Information inequalities and Generalized Graph Entropies

In this article, we discuss the problem of establishing relations between information measures assessed for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the R\'{e}nyi entropy have been considered for this study. Our main results involve establishing formal relationship, in the form of implicit inequalities, between these two kinds of measures when defined for graphs. Further, we also state and prove inequalities connecting the classical partition-based graph entropies and the functional-based entropy measures. In addition, several explicit inequalities are derived for special classes of graphs.Comment: A preliminary version. To be submitted to a journa

Spectral analysis of Gene co-expression network of Zebrafish

We analyze the gene expression data of Zebrafish under the combined framework of complex networks and random matrix theory. The nearest neighbor spacing distribution of the corresponding matrix spectra follows random matrix predictions of Gaussian orthogonal statistics. Based on the eigenvector analysis we can divide the spectra into two parts, first part for which the eigenvector localization properties match with the random matrix theory predictions, and the second part for which they show deviation from the theory and hence are useful to understand the system dependent properties. Spectra with the localized eigenvectors can be characterized into three groups based on the eigenvalues. We explore the position of localized nodes from these different categories. Using an overlap measure, we find that the top contributing nodes in the different groups carry distinguished structural features. Furthermore, the top contributing nodes of the different localized eigenvectors corresponding to the lower eigenvalue regime form different densely connected structure well separated from each other. Preliminary biological interpretation of the genes, associated with the top contributing nodes in the localized eigenvectors, suggests that the genes corresponding to same vector share common features.Comment: 6 pages, four figures (accepted in EPL

Potentielle Wirkung von Unkräutern auf die P-Mobilisierung unter Mais

Die Rhizosphäre ist ein Hot Spot pflanzlicher und mikrobieller Aktivität zur Nährstoffmobilisierung und die Effizienz der Nutzung von Phosphor (P) unterscheidet sich pflanzen- artenspezifisch. Während die P-Mobilisierung in der Rhizosphäre verschiedener Kulturpflanzen intensiv untersucht wurde, ist die Bedeutung der Unkräuter auf die P-Verfügbarkeit für die vergesellschafteten Kulturpflanzen in Balance von Nährstoffkonkurrenz und Mobilisierungsleistung wenig bekannt. In der vorliegenden Untersuchung wird geprüft, ob eine zeitweise Toleranz von Unkräutern im Bestand die P-Verfügbarkeit für die Nutzpflanze Mais (Zea mays) durch die Mobilisierungsaktivität der Unkrautarten verbessern kann. Zu diesem Zweck wurden in zwei Versuchsjahren (2015 und 2016) Gefäßversuche unter Halbfreilandbedingungen mit einem P-defizienten Boden etabliert. Mais als mykorrhizierte Testpflanze wurde alleine und in Kombination mit sechs verschiedenen sowohl mykorrhizierten als auch nicht mykorrhizierten Unkrautarten kultiviert (Chenopodium album, Echinochloa crus-galli, Tripleurospermum perforatum, Polygonum convolvulus, Solanum nigrum, Viola arvensis). Um einen möglichen unkrautartspezifischen Einfluss auf die P-Mobilisierung unter Mais zu erfassen, wurden Boden- (u.a. Phosphatasen-Aktivitäten, mikrobieller Biomasse-P, pflanzenverfügbarer P) und Pflanzenparameter (Ertrag, Nährstoffgehalte und Mykorrhizierungsgrad der Feinwurzeln) untersucht. Die Ergebnisse belegen signifikante pflanzenkombinationsspezifische Unterschiede in der P-Mobilisierung und P-Aufnahme

Connections between Classical and Parametric Network Entropies

This paper explores relationships between classical and parametric measures of graph (or network) complexity. Classical measures are based on vertex decompositions induced by equivalence relations. Parametric measures, on the other hand, are constructed by using information functions to assign probabilities to the vertices. The inequalities established in this paper relating classical and parametric measures lay a foundation for systematic classification of entropy-based measures of graph complexity

Persistent topology for natural data analysis - A survey

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classification of cells, lesions, music pieces, gait, oil and gas reservoirs, cyclones, galaxies, bones, brain connections, languages, handwritten and gestured letters are shown

An Examination of Not-For-Profit Stakeholder Networks for Relationship Management: A Small-Scale Analysis on Social Media

Using a small-scale descriptive network analysis approach, this study highlights the importance of stakeholder networks for identifying valuable stakeholders and the management of existing stakeholders in the context of mental health not-for-profit services. We extract network data from the social media brand pages of three health service organizations from the U.S., U.K., and Australia, to visually map networks of 579 social media brand pages (represented by nodes), connected by 5,600 edges. This network data is analyzed using a collection of popular graph analysis techniques to assess the differences in the way each of the service organizations manage stakeholder networks. We also compare node meta-information against basic topology measures to emphasize the importance of effectively managing relationships with stakeholders who have large external audiences. Implications and future research directions are also discussed

New Polynomial-Based Molecular Descriptors with Low Degeneracy

In this paper, we introduce a novel graph polynomial called the ‘information polynomial’ of a graph. This graph polynomial can be derived by using a probability distribution of the vertex set. By using the zeros of the obtained polynomial, we additionally define some novel spectral descriptors. Compared with those based on computing the ordinary characteristic polynomial of a graph, we perform a numerical study using real chemical databases. We obtain that the novel descriptors do have a high discrimination power

Angle-resolved photoelectron spectrometry studies of the autoionization of the 2s22p 2P triply excited state of atomic lithium: experimental results and R-matrix calculations

We have measured the angle-resolved energy dependence of the electrons emitted over the energy range of the triply excited 2s22p2P lithium resonance using synchrotron radiation. We have also calculated the behavior of the angular distribution parameter β using the R-matrix approximation. Experimental and theoretical results are in good agreement and show deep minima in the 1s2p1,3P ionic channels. The energy at which the minima occur does not coincide with the resonance energy, but is shifted towards higher energy

An approach for the identification of targets specific to bone metastasis using cancer genes interactome and gene ontology analysis

Metastasis is one of the most enigmatic aspects of cancer pathogenesis and is a major cause of cancer-associated mortality. Secondary bone cancer (SBC) is a complex disease caused by metastasis of tumor cells from their primary site and is characterized by intricate interplay of molecular interactions. Identification of targets for multifactorial diseases such as SBC, the most frequent complication of breast and prostate cancers, is a challenge. Towards achieving our aim of identification of targets specific to SBC, we constructed a 'Cancer Genes Network', a representative protein interactome of cancer genes. Using graph theoretical methods, we obtained a set of key genes that are relevant for generic mechanisms of cancers and have a role in biological essentiality. We also compiled a curated dataset of 391 SBC genes from published literature which serves as a basis of ontological correlates of secondary bone cancer. Building on these results, we implement a strategy based on generic cancer genes, SBC genes and gene ontology enrichment method, to obtain a set of targets that are specific to bone metastasis. Through this study, we present an approach for probing one of the major complications in cancers, namely, metastasis. The results on genes that play generic roles in cancer phenotype, obtained by network analysis of 'Cancer Genes Network', have broader implications in understanding the role of molecular regulators in mechanisms of cancers. Specifically, our study provides a set of potential targets that are of ontological and regulatory relevance to secondary bone cancer.Comment: 54 pages (19 pages main text; 11 Figures; 26 pages of supplementary information). Revised after critical reviews. Accepted for Publication in PLoS ON