Canonical Variables Research Articles

A demonstration of the effect of fringe-rate filtering in the hydrogen epoch of reionization array delay power spectrum pipeline

Abstract Radio interferometers targeting the 21cm brightness temperature fluctuations at high redshift are subject to systematic effects that operate over a range of different timescales. These can be isolated by designing appropriate Fourier filters that operate in fringe-rate (FR) space, the Fourier pair of local sidereal time (LST). Applications of FR filtering include separating effects that are correlated with the rotating sky vs. those relative to the ground, down-weighting emission in the primary beam sidelobes, and suppressing noise. FR filtering causes the noise contributions to the visibility data to become correlated in time however, making interpretation of subsequent averaging and error estimation steps more subtle. In this paper, we describe fringe rate filters that are implemented using discrete prolate spheroidal sequences, and designed for two different purposes – beam sidelobe/horizon suppression (the ‘mainlobe’ filter), and ground-locked systematics removal (the ‘notch’ filter). We apply these to simulated data, and study how their properties affect visibilities and power spectra generated from the simulations. Included is an introduction to fringe-rate filtering and a demonstration of fringe-rate filters applied to simple situations to aid understanding.

Canonical correlation-based relationships between social support and sleep quality in a hospital psychiatric outpatient population with examining the mediating roles of anxiety and depressive symptoms

Objective: This study aims to examine the associations between various dimensions of social support and sleep quality in a hospital psychiatric outpatient population using canonical correlation analysis, while also investigating the potential mediating roles of anxiety and depressive symptoms. Methods: Employing a cross-sectional design, survey data were collected from 10,071 individuals visiting Hangzhou Seventh People’s Hospital between October 2020 and October 2023. After excluding invalid cases, a total of 10,063 participants were included for analysis. The survey encompassed gathering basic demographic information as well as administering the Social Support Rating Scale, Self-rating Depression Scale, Self-rating Anxiety Scale, and Pittsburgh Sleep Quality Index Scale. Data analysis was conducted using SPSS 27.0 statistical software with canonical correlation analysis employed to examine the relationships. Additionally, the mediating effects of anxiety and depression symptoms were examined using the SPSS PROCESS macro. Results: Canonical correlation analysis reveals a significant positive correlation between social support dimensions and various aspects of sleep quality. The first pair of canonical variables (r = 0.586, p < 0.001) accounts for an impressive 97% of the cumulative contribution. It is found that this pair of canonical variables explains 68.9% of the variance in social support and 49.0% in sleep quality. Mediation analysis revealed that anxiety and depressive symptoms significantly mediated the relationship between social support and sleep quality, accounting for 88% of the total effect. Specifically, anxiety accounted for 47% mediation while depression accounted for 41%. Conclusion: The study findings revealed a significant positive correlation between social support and sleep quality dimensions, indicating a robust association between increased social support and enhanced individual sleep quality. Furthermore, the results indicated that anxiety and depression partially mediated the relationship between social support and sleep quality, offering novel insights into the intricate connection between mental health and sleep quality.

On the Limited Role of Conservation Laws in the Double Reduction Routine for Partial Differential Equations

The double reduction method for finding invariant solutions of a given partial differential equation (PDE) provides for the reduction of a $ q $-th order PDE that admits a nontrivial Lie symmetry and an associated nontrivial conservation law to an ordinary differential equation (ODE) of order $ q-1. $ In all the articles we have seen where the method has been used, the algorithm has involved writing the conservation law in canonical variables determined by the associated symmetry. In this paper, we illustrate that it is not necessary to use or even have the associated conservation law. It is enough to know that there exists a conservation law associated with a given Lie symmetry. Canonical variables derived from the symmetry are sufficient to achieve double reduction. In the canonical variables, the PDE is transformed after routine calculations into an ODE of order one less than that of the PDE. We have outlined steps involved in this variation of the double reduction method and illustrated the routine using five PDEs.

A neural implementation of cognitive reserve: Insights from a longitudinal fMRI study of set-switching in aging

Aging is often accompanied by changes in brain structure and executive functions, particularly in tasks involving cognitive flexibility, such as task-switching. However, substantial individual differences in the degree of cognitive impairment indicate that some individuals can cope with brain changes more effectively than others, suggesting higher cognitive reserve (CR). This study identified a neural basis for CR by examining the longitudinal relationship between task-related brain activation, structural brain changes, and changes in cognitive performance during an executive task-switching paradigm including single and dual conditions. Fifty-two older individuals were assessed at baseline and followed up after five years. Structural brain changes related to task-switching performance were analyzed using elastic net regression. Task-related functional brain activation was measured using ordinal trends canonical variate analysis (OrT CVA), capturing patterns of activation increasing from single to dual conditions. A differential task-related expression score (dOrT) was calculated as the difference in pattern expression scores between single and dual conditions at baseline. A linear regression model tested whether dOrT moderated the impact of brain changes on changes in switch cost over five years. Results showed a significant interaction between changes in brain structure and dOrT activation on switch cost change, indicating a moderation effect of task-related activation. Higher dOrT buffered the impact of brain structural decline on switch costs, enabling older adults to better cope with age-related brain structural changes and preserve cognitive flexibility. These findings suggest that these task-related activation patterns represent a neural basis for CR.

Lifetime Adversity and Risky Substance Use among Transgender Emerging Adults: Selected Interventions and Clinical Social Work Practice

AbstractThis study investigated multivariate relations between indicators of lifetime adversity and past year risky substance use reported by an Internet-recruited sample of transgender emerging adults from the United States (N = 248, age M = 22.61 years). Canonical correlation analysis (CCA) documented the canonical correlation between canonical variates in this sample (.362), as well as the amount of shared variance (13.1%) between set of variables representing lifetime adversity and past year risky substance use. Examination of the standardized canonical coefficients and structure coefficients highlighted the important contributions of (a) past year drug use and negative consequences of substance use to the synthetic criterion variable and (b) lifetime intimate partner violence to the synthetic predictor variable. Information generated in this study about how specific observed variables contributed to canonical variates may be used to tailor trauma-informed selected interventions in clinical socialwork practice with transgender emerging adults who report substance use problems.

Shape analysis of the craniofacial skeleton in children prenatally exposed to anticonvulsant medications using geometric morphometrics.

Children exposed prenatally to antiepileptic drugs may have a typical facies characterized by midfacial retrusion, a short nose, and anteverted nares. Our aim was to determine whether the shape of the maxilla was altered in its sagittal displacement, or whether the defect in the underlying articulation with the cranial base was responsible for the appearance of midface retrusion. Our hypothesis was that the sphenoid bone as well as the maxilla and other bones in the cranial base were affected by the anticonvulsant medication. The lateral cephalograms of 65 children exposed prenatally to monotherapy (phenobarbital, phenytoin, or carbamazepine) were evaluated using various analyses derived from geometric morphometrics (GM) on different studied areas (maxilla, entire cranial base, spheno-occipital region, and the total study area) and the resulting configurations compared with those of control children. Procrustes ANOVA suggested that shape variation for all the regions correlated significantly (p < 0.0001) with exposure to antiepileptic drugs, and principal component analysis revealed a noticeable separation between the means of the two groups when PC1 was plotted against PC2 for all the areas studied. The cross-validation resulting from the discriminant function analysis accurately classified between 79.5% and 88.6% of the control group and between 73.8% and 90.7% of the study group when looking at the different anatomic regions. Canonical variate analysis, applied to the sample after its separation following biological sex and stratification into two age groups, showed unequal results between males and females as well as during circumpubertal growth of the cranial base. Thus, in the exposed subjects, while the glabella was projected forward with a similar prominence in males and females, the rhinion, which is relocated more posteriorly, was more severely displaced in females as opposed to the sella, where the most important displacement occurred in males. Regarding the age groups, it revealed that patients in the younger group of both sexes exhibited a facial shape difference very early (p < 0.0001) when the comparison was performed between exposed and non-exposed subjects. This difference was maintained in females at older ages but not in males. These details may help isolate the mechanism for the anomalies because of GM's use of shape instead of traditional linear and angular cephalometric measurements.

Which Attributes Explain Gender Differences in Impostor Syndrome Scores in Medicine and Health Sciences Students: A Secondary Multivariate Analysis

Impostor Syndrome (IS) is a psychological pattern where individuals doubt their accomplishments and fear being exposed as frauds, despite evidence of success. This study investigates gender differences in IS among 753 medical and health sciences students and graduates, using the Clance Impostor Phenomenon Scale. We aim to discern item-specific gender disparities in IS manifestations and develop a canonical variable that encapsulates these differences. Our findings reveal significant disparities: women display higher scores related to self-doubt and fear of failure, while specific IS aspects in men are associated with overcompensation. These insights suggest the need for gender-specific educational and clinical strategies to address IS in medicine and health sciences. By employing a multivariate analysis of variance, this study refines our understanding of how IS differently affects genders, aiding in the design of targeted interventions that can enhance well-being and professional efficacy among future healthcare professionals. Such strategies are crucial, emphasizing the importance of creating supportive environments to foster resilience in these high-stakes fields.

Integrating Canonical Correlation Analysis with Random Forest for Heart Disease Prediction

Heart disease, a leading global cause of death over the past several decades, encompasses a range of disorders affecting the heart. Researchers use various data mining and machine learning techniques to analyze complex medical data, aiding healthcare professionals in predicting cardiac conditions. Despite these advances, existing models often struggle with effectively modelling non-linear relationships, maximizing feature correlation, and addressing challenges related to dimensionality and overfitting. This research paper introduces the Hybrid CCRF model for heart disease prediction, which integrates Canonical Correlation Analysis (CCA) with Random Forest. The proposed model generates polynomial features to capture non-linear relationships and applies Canonical Correlation Analysis to identify canonical variables that maximize correlations between heart disease features and chronic condition features. By combining these canonical variables into a single feature set, the model enhances prediction accuracy. The objectives of the Hybrid CCRF model are threefold: 1) To capture complex non-linear relationships between heart disease and chronic condition features by integrating polynomial feature generation with Canonical Correlation Analysis, thereby improving the model’s ability to represent intricate data patterns; 2) To use CCA to identify and integrate canonical variables that enhance feature correlation, creating a more informative feature set; and 3) To address high-dimensional data and overfitting issues by combining canonical variables with polynomial features in a Random Forest model, balancing complexity and performance for improved generalization and robustness across various datasets. The proposed model achieved an accuracy of 99.45%, with a sensitivity of 98.53%, specificity of 99.54%, precision of 95.73%, and an F1 Score of 0.9711, outperforming all existing models.

Genetic variability increase by gamma irradiation of soybean seeds

The increase of genetic variability by the appearance of new genes of agronomic interest may be favored by the use of gamma radiation. The objective of this study was to evaluate different doses of gamma irradiation on dry seeds of VX04-5692 soybean line, aiming to increase the genetic variability and, with this, the identification of possible mutant plants. The doses of 0, 50, 150 and 250 Gy of gamma radiation were applied from a60Co source. The newly irradiated seeds were sown in the field, giving rise to the M1 cycle. Selected plants originated the M2 cycle. The number of seedlings was counted on the 21st day after sowing. Ten plants of each row were identified and evaluated for the various agronomic characteristics and for chemical composition. The data were submitted to analysis of variance. The F test was applied and the results were presented by boxplots and biplot (canonical variables). There was effect of gamma radiation doses at plant height at full bloom and maturity, number of nodes, pods with one seed and seeds per pod. The use of gamma radiation increases the variability in soybean, with consequent increase in the probabilities of identification of new mutants and gains in the chemical composition, useful for breeding programs that aim at better agronomic performance and gains in oil and protein contents. More satisfactory results in the generation of variability are obtained by the application of gamma radiation on soybean dry seeds between 50 and 150 Gy.

Constraints of the teleparallel equivalent of general relativity in a gauge

We consider a specific Hamiltonian formulation of the Teleparallel Equivalent of General Relativity, where the canonical variables are expressed by means of differential forms. We show that some “position” variables of this formulation can be always gauge-transformed to zero. In this gauge the constraints of the theory become simpler, and the other “position” variables acquire a nice geometric interpretation that allows for an alternative, clearer form of the constraints. Based on these results we derive some exact solutions to the constraints.

Association of hospital safety climate and compliance with occupational safety practices among nurse interns: A cross-sectional study using canonical correlation analysis.

Nurse interns may be at a similar or higher risk than registered nurses. The key elements and mechanisms involved in the effects of safety climate on safety performance are not well understood. This study explores the relationship between the perceived hospital safety climate and compliance with occupational safety practices among nurse interns. A cross-sectional study was conducted among 178 nurse interns in three tertiary university hospitals in Chongqing city, China. The Chinese version of the Hospital Safety Climate Scale (HSCS) was used to measure the perceived hospital safety climate of nurse interns. Compliance behavior was measured using the Compliance with Occupational Safety Practice Scale (COSPS). Canonical correlation analysis and multiple linear regression modeling were used to examine their relationship. Total scores for the HSCS and COSPS were 92 (80,100) and 185 (175,185) [M (P25, P75)], respectively. Canonical correlation coefficients for canonical variates 1 and 2 were 0.636 (p < 0.001) and 0.414 (p < 0.001), respectively. Nurse interns' compliance with occupational safety practices was mainly influenced by management support, feedback/training, personal protective and engineering control equipment availability, and absence of job hindrance. Multiple linear regression showed that management support of HSCS accounted for 37.1% of the variance in compliance (β = 0.283, p = 0.039). Nurse interns reported high levels of perceived hospital safety climate and compliance with occupational safety practices. Younger nurse interns reported a lower level of perceived hospital safety climate. Nurse educators can improve interns' compliance by promoting better management support, feedback/training, personal protective and engineering control equipment availability, and fewer job hindrance.

Analysis of the pharyngeal structure of the genus Oreochromis for species identification through geometric morphometrics in the Aguamilpa reservoir, Nayarit, Mexico

Tilapia is an important fishing resource in economic terms for continental ecosystems such as dam reservoirs and lagoons. In Nayarit, the Aguamilpa Dam reservoir contributes around 50 % of the tilapia production in the state. However, despite the social and economic importance of the resource, there are few studies on it in this reservoir, and it is still unknown with certainty which species are found in the reservoir. This work is the first report for the Aguamilpa reservoir, where geometric morphometrics was used as a tool for the identification of tilapia species. The pharyngeal plate of 230 organisms was used for the geometric morphometrics analysis. According to this study, the existence of three species of the genus Oreochromis (O. aureus, O. niloticus and Oreochromis mossambicus) is confirmed; according to the analysis of canonical variables, the three species were correctly discriminated. This allows us to conclude that the use of geometric morphometrics in the pharyngeal plate is a useful structure for the identification of species in the reservoir.

CONSTRUCTING QUANTUM ANGULAR MOMENTUM L3 IN SPECIFIC DIRECTION BY USING U(1) GROUP

The purpose of this work is to investigate the mathematical structure of finite quantum angular momentum in a specific direction L3 which can be constructed from the representation of the U(1) group. The angular momentum eigenstate is invariant under Abelian rotation symmetry. The character group of U(1) is constructed to show that there exists an additive unitary operator for the angular momentum eigenstate, and the rotation eigenstate is invariant under it. The Weyl relation is proved by showing that the angle and angular momentum L3 are the canonical conjugate pair of observables.

Microplastics contamination through a mighty estuarine island: Distribution, influencing factors, and risk assessment

The global concern over microplastic (MP) contamination in diverse ecosystems is well-established, yet Nijhum Dwip Island (NDI), known for its ecological diversity, has not undergone a comprehensive study addressing the extent of MP pollution. This research aims to evaluate the spatial distribution, influencing factors, and ecological risks of MPs in both sediment and surface water surrounding NDI, situated in the Northern Bay of Bengal. A meticulous collection of 40 sediment and 40 tidal water samples from various sites facilitated a detailed analysis. The mean abundance of MPs in sediment was 138.39 ± 34.15 pieces/kg, while in water, it was 72.83 ± 30.76 pieces/m³. Various shapes observed on NDI included films, fragments, fibers, and foams, with fragments dominating in sediment (64.05 %) and water (61.51 %). Analysis of FTIR spectra identified two primary polymer types, namely polyethylene (PE) at 57 % and polypropylene (PP) at 40 %. The results indicated elevated pollution levels on NDI, with sediment and water pollution load index measuring 1.32 and 2.01, respectively, signifying significant MP contamination in both compartments. Given the island's rare biodiversity, the vicinity of wastewater sewages, anthropogenic activities, and atmospheric deposition, could be behind MP contamination in water and sediments. No strong correlation between MP and physiochemical properties in water and PCA biplots showed their similar distribution, whereas MP abundances in sediment were significantly correlated with pH and organic matter (p<0.05), signifying a pivotal role in transporting MPs in the aquatic environment. Two canonical variables were identified as important by canonical correlation analysis, demonstrating the interdependence of MP contamination at the sample sites. This research contributes to better insights into the occurrence of MP in the rare islands, which are ecosystems that have been hardly examined for this type of pollution, and it can report sustainable interventions to lessen MP inputs to the Bay of Bengal.

Dimers for type D relativistic Toda model

We construct dimer graphs for type D relativistic Toda models by introducing impurities into the Y2N,0 square dimer graphs. By properly placing the impurities and changing the canonical variables assigned to the 1-loops on the dimer graph, we perform a “folding” of the graphs, which yields the type D relativistic Toda lattice Hamiltonian and monodromy matrix.

Molar enamel–dentine junction shape of Pliobates cataloniae and other Iberian pliopithecoids

The phylogenetic relationships of the small-bodied catarrhine Pliobates cataloniae (∼11.6 Ma, NE Iberian Peninsula) have been controversial since its original description. However, the recent report of additional dentognathic remains has supported its crouzeliid pliopithecoid status. Based on the available hypodigm, the molar enamel–dentine junction (EDJ) shape of P. cataloniae is compared with that of other pliopithecoids from the same basin as well as both extinct and extant hominoids to further evaluate its pliopithecoid affinities. We also quantitatively compare the EDJ shape among these taxa by means of landmark-based three-dimensional geometric morphometrics using principal component analysis (PCA), canonical variate analysis, and between-group PCA. Permutation tests are performed to test whether Pliobates variation exceeds that of extant hominoid genera. Results indicate that Pliobates is similar in molar EDJ shape to other pliopithecoids, particularly crouzeliids. The variation displayed by Pliobates upper molars is less marked at the EDJ level than at the outer enamel surface, probably owing to differential enamel wear and intraspecific differences in enamel thickness. Multivariate analyses of EDJ shape show that all pliopithecoids (including Pliobates) cluster together in the PCAs, canonical variate analyses, and between-group PCAs and occupy a different portion of the morphospaces from extinct and extant hominoids. Posterior and typicality probabilities strongly support the classification of Pliobates as a pliopithecoid, wheras permutation tests fail to reject the single-genus hypothesis for the P. cataloniae hypodigm. We conclude that P. cataloniae is a crouzeliid pliopithecoid, as recently supported by cladistic analyses of craniodental characters, and that previous cladistic results that supported a stem hominoid status are attributable to postcranial convergences with crown hominoids. Our results further highlight the potential of three-dimensional geometric morphometrics analyses of the EDJ shape for better informing fossil primate alpha-taxonomy by means of quantitatively testing hypotheses about tooth shape variation.

Dynamic Inner Canonical Variate Network for Incipient Fault Monitoring

Dynamic Inner Canonical Variate Network for Incipient Fault Monitoring

Multidimensional analysis of heart rate variability and burden of illness in bipolar disorder

IntroductionPatients with bipolar disorder (BD) face disproportionate rates of cardiovascular disease. While several mechanisms have been proposed for this association, both are multifactorial and heterogeneous illnesses, and it is unlikely that any individual factor can account for a significant portion of their association. Potential mediators have been mostly studied in isolation even though they are interrelated. Furthermore, few studies have accounted for baseline cardiovascular functioning or burden of illness. MethodsWe sought to analyze the association between burden of illness, phase of the illness (e.g., depressive) and heart rate variability (HRV) in 48 patients diagnosed with BD using canonical correlation analysis. We hypothesized that the association between burden of illness and HRV measures would be different depending on the clinical phase (i.e., euthymia, depression or (hypo)mania). ResultsA longer duration of (hypo)manic episodes was associated with higher rates of hypertension and increased sympathetic activation, along with lower rates of migraine and family history of suicide. In the second canonical variable, a later age at onset of (hypo)manic episodes was associated with higher parasympathetic activity. LimitationsSmall sample size; while the magnitudes of correlations for these top functions were large, none of the models were statistically significant. ConclusionsThere are different dimensions to the association between burden of illness and HRV in BD. The first dimension could comprise higher sympathetic activation in the context of longer (hypo)manic episodes, with lower rates for clinical variables that have been associated with a predominant depressive polarity (e.g., family history of suicide and migraine).

Statistical uncertainty principle in Markov kinetics

A reciprocality between the statistical variance of observables of a thermodynamic state and that of their conjugate variables, as entropic forces, originates from the thermodynamic conjugacy with respect to an entropy function. This thermodynamic uncertainty principle in equilibrium can be derived from the Maximum Entropy principle and is independent upon underlying mechanistic details. We present, based on the Maximum Caliber principle as the dynamic generalization of Maximum Entropy, the formalism of the uncertainty principle in kinetics in time homogeneous Markov processes between transitional observables and their conjugate path entropic forces. A stochastic biophysical model for molecular motors is used as an illustrating example. The present work generalizes the phenomenological thermodynamics of uncertainties/fluctuations and is applicable to data ad infinitum.

Quantum geometrodynamics revived: II. Hilbert space of positive definite metrics

Abstract This paper represents the second in a series of works aimed at reinvigorating the quantum geometrodynamics program. Our approach introduces a lattice regularization of the hypersurface deformation algebra, such that each lattice site carries a set of canonical variables given by the components of the spatial metric and the corresponding conjugate momenta. In order to quantize this theory, we describe a representation of the canonical commutation relations that enforces the positivity of the operators q_{ab} s^a s^b for all choices of s. Moreover, symmetry of q_{ab} and p^{ab} is ensured. This reflects the physical requirement that the spatial metric should be a positive definite, symmetric tensor. To achieve this end, we resort to the Cholesky decomposition of the spatial metric into upper triangular matrices with positive diagonal entries. Moreover, our Hilbert space also carries a representation of the vielbein fields and naturally separates the physical and gauge degrees of freedom. Finally, we introduce a generalization of the Weyl quantization for our representation. We want to emphasize that our proposed methodology is amenable to applications in other fields of physics, particularly&amp;#xD;in scenarios where the configuration space is restricted by complicated relationships among the degrees of freedom.