Relevance of soft modes for order parameter fluctuations in the Two-Dimensional XY model

We analyse the spin wave approximation for the 2D-XY model, directly in reciprocal space. In this limit the model is diagonal and the normal modes are statistically independent. Despite this simplicity non-trivial critical properties are observed and exploited. We confirm that the observed asymmetry for the probability density function for order parameter fluctuations comes from the divergence of the mode amplitudes across the Brillouin zone. We show that the asymmetry is a many body effect despite the importance played by the zone centre. The precise form of the function is dependent on the details of the Gibbs measure, giving weight to the idea that an effective Gibbs measure should exist in non-equilibrium systems, if a similar distribution is observed.Comment: 12 pages, 9 figure

Universal Fluctuations of the Danube Water Level: a Link with Turbulence, Criticality and Company Growth

A global quantity, regardless of its precise nature, will often fluctuate according to a Gaussian limit distribution. However, in highly correlated systems, other limit distributions are possible. We have previously calculated one such distribution and have argued that this function should apply specifically, and in many instances, to global quantities that define a steady state. Here we demonstrate, for the first time, the relevance of this prediction to natural phenomena. The river level fluctuations of the Danube are observed to obey our prediction, which immediately establishes a generic statistical connection between turbulence, criticality and company growth statistics.Comment: 5 pages, 1 figur

Generalised extreme value statistics and sum of correlated variables

We show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and (generally) correlated random variables with a sum distributed according to one of the three (k-dependent) asymptotic distributions of extreme value statistics, namely the Gumbel, Frechet and Weibull distributions. These classes, as well as the limit distributions, are naturally extended to real values of k, thus providing a clear interpretation to the onset of Gumbel distributions with non-integer index k in the statistics of global observables. This is one of the very few known generalisations of the central limit theorem to non-independent random variables. Finally, in the context of a simple physical model, we relate the index k to the ratio of the correlation length to the system size, which remains finite in strongly correlated systems.Comment: To appear in J.Phys.

Temperature dependent fluctuations in the two-dimensional XY model

We present a detailed investigation of the probability density function (PDF) of order parameter fluctuations in the finite two-dimensional XY (2dXY) model. In the low temperature critical phase of this model, the PDF approaches a universal non-Gaussian limit distribution in the limit T-->0. Our analysis resolves the question of temperature dependence of the PDF in this regime, for which conflicting results have been reported. We show analytically that a weak temperature dependence results from the inclusion of multiple loop graphs in a previously-derived graphical expansion. This is confirmed by numerical simulations on two controlled approximations to the 2dXY model: the Harmonic and ``Harmonic XY'' models. The Harmonic model has no Kosterlitz-Thouless-Berezinskii (KTB) transition and the PDF becomes progressively less skewed with increasing temperature until it closely approximates a Gaussian function above T ~ 4\pi. Near to that temperature we find some evidence of a phase transition, although our observations appear to exclude a thermodynamic singularity.Comment: 15 pages, 5 figures and 1 tabl

Statistics of extremal intensities for Gaussian interfaces

The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not coincide with the distribution of the integrated power spectrum (i.e. roughness of the surface), nor does it obey any of the known extreme statistics limit distributions. The Fisher-Tippett-Gumbel limit distribution is, however, recovered in three cases: (i) in the non-dispersive (white noise) limit, (ii) for high dimensions, and (iii) when only short-wavelength modes are kept. In the last two cases the limit distribution emerges in novel scenarios.Comment: 15 pages, including 7 ps figure

Numerical convergence of the block-maxima approach to the Generalized Extreme Value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. [2006] have found analytical results.Comment: 34 pages, 7 figures; Journal of Statistical Physics 201

Ancient DNA of guinea pigs (Cavia spp.) indicates a probable new center of domestication and pathways of global distribution

Guinea pigs (Cavia spp.) have a long association with humans. From as early as 10,000 years ago they were a wild food source. Later, domesticated Cavia porcellus were dispersed well beyond their native range through pre-Columbian exchange networks and, more recently, widely across the globe. Here we present 46 complete mitogenomes of archaeological guinea pigs from sites in Peru, Bolivia, Colombia, the Caribbean, Belgium and the United States to elucidate their evolutionary history, origins and paths of dispersal. Our results indicate an independent centre of domestication of Cavia in the eastern Colombian Highlands. We identify a Peruvian origin for the initial introduction of domesticated guinea pigs (Cavia porcellus) beyond South America into the Caribbean. We also demonstrate that Peru was the probable source of the earliest known guinea pigs transported, as part of the exotic pet trade, to both Europe and the southeastern United States. Finally, we identify a modern reintroduction of guinea pigs to Puerto Rico, where local inhabitants use them for food. This research demonstrates that the natural and cultural history of guinea pigs is more complex than previously known and has implications for other studies regarding regional to global-scale studies of mammal domestication, translocation, and distribution.Fil: Lord, E.. Stockholms Universitet; Suecia. University of Otago; Nueva ZelandaFil: Collins, C.. University of Otago; Nueva ZelandaFil: deFrance, S.. University of Florida; Estados UnidosFil: LeFebvre, M. J.. University of Florida; Estados UnidosFil: Pigière, F.. Universidad de Dublin; IrlandaFil: Eeckhout, P.. Université Libre de Bruxelles; BélgicaFil: Erauw, C.. Université Libre de Bruxelles; BélgicaFil: Fitzpatrick, S. M.. State University of Oregon; Estados UnidosFil: Healy, P. F.. Trent University; CanadáFil: Martínez Polanco, M. F.. Muséum National d'Histoire Naturelle; Francia. Universitat Rovira I Virgili; España. Institut Català de Paleoecologia Humana i Evolució Social; EspañaFil: Garcia, J. L.. Stetson University; Estados UnidosFil: Ramos Roca, E.. Universidad de los Andes. Facultad de Ciencias Sociales. Departamento de Antropología; ColombiaFil: Delgado Burbano, Miguel Eduardo. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo. Área Antropológica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. School of Life Sciences and Human Phenome Institute Fudan University; ChinaFil: Sánchez Urriago, A.. Instituto Colombiano de Antropología e Historia; ColombiaFil: Peña Léon, G. A.. Universidad Nacional de Colombia; ColombiaFil: Toyne, J. M.. University of Florida; Estados UnidosFil: Dahlstedt, A.. Arizona State University; Estados UnidosFil: Moore, K. M.. State University of Pennsylvania; Estados UnidosFil: Laguer Diaz, C.. University of Florida; Estados UnidosFil: Zori, C.. Baylor University; Estados UnidosFil: Matisoo-Smith, E.. University of Otago; Nueva Zeland

Identifying Suitable Representation Techniques for the Prioritization of Requirements and Their Interdependencies for Multiple Software Product Lines

Software requirements typically do not exist independently of each other, rather most requirements have some type of dependency on another requirement [4]. For companies developing software products, which depend on each other, in so-called multiple software product lines (SPLs), systematic requirements management, including consideration for prioritization and inter‐ dependencies, is a time-consuming and convoluted task. Representation techniques for complex requirements can convey critical requirements interdependency information to make prioritization of requirements quicker and more accurate [1]. Based on reviewing the foremost literature, this paper identifies the representation techniques for requirements management which are most suitable for multiple software product lines (SPLs