Index Theory Research Articles

On the Szeged and Wiener complexities in graphs

When characterizing networks structurally, the discriminating ability of a topological index is crucial. This relates to investigate its discrimination power (also called uniqueness or degeneracy) that indicates how meaningful the given measure can distinguish nonisomorphic networks. Assume G is a connected graph. The Szeged complexity (or briefly Sz-complexity) of a graph G is the number of different portions in the Szeged index formula. Also, the Wiener complexity (or briefly W-complexity) can be defined similarly. In the current work, we study graphs with small Sz-complexity. We characterize trees with Sz-complexity two and bicyclic graphs with Sz-complexity one. In this way, first we introduce some graphs with Sz-complexity one. For instance, we investigate Θ-graph and two categories of k-cyclic graphs. Besides, we classify bicyclic graphs with Sz-complexity equal to the number of edge-orbits. Finally, we determine W-complexity of these graphs.

LAJU TUMBUH GULMA PADA BERBAGAI PUPUK ORGANIK DAN UKURAN BENIH DI PERTANAMAN KENTANG (Solanum tuberosum L.) DATARAN MEDIUM

Weeds are one of the causes of the decline in potato production in the central plains. This research aimed to assess the diversity of weeds that appear on granola-variety potato plants (Solanum tuberosum L.) This research uses a quantitative approach by arranging frames measuring 50x50 cm in five locations spread diagonally. Weed samples were taken at 20 and 40 days after planting, and then the weed vegetation was analyzed using the index formula and weed dominance. The research found nine types of weeds, namely: Cyperus rotundus, Ageratum conyzoides L., Common purslane, Eleusine indica L. Gaertn, Commelia benghalensis, Panicum repens L., Amaranthus spinosus L., Gynura procumbens, and Bidens pilosa L. Analysis result the variety shows the level of weed diversity at 20 days after planting in the P0 treatment wich gives the best result with the lowest average value. Meanwhile, in weed diversity parameters at 60 days after planting, the highest average value was achieved by treatment P1, while the lowest average value was seen in treatment P3.

Information flow in non-unitary quantum cellular automata

The information flow in a quantum system is a fundamental feature of its dynamics. An important class of dynamics are quantum cellular automata (QCA), systems with discrete updates invariant in time and space, for which an index theory has been proposed for the quantification of the net flow of quantum information across a boundary. While the index is rigid in the sense of begin invariant under finite-depth local circuits, it is not defined when the system is coupled to an environment, i.e.for non-unitary time evolution of open quantum systems. We propose a new measure of information flow for non-unitary QCA denoted the information current which is not rigid, but can be computed locally based on the matrix-product operator representation of the map.

Existence and bifurcation of positive solutions to a class of predator-prey models with mutual interference among the predators

In this work, we study a class of diffusive predator-prey models with mutual interference among the predators while searching for food. Under Dirichlet boundary condition, by the fixed point index theory, we provide the necessary and sufficient conditions for the existence of coexistence states (i.e., stationary pattern). This is a strong contrast to the corresponding Neumann boundary problem, which exhibits bistability and admits no patterns.

Experiment and theory of the complex refractive index of dense colloidal media.

The complex refractive index is analyzed by measuring its scattering attenuation μ s, group index n g, and group velocity dispersion (GVD) for 100nm diameter silica nanoparticles dispersed in water. The experiments were performed for wavelengths between 410nm and 930nm. The experimental results were compared with different mixing models for the complex refractive index of colloidal suspensions. The group index linearly scaled with the volume fraction both in experiment and for all tested models. It was found that the GVD has a nonlinear dependence on volume fraction in agreement with the coupled dipole model of Parola etal. [J. Chem. Phys.141, 124902 (2014)JCPSA60021-960610.1063/1.4895961] The scattering attenuation is in good agreement with both the coupled dipole model and the low frequency quasi-crystalline approximation [J. Electromagn. Waves Appl.2, 757 (1988)JEWAE50920-507110.1163/156939388X00053] that take particle correlations into account. With an iterative fitting procedure of all the data based on both the coupled dipole model and the quasi-crystalline approximation, the refractive index, porosity, and size of the nanoparticles were determined. We determined that the coupled dipole model is in best agreement with the data.

Effects of Dietary Plant Protein Replacement with Insect and Poultry By-Product Meals on the Liver Health and Serum Metabolites of Sea Bream (Sparus aurata) and Sea Bass (Dicentrarchus labrax).

The liver health of Gilthead sea bream and European sea bass, fed with fish meal-free diets, including various proportions of plant proteins, as well as insect and poultry by-product meals, was investigated through biochemical and histological analyses using a new liver index (LI) formula. Four isoproteic (45% Dry Matter, DM) and isolipidic (20% DM) diets were compared, including a plant-based control diet (CV) and three other test diets, in which 40% of a plant protein-rich ingredient mixture was replaced with meals from Hermetia illucens (H40) or poultry by-product (P40) alone, or in combination (H10P30). The trials lasted 12 and 18 weeks for sea bream and sea bass, respectively. The results obtained thus far highlighted species-specific differences in the physiological response to dietary changes. In sea bream, the biochemical and histological responses suggest favorable physiological and liver health statuses, with higher serum cholesterol (CHO) and triglyceride (TAG) levels, as well as moderate hepatocyte lipid accumulation, with the H10P30 diet compared to the CV (p < 0.05). In sea bass, all diets resulted in elevated serum TAG levels and lipid accumulation in the liver, particularly in fish fed the P40 one (p < 0.05), which resulted in the highest LI, coupled with a higher frequency of severe lipid accumulation, hypertrophy, cord loss, peripheral nuclei displacement, and pyknosis. In conclusion, sea bream adapted well to the test diets, whereas sea bass exhibited altered hepatic lipid metabolism leading to incipient liver steatosis, likely due to the high lipid contents of the diets, including the insect and poultry meals. The LI formula developed in this study proved to be a reliable tool for assessing the effects of dietary changes on the liver health of sea bream and sea bass, consistent with biochemical and histological findings.

Evaluate Human Perception of the Built Environment in the Metro Station Area

Transit-oriented development (TOD) has become a dominant form of spatial planning and land use in large cities internationally. As the intersections of urban space and rail transportation, metro station areas play a key public service function in the lives of city residents. Based on the “5D” index and Node-Place theory in the metro station area, current research on the built environment in metro station areas focuses on improving the economic and transportation efficiency while neglecting public perception of the construction of station space. Sentiments, as an important part of the individual’s perception, are closely related to the built environment. Therefore, this study takes 187 metro stations within the fifth ring road of Beijing, China, as an example and extracts public sentiment information from social media data using a wide range of natural language processing techniques to quantitatively analyze the distribution of the public’s sentiment characteristics (including intensity, polarity, and category) in the metro station area and deeply explores the spatial correlation with the distribution of the objective built environment elements. The study shows that influenced by the spatial design of the metro station, density, land use functions, etc., the sentiment intensity of the station area within the Fifth Ring Road of Beijing is “strong in the east and weak in the west, strong in the north and weak in the south”, and the sentiment polarity has the characteristic of gradually negative from inside to outside in a circular pattern. Synthesizing the sentiment perception in the metro station area, our study further divided the Beijing metro station area into four major categories and eight specific subtypes.

Deformation theory of asymptotically conical Spin(7)-instantons

We develop the deformation theory of instantons on asymptotically conical Spin(7)-manifolds where the instanton is asymptotic to a fixed nearly G2-instanton at infinity. By relating the deformation complex with spinors, we identify the space of infinitesimal deformations with the kernel of the twisted negative Dirac operator on the asymptotically conical Spin(7)-manifold.Finally we apply this theory to describe the deformations of Fairlie–Nuyts–Fubini–Nicolai Spin(7)-instantons on R8, where R8 is considered to be an asymptotically conical Spin(7)-manifold asymptotic to the cone over S7. We calculate the virtual dimension of the moduli space using Atiyah–Patodi–Singer index theorem and the spectrum of the twisted Dirac operator.

A multi-attribute group decision making method based on novel distance measures and regret theory under probabilistic dual hesitant fuzzy sets

As a decision information preference which includes membership degree (MD), non-membership degree (NMD), and probability, the probabilistic dual hesitant fuzzy set (PDHFS) is a crucial tool for effectively expressing uncertain information. In the domains of multi-attribute decision making (MADM) and multi-attribute group decision making (MAGDM), distance measures are extremely helpful tools. In this study, a novel PDHFS distance measure is put out, on which a MAGDM method that takes decision-makers’ (DMs’) psychological behavior into account is proposed. First, a novel distance measure is put forward to effectively assess the difference between different PDHFSs by adding consideration of the distances between MDs and between NMDs. Second, a similarity-trust analysis method based on the new distance measure is employed to calculate expert weights for integrating group decisions, and the group satisfaction index and regret theory are extended to a probabilistic dual hesitant fuzzy information environment. A MAGDM method based on the novel distance measure and regret theory is proposed. Finally, the proposed method is applied to the selection of radiation protection strategies in nuclear power plants, and it is also determined through parametric analysis that DMs’ tendency to avoid regret has an impact on the outcomes of decisions. When the method proposed in this study is compared to existing approaches, the findings demonstrate that the method’s performance in resolving MAGDM issues in a PDHFS environment is superior.

Complements, index theorem, and minimal log discrepancies of foliated surface singularities

Complements, index theorem, and minimal log discrepancies of foliated surface singularities

Exploring the effect of substituents on the supramolecular assemblies built by non-covalent interactions in three closely related 1,3,4-oxadiazole-2(3H)-thione derivatives: An evaluation of antimicrobial and anti-proliferative activities

Three closely related 1,3,4-oxadiazole-2(3H)-thione N-Mannich bases were synthesized and characterized by spectroscopic and single crystal X-ray diffraction methods. X-ray analysis reveals that the title molecules adopt l-shaped conformation, and a slight structural deviation around substituent groups is noted. The Hirshfeld surface and 2D fingerprint plots demonstrate the effect of substituents (piperidine, morpholine, and thiomorpholine) on the intermolecular interactions. The CLP-PIXEL energy analysis identified the most significant interactions in the molecular dimers (that characterize the crystal packing) with respect to the total intermolecular interaction energies. These dimers are held together by various non-covalent interactions including C–H⋅⋅⋅S/N/O/Cl/π interactions in addition to unconventional lone pair⋅⋅⋅π interactions. A molecule with thiomorpholine substituent is favoured by two σ-hole interactions (Cl⋅⋅⋅Cl halogen bond and S⋅⋅⋅N chalcogen bond) in the solid state. Furthermore, the molecular electrostatic potential (MEP) surfaces and deformation electron density help to describe the existence of σ-hole on the Cl and thione S atoms. Noncovalent interaction index (NCI) and quantum theory of atoms in molecules (QTAIM) methods are used to delineate the nature of observed noncovalent interactions in the molecular dimers. In vitro data of antibacterial and anti-proliferative activities indicate that compound with morpholine substituent showed a moderate antibacterial activity against all tested Gram-positive bacterial strains. However, molecules with piperidine and thiomorpholine showed notable effectiveness against the HepG-2 cell line. Molecular docking analysis was performed with two liver cancer targets, VEGFR2 and RET, in order to understand the interactions between the ligand and the active site residues of these targets.

Generalized Ginsparg-Wilson relations

We give a general derivation of Ginsparg-Wilson relations for both Dirac and Majorana fermions in any dimension. These relations encode continuous and discrete chiral, parity and time-reversal anomalies and will apply to the various classes of free-fermion topological insulators and superconductors (in the framework of a relativistic quantum field theory in Euclidean spacetime). We show how to formulate the exact symmetries of the lattice action and the relevant index theorems for the anomalies. Published by the American Physical Society 2024

EDGE-WIENER INDEX OF SIERPINSKI FRACTAL NETWORKS

The edge-Wiener index, an invariant index representing the summation of the distances between every pair of edges in the graph, has monumental influence on the study of chemistry and materials science. In this paper, drawing inspiration from Gromov’s idea, we use the finite pattern method proposed by Wang et al. [Average geodesic distance of Sierpinski gasket and Sierpinski networks, Fractals 25(5) (2017) 1750044] to figure out the exact formula of edge-Wiener index of the Sierpinski fractal networks.

Degree-weighted Wiener index of a graph

&lt;abstract&gt;&lt;p&gt;From geometric point of view, we introduced the Sombor-Wiener index of a graph and studied the basic properties of the new index. It was shown that the Sombor-Wiener index was useful in predicting the acentric factor of octane isomers. In addition, we proposed a degree-weighted Wiener index to generalize the Schultz index, the Gutman index, and the Sombor-Wiener index. Meanwhile, we gave the calculation formula of degree-weighted Wiener index for generalized Bethe trees.&lt;/p&gt;&lt;/abstract&gt;

The multiplicative degree-Kirchhoff index and complexity of a class of linear networks

&lt;abstract&gt;&lt;p&gt;In this paper, we focus on the strong product of the pentagonal networks. Let $ R_{n} $ be a pentagonal network composed of $ 2n $ pentagons and $ n $ quadrilaterals. Let $ P_{n}^{2} $ denote the graph formed by the strong product of $ R_{n} $ and its copy $ R_{n}^{\prime} $. By utilizing the decomposition theorem of the normalized Laplacian characteristics polynomial, we characterize the explicit formula of the multiplicative degree-Kirchhoff index completely. Moreover, the complexity of $ P_{n}^{2} $ is determined.&lt;/p&gt;&lt;/abstract&gt;

Analyzing the normalized Laplacian spectrum and spanning tree of the cross of the derivative of linear networks

&lt;abstract&gt;&lt;p&gt;In this paper, we focus on the strong product of the pentagonal networks. Let $ R_{n} $ be a hexagonal network composed of $ 2n $ pentagons and $ n $ quadrilaterals. Let $ P_{n}^{2} $ denote the graph formed by the strong product of $ R_{n} $ and its copy $ R_{n}^{\prime} $. By utilizing the decomposition theorem of the normalized Laplacian characteristics polynomial, we characterize the explicit formula of the multiplicative degree-Kirchhoff index completely. Moreover, the complexity of $ P_{n}^{2} $ is determined.&lt;/p&gt;&lt;/abstract&gt;

Aluminium phosphide (Al12P12) nanocage as a potential sensor for volatile organic compounds: A DFT study.

The efficacy of aluminium phosphide (Al12P12) nanocage toward sensing methanol (MeOH) and ethanol (EtOH) volatile organic compounds (VOCs) was herein thoroughly elucidated utilizing various density functional theory (DFT) computations. In this perspective, MeOH⋯ and EtOH⋯Al12P12 complexes were investigated within all plausible configurations. According to the energetic features, the EtOH⋯Al12P12 complexes exhibited larger negative values of adsorption and interaction energies with values up to -27.23 and -32.84 kcal mol-1, respectively, in comparison to the MeOH⋯Al12P12 complexes. Based on the symmetry-adapted perturbation theory (SAPT) results, the electrostatic forces were pinpointed as the predominant component beyond the adsorption process within the preferable MeOH⋯ and EtOH⋯Al12P12 complexes. The findings of the noncovalent interaction (NCI) index and quantum theory of atoms in molecules (QTAIM) outlined the closed-shell nature of the interactions within the studied complexes. Substantial variations were found in the molecular orbitals distribution patterns of MeOH/EtOH molecules and Al12P12 nanocage, outlining the occurrence of the adsorption process within the complexes under investigation. Thermodynamic parameters were denoted with negative values, demonstrating the spontaneous exothermic nature of the most favorable complexes. New energy states were observed within the extracted density of states plots, confirming the impact of adsorbing MeOH and EtOH molecules on the electronic properties of the Al12P12 nanocage. The appearance of additional peaks in Infrared Radiation (IR) and Raman spectra revealed the apparent effect of the adsorption process on the features of the utilized sensor. The emerging results declared the potential uses of Al12P12 nanocage as a promising candidate for sensing VOCs, particularly MeOH and EtOH.

Microhydration of small protonated polyaromatic hydrocarbons: a first principles study.

Using first principles methodology, we investigate the microsolvation of protonated benzene (BzH+), protonated coronene (CorH+) and protonated dodecabenzocoronene (DbcH+). Gas phase complexes of these small protonated polyaromatic hydrocarbons (H+PAHs) with mono-, di-, and tri-hydrated water molecules are considered. Their most stable forms are presented, where we discuss their structural, energetic aromaticity and IR and UV spectral features. In particular, we focus on the analysis of the bonding and various non-bonded interactions between these protonated aromatics and water clusters. The strength of non-bonded interactions is quantified and correlated with their electron density profiles. Furthermore, insights into the interfacial interactions and stability of these complexes were obtained through non-covalent index and symmetry-adapted perturbation theory (SAPT0) analyses. We also discuss the effects of the extension of the π aromatic cloud on the water solvation of these protonated aromatics. In particular, we extended our predictions for the S0 → S1 and S0 → T1 wavelength transitions of micro hydrated H+PAHs to deduce those of these species solvated in aqueous solution. The present findings should be useful for understanding, at the microscopic level, the effects of water interacting with H+PAHs, which are relevant for organic chemistry, astrochemistry, atmospheric chemistry, combustion and materials science.

Existence results for a class of nonlinear singular $ p $-Laplacian Hadamard fractional differential equations

&lt;abstract&gt;&lt;p&gt;Based on properties of Green's function and the some conditions of $ f(t, u) $, we found a minimal and a maximal positive solution by the method of sequence approximation. Moreover, based on the properties of Green's function and fixed point index theorem, the existence of multiple positive solutions for a singular $ p $-Laplacian fractional differential equation with infinite-point boundary conditions was obtained and, at last, an example was given to demonstrate the validity of our main results.&lt;/p&gt;&lt;/abstract&gt;

Comparative Analysis of FSE T2 Weighted, Chemical Shift and Dynamic Contrast-Enhanced MR Imaging in the Characterization of Adrenal Masses Based on Qualitative and Quantitative Parameters.

The purpose of our study was to investigate the role of different magnetic resonance imaging (MRI) parameters in the characterization of adrenal masses. A total of 150 patients who presented with 186 adrenal tumors were retrospectively evaluated in this study. Final patient cohort consisted of 17 pheochromocytomas, 3 adrenocortical carcinomas, 24 metastases, 31 lipid-poor adenomas and 111 lipid-rich adenomas. We carried out a visual assessment on FSE (Fast spin echo)T2 weighted images and also calculated T2 signal intensity ratio of all adrenal masses and also performed a qualitative assessment on chemical shift imaging (CSI) together with quantitative calculation using Adrenal to spleen signal intensity (si) ratio and Adrenal si index formulas. On dynamic contrast-enhanced sequences, visual assessment based on enhancement patterns on late-arterial phase images was performed and also mean signal intensity measurements were carried out. All examinations were interpreted by two abdominal radiologists in consensus who were blinded to the clinical and pathological findings. Statistical analysis was performed. On FSE T2 weighted imaging, isointense to liver and slightly hyperintense than liver was found higher in benign cases, however, in malignant cases moderately and strikingly hyperintense than liver was higher than in benign cases (p=0.001, p<0.01). There was a statistically significant difference between the T2 signal intensity ratio values of adrenal tumor groups (p=0.001, p<0.01). In lipid-rich and lipid-poor adenoma groups, T2 signal intensity ratio values was significantly lower than in pheochromocytoma and metastasis cases. In malignant group, T2 signal intensity ratio values were found statistically significantly higher than in the benign group (p=0.001, p<0.01). There was a statistically significant difference between CSI visual assessment of adrenal tumor groups (p=0.001, p<0.01). Although moderate and significant signal intensity loss was usually detected in lipid-rich adenoma group, never detected in other tumor groups. There was also a statistically significant difference between benign and malignant adrenal tumor groups (p=0.001, p<0.01). In the malignant group, Adrenal to spleen si ratio values were found significantly higher whereas, Adrenal si index values were significantly lower compared to benign tumors (p=0.001, p<0.01). Based on malignancy, there was a statistically significant difference between adrenal tumor groups (p=0.001, p<0.01). Although capillary blush and homogenous type enhancement were more common in benign cases than in malignant ones, peripheral-patchy and strikingly capillary blush type enhancement was more frequent in malignant tumors. Based on malignancy, mean arterial signal intensity values of malignant tumors were statistically higher than benign tumors (p=0.001; p<0.01). Dynamic contrast-enhanced MRI protocol including CSI aids in the characterization of indeterminate adrenal masses. Herein, the combined use of qualitative and quantitative parameters enables more tumors to be recognized that otherwise would be indeterminate.