GTI-space : the space of generalized topological indices

A new extension of the generalized topological indices (GTI) approach is carried out torepresent 'simple' and 'composite' topological indices (TIs) in an unified way. Thisapproach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randićconnectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index andreverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given

Generalized graph theoretic indices in chemistry

In the development of any scientific theory, the initial stage based on the accumulation of observational facts is necessarily followed by the formalization and generalization of the concepts involved. Graph theoretic molecular descriptors, which are referred as topological indices (TI) have been around for more than half century [1]. During this time many TIs have been defined [1], their mathematical properties have been scrutinized [2, 3], and more importantly they have proved to be useful in predicting molecular properties beyond any reasonable doubt [4]. Then, the field is mature enough to jump to the next stage of development. That is, the formalization and generalization of concepts that permits the elaboration of a physical theory for topological indices in molecular sciences. In 2001 one of the current authors (EE) proposed a graph theoretic scheme that permitted the generalization of several of the best known TIs [5]. In a subsequent series of papers we have shown several of the principal characteristics of this generalized scheme for graph theoretic indices in chemistry, hereafter named G-GTI [6-12]. Among the most relevant characteristics of G-GTI we can mention the following ones: It groups the definition of many known TIs into one graph theoretic invariant, namely a quadratic form based on a generalized graph matrix and vectors [5, 10]. TIs are designed a-la-carte more than in ad hoc way to describe a particular experimental property, which improves significantly the predictability of the methods used [7-9]. The generalized graph matrix can be used to generalize quantum chemical concepts, such as the Hückel Molecular Orbital method or the Lennard-Jones potentials for united-atoms [6, 12]. The method permits the optimization of local vertex invariants (LOVIs) to account for atomic properties, which is an avenue to be explored for introducing heteroatoms in the G-GTI scheme. The structural interpretation of the TIs can be carried out in a generalized way accounting for through-bonds and through-space inter-atomic interactions in molecules [5-12]. The aim of the current work is to review the G-GTI method with special emphasis in the methodological aspects of the method and its applications for predicting physico-chemical properties. Our objective is two-fold. First, that chemists interested in the prediction of molecular properties are aware of the generality and simplicity of the G-GTI approach in such a way that they can use it in modelling physical, chemical pharmacological, toxicological and environmental properties of organic molecules. Secondly, that graph theorists, both mathematicians and chemists, explore more deeply the possibilities of G-GTI for studying molecular graphs. We hope that this chapter be of interest for both communities

A graph theoretic approach to atomic displacements in fullerenes

We consider a classical mechanics approach to atomic displacements in fullerene molecules. The problem is reduced to the study of the graph Laplacian spectra by deriving an analytical expression for the atomic displacement due to thermal vibrations/oscillations. We then use the concepts of graph isoperimetric constant and graph expansion to prove that "among all graphs on n nodes, those with good expansion properties display the smallest topological displacements of their nodes." Consequently, fullerenes with the property of being Ramanujan graphs, i.e., Ramafullerenes, are those that exhibit the smallest atomic displacements due to thermal movement. We show that fullerenes with the smallest atomic perturbations due to thermal effects are the most stable ones. Then, relationships between atomic displacements, spectral gap, and energy are presented for different families of fullerenes

Author Correction: The FLUXNET2015 dataset and the ONEFlux processing pipeline for eddy covariance data (Scientific Data, (2020), 7, 1, (225), 10.1038/s41597-020-0534-3)

The following authors were omitted from the original version of this Data Descriptor: Markus Reichstein and Nicolas Vuichard. Both contributed to the code development and N. Vuichard contributed to the processing of the ERA-Interim data downscaling. Furthermore, the contribution of the co-author Frank Tiedemann was re-evaluated relative to the colleague Corinna Rebmann, both working at the same sites, and based on this re-evaluation a substitution in the co-author list is implemented (with Rebmann replacing Tiedemann). Finally, two affiliations were listed incorrectly and are corrected here (entries 190 and 193). The author list and affiliations have been amended to address these omissions in both the HTML and PDF versions. © 2021, This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply

The FLUXNET2015 dataset and the ONEFlux processing pipeline for eddy covariance data

The FLUXNET2015 dataset provides ecosystem-scale data on CO2, water, and energy exchange between the biosphere and the atmosphere, and other meteorological and biological measurements, from 212 sites around the globe (over 1500 site-years, up to and including year 2014). These sites, independently managed and operated, voluntarily contributed their data to create global datasets. Data were quality controlled and processed using uniform methods, to improve consistency and intercomparability across sites. The dataset is already being used in a number of applications, including ecophysiology studies, remote sensing studies, and development of ecosystem and Earth system models. FLUXNET2015 includes derived-data products, such as gap-filled time series, ecosystem respiration and photosynthetic uptake estimates, estimation of uncertainties, and metadata about the measurements, presented for the first time in this paper. In addition, 206 of these sites are for the first time distributed under a Creative Commons (CC-BY 4.0) license. This paper details this enhanced dataset and the processing methods, now made available as open-source codes, making the dataset more accessible, transparent, and reproducible