Weighted Distance Matrix Research Articles

On COVID-19 country containment metrics: a new approach

ABSTRACT The containment of COVID-19 is an important issue. We obtain the raw COVID-19 data of 3144 counties and equivalents in the USA regarding the confirmed cases and death cases from 22 January to 1 July. We devise a free interval metric to measure the distance between case distributions at different dates. This metric is useful in taking structures into consideration. Based on this metric, we calculate the distance matrices for both the confirmed cases and death cases with respect to dates. Then, we combine them to yield a weighted distance matrix. With this matrix, we compute the time series of average variance and average distance – both could serve the indicators for the containment of COVID-19. Our approaches and definitions show that COVID-19 is not yet contained in the USA. We also provide some graphical results to demonstrate our findings and compare ours with the other typical approach.

A new method for isomorphism identification of planetary gear trains

Abstract. Planetary gear trains (PGTs) are widely used in machinery such as vehicles, pulley blocks, wrist watches, machine tools, and robots. During the process of structural synthesis of PGTs using graph theory, isomorphism identification of graphs is an important and complicated problem. The reliability of the isomorphism detection method directly determines the accuracy of the synthesis result. In this paper, a novel isomorphism identification method for PGTs is proposed. First, a new weighted adjacent matrix is presented to describe the topological graph of PGTs, which has is unique in describing the structure of PGTs. Then, the weighted distance matrix is proposed and the sum of the matrix is obtained, which can determine whether the planetary gear trains is isomorphic or not. Eventually, the examples demonstrate that this new method can be accurately and effectively performed.

Molecular descriptors-based models for estimating net heat of combustion of chemical compounds

The heating values of fuels are determined by Heat of Combustion (ΔHC∘)in which the higher amount is more lucrative. Moreover, one of the best methods to compare the stabilities of chemical materials is using ΔHC∘. Therefore, improving precise and general models to estimate this property in different areas such as industries and academic perspective should be considered. In this study, three models namely Least Square Support Vector Machine optimized by Coupled Simulated Annealing optimization algorithm (CSA-LSSVM), Genetic Programming (GP) and Adaptive-Neuro Fuzzy Inference System optimized by PSO, and GA methods (PSO-ANFIS and GA-ANFIS) were applied to estimate ΔHC∘ Also, ΔHC∘ can be expressed by the GP model with an equation. The input parameters of the models are total carbon atoms in a molecule (nC), sum of atomic van der Waals volumes (scaled on carbon atom) (Sv), Broto–Moreau autocorrelation of a topological structure (ATS2m), and total Eigenvalue from electronegativity weighted distance matrix (siege). In addition, two parameter models based on measureable variables of nC and Sv are proposed. In a comprehensive set, 1714 data points were used to fulfill and develop the models. Results demonstrate that the models are trustworthy and accurate (especially the PSO-ANFIS model) in comparison with other recently developed literature models.

The asymptotic value of energy for matrices with degree-distance-based entries of random graphs

For a graph G=(V,E) and i,j∈V, denote the distance between i and j in G by D(i,j) and the degrees of i, j by di, dj, respectively. Let f(D(i,j),di,dj) be a function symmetric in i and j. Define a matrix Wf(G), called the weighted distance matrix, of G, with the ij-entry Wf(G)(i,j)=f(D(i,j),di,dj) if i≠j and Wf(G)(i,j)=0 if i=j. In this paper, we prove that if the symmetric function f satisfies that f(D(i,j),(1+o(1))np,(1+o(1))np)=(1+o(1))f(D(i,j),np,np), then for almost all graphs Gp in the Erdo¨s-Re´nyi random graph model Gn,p, the energy of Wf(Gp) is {(83πp(1−p)+o(1))⋅|f(1,np,np)−f(2,np,np)|+o(|f(2,np,np)|)}⋅n3/2. As a consequence, we give the asymptotic values of energies of a variety of weighted distance matrices with function f from distance-based only and mixed with degree-distance-based topological indices of chemical use. This generalizes our former result with only degree-based weights.

Cross-View Self-Similarity Using Shared Dictionary Learning for Cervical Cancer Staging

Dictionary Learning (DL) has gained large popularity in solving different computer vision and medical image problems. However, to the best of our knowledge, it has not been used for cervical tumor staging. More importantly, there have been very limited works on how to aggregate different interactions across data views using DL. As a contribution, we propose a novel cross-view self-similarity low rank shared dictionary learning-based (CVSS-LRSDL) framework, which introduces three major contributions in medical image-based cervical cancer staging: (1) leveraging the complementary of axial and sagittal T2w-magnetic resonance (MR) views for cervical cancer diagnosis, (2) introducing self-similarity (SS) patches for DL training, which explore the unidirectional interaction from a source view to a target one, and (3) extracting features that are shared across tumor grades and grade-specific features using the CVSS-LRSDL learning approach. For the first and second contributions, given an input patch in the source view (axial T2w-MR images), we generate its SS patches within a fixed neighborhood in the target view (sagittal T2w-MR images). Specifically, we produce a unidirectional patch-wise SS from a source to a target view, based on mutual and additional information between both views. As for the third contribution, we represent each individual subject using the weighted distance matrix between views, which is used to train our DL-based classifier to output the label for a new testing subject. Overall, our framework outperformed several DL based multi-label classification methods trained using: (i) patch intensities, (ii) SS single-view patches, and (iii) weighted-SS single-view patches. We evaluated our CVSS-LRSDL framework using 15 T2w-MRI sequences with axial and sagittal views. Our CVSS-LRSDL significantly ( $\text{p} ) outperformed several comparison methods and obtained an average accuracy of 81.73% for cervical cancer staging.

A nomenclature algorithm for a potentially global soil taxonomy

Previous work has been put into the creation of a global soil taxonomy using a harmonised dataset of 23 soil properties at 18 depth intervals. The taxonomy consisted of selected soil taxa from the US Soil Taxonomy, World Reference Base for Soil Resources, the Australian Soil Classification, and the New Zealand Soil Classification. In this paper, a nomenclature algorithm was proposed for this established comprehensive taxonomy. Firstly, a Ward dendrogram was calculated from a weighted distance matrix determined from principal components of the taxa. This dendrogram was then cut at three levels, creating 15 groups, 86 subgroups, and 493 sub-subgroups at tiers 1, 2 and 3, respectively. A sequence of consonants was used to name the taxa at each tier alphabetically with “A” and “E” inserted between the consonants of tiers 2 and 3 and “OZEM” appended after the consonants of tier 1. In addition, a distance-based algorithm was used to allocate and name 10 unknown soil profiles to the comprehensive soil taxonomy. It was concluded that the nomenclature algorithm can be easily disaggregated by computer and can be used to understand the inter-relationships between soil profiles from different classification systems. In the future, there is a need to include other soil classification systems to the comprehensive system and assign different weights to the soil properties and depths used to construct the comprehensive soil classification system.

Health, emergency facilities and development: Locating facilities to serve people and development better

Health is a major factor in development and it is central to the theory about human capital and endogenous growth. This is because health affects all other economic and development activities. The World Health Organization’s (2003) call for “Health for all” which argues that “everybody needs and is entitled to the highest possible standard of health” is a coherent and indispensable vision for global health and development. The importance of health for development is also highlighted in the Millennium Development Goals (MDGs) where three of the eight MDGs goals focused on health. So far global actions to promote health for development have focused heavily on primary health care and it is right to do so given the importance of the burden of diseases in low and middle income countries (LMICs). However, there is a missing link. Despite their importance, emergency facilities and emergency services have become the poorer cousins of the global health and development effort. We analyze the relationship between emergency facilities, health care delivery and development and develop a simple heuristic or mathematical algorithm for effective location of facilities for regional or diversified health care systems. We modified a greedy (myopic) algorithm of the p -median location problem by using a reduced matrix for the determination of facilities. We illustrate how additional facilities can be located using a 5-node weighted distance matrix. We locate two facilities using the Myopic algorithm and showed how the two facilities could serve all the customers (demands) at nodes 1, 2, 3, 4 and 5. Our heuristic reduced the computational and time costs as well as performance of existing location problems as well as made location of additional facilities more user friendly in our view. We compare our new method with the original greedy algorithm using a 400 random problem. The results demonstrate the efficiency and superiority of our new method resulting in the reduction cost of locating a facility using our new algorithm by up to 64%.

Genetic characterization of Brucella melitensis and Brucella abortus geographical clusters in Italy.

The genetic diversity of Brucella melitensis and Brucella abortus strains isolated in 199 cattle and sheep from 156 brucellosis outbreaks which occurred in 8 regions of Southern Italy in 2011, was determined using a Multiple-Locus Variable Number of Tandem Repeats Analysis approach. The existence of possible genetic clusters was verified through a hierarchical cluster analysis based on 'single link', which is closely related to the minimum spanning tree. The Hamming weighted distance matrix was adopted in the analysis. All calculations were performed using R and the additional libraries phangorn and Cluster. For a number of clusters, ranging from 2 to 15, the average silhouette width was calculated. The number of clusters adopted was identified according to the maximum average silhouette width. For B. abortus and B. melitensis, 6 and 11 genetic clusters were identified, respectively. Three out of 6 B. abortus clusters included the 96.7% of all B. abortus isolates. Clusters were clearly geographically separated, and this highlighted the known epidemiological links among them. Brucella melitensis genotypes resulted more heterogeneous; the 3 more representative genetic clusters included 79.7% of all B. melitensis isolates. A clear geographical clusterization of genotypes is recognizable only for 1 cluster, whereas the others are more widespread across Southern Italy. The genetic characterization of Brucella strains isolated from animals may be a useful tool to better understand the epidemiology and dissemination patterns of this pathogen through host populations.

Chemometric Descriptor Based QSAR Rationales for the MMP-13 Inhibition Activity of Non-Zinc-Chelating Compounds

The MMP-13 inhibition activity of non-zinc-chelating compounds has been quantitatively analyzed in terms of chemometric descriptors. The statistically validated quantitative structure-activity relationship (QSAR) models provided rationales to explain the inhibition activity of these compounds. The descriptors, identified through combinatorial protocol in multiple linear regression (CP-MLR) analysis, have highlighted the role of 3-path Kier alpha-modified shape index (S3K), complementary information content index of 1-order neighborhood symmetry (CIC1), eigenvalue sum from mass weighted distance matrix (SEigm), lowest eigenvalue n. 6 of Burden matrix / weighted by atomic van der Waals volumes (BELv6) and by atomic polarizabilities (BELp6), 3-order topological charge index (GGI3) and the functionality, R--CR--R (C-025). From statistically validated models, it appeared that the descriptors S3K, BELv6, BELp6 and SEigm make positive contribution to activity and their higher values are conducive in improving the MMP- 13 inhibition activity of a compound. On the other hand, the descriptors CIC1, GGI3 and C-025 render detrimental effects to activity. Therefore, the absence of functionality, R--CR--R and lower values of descriptors CIC1 and GGI3 would be advantageous. PLS analysis has further corroborated the dominance of the CP-MLR identified descriptors. Applicability domain analysis revealed that the suggested models have acceptable predictability. All the compounds are within the applicability domain of the proposed models and were evaluated correctly.

Structural Findings of 2‐Phenylindole‐3‐Carbaldehyde Derivatives for Antimitotic Activity by FA‐sMLR QSAR Analysis

Antimitotic agents prevent the mitosis process of cell cycle and are generally used for the treatment of cancer with good clinical success. QSAR analysis was performed on 33 reported 2-phenylindole-3-carbaldehyde derivatives to find out the structural requirements of these compounds for higher antimitotic activity. The dataset was divided into test set and training set by k-MCA. Factor analysis-stepwise multiple linear regression (FA-sMLR) method was used to develop statistically significant QSAR equations. QSAR analysis showed importance of topological indices like RTSA indices, structural information content indices, Balaban-type index from van der Waals weighted distance matrix Jhetv, rotatable bond fraction RBF, and Lovasz-Pelikan index LP1 on biological activity. The study also shows significance of electrostatic potential charges of different atoms as well as principal moment of inertia along Y axis and number of nitrogen atoms toward antimitotic activity of these compounds.

CP-MLR directed QSAR study of carbonic anhydrase inhibitors: sulfonamide and sulfamate inhibitors

Abstract The inhibition activities of sulfonamide and sulfamate derivatives for human carbonic anhydrases have been quantitatively analyzed using DRAGON descriptors. QSAR models have been obtained through combinatorial protocol-multiple linear regression (CP-MLR) computational procedure. For the hCA I inhibition activity, a higher value of information content index of the 1-order neighborhood symmetry (IC1) and a lower value of the Moran autocorrelations, MATS2v and MATS1p, along with a lower number of sulfur atoms in a molecular structure (nRSR) is beneficial to the activity. A higher number of 5-membered rings (nR05), a bigger distance between nitrogen and sulfur T(N..S), and a higher value of van der Waals volume weighted descriptor (GATS6v), are helpful to improve the hCA II inhibition activity. For the inhibition of hpCA, a lower value of the descriptors Jhetv and PW5, and higher values of the eigenvalue sum from Z weighted distance matrix, SEigZ, the Moran autocorrelation of lag 8 weighted by atomic van der Waals volumes, MATS8v and the Moran autocorrelation of lag 4 weighted by atomic Sanderson electronegativities, MATS4e are favorable. The derived significant models in such descriptors may further be used to synthesize new potential compounds and to decipher the mode of their actions at molecular level.

Comparative structure–toxicity relationship study of substituted benzenes to Tetrahymena pyriformis using shuffling-adaptive neuro fuzzy inference system and artificial neural networks

The purpose of this study was to develop the structure–toxicity relationships for a large group of 268 substituted benzene to the ciliate Tetrahymena pyriformis using mechanistically interpretable descriptors. The shuffling-adaptive neuro fuzzy inference system (Shuffling-ANFIS) has been successfully applied to select the important factors affecting the toxicity of substituted benzenes to T. pyriformis. The results of the proposed model were compared with the model of linear-free energy response surface and also the principal component analysis Bayesian-regularized neural network (PCA-BRANN) trained using the same data. The presented model shows a better statistical parameter in comparison with the previous models. The results of the model are promising and descriptive. Five descriptors of octanol–water partition coefficient (log P), bond information content (BIC0), number of R-CX-R (C-026), eigenvalue sum from Z weighted distance matrix (SEigZ) and fragment based polar surface area (PSA) selected by Shuffling-ANFIS reveal the role of hydrophobicity, electronic and steric interactions in the mechanism of toxic action. Sequential zeroing of weights (SZW) as a sensitivity analysis method revealed that the hydrophobicity and electronic interactions play a major role in toxicity of these compounds. Satisfactory results ( q 2 = 0.828 and RMSE = 0.348) in comparison with the previous works indicate that the Shuffling-ANFIS-ANN technique is able to model a diverse chemical class with more than one mechanism of toxicity by using simple and interpretable descriptors. Shuffling-ANFIS can be used as powerful feature selection technique, because its application in prediction of toxicity potency results in good statistical and interpretable physiochemical parameters.