Fully dynamic data structure for LCE queries in compressed space

A Longest Common Extension (LCE) query on a text $T$ of length $N$ asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding $\mathcal{G}$ of size $w = O(\min(z \log N \log^* M, N))$ [Mehlhorn et al., Algorithmica 17(2):183-198, 1997] of $T$, which can be seen as a compressed representation of $T$, has a capability to support LCE queries in $O(\log N + \log \ell \log^* M)$ time, where $\ell$ is the answer to the query, $z$ is the size of the Lempel-Ziv77 (LZ77) factorization of $T$, and $M \geq 4N$ is an integer that can be handled in constant time under word RAM model. In compressed space, this is the fastest deterministic LCE data structure in many cases. Moreover, $\mathcal{G}$ can be enhanced to support efficient update operations: After processing $\mathcal{G}$ in $O(w f_{\mathcal{A}})$ time, we can insert/delete any (sub)string of length $y$ into/from an arbitrary position of $T$ in $O((y+ \log N\log^* M) f_{\mathcal{A}})$ time, where $f_{\mathcal{A}} = O(\min \{ \frac{\log\log M \log\log w}{\log\log\log M}, \sqrt{\frac{\log w}{\log\log w}} \})$. This yields the first fully dynamic LCE data structure. We also present efficient construction algorithms from various types of inputs: We can construct $\mathcal{G}$ in $O(N f_{\mathcal{A}})$ time from uncompressed string $T$; in $O(n \log\log n \log N \log^* M)$ time from grammar-compressed string $T$ represented by a straight-line program of size $n$; and in $O(z f_{\mathcal{A}} \log N \log^* M)$ time from LZ77-compressed string $T$ with $z$ factors. On top of the above contributions, we show several applications of our data structures which improve previous best known results on grammar-compressed string processing.Comment: arXiv admin note: text overlap with arXiv:1504.0695

Effect of an InP/In0.53_{0.53}Ga0.47_{0.47}As Interface on Spin-orbit Interaction in In0.52_{0.52}Al0.48_{0.48}As/In0.53_{0.53}Ga0.47_{0.47}As Heterostructures

We report the effect of the insertion of an InP/In$_{0.53}$Ga$_{47}$As Interface on Rashba spin-orbit interaction in In$_{0.52}$Al$_{0.48}$As/In$_{0.53}$Ga$_{0.47}$As quantum wells. A small spin split-off energy in InP produces a very intriguing band lineup in the valence bands in this system. With or without this InP layer above the In$_{0.53}$Ga$_{47}$As well, the overall values of the spin-orbit coupling constant $\alpha$ turned out to be enhanced or diminished for samples with the front- or back-doping position, respectively. These experimental results, using weak antilocalization analysis, are compared with the results of the $\mathbf{k\cdot p}$ theory. The actual conditions of the interfaces and materials should account for the quantitative difference in magnitude between the measurements and calculations.Comment: Submitted for publication; v2 to adjust Eq.6; v3 to correct the figure file name; v4, a revised version accepted for publication in Phys. Rev.

An alternative gauged U(1)RU(1)_R symmetric model in light of the CDF II WW boson mass anomaly

We consider an explanation of CDF II W bosom mass anomaly by $Z-Z'$ mixing with $U(1)_R$ gauge symmetry under which right-handed fermions are charged. It is found that $U(1)_R$ is preferred to be leptophobic to accommodate the anomaly while avoiding other experimental constraints. In such a case we require extra charged leptons to cancel quantum anomalies and the SM charged leptons get masses via interactions with the extra ones. These interactions also induce muon $g-2$ and lepton flavor violations. We discuss muon $g-2$, possible flavor constraints, neutrino mass generation via inverse seesaw mechanism, and collider physics regarding $Z'$ production for parameter space explaining the W boson mass anomaly.Comment: 22 pages, 3 figures, 2 tables; version accepted for publication in Physical Review

Spin-orbit induced interference in polygon-structures

We investigate the spin-orbit induced spin-interference pattern of ballistic electrons travelling along any regular polygon. It is found that the spin-interference depends strongly on the Rashba and Dresselhaus spin-orbit constants as well as on the sidelength and alignment of the polygon. We derive the analytical formulae for the limiting cases of either zero Dresselhaus or zero Rashba spin-orbit coupling, including the result obtained for a circle. We calculate the nonzero Dresselhaus and Rashba case numerically for the square, triangle, hexagon, and circle and discuss the observability of the spin-interference which can potentially be used to measure the Rashba and Dresselhaus coefficients.Comment: 17 pages, 4 figure

Neutrinophilic DM annihilation in a model with U(1)Lμ−Lτ×U(1)HU(1)_{L_\mu-L_\tau} \times U(1)_{H} gauge symmetry

We propose a model with two different extra $U(1)$ gauge symmetries; muon minus tauon symmetry $U(1)_{{L_\mu}-L_{\tau}}$ and hidden symmetry $U(1)_H$. Then, we explain muon anomalous magnetic moment, semi-leptonic decays $b\to s\ell\bar\ell$, and dark matter. In particular, we find an intriguing dark matter candidate to be verified by Hyper-Kamiokande and JUNO in the future that request neutrinophilic DM with rather light dark matter mass$\sim{\cal O}(10)$ MeV.Comment: 23 pages, 6 figures, 2 table