A set of intervals is independent when the intervals are pairwise disjoint. In the interval selection problem we are given a set I of intervals and we want to find an independent subset of intervals of largest cardinality. Let α(I) denote the cardinality of an optimal solution. We discuss the estimation of α(I) in the streaming model, where we only have one-time, sequential access to the input ...

In this paper we consider a sequential, coarse-to-fine estimation of a piecewise constant function with smooth boundaries. Accurate detection and localization of the boundary (a manifold) is the key aspect of this problem. In general, algorithms capable of achieving optimal performance require exhaustive searches over large dictionaries that grow exponentially with the dimension of the observat...

We analyse sequential Markov coalescent algorithms for populations with demographic structure: for a bottleneck model, a population-divergence model, and for a two-island model with migration. The sequential Markov coalescent method is an approximation to the coalescent suggested by McVean and Cardin, and by Marjoram and Wall. Within this algorithm we compute, for two individuals randomly sampl...

We present an algorithm to build covering polyhedra for digital 3D objects, by iteratively filling local concavities. The resulting covering polyhedron is convex and is a good approximation of the convex hull of the object. The algorithm uses 3 x 3 x 3 operators and requires a few minutes for a 128 x 128 x 128 image, when implemented on a sequential computer. Once the covering polyhedron has be...

The problem associated with the stiff ordinary differential equation (ODE) systems in parallel processing is that the calculus can not be started simultaneously on many processors with an explicit formula. The proposed algorithm is constructed for a special classes of stiff ODE, those of the form y'(t)=A(t)y(t)+g(t). It has a high efficiency in the implementation on a distributed memory multipr...

We consider an online linear optimization problem over the set of permutations under some precedence constraints. In this problem, the player is supposed to predict a permutation of n fixed objects at each trial, under the constraints that some objects have higher priority than other objects in each permutation. This problem is naturally motivated by a scheduling problem whose objective is to m...

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.’s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine im...

We introduce a class of Multigrid based temporal difference algorithms for reinforcement learning with linear function approximation. Multigrid methods are commonly used to accelerate convergence of iterative numerical computation algorithms. The proposed Multigrid-enhanced TD(λ) algorithms allows to accelerate the convergence of the basic TD(λ) algorithm while keeping essentially the same per-...

This paper presents an improved method of speaker verification using the sequential probability ratio test (SPRT), which can treat the correlation between successive feature vectors. The hidden Markov model with the mean field approximation enables us to consider the correlation in the SPRT, i.e., using the mean field of previous state, probability computation can be carried out as if input sam...