Analytical controllability of deterministic scale-free networks and Cayley trees

According to the exact controllability theory, the controllability is investigated analytically for two typical types of self-similar bipartite networks, i.e., the classic deterministic scale-free networks and Cayley trees. Due to their self-similarity, the analytical results of the exact controllability are obtained, and the minimum sets of driver nodes (drivers) are also identified by elementary transformations on adjacency matrices. For these two types of undirected networks, no matter their links are unweighted or (nonzero) weighted, the controllability of networks and the configuration of drivers remain the same, showing a robustness to the link weights. These results have implications for the control of real networked systems with self-similarity.Comment: 7 pages, 4 figures, 1 table; revised manuscript; added discussion about the general case of DSFN; added 3 reference

Design of Compact Planar Diplexer Based on Novel Spiral-Based Resonators

A miniaturized planar diplexer utilizing the novel spiral-based resonators is proposed. The given cell which is initially proposed in this article is composed of two separated rectangular spirals which are asymmetrical to each other and thus, it is called as ‘asymmetrical separated spirals resonator’ (ASSR). ASSR has more superior transmission property than the previous prototype and extremely compact dimension is also achieved. It is demonstrated that ASSR can exhibit bandpass performance with high frequency selectivity and good transmission property within the relatively low frequency band. Based on the given characteristic, one planar diplexer composed of T-junction and two ASSRs is synthesized and the fabricated prototype with compact dimension is achieved, thanks to ASSRs explored. Simultaneously, the transversal dimension of each channel is extremely compact because ASSRs are completely embedded in the feed lines. Both the simulated and measured results indicate that satisfactory impedance matching and high isolation between two channels are achieved. Furthermore, the proposed diplexer is uniplanar and no defected ground structure is introduced

Proving Expected Sensitivity of Probabilistic Programs with Randomized Variable-Dependent Termination Time

The notion of program sensitivity (aka Lipschitz continuity) specifies that changes in the program input result in proportional changes to the program output. For probabilistic programs the notion is naturally extended to expected sensitivity. A previous approach develops a relational program logic framework for proving expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded. In this work, we consider probabilistic while loops where the number of iterations is not fixed, but randomized and depends on the initial input values. We present a sound approach for proving expected sensitivity of such programs. Our sound approach is martingale-based and can be automated through existing martingale-synthesis algorithms. Furthermore, our approach is compositional for sequential composition of while loops under a mild side condition. We demonstrate the effectiveness of our approach on several classical examples from Gambler's Ruin, stochastic hybrid systems and stochastic gradient descent. We also present experimental results showing that our automated approach can handle various probabilistic programs in the literature