Stochastic comparisons of series and parallel systems with randomized independent components

Consider a series or parallel system of independent components and assume that the components are randomly chosen from two different batches, with the components of the first batch being more reliable than those of the second. In this note it is shown that the reliability of the system increases, in usual stochastic order sense, as the random number of components chosen from the first batch increases in increasing convex order. As a consequence, we establish a result analogous to the Parrondo's paradox, which shows that randomness in the number of components extracted from the two batches improves the reliability of the series syste

Parallel Batch-Dynamic Graph Connectivity

In this paper, we study batch parallel algorithms for the dynamic connectivity problem, a fundamental problem that has received considerable attention in the sequential setting. The most well known sequential algorithm for dynamic connectivity is the elegant level-set algorithm of Holm, de Lichtenberg and Thorup (HDT), which achieves $O(\log^2 n)$ amortized time per edge insertion or deletion, and $O(\log n / \log\log n)$ time per query. We design a parallel batch-dynamic connectivity algorithm that is work-efficient with respect to the HDT algorithm for small batch sizes, and is asymptotically faster when the average batch size is sufficiently large. Given a sequence of batched updates, where $\Delta$ is the average batch size of all deletions, our algorithm achieves $O(\log n \log(1 + n / \Delta))$ expected amortized work per edge insertion and deletion and $O(\log^3 n)$ depth w.h.p. Our algorithm answers a batch of $k$ connectivity queries in $O(k \log(1 + n/k))$ expected work and $O(\log n)$ depth w.h.p. To the best of our knowledge, our algorithm is the first parallel batch-dynamic algorithm for connectivity.Comment: This is the full version of the paper appearing in the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 201

Low order harmonic cancellation in a grid connected multiple inverter system via current control parameter randomization

In grid connected multiple inverter systems, it is normal to synchronize the output current of each inverter to the common network voltage. Any current controller deficiencies, which result in low order harmonics, are also synchronized to the common network voltage. As a result the harmonics produced by individual converters show a high degree of correlation and tend to be additive. Each controller can be tuned to achieve a different harmonic profile so that harmonic cancellation can take place in the overall system, thus reducing the net current total harmonic distortion level. However, inter-inverter communication is required. This paper presents experimental results demonstrating an alternative approach, which is to arrange for the tuning within each inverter to be adjusted automatically with a random component. This results in a harmonic output spectrum that varies with time, but is uncorrelated with the harmonic spectrum of any other inverter in the system. The net harmonics from all the inverters undergo a degree of cancellation and the overall system yields a net improvement in power quality