Canonical Variables Research Articles

Nonmetric geometric flows and quasicrystalline topological phases for dark energy and dark matter in f(Q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(Q)$$\\end{document} cosmology

We elaborate on nonmetric geometric flow theory and metric-affine gravity with applications in modern cosmology. Two main motivations for our research follow from the facts that (1) cosmological models for f(Q) modified gravity theories, MGTs, are efficient for describing recent observational data provided by the James Webb Space Telescope; and (2) the statistical thermodynamic properties of such nonmetric locally anisotropic cosmological models can be studied using generalizations of the concept of G. Perelman entropy. We derive nonmetric distorted R. Hamilton and Ricci soliton equations in such canonical nonholonomic variables when corresponding systems of nonlinear PDEs can be decoupled and integrated in general off-diagonal forms. This is possible if we develop and apply the anholonomic frame and connection deformation method involving corresponding types of generating functions and generating sources encoding nonmetric distortions. Using such generic off-diagonal solutions (when the coefficients of metrics and connections may depend generically on all spacetime coordinates), we model accelerating cosmological scenarios with quasi-periodic gravitational and (effective) matter fields; and study topological and nonlinear geometric properties of respective dark energy and dark matter, DE and DM, models. As explicit examples, we analyze some classes of nonlinear symmetries defining topological quasicrystal, QC, phases which can modified to generate other types of quasi-periodic and locally anisotropic structures. The conditions when such nonlinear systems possess a behaviour which is similar to that of the Lambda cold dark matter (Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM) scenario are stated. We conclude that nonmetric geometric and cosmological flows can be considered as an alternative to the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM concordance models and speculate on how such theories can be elaborated. This is a partner work with generalizations and applications of the results published by Bubuianu, Vacaru et all. EPJC 84 (2024) 211; 80 (2020) 639; 78 (2018) 393; 78 (2018) 969; and CQG 35 (2018) 245009.

Linear measurements and shape analysis in the calcaneus of selected dog breeds.

The vast array of dog breeds showcases a remarkable diversity that extends to osteological differences. Exploring these morphological distinctions and establishing reference data for various dog breeds are essential steps in comprehending the evolutionary changes that dogs have undergone. In this study, we conducted linear measurements of the calcaneus and performed shape analyses on selected dog breeds to elucidate distinctive characteristics among them. X-ray images of the calcaneus from six different dog breeds-Maltese Terrier, Toy Poodle, Pomeranian, Cavalier King Charles Spaniel, French Bulldog and Golden Retriever-were utilized for this investigation. Radiological images were obtained from a medio-lateral exposure, positioned 30 cm away from the x-ray device. From these images, four linear length measurements and two angle values were extracted. Additionally, a 2D geometric morphometric analysis was conducted using 32 semi landmarks placed on the radiological images. Linear measurements were assessed using ANOVA, while principal component analysis was employed to examine shape variations across all individuals. Shape differences between species were further elucidated through canonical variates analysis. The results revealed that the Golden Retriever exhibited the highest values for linear measurements, while the Pomeranian showed the lowest. Maltese Terriers displayed the highest dorsal calcaneal angle value. Notably, there were significant differences in calcaneal body length among all breeds, except for the Toy Poodle and Cavalier King Charles Spaniel. Moreover, Maltese Terriers exhibited statistically distinct angular measurements compared to other breeds. Principal component analysis unveiled that the first principal component explained 32.69% of the total variation, with the cranial edge of the calcaneal body being closer to the body in individuals with higher values. Shape variations also indicated that Golden Retrievers displayed a broader range of shapes compared to French Bulldogs, which exhibited a more conservative distribution. While there was no clear breed-specific distinction according to the first principal component, Cavalier King Charles Spaniels generally showed lower values. In canonical variates analysis, distinctions in calcaneal shape between species were apparent, with Golden Retrievers, Cavalier King Charles Spaniels and French Bulldogs displaying positive values for the first canonical variates. The highest Procrustes distance was observed between Maltese Terriers and Cavalier King Charles Spaniels. Notably, allometry was found to be statistically insignificant. This comprehensive study utilized both linear and geometric morphometric analyses based on x-ray images, yielding promising results. The integration of imaging systems in veterinary anatomy research presents numerous opportunities for studying animal welfare and health, utilizing various materials such as bones and cadavers. These advancements hold the potential for further enhancing our understanding of animal morphology and well-being.

Thermodynamics and Decay of de Sitter Vacuum

We discuss the consequences of the unique symmetry of de Sitter spacetime. This symmetry leads to the specific thermodynamic properties of the de Sitter vacuum, which produces a thermal bath for matter. de Sitter spacetime is invariant under the modified translations, r→r−eHta, where H is the Hubble parameter. For H→0, this symmetry corresponds to the conventional invariance of Minkowski spacetime under translations r→r−a. Due to this symmetry, all the comoving observers at any point of the de Sitter space perceive the de Sitter environment as the thermal bath with temperature T=H/π, which is twice as large as the Gibbons–Hawking temperature of the cosmological horizon. This temperature does not violate de Sitter symmetry and, thus, does not require the preferred reference frame, as distinct from the thermal state of matter, which violates de Sitter symmetry. This leads to the heat exchange between gravity and matter and to the instability of the de Sitter state towards the creation of matter, its further heating, and finally the decay of the de Sitter state. The temperature T=H/π determines different processes in the de Sitter environment that are not possible in the Minkowski vacuum, such as the process of ionization of an atom in the de Sitter environment. This temperature also determines the local entropy of the de Sitter vacuum state, and this allows us to calculate the total entropy of the volume inside the cosmological horizon. The result reproduces the Gibbons–Hawking area law, which is attributed to the cosmological horizon, Shor=4πKA, where K=1/(16πG). This supports the holographic properties of the cosmological event horizon. We extend the consideration of the local thermodynamics of the de Sitter state using the f(R) gravity. In this thermodynamics, the Ricci scalar curvature R and the effective gravitational coupling K are thermodynamically conjugate variables. The holographic connection between the bulk entropy of the Hubble volume and the surface entropy of the cosmological horizon remains the same but with the gravitational coupling K=df/dR. Such a connection takes place only in the 3+1 spacetime, where there is a special symmetry due to which the variables K and R have the same dimensionality. We also consider the lessons from de Sitter symmetry for the thermodynamics of black and white holes.

Sparse Generalized Canonical Correlation Analysis: Distributed Alternating Iteration-Based Approach.

Sparse canonical correlation analysis (CCA) is a useful statistical tool to detect latent information with sparse structures. However, sparse CCA, where the sparsity could be considered as a Laplace prior on the canonical variates, works only for two data sets, that is, there are only two views or two distinct objects. To overcome this limitation, we propose a sparse generalized canonical correlation analysis (GCCA), which could detect the latent relations of multiview data with sparse structures. Specifically, we convert the GCCA into a linear system of equationsand impose $\ell _1$ minimization penalty to pursue sparsity. This results in a nonconvex problem on the Stiefel manifold. Based on consensus optimization, a distributed alternating iteration approach is developed, and consistency is investigated elaborately under mild conditions. Experiments on several synthetic and real-world data sets demonstrate the effectiveness of the proposed algorithm.

Shape variation in cranium, mandible and teeth in selected mouse strains.

There are different strains of laboratory mouse used in many different fields. These strains differ anatomically. In order to determine these anatomical differences, shape analysis was conducted according to species. CD-1, C57bl/6 and Balb-c strains were preferred to study these differences. Forty-eight adult mouse strains belonging to these strains were utilized. The bones were photographed and geometric morphometry was applied to these photographs. Principal Component Analysis was applied to determine shape variations. In Principal component 1 for cranium, CD-1 and C57bl/6 strain groups showed different shape variations, while Balb-c strain group showed similar shape variations to the other strain groups. Principal Component 1 for the mandible separated the CD-1 and C57bl/6 strain groups in terms of shape variation. Principal Component 2 explained most of the variation between the C57bl/6 and CD-1 lineage groups. In PC1 for molars, the CD-1 group showed a different shape variation from the other groups. Mahalanobis distances and Procrustes distances were measured using Canonical variance analysis to explain the differences between the lineage groups. These measurements were statistically significant. For cranium, in canonical variate 1, CD-1 group of mouse and Balb-c group of mouse were separated from each other. In canonical variate 2, C57bl/6 group of mouse were separated from the other groups. For mandible, Balb-c group of mouse in canonical variate 1 and CD-1 group of mouse in canonical variate 2 were separated from the other groups. For molars, CD-1 group of mouse in canonical variate 1 and Balb-c group of mouse in canonical variate 2 were separated from the other groups. It was thought that these anatomical differences could be caused by genotypic factors as well as dietary differences and many different habits that would affect the way their muscles work.

Domestic Competition, Trade Openness and Entrepreneurial Culture: Canonical Correlation Analysis

Abstract The paper analyses canonical correlations between domestic competition, trade openness and entrepreneurial culture. The research covered 141 countries ranked by World Competitiveness Index in 2019. Canonical correlation analysis is applied to find relationship between two canonical variables. The first canonical variable includes sub-indexes from Domestic competition and Trade openness pillars. The second variable contains sub-indexes from Entrepreneurial culture pillar. The results of the analysis showed there is a strong, positive, statistically significant canonical correlation between these canonical variables with a Pearson coefficient of 0.86. The linear regression analysis is also applied. The regression analysis shows that the variable Distortive effects of taxes and subsidies on competition is the most important for all dependent variables. The extent of market dominance, Competition in services and Border clearance efficiency are important, but not as much as taxes and subsidies. It confirms that regulation of domestic competition and trade openness are supreme for entrepreneurial culture.

Association between the three-dimensional facial shape and its color in a boundary group of young to middle-aged Asian women

Visual cues strongly influence an individual's self-esteem and have fundamental sociopsychological functions. The color and shape of the face are important information for visual cues and are hypothesized to be correlated with each other. However, few studies have examined these relationships. Thus, this study determined the association between color and shape of the face. For this purpose, we evaluated Chinese women in their 30s and 40s (n = 166). Three-dimensional (3D) image-capture devices that provide shape morphology along with standardized photographs (color information) were used to obtain 3D images of women. The coordinates and red‒green–blue color data on the 3D images were utilized to perform principal component (PC) analysis, and shape and color PCs were generated. A canonical variate analysis was then conducted to check for significant correlations between the shape and color PCs. As a result, 6 significant correlations were found (p < 0.05). In detail, in addition to the physical correlations (i.e., steric faces or faces with protrusion of the cheek showed greater shadows, retrognathism was related to a shadow under the lower lip and vice versa), biological correlations (fatty faces showed greater redness and remarkable marionette lines; faces with age-related sagging showed greater darkness, possibly related to cumulative ultraviolet radiation exposure of the skin; and robust mandibles and supraorbital ridges were related to thick eyebrows) were found. This insight can aid both medical and cosmetic practitioners in comprehending the intricate details conveyed by facial features, thereby facilitating more comprehensive diagnosis and treatment planning, including makeup.

Latent Demographic and Clinical Correlates of Drug Resistant Tuberculosis Among Treated Patients

Demographic and Clinical variables (data) collected from tuberculosis patients whose cases were drug resistant were analysed. The tuberculosis patients studied were those treated in the 11 Local Governments Areas and a treatment centre of Anambra State, Nigeria, for six years (2017 – 2022). Data from 197 Drug Resistant Tuberculosis (DR-TB) patients were analysed. The pair of data collected, being multivariate in nature, were analysed using the Canonical Correlation Analysis (CCA) and the Canonical loadings (structure coefficients) between the Demographic and Clinical Variables were extracted. Data obtained showed that mean age of the study participants was 40.2 ± 18.9 years (95% Confidence Interval). Males were 60.9%. Participants with HIV co-infection was 22.3%. The CCA showed that the first canonical variate was significant with 79% contribution, extracting 28.5% of the variance from demographic variables and 6.7% variance from the clinical variables. The variables that significantly contributed to the relationship include Age, Location and Body Mass Index (BMI). Human Immuno-Deficiency Virus (HIV) negative was protective in the relationship but not statistically significant.

Heisenberg soft hair on Robinson-Trautman spacetimes

We study 4 dimensional (4d) gravitational waves (GWs) with compact wavefronts, generalizing Robinson-Trautman (RT) solutions in Einstein gravity with an arbitrary cosmological constant. We construct the most general solution of the GWs in the presence of a causal, timelike, or null boundary when the usual tensor modes are turned off. Our solution space besides the shape and topology of the wavefront which is a generic compact, smooth, and orientable 2d surface Σ, is specified by a vector over Σ satisfying the conformal Killing equation and two scalars that are arbitrary functions over the causal boundary, the boundary modes (soft hair). We work out the symplectic form over the solution space using covariant phase space formalism and analyze the boundary symmetries and charges. The algebra of surface charges is a Heisenberg algebra. Only the overall size of the compact wavefront and not the details of its shape appears in the boundary symplectic form and is canonical conjugate to the overall mass of the GW. Hence, the information about the shape of the wavefront can’t be probed by the boundary observer. We construct a boundary energy-momentum tensor and a boundary current, whose conservation yields the RT equation for both asymptotically AdS and flat spacetimes. The latter provides a hydrodynamic description for our RT solutions.

Carrollian hydrodynamics and symplectic structure on stretched horizons

The membrane paradigm displays underlying connections between a timelike stretched horizon and a null boundary (such as a black hole horizon) and bridges the gravitational dynamics of the horizon with fluid dynamics. In this work, we revisit the membrane viewpoint of a finite-distance null boundary and present a unified geometrical treatment of the stretched horizon and the null boundary based on the rigging technique of hypersurfaces. This allows us to provide a unified geometrical description of null and timelike hypersurfaces, which resolves the singularity of the null limit appearing in the conventional stretched horizon description. We also extend the Carrollian fluid picture and the geometrical Carrollian description of the null horizon, which have been recently argued to be the correct fluid picture of the null boundary, to the stretched horizon. To this end, we draw a dictionary between gravitational degrees of freedom on the stretched horizon and the Carrollian fluid quantities and show that Einstein’s equations projected onto the horizon are the Carrollian hydrodynamic conservation laws. Lastly, we report that the gravitational pre-symplectic potential of the stretched horizon can be expressed in terms of conjugate variables of Carrollian fluids and also derive the Carrollian conservation laws and the corresponding Noether charges from symmetries.

Information entropies with Varshni-Hellmann potential in higher dimensions

This work investigates the behavior of Shannon entropy and Fisher information for the Varshni-Hellmann potential (VHP) in one and three dimensions using the Nikiforov-Uvarov method. We employ the Greene-Aldrich approximation scheme to obtain the energy eigenvalues and normalized wavefunctions, which are then used to calculate these information-theoretic quantities. Our analysis revealed remarkably similar high-order features in both position and momentum spaces. Notably, our calculations showed enhanced accuracy in predicting particle localization within position space. Furthermore, the combined position and momentum entropies obeyed the lower and upper bounds established by the Berkner-Bialynicki-Birula-Mycieslki inequality. Additionally, for three-dimensional systems, the Stam-Cramer-Rao inequalities were fulfilled for different eigenstates with respect to the calculated Fisher information. It is observed that as the position Fisher entropy decreases, indicating a more precise measurement of position, the momentum Fisher entropy must increase. This implies that the Fisher information regarding momentum decreases, resulting in a decrease in the precision of momentum measurement. This demonstrates how position and momentum uncertainties complement each other in quantum mechanics. Exploring the balance between position and momentum Fisher entropy reveals a fundamental aspect of the uncertainty principle in quantum mechanics, highlighting the restrictions on measuring certain pairs of conjugate variables simultaneously with high precision.

A two-group canonical variate analysis biplot for an optimal display of both means and cases

AbstractCanonical variate analysis (CVA) entails a two-sided eigenvalue decomposition. When the number of groups, J, is less than the number of variables, p, at most $$J-1$$ J - 1 eigenvalues are not exactly zero. A CVA biplot is the simultaneous display of the two entities: group means as points and variables as calibrated biplot axes. It follows that with two groups the group means can be exactly represented in a one-dimensional biplot but the individual samples are approximated. We define a criterion to measure the quality of representing the individual samples in a CVA biplot. Then, for the two-group case we propose an additional dimension for constructing an optimal two-dimensional CVA biplot. The proposed novel CVA biplot maintains the exact display of group means and biplot axes, but the individual sample points satisfy the optimality criterion in a unique simultaneous display of group means, calibrated biplot axes for the variables, and within group samples. Although our primary aim is to address two-group CVA, our proposal extends immediately to an optimal three-dimensional biplot when encountering the equally important case of comparing three groups in practice.

Fault detection and isolation for dynamic non-stationary processes with stationary subspace-based canonical variate analysis

As modern science and technology advance, industrial processes have grown more complex, characterized by dynamic and non-stationary features. Existing methods often focus on single features, necessitating the development of approaches capable of addressing multiple characteristics. This study introduces a novel approach based on stationary subspace canonical variate analysis for fault detection and isolation in dynamic non-stationary processes. The proposed model combines the strengths of stationary subspace analysis and canonical variate analysis (CVA) by introducing new detection indices and their corresponding contributions. These new indices, derived from CVA indices, are further transformed into quadratic form to facilitate easy calculation of contributions, which are based on reconstruction. A numerical example and simulation of the continuous stirred tank reactor process are carried out to demonstrate the superior sensitivity and accuracy of the proposed approach.

Geographical variation in the forewing shape of the red dwarf honeybees revealed by landmark-based geometric morphometrics

Accurate intraspecific variation assessment is the prerequisite for determining subspecies, evolutionarily significant units, or management units across a species' range. However, intraspecific variation assessment is often hindered by inaccurate morphological results from traditional methods or high-cost genetic analyses. Geometric morphometrics is a promising technique for quantifying and visualising intraspecific diversity. We used landmark-based geometric morphometrics to investigate forewing shape variation and microtaxonomy of populations of Apis florea Fabricius 1787 (Apidae: Apini), which originated from some parts of Asia and Africa based on the 19 landmarks plotted at the venation intersections of forewings. We collected samples of 162 colonies from 36 different localities. On average, 13 workers per colony were analysed (1851 bees in total). Distinct spatial structures and significant differences in wing shape between the studied populations were revealed using canonical variate analysis, and no considerable overlap was detected between the colonies belonging to the western and eastern populations. The populations at higher latitudes showed significantly larger centroid sizes than those at lower latitudes, and a clinal variation in forewing size was confirmed. Significant distance-decay relationships between the studied populations were observed so that the populations located at the maximum geographical distance showed the most significant distance from each other and vice versa. Wing geometric morphometrics was an accurate tool for the reliable estimation of the population structure of the red dwarf honeybees. It is essential to increase the reliability of these variations by combining the results with further molecular data.

Geometric morphometric evaluation of mandibles of four sheep breeds: Bardoka, İvesi, Polish Mountain sheep and Turcana.

The enduring relationship between humans and domestic sheep has evolved over millennia, showcasing diverse uses such as meat, milk, wool, leather and fur, shaped by geographical, historical, cultural and social factors. The sheep breeds discussed include the Ivesi from Southeastern Anatolia, known for its varied animal products; the resilient Turcana breed of Romania; Kosovo's Bardoka, valued for its triple-purpose characteristics; and Poland's Polish Mountain Sheep, uniquely utilized for milk production in cheese making. Sheep, with their enduring relationship with humans and significant economic importance, have attracted scientific interest in morphometric studies of their mandibles, yielding valuable data applicable across various fields including basic anatomy, veterinary clinical anatomy, zooarchaeology and veterinary forensic medicine. Traditional morphometric studies rely on statistical methods to compare length, depth and angular ratios between anatomical formations, often highlighting differences between specific points but not fully revealing shape variations between distinct groups. Geometric morphometric analysis has emerged as a preferred method in recent years, enabling shape analyses using coordinate data from various imaging techniques, facilitating a comprehensive examination of mandibular morphometrics among sheep breeds across different countries. This study involved four sheep breeds from different countries, namely İvesi from Turkey, Bardoka from Kosovo, Polish Mountain Sheep from Poland and Turcana from Romania, with a total of 70 mandibles sourced from various veterinary faculties. Mandibular photographs were meticulously captured, focusing on the right side of mandible pairs and placing landmarks and semi-landmarks along the entire edge, enabling geometric morphometric analysis using tpsUtil, tpsDig2 and MorphoJ software. The analysis included principal component analysis, canonical variate analysis and discriminant function analysis for pairwise comparisons, facilitating a comprehensive examination of mandibular shape variations among the different sheep breeds. Using geometric morphometric methods, this study analysed mandibles from four distinct sheep breeds sourced from different countries, revealing notable variations in regions such as the ramus mandibula, angulus mandibula and incisive areas, attributed to genetic, geographical and dietary influences, highlighting the importance of continued research to better comprehend these shape differences.

Hamiltonian Computational Chemistry: Geometrical Structures in Chemical Dynamics and Kinetics.

The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show that the physical states of integrable dynamical systems are depicted by Lagrangian submanifolds embedded in phase space. Observable quantities are calculated by properly transforming the extended phase space onto a reduced space, and trajectories are integrated by solving Hamilton's equations of motion. After defining a Riemannian metric, we can also estimate the length between two states. Local constants of motion are investigated by integrating Jacobi fields and solving the variational linear equations. Diagonalizing the symplectic fundamental matrix, eigenvalues equal to one reveal the number of constants of motion. For conservative systems, geometrical quantum mechanics has proved that solving the Schrödinger equation in extended Hilbert space, which incorporates the quantum phase, is equivalent to solving Hamilton's equations in the projective Hilbert space. In classical thermodynamics, we take entropy and energy as canonical variables to construct the extended phase space and to represent the Lagrangian submanifold. Hamilton's and variational equations are written and solved in the same fashion as in classical mechanics. Solvers based on high-order finite differences for numerically solving Hamilton's, variational, and Schrödinger equations are described. Employing the Hénon-Heiles two-dimensional nonlinear model, representative results for time-dependent, quantum, and dissipative macroscopic systems are shown to illustrate concepts and methods. High-order finite-difference algorithms, despite their accuracy in low-dimensional systems, require substantial computer resources when they are applied to systems with many degrees of freedom, such as polyatomic molecules. We discuss recent research progress in employing Hamiltonian neural networks for solving Hamilton's equations. It turns out that Hamiltonian geometry, shared with all physical theories, yields the necessary and sufficient conditions for the mutual assistance of humans and machines in deep-learning processes.

Morphometric study of the legs of the main Chagas vector, Triatoma infestans (Hemiptera: Reduviidae)

In triatomines, vectors of Chagas disease, active dispersal takes place by walking and flying. Flight has received more attention than walking although the last is the dispersal modality used by nymphs due to their lack of wings and also used by adults, which would facilitate the colonization and reinfestation of houses after vector control actions. The present work studied the morphometrical variation of Triatoma infestans legs, the main vector of Chagas disease the Southern Cone of South America. We described morphometric traits and the natural variation of each leg segment. Different linear, size and shape variables of each component of the three right legs of fifth instar nymphs of T. infestans were analyzed using morphometric tools. We analyzed differentiation, variation and correlation for each segment across the fore-, mid and hind legs using different statistical approaches such as general linear model, canonical variates analysis, test of equality of coefficient of variation and partial least square analysis. We also analyzed variation and correlation between segments within each leg with partial least square and morphometric disparity analyses. Our results showed that the segments differed between legs, as general trends, the dimensions (length, width and/or size) were greater in the hind legs, smaller in the forelegs and intermediate in the mid ones. The femur and tibia (length and/or width) showed differences in morphometric variation between legs and the femur and tibia showed the highest levels of correlation between legs. On the other hand, in the fore- and mid legs, the femur (length or width) showed similar variation with tibia and tarsus lengths, but in the hind legs, the femur showed similar variation with all segments and not with the tibia length, and there were strong correlations between linear measurement within each leg. Our results suggest that the femur and tibia could play a determining role in the coordination between the legs that determines the walking pattern. Considering that these segments would also be linked to the specific function that each leg has, this study suggests a preponderant role of the femur and tibia in the walking locomotion of T. infestans.

Influence of insular conditions on wing phenotypic variation in two dominant mosquito vectors, Aedes albopictus and Armigeres subalbatus (Diptera: Culicidae), in the border archipelagos of Thailand.

Insects geographically separated into island and mainland populations often exhibit phenotypic variations, a phenomenon known as insular conditions. These conditions can lead to rapid evolutionary changes that affect the morphological characteristics of mosquito vectors. Nevertheless, studies that specifically examine phenotype differences between island and mainland mosquito populations have been limited. In this study, wing variation in size and shape was investigated using the geometric morphometric (GM) technique in two dominant mosquito vectors, Aedes albopictus and Armigeres subalbatus, in the Ranong and Trat archipelagos of Thailand. Significant differences in average wing centroid size (CS) were found in 6 out of 15 population pairs for Ae. albopictus (p < 0.05) and in 5 population pairs for Ar. subalbatus (p < 0.05). After removing the allometric effect, canonical variate analyses (CVA) based on wing shape analysis revealed overlap across all populations for both Ae. albopictus and Ar. subalbatus. However, the statistical analysis indicated that Ar. subalbatus exhibited wing shape differences across all populations (p < 0.05), and most Ae. albopictus populations also displayed distinct wing shapes (p < 0.05), except for the populations from Chang Island and the mainland of Ranong, which showed no significant differences (p > 0.05). These findings enhance our understanding of mosquito adaptability in island regions and provide valuable data for the surveillance and monitoring of vector evolution.

Manifold regularized deep canonical variate analysis with interpretable attribute guidance for three-phase flow process monitoring

Oil–gas–water three-phase flow has multiple flow states, exhibiting dynamic, nonlinear, and instantaneous behaviors. Monitoring and analysis of flow state are crucial for ensuring safe operation of industrial processes. However, the absence of a universal definition for three-phase flow states, owing to the complex flow characteristics and structures, leads to that labeling three-phase flow states by categories is impractical. For comprehensive monitoring and analysis, the flow states should be described from both global (e.g., the dominant phase) and local (e.g., the interphase structure) aspects. Given the aforementioned challenges, the work aims to address the accurate identification of typical three-phase flow states and to meticulously monitor and analyze the continuous evolutionary process of three-phase flow. To achieve it, the manifold regularized deep canonical variate analysis with attribute guidance (Ag-MRDCVA) is proposed, which not only introduces an innovative monitoring paradigm that designs state attributes for process description but also facilitates knowledge transfer from typical flow states to transition states. For enhancing the model’s feature embedding capabilities, an attribute guidance module is introduced to increase supervision information at both class and attribute levels. Then, convolutional neural network (CNN) backbones are developed with a dual objective of global serial correlation and local manifold regularization, which capture spatiotemporal information at both global and local scales, facilitating effective attribute encoding and characterization of flow states. Finally, the attribute evolution heat map and a monitoring metric (MM) collectively offer a compelling and comprehensive analysis of the three-phase flow process. Extensive experiments demonstrate that Ag-MRDCVA surpasses existing methods, showcasing its ability to minutely monitor the process while providing reasonable explanations.

Screwon spectral statistics and dispersion relation in the quantum Rajeev–Ranken model

The Rajeev–Ranken (RR) model is a Hamiltonian system describing screw-type nonlinear waves (screwons) of wavenumber k in a scalar field theory pseudodual to the 1+1D SU(2) principal chiral model. Classically, the RR model based on a quadratic Hamiltonian on a nilpotent/Euclidean Poisson algebra is Liouville integrable. Upon adopting canonical variables in a slightly extended phase space, the model was interpreted as a novel 3D cylindrically symmetric quartic oscillator with a rotational energy. Here, we examine the spectral statistics and dispersion relation of quantized screwons via numerical diagonalization validated by variational and perturbative approximations. We also derive a semiclassical estimate for the cumulative level distribution which compares favorably with the one from numerical diagonalization. The spectrum shows level crossings typical of an integrable system. The ith unfolded nearest neighbor spacings are found to follow Poisson statistics for small i. Nonoverlapping spacing ratios also indicate that successive spectral gaps are independently distributed. After displaying universal linear behavior over energy windows of short lengths, the spectral rigidity saturates at a length and value that scales with the square-root of energy. For strong coupling λ and intermediate k, we argue that reduced screwon energies can depend only on the product λk. Numerically, we find power law dependences on λ and k with an approximately common exponent 2/3 provided the angular momentum quantum number l is small compared to the number of nodes n in the radial wavefunction. On the other hand, for the ground state n=l=0, the common exponent becomes 1.