AbstractThis paper considers the scenario where multiple robots collaboratively cover a region in which the exact distribution of workload is unknown prior to the operation. The workload distribution is not uniform in the region, meaning that the time required to cover a unit area varies at different locations of the region. In our approach, we divide the target region into multiple horizontal stripes, and the robots sweep the current stripe while partitioning the next stripe concurrently. We propose a distributed workload partition algorithm and prove that the operation time on each stripe converges to the minimum under the discrete-time update law. We conduct comprehensive simulation studies and compare our method with the existing methods to verify the theoretical results and the advantage of the proposed method. Flight experiments on mini drones are also conducted to demonstrate the practicality of the proposed algorithm.
We propose an optimal combining strategy to mitigate estimation risk for the popular mean-variance portfolio choice problem in the case without a risk-free asset. We find that our strategy performs well in general, and it can be applied to known estimated rules and the resulting new rules outperform the original ones. We further obtain the exact distribution of the out-of-sample returns and explicit expressions of the expected out-of-sample utilities of the combining strategy, providing not only a fast and accurate way of evaluating the performance, but also analytical insights into the portfolio construction. This paper was accepted by Tyler Shumway, finance.
In this study, a multivariate gamma distribution is first introduced. Then, by defining a new statistic, three control charts called the MG charts, are proposed for this distribution. The first control chart is based on the exact distribution of this statistic, the second control chart is based on the Satterthwaite approximation, and the last is based on the normal approximation. Efficiency of the proposed control charts is evaluated by average run length (ARL) criterion.
Stochastic transcription and translation dynamics of protein accumulation up to some concentration threshold sets the timing of many cellular physiological processes. Here we obtain the exact distribution of first threshold-crossing times of protein concentration, in either Laplace or time domain, and its associated cumulants: mean, variance and skewness. The distribution is asymmetric and its skewness non-monotonically varies with the threshold. We study lysis times of E-coli cells for holin gene mutants of bacteriophage-λ and find a good match with theory. Mutants requiring higher holin thresholds show more skewed lysis time distributions as predicted.
In a classical chess round-robin tournament, each of
$n$
players wins, draws, or loses a game against each of the other
$n-1$
players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested in the distribution of the scores associated with ranks of
$n$
players after
${{n \choose 2}}$
games, that is, the distribution of the maximal score, second maximum, and so on. The exact distribution for a general
$n$
seems impossible to obtain; we obtain a limit distribution.
Distributed multi-robot sweep coverage for a region with unknown workload distribution
