak fairness implemented in Spin. We show that this recipe can be applied to several PP models. In the second recipe, we show how to use probabilistic model-checking and, in particular, Prism to take completely in consideration the fairness of the PP models. The correctness of this recipe is based on existing theorems involving finite discrete Markov chains.

Brief announcement: non-self-stabilizing and self-stabilizing gathering in networks of mobile agents--the notion of speed

We present a model for <i>asynchronous mobile agent</i> networks that takes into account the <i>notion of speed</i> of the agents. Then, we study the <i>gathering problem</i> (GP), in which an <i>unknown</i> number of <i>anonymous</i> agents have constant values they must deliver (only once) to a non mobile agent, the base station.

On the Complexity of a Self-Stabilizing Spanning Tree Algorithm for Large Scale Systems

Many large scale systems, like grids and structured peer to peer systems, operate on a constrained topology. Since underlying networks do not expose the real topology to the applications, an algorithm should build and maintain a virtual topology for the application. This algorithm has to bootstrap the system and react to the arrival and departures of processes. In a previous article, we introduced a computing model designed for scalability in which we gave a self-stabilizing algorithm that builds a spanning tree. At that time, we provided a proof of stabilization and performance measurements of a prototypal implementation. In this work, we present a probabilistic method to evaluate the theoretical performances of algorithms in this model, and provide a probabilistic analysis of the convergence time of the algorithm.