Symmetric Index Research Articles

UNVEILING THE RELATIONSHIP BETWEEN M-POLYNOMIAL BASED TOPOLOGICAL INDICES AND INVERSE GRAPHS OF FINITE CYCLIC GROUPS: A COMPREHENSIVE STUDY

In the discipline of graph theory, topological indices are extremely important. The M-polynomial is a powerful tool for determining a graph's topological indices. The use of M-polynomials to describe macro-molecules and biochemical networking is a novel concept. Also, the M-polynomial of various micro-structural allows us to calculate a variety of topological indices. The chemical substances and biochemical networks are correlated with their chemical characteristics and bio-active compounds using these findings. In this research, we use the M-polynomial to create special essential topological indices of inverse graphs on finite cyclic groups, such as Randic, Zagreb, Augmented Zagreb, Harmonic, Inverse sum, and Symmetric division degree indices.

On Bond Incident Degree Indices of Fixed-Size Bicyclic Graphs with Given Matching Number

A connected graph with p vertices and q edges satisfying q=p+1 is referred to as a bicyclic graph. This paper is concerned with an optimal study of the BID (bond incident degree) indices of fixed-size bicyclic graphs with a given matching number. Here, a BID index of a graph G is the number BIDf(G)=∑vw∈E(G)f(dG(v),dG(w)), where E(G) represents G’s edge set, dG(v) denotes vertex v’s degree, and f is a real-valued symmetric function defined on the Cartesian square of the set of all different members of G’s degree sequence. Our results cover several existing indices, including the Sombor index and symmetric division deg index.

On Unicyclic Graphs with a Given Number of Pendent Vertices or Matching Number and Their Graphical Edge-Weight-Function Indices

Consider a unicyclic graph G with edge set E(G). Let f be a real-valued symmetric function defined on the Cartesian square of the set of all distinct elements of G’s degree sequence. A graphical edge-weight-function index of G is defined as If(G)=∑xy∈E(G)f(dG(x),dG(y)), where dG(x) denotes the degree a vertex x in G. This paper determines optimal bounds for If(G) in terms of the order of G and a parameter z, where z is either the number of pendent vertices of G or the matching number of G. The paper also fully characterizes all unicyclic graphs that achieve these bounds. The function f must satisfy specific requirements, which are met by several popular indices, including the Sombor index (and its reduced version), arithmetic–geometric index, sigma index, and symmetric division degree index. Consequently, the general results obtained provide bounds for several well-known indices.

Analyzing the modified symmetric division deg index: mathematical bounds and chemical relevance

Abstract The modified symmetric division deg (MSD) index of a graph G is precisely defined as MSD ( G ) = ∑ j ∼ k 1 2 d j d k + d k d j , where d j and d k represent the degrees of j and k respectively. In this paper, we present precise bounds for the modified symmetric division deg index, expressed in the relation to the minimum and maximum degrees, the order and size of the graph, the number of pendant vertices and the minimum degree of a non-pendant vertex, the forgotten topological index, the modified second Zagreb index. We determine the upper bounds for the modified symmetric division deg index of unicyclic, bicyclic and k-cyclic graphs. Moreover, upon analyzing the modified symmetric division deg index, we observe its correlation with other well-known indices and its chemical applicability on the molecular graphs of octane isomers. At the end, we find the chemical applicability of the modified symmetric division deg index on benzenoid hydrocarbons and observe that the modified symmetric division deg index has a very strong correlation with the physical properties of benzenoid hydrocarbons.

Topological Characterization of Coronoid Structures via Valency Based Topological Indices.

The number of atoms producing a bond with an atom a in a molecular structure (graph) is regarded as the valency of a. A number of molecular structures have been topologically characterized via a large number of valency-based topological indices, which correlate certain physio-chemical properties like boiling point, stability, strain energy, and many more chemical compounds. Our intention is to perform the topological characterization of primitive coronoid structures initially on the base of seven different valency-based topological indices. Fundamentally, our purpose is to provide the universal formula by using the topological characterization of any primitive coronoid structures with any valency-based topological index. The technique of atom-bonds partitions according to the valency of atoms besides counting principals are used to find the results. Exact values of valency-based topological index, namely the Randic index, sum connectivity index, harmonic index, atom bond connectivity index, geometric arithmetic index, forgotten index, and symmetric division index are calculated coronoid structures initially constructed with at most three benzene lyres. All these indices are valency-dependent structural invariants that have been used to elaborate several chemical properties of compounds of the structure. Moreover, we provide the general formula to compute any valency-based topological index for any type of coronoid structure constructed with any number of benzene lyres.

A review on the direct and inverse transmission eigenvalue problem for the spherically symmetric refractive index

A review on the direct and inverse transmission eigenvalue problem for the spherically symmetric refractive index

On unicyclic graphs with a given girth and their minimum symmetric division deg index

On unicyclic graphs with a given girth and their minimum symmetric division deg index

NATURAL OR ARTIFICIAL TRITIUM IN RIVERS – THE ASSESSMENT USING SYMMETRICAL INDEX

Tritium, hydrogen isotope, with a half-life of 12.3 years, is produced in two ways: naturally and artificially. Naturally, tritium is generated through the interaction of cosmic radiation protons and neutrons with gases in the upper atmosphere. Artificially, tritium origins from the atmospheric nuclear tests, production from nuclear reactors, future fusion reactors, fuel reprocessing plants, heavy water production facilities and commercial production for medical diagnostics, radiopharmaceuticals, luminous paints. Elevated concentrations of tritium in the environment are of great public concern. Considering the fact that nuclear power plants are located on rivers, knowing the activity concentration of this isotope in rivers is of great importance. This work presents the results for tritium determination in Danube and Sava River in Belgrade, Serbia. The origin of tritium was estimated using a mathematical parameter, symmetrical index.

Design and optimization of a long-range surface plasmon resonance-based plasmonic SERS biosensor

In this paper, we designed and studied a novel type of hybrid chip based on long-range surface plasmon resonance (LRSPR) and surface-enhanced Raman scattering (SERS). The substrate has periodic arrangement gold nanoring cavity arrays structure, which can obtain a uniform and stable electromagnetic field distribution. In addition, due to the clever design of the long-range configuration (a “sandwich” structure with symmetric refractive index), the chip has a significant extended electromagnetic field enhancement ability. In numerous existing studies focusing on SERS performance, the consideration of plasmonic structure is limited to its shape and size, while neglecting the significance of spacer layer parameters. Thus, we use the Finite Difference Time Domain (FDTD) software to design and optimize the chip substrate configuration by investigating the impact of various parameters such as refractive index, spacer layer thickness, plasmonic structure's inner and outer radius, and period of array on the long-range effect. The presented geometrically-tunable long-range plasmonic chip provides a way to identify the governing factors for SERS and presents a design principle for optimizing SERS substrates.

Analyzing global competitiveness of Turkish air conditioning industry

The global economy significantly relies on the air conditioning sector, which has been gaining increased importance worldwide and in Türkiye due to the impact of global warming, climate change, and the diminishing energy resources. As a multifaceted industry encompassing air conditioning, heating, installation, insulation, refrigeration and ventilation sector has been adapting to the growing demand for environmentally friendly and energy-efficient solutions. This study analyzes air conditioning industry of Türkiye and its sub-product groups in terms of its ability to compete internationally, spanning from 2001 to 2021. To assess competitiveness, we employed various analytical tools, including Balassa's Revealed Comparative Advantages Index (RCA), Vollrath Indices (RXA, RMP, RTA, RC), Revealed Symmetric Comparative Advantages Index (RSCA), Trade Balance Index (TBI), and Product Mapping method. Notably, there is no research that scrutinize the competitiveness of the Turkish air conditioning industry utilizing the Product Mapping. The study findings emphasize that air conditioning industry of Türkiye has competitiveness. Within the sub-product group, the analysis reveals that Türkiye has competitiveness for 11 products, a near-limit competitiveness for 3 products, and a lack of competitiveness for 10 products.

Determinants of the competitiveness of world palm oil exports: A cointegration analysis

The purpose of this research is to determine the impact of international palm oil prices, prices of its substitute and complementary goods, and the exchange rate on the competitiveness of 30 palm oil exporting countries over the period from 2011 to 2019, using monthly data. The symmetric comparative advantage index was estimated, and a convergence effect was found, whereby emerging countries exhibited greater specialization than industrialized countries. Unit root and cointegration tests were applied, in addition to FMOLS and DOLS methods. The analysis revealed that decreases in palm and vegetable oil prices, coupled with an increase in the exchange rate and prices of soybeans and biodiesel, enhanced the competitiveness of palm oil exports.

Machine learning methods to improve spatial predictions of coastal wind speed profiles and low-level jets using single-level ERA5 data

Abstract. Observations of the wind speed at heights relevant for wind power are sparse, especially offshore, but with emerging aid from advanced statistical methods, it may be possible to derive information regarding wind profiles using surface observations. In this study, two machine learning (ML) methods are developed for predictions of (1) coastal wind speed profiles and (2) low-level jets (LLJs) at three locations of high relevance to offshore wind energy deployment: the US Northeastern Atlantic Coastal Zone, the North Sea, and the Baltic Sea. The ML models are trained on multiple years of lidar profiles and utilize single-level ERA5 variables as input. The models output spatial predictions of coastal wind speed profiles and LLJ occurrence. A suite of nine ERA5 variables are considered for use in the study due to their physics-based relevance in coastal wind speed profile genesis and the possibility to observe these variables in real-time via measurements. The wind speed at 10 ma.s.l. and the surface sensible heat flux are shown to have the highest importance for both wind speed profile and LLJ predictions. Wind speed profile predictions output by the ML models exhibit similar root mean squared error (RMSE) with respect to observations as is found for ERA5 output. At typical hub heights, the ML models show lower RMSE than ERA5 indicating approximately 5 % RMSE reduction. LLJ identification scores are evaluated using the symmetric extremal dependence index (SEDI). LLJ predictions from the ML models outperform predictions from ERA5, demonstrating markedly higher SEDIs. However, optimization utilizing the SEDI results in a higher number of false alarms when compared to ERA5.

A Study on Degree Based Topological Indices of Harary Subdivision Graphs With Application

Combinatorial design theory and graph decompositions play a critical role in the exploration of combinatorial design theory and are essential in mathematical sciences. The process of graph decomposition involves partitioning the set of edges in a graph G. An n-sun graph, characterized by a cycle with an edge connecting each vertex to a terminating vertex of degree one, is introduced in this study. The concept of n-sun decomposition is applied to certain even-order graphs. The indices covered in this study include the general connectivity index of the harary graphs, Zagreb indices, symmetric division degree indices and randic indices.

The role of the paraspinal muscles in the development of adolescent idiopathic scoliosis based on surface electromyography and radiographic analysis

BackgroundPatients with idiopathic scoliosis commonly present with an imbalance of the paraspinal muscles. However, it is unclear whether this muscle imbalance is an underlying cause or a result of idiopathic scoliosis. This study aimed to investigate the role of paraspinal muscles in the development of idiopathic scoliosis based on surface electromyography (sEMG) and radiographic analyses.MethodsThis was a single-center prospective study of 27 patients with single-curve idiopathic scoliosis. Posteroanterior whole-spine radiographs and sEMG activity of the erector spinae muscles were obtained for all patients in the habitual standing position (HSP), relaxed prone position (RPP), and prone extension position (PEP). The Cobb angle, symmetrical index (SI) of the sEMG activity (convex/concave), and correlation between the two factors were analyzed.ResultsIn the total cohort, the mean Cobb angle in the HSP was significantly greater than the mean Cobb angle in the RPP (RPP-Cobb) (p < 0.001), whereas the mean Cobb angle in the PEP (PEP-Cobb) did not differ from the RPP-Cobb. Thirteen patients had a PEP-Cobb that was significantly smaller than their RPP-Cobb (p = 0.007), while 14 patients had a PEP-Cobb that was significantly larger than their RPP-Cobb (p < 0.001). In the total cohort and two subgroups, the SI of sEMG activity at the apex vertebra (AVSI) in the PEP was significantly greater than 1, revealing significant asymmetry, and was also significantly larger than the AVSI in the RPP. In the RPP, the AVSI was close to 1 in the total cohort and two subgroups, revealing no significant asymmetry.ConclusionThe coronal Cobb angle and the SI of paraspinal muscle activity in AIS patients vary with posture changes. Asymmetrical sEMG activity of the paraspinal muscles may be not an inherent feature of AIS patients, but is evident in the challenging tasks. The potential significance of asymmetric paraspinal muscle activity need to be explored in further research.

Some New Bounds on the Modified Symmetric Division Deg Index

The use of graph theory in the fields of chemistry, pharmacy, communication, maps, and aeronautics is significant. In order to study the properties of chemical compounds, the molecules of those compounds are modeled as graphs. Boiling point, enthalpy, π -electron energy, and molecular weight are a few examples of physical properties that are related to the geometric structure of the compound. Recently, the modified symmetric division deg (mSDD(G), in short) index is {defined} as the total of all adjacent vertices in pairs μυ of the term 12(dμdν+dνdμ)−−−−−−−−−−−−√. The purpose of this article is to demonstrate the usefulness of mSDD(G) index through the resolution of an interdisciplinary problem describing the structure of benzenoid hydrocarbons. With the help of linear regression models, we have studied the physicochemical properties of benzenoid hydrocarbons. Strong correlations were obtained, and the bounds for the same index were subsequently established.

The margin of stability is affected differently when walking under quasi-random treadmill perturbations with or without full visual support.

Sensory-motor perturbations have been widely used to assess astronauts' balance in standing during pre-/post- spaceflight. However, balance control during walking, where most falls occur, was less studied in these astronauts. A study found that applying either visual or platform oscillations reduced the margin of stability (MOS) in the anterior-posterior direction (MOSap) but increased MOS in the medial-lateral direction (MOSml) as a tradeoff. This tradeoff induced an asymmetric gait. This study extended the current knowledge to investigate overall stability under unpredictable environments. This study aimed to determine (1) whether quasi-random treadmill perturbations with or without full vision support would result in a significant reduction in MOSap but an increase in MOSml and (2) regardless of whether vision support was provided, quasi-random treadmill perturbations might result in asymmetric gait patterns. Twenty healthy young adults participated in this study. Three experimental conditions were semi-randomly assigned to these participants as follows: (1) the control condition (Norm), walking normally with their preferred walking speed on the treadmill; (2) the treadmill perturbations with full vision condition (Slip), walking on the quasi-random varying-treadmill-belt-speeds with full vision support; and (3) the treadmill perturbations without full vision condition (Slip_VisionBlocked, blackout vision through customized vision-blocked goggles), walking on the quasi-random varying-treadmill-belt-speeds without full vision support. The dependent variables were MOSap, MOSml, and respective symmetric indices. A one-way repeated ANOVA measure or Friedman Test was applied to investigate the differences among the conditions mentioned above. There was an increase in MOSap in Slip (p=0.001) but a decrease in MOSap in Slip_VisionBlocked (p=0.001) compared to Norm condition. The MOSml was significantly greater in both Slip and Slip_VisionBlocked conditions compared to the Norm condition (p=0.011; p<0.001). An analysis of Wilcoxon signed-rank tests revealed that the symmetric index of MOSml in Slip_VisionBlocked (p=0.002) was greater than in the Norm condition. The novelty of this study was to investigate the effect of vision on the overall stability of walking under quasi-random treadmill perturbations. The results revealed that overall stability and symmetry were controlled differently with/without full visual support. In light of these findings, it is imperative to take visual support into consideration while developing a sensory-motor training protocol. Asymmetric gait also required extra attention while walking on the quasi-random treadmill perturbations without full vision support to maintain overall stability.

The clinical and neuroimaging differences between vascular parkinsonism and Parkinson's disease: a case-control study.

Parkinson's disease (PD) and vascular parkinsonism (VaP) have highly overlapping phenotypes, and different prognosis. This study comprehensively investigated the clinical, brain MRI and transcranial sonography differences between VaP and PD. Forty-eight patients with PD, 27 patients with VaP, and 29 healthy controls were compared. All patients were assessed using the MDS-UPDRS, Berg Balance Scale (BBS), Ten-Meter Walking Test (10-MWT), Time Up and Go Test, and Non-Motor Symptoms Scale. Beck Depression Inventory, PD questionnaire- 39, international urine incontinence scale, cognitive assessment scales, MRI brain and transcranial colour-coded doppler. The study was registered on clinical-Trial.gov (NCT04308135) on 03/12/2020. VaP patients showed significantly older age of onset, shorter disease duration, lower drug doses and levodopa responsiveness, higher On and Off axial scores, On and Off BBS, higher On scores for PIGD, rigidity, bradykinesia and total motor MDS-UPDRS, lower On and Off tremor, lower-half predominance, lower asymmetrical presentation and symmetric index than PD patients. VaP patients had worse non-motor symptoms Scale (NMSS) than controls except for perceptual problems/hallucinations but better symptoms than PD patients except for urinary dysfunction. Quality of life (QoL) was impaired in VaP patients and was correlated with motor function and NMSs. The VaP group had significantly higher white matter lesions and brain atrophy, with lower hyperechogenicity of the substantia nigra and more impaired cerebral vascular resistance and vasoreactivity than the PD group. VaP has a characteristic motor and non-motor profile, with impaired QoL, white matter, and transcranial sonography abnormalities that differentiate it from PD. Further studies are warranted to explore the role of vascular lesions in the pathogenesis of VaP. The registered identifier NCT04308135 on clinical-Trial.gov. Registered on 03/12/2020.

Advanced waveform analysis of the photoplethysmogram signal using complementary signal processing techniques for the extraction of biomarkers of cardiovascular function.

Photoplethysmogram signals from wearable devices typically measure heart rate and blood oxygen saturation, but contain a wealth of additional information about the cardiovascular system. In this study, we compared two signal-processing techniques: fiducial point analysis and Symmetric Projection Attractor Reconstruction, on their ability to extract new cardiovascular information from a photoplethysmogram signal. The aim was to identify fiducial point analysis and Symmetric Projection Attractor Reconstruction indices that could classify photoplethysmogram signals, according to age, sex and physical activity. Three datasets were used: an in-silico dataset of simulated photoplethysmogram waves for healthy male participants (25-75 years old); an in-vivo dataset containing 10-min photoplethysmogram recordings from 57 healthy subjects at rest (18-39 or > 70 years old; 53% female); and an in-vivo dataset containing photoplethysmogram recordings collected for 4 weeks from a single subject, in daily life. The best-performing indices from the in-silico study (5/48 fiducial point analysis and 6/49 Symmetric Projection Attractor Reconstruction) were applied to the in-vivo datasets. Key fiducial point analysis and Symmetric Projection Attractor Reconstruction indices, which showed the greatest differences between groups, were found to be consistent across datasets. These indices were related to systolic augmentation, diastolic peak positioning and prominence, and waveform variability. Both fiducial point analysis and Symmetric Projection Attractor Reconstruction techniques provided indices that supported the classification of age and physical activity, but not sex. Both fiducial point analysis and Symmetric Projection Attractor Reconstruction techniques demonstrated utility in identifying cardiovascular differences between individuals and within an individual over time. Future research should investigate the potential utility of these techniques for extracting information on fitness and disease, to support healthcare-decision making.

Bond Incident Degree Indices of Connected (n,m)-Graphs With Fixed Maximum Degree

This article gives bounds on a substantial number of BID (bond incident degree) indices for connected graphs in terms of their order, size, and maximum degree. The considered BID indices include, among others, the Sombor index (together with its reduced version), atom-bond sum-connectivity index, symmetric division deg index, sum-connectivity index, harmonic index, and Randi´c index. All the graphs that attain the obtained bounds are also characterized. All the established bounds are valid also for molecular graphs. A graph of order n and size m is called an (n,m)-graph. The obtained bounds provide a partial solution to the problem of finding graphs with extremum (considered) BID indices over the class of all connected (n,m)-graphs with a fixed maximum degree under certain constraints.

Using Patent Data to Evaluate the Knowledge Dissemination of the Offshore Wind Power Industry

Many countries use the offshore wind power technology as renewable energy for sustainable development. In this study, we will focus on the knowledge dissemination of the offshore wind power technology. Not every country has the ability to develop their own offshore wind power technologies. The knowledge dissemination on sustainable technology could bridge the technology gap among the developer and promote the development of sustainable clean energy technology. Some objective evaluation indicators of knowledge dissemination will be carried out in this research and help to find appropriate companies to assist the local industry on offshore wind power industry. The public patent information is used to build a model to bring evaluation indicators about knowledge dissemination. These evaluation indicators include the revealed symmetric technological advantage index (RSTA), the knowledge density index ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D_c,m,t</i> ), and the relatedness knowledge base index ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_c,r,t</i> ). For RSTA, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> indicators, Siemens Aktiengesellschaft, Vestas Wind Systems, Siemens Gamesa Renewable Energy, and Aloys Wobben have higher values, which can be evaluated to have the higher degree of knowledge dissemination in the field of offshore wind power technology. Unlike previous studies that only using patent bibliographic data alone, employ evaluation indicators can extract more information about the knowledge dissemination. This study presents a promising method to evaluate the degree of knowledge dissemination in offshore wind power technology by using patent data.