We are interested in the asymptotic analysis of the binary search tree (BST) under the random permutation model. Via an embedding in a continuous time model, we get new results, in particular the asymptotic behavior of the profile.
X 3 2. Asymptotic properties: exact model 4 2.1. Consistency and asymptotic normality 4 2.2. Asymptotic efficiency 6 3. Asymptotic properties: metamodel 8 3.
In a model of the form Y = h(X1,. .. , X d) where the goal is to estimate a parameter of the probability distribution of Y , we define new sensitivity indices which quantify the importance of each variable Xi with respect to this parameter of interest. The aim of this paper is to define goal oriented sensitivity indices and we will show that Sobol indices… (More)
In this paper, we develop new algorithms for parameter estimation in the case of models type Input/Output in order to represent and to characterize a phenomenon Y. From experimental data Y 1 , ..., Y n supposed to be i.i.d from Y , we prove a risk bound qualifying the proposed procedures in terms of the number of experimental data n, computing budget m and… (More)
We define a notion of barycenter for random probability measures in the Wasserstein space. We study the population barycenter in terms of existence and uniqueness. Using a duality argument, we give a precise characterization of the population barycenter for compactly supported measures, and we make a connection between averaging in the Wasserstein space and… (More)
We present a TCP mobility solution for the mobile Internet which enables seamless session end-point migration across multi-provider network environments. The solution can be applied by mobile devices to conduct energy-efficient network selection and dynamic spectrum sharing or by data centers to facilitate service migration across IP domains. We leverage… (More)
Given (M t) t∈R + and (M * t) t∈R + respectively a forward and a backward mar-tingale with jumps and continuous parts, we prove that E[φ(M t + M * t)] is non-increasing in t when φ is a convex function, provided the local characteristics of (M t) t∈R + and (M * t) t∈R + satisfy some comparison inequalities. We deduce convex concentration inequalities and… (More)
—We study the cost of improving the goodput, or the useful data rate, to user in a wireless network. We measure the cost in terms of number of base stations, which is highly correlated to the energy cost as well as capital and operational costs of a network provider. We show that increasing the available bandwidth, or throughput, may not necessarily lead to… (More)
We present a mobility solution for stateless applications, where the mobile host can change its IP address as well as the content servers used by ongoing client sessions. This allows content retrieval to always use the locally optimal source when the host moves between networks. We refer to this approach as “stateless mobility” since neither… (More)
—We analyze the performance of TCP and TCP with network coding (TCP/NC) in lossy networks. We build upon the framework introduced by Padhye et al. and characterize the throughput behavior of classical TCP and TCP/NC as a function of erasure probability, round-trip time, maximum window size, and duration of the connection. Our analytical results show that… (More)