Irregularity Descriptors Research Articles

Measuring Irregularities in the Chemical Compound: Porous Graphene

This study is based on the applications of many irregularity descriptors (IDs) which help us to discover the irregularity measurements (IMs) in the chemical compound named porous graphene. It is symbolized as PGRz×z , for z = 1, 2, 3 and 4. These IDs and IMs are used in this article to get new bounds for measurements. A graphical depiction and analysis have also been made over the molecular structure of Porous Graphene. Different IMs like IRDIF(ֆz), AL(ֆz), IRL(ֆz), IRLU(ֆz), IRLF(ֆz), IRF(ֆz), IRLA(ֆz), IRD1(ֆz), IRA(ֆz), IRGA(ֆz), IRB(ֆz), and IRR t (ֆz) have been considered. By using above-mentioned descriptors, we will be able to produce new formulas which are related to the IMs in PGRz × z , for z = 1, 2, 3, and 4.

A seismic fragility model accounting for torsional irregularity in low‐rise non‐ductile RC moment‐resisting frames

AbstractBuildings characterized by torsional irregularity are notorious for their vulnerability to earthquakes. However, most fragility/vulnerability models used for regional seismic risk assessment fail to distinguish between buildings with torsionally balanced and unbalanced configurations. The present study aims to develop a seismic fragility model sensitive to torsional irregularity for low‐rise non‐ductile RC moment frame buildings. To this end, a numerical investigation centred on 13 three‐storied plan‐asymmetric models, each characterized by a distinct combination of normalized stiffness eccentricity, torsional radius to mass radius of gyration ratio and normalized strength eccentricity, is presented. Using high‐dimensional model representation (HDMR), a metamodel for the maximum inter‐storey drift under bi‐directional seismic action is calibrated, considering average spectral acceleration and the above trio of torsional irregularity descriptors (TIDs) as the predictor variables. Carrying out numerical simulations on limit state functions formulated using the above demand model and appropriate capacity thresholds, the seismic fragility is estimated. The parameters of a lognormal fragility function compatible with the above estimates are determined using the method of maximum likelihood. A strong correlation is observed between the TIDs and the fragility function parameters. This reinforces the importance of accounting for all three TIDs while rating the seismic fragility of a building. Using least‐square error minimization technique, a functional relationship is established between the fragility model parameters and the TIDs. The framework described herein provides a simple, yet rational means to develop the next generation of seismic fragility models accounting for one of the most critical factors governing seismic behaviour––‘torsional irregularity’.

A Comparison Study of Irregularity Descriptors of Benzene Ring Embedded in P-Type Surface Network and Its Derived Network

Topological indices are atomic auxiliary descriptors which computationally and hypothetically portray the natures of the basic availability of nanomaterials and chemical mixes, and henceforth, they give faster techniques to look at their exercises and properties. Anomaly indices are for the most part used to describe the topological structures of unpredictable graphs. Graph anomaly examines are helpful not only for quantitative structure-activity relationship (QSAR) and also quantitative structure-property relationship (QSPR) but also for foreseeing their different physical and compound properties, including poisonousness, obstruction, softening and breaking points, the enthalpy of vanishing, and entropy. In this article, we discuss the irregularities of benzene ring and its line graph and compare them by its irregularity indices. We present graphical comparison by using Mathematica.

NIMG-57. ASSOCIATION OF RADIOMICS BASED TUMOR SHAPE IRREGULARITY MEASURES AND GAMMA KNIFE DOSE PLANNING INDICES IN VESTIBULAR SCHWANNOMAS

Abstract Gamma knife radiosurgery (GKRS) delivers an unevenly distributed radiation dose to a tumor, with a sharp falloff outside the target. Although the dose inhomogeneity within a tumor is strongly influenced by its shape, routine GKRS dose planning does not account for it. We hypothesized that shape irregularity measures were correlated with treatment planning indices, and might provide insight during treatment planning. The aims of this study were to quantify the shape irregularity measures in vestibular schwannomas, estimate their correlations with core radiosurgical planning measures, and define the most predictive shape feature for dose effectiveness. METHODS: Four dose plan indices, which were the selectivity index (SI), gradient index (GI), efficiency index (EI), and Paddick’s conformity index (PCI) were estimated from the GKRS plans of 234 vestibular schwannomas. All dose plans were prepared using Gamma Plan 10.0 and above and all treatments were delivered using a perfexion/ICON platform. Three-dimensional (3D) tumor models were rendered using 3D Slicer Software from segmented T1-weighted MR images. Sixteen irregularity measures were calculated for each tumor using Radiomics in MATLAB. Spearman correlation coefficients (r) were computed to find associations of the dose plan indices with the irregularity descriptors. The most predictive shape feature for dose efficiency was identified using the least absolute shrinkage and selection operator (Lasso). RESULTS: The shape irregularity measures were negatively correlated with SI, EI, and PCI, and positively correlated with GI. Volumetric index of sphericity (VioS) had the highest correlations with SI (r = 0.63, p= 3.27E-23), GI (r= -0.58, p= 1.10E-19), EI (r = 0.69, p= 0.00), and PCI(r= 0.68, p = 6.73E-28), and Lasso feature selection identified VioS as the most important feature for predicting all dose plan indices. CONCLUSION: VioS provides a numerical quantification of tumor shape irregularity, and it is highly correlated with the GKRS dose planning indices. *indicates co-senior authors

Torsional irregularity indices for the seismic demand assessment of RC moment resisting frame buildings

Design standards across the world use different parameters to quantify degree of torsional irregularity of buildings. Popular among such descriptors are the normalized static eccentricity ratio, torsional radius to mass radius of gyration ratio, maximum to minimum (or average) elastic floor displacement ratio, etc. However prior research, particularly on idealized single storey systems have indicated that these parameters do not correlate well with the seismic demands at all stages of structural behaviour (i.e. elastic and inelastic). The present study aims to identify a robust torsional irregularity index that captures the susceptibility of a structure to torsional effects at all ground motion intensity levels. To this end, the correlation between the maximum interstorey drift demands and popular torsional irregularity descriptors is first examined under different intensities of ground shaking using an approach that integrates multiple stripe analysis and statistical regression analysis. The numerical study is based on the nonlinear seismic assessment of thirteen three-storey gravity designed RC moment frame buildings subjected to bidirectional seismic excitation. The results indicate that none of the scalar indices considered correlate well with the drift demands at all intensities of ground shaking. A vector comprising of the normalized static eccentricity ratio and the torsional radius to mass radius of gyration ratio is found to perform well at low shaking intensity levels, where the structure responds in an elastic manner. However, at high intensity levels where the structure undergoes significant excursions into the inelastic range of behaviour, the strength eccentricity is observed to be a better descriptor of torsional irregularity. A three-element vector comprising of the above indices is found to capture the maximum interstorey drifts accurately at all ground motion intensity levels. A seismic demand model for maximum interstorey drift, sensitive to the above torsional irregularity descriptors, is also defined.

On irregularity descriptors of derived graphs

Topological indices are molecular structural descriptors which computationally and theoretically describe the natures of the underlying connectivity of nanomaterials and chemical compounds, and hence they provide quicker methods to examine their activities and properties. Irregularity indices are mainly used to characterize the topological structures of irregular graphs. Graph irregularity studies are useful not only for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies, but also for predicting their various physical and chemical properties, including toxicity, resistance, melting and boiling points, the enthalpy of evaporation and entropy. In this article, we establish the expressions for the irregularity indices named as the variance of vertex degrees, σ irregularity index, and the discrepancy index of subdivision graph, vertex-semi total graph, edge-semi total graph, total graph, line graph, paraline graph, double graph, strong double graph and extended double cover of a graph.

Analysis of the contour structural irregularity of skin lesions using wavelet decomposition

The boundary irregularity of skin lesions is of clinical significance for the early detection of malignant melanomas and to distinguish them from other lesions such as benign moles. The structural components of the contour are of particular importance. To extract the structure from the contour, wavelet decomposition was used as these components tend to locate in the lower frequency sub-bands. Lesion contours were modeled as signatures with scale normalization to give position and frequency resolution invariance. Energy distributions among different wavelet sub-bands were then analyzed to extract those with significant levels and differences to enable maximum discrimination.Based on the coefficients in the significant sub-bands, structural components from the original contours were modeled, and a set of statistical and geometric irregularity descriptors researched that were applied at each of the significant sub-bands. The effectiveness of the descriptors was measured using the Hausdorff distance between sets of data from melanoma and mole contours. The best descriptor outputs were input to a back projection neural network to construct a combined classifier system. Experimental results showed that thirteen features from four sub-bands produced the best discrimination between sets of melanomas and moles, and that a small training set of nine melanomas and nine moles was optimum.

A new method describing border irregularity of pigmented lesions

Automatic quantitative characterization of border irregularity generating useful descriptors is a highly important task for computer-aided diagnosis of melanoma. This paper proposes a novel approach to describe the border irregularity of melanomas aiming at achieving higher recognition rates. By introducing a boundary characteristic description, which we call a centroid distance diagram (CDD), a compact-supported mapping, called the centroid distance curve, can be extracted from this diagram. The centroid distance curve establishes the projection from angular orientations to the sum of the lengths of those line segments connecting the lesion centroid and border points. Border irregularity descriptors generated from CDDs include the non-centroid-convexity index, the maximum-minimum distance indicator, the standard deviation of centroid distance curves and the maximum magnitude of non-zero frequency elements of centroid distance curves after discrete Fourier transforms. Upper limits of the error boundaries involved in these descriptors are estimated. Experimental studies are based on 60 melanoma and 107 benign lesion images collected from local pigmented lesion clinics. By applying the proposed descriptors, receiver operating characteristic (ROC) curves are constructed by projecting the features into a linear space learned from samples. The optimal sensitivity and specificity for the proposed method are 74.2% and 72.6%. The total area enclosed by the corresponding ROC curve is 0.788. In addition, as the training and testing study for melanoma recognition in the literature is largely missing, a comprehensive comparative study is conducted by randomly dividing the data into two groups: one for training and one for testing. For the testing group, the best mean sensitivity obtained with the descriptors proposed in this paper reaches 71.8% and the standard deviation is 10.1%. The specificity for the testing group corresponding to the optimal sensitivity is 69.8%, with a standard deviation of 7.2%. This study suggests that in terms of sensitivity, descriptors extracted from CDDs are the most powerful ones in characterizing the border irregularity of melanomas.

Analysis of impulsive modes and Luenberger observers for descriptor systems

In this paper, the distinction between impulsive modes that can be generated by inputs and impulsive modes that can only be generated by initial conditions is investigated for linear time-invariant descriptor systems. It reveals that the input-generatable impulsive modes are very crucial to the existence of normal Luenberger observers of the systems. Based on this observation, an earlier known concept called strongly detectability for regular descriptor systems is extended to irregular case that is shown to be of much clearer physical meanings in classical sense than a recently proposed equivalent notion of causal detectability does. Thus, similar to the regular case, strong detectability is also a sufficient and necessary condition for the existence of normal Luenberger observers of irregular descriptor systems.