In this paper we investigate the asymptotic optimality property of a randomized sampling based motion planner, namely RRT. We prove that a RRT planner is not an asymptotically optimal motion planner. Our result, while being consistent with similar results which exist in the literature, however, brings out an important characteristics of a RRT planner. We show that the degree distribution of the...

The spectrum of a weighted Dirac comb on the Thue-Morse quasicrystal is investigated, and characterized up to a measure zero set, by means of the BombieriTaylor conjecture, for Bragg peaks, and of another conjecture that we call AubryGodrèche-Luck conjecture, for the singular continuous component. The decomposition of the Fourier transform of the weighted Dirac comb is obtained in terms of temp...

The asymptotic distribution of sample quantiles in the classical definition is well-known to be normal for absolutely continuous distributions. However, this is no longer true for discrete distributions or sampleswith ties.We show that the definition of sample quantiles based on mid-distribution functions resolves this issue and provides a unified framework for asymptotic properties of sample q...

The temperature of a gas corresponds to the average kinetic energy of the molecules in the gas. What can we say about the distribution of velocities in the gas at a given temperature? We know from physics that this distribution is the maximum entropy distribution under the temperature constraint, otherwise known as the Maxwell-Boltzmann distribution. The maximum entropy distribution corresponds...

In this paper we estimate R = P{X ≤ Y } when X and Y are independent random variables from geometric and Poisson distribution respectively. We find maximum likelihood estimator of R and its asymptotic distribution. This asymptotic distribution is used to construct asymptotic confidence intervals. A procedure for deriving bootstrap confidence intervals is presented. UMVUE of R and UMVUE of its v...

This paper presents the number of results concerning problems of asymptotic densities in the variety of propositional logics. We investigate, for propositional formulas, the proportion of tautologies of the given length n against the number of all formulas of length n. We are specially interested in asymptotic behavior of this fraction. We show what the relation between a number of premises of ...

We study the blocks of interpoint distances, their distributions, correlations, independence and the homogeneity of their total variances. We discuss the exact and asymptotic distribution of the interpoint distances and their average under three models and provide connections between the correlation of interpoint distances with their vector correlation and test of sphericity. We discuss testing...