Parametrized Research Articles

Factors associated with time to first birth interval among ever married Bangladeshi women: A comparative analysis on Cox-PH model and parametric models.

The fertility rate of a married woman can be measured by the length of the first birth interval (FBI). This length is influenced by some significant factors. Better knowledge about the factors affecting the birth interval can help in controlling population growth and fertility progress. The main focus of this study was to compare the performance of Cox-Proportional Hazard (Cox-PH) and the parametric Accelerated Failure Time (AFT) model in assessing the impact of significant factors affecting the time to FBI of ever-married Bangladeshi women. Information of 14941 women having at least one birth was included in this study from the most recent nationally representative data 2017-18 Bangladesh Demographic and Health Survey (BDHS). We used the Cox-PH model and AFT model under various parametric forms of survival time distributions (Weibull, Exponential, and Log-normal distribution) to measure the effect of factors influencing FBI. And then, a respective Akaike information criterion (AIC) was calculated for selecting the best-fitted model. According to the AIC and BIC values, the log-normal model fitted better than other AFT models. Based on the log-normal model, women's age and age at first marriage, maternal and paternal education, contraceptive use status, used anything to avoid pregnancy, sex of household head, and spousal age difference had a significant association with FBI of ever married Bangladeshi women. The parametric AFT model (log-normal distribution) was a better fitted model in evaluating the covariates associated with FBI of ever-married Bangladeshi Women. Higher education, the right age at marriage, and proper knowledge about family planning (i.e., contraception use) should be ensured for every married person to control the gap of the first birth.

Anisotropy of the zigzag order in the Kitaev honeycomb magnet α−RuBr3

Kitaev materials often order magnetically at low temperatures due to the presence of non-Kitaev interactions. Torque magnetometry is a very sensitive technique for probing the magnetic anisotropy, which is critical in understanding the magnetic ground state. In this paper, we report detailed single-crystal torque measurements in the proposed Kitaev candidate honeycomb magnet α−RuBr3, which displays zigzag order below 34 K. Based on angular-dependent torque studies in magnetic fields up to 16 T rotated in the plane normal to the honeycomb layers, we find an easy-plane anisotropy with a temperature dependence of the torque amplitude following closely the behavior of the powder magnetic susceptibility. The torque for the field rotated in the honeycomb plane has a clear sixfold periodicity with a sawtooth shape, reflecting the threefold symmetry of the crystal structure and stabilization of different zigzag domains depending on the field orientation, with a torque amplitude that follows an order parameter form inside the zigzag phase. By comparing experimental data with theoretical calculations we highlight the importance of relevant anisotropic interactions and the role of the competition between different zigzag domains in this candidate Kitaev magnet. Published by the American Physical Society 2024

Unified genus-1 potential and a parametric perturbative/nonperturbative relation

We study a parametric deformation of the unified genus-1 anharmonic potential and derive a parametric form of perturbative/nonperturbative (P/NP) relation, applicable across all parameter values. We explicitly demonstrate that the perturbative expansion around the perturbative saddle is sufficient to generate all the nonperturbative information in these systems. Our results confirm the known results in the literature, where the cubic and quartic anharmonic potentials are reproduced under extreme parameter values, and go beyond these known results by developing the nonperturbative function of real and complex instantons solely from perturbative data. Published by the American Physical Society 2024

Modified Successive Approximations Method for Solving Fuzzy Second Kind Fredholm Integral Equations with Separable Kernel

This paper presents an analysis, development, and application of a modified method of successive approximations to solve fuzzy second kind Fredholm integral equations with a separable kernel. The fuzziness in the equations is represented utilizing convex normalized triangular fuzzy numbers, which are based on a single and double parametric form of fuzzy numbers. In the single parametric form of the fuzzy number, a fuzzy equation converts to two crisp equations for the solution which increases the computational cost. Therefore, to reduce the computational cost and increase the solution's accuracy, the double parametric form of the fuzzy number will be used in this study. The feasibility of the proposed methods is illustrated through a numerical example. The results obtained using the presented approach demonstrate adequate agreement with relevant theoretical aspects.

Anthropometric Study of Auricular Development in Human Fetal Cadavers

The aim of the study is to comprehensively examine the composition and localization of the auricle in formalin-fixed human fetuses during the second and third trimesters of the antenatal period. Ninety-seven auricles were evaluated (33 females and 31 males in the second, and 22 females and 11 males in the third trimester). Nine morphometric dimensions were directly measured from auricles. The position of the auricula relative to lateral cantus and oral commissure levels, and the ear inclination angle were determined. The frequency of lobule attachment types was also noted. All fetuses exhibited normal development within the 50% to 97% percentile range. Morphometric data (ear length, ear width, distance from tragus to helix, auricular base length, concha length, conchal width, lobule length, and lobule width) for the second and third trimesters were presented, along with comparisons of ear dimensions by side and sex. Attachment types of lobules in fetuses were with pendulous lobules being the most common at 62.5%, nonpendulous lobules at 21.88%, and partial pendulous lobules the least common at 15.62%. None of the fetuses exhibited low-set ears. Dimensional measurements revealed no statistically significant differences between fetuses, except for the left auricular base length in females, left concha length in males, and left lobule width in males, which were higher. Scatter plots of parameters with age and regression analysis were provided. These results contribute to a deeper understanding of fetal auricle development and serve as a reference during the second and third trimesters. Quantitative values of normal fetal ear growth can aid specialists in distinguishing congenital or developmental anomalies from normal ears.

Covariate-adjusted response-adaptive designs for semiparametric survivalmodels.

Covariate-adjusted responseadaptive (CARA) designs are effective in increasing the expected number of patients receiving superior treatment inan ongoing clinical trial, given a patient's covariate profile. There has recently been extensive research on CARA designs with parametric distributional assumptions on patient responses. However, the range of applications for such designs becomes limited in real clinical trials. Sverdlov etal. have pointed out that irrespective of a specific parametric form of the survival outcomes, their proposed CARA designs based on the exponential model provide valid statistical inference, provided the final analysis is performed using the appropriate accelerated failure time (AFT) model. In real survival trials, however, the planned primary analysis is rarely conducted using an AFT model. The proposed CARA designs are developed obviating any distributional assumptions about the survival responses, relying only on the proportional hazards assumption between the two treatment arms. To meet the multiple experimental objectives of a clinical trial, the proposed designs are developed based on an optimal allocation approach. The covariate-adjusted doubly adaptive biased coin design and the covariate-adjusted efficient-randomized adaptive design are used to randomize the patients to achieve the derived targets on expectation. These expected targets are functions of the Cox regression coefficients that are estimated sequentially with the arrival of every new patient into the trial. The merits of the proposed designs are assessed using extensive simulation studies of their operating characteristics and then have been implemented to re-design a real-life confirmatory clinical trial.

Bivariate Generalized Exponential Distribution with Positive Probability at (X = 0, Y = 0) and Estimation of Parameters for a Particular Case

Kundu and Gupta, 2009, J Multivar Anal, 100, 581–593, provided a bivariate generalized exponential distribution (BVGED [Formula: see text]), which is a bivariate continuous lifetime distribution. In practice, however, sometimes both the components may fail instantaneously. Thus, we get a mixture bivariate distribution with positive probability at instantaneous failure of each component. The main aim of this article is to define a BVGED with positive probability at instantaneous failure of each component (BVGEDP [Formula: see text]), where PX=0P(X = 0) and P(Y = 0) is a function of parameter [Formula: see text]. It is observed that the joint probability density function and the cumulative distribution function can be expressed in compact forms. Several properties of the distribution have been discussed. For a particular case (BVGEDP ([Formula: see text] 1, 1, 1)), moment type estimators are obtained which are in closed form and maximum likelihood estimators of parameters ([Formula: see text]) are obtained using an iterative procedure. Also, their finite sample and asymptotic properties are discussed using simulation. A final section presents an application to a real data set on which the proposed BVGEDP ([Formula: see text], 1, 1, 1) distribution is fitted. AMS Subject Classification: 62E99

Multi-objective optimization framework based on review of form-finding of architectural parametric forms

Parametric architecture has played a vital role in architectural design in recent times. Research on early form-finding of architectural forms represents a notable area of study. Despite the significance of energy performance, digital fabrication, and aesthetics as design objectives, there is a lack of a comprehensive framework that integrates them in the form-finding process. To address this gap, this research conducts a systematic review of previous studies on form-finding and optimization of architectural forms, focusing on the three aforementioned objectives. Then, based on the analysis of the selected studies, the research proposes a multi-objective optimization framework for form-finding of architectural parametric forms, considering energy performance, digital fabrication, and aesthetics. The framework comprises five phases: form generation, multi-objective optimization, aesthetic evaluation, geometry rationalization, and digital fabrication of a prototype. This framework is usable by any architect, regardless of their programming knowledge, and is applicable to any new architectural design.

MARS CHRONOLOGY DERIVED FROM CRATERS HETEROGENEITY AT GALE CRATER

Craters sample into diachronic surfaces and different depths on Mars and other planetary surfaces. These surfaces are affected by cosmonuclide radiation that offers one of the most reliable age anchors to date. Craters also accumulate, evolve and display an universal characteristic that can be measured at any scale, regardless of the geologic unit they sample, in the form of the heterogeneity parameter (Capitan, 2021). Here we use an age equation, which is based on the measurements of craters diameter, depths and area they occupy, to derive the ages of deposits that are sampled by medium-scale craters (meters to few hundred meters in diameter). We show that units sampled by the deepest craters near MSL exploration area are formed during the early stages of Gale crater formation before 2870 Ma. In contrast, units sampled by shallower craters were formed during the stages that correspond to the time of sediment recycling and lithification periods, near 2129 Ma to present. Given the heterogeneity of initial formation conditions of craters of diverse diameters and their different depths of sampling, our proposed synchronous ages with ground-truth ages has the potential to redefine the paradigm of using the impact crater morphometry as a tool to date the planetary surfaces.

Double parametric based solution of fuzzy unconfined aquifer problem using Laplace transforms method

The Boussinesq equation describes the model for horizontal water flow in unconfined aquifers without precipitation, a topic that has been extensively studied in the literature. However, the parameters, as well as the initial and boundary conditions, are often assumed to be exact. In reality, these conditions may be incomplete or uncertain due to limited knowledge, insufficient information, or errors introduced by humans or machines. The fuzzy set theory has recently been successfully employed to model such uncertainties. This article investigates the analytical solution of the one-dimensional Boussinesq equation in a fuzzy environment. The objective of this research is to investigate the recharge and discharge of a semi-infinite unconfined aquifer adjacent to a lake. For the present investigation, uncertainties in terms of fuzzy are considered only for the involved initial and boundary conditions of the problem, whereas other parameters are considered as crisp or exact. The analysis employed the double parametric form of a fuzzy number alongside Laplace transform techniques. The obtained solutions were then compared with existing results in specific cases to validate their accuracy.

Variable offsets and processing of implicit forms toward the adaptive synthesis and analysis of heterogeneous conforming microstructure

AbstractThe synthesis of porous, lattice, or microstructure geometries has captured the attention of many researchers in recent years. Implicit forms, such as triply periodic minimal surfaces (TPMS) has captured a significant attention, recently, as tiles in lattices, partially because implicit forms have the potential for synthesizing with ease more complex topologies of tiles, compared to parametric forms. In this work, we show how variable offsets of implicit forms could be used in lattice design as well as lattice analysis, while graded wall and edge thicknesses could be fully controlled in the lattice and even vary within a single tile. As a result, (geometrically) heterogeneous lattices could be created and adapted to follow analysis results while maintaining continuity between adjacent tiles. We demonstrate this ability on several 3D models, including TPMS.

Interactions between a toroidal bubble and a free surface

Toroidal bubbles (TBs) represent cases of vortex rings with a gas–liquid interface where a gas vortex ring is encased within a liquid vortex ring, and can serve as effective media for mass conveyance, process mixing, noise reduction and reaction regulation. In this study, we carry out a systematic study on the interaction between a TB and a free surface. According to the high-speed photographic images from the experiments, we identify strong and weak interactions in terms of the normalized maximum free surface deformation $h_{max}^*$ . Then, we perform numerical simulations based on the volume of fluid (VOF) method in the OpenFOAM platform. Based on both the experimental and the numerical results, we conclude that the Froude number, $Fr$ , determines the main characteristics during the interaction process. The TB–free surface interaction is essentially the interaction between the liquid vortex ring enveloping the TB and the free surface, supplemented by the TB's complex behaviour. Next, we establish the scaling law of $h_{max}^*$ based on the energy balance condition. Based on this, we provide the critical $Fr$ and the slenderness of the TB, $\eta$ , for identifying the strong and weak interactions, and a parametric plot of the interactions in terms of $Fr$ and $\eta$ .

Symmetric teleparallel gravity with variable deceleration parameter

In this paper, our investigation focuses on the cosmic history in modified [Formula: see text] gravity, a different theory that describes the gravitational force using a non-metricity scalar. The equations of the theory are solved by assuming a parametric form for the deceleration parameter. The parameters of the model are estimated by using the Cosmic Chronometer dataset. A number of parameters, like the deceleration parameter, whose signature changes with redshift and shows typical behavior in late-time cosmology, are subject of our analysis. We also show the evolution of other parameters, such as the equation of state parameter and energy density. The parametrization approach used here in [Formula: see text] modified gravity provides a better description of the late-time cosmic evolution without dark energy.

Modelling nonlinear moderation effects with local structural equation modelling (LSEM): A non-technical introduction.

Understanding the differential strength of effects in the presence of a third variable, known as a moderation effect, is a common research goal in many psychological and behavioural science fields. If structural equation modelling is applied to test effects of interest, the investigation of differential strength of effects will typically ask how parameters of a latent variable model are influenced by categorical or continuous moderators, such as age, socio-economic status, personality traits, etc. Traditional approaches to continuous moderators in SEMs predominantly address linear moderation effects, risking the oversight of nonlinear effects. Moreover, some approaches have methodological limitations, for example, the need to categorise moderators or to pre-specify parametric forms of moderation. This tutorial introduces local structural equation modelling (LSEM) in a non-technical way. LSEM is a nonparametric approach that allows the analysis of nonlinear moderation effects without the above-mentioned limitations. Using an empirical dataset, we demonstrate the implementation of LSEM through the R-sirt package, emphasising its versatility in both exploratory analysis of nonlinear moderation without prior knowledge and confirmatory testing of hypothesised moderation functions. The tutorial also addresses common modelling issues and extends the discussion to different application scenarios, demonstrating its flexibility.

Unified specification tests in partially linear time series models

Based on a residual marked empirical process, Cramér–von Mises and Kolmogorov–Smirnov tests are proposed for the correct specification of the nonparametric components in partially linear time series models. The tests are unified in the sense that the asymptotic distribution of residual marked empirical process is invariant across different nν-consistent estimators in calculating residuals (where ν>1/4) under the null. In addition, the residual marked empirical process has the same power property under the sequence of local alternatives regardless of the estimators used. Achieved through a projection method, these features also enable using a computationally convenient multiplier bootstrap to approximate the unified null distributions of the test statistics. Simulations show satisfactory finite-sample performance of the proposed method. The application to validate the parametric form of conditional variance in the ARCH-X model is also highlighted, along with an empirical analysis of the conditional variance of the FTSE 100 index return series.

Dimensional Synthesis of the Compliant Mechanism Using the Parametric Fuzzy Form of the Freudenstein Equation

The dimensional synthesis of compliant mechanisms (CMs) leverages the flexibility of their components to achieve precise motion and functionality. This study introduces a novel approach using the parametric fuzzy form of the Freudenstein equation with triangular fuzzy numbers (TFNs) to address the complexities and uncertainties inherent in CM design. By integrating fuzzy logic with advanced computational techniques such as Newton’s method, the proposed methodology offers a robust framework for synthesizing CMs that can adapt to varying conditions. This approach enables the creation of flexible links modeled as fuzzy regions, allowing for optimized performance and reliability across a range of operational scenarios. Numerical examples illustrate the practical application and efficacy of the proposed methods, highlighting significant improvements in the design and synthesis of CMs. The integration of fuzzy logic in the synthesis process not only enhances the resilience of the mechanisms but also paves the way for future advancements in the field. This study demonstrates the potential of fuzzy logic principles in optimizing CM designs, ensuring they meet specific functional requirements with high precision.

Exact analytical solution of the equations for a quasiequilibrium two-phase domain: permeability and interdendritic spacing

This study is concerned with the theoretical description of a quasi-stationary process of directional crystallization of binary melts and solutions in the presence of a quasi-equilibrium two-phase region. The quasi-equilibrium process is ensured by the fact that the system supercooling is almost completely compensated by heat released during the phase transformation. Quasi-stationarity of the process determining constancy of the crystallization rate is ensured by given temperature gradients in the solid and liquid phases. The system of heat and mass transfer equations and boundary conditions to them under these assumptions is dependent on a single spatial variable in the reference frame moving with the crystallization rate relative to a laboratory coordinate system. Exact analytical solutions to the formulated problem in parametric form are obtained. The parameter of the solution is the solid phase fraction in a two-phase region. The distributions of temperature and impurity concentration in the solid, liquid and two-phase regions of the crystallizing system, the rate of solidification, and the spatial coordinate in the two-phase region depending on the solid phase fraction in it are found. An algebraic equation for the solid phase fraction at the interface between the solid material and the two-phase region is derived. Exact analytical solutions show that the impurity concentration in the two-phase layer increases as the solid phase fraction increases. Moreover, the solid phase fraction at the interface solid phase — two phase region and its thickness increase as the temperature gradient in the solid phase and the solidification rate increase. The developed theory allows us to determine analytically the permeability of the two-phase region and a characteristic interdendritic spacing in it. Analytical solutions show that the relative permeability in the two-phase region increases from a certain value at the interface with the solid phase to unity at the interface with the liquid phase. The selection theory of stable dendritic growth allows us to determine analytically a characteristic interdendritic distance in the two-phase layer that decreases as the temperature gradient in the solid phase increases. An increase of impurity in the molten phase gives a decrease in the interdendritic spacing within a two-phase region.

Filter transfer learning algorithm for nonlinear systems modeling with heterogeneous features

Transfer learning can handle the domain adaptation of different feature spaces in nonlinear systems. Most existing studies only focus on common features between heterogeneous scenes rather than specific features that account for latent similarities between them. To deal with this problem, a filter transfer learning algorithm for nonlinear systems modeling with heterogeneous features is proposed. First, nonlinear mapping is constructed to learn the potential relationships between different feature attributes, including common features and specific features. Then, source knowledge from different domains can be obtained in the form of process parameters according to the mapping relationship. Second, a hierarchical filter framework is presented to reconstruct source knowledge in different transfer phases. In the pre-transfer phase, a knowledge filter is designed to increase the diversity of knowledge through selection, crossover, and mutation operations. In the post-transfer phase, a guided filter is established to achieve a coupling balance between source knowledge and target domain by using target samples as guidance information. Third, a dynamic parameter learning strategy is given to promote the learning performance of heterogeneous tasks. Finally, the effectiveness of innovations and the superiority of this proposed algorithm are verified by the experimental results in nonlinear systems with heterogeneous features.

Exact solution of a mathematical model for human muscular motion

An ordinary differential equation (ODE) which models human muscular movement is considered. A functional form of the model parameter is specified through the Lie symmetry approach, yielding a different expression from the one derived in the previous study (Kosugi et al., 2019). The Lie point symmetries corresponding to the model parameter are employed for derivation of exact solution.

The Reliability of Type Ia Supernovae Delay-time Distributions Recovered from Galaxy Star Formation Histories

We present a numerical analysis investigating the reliability of Type Ia supernova (SN Ia) delay-time distributions recovered from individual host galaxy star formation histories. We utilize star formation histories of mock samples of galaxies generated from the IllustrisTNG simulation at two redshifts to recover delay-time distributions. The delay-time distributions are constructed through piecewise constants as opposed to typically employed parametric forms such as power laws or Gaussian or skew/lognormal functions. The SN Ia delay-time distributions are recovered through a Markov Chain Monte Carlo exploration of the likelihood space by comparing the expected SN Ia rate within each mock galaxy to the observed rate. We show that a reduced representative sample of nonhost galaxies is sufficient to reliably recover delay-time distributions while simultaneously reducing the computational load. We also highlight a potential systematic between recovered delay-time distributions and the mass-weighted ages of the underlying host galaxy stellar population.