Singularity Index Research Articles

Research on comprehensive assessment of coastal erosion intensity based on multi index method

The intensity of coastal erosion is a measure of the strength of erosion processes affecting coastal areas. Traditionally, assessments of coastal erosion intensity have relied on singular indices, such as the rate of shoreline retreat or erosion, often prioritizing higher rates over lower ones. This approach, however, lacks comprehensive consideration and scientific rigor. In this study, we adopt a more holistic approach by examining the Qionghai-Wanning coast on the eastern side of Hainan Island. We selected four indices that reflect local conditions and influence coastal erosion strength: Annual rate of shoreline change (T1), Beach annual down-cutting rate (T2), Beach slope (T3), Average particle size of the beach (T4). These indices were used to comprehensively evaluate the erosion intensity of the Qionghai-Wanning coast. The evaluation results categorized the study area into six grades: serious erosion (3.45%), strong erosion (6.90%), erosion (20.69%), micro erosion (44.38%), stabilization (20.69%), and accretion (3.45%). The findings indicate that, under the broader environmental trends of global warming and rising sea levels, most sandy coasts exhibit micro-erosion intensity. Areas experiencing strong and serious erosion are predominantly influenced by human activities, such as those occurring in promenade bays, artificial islands, and harbors. To further understand the relationship between these factors and erosion intensity, we employed the Spearman correlation coefficient method. The analysis revealed that the T1 and the T2 are the primary factors influencing coastal erosion intensity, with the T4 serving as a secondary factor. These factors collectively impact the force and energy absorption of the coast through wave and tidal actions, ultimately determining the intensity of coastal erosion. The multi-index assessment method for coastal erosion intensity demonstrated an accuracy of 82.75%, providing a scientific basis for the management, protection, and restoration of coastal areas.

Strain energy density maximization principle for material design and the reflection in trans-scale continuum theory

Traditional efforts in the design of damage-tolerant structural materials were largely exercises in optimizing the combination of strength and ductility. However, the simultaneous consideration of these two conflicting mechanical indices, improving one inevitably sacrifices the other, makes the design extremely complex and difficult, due to the dilemma of choosing between them. Here, physically guided by the energy variational expression in trans-scale continuum mechanics theory, we propose a general mechanics principle for material design that involving only one index: towards strong and tough material the strain energy density limit (w) should be maximized, i.e., strain energy density maximization principle, referred to as wmax principle. It aims to guide the attainment of exceptional comprehensive mechanical properties, while circumventing the dual-index dilemma by employing a singular index w. Extensive experimental data analyses prove that (i) the maximum wmax always exists, at a critical dimension of characteristic microstructure dc,micro, and (ii) w can effectively index strength-ductility synergy and the wmax is conjugated with both high strength and high ductility, verifying the validity of wmax principle. The universality, practicality and downward compatibility are also examined. The dc,micro approaches twice the span of strain gradient region around internal boundary, suggesting that the microstructure state with wmax is the critical state with strongest strain gradient. Importantly, the w improvement as a function of the characteristic size of either microstructure or deformation field can be well captured by strain gradient theory, confirming the consistence between the wmax principle, experimental results and trans-scale continuum theories. This principle opens up a new design concept for advanced structural materials from the perspective of microstructure-w-mechanical properties relationship.

Electrolyte prognosis scoring system can predict overall survival in patients with osteosarcoma.

Osteosarcoma stands as the most prevalent bone tumor, characterized by a heightened tendency for local recurrence and distant metastasis, resulting in a bleak prognosis. Presently, there exists a shortage of novel markers to effectively determine the prognosis of osteosarcoma patients. Recent research indicates that hematological markers partially mirror an individual's microenvironment, offering potential insights into predicting patient prognosis. However, prior studies predominantly focused on the prognostic significance of singular hematological indices, failing to comprehensively represent the tumor microenvironment of patients. In our investigation, we meticulously gathered data on 22 hematological and electrolyte markers, utilizing LASSO Cox regression analysis to devise an Electrolyte Prognostic Scoring System (EPSS). The EPSS encompasses various indicators, including immunity, inflammation, coagulation, and electrolyte levels. Our findings indicate that the EPSS stands as an independent prognostic factor for overall survival among osteosarcoma patients. It serves as a valuable addition to clinical characteristics, adept at discerning high-risk patients from those deemed clinically low-risk. Furthermore, EPSS-based nomograms demonstrate commendable predictive capabilities.

Feature extraction for periodic impacts based on singular gini index

Feature extraction for periodic impacts based on singular gini index

Unsupervised Machine Learning-Based Singularity Models: A Case Study of the Taiwan Strait Basin

The identification of geochemical anomalies in oil and gas indicators is a fundamental task in oil and gas exploration, as the process of oil and gas accumulation is a low probability event. Machine learning algorithms for anomaly detection are applicable to the identification of oil and gas geochemical anomalies related to oil and gas accumulation. However, when using oil and gas indicators for anomaly detection, the diversity of these indicators often leads to the influence of the indicator redundancy on the identification of such features. Therefore, it is particularly important to select appropriate oil and gas indicators for anomaly detection. In this study, a hybrid model combining unsupervised machine learning methods and singularity analysis methods was used to evaluate oil and gas indicator anomalies using geochemical data from the Taiwan Strait Basin. The models used in this study include the singularity index model (LSP), the principal component model combined with the singularity index model (PCA and LSP), and the cluster analysis combined with the principal component model and the singularity index model (CLA-PCA-LSP). PCA models can reduce the dimensions of the data and retain as much information as possible. CLA divides data samples into different groups, so that samples within the same group are more similar and samples between different groups are less similar. LSP is mainly used for measuring the setting and singular degree of local anomalies in multi-scale geochemistry, geophysics, and other types of local anomalies, and it has a unique advantage in extracting low and weak anomalies and nonlinear characteristics. The results of the study show that the results obtained using the CLA-PCA-LSP hybrid model are very similar to those obtained by performing PCA on the entire index and then calculating the singularity index. This also verifies that, for the study areas of the Jiulongjiang Depression and Jinjiang Depression, we can select oil and gas indicators that are favorable for exploration analysis, without including all indicators in the analysis scope, thereby improving the computational efficiency. The application of a singularity analysis method and generalized self-similarity principle in extracting the geochemical information of oil and gas indicators in the Taiwan Strait Basin highlights key technologies such as the identification of weak anomalies, decomposition of composite anomalies, and integration of spatial information. The combination anomalies delineated by the singularity analysis method and S-A method not only reflect the spatial relationship with known oil and gas reservoir distribution, but also show the multiple combination anomalies in unknown areas, providing favorable guidance for the next exploration direction in the Taiwan Strait Basin.

Research progress of lipid-derived parameters in atherosclerotic cardiovascular disease

Dyslipidemia stands as an autonomous peril in the realm of atherosclerotic cardiovascular maladies. Prompt identification and timely intervention in the case of dyslipidemia hold promise for substantially curbing the onset and fatality rates associated with coronary heart disease. Traditional lipid surveillance metrics employed in clinical settings, such as low-density lipoprotein cholesterol, exhibit notable limitations. Conversely, lipid-derived parameters emerge as formidable contenders, demonstrating a capacity to amalgamate and quantify disparate risk factors and multifactorial etiologies inherent in a given disease. By encompassing a broader spectrum of information than singular indices, these parameters offer a more profound insight into disease progression by virtue of their grounding in the physiological intricacies of lipid metabolism. Drawing upon extant domestic and international guidelines and research, this discourse delineates and synthesizes four lipid-derived parameters with promising clinical applications: atherogenic index of plasma, non-high-density lipoprotein cholesterol to high-density lipoprotein cholesterol ratio, apolipoprotein B/A1 ratio, and lipoprotein combine index, and forwards a perspective grounded in current strides in clinical research.

Spatio-temporal analysis of Permian-Cretaceous magmatic activities in the Tengchong block: Implications for tectono-magmatic evolution

Understanding the tectono-magmatic evolution history of the Tengchong block is crucial for elucidating the formation of the Eastern Tethys tectonic domain. However, the correlation and evolution of the Tengchong block with the Sibumasu and Lhasa blocks is controversial during the Permian and Cretaceous. This study explores the information contained within magmatic rocks using big data and spatio-temporal analysis, providing quantitative constraints for the discussion of the tectono-magmatic evolution of the Tengchong block. To more accurately assess true magma activities and reduce errors caused by preservation and sampling processes, we utilized local singularity analysis to obtain the singularity index time-series. Correlation analysis of zircon ages and εHf(t) (correlation coefficient ≥ 0.5) values indicates that the Tengchong block is more similar to the Sibumasu block. Results from time-lagged cross-correlation analysis indicate that the Tengchong block and Sibumasu block exhibit a shorter lag in magmatic activities (3 Myr). Wavelet analysis reveals similar periods of collision-related magmatic activities (57 Myr and 43 Myr). Integrating evidence from paleontology and ophiolite belts, we propose that the Tengchong block co-evolved more closely with the Sibumasu block than with the Lhasa block, suggesting similar tectonic processes during the Early Permian to Early Cretaceous. Approximately 250–236 Ma, in the western Tengchong block, partial melting of the lower crust occurs due to crustal thickening. Around 219–213 Ma and 198–180 Ma, after the Tengchong block collided with the Eurasian continent, the subduction of the Meso-Tethys Ocean commenced. Around 130–111 Ma, the overall tectonic feature was a scissor-like closure of the Meso-Tethys Ocean from north to south.

Optimizing Fractional Differential Equation Solutions with Novel Müntz Space Basis Functions

This paper introduces innovative basis functions derived from Müntz spaces, aimed at addressing the computational challenges of Fractional Differential Equations (FDEs). Our primary focus is the creation of these functions using singular indices linked to the solutions of FDEs. We thoroughly investigate the properties of these fundamental functions to understand their operational potential. These functions are particularly adept at capturing initial singular indices, making them highly suitable for solving FDEs. The proposed numerical method is distinguished by its rapid convergence rates, showcasing its efficiency in computational evaluations. We validate our approach by presenting numerical examples that highlight its accuracy and reliability. These examples confirm the effectiveness and efficiency of the new basis functions from Müntz spaces in accurately solving FDEs. This research advances numerical methods for FDEs and serves as a valuable resource for researchers seeking robust and reliable techniques

Comparative Bibliometric Analysis of Established and Emerging Databases on Salivary Biomarkers for Early Oral Cancer Diagnosis.

Salivary biomarkers play an important role in the preventive strategy for oral cancer detection at an early stage. The aim of this study was to carry out a comparative quantitative analysis of the research material on the topic in one established database, Scopus and another emerging database, Dimensions. An electronic search was performed in Scopus and Dimensions in April 2024 with the search subjects "Saliva," "Biomarkers," "Diagnosis," and "Oral Cancer." The retrieved data were analyzed using Biblioshiny for RStudio and MS Excel. The search yielded 229 and 158 documents in Scopus and Dimensions, respectively. The data were studied to understand the coverage, concentration, and diversion of research articles. The analysis revealed high singularity index for Scopus and low overlap percentage between the two databases. Scopus was found to have higher citation count per article, however, the citation correlation between Scopus and Dimensions was found to be strong. Author productivity was found to be low in both the databases. Scopus and Dimensions vary in their scope, volume of data, and coverage policies. Both the databases have complimentary coverage on salivary biomarkers for oral cancer diagnosis. However, Scopus has a greater number of articles, sources, and citations resulting in better coverage of the topic.

Geochemical anomaly separation based on geology, geostatistics, compositional data and local singularity analyses: A case study from the kuh panj copper deposit, Iran

This study combines geochemical anomaly separation with geostatistical approaches and compositional data analysis. To have a reasonable model for abnormal areas, suggesting the optimal drilling coordinates, one needs to consider some effective geological controllers on the mineralization such as lithology, alteration, and tectonic processes. The lithogeochemical samples at 608 locations were processed from the copper porphyry mineralization area of Kuh Panj, Iran, to illustrate the proposed approach. The heterogeneity of rock type domains was detected using contact analysis. Based on this, plurigaussian simulation made it possible to model the uneconomic dykes of the area. Copper-molybdenum grades and filler as geochemical components were transformed into multivariate normal data using isometric logarithmic ratio-flow anamorphosis. Hierarchical rock type-grade simulation reproduced the grade behavior at hard rock type boundaries. Selection of a dense and regular simulation grid minimized the smoothing effect caused by interpolation of the singularity index values. Finally, unsupervised machine learning identified the anomaly zone by clustering the results of the singularity analysis. Validation using drilling data and the geological map shows that the anomaly separation, considering the geological conditions and the compositional nature of the geochemical data, can provide a reliable model of the geochemical anomalies in the Kuh Panj deposit.

Feasibility study of the use of a wearable vital sign patch in an intensive care unit setting.

Multiple studies and review papers have concluded that early warning systems have a positive effect on clinical outcomes, patient safety and clinical performances. Despite the substantial evidence affirming the efficacy of EWS applications, persistent barriers hinder their seamless integration into clinical practice. Notably, EWS, such as the National Early Warning Score, simplify multifaceted clinical conditions into singular numerical indices, thereby risking the oversight of critical clinical indicators and nuanced fluctuations in patients' health status. Furthermore, the optimal deployment of EWS within clinical contexts remains elusive. Manual assessment of EWS parameters exacts a significant temporal toll on healthcare personnel. Addressing these impediments necessitates innovative approaches. In this regard, wearable medical technologies emerge as promising solutions capable of continual monitoring of hospitalized patients' vital signs. To overcome the barriers of the use of early warning scores, wearable medical technology has the potential to continuously monitor vital signs of hospitalised patients. However, a fundamental inquiry arises regarding the comparability of their reliability to the current used golden standards. This inquiry underscores the imperative for rigorous evaluation and validation of wearable medical technologies to ascertain their efficacy in augmenting extant clinical practices. This prospective, single-center study aimed to evaluate the accuracy of heart rate and respiratory rate measurements obtained from the Vivalink Cardiac patch in comparison to the ECG-based monitoring system utilized at AZ Maria Middelares Hospital in Ghent. Specifically, the study focused on assessing the concordance between the data obtained from the Vivalink Cardiac patch and the established ECG-based monitoring system among a cohort of ten post-surgical intensive care unit (ICU) patients. Of these patients, five were undergoing mechanical ventilation post-surgery, while the remaining five were not. The study proceeded by initially comparing the data recorded by the Vivalink Cardiac patch with that of the ECG-based monitoring system. Subsequently, the data obtained from both the Vivalink Cardiac patch and the ECG-based monitoring system were juxtaposed with the information derived from the ventilation machine, thereby providing a comprehensive analysis of the patch's performance in monitoring vital signs within the ICU setting. For heart rate, the Vivalink Cardiac patch was on average within a 5% error range of the ECG-based monitoring system during 85.11±10.81% of the measured time. For respiratory rate this was during 40.55±17.28% of the measured time. Spearman's correlation coefficient showed a very high correlation of 8 for heart rate and a moderate correlation of for respiratory rate. In comparison with the ventilated respiratory rate (ventilation machine) the Vivalink and ECG-based monitoring system both had a moderate correlation of A very high correlation was found between the heart rate measured by the Vivalink Cardiac patch and that of the ECG-based monitoring system of the hospital. Concerning respiratory rate the correlation between the data from the Vivalink Cardiac patch, the ECG-based monitoring system and the ventilation machine was found to be moderate.

Polarization Möbius strip at the tight focus of a generalized Poincaré beam

Based on the Richards-Wolf formalism, we investigate tight focusing of a generalized Poincaré beam. Analytical expressions are derived for all components of the electric field strength vector in the focal plane. For superposition of a right-handed circularly polarized plane wave with a left-handed circularly polarized optical vortex with topological charge –1, we obtain expressions for the intensity distribution and the longitudinal component of the spin angular momentum vector at the tight focus. We demonstrate both theoretically and numerically that the initial beam has topological charge –1/2 and, in the center of the focal plane, there is a C-point (a point with circular polarization which makes a C-line along the optical axis) with the singularity index of –1/2 (star), whereas the vector of major axis of the polarization ellipse makes along a certain-radius circle around the optical axis a single-side polarization Möbius stripe of the order –3/2, which has three half-turnovers and one stitching, where two opposite major axis vectors of the polarization ellipse meet.

Optical spin and orbital Hall effects at the tight focus of the superposition of two coaxial cylindrical vector beams with different-parity numbers

We study properties of a light field at the tight focus of the superposition of two different-order cylindrical vector beams (CVBs). In the source plane, this superposition has a polarization singularity index amounting to the half-sum of the numbers of two constituent CVBs, while having neither spin angular momentum (SAM) nor transverse energy flow. We show that if the constituent CVBs have different-parity numbers, in the focal plane there occur areas that have opposite-sign longitudinal SAM projections, alongside areas of opposite-handed energy flows rotating on closed paths (clockwise and anticlockwise). The observed phenomena indicate that longitudinal optical spin/orbital Hall effects occur in the focal plane. It is found that if the two constituent CVBs have the same-parity numbers, in the focal plane the light field is inhomogeneously linearly polarized and the energy flow (Umov-Poytning vector) has just a longitudinal component. It is also shown that in the focal plane, the intensity of the on-axis superposition of two opposite-parity CVBs is defined by the sum of the constituent beams’ intensities, as though the two beams would be orthogonally polarized. Meanwhile, in the source plane, the beams under study are not orthogonally polarized and the relation for the intensity contains an interference term.

Optimal signal quality index for remote photoplethysmogram sensing

Remote photoplethysmography (rPPG) enables non-invasive monitoring of circulatory signals using mobile devices, a crucial advancement in biosensing. Despite its potential, ensuring signal quality amidst noise and artifacts remains a significant challenge, particularly in healthcare applications. Addressing this, our study focuses on a singular signal quality index (SQI) for rPPG, aimed at simplifying high-quality video capture for heart rate detection and cardiac assessment. We introduce a practical threshold for this SQI, specifically the signal-to-noise ratio index (NSQI), optimized for straightforward implementation on portable devices for real-time video analysis. Employing (NSQI < 0.293) as our threshold, our methodology successfully identifies high-quality cardiac information in video frames, effectively mitigating the influence of noise and artifacts. Validated on publicly available datasets with advanced machine learning algorithms and leave-one-out cross-validation, our approach significantly reduces computational complexity. This innovation not only enhances efficiency in health monitoring applications but also offers a pragmatic solution for remote biosensing. Our findings constitute a notable advancement in rPPG signal quality assessment, marking a critical step forward in the development of remote cardiac monitoring technologies with extensive healthcare implications.

Mapping exploration targets through multifractal modelling of soil geochemical data in the Xiaohongshilazi Pb–Zn–(Ag) ore district, Jilin Province, NE China

The Xiaohongshilazi Pb–Zn–(Ag) ore district, located in the Jizhong–Yanbian Metallogenic Belt in NE China, presents challenges in identifying geochemical anomalies and prospecting minerals due to thick covers, complex geological evolution and mining activities. To overcome these obstacles, we adopted an innovative approach that combines multifractal theory with concentration-area (C-A) modelling and local singularity analysis (LSA) to characterize the geochemical signature. Initially, factor analysis of log-transformed data was used to identify ore-forming factors, which were then modelled using C-A and LSA. Subsequently, modelling results were compared to conventional maps generated using inverse distance weighted (IDW) interpolation. Additionally, the C-A model was employed to establish thresholds for singularity indices generated by LSA for target mapping. The results revealed a close relationship between Factor 1 (F1) and mineralization. The C-A model of F1 failed to detect weak anomalies compared to the IDW-interpolated map, while LSA not only identified weak anomalies but also enhanced the detection of reliable anomalies. Three prospecting targets (PT-01, PT-02 and PT-03) were identified. Validation of PT-01 using new drillholes and existing mineralization confirms the effectiveness of targets and the accuracy of the model. Our approach provides a robust alternative for prospecting at ore districts encountering similar challenges.

Research on SAR image denoising method based on feature extraction

AbstractDue to the excellent characteristics of Synthetic Aperture Radar (SAR), it has become an important technical means for land and sea target detection applications worldwide. However, the SAR image imaging process is often accompanied by speckle noise, which affects the accuracy of target detection. For this problem, this paper proposes an SAR image reconstruction model based on image denoising and feature extraction. Given a noisy SAR image, at each pixel of the image, the value of the singularity index of a metric defined by the signal gradient norm density is calculated. Then through a hierarchical decomposition of these singular indices, a set of pixels containing the most informative feature set of the image is extracted, and a denoised image is reconstructed using the extracted features. In comparison to traditional filtering and denoising techniques such as non‐local filtering, this algorithm achieves remarkable local filtering and denoising effects while preserving the image's texture information. The denoising performance of the proposed method is evaluated through a series of quantitative indicators and visual comparisons. The results demonstrate that this method effectively reduces background clutter, resulting in a higher contrast between the target and the background.

Development of a Probability-Based In Vitro Eye Irritation Screening Platform.

Traditional eye irritation assessments, which rely on animal models or ex vivo tissues, face limitations due to ethical concerns, costs, and low throughput. Although numerous in vitro tests have been developed, none have successfully reconciled the need for high experimental throughput with the accurate prediction of irritation potential, attributable to the complexity of irritation mechanisms. Simple cell models, while suitable for high-throughput screening, offer limited mechanistic insights, contrasting with more physiologically relevant but less scalable complex organotypic corneal tissue constructs. This study presents a novel strategy to enhance the predictive accuracy of screening-compatible simple cell models in eye irritation testing. Our method combines the results of two in vitro assays-cell apoptosis and nociceptor (TRPV1) activation-using micropatterned chips to partition human corneal epithelial cells into numerous discrete small populations. Following exposure to test compounds, we measure apoptosis and nociceptor activation responses. The large datasets collected from the cell micropatterns facilitate binarization and statistical fitting to calculate a mathematical probability, which assesses the compound's potential to cause eye irritation. This method potentially enables the amalgamation of multiple mechanistic readouts into a singular index, providing a more accurate and reliable prediction of eye irritation potential in a format amenable to high-throughput screening.

Polarization singularity index determination using wedge plate lateral shear interferometry

Polarization singularity is a point in an inhomogeneous polarization distribution at which the azimuth of the polarization ellipse is indeterminate. The azimuth gradient is solenoidal around the polarization singular point. In metrology, shear interferometry enables the visualization of phase gradients in optical beams. Since the polarization azimuth gradient is related to the Stokes phase gradient, we adopt the shear interferometry technique to visualize these phase gradients for the detection of polarization singularity. We use a wedge plate lateral shear interferometer (LSI) in our experiments for the detection of the ellipse and vector field singularities. Being a self-referencing and intensity-based technique, this method is convenient for practical use. Unlike the traditional Stokes polarimetry method, where the polarization distribution at every spatial point is evaluated, this technique can distinguish degenerate states of polarization singularities simply by visual observation of intensity fringes. Index and helicity measurement of these polarization singularities without using polarization measurement methods are novel aspects of this scheme. Both theoretical and experimental results are presented to support our claim.

Chain position optimization of a 4UPS−UPU parallel mechanism considering dynamic coupling effects

The strong dynamic coupling effects among kinematic chains are not beneficial to the control of parallel mechanisms. This paper deals with the chain position optimization of a 4UPS−UPU parallel mechanism to reduce dynamic coupling effects among kinematic chains. Using the kinematic model, the Jacobian matrix is derived, and a method is proposed to transform it into a non-dimensional form and being independent of scaling factors. A singularity index is formulated based on the normalized determinant of the modified Jacobian matrix, guiding the optimization of chain positions at the base platform. Subsequently, the dynamic model is derived by using the principle of virtual work and a novel dynamic coupling index is proposed by taking both the inertia and centrifugal terms in the dynamic model into account. The neural network is then employed to enhance the calculation efficiency of the dynamic coupling index. Finally, the chain positions at the moving platform are optimized using Particle Swarm Optimization algorithm. This optimization process significantly reduces the dynamic coupling effects among kinematic chains in the parallel mechanism, thereby conferring advantageous benefits to its overall control.

Influence of Primary Coma on the Tightly Focusing Characteristics of Circular Basis Hybrid Order Poincaré Sphere Beams

Analogous to the Poincaré sphere, a hybrid order Poincaré sphere is used to represent the ellipse field singularities (C-points). We study the tight focusing properties of generic bright and dark hybrid order Poincaré sphere beams in the presence of primary coma. The role of the polarization singularity index and handedness of the polarization of the hybrid order Poincaré sphere beams on the focused structure has been discussed. Results have been presented for the total intensity, component intensities, and component phase distributions for left- and right-handed bright and dark star and lemon types singularities. The presence of primary coma distorted the focal plane intensity distributions for both positive and negative index generic C-points. Coma is known to disturb the circular symmetry of the focal plane intensity distribution. Similarly in tight focusing polarization is known to disturb the symmetry. Therefore, a beam with structured and inhomogeneous polarization distribution tightly focused under the influence of coma is a fit case to study. It is found that the presence of primary coma aberration in the focusing system produces a positional shift of the high-intensity peaks and a reduction of the intensity on one side of the center. As the strength of the primary coma increases, the focal plane intensity distributions shift more and more toward the right from the initial position. Unlike the scalar vortex case, in the case of hybrid order Poincaré sphere beams, the focal plane intensity distribution undergoes rotation, as the helicity of the hybrid order Poincaré sphere beams is inverted, in addition to shifting. All the component phase distributions are found to be embedded with phase vortices of charge ±1.