Inverse Sum Research Articles

A new spectral-based index for graphs and its application to polyaromatic compounds

In this study, we introduce a novel index called the modified inverse sum indeg (MISI) energy as an extension of the traditional inverse sum indeg (ISI) energy and neighbor degree sum energy. We devised an algorithm that employs the simplified molecular input line entry system (SMILES) formula of compounds to compute the MISI energy of polycyclic aromatic hydrocarbon (PAH). Additionally, we established the bounds of the MISI energy for certain classes of graphs with fixed number of vertices. A strong correlation between the MISI energy and the total [Formula: see text]-electron energy of PAHs is observed through regression analysis. Remarkably, this correlation outperforms that achieved by the classical ISI energy. These findings highlight the enhanced effectiveness of the MISI energy as a descriptor for capturing significant molecular properties. Moreover, our study establishes a foundation for further theoretical extensions and practical applications in the field of chemical graph theory.

The causal association between epilepsy and amyotrophic lateral sclerosis: A two-sample Mendelian randomization study.

Epilepsy and amyotrophic lateral sclerosis (ALS) are common neurological disorders. The association between the two disorders has been raised in observational studies. However, it is uncertain to what extent they have mutual causal effects. In this study, we aimed to investigate their causal association using a two-sample Mendelian randomization (MR) method. We performed a two-sample bidirectional MR analysis to evaluate the causal association of epilepsy with the risk of ALS. Publicly published genome-wide association study statistics for epilepsy and ALS were used in the study. The primary analysis included genetic variants with a p value of less than 1 × 10-5 as instrumental variables. We applied several alternative methods, including inverse variance weighting, weighted median, simple mode, weighted mode, MR-Egger regression and MR pleiotropy residual sum and outlier, and statistical graphs to assess the associations of epilepsy and its subtype with the risk of ALS. Reverse MR analyses were also performed to examine the association of ALS with the risk of epilepsy. The primary MR analysis found no causal effect of epilepsy on risk of ALS (odds ration [OR]: 1.133, 95% confidence interval [CI]: 0.964-1.332, p=.130). Among subtypes of epilepsy, it also failed to observe any causal association between general epilepsy and ALS (OR: 1.036, 95% CI: 0.969-1.108, P=.300). However, focal epilepsy contributed to an increase in the risk of ALS (OR: 1.177, 95% CI: 1.027-1.348, p=.019). Moreover, the investigation of reverse causalities did not reveal significant results. The current study supports a causal influence of focal epilepsy on ALS risk. Future studies are needed to explore its potential role in ALS.

Analyzing topological descriptors of guar gum and its derivatives for predicting physical properties in carbohydrates

Guar gum is a non-ionic polysaccharide found in abundance in nature. It may be used as a thickening agent, stabilizer, or emulsifier in pharmaceutical formulations, food products, or cosmetics. Its ability to form viscous solutions makes it useful in drug delivery systems, controlled release formulations, and as a matrix for oral drug delivery. The investigation of chemical structures through graph invariants is of great concern. Topological descriptors are numerical numbers associated with the molecular structure and have the ability to predict certain physical and chemical properties of the underlying structure. In this paper, we have calculated the harmonic index, the inverse sum indeg index, the third Zagreb index, the Hyper Zagreb index, the sigma index, the reformulated first Zagreb index, the reformulated multiplicative first Zagreb index, the Harmonic–arithmetic index, and the Atom Bond sum connectivity indices of guar gum and its chemical derivatives. Finally, the chemical applicability of these topological descriptors is checked for different carbohydrates (monosaccharides, disaccharides, and polysaccharides) by using straight-line, parabolic and logarithmic regression models. It has been observed that these topological descriptors are useful to predict two physical properties, namely density and molecular weight.

Molecular structure of DNA via Zagreb connection descriptors.

Topological indices quantify the connectivity and structural properties of chemical compounds. We use the topological indices for predicting and evaluating the numerous properties of molecules, such as boiling temperatures, toxicity, and biological activity. Zagreb connection indices are a useful tool for studying the structural characteristics of the DNA backbone network. These indices provide important information on the arrangement and connections between nucleotide bases inside the DNA molecule. These indices show compactness, complexity, and topological properties in order to predict DNA bending propensity, DNA-protein interaction, and DNA stability. DNA folding patterns and the impact of mutations on DNA networks are areas of further research for these topological indices. In this study, we calculate Zagreb connection indices and modified Zagreb connection indices for backbone DNA network and subdivided backbone DNA network. Furthermore, we compute the hyper-Zagreb connection index, the inverse sum connection index, and the harmonic connection index.

Computation of differential and integral operators using [formula omitted]-polynomials of gold crystal

Gold is generally considered a noble metal since it is inherently inert in its bulk state. However, gold demonstrates reactivity when it is in its ionic state. The inherent inertness of bulk gold has resulted in its widespread recognition as a vital raw material in various biomedical processes. The applications of these technologies include drug delivery microchips, dental prostheses, reconstructive surgery, culinary additives, and cardiovascular stents. Gold can also exist in molecules or ions, particularly gold ions, which facilitates the production of gold nanomaterials. In this paper, we have computed differential and integral operators by using the M-Polynomial of gold crystals and by utilizing this polynomial, we have also computed eleven topological indices like 1st Zagreb, 2nd Zagreb, Hyper, Sigma, Second Modified, General Randic, General Reciprocal Randic, 3rd Redefined Zagreb, Symmetric Division Degree, Harmonic, Inverse Sum indices for the structure of Gold crystal.

Tridiagonal and single-pair matrices and the inverse sum of two single-pair matrices

A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent factorizations are established, leading to semi-closed-form formulas for the inverse sum of two single-pair matrices. An application to derive the symbolic inverse of a particular Gram matrix is presented, and the numerical stability of the formulas is studied.

New bounds for variable topological indices and applications

One of the most important information related to molecular graphs is given by the determination (when possible) of upper and lower bounds for their corresponding topological indices. Such bounds allow to establish the approximate range of the topological indices in terms of molecular structural parameters. The purpose of this paper is to provide new inequalities relating several classes of variable topological indices including the first and second general Zagreb indices, the general sum-connectivity index, and the variable inverse sum deg index. Also, upper and lower bounds on the inverse degree in terms of the first general Zagreb are found. Moreover, the characterization of extremal graphs with respect to many of these inequalities is obtained. Finally, some applications are given.

A Computational Approach on Fenofibrate Drug Using Degree-Based Topological Indices and M-polynomials

Fenofibrate is a drug approved by FDA Food and Drugs Administration used to treat patients with Hypertrigly ceridemia primary hypercholesterolemia or mixed dyslipidemia. It reduces low-density lipoprotein cholesterol (LDL-c), total cholesterol, triglycerides, and apolipoprotein B and increases high -density lipoprotein cholesterol (HDL-C) in adults. The sum and multiplicative versions of several topological indices such as General Zagreb, General Randic, Arithmetic Geometric Index, Inverse sum (Indeg) Index, Symmetric Division (Deg) Index, Forgotten Indices M-polynomials of Fenofibrate are computed in this article.

Topological Invariants of Hexagonal Cage Network by Using Algebraic Polynomials

In this article, we go beyond earlier limits in the analysis by using algebraic polynomials to compute the topological indices for hexagonal cage networks. We investigate hexagonal cage networks of different orders and copies by introducing M-Polynomials and Forgotten polynomials, and we derive novel closed formulae and conclusions for a broad range of topological indices. We also create an efficient technique to compute , a pivotal polynomial, as part of our work. In addition to computing, we apply algebraic polynomials to the analysis of these indices, providing more insights into their structural significance in hexagonal cage networks. This work illuminates the algebraic underpinnings of these intricate networks and broadens the scope of topological index computation, with implications for a variety of scientific domains. These polynomials allow us to calculate several features of the network, such as the first and second Zagreb, modified Zagreb, General Randić, inverse General Randić, harmonic, symmetric division, inverse sum, and so on. There are now new closed formulae and outcomes available. Additionally, we offer a technique for calculating the polynomial . We also use algebraic polynomials to analyses all of the aforementioned indices.

Potential causal associations between leisure sedentary behaviors, physical activity, sleep traits, and myopia: a Mendelian randomization study

BackgroundMyopia is the most prevalent refractive error and a growing global health concern that significantly affects visual function. Researchers have recently emphasized considerably on the influence of lifestyle on myopia incidence and development. This study investigates the relationship between leisure sedentary behaviors (LSB)/physical activity (PA)/sleep traits and myopia.MethodsLSB, PA, and sleep trait-associated genetic variants were used as instrument variables in a Mendelian randomization (MR) study to examine their causal effects on myopia. Summary genome-wide association studies (GWASs) statistical data for LSB and PA were obtained from UK Biobank, and the data of sleep traits was obtained from UK Biobank, UK Biobank and 23andMe, and FinnGen. We used summary statistics data for myopia from MRC IEU. The MR analyses was performed using the inverse variance-weighted (IVW), MR-Egger, weighted median, and MR Pleiotropy RESidual Sum and Outlier methods.ResultsComputer use was genetically predicted to increase the myopia risk [IVW odds ratio (OR) = 1.057; 95% confidence interval (CI), 1.038–1.078; P = 7.04 × 10− 9]. The self-reported moderate-to-vigorous physical activity (MVPA) (IVW OR = 0.962; 95% CI, 0.932–0.993; P = 1.57 × 10− 2) and television watching (IVW OR = 0.973; 95% CI, 0.961–0.985, P = 1.93 × 10− 5) were significantly associated with a lower myopia risk. However, genetically predicted sleep traits or accelerometer-measured physical activity had no significant associations with myopia.ConclusionOur results indicated that computer use is a risk factor for myopia, whereas television watching and MVPA may protect against myopia. These findings shed new light on possible strategies for reducing the prevalence of myopia.

On the neighborhood inverse sum indeg index of fuzzy graph with application

On the neighborhood inverse sum indeg index of fuzzy graph with application

The first–order factorizable contributions to the three–loop massive operator matrix elements [formula omitted] and [formula omitted

The unpolarized and polarized massive operator matrix elements AQg(3) and ΔAQg(3) contain first–order factorizable and non–first–order factorizable contributions in the determining difference or differential equations of their master integrals. We compute their first–order factorizable contributions in the single heavy mass case for all contributing Feynman diagrams. Moreover, we present the complete color–ζ factors for the cases in which also non–first–order factorizable contributions emerge in the master integrals, but cancel in the final result as found by using the method of arbitrary high Mellin moments. Individual contributions depend also on generalized harmonic sums and on nested finite binomial and inverse binomial sums in Mellin N–space, and correspondingly, on Kummer–Poincaré and square–root valued alphabets in Bjorken–x space. We present a complete discussion of the possibilities of solving the present problem in N–space analytically and we also discuss the limitations in the present case to analytically continue the given N–space expressions to N∈C by strict methods. The representation through generating functions allows a well synchronized representation of the first–order factorizable results over a 17–letter alphabet. We finally obtain representations in terms of iterated integrals over the corresponding alphabet in x–space, also containing up to weight w = 5 special constants, which can be rationalized to Kummer–Poincaré iterated integrals at special arguments. The analytic x–space representation requires separate analyses for the intervals x∈[0,1/4],[1/4,1/2],[1/2,1] and x>1. We also derive the small and large x limits of the first–order factorizable contributions. Furthermore, we perform comparisons to a number of known Mellin moments, calculated by a different method for the corresponding subset of Feynman diagrams, and an independent high–precision numerical solution of the problems.

Rapid inverse radiative transfer solver for multiparameter spectrophotometry without integrating sphere.

Multiparameter spectrophotometry (MPS) provides a powerful tool for accurate characterization of turbid materials in applications such as analysis of material compositions, assay of biological tissues for clinical diagnosis and food safety monitoring. This work is aimed at development and validation of a rapid inverse solver based on a particle swarm optimization (PSO) algorithm to retrieve the radiative transfer (RT) parameters of absorption coefficient, scattering coefficient and anisotropy factor of a turbid sample. Monte Carlo (MC) simulations were performed to obtain calculated signals for comparison to the measured ones of diffuse reflectance, diffuse transmittance and forward transmittance. An objective function has been derived and combined with the PSO algorithm to iterate MC simulations for MPS. We have shown that the objective function can significantly reduce the variance in calculated signals by local averaging of an inverse squared error sum function between measured and calculated signals in RT parameter space. For validation of the new objective function for PSO based inverse solver, the RT parameters of 20% Intralipid solutions have been determined from 520 to 1000nm which took about 2.7 minutes on average to complete signal measurement and inverse calculation per wavelength. The rapid solver enables MPS to be translated into easy-to-use and cost-effective instruments without integrating sphere for material characterization by separating and revealing compositional profiles at the molecular and particulate scales.

Some polynomials and degree-based topological indices of molecular graph and line graph of Titanium dioxide nanotubes

Graph polynomials based on distance and degree are helpful and necessary because they contain much information about topological indices. In this article, the general inverse sum indeg index and the generalized inverse sum indeg polynomials are calculated for the molecular graph and the line graph of the Titanium dioxide nanotubes. Then, with their help, some polynomials and some degree-based topological indices of the molecular graph and the line graph of Titanium dioxide nanotubes are obtained.

On Lanzhou Index of Graphs

Let G = ( V , E ) be a simple graph with vertex set V ( G ) and edge set E ( G ) . The Lanzhou index of a graph G is defined by L z ( G ) = ∑ u ∈ V ( G ) d 2 u ¯¯¯ d u , where d u ( ¯¯¯ d u resp.) denotes the degree of the vertex u in G ( ¯¯¯¯ G , the complement graph of G resp.). It has predictive powers to provide insights of chemical relevant properties of chemical graph structures. In this paper we discuss some properties of Lanzhou index. Several inequalities having lower and upper bound for the Lanzhou index in terms of first, second and third Zagreb indices, radius of graph, eccentric connectivity index, Schultz index, inverse sum indeg index and symmetric division deg index, are discussed. At the end the Lanzhou index of corona and join of graphs have been derived.

Approximating the properties of some chemical solvents by two‐dimensional molecular descriptors

AbstractThe selection and design of suitable chemical solvents are essential in numerous industrial and laboratory processes. To facilitate this task, the use of molecular descriptors has gained significant attention in recent years. Chemical solvents constitute around 80 percent of all chemicals used in major chemical processes, particularly fine chemical manufacture. Solvents are the most vital materials used in every industry. Two‐dimensional (2D) molecular descriptors, which are derived from the structural representation of chemical compounds, offer a computationally efficient way to approximate various properties of solvents. The graph descriptors are already used to examine many chemical structures; however, they are not used to analyze the structures of various solvents. Water is the most important solvent required for the maintenance of life, and life on Earth would be unimaginable without it. We try to examine various solvents using degree‐based additive topological indices because solvents are extensively used. In this article, we investigated the important physical and chemical characteristics of 68 solvents using zagreb indices: the inverse sum index, the hyper zagreb index, the forgotten index, and the sum connectivity index. We calculate the correlation between experimental and estimated values of chemical solvents to demonstrate the significance of this research.

Connection number topological aspect for backbone DNA networks.

The present study investigates the complex topological characteristics of DNA networks, with a specific emphasis on the innovative metric known as Connection Number (CN) as a key factor in determining network structure. The Connection Number, represented as CN(v) for a vertex v, measures the count of unique paths that link v to every other vertex in the network. By employing rigorous mathematical modeling and analysis techniques, we are able to reveal the profound implications of CN (complex networks) in characterizing the structural robustness and dynamics of information flow within DNA networks. The study of how the theory of graphs and chemicals interact is known as chemical graph theory. This paper, computing the hyper Zagreb connection index, augmented connection index, inverse sum connection index, harmonic connection index, symmetric division connection index, geometric arithmetic connection index, and atom bond connectivity connection index, of two significant types of backbone DNA and Barycentric subdivision of backbone DNA networks. Direct method computation is used to produce these Connection-based topological descriptors.

Impact of respiratory motion on 18 F-FDG PET radiomics stability: Clinical evaluation with a digital PET scanner.

18 F-FDG PET quantitative features are susceptible to respiratory motion. However, studies using clinical patient data to explore the impact of respiratory motion on 18 F-FDG PET radiomic features are limited. In this study, we investigated the impact of respiratory motion on radiomics stability with clinical 18 F-FDG PET images using a data-driven gating (DDG) algorithm on the digital PET scanner. A total of 101 patients who underwent oncological 18 F-FDG PET scans were retrospectively included. A DDG algorithm combined with a motion compensation technique was used to extract the PET images with respiratory motion correction. 18 F-FDG-avid lesions from the thorax to the upper abdomen were analyzed on the non-DDG and DDG PET images. The lesions were segmented with a 40% threshold of the maximum standardized uptake. A total of 725 radiomic features were computed from the segmented lesions, including first-order, shape, texture, and wavelet features. The intraclass correlation coefficient (ICC) and coefficient of variation (COV) were calculated to evaluate feature stability. An ICC above 0.9 and a COV below 5% were considered high stability. In total, 168 lesions with and without respiratory motion correction were analyzed. Our results indicated that most 18 F-FDG PET radiomic features are sensitive to respiratory motion. Overall, only 27 out of 725 (3.72%) radiomic features were identified as highly stable, including one from the first-order features (entropy), one from the shape features (sphericity), four from the gray-level co-occurrence matrix features (normalized and unnormalized inverse difference moment, joint entropy, and sum entropy), one from the gray-level run-length matrix features (run entropy), and 20 from the wavelet filter-based features. Respiratory motion has a significant impact on 18 F-FDG PET radiomics stability. The highly stable features identified in our study may serve as potential candidates for further applications, such as machine learning modeling.

On topological indices of some chemical graphs

This research delves into the application of topological indices in predicting the physico-chemical properties of chemical materials. These indices have been employed in various QSAR and QSPR studies, providing a mathematical formulation to predict properties such as viscosity and radius of gyrations Rucker and Rucker [J. Chem. Inf. Comput. Sci. 39, 788–802, (1999)]. We explore several indices, including the forgotten topological index, inverse sum index, general sum connectivity index and first multiplicative atom bond connectivity index, and investigate their usefulness in predicting bio-activity and anti-inflammatory activities of certain chemical compounds. Specifically, we focus on the allotrope structure, nanotubes and dominating oxide and silicate chemical networks. We present a graphical trend of these indices and perform a comparison to facilitate the observation of physical-chemical properties of these materials for researchers.

Topological indices and QSPR analysis of some chemical structures applied for the treatment of heart patients

AbstractIn this study, various beta‐blocker drugs used for heart disease were analyzed, and their degree‐based topological indices derived from the M‐polynomial were calculated. Linear and quadratic regression analysis was used to obtain quantitative structure‐property relationship models between the topological indices and eight the physicochemical properties of the drugs to determine their effectiveness. The results show that the harmonic index was the best predictor for boiling point, flashpoint, and enthalpy of vaporization, while the redefined third Zagreb index was effective for polarizability, molar refractivity, and molar volume. The inverse sum indeg index was found to be effective for molar refractivity, and the second modified Zagreb index was surface tension in linear regression models. In addition, the redefined third Zagreb index was the best predictor for polarizability and molar refractivity, while the second modified Zagreb index was effective for molar volume. The SDD index was found to be effective for surface tension in quadratic regression models.