Spectral analysis and an area-preserving extension of a piecewise linear intermittent map

We investigate spectral properties of a 1-dimensional piecewise linear intermittent map, which has not only a marginal fixed point but also a singular structure suppressing injections of the orbits into neighborhoods of the marginal fixed point. We explicitly derive generalized eigenvalues and eigenfunctions of the Frobenius--Perron operator of the map for classes of observables and piecewise constant initial densities, and it is found that the Frobenius--Perron operator has two simple real eigenvalues 1 and $\lambda_d \in (-1,0)$, and a continuous spectrum on the real line $[0,1]$. From these spectral properties, we also found that this system exhibits power law decay of correlations. This analytical result is found to be in a good agreement with numerical simulations. Moreover, the system can be extended to an area-preserving invertible map defined on the unit square. This extended system is similar to the baker transformation, but does not satisfy hyperbolicity. A relation between this area-preserving map and a billiard system is also discussed.Comment: 12 pages, 3 figure

Quantum walk approach to search on fractal structures

We study continuous-time quantum walks mimicking the quantum search based on Grover's procedure. This allows us to consider structures, that is, databases, with arbitrary topological arrangements of their entries. We show that the topological structure of the database plays a crucial role by analyzing, both analytically and numerically, the transition from the ground to the first excited state of the Hamiltonian associated with different (fractal) structures. Additionally, we use the probability of successfully finding a specific target as another indicator of the importance of the topological structure.Comment: 15 pages, 14 figure

Understanding Anomalous Transport in Intermittent Maps: From Continuous Time Random Walks to Fractals

We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a dynamical phase transition from normal to anomalous diffusion marked by strong suppression of diffusion. Similarly, the probability density of moving particles is governed by a time-fractional diffusion equation on coarse scales while exhibiting a specific fine structure. Approximations beyond stochastic theory are derived from a generalized Taylor-Green-Kubo formula.Comment: 4 pages, 3 eps figure

The relationship between quality of life (EORTC QLQ-C30) and survival in patients with gastro-oesopohageal cancer

It remains unclear whether any aspect of quality of life has a role in predicting survival in an unselected cohort of patients with gastro-oesophageal cancer. Therefore the aim of the present study was to examine the relationship between quality of life (EORTC QLQ-C30), clinico-pathological characteristics and survival in patients with gastro-oesophageal cancer. Patients presenting with gastric or oesophageal cancer, staged using the UICC tumour node metastasis (TNM) classification and who received either potentially curative surgery or palliative treatment between November 1997 and December 2002 (n=152) participated in a quality of life study, using the EORTC QLQ-C30 core questionnaire. On univariate analysis, age (P < 0.01), tumour length (P < 0.0001), TNM stage (P<0.0001), weight loss (P<0.0001), dysphagia score (P<0.001), performance status (P<0.1) and treatment (P<0.0001) were significantly associated with cancer-specific survival. EORTC QLQ-C30, physical functioning (P<0.0001), role functioning (P<0.001), cognitive functioning (P<0.01), social functioning (P<0.0001), global quality of life (P<0.0001), fatigue (P<0.0001), nausea/vomiting (P<0.01), pain (P<0.001), dyspnoea (P<0.0001), appetite loss (P<0.0001) and constipation (P<0.05) were also significantly associated with cancer-specific survival. On multivariate survival analysis, tumour stage (P<0.0001), treatment (P<0.001) and appetite loss (P<0.0001) were significant independent predictors of cancer-specific survival. The present study highlights the importance of quality of life (EORTC QLQ-C30) measures, in particular appetite loss, as a prognostic factor in these patients

Pointwise convergence of Birkhoff averages for global observables

It is well-known that a strict analogue of the Birkhoff Ergodic Theorem in infinite ergodic theory is trivial; it states that for any infinite-measure-preserving ergodic system the Birkhoff average of every integrable function is almost everywhere zero. Nor does a different rescaling of the Birkhoff sum that leads to a non-degenerate pointwise limit exist. In this paper we give a version of Birkhoff's theorem for conservative, ergodic, infinite-measure-preserving dynamical systems where instead of integrable functions we use certain elements of $L^\infty$, which we generically call global observables. Our main theorem applies to general systems but requires an hypothesis of "approximate partial averaging" on the observables. The idea behind the result, however, applies to more general situations, as we show with an example. Finally, by means of counterexamples and numerical simulations, we discuss the question of finding the optimal class of observables for which a Birkhoff theorem holds for infinite-measure-preserving systems.Comment: Final version. 33 pages, 10 figure

Classical and quantum partition bound and detector inefficiency

We study randomized and quantum efficiency lower bounds in communication complexity. These arise from the study of zero-communication protocols in which players are allowed to abort. Our scenario is inspired by the physics setup of Bell experiments, where two players share a predefined entangled state but are not allowed to communicate. Each is given a measurement as input, which they perform on their share of the system. The outcomes of the measurements should follow a distribution predicted by quantum mechanics; however, in practice, the detectors may fail to produce an output in some of the runs. The efficiency of the experiment is the probability that the experiment succeeds (neither of the detectors fails). When the players share a quantum state, this gives rise to a new bound on quantum communication complexity (eff*) that subsumes the factorization norm. When players share randomness instead of a quantum state, the efficiency bound (eff), coincides with the partition bound of Jain and Klauck. This is one of the strongest lower bounds known for randomized communication complexity, which subsumes all the known combinatorial and algebraic methods including the rectangle (corruption) bound, the factorization norm, and discrepancy. The lower bound is formulated as a convex optimization problem. In practice, the dual form is more feasible to use, and we show that it amounts to constructing an explicit Bell inequality (for eff) or Tsirelson inequality (for eff*). We give an example of a quantum distribution where the violation can be exponentially bigger than the previously studied class of normalized Bell inequalities. For one-way communication, we show that the quantum one-way partition bound is tight for classical communication with shared entanglement up to arbitrarily small error.Comment: 21 pages, extended versio

Peculiar Velocities of 3000 Spiral Galaxies from the 2MFGC Catalog

The 2MFGC catalog we have used contains 18020 galaxies selected from the extended objects in the 2MASS infrared sky survey as having apparent ratios of the axes b/a<0.3. Most of them are spiral galaxies of later morphological types whose disks are seen almost edge-on. The individual distances to the 2724 2MFGC galaxies with known rotation velocities and radial velocities are determined using a multiparameter infrared Tully-Fisher relation. A list of the distances and peculiar velocities of these galaxies is presented. The collective motion of the 2MFGC galaxies relative to the cosmic microwave background is characterized by a velocity V = 199 +- 37 km/s in the direction l = 304o +- 11o, b = -8o +- 8o. Our list is currently the most representative and uniform sample for analyzing non-Hubble motions of galaxies on a scale of ~100 Mpc.Comment: 12 pages, 5 figures, 1 table (here we present the beginning of the table as an illustration). Astrophysics, Vol. 49, No. 4, 2006. Original article submitted June 13, 2006. Translated from Astrofizika, Vol. 49, No. 4, pp. 527-540 (November 2006

Approximating Fractional Time Quantum Evolution

An algorithm is presented for approximating arbitrary powers of a black box unitary operation, $\mathcal{U}^t$, where $t$ is a real number, and $\mathcal{U}$ is a black box implementing an unknown unitary. The complexity of this algorithm is calculated in terms of the number of calls to the black box, the errors in the approximation, and a certain `gap' parameter. For general $\mathcal{U}$ and large $t$, one should apply $\mathcal{U}$ a total of $\lfloor t \rfloor$ times followed by our procedure for approximating the fractional power $\mathcal{U}^{t-\lfloor t \rfloor}$. An example is also given where for large integers $t$ this method is more efficient than direct application of $t$ copies of $\mathcal{U}$. Further applications and related algorithms are also discussed.Comment: 13 pages, 2 figure

A near-infrared study of AGB and red giant stars in the Leo I dSph galaxy

A near-infrared imaging study of the evolved stellar populations in the dwarf spheroidal galaxy Leo I is presented. Based on JHK observations obtained with the WFCAM wide-field array at the UKIRT telescope, we build a near-infrared photometric catalogue of red giant branch (RGB) and asymptotic giant branch (AGB) stars in Leo I over a 13.5 arcmin square area. The V-K colours of RGB stars, obtained by combining the new data with existing optical observations, allow us to derive a distribution of global metallicity [M/H] with average [M/H] = -1.51 (uncorrected) or [M/H] = -1.24 +/- 0.05 (int) +/- 0.15 (syst) after correction for the mean age of Leo I stars. This is consistent with the results from spectroscopy once stellar ages are taken into account. Using a near-infrared two-colour diagram, we discriminate between carbon- and oxygen-rich AGB stars and obtain a clean separation from Milky Way foreground stars. We reveal a concentration of C-type AGB stars relative to the red giant stars in the inner region of the galaxy, which implies a radial gradient in the intermediate-age (1-3 Gyr) stellar populations. The numbers and luminosities of the observed carbon- and oxygen-rich AGB stars are compared with those predicted by evolutionary models including the thermally-pulsing AGB phase, to provide new constraints to the models for low-metallicity stars. We find an excess in the predicted number of C stars fainter than the RGB tip, associated to a paucity of brighter ones. The number of O-rich AGB stars is roughly consistent with the models, yet their predicted luminosity function is extended to brighter luminosity. It appears likely that the adopted evolutionary models overestimate the C star lifetime and underestimate their K-band luminosity.Comment: MNRAS, accepte

Dark Matter and the CACTUS Gamma-Ray Excess from Draco

The CACTUS atmospheric Cherenkov telescope collaboration recently reported a gamma-ray excess from the Draco dwarf spheroidal galaxy. Draco features a very low gas content and a large mass-to-light ratio, suggesting as a possible explanation annihilation of weakly interacting massive particles (WIMPs) in the Draco dark-matter halo. We show that with improved angular resolution, future measurements can determine whether the halo is cored or cuspy, as well as its scale radius. We find the relevant WIMP masses and annihilation cross sections and show that supersymmetric models can account for the required gamma-ray flux. The annihilation cross section range is found to be not compatible with a standard thermal relic dark-matter production. We compute for these supersymmetric models the resulting Draco gamma-ray flux in the GLAST energy range and the rates for direct neutralino detection and for the flux of neutrinos from neutralino annihilation in the Sun. We also discuss the possibility that the bulk of the signal detected by CACTUS comes from direct WIMP annihilation to two photons and point out that a decaying-dark-matter scenario for Draco is not compatible with the gamma-ray flux from the Galactic center and in the diffuse gamma-ray background.Comment: 24 pages, 10 figures; version accepted for publication in JCA