Modulo Three Problem With A Cellular Automaton Solution

An important global property of a bit string is the number of ones in it. It has been found that the parity (odd or even) of this number can be found by a sequence of deterministic, translational invariant cellular automata with parallel update in succession for a total of O(N^2) time. In this paper, we discover a way to check if this number is divisible by three using the same kind of cellular automata in O(N^3) time. We also speculate that the method described here could be generalized to check if it is divisible by four and other positive integers.Comment: 10 pages in revtex 4.0, using amsfont

Rate Splitting for MIMO Wireless Networks: A Promising PHY-Layer Strategy for LTE Evolution

MIMO processing plays a central part towards the recent increase in spectral and energy efficiencies of wireless networks. MIMO has grown beyond the original point-to-point channel and nowadays refers to a diverse range of centralized and distributed deployments. The fundamental bottleneck towards enormous spectral and energy efficiency benefits in multiuser MIMO networks lies in a huge demand for accurate channel state information at the transmitter (CSIT). This has become increasingly difficult to satisfy due to the increasing number of antennas and access points in next generation wireless networks relying on dense heterogeneous networks and transmitters equipped with a large number of antennas. CSIT inaccuracy results in a multi-user interference problem that is the primary bottleneck of MIMO wireless networks. Looking backward, the problem has been to strive to apply techniques designed for perfect CSIT to scenarios with imperfect CSIT. In this paper, we depart from this conventional approach and introduce the readers to a promising strategy based on rate-splitting. Rate-splitting relies on the transmission of common and private messages and is shown to provide significant benefits in terms of spectral and energy efficiencies, reliability and CSI feedback overhead reduction over conventional strategies used in LTE-A and exclusively relying on private message transmissions. Open problems, impact on standard specifications and operational challenges are also discussed.Comment: accepted to IEEE Communication Magazine, special issue on LTE Evolutio

Spin transport properties of a quantum dot coupled to ferromagnetic leads with noncollinear magnetizations

A correct general formula for the spin current through an interacting quantum dot coupled to ferromagnetic leads with magnetization at an arbitrary angle $\theta$ is derived within the framework of the Keldysh formalism. Under asymmetric conditions, the spin current component J_{z} may change sign for $0<\theta<\pi$. It is shown that the spin current and spin tunneling magnetoresistance exhibit different angle dependence in the free and Coulomb blockade regimes. In the latter case, the competition of spin precession and the spin-valve effect could lead to an anomaly in the angle dependence of the spin current.Comment: 7 pages, 4 figures; some parts of the text has been revised in this version accepted by J. Phys.: Condens. Matte

Interlayer Exchange Coupling Beyond the Proximity Force Approximation

Ion bombardment has been shown to be capable of enhancing the interlayer exchange coupling in a trilayer system that exhibits giant magnetoresistance. We demonstrate that this phenomenon can be derived from the phase coherence among scattered paths within the two rough interfaces when their topographies are correlated. In the case of mild corrugations, our method reproduces the predictions by the proximity force approximation which does not consider the interference. When the characteristic Fourier conjugate of the tomography becomes large and comparable to the Fermi momentum, interesting new features arise and can only be captured by our more general approach. Among our findings, the scenario of an enhanced interlayer exchange coupling due to the interface roughness is explained, along with how it depends on the sample parameters. An additional channel for the resonant transmission is identified due to extra scattering paths from the roughness.Comment: 9 pages, 7 figures, submitted to PRB (2010

Maximized string order parameters in the valence bond solid states of quantum integer spin chains

We propose a set of maximized string order parameters to describe the hidden topological order in the valence bond solid states of quantum integer spin-S chains. These optimized string order parameters involve spin-twist angles corresponding to $Z_{S+1}$ rotations around $z$ or $x$-axes, suggesting a hidden $Z_{S+1}\times Z_{S+1}$ symmetry. Our results also suggest that a local triplet excitation in the valence bond solid states carries a $Z_{S+1}$ topological charge measured by these maximized string order parameters.Comment: 5 pages, 1 figur

Operando STM study of the interaction of imidazolium-based ionic liquid with graphite

Understanding interactions at the interfaces of carbon with ionic liquids (ILs) is crucially beneficial for the diagnostics and performance improvement of electrochemical devices containing carbon as active materials or conductive additives in electrodes and ILs as solvents or additives in electrolytes. The interfacial interactions of three typical imidazolium-based ILs, 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide (AMImTFSI) ILs having ethyl (C2), butyl (C4) and octyl (C8) chains in their cations, with highly oriented pyrolytic graphite (HOPG) were studied in-situ by electrochemical scanning tunneling microscopy (EC-STM). The etching of HOPG surface and the exfoliation of graphite/graphene flakes as well as cation intercalation were observed at the HOPG/C2MImTFSI interface. The etching also takes place in C4MImTFSI at −1.5 V vs Pt but only at step edges with a much slower rate, whereas C8MIm+ cations adsorbs strongly on the HOPG surface under similar conditions with no observable etching or intercalation. The EC-STM observations can be explained by the increase in van der Waals interaction between the cations and the graphite surface with increasing length of alkyl chains

Effects of force load, muscle fatigue and extremely low frequency magnetic stimulation on EEG signals during side arm lateral raise task

Objective: This study was to quantitatively investigate the effects of force load, muscle fatigue and extremely low frequency (ELF) magnetic stimulation on electroencephalography (EEG) signal features during side arm lateral raise task. Approach: EEG signals were recorded by a BIOSEMI Active Two system with Pin-Type active-electrodes from 18 healthy subjects when they performed the right arm side lateral raise task (90° away from the body) with three different loads (0 kg, 1 kg and 3 kg; their order was randomized among the subjects) on the forearm. The arm maintained the loads until the subject felt exhausted. The first 10 s recording for each load was regarded as non-fatigue status and the last 10 s before the subject was exhausted as fatigue status. The subject was then given a 5 min resting between different loads. Two days later, the same experiment was performed on each subject except that ELF magnetic stimulation was applied to the subject's deltoid muscle during the 5 min resting period. EEG features from C3 and C4 electrodes including the power of alpha, beta and gamma and sample entropy were analyzed and compared between different loads, non-fatigue/fatigue status, and with/without ELF magnetic stimulation. Main results: The key results were associated with the change of the power of alpha band. From both C3-EEG and C4-EEG, with 1 kg and 3 kg force loads, the power of alpha band was significantly smaller than that from 0 kg for both non-fatigue and fatigue periods (all p    0.05 for all the force loads except C4-EEG with ELF simulation). The power of alpha band at fatigue status was significantly increased for both C3-EEG and C4-EEG when compared with the non-fatigue status (p    0.05, except between non-fatigue and fatigue with magnetic stimulation in gamma band of C3-EEG at 1 kg, and in the SampEn at 1 kg and 3 kg force loads from C4-EEG). Significance: Our study comprehensively quantified the effects of force, fatigue and the ELF magnetic stimulation on EEG features with difference forces, fatigue status and ELF magnetic stimulation

String order and hidden topological symmetry in the SO(2n+1) symmetric matrix product states

We have introduced a class of exactly soluble Hamiltonian with either SO(2n+1) or SU(2) symmetry, whose ground states are the SO(2n+1) symmetric matrix product states. The hidden topological order in these states can be fully identified and characterized by a set of nonlocal string order parameters. The Hamiltonian possesses a hidden $(Z_{2}\times Z_{2})^{n}$ topological symmetry. The breaking of this hidden symmetry leads to $4^{n}$ degenerate ground states with disentangled edge states in an open chain system. Such matrix product states can be regarded as cluster states, applicable to measurement-based quantum computation.Comment: 5 pages, 1 figur

On the linear extension complexity of stable set polytopes for perfect graphs

We study the linear extension complexity of stable set polytopes of perfect graphs. We make use of known structural results permitting to decompose perfect graphs into basic perfect graphs by means of two graph operations: 2-join and skew partitions. Exploiting the link between extension complexity and the nonnegative rank of an associated slack matrix, we investigate the behaviour of the extension complexity under these graph operations. We show bounds for the extension complexity of the stable set polytope of a perfect graph G depending linearly on the size of G and involving the depth of a decomposition tree of G in terms of basic perfect graphs