The oscillatory distribution of distances in random tries

We investigate \Delta_n, the distance between randomly selected pairs of nodes among n keys in a random trie, which is a kind of digital tree. Analytical techniques, such as the Mellin transform and an excursion between poissonization and depoissonization, capture small fluctuations in the mean and variance of these random distances. The mean increases logarithmically in the number of keys, but curiously enough the variance remains O(1), as n\to\infty. It is demonstrated that the centered random variable \Delta_n^*=\Delta_n-\lfloor2\log_2n\rfloor does not have a limit distribution, but rather oscillates between two distributions.Comment: Published at http://dx.doi.org/10.1214/105051605000000106 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Lasing in metamaterial nanostructures

A self-consistent computational scheme is presented for one dimensional (1D) and two dimensional (2D) metamaterial systems with gain incorporated into the nanostructures. The gain is described by a generic four-level system. The loss compensation and the lasing behavior of the metamaterial system with gain are studied. A critical pumping rate exists for compensating the losses of the metamaterial. There exists a wide range of input signals where the composite system behaves linearly. Nonlinearities arise for stronger signals due to gain depletion. The retrieved effective parameters are presented for one layer of gain embedded in two layers of Lorentz dielectric rods and split ring resonators with two different gain inclusions: (1) gain is embedded in the gaps only and (2) gain is surrounding the SRR. When the pumping rate increases, there is a critical pumping rate that the metamaterial system starts lasing.Comment: 18 pages, 19 figures, submitted to Journal of Optics A: Pure and Applied Optic

The Swap Matching Problem Revisited

In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using the model, we devise two efficient algorithms to solve the swap matching problem. The resulting algorithms are adaptations of the classic shift-and algorithm. For patterns having length similar to the word-size of the target machine, both the algorithms run in linear time considering a fixed alphabet.Comment: 23 pages, 3 Figures and 17 Table

Nonplanar Chiral Metamaterials with Negative Index

We demonstrate experimentally and numerically that nonplanar chiral metamaterials give giant optical activity, circular dichroism, and negative refractive index. The transmission, reflection, and the retrieval results of the experiments agree pretty well with the simulations. This is an important step toward the design and fabrication of three-dimensional isotropic chiral metamaterials.Comment: 3 pages 4 figure

Optical anisotropic metamaterials: Negative refraction and focusing

We design three-dimensional (3D) metallic nanowire media with different structures and numerically demonstrate that they can be homogeneous effective indefinite anisotropic media by showing that their dispersion relations are hyperbolic. For a finite slab, a nice fitting procedure is exploited to obtain the dispersion relations from which we retrieve the effective permittivities. The pseudo focusing for the real 3D wire medium agrees very well with the homogeneous medium having the effective permittivity tensor of the wire medium. Studies also show that in the long-wavelength limit, the hyperbolic dispersion relation of the 3D wire medium can be valid even for evanescent modes.Comment: 7 pages, 9 figure

Non-Perturbative Gravitational Corrections in a Class of N=2 String Duals

We investigate the non-perturbative equivalence of some heterotic/type II dual pairs with N=2 supersymmetry. The perturbative heterotic scalar manifolds are respectively SU(1, 1)/U(1) x SO(2, 2+NV)/ SO(2) x SO(2+NV) and SO(4, 4+NH)/ SO(4) x SO(4+NH) for moduli in the vector multiplets and hypermultiplets. The models under consideration correspond, on the type II side, to self-mirror Calabi-Yau threefolds with Hodge numbers h(1,1)= NV +3= h(2,1)= NH +3, which are K3 fibrations. We consider three classes of dual pairs, with NV=NH=8, 4 and 2. The models with h(1,1)=7 and 5 provide new constructions, while the h(1,1)=11, already studied in the literature, is reconsidered here. Perturbative R2-like corrections are computed on the heterotic side by using a universal operator whose amplitude has no singularities in the (T,U) space, and can therefore be compared with the type II side result. We point out several properties connecting K3 fibrations and spontaneous breaking of the N=4 supersymmetry to N=2. As a consequence of the reduced S- and T- duality symmetries, the instanton numbers in these three classes are restricted to integers, which are multiples of 2, 2 and 4, for NV=8, 4 and 2, respectively

Dielectric Metamaterials with Toroidal Dipolar Response

Toroidal multipoles are the terms missing in the standard multipole expansion; they are usually overlooked due to their relatively weak coupling to the electromagnetic fields. Here we propose and theoretically study all-dielectric metamaterials of a special class that represent a simple electromagnetic system supporting toroidal dipolar excitations in the THz part of the spectrum. We show that resonant transmission and reflection of such metamaterials is dominated by toroidal dipole scattering, the neglect of which would result in a misunderstanding interpretation of the metamaterials macroscopic response. Due to the unique field configuration of the toroidal mode the proposed metamaterials could serve as a platform for sensing, or enhancement of light absorption and optical nonlinearities

Tempo and intensity of pre-task music modulate neural activity during reactive task performance

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2013 The Authors.Research has shown that not only do young athletes purposively use music to manage their emotional state (Bishop, Karageorghis, & Loizou, 2007), but also that brief periods of music listening may facilitate their subsequent reactive performance (Bishop, Karageorghis, & Kinrade, 2009). We report an fMRI study in which young athletes lay in an MRI scanner and listened to a popular music track immediately prior to performance of a three-choice reaction time task; intensity and tempo were modified such that six excerpts (2 intensities × 3 tempi) were created. Neural activity was measured throughout. Faster tempi and higher intensity collectively yielded activation in structures integral to visual perception (inferior temporal gyrus), allocation of attention (cuneus, inferior parietal lobule, supramarginal gyrus), and motor control (putamen), during reactive performance. The implications for music listening as a pre-competition strategy in sport are discussed

Negative refractive index due to chirality

We demonstrate experimentally and numerically that metamaterials based on bilayer cross wires give giant optical activity, circular dichroism, and negative refractive index. The presented chiral design offers a much simpler geometry and more efficient way to realize negative refractive index at any frequency. We also developed a retrieval procedure for chiral materials which works successfully for circularly polarized waves

The X-ray Properties of the Nearby Star-Forming Galaxy IC 342: The XMM-Newton View

We present the X-ray properties of IC342 using XMM-Newton. Thirty-five sources are detected coincident with the disk of IC342 (more than tripling the number known), of which ~31 are likely to be intrinsic to IC342. This population shows a range of spectral properties and has an X-ray luminosity function slope and infrared luminosity comparable to that of starburst galaxies such as M82 and the Antennae, while its relative lack of extended X-ray emission is similar to the properties of quiescent spirals. We do detect long-term variability between this observation and the 1991 ROSAT and 1993/2000 ASCA observations for five sources. Notably, the second most luminous source IC342 X-2 is is found to be in its the lowest luminosity state observed for X-2 to date, although the slope of the spectrum is intermediate between the previously observed low/hard and high/soft states. IC342 X-1, on the other hand, is found to be in an identical state to that observed in 2000 with ASCA. Assuming X-1 is in an anomalous very high (VH) state, then either (1) X-1 has remained in this state between 2000 and 2002, and is therefore the longest duration VH-state binary ever observed, or (2) it was simply caught in a VH state by chance in both the 2000 ASCA and 2002 XMM-Newton observations. We have also confirmed the ROSAT HRI result that the nucleus of IC342 is made up of both point-like and extended emission. The relative fluxes of the two spectral components suggest that the nucleus is complex, with a soft extended component contributing approximately half of the total luminosity. (Abridged)Comment: AJ in press (December 2003), 9 pages, 7 figures, 2 tables, emulateapj.cls use