Exact Distribution of the Local Score for Markovian Sequences,

International audienceWe provide the exact distribution of the local score in random sequences in several models. We will first consider a Markov model on the score sequence, and then on the letter sequence. The exact P-value of the local score obtained with both models are compared thanks to several datasets. they are elso comparde with previous results using the independent model

Distribution exacte du score local, cas Markovien

National audienceSoit X = (Xk)k≥1 une suite de variables à valeurs dans {−v, ..., 0, ...,+u}. On définit le score local d'une séquence par Hn = max1≤i≤j≤n j k=iXk . Le score local est utilisé notamment dans l'analyse des séquences biologiques afin de mettre en évidence des régions de séquences ayant des propriétés biologiques intéressantes. La signification statistique des scores locaux calculés permet alors de mettre en évidence ce qui est réellement intéressant et il est donc nécessaire de connaître la distribution du score local. Nous établissons ici la loi exacte du score local dans le cas où la suite des Xi est une chaîne de Markov d'ordre 1

Unbiased risk estimation method for covariance estimation

We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (URE) method, we build an estimator of the risk which allows to select an estimator in a collection of model. Then, we present an oracle inequality which ensures that the risk of the selected estimator is close to the risk of the oracle. Simulations show the efficiency of this methodology

New approximate P-value of gapped local sequence alignments,

International audienceWe propose a new method to approximate the signi cativity of gapped local sequence alignments. We focus on short sequences for which standard methods are known to be less accurate since they have been developed under asymptotics. Our approach combines an approximate distribution of ungapped local score of two sequences and a special scoring scheme that allows the insertion of gaps. For a positive integer h, the scoring scheme is de ned on h-tuples of the components of the sequences and corresponds to the gapped global score. The in uence of h and the accuracy of the p-value are numerically studied

Elements related to the largest complete excursion of a reflected BM stopped at a fixed time. Application to local score.

International audienceElements related to the largest complete excursion of a reflected BM stopped at a fixed time. Application to local score

Unbiased risk estimation method for covariance estimation

We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (U.R.E.) method, we build an estimator of the risk which allows to select an estimator in a collection of models. Then, we present an oracle inequality which ensures that the risk of the selected estimator is close to the risk of the oracle. Simulations show the efficiency of this methodology

Affectation of Emergency Vehicles in Rescue Centers under Random Demand

International audienceThe aim of this paper is to improve the operational response of the Fire and Rescue Services (SDIS). More precisely, the allocation of emergency vehicle (EV) to Rescue Center (RC) in department(France) is studied. The problem is to allocate the capacity (number of EV by RC) under random apparition of accidents and random durations. A mathematical model based on the notion of simultaneous requirements of EV is proposed. This notion allows us to dispense with the time dimension and just focus on the probability to have simultaneous required quantity of EVs. Hence, the problem can be formulated as a kind of transportation problem under random demand. An approximation of the model is done using the simulation approach and an algorithm to find the optimal solution of approximate model is proposed