Topological Indices Research Articles

3D molecular structural modeling and characterization of indium phosphide via irregularity topological indices

Indium phosphide (InP) is a binary semiconductor composed of indium and phosphorus. It has a zinc blende crystal structure, which is a type of cubic lattice structure. This lattice is composed of indium and phosphorus atoms arranged in a lattice of cube-shaped cells, with each cell containing four indium atoms and four phosphorus atoms. This lattice structure is the same for all materials with a zinc blende crystal structure and is the most common type of lattice structure in semiconductors. Indium phosphide (InP) has several chemical applications. It is commonly used as a dopant in the production of semiconductors, where it helps control the electrical properties of the material. InP is also utilized in the synthesis various indium-containing compounds, which can have applications in catalysts and chemical reactions. Additionally, InP nanoparticles have been investigated for their potential use in biomedical imaging and drug delivery systems. The topological characterization of 3D molecular structures can be performed via graph theory. In graph theory, the connections between atoms are represented as edges and the atoms themselves are represented as nodes. Furthermore, graph theory can be used to calculate the topological descriptors of the molecule such as the degree-based and reverse degree-based irregularity toplogical indices. These descriptors can be used to compare the topology of different molecules. This paper deals with the modeling and topological characterization of indium phosphide (InP)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\ ext{InP}})$$\\end{document} via degree-based and reverse irregularity indices. The 3D crystal structure of the InP is topologically modeled via partition of the edges, and derived closed form expressions for its irregularity indices. Our obtained results will be surely be helpful in investigating the QSPR/QSAR analysis as well as understanding the deep irregular behavior of the indium phosphide (InP)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\ ext{InP}})$$\\end{document}.

Exploring supply chain and regional resilience through the analysis of the transport dimension

Despite the key role that global supply chains (GSC), and more specifically, the transport and logistics function, might play in the performance of regions, there is a lack of analytical tools that turn the data generated by supply chain operations into quantitative metrics allowing policymakers to identify early signals of potential vulnerabilities and assess how resilient the GSC are at regional level. In an effort to fill this gap, we present a Transportation Resilience Index (TRI) that permits evaluating how transport chains affect supply chain resilience and, consequently, regional resilience. Our index, based on publicly available data –statistics on foreign trade flows provided by the Spanish Customs, the World Bank’ Logistics Performance Index and the UNCTAD’ Bilateral Liner Shipping Connectivity Index − differentiates between the determinants over which the company has direct decision-making control, and those linked to the selection of the supply market (market and macro dimensions). The TRI is applied to the Spanish regions (NUTS2) by using the Benefit-of-the-Doubt (BoD) approach to Data Envelopment Analysis (DEA) and applying a Common Set of Weights (CSW) for the selection of the weights to the index components. In our specific analysis, the market and macroeconomic components account for 84% of the total weight of the TRI. Despite the lower relative weight of the company dimension, the high degree of homogeneity in the market and macroeconomic scores means the company dimension plays a key role in the relative resilience of the Spanish regions.

Cognitive Technology to Evaluate the Academic Learning of Computational Cognition in Psychology Students

<p style="text-align:justify">This study illustrated an alternative way to evaluate students’ academic learning. It involved the joint and intertwined application of the natural semantic network technique, computer simulations, and semantic priming experiments to assess the cognitive changes in knowledge structures due to academic learning in two groups of psychology students. The experimental group was enrolled in a course on computational cognition, while the control group was oblivious to this course. The results indicated that the cognitive assessment tools discriminate the cognitive changes produced as a result of general training undertaken in a psychology degree versus the influence of a specific course. After the course, the experimental group increased their technical vocabulary, changed their conceptual valuation of definers related to computational theories of mind, and reorganized the relations among definers according to the computational cognition approach. Also, this group presented a higher connectivity index between the concepts of the semantic network, their conceptual activation level and conceptual co-activation pattern changed, and their access level to the evaluated schema’s concepts improved. In contrast, the control group did not show significant changes in their cognitive patterns after the course. These findings suggest that cognitive tools may be helpful in the diagnosis of academic learning.</p>

Framework for a High-Throughput Screening Method to Assess Polymer/Plasticizer Miscibility: The Case of Hydrocarbons in Polyolefins.

Polymer composite materials require softening to reduce their glass transition temperature and improve processability. To this end, plasticizers (PLs), which are small organic molecules, are added to the polymer matrix. The miscibility of these PLs has a large impact on their effectiveness and, therefore, their interactions with the polymer matrix must be carefully considered. Many PL characteristics, including their size, topology, and flexibility, can impact their miscibility and, because of the exponentially large number of PLs, the current trial-and-error approach is very ineffective. In this work, we show that using coarse-grained molecular simulations of a small dataset of 48 PLs, it is possible to identify topological and thermodynamic descriptors that are proxy for their miscibility. Using ad-hoc molecular dynamics simulation setups that are relatively computationally inexpensive, we establish correlations between the PLs' topology, internal flexibility, thermodynamics of aggregation, and degree of miscibility, and use these descriptors to classify the molecules as miscible or immiscible. With all available data, we also construct a decision tree model, which achieves a F1 score of 0.86 ± 0.01 with repeated, stratified 5-fold cross-validation, indicating that this machine learning method can be a promising route to fully automate the screening. By evaluating the individual performance of the descriptors, we show this procedure enables a 10-fold reduction of the test space and provides the basis for the development of workflows that can efficiently screen PLs with a variety of topological features. The approach is used here to screen for apolar PLs in polyisoprene melts, but similar proxies would be valid for other polyolefins, while, in cases where polar interactions drive the miscibility, other descriptors are likely to be needed.

Hemodynamics and wall shear metrics in a pulmonary autograft: Comparing a fluid-structure interaction and computational fluid dynamics approach

ObjectiveIn young patients, aortic valve disease is often treated by placement of a pulmonary autograft (PA) which adapts to its new environment through growth and remodeling. To better understand the hemodynamic forces acting on the highly distensible PA in the acute phase after surgery, we developed a fluid-structure interaction (FSI) framework and comprehensively compared hemodynamics and wall shear-stress (WSS) metrics with a computational fluid dynamic (CFD) simulation. MethodsThe FSI framework couples a prestressed non-linear hyperelastic arterial tissue model with a fluid model using the in-house coupling code CoCoNuT. Geometry, material parameters and boundary conditions are based on in-vivo measurements. Hemodynamics, time-averaged WSS (TAWSS), oscillatory shear index (OSI) and topological shear variation index (TSVI) are evaluated qualitatively and quantitatively for 3 different sheeps. ResultsDespite systolic-to-diastolic volumetric changes of the PA in the order of 20 %, the point-by-point correlation of TAWSS and OSI obtained through CFD and FSI remains high (r > 0.9, p < 0.01) for TAWSS and (r > 0.8, p < 0.01) for OSI). Instantaneous WSS divergence patterns qualitatively preserve similarities, but large deformations of the PA leads to a decrease of the correlation between FSI and CFD resolved TSVI (r < 0.7, p < 0.01). Moderate co-localization between FSI and CFD is observed for low thresholds of TAWSS and high thresholds of OSI and TSVI. ConclusionFSI might be warranted if we were to use the TSVI as a mechano-biological driver for growth and remodeling of PA due to varying intra-vascular flow structures and near wall hemodynamics because of the large expansion of the PA.

Computation of molecular description of supramolecular Fuchsine model useful in medical data

Supramolecular chemistry is a fascinating field that explores the interactions between molecules to create higher-order structures. In the case of the supramolecular chain of Fuchsine acid, which is a type of dye molecule, several chemical applications are possible. Fuchsine acid helps to make better medicine carriers that deliver drugs where they’re needed in the body, making treatments more effective and reducing side effects. It also helps create smart materials like sensors and self-fixing plastics, which are useful in electronics, keeping our environment clean, and making new materials. In sensing and detection, the supramolecular chain of Fuchsine acid utilizes as a sensor or detector for specific analyzes. In drug delivery, the supramolecular chains of Fuchsine acid incorporated into drug delivery systems. In recent years, a common method is linking a graph to a chemical structure and using topological descriptors to study it. This technique is becoming increasingly important over time. Topological descriptors gives very useful information while studying the topology of chemical graph. In this paper, we have computed the 3D structure of supramolecular graph of Fuchsine acid. We have computed an explicit expressions of ABC index, GA index, General Randic´\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\acute{c}$$\\end{document} index, first and second Zagreb index, hyper Zagreb index, H-index and F-index of supramolecular structure of Fushine acid.

Analyzing polycyclic aromatic hydrocarbons using topological indices and QSPR analysis to reveal molecular complexity

Polycyclic aromatic hydrocarbons (PAHs) have distinctive chemical structures and are well known for their wide range of uses and environmental relevance. This work explores the impact of these structural characteristics on eccentricity-based topological indices offering information about the arrangement of atoms within the molecules. This study uses quantitative structure-property relationship (QSPR) analysis to construct prediction models for understanding and forecasting specific PAHs including Dibenzo[e,l]Pyrene, Heptacence, Heptaphene, Naphthacene, Naphthalene, Naphto[1,2a]pyrene, Naphtho[2,3a]pyrene, perylene, Perylene, Picene, Phenanthrene, Pyrene, Tetraphene, Tribenzo[b,n,pqr]perylene, Tribenzo[a,fg,op]tetracene and Triphenylene. Furthermore, regression analysis applies to clarify the quantitative correlations between the factors under study and improves the interpretability of the data produced. The combined use of these diverse approaches advances a thorough comprehension of the mutual influence of chemical structure, topological indices and predictive modeling about PAHs.

Extremal values of degree-based entropies of bipartite graphs

We characterize the bipartite graphs that minimize the (first degree-based) entropy among all bipartite graphs of given size. For bipartite graphs given size and (upper bound on the) order, we give a lower bound for this entropy. The extremal graphs turn out to be complete bipartite graphs, or nearly complete bipartite. Here we make use of an equivalent representation of bipartite graphs by means of Young diagrams, which make it easier to compare the entropy of related graphs. We conclude that the general characterization of the extremal graphs is a difficult problem, due to its connections with number theory. However, it is easier to identify them for particular values of the order n and size m because we have narrowed down the possible extremal graphs. We indicate that some of our ideas extend to other degree-based topological indices as well.

Computing Certain Topological Indices of Silicate Triangle Fractal Network Modeled by the Sierpiński Triangle Network

The study of Sierpiński triangle network and extended Sierpiński graph is quite interesting in the field of fractal networks. In nature, fractal networks (FN) and silicate structure networks (Sio4) play vital roles and in architecture to analyze the dimension of the above-mentioned FN and Sio4 networks it is necessary to identify the number of copies of the network. In this paper, we introduced a silicate triangle fractal network (Sin) which is a planar fractal and it is created using a related sequence of graphs named (Sin)n≥0, where n is the nth level of silicate triangle fractal network. We analyze the topological indices (TI) of the silicate triangle fractal network Sin graph and compare the calculated topological indices to the number of copies of silicate structure (Sio4) in each iteration of Sin for a sequence of a graph.

Stress-difference index for graphs

The stress of a vertex is a node centrality index, which has been introduced by Shimbel (1953). The stress of a vertex in a graph is the number of geodesics (shortest paths) passing through it. A topological index of a chemical structure (graph) is a number that correlates the chemical structure with chemical reactivity or physical properties. In this paper, we introduce a new topological index for graphs called stress-difference index using stresses of vertices. Further, we establish some inequalities, prove some results and compute stress-difference index for some standard graphs. Also, we found that there is a positive correlation between the stress-difference index and some physical properties of lower alkanes.

Coexistence of superconductivity and topological phase in kagome metals ANb3Bi5 (A = K, Rb, Cs)

The AV3Sb5 prototype kagome materials have been demonstrated as a versatile platform for exploring exotic properties in condensed matter physics, including charge density waves, superconductivity, non-trivial electron topology, as well as topological superconductivity. Here we identify that ANb3Bi5 (A = K, Rb, Cs) exhibit non-trivial coexisting superconductivity and topological properties via first-principles calculations. The negative formation energy and the absence of imaginary phonon dispersion demonstrate both thermodynamics and dynamics stabilities of ANb3Bi5 (A = K, Rb, Cs) under ambient conditions. By analytically solving the Allen-Dynes-modified McMillan formula, the superconducting transition temperatures are predicted to be 2.11, 2.15 and 2.21 K for KNb3Bi5, RbNb3Bi5, and CsNb3Bi5, respectively. More importantly, the kagome materials proposed here can be classified into Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb{Z}}}_{2}$$\\end{document} topological metals due to the non-trivial topological index and the obvious surface states around the Fermi level. Such coexistence of superconductivity and non-trivial band characters in ANb3Bi5 (A = K, Rb, Cs) offer us more insights to study the relationship between superconductivity and topological properties, and to design innate topological superconductors.

A Corpus-Based Study on Cohesion Development in Writing by EFL Novices

This corpus-based study explored the development of cohesive devices in the writing of Chinese beginner learners of English as a foreign language (EFL) over a three-year span. Quantitative analysis utilizing the Tool for Automatic Analysis of Cohesion (TAACO) was conducted on a longitudinal learner corpus comprising over 500 exam essays. Lexical, syntactic, semantic, and discourse features were examined to identify reliable indices for tracking learners’ progressive mastery of cohesion. Results revealed that pronoun-related features, including pronoun density and repetition, significantly differed across year pairs and robustly predicted writing development. However, most lexical and connective indices showed ambiguous trajectories over time. The findings highlight the vital role of pronouns in building coherence for novice writers and underscore persistent difficulties in acquiring sophisticated content words and their collocations. This study contributes data-driven insights into the nonlinear processes and enduring challenges shaping EFL beginners’ cohesive competence. It demonstrates the value of computational tools and learner corpora in exploring discourse acquisition.

Multicriteria decision making attributes and estimation of physicochemical properties of kidney cancer drugs via topological descriptors.

Based on topological descriptors, QSPR analysis is an incredibly helpful statistical method for examining many physical and chemical properties of compounds without demanding costly and time-consuming laboratory tests. Firstly, we discuss and provide research on kidney cancer drugs using topological indices and done partition of the edges of kidney cancer drugs which are based on the degree. Secondly, we examine the attributes of nineteen drugs casodex, eligard, mitoxanrone, rubraca, and zoladex, etc and among others, using linear QSPR model. The study in the article not only demonstrates a good correlation between TIs and physical characteristics with the QSPR model being the most suitable for predicting complexity, enthalpy, molar refractivity, and other factors and a best-fit model is attained in this study. This theoretical approach might benefit chemists and professionals in the pharmaceutical industry to forecast the characteristics of kidney cancer therapies. This leads towards new opportunities to paved the way for drug discovery and the formation of efficient and suitable treatment options in therapeutic targeting. We also employed multicriteria decision making techniques like COPRAS and PROMETHEE-II for ranking of said disease treatment drugs and physicochemical characteristics.

Data-driven, explainable machine learning model for predicting volatile organic compounds’ standard vaporization enthalpy

The accurate prediction of standard vaporization enthalpy (ΔvapHm°) for volatile organic compounds (VOCs) is of paramount importance in environmental chemistry, industrial applications and regulatory compliance. To overcome traditional experimental methods for predicting ΔvapHm° of VOCs, machine learning (ML) models enable a high-throughput, cost-effective property estimation. But despite a rising momentum, existing ML algorithms still present limitations in prediction accuracy and broad chemical applications.In this work, we present a data driven, explainable supervised ML model to predict ΔvapHm° of VOCs. The model was built on an established experimental database of 2410 unique molecules and 223 VOCs categorized by chemical groups. Using supervised ML regression algorithms, the Random Forest successfully predicted VOCs' ΔvapHm° with a mean absolute error of 3.02 kJ mol−1 and a 95% test score. The model was successfully validated through the prediction of ΔvapHm° for a known database of VOCs and through molecular group hold-out tests. Through chemical feature importance analysis, this explainable model revealed that VOC polarizability, connectivity indexes and electrotopological state are key for the model's prediction accuracy. We thus present a replicable and explainable model, which can be further expanded towards the prediction of other thermodynamic properties of VOCs.

QSPR analysis of anti‐asthmatic drugs using some new distance‐based topological indices: A comparative study

AbstractAsthma is a widespread disease that has affected more than 300 million people worldwide. There is no efficient or preventive treatment for this disease yet. Drug scientists are striving hard to discover a variety of medicines that can treat asthma effectively. Quantitative structure‐property relationship (QSPR) analysis of drugs used in the treatment of a specific disease through topological descriptors is one of the best techniques adopted by drug scientists to cut down unnecessary laboratory expenses. In this article, we have done a QSPR analysis to identify the best predictor for the six properties namely, boiling point, enthalpy, flash point, log P, molar volume, and molar refractivity of 19 different anti‐asthmatic drugs using a set of 16 distance‐based topological indices. Also, we compare our results with QSPR analysis done by using certain degree‐based indices for the chosen drugs and obtain new directions.

Variation in Debris-Flow-Prone Areas with Ecosystem Stability: A Case Study of the Qipan Catchment in the Wenchuan Earthquake Region

The spatial distribution of vegetation in a basin has a far-reaching influence on the potential for sediment separation and transport capacity. However, many landslides induced by strong earthquakes have greatly changed the existing pattern, which further increases the probability of debris flow in a basin during heavy rainfall and has a significant impact on the stability of the basin. Thus, this study selected the debris flow basin in the Qipan catchment of the Wenchuan earthquake area as the research object. Multisource and high-precision remote sensing images were used to analyze the land use changes in the basin, and the index of connectivity (IC) was introduced to analyze the evolution of sediment transport capacity. An ecosystem stability assessment method suitable for post-earthquake debris flow basins was proposed. Through quantitative assessment of the ecosystem stability of the basin after the Wenchuan earthquake in 2008 and the two debris flow events after the earthquake, the dynamic relationship between the debris-flow-prone area and the ecosystem stability of the basin was revealed. The results showed that the stability of the ecosystem in the Qipan catchment increased annually, indicating a stable and substable state. The spatial distribution characteristics were lower in the north and south and greater in the middle. By comparing the evaluation results with the actual terrain change trend, the accuracy and feasibility of the evaluation method are verified. The results of this study provide a scientific basis for the formulation of regional disaster prevention strategies and help to accelerate the improvement of regional stability in debris-flow-prone areas.

Spatial variation characteristics and influencing factors of sediment connectivity in the black soil region of northeast China

Connectivity has become an important indicator of the sediment transfer potential through sediment sources to catchment sinks. Connectivity plays a vital role in investigating the rate of soil erosion caused by runoff and sediment output across the watershed landscape. However, there have been few quantitative studies on the spatial variations in sediment connectivity in the black soil region of Northeast China. Seven classic watersheds in the northeast black soil region were selected to discover spatial variations in sediment connectivity and their influencing factors. The connectivity index (IC) was used to study the spatial variation of sediment connectivity, and the weight of IC was calculated using the vegetation cover management factor (C), which reflected the influence of human activities on the soil erosion process caused by cultivated land expansion and encroachment of forest grassland. The redundancy analysis method (RDA) was used to determine the main factors affecting the spatial variation of IC. The results showed that IC decreased from north (0.45) to south (0.12). The spatial variations of watersheds in sediment connectivity showed significant spatial heterogeneity. IC was correlated with topographic, climatic, and artificial management characteristics at 0.01 or 0.05 levels except soil structural index; RDA results showed that topography and human activities were the main factors affecting sediment connectivity. Topographic and climatic factors explained more sediment connectivity changes in the southern watersheds than in the northern watersheds, while the human activities factor explanation was the opposite of topographic factors. Human activities refer to changes in vegetation cover and soil structure and properties resulting from human logging and farming that affect sediment connectivity.

Topological indices & Hirshfeld pseudo-surfaces synergy to understand the radiation attenuation in materials: Case of study spinel mineral crystals

The present work deals with the radiation attenuation characteristics of spinel minerals, a unique class of minerals with diverse crystalline structures and chemical compositions. We analyze the MAC and LAC in various photon energy spectrum using XCOM and Phys-X software tools. In addition to traditional methods, we employ topological indices (TIs) and Hirshfeld pseudo-surfaces (HPSs) to explore the atomic interactions and electron density distributions within these minerals to pinpointed their effects on the on these γ-radiation attenuation coefficients. Our findings reveal that MAC values decrease with increasing photon energy, a trend observed across all studied spinel minerals. The use of the HPSs provides visual insights into electron density distributions and intermolecular interactions mastered by 2D fingerprints which are correlated with the γ-attenuation of these spinels crystal. Linear regression correlations between TIs and MAC, LAC values demonstrate strong relationships, with the first Zagreb coindex and the Forgotten Index (F-index) emerging as reliable predictors of γ-rays radiations shield properties.

A mathematical approach to optimizing brand school placement via intuitionistic Sombor indices

The property of fuzziness is advantageous for any setting where a problem prediction and solution are intended. In comparison to the classical approach (crisp set), fuzzy graphs are beneficial as they provide greater precision and flexibility. Intuitionistic fuzzy graphs (IFGs) are generalizations of fuzzy graphs, in which each vertex is allocated an ordered pair whose first coordinate represents the membership value and whose second coordinate gives the non-membership value. Sombor indices are recently invented indices and are prime indices in describing the topology of a graph. They have demonstrated strong prediction ability in mathematical chemistry. The main aim of this research draft is to define two milestones, the fifth and sixth versions of Sombor indices in an intuitionistic fuzzy environment, IFGs are much more generalized and universal as compared to crisp graph theory, so we converted these two topological indices in this environment and then formulae for some fundamental families of graphs such as path graph, cycle graph, complete graph etc. are being derived. Our manuscript presents a novel application of opening a chain of schools of a popular brand in a certain vicinity, including the cluster center of the chain and applying intuitionistic fuzzy-based topological indices to assess their performance. With the help of this application, we highlight the practical implications and benefits of employing intuitionistic fuzzy-based techniques on the performance of schools through a comparative analysis. We checked the importance of intuitionistic fuzzy Sombor indices by presenting the application and concluded these indices can be applied to decision-making problems. With the help of the application, the efficiency of both of the intuitionistic fuzzy Sombor indices is also characterized, which must be a future efficacious tool in decision-making issues.

Differential equations with maximal monotone operators

The paper deals with multivalued differential equations in abstract spaces. Nonlocal conditions are assumed. The model includes an m-dissipative multioperator which generates an equicontinuous, not necessarily compact, semigroup. The regularity of the nonlinear term also depends on the Hausdorff measure of noncompactness. The existence of integral solutions is discussed, with a topological index argument. A transversality condition is required. The results are applied to a partial differential inclusion in a bounded domain in Rn with nonlocal integral conditions. The model also includes an m-dissipative but not necessarily compact semigroup generated by a suitable subdifferential operator.