Quantifying structure in networks

We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of subgraphs with no more than k links are a sufficient statistics for the exponential families of graphs with interactions between at most k links. In this framework we investigate the dependencies between several observables commonly used to quantify structure in networks, such as the degree distribution, cluster and assortativity coefficients.Comment: 17 pages, 3 figure

Social inertia in collaboration networks

This work is a study of the properties of collaboration networks employing the formalism of weighted graphs to represent their one-mode projection. The weight of the edges is directly the number of times that a partnership has been repeated. This representation allows us to define the concept of "social inertia" that measures the tendency of authors to keep on collaborating with previous partners. We use a collection of empirical datasets to analyze several aspects of the social inertia: 1) its probability distribution, 2) its correlation with other properties, and 3) the correlations of the inertia between neighbors in the network. We also contrast these empirical results with the predictions of a recently proposed theoretical model for the growth of collaboration networks.Comment: 7 pages, 5 figure

Estimating the number of planets that PLATO can detect

The PLATO mission is scheduled for launch in 2026. This study aims to estimate the number of exoplanets that PLATO can detect as a function of planetary size and period, stellar brightness, and observing strategy options. Deviations from these estimates will be informative of the true occurrence rates of planets, which helps constraining planet formation models. For this purpose, we developed the Planet Yield for PLATO estimator (PYPE), which adopts a statistical approach. We apply given occurrence rates from planet formation models and from different search and vetting pipelines for the Kepler data. We estimate the stellar sample to be observed by PLATO using a fraction of the all-sky PLATO stellar input catalog (PIC). PLATO detection efficiencies are calculated under different assumptions that are presented in detail in the text. The results presented here primarily consider the current baseline observing duration of four years. We find that the expected PLATO planet yield increases rapidly over the first year and begins to saturate after two years. A nominal (2+2) four-year mission could yield about several thousand to several tens of thousands of planets, depending on the assumed planet occurrence rates. We estimate a minimum of 500 Earth-size (0.8-1.25 RE) planets, about a dozen of which would reside in a 250-500d period bin around G stars. We find that one-third of the detected planets are around stars bright enough (V $\leq 11$) for RV-follow-up observations. We find that a three-year-long observation followed by 6 two-month short observations (3+1 years) yield roughly twice as many planets as two long observations of two years (2+2 years). The former strategy is dominated by short-period planets, while the latter is more beneficial for detecting earths in the habitable zone.Comment: 14 pages, 11 figures, accepted by A&A (July 5, 2023

Conformally invariant wave-equations and massless fields in de Sitter spacetime

Conformally invariant wave equations in de Sitter space, for scalar and vector fields, are introduced in the present paper. Solutions of their wave equations and the related two-point functions, in the ambient space notation, have been calculated. The ``Hilbert'' space structure and the field operator, in terms of coordinate independent de Sitter plane waves, have been defined. The construction of the paper is based on the analyticity in the complexified pseudo-Riemanian manifold, presented first by Bros et al.. Minkowskian limits of these functions are analyzed. The relation between the ambient space notation and the intrinsic coordinates is then studied in the final stage.Comment: 21 pages, LaTeX, some details adde

Deterministic and stochastic influence of nutrients on phytoplankton function and structure in coastal waters

Knowledge of how phytoplankton responds to nutrient inputs is essential for water management and for minimizing eutrophication. Only processes that are deterministic, i.e. that can respond as algorithms, are controllable. The study area is the chain of inshore waters (so-called Bodden) south of the Darss-Zingst peninsula - shallow eutrophic waters of estuarine character in the Southern Baltic. Monitoring programmes and laboratory experiments have revealed an annual periodicity of the phytoplankton and of the physico-chemical factors influencing it. On the basis of these results, experiments were carried out in enclosures to study the effects of nutrient loading on phytoplankton. The purpose was to test the feasibility of influencing phytoplankton development under field conditions during the transition period from late spring to mid-summer. This contribution presents results from the 1985 shallow water enclosure experiments (FLAK 85) which demonstrate that - the scale of phytoplankton reactions and the species involved are stochastic in character and are governed by stochastic interactions between meteorological events and water exchange processes in the chain of Bodden; - all processes affecting phytoplankton growth are deterministic in character, conforming to simple batch theories: simultaneous addition of nitrogen and phosphorus favours green algae, and in exceptional cases one algal species became dominant; - nutrient loadings do not affect the time of transition to the mid-summer phytoplankton population, the most important regulating factor obviously being temperature

QTLs for salt tolerance in three different barley mapping populations 2006

Soil salinity is one of the crucial factors limiting crop production. Progression of salinisation of agriculturally arable land is mainly connected with mismanagement of water in irrigation systems, in particular under arid and semiarid climate conditions and global changes of water flow in the landscape. Selection of salt tolerant genotypes is necessary to ensure yield and to reclaim salt affected soils. The development of molecular marker(s) could facilitate the selection process. Phenotyping of mapping populations under salt stress conditions and calculation of QTLs are suitable instruments to detect markers that are responsible for tolerance/sensitivity. However, a quantitative inherited trait like salt tolerance requires a range of adaptations, with a whole host of genes interacting with each other to produce the visible phenotype

Anharmonic double-phonon excitations in the interacting boson model

Double-$\gamma$ vibrations in deformed nuclei are analyzed in the context of the interacting boson model. A simple extension of the original version of the model towards higher-order interactions is required to explain the observed anharmonicities of nuclear vibrations. The influence of three- and four-body interactions on the moments of inertia of ground- and $\gamma$-bands, and on the relative position of single-$\gamma$ and double-$\gamma$ bands is studied in detail. As an example of a realistic calculation, spectra and transitions of the highly $\gamma$-anharmonic nuclei $^{164}$Dy, $^{166}$Er, and $^{168}$Er are interpreted in this approach.Comment: 38 pages, TeX (ReVTeX). 15 ps figures. Submitted to Phys. Rev.

Group theoretical approach to quantum fields in de Sitter space I. The principal series

Using unitary irreducible representations of the de Sitter group, we construct the Fock space of a massive free scalar field. In this approach, the vacuum is the unique dS invariant state. The quantum field is a posteriori defined by an operator subject to covariant transformations under the dS isometry group. This insures that it obeys canonical commutation relations, up to an overall factor which should not vanish as it fixes the value of hbar. However, contrary to what is obtained for the Poincare group, the covariance condition leaves an arbitrariness in the definition of the field. This arbitrariness allows to recover the amplitudes governing spontaneous pair creation processes, as well as the class of alpha vacua obtained in the usual field theoretical approach. The two approaches can be formally related by introducing a squeezing operator which acts on the state in the field theoretical description and on the operator in the present treatment. The choice of the different dS invariant schemes (different alpha vacua) is here posed in very simple terms: it is related to a first order differential equation which is singular on the horizon and whose general solution is therefore characterized by the amplitude on either side of the horizon. Our algebraic approach offers a new method to define quantum field theory on some deformations of dS space.Comment: 35 pages, 2 figures ; Corrected typo, Changed referenc