Re-parameterization Invariance in Fractional Flux Periodicity

We analyze a common feature of a nontrivial fractional flux periodicity in two-dimensional systems. We demonstrate that an addition of fractional flux can be absorbed into re-parameterization of quantum numbers. For an exact fractional periodicity, all the electronic states undergo the re-parameterization, whereas for an approximate periodicity valid in a large system, only the states near the Fermi level are involved in the re-parameterization.Comment: 4 pages, 1 figure, minor changes, final version to appear in J. Phys. Soc. Jp

On Energy Efficient Inter-Frequency Small Cell Discovery in Heterogeneous Networks

In this paper, we investigate the optimal inter-frequency small cell discovery (ISCD) periodicity for small cells deployed on carrier frequency other than that of the serving macro cell. We consider that the small cells and user terminals (UTs) positions are modelled according to a homogeneous Poisson Point Process (PPP). We utilize polynomial curve fitting to approximate the percentage of time the typical UT missed small cell offloading opportunity, for a fixed small cell density and fixed UT speed. We then derive analytically, the optimal ISCD periodicity that minimizes the average UT energy consumption (EC). Furthermore, we also derive the optimal ISCD periodicity that maximizes the average energy efficiency (EE), i.e. bit-per-joule capacity. Results show that the EC optimal ISCD periodicity always exceeds the EE optimal ISCD periodicity, with the exception of when the average ergodic rates in both tiers are equal, in which the optimal ISCD periodicity in both cases also becomes equal

Fractional Flux Periodicity in Doped Carbon Nanotubes

An anomalous magnetic flux periodicity of the ground state is predicted in two-dimensional cylindrical surface composed of square and honeycomb lattice. The ground state and persistent currents exhibit an approximate fractional period of the flux quantum for a specific Fermi energy. The period depends on the aspect ratio of the cylinder and on the lattice structure around the axis. We discuss possibility of this nontrivial periodicity in a heavily doped armchair carbon nanotube.Comment: 5 pages, 4 figure

Wave packet revivals and the energy eigenvalue spectrum of the quantum pendulum

The rigid pendulum, both as a classical and as a quantum problem, is an interesting system as it has the exactly soluble harmonic oscillator and the rigid rotor systems as limiting cases in the low- and high-energy limits respectively. The energy variation of the classical periodicity ($\tau$) is also dramatic, having the special limiting case of $\tau \to \infty$ at the 'top' of the classical motion (i.e. the separatrix.) We study the time-dependence of the quantum pendulum problem, focusing on the behavior of both the (approximate) classical periodicity and especially the quantum revival and superrevival times, as encoded in the energy eigenvalue spectrum of the system. We provide approximate expressions for the energy eigenvalues in both the small and large quantum number limits, up to 4th order in perturbation theory, comparing these to existing handbook expansions for the characteristic values of the related Mathieu equation, obtained by other methods. We then use these approximations to probe the classical periodicity, as well as to extract information on the quantum revival and superrevival times. We find that while both the classical and quantum periodicities increase monotonically as one approaches the 'top' in energy, from either above or below, the revival times decrease from their low- and high-energy values until very near the separatrix where they increase to a large, but finite value.Comment: 27 pages, 8 embedded .eps figures; to appear, Annals of Physic

Convergence Rates and H\"older Estimates in Almost-Periodic Homogenization of Elliptic Systems

For a family of second-order elliptic systems in divergence form with rapidly oscillating almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the coefficients. The results are used to investigate the problem of convergence rates. We also establish uniform H\"older estimates for the Dirichlet problem in a bounded $C^{1, \alpha}$ domain.Comment: 41 pages; minor revision of the previous versio

Approximate periodicity in strings

In many application areas (for instance, DNA sequence analysis) it becomes important to compute various kinds of “approximate period” of a given string y. Here we discuss three such approximate periods and the algorithms which compute them: an Abelian generator, a cover, and a seed. Let u be a substring of y. Then u is an Abelian generator of y iff y is a concatenation of substrings which are permutations of u: u is a cover of y iff every letter of y is contained in an occurrence of u in y and u is a seed of y iff y is a substring of a string y with cover u. Observe that, according to these definitions, y is an Abelian generator, a cover, and a seed of itself

Improved Periodicity Mining in Time Series Databases

Time series data represents information about real world phenomena and periodicity mining explores the interesting periodic behavior that is inherent in the data. Periodicity mining has numerous applications such as in weather forecasting, stock market prediction and analysis, pattern recognition, etc. Recently, the suffix tree, a powerful data structure that efficiently solves many strings related problems has been used to gather information about repeated substrings in the text and then perform periodicity mining. However, periodicity mining deals with large amounts of data which makes it difficult to perform mining in main memory due to the space constraints of the suffix tree. Thus, we first propose the use of the Compressed Suffix Tree (CST) for space efficient periodicity mining in very large datasets. Given the time-space trade-off that comes with any practical usage of the CST, we provide a comprehensive empirical analysis on the practical usage of CSTs and traditional suffix trees for periodicity mining.;Noise is an inherent part of practical time series data, and it is important to mine periods in spite of the noise. This leads to the problem of approximate periodicity mining. Existing algorithms have dealt with the noise introduced between the occurrences of the periodic pattern, but not the noise introduced in the structure of the pattern itself. We present a taxonomy for approximate periodicity and then propose an algorithm that performs periodicity mining in the presence of noise introduced simultaneously in both the structure of the pattern and between the periodic occurrences of the pattern

Approximate Quantum Fourier Transform and Decoherence

We discuss the advantages of using the approximate quantum Fourier transform (AQFT) in algorithms which involve periodicity estimations. We analyse quantum networks performing AQFT in the presence of decoherence and show that extensive approximations can be made before the accuracy of AQFT (as compared with regular quantum Fourier transform) is compromised. We show that for some computations an approximation may imply a better performance.Comment: 14 pages, 10 fig. (8 *.eps files). More information on http://eve.physics.ox.ac.uk/QChome.html http://www.physics.helsinki.fi/~kasuomin http://www.physics.helsinki.fi/~kira/group.htm