572 research outputs found
Spectral properties of geometric-arithmetic index
The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. One of the main aims of algebraic graph theory is to determine how, or whether, properties of graphs are reflected in the algebraic properties of some matrices. The aim of this paper is to study the geometric-arithmetic index GA(1) from an algebraic viewpoint. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix that is a modification of the classical adjacency matrix involving the degrees of the vertices. Moreover, using this matrix, we define a GA Laplacian matrix which determines the geometric-arithmetic index of a graph and satisfies properties similar to the ones of the classical Laplacian matrix. (C) 2015 Elsevier Inc. All rights reserved.This research was supported in part by a Grant from Ministerio de EconomĂa y Competitividad (MTM 2013-46374-P), Spain, and a Grant from CONACYT (FOMIX-CONACyT-UAGro 249818), MĂ©xico
Applications of Multidimensional Space of Mathematical Molecular Descriptors in Large-Scale Bioactivity and Toxicity Prediction- Applications to Prediction of Mutagenicity and Blood-Brain Barrier Entry of Chemicals
In this chapter, we review our QSAR research in the prediction of toxicities, bioactivities and properties of chemicals using computed mathematical descriptors. Robust statistical methods have been used to develop high quality predictive quantitative structure-activity relationship (QSAR) models for the prediction of mutagenicity and BBB (blood-brain barrier) entry of two large and diverse sets chemicals.
This work is licensed under a Creative Commons Attribution 4.0 International License
Embeddings of Decomposition Spaces into Sobolev and BV Spaces
In the present paper, we investigate whether an embedding of a decomposition
space into a given Sobolev space
exists. As special cases, this includes embeddings
into Sobolev spaces of (homogeneous and inhomogeneous) Besov spaces,
()-modulation spaces, shearlet smoothness spaces and also of a large
class of wavelet coorbit spaces, in particular of shearlet-type coorbit spaces.
Precisely, we will show that under extremely mild assumptions on the covering
, we have
as soon as and
hold. Here, and the weight
can be easily computed, only based on the covering
and on the parameters .
Conversely, a necessary condition for existence of the embedding is that
and
hold, where denotes the space of finitely supported
sequences on .
All in all, for the range , we obtain a complete
characterization of existence of the embedding in terms of readily verifiable
criteria. We can also completely characterize existence of an embedding of a
decomposition space into a BV space
Preliminary Analysis of an Aquatic Toxicity Dataset and Assessment of QSAR Models for Narcosis
The purpose of the analyses presented in this report was to contribute to an evaluation of the possibility of using QSAR predictions for regulatory purposes. To this end QSAR predictions were compared with SIDS test data. Furthermore, the models were also assessed according to the extent to which they meet OECD principles for QSAR validation. The comparisons are not intended to be scientific validations, because the SIDS test chemicals were not selected to ensure that they are sufficiently representative for the entire applicability domain of the individual models. Nevertheless, many of the analyses presented form the basis for scientific validationJRC.I.3-Toxicology and chemical substance
Models for Antitubercular Activity of 5âČ-O-[(N-Acyl)sulfamoyl]adenosines
The relationship between topological indices and antitubercular activity of 5âČ-O-[(N-Acyl)sulfamoyl]adenosines has been investigated. A data set consisting of 31 analogues of 5âČ-O-[(N-Acyl)sulfamoyl]adenosines was selected for the present study. The values of numerous topostructural and topochemical indices for each of 31 differently substituted analogues of the data set were computed using an in-house computer program. Resulting data was analyzed and suitable models were developed through decision tree, random forest and moving average analysis (MAA). The goodness of the models was assessed by calculating overall accuracy of prediction, sensitivity, specificity and Mathews correlation coefficient. Pendentic eccentricity index â a novel highly discriminating, non-correlating pendenticity based topochemical descriptor â was also conceptualized and successfully utilized for the development of a model for antitubercular activity of 5âČ-O-[(N-Acyl)sulfamoyl]adenosines. The proposed index exhibited not only high sensitivity towards both the presence as well as relative position(s) of pendent/heteroatom(s) but also led to significant reduction in degeneracy. Random forest correctly classified the analogues into active and inactive with an accuracy of 67.74%. A decision tree was also employed for determining the importance of molecular descriptors. The decision tree learned the information from the input data with an accuracy of 100% and correctly predicted the cross-validated (10 fold) data with accuracy up to 77.4%. Statistical significance of proposed models was also investigated using intercorrelation analysis. Accuracy of prediction of proposed MAA models ranged from 90.4 to 91.6%
Angular distribution of cosmic rays from an individual source in a turbulent magnetic field
We obtain the angular distribution of the cosmic rays reaching an observer
from an individual source and after propagation through a turbulent magnetic
field, for different ratios between the source distance and the diffusion
length. We study both the high-energy quasi-rectilinear regime as well as the
transition towards the diffusive regime at lower energies where the deflections
become large. We consider the impact of energy losses, showing that they tend
to enhance the anisotropy of the source at a given energy. We also discuss
lensing effects, in particular those that could result from the regular
galactic magnetic field component, and show that the effect of the turbulent
extragalactic magnetic fields can smooth out the divergent magnification peaks
that would result for point-like sources in the limit of no turbulent
deflections.Comment: matches published versio
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