Analysis Of Variation Research Articles

The Prognostic Significance of Plasma Beta2-Glycoprotein I Levels in Hepatocellular Carcinoma Patients.

Beta2-glycoprotein I (β2-GPI) is a plasma glycoprotein with multiple physiological functions, but its relationship with hepatocellular carcinoma (HCC) is still poorly understood. HCC is one of the most common forms of liver cancer and is a leading cause of cancer-related death worldwide. This study aimed to investigate the association between β2-GPI and liver cancer and further validate its potential as a biomarker for HCC. Thirty-six patients diagnosed with HCC at the Division of Gastroenterology and Hepatology, E-Da Hospital, Taiwan, were included in the study. The expression levels of β2-GPI in plasma specimens from patients with HCC were determined by enzyme immunoassay and analyzed in relation to clinicopathological variables using the Chi-square test or Fisher's exact test. The predictive significance of β2-GPI for both overall survival (OS) and disease-free survival (DFS) was assessed using Kaplan-Meier estimates, and the statistical significance of differences was evaluated through the log-rank test. Cox proportional hazards regression models were used to evaluate the association between OS/DFS time and clinicopathological characteristics. Results: Plasma β2-GPI levels were significantly lower in patients with HCC compared to non-cancer controls and significantly correlated with aspartate aminotransferase (AST) levels of HCC. High plasma β2-GPI levels were significantly associated with better OS and DFS in HCC patients. Furthermore, in multiple variates analyses, OS was found to be significantly better in HCC patients with higher plasma β2-GPI expression. Elevated levels of β2-GPI protein in the plasma of HCC patients were identified as an independent factor predictive of improved OS and DFS. Activating β2-GPI in individuals at high risk could serve as a promising way for mitigating the progression of HCC.

Nonlinear Dynamic Process Monitoring Based on Discriminative Denoising Autoencoder and Canonical Variate Analysis

Modern industrial processes are characterized by increasing complexity, often exhibiting pronounced dynamic behaviors and significant nonlinearity. Addressing these dynamic and nonlinear characteristics is essential for effective process monitoring. However, many existing methods for process monitoring and fault diagnosis are insufficient in handling these challenges. In this article, we present a novel process monitoring approach, CVA-DisDAE, which integrates an improved Denoising Autoencoder (DAE) with Canonical Variate Analysis (CVA) to address the challenges posed by dynamic behaviors and nonlinear relationships in industrial processes. First, CVA is employed to reduce data dimensionality and minimize information redundancy by maximizing correlations between past and future observations, thereby effectively capturing process dynamics. Following this, we introduce a discriminative DAE model (DisDAE) designed to serve as a semi-supervised denoising autoencoder for precise feature extraction. This is achieved by incorporating both between-class separability and within-class variability into the traditional DAE framework. The key distinction between the proposed DisDAE and the conventional DAE lies in the integration of a linear discriminant analysis (LDA) penalty into the DAE’s loss function, resulting in extracted features that are more conducive to fault classification. Finally, we validate the effectiveness of the proposed semi-supervised dynamic process monitoring approach through its application to the Tennessee Eastman benchmark process, demonstrating its superior performance.

Shape variability and morphological discrimination of haptoral attachment structures in Urocleidoides spp. Mizelle et Price, 1964 (Monogenea: Dactylogyridae) parasitizing fish from neotropical rivers in southern Mexico.

The morphology of attachment organs in Monogenea is an essential source of evidence for taxonomic assessments and understanding of ecology and evolutionary history. It has been demonstrated that geometric morphometry analysis of the haptoral attachment organs provides rich and precise information about monogeneans morphology. In this study, we consider three monogenean species of Urocleidoides, U. simonae, U. vaginoclaustrum, U. vaginoclaustroides, and the incertae sedis species U. strombicirrus that parasitize fish of the Poeciliidae, Profundulidae and Characidae in neotropical rivers in southern Mexico. We aimed to identify new morphological characteristics that can be used to describe these populations with greater certainty and to test whether these characteristics present geographic variation. Anchor shape data (n = 69) were generated using geometric morphometric methods. We discriminated species using principal components and canonical variate analysis of shape data. Our results showed that there was discernible interspecific variation. The four species contributed four new morphological characteristics: anchor point length, short versus long anchor roots, elongated versus wide anchor shape, and the relative length of inner versus outer roots. Intraspecific variation was relatively low compared to interspecific anchor shape variation in Urocleidoides spp. These new morphological characteristics may also be useful for delimiting other similar species in Monogenea.

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.

“Saying ‘thank you’ or something more than lip service”: a variational analysis of the influence of gender and social status on responses to congratulations on Chinese WeChat

Abstract Existing studies on responses to congratulations to date have displayed a general culturally-bound finding that Chinese speakers prefer to take a detour approach. However, the effect of social constraints on response strategies have not received the attention it deserves. Drawing on a variational pragmatic approach, this study explores the constraints of gender and social status on the pragmatic variation of Chinese WeChat users’ responses to congratulations. Building upon an integrative data set of congratulatory interactions in actual online messages, the findings suggest that gender and social status overlap in complex ways, but with a clear tendency: both men and women significantly tend towards an acceptance strategy when responding to congratulations on WeChat, while social status influences the sub-strategies used in accepting congratulations across both male and female groups. The findings challenge previous stereotypes about Chinese language variation in responses to congratulations. The current results suggest that Chinese speakers have already made a transition from following the Modesty Maxim to using the Agreement Maxim, and have also incorporated the Obligation Maxim. Chinese speakers also consider rapport and reciprocity when responding to kind congratulatory remarks.

Normal Approximation of Random Gaussian Neural Networks

In this paper, we provide explicit upper bounds on some distances between the (law of the) output of a random Gaussian neural network and (the law of) a random Gaussian vector. Our main results concern deep random Gaussian neural networks with a rather general activation function. The upper bounds show how the widths of the layers, the activation function, and other architecture parameters affect the Gaussian approximation of the output. Our techniques, relying on Stein’s method and integration by parts formulas for the Gaussian law, yield estimates on distances that are indeed integral probability metrics and include the convex distance. This latter metric is defined by testing against indicator functions of measurable convex sets and so allows for accurate estimates of the probability that the output is localized in some region of the space, which is an aspect of a significant interest both from a practitioner’s and a theorist’s perspective. We illustrated our results by some numerical examples. Funding: This research was supported by the European Union’s Horizon 2020 research project WARIFA under grant agreement no. 101017385, by the PRIN project 2022 “Variational Analysis of Complex Systems in Materials Science, Physics and Biology” (CUP B53D23009290006), and by the INdAM project “Modelli ed Algoritmi per dati ad elevata dimensionalità” (CUP E53C23001670001).

Micropolar fluid-thin elastic structure interaction: variational analysis

We consider the non-stationary flow of a micropolar fluid in a thin channel with an impervious wall and an elastic stiff wall, motivated by applications to blood flows through arteries. We assume that the elastic wall is composed of several layers with different elastic characteristics and that the domains occupied by the two media are infinite in one direction and the problem is periodic in the same direction. We provide a complete variational analysis of the two dimensional interaction between the micropolar fluid and the stratified elastic layer. For a suitable data regularity, we prove the existence, the uniqueness and the regularity of the solution to the variational problem associated to the physical system. Increasing the data regularity, we prove that the fluid pressure is unique, we obtain additional regularity for all the unknown functions and we show that the solution to the variational problem is solution for the physical system, as well.

Variational Analysis of a Dynamic Contact Problem with Wear and Damage Involving Viscoelastic Materials with Long-Term Memory

We investigate a mathematical problem involving dynamic interaction between a viscoelastic body with long-term memory loss and an obstruction. The contact is frictional and bilateral, with a moving rigid base, resulting in wear of the contacting surface. The problem is expressed as a coupled system, with a hyperbolic quasi-variational inequality for displacement and a parabolic variational inequality for damage. We define a variational formulation for the model and demonstrate the existence of a single weak solution to the problem. The material behaviour is explained using a viscoelastic constitutive law that includes long-term memory and damage. Elastic deformations induce material deterioration, which is depicted by a parabolic inclusion. The proof is based on classical existence.

The clinical outcomes and prognostic factors of dedifferentiated central chondrosarcoma in extremities

ObjectiveThis study was to analyze the clinical outcomes and prognostic factors of dedifferentiated central chondrosarcomas (DCCS) in extremities.MethodsA retrospective study was conducted on 49 patients (27 males, 22 females) who underwent surgical treatment between January 2001 and March 2023 in our institution. All patients were diagnosed with dedifferentiated central chondrosarcomas by needle biopsy or postoperative histopathological examination. The general characters, treatment and clinical outcomes were recorded in the follow-up and all surgical-related complications that occurred were recorded in this study. Overall, these data were used to analyse the prognostic factors of DCCS.Results49 patients were included in this retrospective study and there were no patients lost in the follow-up period. The median diagnosis age of all patients was 57 years old (ranging from 17 to 87) and the median follow-up time was 34 months (range, 1-289). The average tumor size was 9.6 ± 2.4 cm (3.0-15.5). Median overall survival (OS) and progression-free survival (PFS) were 34 and 23 months, respectively. The 1-year, 2-year, 5-year, and 10-year OS were 87.8% (95% CI 77.6%-98.0%), 71.4% (35/49), 28.6% (14/49) and 18.4% (9/49). And the 1-year, 2-year, 5-year, and 10-year PFS were 75.5% (95% CI 63.6%-87.4%), 49.0% (35/49), 26.5% (14/49) and 16.3% (9/49). Multiple variate analyses indicated metastasis, pathological fracture, Enneking staging and surgical margin were independent prognostic factors in extremity dedifferentiated central chondrosarcomas.ConclusionsDedifferentiated central chondrosarcomas in extremities still had a grave prognosis. Metastasis, pathological fracture, Enneking staging, and surgical margin were independent risk factors for prognosis.Evidence levelIV Therapic.

Sea surface wind retrieval from CFOSAT Rotating fan-beam scatterometer in ocean cyclones

ABSTRACT Rotating fan-beam scatterometer (RFSCAT) is a radar scatterometer system for sea surface wind vector measurement. Compared with other available scatterometers, RFSCAT can provide more combination of azimuth angles and incidence angles for a single WVC (wind vector cell), this observation mechanism is more conducive to the sea surface wind direction retrieval. In this paper, the NSCAT-4DS GMF (geophysical model function) with SST (sea surface temperature) correction, and the MSS (Multiple Solution Scheme) combination with a 2DVAR (2-dimensional variational analysis) are adopted to retrieve the sea surface winds from RFSCAT on the CFOSAT (Chinese-French Oceanography Satellite). The retrieved RFSCAT sea surface winds and ASCAT (advanced scatterometer) sea surface winds are compared and tested, and the feasibility of the RFSCAT measuring sea surface winds under high wind speeds is analysed. The results show that the RMSE of the RFSCAT sea surface wind speed using improved algorithm has decreased by 0.292 m s−1, the correlation coefficient has increased by 0.032, and the residual standard deviation has decreased by 0.194 m s−1. The RMSE of RFSCAT sea surface wind direction has decreased by 5.950°, the correlation coefficient has increased by 0.002, and the residual standard deviation has decreased by 5.567°. It is shown that the changes in winds RMSE using pre-improved and improved algorithms have statistical significance. In a word, the spaceborne Ku-band rotating fan-beam scatterometer can capture the winds structure of ocean cyclones. Although there may be high wind speeds saturation phenomena, the detecting sea surface winds at high wind speeds show preferable performance.

Variational Bayes latent class analysis for EHR-based phenotyping with large real-world data

IntroductionBayesian approaches to patient phenotyping in clinical observational studies have been limited by the computational challenges associated with applying the Markov Chain Monte Carlo (MCMC) approach to real-world data. Approximate Bayesian inference via optimization of the variational evidence lower bound, variational Bayes (VB), has been successfully demonstrated for other applications.MethodsWe investigate the performance and characteristics of currently available VB and MCMC software to explore the practicability of available approaches and provide guidance for clinical practitioners. Two case studies are used to fully explore the methods covering a variety of real-world data. First, we use the publicly available Pima Indian diabetes data to comprehensively compare VB implementations of logistic regression. Second, a large real-world data set, Optum™ EHR with approximately one million diabetes patients extended the analysis to large, highly unbalanced data containing discrete and continuous variables. A Bayesian patient phenotyping composite model incorporating latent class analysis (LCA) and regression was implemented with the second case study.ResultsWe find that several data characteristics common in clinical data, such as sparsity, significantly affect the posterior accuracy of automatic VB methods compared with conditionally conjugate mean-field methods. We find that for both models, automatic VB approaches require more effort and technical knowledge to set up for accurate posterior estimation and are very sensitive to stopping time compared with closed-form VB methods.DiscussionOur results indicate that the patient phenotyping composite Bayes model is more easily usable for real-world studies if Monte Carlo is replaced with VB. It can potentially become a uniquely useful tool for decision support, especially for rare diseases where gold-standard biomarker data are sparse but prior knowledge can be used to assist model diagnosis and may suggest when biomarker tests are warranted.

Preventing mass loss in the standard level set method: New insights from variational analyses

For decades, the computational multiphase flow community has grappled with mass loss in the level set method. Numerous solutions have been proposed, from fixing the reinitialization step to combining the level set method with other conservative schemes. However, our work reveals a more fundamental culprit: the smooth Heaviside and delta functions inherent to the standard formulation. Even if reinitialization is done exactly, i.e., the zero contour interface remains stationary, the use of smooth functions lead to violation of mass conservation. We propose a novel approach using variational analysis to incorporate a mass conservation constraint. This introduces a Lagrange multiplier that enforces overall mass balance. Notably, as the delta function sharpens, i.e., approaches the Dirac delta limit, the Lagrange multiplier approaches zero. However, the exact Lagrange multiplier method disrupts the signed distance property of the level set function. This motivates us to develop an approximate version of the Lagrange multiplier that preserves both overall mass and signed distance property of the level set function. Our framework even recovers existing mass-conserving level set methods, revealing some inconsistencies in prior analyses. We extend this approach to three-phase flows for fluid-structure interaction (FSI) simulations. We present variational equations in both immersed and non-immersed forms, demonstrating the convergence of the former formulation to the latter when the body delta function sharpens. Rigorous test problems confirm that the FSI dynamics produced by our simple, easy-to-implement immersed formulation with the approximate Lagrange multiplier method are accurate and match state-of-the-art solvers.

Broadband elastic energy harvesting based on achromatic meta-grating

Energy harvesting exploiting the inverse piezoelectric effect has been the subject of much attention and discussion in the field of elastic and structural dynamics. Recently, the ongoing development of elastic metamaterials and metasurfaces has opened up a new way to improve the quality of energy harvesting. Here, we proposed a new strategy for harvesting elastic energy in a plate, which is the use of the inverse piezoelectric effect to convert the elastic energy into electrical energy after the achromatic meta-grating has focused broadband flexural waves. A new theoretical method to design the achromatic meta-grating is proposed based on derived analytical expression of the phase shift of subunit. When a meta-grating, a thin plate and a piezoelectric patch are combined into an energy harvesting system, the elastic energy can be converted into electric energy by the system, and the output voltage can be amplified by twice that of the system without the meta-grating. A theoretical framework is built to analyze the performance of the energy harvesting system, and variational parametric analyses are carried out to obtain the optimal resistance, the optimal length, thickness and position of piezoelectric patch, which are 870Ω, 18mm, 0.2mm and 30mm, respectively. For the optimized system, the power harvested rate of the system is close to 4 in the frequency band of 6-8kHz. Finally, the design of the system based on the wave focusing principle is extended, and energy harvesters are designed for different frequency bands, which can all work under different excitation conditions (a local and a base excitations). Our work opens up a new route for elastic energy harvesting and may have broad application prospects in the development of self-powered sensors.

Morphogenesis analysis of icosahedral and prismatic tensegrity modules

Morphogenesis is a critical aspect of tensegrity system design. This paper explores icosahedral and prismatic tensegrity modules' pattern formation and foundational theories. First, a material consumption functional and self-strain energy functional are introduced from an engineering perspective, along with a variational principle involving independent dual-variable in the morphogenesis process of tensegrity structures. Next, a Symbol Parsing Method is proposed and successfully applied to the optimal morphology analysis of the icosahedral tensegrity module. Due to memory limitations in personal computers, the Singular Value Decomposition of the symbolic equilibrium matrix for the prismatic tensegrity module is constrained. As an alternative, a discrete numerical solution, the semi-symbolic parsing method, is obtained by directly utilizing a numerical equilibrium matrix. This method was recently employed to analyze and optimize a practical tensegrity footbridge designed by the authors. Lastly, the paper delves into the stability of self-equilibrium states in icosahedral and classical prismatic tensegrity modules by employing a second-order variational analysis of the self-strain energy functional. The findings presented are expected to contribute to future research on the morphogenesis of tensegrity structures.

Odd-parity nucleon electromagnetic transitions in lattice QCD

The parity-expanded variational analysis (PEVA) technique enables the isolation of opposite-parity eigenstates at finite momentum. The approach has been used to perform the first lattice QCD calculations of excited-baryon form factors. In particular, these calculations show that the low-lying odd-parity nucleon excitations are described well by constituent quark models at moderate u and d quark masses approaching the strange quark mass. Herein, we extend the PEVA technique to establish a formalism for the determination of odd-parity nucleon electromagnetic transition form factors in lattice QCD. The formalism is implemented in the first calculation of the helicity amplitudes for transitions from the ground state nucleon to the first two odd-parity excitations. Through a comparison with constituent quark-model calculations of these amplitudes, these new results give important insight into the structure of these excitations. This work is a critical step towards confronting experimental electroproduction amplitudes for the N*(1535) and N*(1650) resonances with lattice QCD calculations. Published by the American Physical Society 2024

Fixed points of regular set-valued mappings in quasi-metric spaces

Metric fixed point theory is becoming increasingly significant across various fields, including data science and iterative methods for solving optimization problems. This paper aims to introduce new fixed point theorems for set-valued mappings under novel regularity conditions, such as orbital regularity and orbital pseudo-Lipschitzness. Instead of traditional metric spaces, we adopt the framework of quasi-metric spaces, motivated by the need to address problems in spaces that are not necessarily metric, such as function spaces of homogeneous type. We also explore the stability of the set of fixed points under variations of the set-valued mapping. Additionally, we provide estimates for the distances from a given point to the set of fixed points and between two sets of fixed points. Building on these findings, we extend the discussion to similar problems involving fixed, coincidence, and cyclic/double fixed points within this framework. Our results generalize recent findings from the literature, including those in Ait Mansour M, Bahraoui MA, El Bekkali A. [Metric regularity and Lyusternik-Graves theorem via approximate fixed points of set-valued maps in noncomplete metric spaces. Set-Valued Var Anal. 2022;30(1):233–256. doi: 10.1007/s11228-020-00553-1], Dontchev AL, Rockafellar RT. [Implicit functions and solution mappings. a view from variational analysis. Dordrecht: Springer; 2009. Springer Monographs in Mathematics], Ioffe AD. [Variational analysis of regular mappings. Springer, Cham; 2017. Springer Monographs in Mathematics; theory and applications. doi: 10.1007/978-3-319-64277-2], Lim TC. [On fixed point stability for set-valued contractive mappings with applications to generalized differential equations. J Math Anal Appl. 1985;110(2):436–441. doi: 10.1016/0022-247X(85)90306-3] and Tron NH. [Coincidence and fixed points of set-valued mappings via regularity in metric spaces. Set-Valued Var Anal. 2023;31(2):22. Paper No. 17. doi: 10.1007/s11228-023-00680-5].

Variational analysis of sensory feedback mechanisms in powerstroke-recovery systems.

Although the raison d'etre of the brain is the survival of the body, there are relatively few theoretical studies of closed-loop rhythmic motor control systems. In this paper we provide a unified framework, based on variational analysis, for investigating the dual goals of performance and robustness in powerstroke-recovery systems. To demonstrate our variational method, we augment two previously published closed-loop motor control models by equipping each model with a performance measure based on the rate of progress of the system relative to a spatially extended external substrate-such as a long strip of seaweed for a feeding task, or progress relative to the ground for a locomotor task. The sensitivity measure quantifies the ability of the system to maintain performance in response to external perturbations, such as an applied load. Motivated by a search for optimal design principles for feedback control achieving the complementary requirements of efficiency and robustness, we discuss the performance-sensitivity patterns of the systems featuring different sensory feedback architectures. In a paradigmatic half-center oscillator-motor system, we observe that the excitation-inhibition property of feedback mechanisms determines the sensitivity pattern while the activation-inactivation property determines the performance pattern. Moreover, we show that the nonlinearity of the sigmoid activation of feedback signals allows the existence of optimal combinations of performance and sensitivity. In a detailed hindlimb locomotor system, we find that a force-dependent feedback can simultaneously optimize both performance and robustness, while length-dependent feedback variations result in significant performance-versus-sensitivity tradeoffs. Thus, this work provides an analytical framework for studying feedback control of oscillations in nonlinear dynamical systems, leading to several insights that have the potential to inform the design of control or rehabilitation systems.

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.

Prediction of sectional collapse of thin-walled structure under pure bending by nonlinear composite beam theory

Brazier (1927) found that when one dimension of the beam cross-section was relatively smaller than the others, large in-plane displacements over the cross-section might occur, even though the strains could remain very small. Under this circumstance, the so-called Brazier effect refers to the cross-sectional ovalization, which leads to nonlinear bending buckling and collapses. This paper studies the Brazier effect by the nonlinear Variational Asymptotic Beam Sectional Analysis (VABS) theory which considers finite cross-sectional deformations. Nonlinear VABS reduces three-dimensional (3D) continuum to a one-dimensional (1D) beam analysis and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities without unnecessary kinematic assumptions. The present theory is implemented using the finite element method (FEM) in the VABS code, a general-purpose beam cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model using the Euler–Bernoulli beam theory. The deformation gradient tensor is directly used to deal with finite deformation, various strain definitions, and several types of material laws. Numerical examples demonstrate the capabilities of VABS to predict the sectional collapse of thin-walled structures under pure bending.

Investigation of the shape of goat (capra hircus) astragalus via geometric morphometry method

The aim of this study is to determine the effect of sex on shape of goat astragalus via geometric morphometry method. A total of 37 astragalus bone samples collected from 16 female and 21 male goats were used as material. Bone samples were cleaned from skin and soft tissue and then macerated by boiling. Astragalus bone samples were photographed from a distance of 20 cm dorsally by focusing on the center of the bone. The photographs were transferred to the computer in JPEG format. Principal Component Analysis, Regression Analysis, Canonical Variate Analysis, and Discriminant Function Analysis were conducted using the Cartesian coordinate values, which were obtained by homologous landmark marking. The first two principal components accounted for 75.967% of the total shape variation. Shape variation was determined in different regions of the astragalus. According to the scatter plot of male and female individuals, male individuals were completely placed within the confidence interval ellipse of female individuals. It was found that allometric effect on the shape of astragalus bone was not statistically significant. As a result of Canonical Variate Analysis, mahalanobis and procrustes distances were detected as 2.9216 (p