Decentralized pole assignment for interconnected systems

Given a general proper interconnected system, this paper aims to design a LTI decentralized controller to place the modes of the closed-loop system at pre-determined locations. To this end, it is first assumed that the structural graph of the system is strongly connected. Then, it is shown applying generic static local controllers to any number of subsystems will not introduce new decentralized fixed modes (DFM) in the resultant system, although it has fewer inputoutput stations compared to the original system. This means that if there are some subsystems whose control costs are highly dependent on the complexity of the control law, then generic static controllers can be applied to such subsystems, without changing the characteristics of the system in terms of the fixed modes. As a direct application of this result, in the case when the system has no DFMs, one can apply generic static controllers to all but one subsystem, and the resultant system will be controllable and observable through that subsystem. Now, a simple observer-based local controller corresponding to this subsystem can be designed to displace the modes of the entire system arbitrarily. Similar results can also be attained for a system whose structural graph is not strongly connected. It is worth mentioning that similar concepts are deployed in the literature for the special case of strictly proper systems, but as noted in the relevant papers, extension of the results to general proper systems is not trivial. This demonstrates the significance of the present work

Rotating Hayward's regular black hole as particle accelerator

Recently, Ban\~{a}dos, Silk and West (BSW) demonstrated that the extremal Kerr black hole can act as a particle accelerator with arbitrarily high center-of-mass energy ($E_{CM}$) when the collision takes place near the horizon. The rotating Hayward's regular black hole, apart from Mass ($M$) and angular momentum ($a$), has a new parameter $g$ ($g>0$ is a constant) that provides a deviation from the Kerr black hole. We demonstrate that for each $g$, with $M=1$, there exist critical $a_{E}$ and $r_{H}^{E}$, which corresponds to a regular extremal black hole with degenerate horizon, and $a_{E}$ decreases and $r_{H}^{E}$ increases with increase in $g$. While $a<a_{E}$ describe a regular non-extremal black hole with outer and inner horizons. We apply BSW process to the rotating Hayward's regular black hole, for different $g$, and demonstrate numerically that $E_{CM}$ diverges in the vicinity of the horizon for the extremal cases, thereby suggesting that a rotating regular black hole can also act as a particle accelerator and thus in turn may provide a suitable framework for Plank-scale physics. For a non-extremal case, there always exist a finite upper bound of $E_{CM}$, which increases with deviation parameter $g$.Comment: 10 pages, 10 figures, 4 tables, accepted to be published in Journal of High Energy Physic

Dictionary Matching with One Gap

The dictionary matching with gaps problem is to preprocess a dictionary $D$ of $d$ gapped patterns $P_1,\ldots,P_d$ over alphabet $\Sigma$, where each gapped pattern $P_i$ is a sequence of subpatterns separated by bounded sequences of don't cares. Then, given a query text $T$ of length $n$ over alphabet $\Sigma$, the goal is to output all locations in $T$ in which a pattern $P_i\in D$, $1\leq i\leq d$, ends. There is a renewed current interest in the gapped matching problem stemming from cyber security. In this paper we solve the problem where all patterns in the dictionary have one gap with at least $\alpha$ and at most $\beta$ don't cares, where $\alpha$ and $\beta$ are given parameters. Specifically, we show that the dictionary matching with a single gap problem can be solved in either $O(d\log d + |D|)$ time and $O(d\log^{\varepsilon} d + |D|)$ space, and query time $O(n(\beta -\alpha )\log\log d \log ^2 \min \{ d, \log |D| \} + occ)$, where $occ$ is the number of patterns found, or preprocessing time and space: $O(d^2 + |D|)$, and query time $O(n(\beta -\alpha ) + occ)$, where $occ$ is the number of patterns found. As far as we know, this is the best solution for this setting of the problem, where many overlaps may exist in the dictionary.Comment: A preliminary version was published at CPM 201