Damage spreading in the Bak-Sneppen model: Sensitivity to the initial conditions and equilibration dynamics

The short-time and long-time dynamics of the Bak-Sneppen model of biological evolution are investigated using the damage spreading technique. By defining a proper Hamming distance measure, we are able to make it exhibits an initial power-law growth which, for finite size systems, is followed by a decay towards equilibrium. In this sense, the dynamics of self-organized critical states is shown to be similar to the one observed at the usual critical point of continuous phase-transitions and at the onset of chaos of non-linear low-dimensional dynamical maps. The transient, pre-asymptotic and asymptotic exponential relaxation of the Hamming distance between two initially uncorrelated equilibrium configurations is also shown to be fitted within a single mathematical framework. A connection with nonextensive statistical mechanics is exhibited.Comment: 6 pages, 4 figs, revised version, accepted for publication in Int.J.Mod.Phys.C 14 (2003

Diversity and Polarization of Research Performance: Evidence from Hungary

Measuring the intellectual diversity encoded in publication records as a proxy to the degree of interdisciplinarity has recently received considerable attention in the science mapping community. The present paper draws upon the use of the Stirling index as a diversity measure applied to a network model (customized science map) of research profiles, proposed by several authors. A modified version of the index is used and compared with the previous versions on a sample data set in order to rank top Hungarian research organizations (HROs) according to their research performance diversity. Results, unexpected in several respects, show that the modified index is a candidate for measuring the degree of polarization of a research profile. The study also points towards a possible typology of publication portfolios that instantiate different types of diversity

Experimentally feasible measures of distance between quantum operations

We present two measures of distance between quantum processes based on the superfidelity, introduced recently to provide an upper bound for quantum fidelity. We show that the introduced measures partially fulfill the requirements for distance measure between quantum processes. We also argue that they can be especially useful as diagnostic measures to get preliminary knowledge about imperfections in an experimental setup. In particular we provide quantum circuit which can be used to measure the superfidelity between quantum processes. As the behavior of the superfidelity between quantum processes is crucial for the properties of the introduced measures, we study its behavior for several families of quantum channels. We calculate superfidelity between arbitrary one-qubit channels using affine parametrization and superfidelity between generalized Pauli channels in arbitrary dimensions. Statistical behavior of the proposed quantities for the ensembles of quantum operations in low dimensions indicates that the proposed measures can be indeed used to distinguish quantum processes.Comment: 9 pages, 4 figure

Spectral Generalized Multi-Dimensional Scaling

Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances between each pair of points in the set. Distances in the target space can be computed analytically in this setting. Generalized MDS is an extension that allows mapping one metric space into another, that is, multidimensional scaling into target spaces in which distances are evaluated numerically rather than analytically. Here, we propose an efficient approach for computing such mappings between surfaces based on their natural spectral decomposition, where the surfaces are treated as sampled metric-spaces. The resulting spectral-GMDS procedure enables efficient embedding by implicitly incorporating smoothness of the mapping into the problem, thereby substantially reducing the complexity involved in its solution while practically overcoming its non-convex nature. The method is compared to existing techniques that compute dense correspondence between shapes. Numerical experiments of the proposed method demonstrate its efficiency and accuracy compared to state-of-the-art approaches

Metrics for generalized persistence modules

We consider the question of defining interleaving metrics on generalized persistence modules over arbitrary preordered sets. Our constructions are functorial, which implies a form of stability for these metrics. We describe a large class of examples, inverse-image persistence modules, which occur whenever a topological space is mapped to a metric space. Several standard theories of persistence and their stability can be described in this framework. This includes the classical case of sublevelset persistent homology. We introduce a distinction between `soft' and `hard' stability theorems. While our treatment is direct and elementary, the approach can be explained abstractly in terms of monoidal functors.Comment: Final version; no changes from previous version. Published online Oct 2014 in Foundations of Computational Mathematics. Print version to appea

Quantification of habitat fragmentation reveals extinction risk in terrestrial mammals

Although habitat fragmentation is often assumed to be a primary driver of extinction, global patterns of fragmentation and its relationship to extinction risk have not been consistently quantified for any major animal taxon. We developed high-resolution habitat fragmentation models and used phylogenetic comparative methods to quantify the effects of habitat fragmentation on the world's terrestrial mammals, including 4,018 species across 26 taxonomic Orders. Results demonstrate that species with more fragmentation are at greater risk of extinction, even after accounting for the effects of key macroecological predictors, such as body size and geographic range size. Species with higher fragmentation had smaller ranges and a lower proportion of high-suitability habitat within their range, andmost high-suitability habitat occurred outside of protected areas, further elevating extinction risk. Our models provide a quantitative evaluation of extinction risk assessments for species, allow for identification of emerging threats in species not classified as threatened, and provide maps of global hotspots of fragmentation for the world's terrestrial mammals. Quantification of habitat fragmentation will help guide threat assessment and strategic priorities for global mammal conservation

On the accuracy of language trees

Historical linguistics aims at inferring the most likely language phylogenetic tree starting from information concerning the evolutionary relatedness of languages. The available information are typically lists of homologous (lexical, phonological, syntactic) features or characters for many different languages. From this perspective the reconstruction of language trees is an example of inverse problems: starting from present, incomplete and often noisy, information, one aims at inferring the most likely past evolutionary history. A fundamental issue in inverse problems is the evaluation of the inference made. A standard way of dealing with this question is to generate data with artificial models in order to have full access to the evolutionary process one is going to infer. This procedure presents an intrinsic limitation: when dealing with real data sets, one typically does not know which model of evolution is the most suitable for them. A possible way out is to compare algorithmic inference with expert classifications. This is the point of view we take here by conducting a thorough survey of the accuracy of reconstruction methods as compared with the Ethnologue expert classifications. We focus in particular on state-of-the-art distance-based methods for phylogeny reconstruction using worldwide linguistic databases. In order to assess the accuracy of the inferred trees we introduce and characterize two generalizations of standard definitions of distances between trees. Based on these scores we quantify the relative performances of the distance-based algorithms considered. Further we quantify how the completeness and the coverage of the available databases affect the accuracy of the reconstruction. Finally we draw some conclusions about where the accuracy of the reconstructions in historical linguistics stands and about the leading directions to improve it.Comment: 36 pages, 14 figure