The stabilization to a desired pose of a nonholonomic mobile robot carrying a manipulator arm, based on sensory data provided by a camera mounted on the end-e ector of the arm, is considered. Instances of this problem occur in practice during docking or parallel parking maneuvers of such vehicles. The visual data obtained as the camera tracks a target of known geometry are used to implement a c...

Abstract The purpose of this work is to investigate a novel class noninstantaneous impulsive stochastic integrodifferential equations (SIDEs) driven by Brownian motion and Rosenblatt process. We construct new set adequate assumptions for the existence uniqueness mild solutions using analysis, analytic semigroup theory, integral equation fixed point methodology. Additionally, we study asymptotic...

We adapt arguments concerning information-theoretic convergence in the Central Limit Theorem to the case of dependent random variables under Rosenblatt mixing conditions. The key is to work with random variables perturbed by the addition of a normal random variable, giving us good control of the joint density and the mixing coefficient. We strengthen results of Takano and of Carlen and Soffer t...

We consider Bickel-Rosenblatt tests of fit for a density f . Their asymptotic properties are studied under local Pitman’s alternatives ; we investigate their power functions. Our goal is to look for the best test in this class, by optimizing the power as done by Mason (1983) in the context of minimax comparisons. This approach leads to a continuous versions of a χ type test. Finally a simulatio...

A simple procedure to map two probability measures in R is the so-called Knothe-Rosenblatt rearrangement, which consists in rearranging monotonically the marginal distributions of the last coordinate, and then the conditional distributions, iteratively. We show that this mapping is the limit of solutions to a class of Monge-Kantorovich mass transportation problems with quadratic costs, with the...

Jay S. Rosenblatt was a pioneer in the study of the neural and endocrine bases of parental behavior in mammals. Jay's research on themechanisms underlyingmaternal behavior in cats, rats, and rabbits, and the development of behavior as a synchronous interaction between caregiver and offspring through weaning, created a genre of international maternal behavior research. He created unique experime...

We consider Riemann sum approximations of stochastic integrals with respect to the fractional Browian motion index H≥1 2. show convergence these schemes at first and second order. The processes obtained in limit case are Rosenblatt process if H>3 4 standard Brownian otherwise. These results under assumption that integrand is a “controlled” process. provide many examples such processes, particul...

The thermal perceptron is a simple extension to Rosenblatt’s perceptron learning rule for training individual linear threshold units. It finds stable weights for nonseparable problems as well as separable ones. Experiments indicate that if a good initial setting for a temperature parameter, To, has been found, then the thermal perceptron outperforms the Pocket algorithm and methods based on gra...