Spectral norm and energy of a digraph with respect to a VDB topological index.

The set of singular values of a digraph with respect to a vertex-degree based topological index is the set of all singular values of its general adjacency matrix. The spectral norm is the largest singular value and the energy the sum of the singular values. In this paper we characterize the digraphs which have exactly one singular value different from zero and the digraphs for which all singular values are equal. As a consequence, we deduce sharp upper and lower bounds for the spectral norm and energy of digraphs. In addition to being a natural generalization, proving the results in the general setting of digraphs allows us to deduce new results on graph energy.

Use of Community SARS-CoV-2 Case Counts and Instantaneous Reproductive Number to Predict Short-Term COVID-19 Hospital Admission Volumes.

The severe acute respiratory syndrome (SARS-CoV-2) pandemic and high hospitalization rates placed a tremendous strain on hospital resources, necessitating the use of models to predict hospital volumes and the associated resource requirements. Complex epidemiologic models have been developed and published, but many require continued adjustment of input parameters. We developed a simplified model for short-term bed need predictions that self-adjusts to changing patterns of disease in the community and admission rates. The model utilizes public health data on community new case counts for SARS-CoV-2 and projects anticipated hospitalization rates. The model was retrospectively evaluated after the second wave of SARS-CoV-2 in New York, New York (October 2020-April 2021) for its accuracy in predicting numbers of coronavirus disease 2019 (COVID-19) admissions 3, 5, 7, and 10 days into the future, comparing predicted admissions with actual admissions for each day at a large integrated health-care delivery network. The mean absolute percent error of the model was found to be low when evaluated across the entire health system, for a single region of the health system or for a single large hospital (6.1%-7.6% for 3-day predictions, 9.2%-10.4% for 5-day predictions, 12.4%-13.2% for 7-day predictions, and 17.1%-17.8% for 10-day predictions).

Extremal values of VDB topological indices over F-benzenoids with equal number of edges.

The utilization of molecular structure topological indices is currently a standing operating procedure in the structure-property relations research, especially in QSPR/QSAR study. In the past several year, generous molecular topological indices related to some chemical and physical properties of chemical compounds were put forward. Among these topological indices, the VDB topological indices rely only on the vertex degree of chemical molecular graphs. The VDB topological index of an $ n $-order graph $ G $ is defined as TI(G) = \sum\limits_{1\leq i\leq j\leq n-1}m_{ij}\psi_{ij}, $ where $ \{\psi_{ij}\} $ is a set of real numbers, $ m_{ij} $ is the quantity of edges linking an $ i $-vertex and another $ j $-vertex. Numerous famous topological indices are special circumstance of this expression. f-benzenoids are a kind of polycyclic aromatic hydrocarbons, present in large amounts in coal tar. Studying the properties of f-benzenoids via topological indices is a worthy task. In this work the extremum $ TI $ of f-benzenoids with given number of edges were determined. The main idea is to construct f-benzenoids with maximal number of inlets and simultaneously minimal number of hexagons in $ \Gamma_{m} $, where $ \Gamma_{m} $ is the collection of f-benzenoids with exactly $ m $ $ (m\geq19) $ edges. As an application of this result, we give a unified approach of VDB topological indices to predict distinct chemical and physical properties such as the boiling point, $ \pi $-electrom energy, molecular weight and vapour pressure etc. of f-benzenoids with fixed number of edges.

Landscape-scale forest cover drives the predictability of forest regeneration across the Neotropics.

Abandonment of agricultural lands promotes the global expansion of secondary forests, which are critical for preserving biodiversity and ecosystem functions and services. Such roles largely depend, however, on two essential successional attributes, trajectory and recovery rate, which are expected to depend on landscape-scale forest cover in nonlinear ways. Using a multi-scale approach and a large vegetation dataset (843 plots, 3511 tree species) from 22 secondary forest chronosequences distributed across the Neotropics, we show that successional trajectories of woody plant species richness, stem density and basal area are less predictable in landscapes (4 km radius) with intermediate (40-60%) forest cover than in landscapes with high (greater than 60%) forest cover. This supports theory suggesting that high spatial and environmental heterogeneity in intermediately deforested landscapes can increase the variation of key ecological factors for forest recovery (e.g. seed dispersal and seedling recruitment), increasing the uncertainty of successional trajectories. Regarding the recovery rate, only species richness is positively related to forest cover in relatively small (1 km radius) landscapes. These findings highlight the importance of using a spatially explicit landscape approach in restoration initiatives and suggest that these initiatives can be more effective in more forested landscapes, especially if implemented across spatial extents of 1-4 km radius.

Randic energy of digraphs.

We assume that D is a directed graph with vertex set V ( D ) = { v 1 , … v n } and arc set E ( D ) . A VDB topological index φ of D is defined as φ ( D ) = 1 2 ∑ u v ∈ E ( D ) φ d u + , d v - , where d u + and d v - denote the outdegree and indegree of vertices u and v, respectively, and φ i , j is a bivariate symmetric function defined on nonnegative real numbers. Let A φ = A φ ( D ) be the n × n general adjacency matrix defined as [ A φ ] i j = φ d v i + , d v j - if v i v j ∈ E ( D ) , and 0 otherwise. The energy of D with respect to a VDB index φ is defined as E φ ( D ) = ∑ i = 1 n σ i ( A φ ) , where σ 1 ( A φ ) ≥ σ 2 ( A φ ) ≥ ⋯ ≥ σ n ( A φ ) ≥ 0 are the singular values of the matrix A φ . We will show that in case φ = R is the Randic index, the spectral norm of A R is equal to 1, and rank of A R is equal to rank of the adjacency matrix of D. Immediately after, we illustrate by means of examples, that these properties do not hold for most well-known VDB topological indices. Taking advantage of nice properties the Randic matrix has, we derive new upper and lower bounds for the Randic energy E R in digraphs. Some of these generalize known results for the Randic energy of graphs. Also, we deduce a new upper bound for the Randic energy of graphs in terms of rank, concretely, we show that E R ( G ) ≤ r a n k ( G ) for all graphs G, and equality holds if and only if G is a disjoint union of complete bipartite graphs.

Computation method of the Hosoya index of primitive coronoid systems.

Coronoid systems are natural graph representations of coronoid hydrocarbons associated with benzenoid systems, but they differ in that they contain a hole. The Hosoya index of a graph G is defined as the total number of independent edge sets, that are called k-matchings in G. The Hosoya index is a significant molecular descriptor that has an important position in QSAR and QSPR studies. Therefore, the computation of the Hosoya index of various molecular graphs is needed for making progress on investigations. In this paper, a method based on the transfer matrix technique and the Hosoya vector for computing the Hosoya index of arbitrary primitive coronoid systems is presented. Moreover, the presented method is customized for hollow hexagons by using six parameters. As a result, the Hosoya indices of both each arbitrary primitive coronoid system and also each hollow hexagon can be computed by means of a summation of four selected multiplications consisting of presented transfer matrices and two vectors.

k-domination and total k-domination numbers in catacondensed hexagonal systems.

In this paper we study the k-domination and total k-domination numbers of catacondensed hexagonal systems. More precisely, we give the value of the total domination number, we find upper and lower bounds for the 2-domination number and the total 2-domination number, characterizing the catacondensed hexagonal systems which attain these bounds, and we give the value of the 3-domination number for any catacondensed hexagonal system with a given number of hexagons. These results complete the study of k-domination and total k-domination of catacondensed hexagonal systems for all possible values of k.

Sombor index of directed graphs.

Let D be a digraph with set of arcs A. The Sombor index of D is defined as SO ( D ) = 1 2 ∑ u v ∈ A ( d u + ) 2 + ( d v - ) 2 , where d u + and d v - are the out-degree and in-degree of the vertices u and v of D. When D is a graph, we recover the Sombor index of graphs, a molecular descriptor recently introduced with a good predictive potential and a great research activity this year. In this paper we initiate the study of the Sombor index of digraphs. Specifically, we find sharp upper and lower bounds for SO over the class D n of digraphs with n non-isolated vertices, the classes C n and S n of connected and strongly connected digraphs on n vertices, respectively, the class of oriented trees OT ( n ) with n vertices, and the class O ( G ) of orientations of a fixed graph G.

From ArrayExpress to BioStudies.

ArrayExpress (https://www.ebi.ac.uk/arrayexpress) is an archive of functional genomics data at EMBL-EBI, established in 2002, initially as an archive for publication-related microarray data and was later extended to accept sequencing-based data. Over the last decade an increasing share of biological experiments involve multiple technologies assaying different biological modalities, such as epigenetics, and RNA and protein expression, and thus the BioStudies database (https://www.ebi.ac.uk/biostudies) was established to deal with such multimodal data. Its central concept is a study, which typically is associated with a publication. BioStudies stores metadata describing the study, provides links to the relevant databases, such as European Nucleotide Archive (ENA), as well as hosts the types of data for which specialized databases do not exist. With BioStudies now fully functional, we are able to further harmonize the archival data infrastructure at EMBL-EBI, and ArrayExpress is being migrated to BioStudies. In future, all functional genomics data will be archived at BioStudies. The process will be seamless for the users, who will continue to submit data using the online tool Annotare and will be able to query and download data largely in the same manner as before. Nevertheless, some technical aspects, particularly programmatic access, will change. This update guides the users through these changes.

The BioStudies database-one stop shop for all data supporting a life sciences study.

BioStudies (www.ebi.ac.uk/biostudies) is a new public database that organizes data from biological studies. Typically, but not exclusively, a study is associated with a publication. BioStudies offers a simple way to describe the study structure, and provides flexible data deposition tools and data access interfaces. The actual data can be stored either in BioStudies or remotely, or both. BioStudies imports supplementary data from Europe PMC, and is a resource for authors and publishers for packaging data during the manuscript preparation process. It also can support data management needs of collaborative projects. The growth in multiomics experiments and other multi-faceted approaches to life sciences research mean that studies result in a diversity of data outputs in multiple locations. BioStudies presents a solution to ensuring that all these data and the associated publication(s) can be found coherently in the longer term.