Live and Dead Nodes

In this paper, we explore the consequences of a distinction between `live' and `dead' network nodes; `live' nodes are able to acquire new links whereas `dead' nodes are static. We develop an analytically soluble growing network model incorporating this distinction and show that it can provide a quantitative description of the empirical network composed of citations and references (in- and out-links) between papers (nodes) in the SPIRES database of scientific papers in high energy physics. We also demonstrate that the death mechanism alone can result in power law degree distributions for the resulting network.Comment: 12 pages, 3 figures. To be published in Computational and Mathematical Organization Theor

Density of states of helium droplets

Accurate analytical expressions for the state densities of liquid He-4 droplets are derived, incorporating the ripplon and phonon degrees of freedom. The microcanonical temperature and the ripplon angular momentum level density are also evaluated. The approach is based on inversions and systematic expansions of canonical thermodynamic properties.Comment: 20 pages, 5 figure

Les bases culturelles de la parenté: un changement de paradigme

French: D’un point de vue conceptuel, les systèmes de parenté reposent sur des modes de représentation culturelle que nous appelons terminologies de parenté et à partir desquelles les limites, la forme et la structure des principes d’organisation sociale sont culturellement élaborés. Contrairement à ce que les anthropologues tiennent depuis longtemps pour acquis, une terminologie n’est pas forcément inhérente aux relations généalogiques, ces dernières découlant de la logique structurelle de la terminologie de parenté. La structure de la terminologie, représentée sous une forme algébrique, peut être produite à partir des principaux termes de parenté, suivant un principe supposé universel de structures terminologiques de la parenté. Les terminologies diffèrent, sur le plan culturel, selon les principales expressions et équations utilisées pour les élaborer. Cela implique un changement de paradigme qui nous ferait passer de la généalogie considérée comme fondement essentiel des relations de parenté à un modèle dans lequel la parenté intégrerait à la fois des termes de parenté propres à un système de représentations culturellement constitué auquel nous nous référons dans la terminologie de parenté, et une dimension généalogique élaborée de manière récursive en utilisant les relations parents/enfants. Ces deux domaines sont fondés sur un espace familial comprenant les positions de parents/enfants, conjoints, germains. English: Kinship systems are conceptually grounded in culturally formulated idea-systems we refer to as kinship terminologies and through which the boundaries, form and structure of human social systems are culturally constituted. A terminology, contrary to a long-standing assumption in anthropology, is not based on a prior categorization of genealogical relations, as the latter is derived from the structural logic of the kinship terminology. The terminology structure, formally represented as an algebraic structure, can be generated from primary kin terms in accordance with a hypothesized universal theory of kinship terminology structures. Terminologies differ culturally according to the primary terms and equations used for generating them. This requires a paradigm shift from the received view of genealogy as the primary basis for kin relations to a new paradigm in which kinship incorporates both a kin term space expressed through a culturally constituted idea-system we refer to as a kinship terminology and a genealogical space constructed recursively using parent-child relations. Both of these spaces are grounded in a family space composed of parent-child, spouse and sibling positions

Isolated effective coherence (iCoh): causal information flow excluding indirect paths

A problem of great interest in real world systems, where multiple time series measurements are available, is the estimation of the intra-system causal relations. For instance, electric cortical signals are used for studying functional connectivity between brain areas, their directionality, the direct or indirect nature of the connections, and the spectral characteristics (e.g. which oscillations are preferentially transmitted). The earliest spectral measure of causality was Akaike's (1968) seminal work on the noise contribution ratio, reflecting direct and indirect connections. Later, a major breakthrough was the partial directed coherence of Baccala and Sameshima (2001) for direct connections. The simple aim of this study consists of two parts: (1) To expose a major problem with the partial directed coherence, where it is shown that it is affected by irrelevant connections to such an extent that it can misrepresent the frequency response, thus defeating the main purpose for which the measure was developed, and (2) To provide a solution to this problem, namely the "isolated effective coherence", which consists of estimating the partial coherence under a multivariate auto-regressive model, followed by setting all irrelevant associations to zero, other than the particular directional association of interest. Simple, realistic, toy examples illustrate the severity of the problem with the partial directed coherence, and the solution achieved by the isolated effective coherence. For the sake of reproducible research, the software code implementing the methods discussed here (using lazarus free-pascal "www.lazarus.freepascal.org"), including the test data as text files, are freely available at: https://sites.google.com/site/pascualmarqui/home/icoh-isolated-effective-coherenceComment: 2014-02-21 pre-print, technical report, KEY Institute for Brain-Mind Research, University of Zurich, et a

Gibrat's law for cities: uniformly most powerful unbiased test of the Pareto against the lognormal

We address the general problem of testing a power law distribution versus a log-normal distribution in statistical data. This general problem is illustrated on the distribution of the 2000 US census of city sizes. We provide definitive results to close the debate between Eeckhout (2004, 2009) and Levy (2009) on the validity of Zipf's law, which is the special Pareto law with tail exponent 1, to describe the tail of the distribution of U.S. city sizes. Because the origin of the disagreement between Eeckhout and Levy stems from the limited power of their tests, we perform the {\em uniformly most powerful unbiased test} for the null hypothesis of the Pareto distribution against the lognormal. The $p$-value and Hill's estimator as a function of city size lower threshold confirm indubitably that the size distribution of the 1000 largest cities or so, which include more than half of the total U.S. population, is Pareto, but we rule out that the tail exponent, estimated to be $1.4 \pm 0.1$, is equal to 1. For larger ranks, the $p$-value becomes very small and Hill's estimator decays systematically with decreasing ranks, qualifying the lognormal distribution as the better model for the set of smaller cities. These two results reconcile the opposite views of Eeckhout (2004, 2009) and Levy (2009). We explain how Gibrat's law of proportional growth underpins both the Pareto and lognormal distributions and stress the key ingredient at the origin of their difference in standard stochastic growth models of cities \cite{Gabaix99,Eeckhout2004}.Comment: 7 pages + 2 figure

Algebras of Measurements: the logical structure of Quantum Mechanics

In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute. Keywords: Quantum measurements, Measurement algebras, Quantum Logic. PACS: 02.10.-v.Comment: Submitted, 30 page

Multiple Components of the Luminous Compact X-ray Source at the Edge of Holmberg II observed by ASCA and ROSAT

We report the results of the analysis of ASCA/ROSAT observations of the compact luminous X-ray source found at the edge of the nearby star-forming dwarf galaxy Holmberg II (UGC 4305).Our ASCA spectrum revealed that the X-ray emission extends to the hard band and can be best described by a power-law with a photon spectral index of 1.9. The ASCA spectrum does not fit with a multi-color disk blackbody. The joint ASCA-ROSAT spectrum suggests two components to the spectrum: the hard power-law component and a warm thermal plasma kT~0.3[keV]. An additional absorption over that of our galaxy is required. The wobble correction of the ROSAT HRI image has clearly unveiled the existence of an extended component which amounts to 27+/-5% of the total X-ray emission. These observations indicate that there are more than one component in the X-ray emission. The properties of the point-like component is indicative of an accretion onto an intermediate mass blackhole, unless a beaming is taking place. We argue that the extended component does not come from electron scattering and/or reflection by scattered optically-thick clouds of the central radiation. Possible explanations of this X-ray source include multiple supernova remnants feeding an intermediate-mass blackhole. (abridged)Comment: 12 pages, 6 figures accepted to Astronomical Journa