Distributional versions of Littlewood's Tauberian theorem

We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We apply these Tauberian results to deduce a number of Tauberian theorems for power series where Ces\`{a}ro summability follows from Abel summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series.Comment: 15 page

Testing CIP and ICA potato selections for late blight resistance and yield at Rionegro La Selva Station in Colombia.

Papa-Solanum tuberosu

Response of a Fermi gas to time-dependent perturbations: Riemann-Hilbert approach at non-zero temperatures

We provide an exact finite temperature extension to the recently developed Riemann-Hilbert approach for the calculation of response functions in nonadiabatically perturbed (multi-channel) Fermi gases. We give a precise definition of the finite temperature Riemann-Hilbert problem and show that it is equivalent to a zero temperature problem. Using this equivalence, we discuss the solution of the nonequilibrium Fermi-edge singularity problem at finite temperatures.Comment: 10 pages, 2 figures; 2 appendices added, a few modifications in the text, typos corrected; published in Phys. Rev.

Functional centrality in graphs

In this paper we introduce the functional centrality as a generalization of the subgraph centrality. We propose a general method for characterizing nodes in the graph according to the number of closed walks starting and ending at the node. Closed walks are appropriately weighted according to the topological features that we need to measure

"Clumpiness" Mixing in Complex Networks

Three measures of clumpiness of complex networks are introduced. The measures quantify how most central nodes of a network are clumped together. The assortativity coefficient defined in a previous study measures a similar characteristic, but accounts only for the clumpiness of the central nodes that are directly connected to each other. The clumpiness coefficient defined in the present paper also takes into account the cases where central nodes are separated by a few links. The definition is based on the node degrees and the distances between pairs of nodes. The clumpiness coefficient together with the assortativity coefficient can define four classes of network. Numerical calculations demonstrate that the classification scheme successfully categorizes 30 real-world networks into the four classes: clumped assortative, clumped disassortative, loose assortative and loose disassortative networks. The clumpiness coefficient also differentiates the Erdos-Renyi model from the Barabasi-Albert model, which the assortativity coefficient could not differentiate. In addition, the bounds of the clumpiness coefficient as well as the relationships between the three measures of clumpiness are discussed.Comment: 47 pages, 11 figure

"Clumpiness" Mixing in Complex Networks

Three measures of clumpiness of complex networks are introduced. The measures quantify how most central nodes of a network are clumped together. The assortativity coefficient defined in a previous study measures a similar characteristic, but accounts only for the clumpiness of the central nodes that are directly connected to each other. The clumpiness coefficient defined in the present paper also takes into account the cases where central nodes are separated by a few links. The definition is based on the node degrees and the distances between pairs of nodes. The clumpiness coefficient together with the assortativity coefficient can define four classes of network. Numerical calculations demonstrate that the classification scheme successfully categorizes 30 real-world networks into the four classes: clumped assortative, clumped disassortative, loose assortative and loose disassortative networks. The clumpiness coefficient also differentiates the Erdos-Renyi model from the Barabasi-Albert model, which the assortativity coefficient could not differentiate. In addition, the bounds of the clumpiness coefficient as well as the relationships between the three measures of clumpiness are discussed.Comment: 47 pages, 11 figure

Is composition of vertebrates an indicator of the prevalence of tick-borne pathogens?

Communities of vertebrates tend to appear together under similar ranges of environmental features. This study explores whether an explicit combination of vertebrates and their contact rates with a tick vector might constitute an indicator of the prevalence of a pathogen in the quest for ticks at the western Palearctic scale. We asked how ‘indicator’ communities could be ‘markers’ of the actual infection rates of the tick in the field of two species of Borrelia (a bacterium transmitted by the tick Ixodes ricinus). We approached an unsupervised classification of the territory to obtain clusters on the grounds of abundance of each vertebrate and contact rates with the tick. Statistical models based on Neural Networks, Random Forest, Gradient Boosting, and AdaBoost were detect the best correlation between communities’ composition and the prevalence of Borrelia afzelii and Borrelia gariniii in questing ticks. Both Gradient Boosting and AdaBoost produced the best results, predicting tick infection rates from the indicator communities. A ranking algorithm demonstrated that the prevalence of these bacteria in the tick is correlated with indicator communities of vertebrates on sites selected as a proof-of-concept. We acknowledge that our findings are supported by statistical outcomes, but they provide consistency for a framework that should be deeper explored at the large scale. © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group