Parametric Approach Research Articles

Energy levels and thermodynamic models of the general molecular oscillator under a 2D electromagnetic potential field

This study employs the parametric Nikiforov-Uvarov approach (PNUA) to resolve the radial Schrödinger equation (RSE) for the general molecular oscillator with a 2D electromagnetic potential coupling. Analytical approximations are developed for the energy levels, molar enthalpy, and constant-pressure molar heat capacity, with a focus on their applicability to diatomic molecules. The generated equations are employed to investigate the physical properties of real substances like BeCl (X 2Σ+), CsF (X 1Σ+), CuCl (X 1Σ+), CO+ (X 2Σ+), 7Li2 (1 3Δg), and P2 (X 1Σg +) molecules. The percentage average absolute deviations (PAAD) deduced with the analytical model equations are found to agree with the findings on diatomic molecules. Analysis of PAAD values also reveals that the predicted molar enthalpy and heat capacity of the diatomic molecules are better if the magnetic and Aharonov-Bohm components of the EM potential fields are finite.

A stableness of resistance model for nonresponse adjustment with callback data

Abstract Nonresponse arises frequently in surveys, and follow-ups are routinely made to increase the response rate. In order to monitor the follow-up process, callback data have been used in social sciences and survey studies for decades. In modern surveys, the availability of callback data is increasing because the response rate is decreasing, and follow-ups are essential to collect maximum information. Although callback data are helpful to reduce the bias in surveys, such data have not been widely used in statistical analysis until recently. We propose a stableness of resistance assumption for nonresponse adjustment with callback data. We establish the identification and the semiparametric efficiency theory under this assumption, and propose a suite of semiparametric estimation methods including doubly robust estimators, which generalize existing parametric approaches for callback data analysis. We apply the approach to a Consumer Expenditure Survey dataset. The results suggest an association between nonresponse and high housing expenditures.

Testing Similarity of Parametric Competing Risks Models for Identifying Potentially Similar Pathways in Healthcare.

The identification of similar patient pathways is a crucial task in healthcare analytics. A flexible tool to address this issue are parametric competing risks models, where transition intensities may be specified by a variety of parametric distributions, thus in particular being possibly time-dependent. We assess the similarity between two such models by examining the transitions between different health states. This research introduces a method to measure the maximum differences in transition intensities over time, leading to the development of a test procedure for assessing similarity. We propose a parametric bootstrap approach for this purpose and provide a proof to confirm the validity of this procedure. The performance of our proposed method is evaluated through a simulation study, considering a range of sample sizes, differing amounts of censoring, and various thresholds for similarity. Finally, we demonstrate the practical application of our approach with a case study from urological clinical routine practice, which inspired this research.

Beyond Parametric Bounds: Exploring Regional Unemployment Patterns Using Semiparametric Spatial Autoregression

Abstract Background It is a well-known phenomenon that nonlinearities that are inherent in the relationship among economic variables negatively affect the commonly used estimators in the econometric models. The nonlinearities cause an instability of the estimated parameters that, in particular, are unable to capture a local relationship between the response and the covariate. Objectives The main aim of the paper is the simultaneous consideration of spatial effects as well as nonlinearities through an advanced semiparametric spatial autoregressive econometric model. The paper seeks to contribute to empirical studies of regional science focused on the application of semiparametric spatial autoregressive econometric models. Methods/Approach We outline an approach that can be used to correct nonlinearities by incorporating a semiparametric idea within the framework of econometric models. We use an expansion by penalised basis splines that are highly flexible and are able to capture local nonlinearities between variables. Results In the empirical study, we fit different econometric models that attempt to explain the dynamics of the European Union's regional unemployment. Conclusions The results show that regional unemployment exhibits significant spatial dependence, indicating interconnectedness among neighbouring regions and suggesting the adoption of a semiparametric spatial autoregressive model for improved modelling flexibility, surpassing traditional parametric approaches.

A fuzzy tuning approach for controller parameters of a parallel manipulator based on clustering analysis

A fuzzy tuning approach for controller parameters of a parallel manipulator based on clustering analysis

Finding robustly fair solutions in resource allocation

In this study, we consider resource allocation settings where the decisions affect multiple beneficiaries and the decision maker aims to ensure that the effect is distributed to the beneficiaries in an equitable manner. We specifically consider stochastic environments where there is uncertainty in the system and propose a robust programming approach that aims at maximizing system efficiency while guaranteeing an equitable benefit allocation even under the worst scenario. Acknowledging the fact that the robust solution may lead to high efficiency loss and may be over-conservative, we adopt a parametric approach that allows controlling the level of conservatism and present the decision maker alternative solutions that reveal the trade-off between efficiency and the degree of conservatism when incorporating fairness. We obtain tractable formulations, leveraging the results we provide on the properties of highly unfair allocations. We demonstrate the usability of our approach on project selection and shelter allocation applications.

Going beyond carbon: Influence of structural parameters on the environmental impacts of typical building structures

The construction sector has a large impact on the environment, be it climate change, biodiversity loss or resources depletion. Part of those impacts comes from construction materials, and more specifically, concrete and steel building structures. Early-stage design tools including environmental damage assessment are therefore required to achieve sustainable construction practices. This article presents a parametric approach aiming at studying the influence of early-stage structural parameters on the environmental impacts of a structure. The developed methodology combines parametric structural design with a multicriteria cradle-to-grave Life Cycle Assessment, applied to typical housing structures such as grid based beam column structures with a central core for lateral stability. Results show that span, number of levels and materials greatly influence the environmental impacts of considered structures. Climate change scores per floor area range from 80 kgCO2/m2 for short span timber structure to 215 kgCO2/m2 for long span steel buildings with few levels. Beams and slabs have the largest contribution in such impacts. Changing the production processes of materials is a way to reduce greenhouse gas emissions. However, decarbonizing steel production processes or reducing the cement content of concrete participate in burdenshifting with increased scores in several impact categories, such as carcinogenic toxicity or ozone depletion.

Advantages of general parametric solution Approach in dynamics courses

Problems of dynamics are treated using a general parametric solution approach. The advantages of treating problems in the parametric way is discussed. The approach has many advantages over the numerical calculations starting from the beginning: 1) Solutions are expressed in the general form suitable for algorithmic programming 2) Unit check on the correctness of the results are easier 3) Effect of each input parameter on the desired output parameter can be easily observed 4) Results can be evaluated for the limiting cases to recognize the soundness of the solutions. 5) Mathematical principles can be more exploited on the solutions 6) Solutions give more insight on the design principles. The ideas are outlined using three sample problems. The advantages of the approach have been tested on Mechanical Engineering Sophomore students for over 16 years with success.

Revisiting the effect of lens mass models in cosmological applications of strong gravitational lensing

Abstract Strong gravitational lens system catalogues are typically used to constrain a combination of cosmological and empirical power-law lens mass model parameters, often introducing additional empirical parameters and constraints from high resolution imagery. We investigate these lens models using Bayesian methods through a novel alternative that treats spatial curvature via the non-FLRW timescape cosmology. We apply Markov Chain Monte Carlo methods using the catalogue of 161 lens systems of Chen et al. (2019) in order to constrain both lens and cosmological parameters for: (i) the standard ΛCDM model with zero spatial curvature; and (ii) the timescape model. We then generate large mock data sets to further investigate the choice of cosmology on fitting simple power-law lens models. In agreement with previous results, we find that in combination with single isothermal sphere parameters, models with zero FLRW spatial curvature fit better as the free parameter approaches an unphysical empty universe, ΩM0 → 0. By contrast, the timescape cosmology is found to prefer parameter values in which its cosmological parameter, the present void fraction, is driven to fv0 → 0.73 and closely matches values that best fit independent cosmological data sets: supernovae Ia distances and the cosmic microwave background. This conclusion holds for a large range of seed values fv0 ∈ {0.1, 0.9}, and for timescape fits to both timescape and FLRW mocks. Regardless of cosmology, unphysical estimates of the distance ratios given from power-law lens models result in poor goodness of fit. With larger datasets soon available, separation of cosmology and lens models must be addressed.

Analysis of Biomechanical Gait Parameters in Patients after Total Hip Replacement in the Early Recovery Period

INTRODUCTION. The widespread use of total hip arthroplasty (THA) places high demands on the restoration of a normal gait pattern and is one of the key goals of rehabilitation. AIM. Determination of key parameters of walking in patients after THA to assess the effectiveness of restoration of the physiological gait pattern. MATERIALS AND METHODS. In a control prospective study, the main group consisted of 23 patients (11 men, 12 women, aged from 41 to 75 years, mean age 63.9 ± 9.4 years), who in the first 8 weeks after planned THA, moved with the help of assistive devices. supports (two crutches or walkers) who underwent stage II of medical rehabilitation; control group — 27 healthy people (12 men and 15 women, aged from 42 to 73 years, average age 60.9 ± 9.9 years). Spatiotemporal and kinematic gait parameters were recorded before and after the rehabilitation course using a gait simulator with biofeedback equipped with three sensors. For each leg, spatiotemporal and kinematic biomechanical parameters were separately recorded. RESULTS. All spatiotemporal gait parameters on both limbs and pelvic mobility in the sagittal plane in patients in the early recovery period after THA before the start of the rehabilitation course are significantly different from healthy people. After a course of rehabilitation, the studied gait parameters approach physiological values. The main asymmetry is observed in the single support phase from 16 % at the beginning of the course, to 10 % at the end; sagittal pelvic mobility are 2 times higher than the physiological normal meaning at the beginning of the course, without significant changes in dynamics. DISCUSSION. Disturbances in the gait pattern are observed in the majority of patients undergoing THA. Step symmetry is one of the significant parameters of walking, according to which the primary global assessment of its quality is carried out. Asymmetry of the single support phase of the limbs is a natural development of compensatory motor reactions after endoprosthetics. CONCLUSION. The gait parameters “step frequency” and “step cycle” quickly change after a course of rehabilitation and can be used to assess the locomotor activity of patients during short courses of medical rehabilitation in the early recovery period. Indicators of stance and swing phases, their symmetry changes much more slowly, can serve as criteria for assessing the effectiveness of measures taken at the stages of rehabilitation in the dynamics of gait restoration.

Quantified asymptotic analysis for the relativistic quantum mechanical system with electromagnetic fields

We study the asymptotic analysis of a relativistic quantum mechanical system interacting with self-consistent electromagnetic fields, with a specific focus on the Maxwell–Klein–Gordon (MKG) system. Firstly, we show that the MKG system is globally well-posed under the Coulomb gauge condition, even in the presence of self-interacting potential. Furthermore, to derive the asymptotic analysis, we consider the non-relativistic and semi-classical regime simultaneously, introducing a single scaling parameter that serves to parameterize both the speed of light and the Planck constant. As the scaling parameter approaches zero, we obtain rigorous and quantified estimates on the asymptotic convergence of the electrostatic MKG system toward the classical Euler–Poisson system. Our analytical framework relies on the modulated energy estimate.

First Joint MUSE, Hubble Space Telescope, and JWST Spectrophotometric Analysis of the Intracluster Light: The Case of the Relaxed Cluster RX J2129.7+0005

We present the most detailed spectrum of intracluster light (ICL) in an individual cluster to date, the relaxed system RX J2129.7+0005, at z ∼ 0.234. Using 15 broadband, deep images observed with the Hubble Space Telescope and JWST in the optical and the infrared, plus deep integral field spectroscopy from MUSE, we computed a total of 3696 ICL maps spanning the spectral range ∼0.4−5 μm with our algorithm CICLE, a method that is extremely well suited to analyzing large samples of data in a fully automated way. We used both parametric and nonparametric approaches to fit the spectral energy distribution of the ICL and infer its physical properties, yielding a stellar mass log10(M*/M⊙) between 11.5 and 12.7 and an average age between 9.7 and 10.5 Gyr, from CIGALE and Prospector results. This implies that the ICL in RX J2129.7+0005 is, on average, older than that of disturbed clusters, suggesting that the contribution from different stellar populations to the ICL is at play depending on the cluster’s dynamical state. Coupled with X-ray observations of the hot gas distribution, we confirm the relaxed state of RX J2129.7+0005, showing clear signs of sloshing after a last major merger with a high-mass-ratio satellite that could have happened ∼6.6 Gyr ago in a relatively radial orbit. The presence of substructure in the ICL, such as shells, clouds with different densities and a certain degree of boxyness, and a clump, supports this scenario.

A compromise solution approach for efficiency measurement with shared input: The case of tourist hotels in Taiwan

Shared input occurs often when a production system performs two or more functions and some of the functions share the same input. To determine the proportion of the shared input devoted to each function, the conventional data envelopment analysis (DEA) models that allow each decision making unit (DMU) to select the most favorable value to attain the highest efficiency score is usually used. The result is that many DMUs assign proportions of different bound values to the same function, which is not reasonable. This paper proposes a compromise solution approach that aggregates the viewpoints of all DMUs to obtain a consensus regarding the proportion of the shared input used by each function. The approach is actually a parametric DEA approach for constructing the production function. To increase the explanation power, transcendental functions are considered. The tourist hotel, where the accommodation and catering functions share the input of management employees is used for illustration. The results show that a transcendental function has stronger explanation power, and reasonable compromised values for the proportions of the effort of the management employees devoted to the two functions are obtained.

Integrating Hybrid Priors for Face Photo-Sketch Synthesis

Benefiting from the advancement of deep learning techniques, face photo-sketch synthesis has witnessed significant progress in recent years. Cutting-edge methods typically treat this task as an image-to-image translation problem and train a conditional generative model to learn the mapping between two domains. However, purely parametric deep learning models often struggle to capture instance-level details due to limited training samples and tend to focus on domain-level mapping. Moreover, sketch-to-photo synthesis is more challenging than photo-to-sketch synthesis and holds greater significance in the realm of public security, but it has not been well-studied in existing methods. To address these challenges, we introduce an innovative framework that synergistically integrates parametric and non-parametric approaches, infusing facial generative priors and instance-level prior knowledge from the target domain to enrich texture detail synthesis. Specifically, our framework employs a semantic-aware network to facilitate coarse cross-domain reconstruction, thereby capturing domain-level information. Moreover, through efficient neural patch matching between the input image and multiple reference (training) samples, we can harness instance-level prior knowledge as a detailed texture representation to enhance detail fidelity. For the sketch-to-photo synthesis task, we further propose a local patch correspondence mechanism that improves the rationality of matching through local constraint. To further enhance the generation of realistic and detailed facial features, we incorporate a pre-trained StyleGAN as the decoder, leveraging its extensive facial generative priors. Additionally, we introduce the relaxed Earth Movers Distance (rEMD) loss to improve the style consistency between the generated results and the target domain. Extensive experiments show that our method achieves state-of-the-art performance on both quantitative and qualitative evaluations.

An investigation of the rheological parameters of slurry composed of ordinary Portland cement, Portland pozzolana cement and Portland slag cement

ABSTRACT This paper compares the rheological parameters of ordinary Portland cement of grade 43 (OPC 43), ordinary Portland cement of grade 53 (OPC 53), Portland pozzolana cement (PPC) and Portland Slag Cement (PSC) to study the thixotropic built. Five slurries with increasing water/cement (w/c) ratios from 0.52 to 0.6 were prepared and examined at resting times of 1 minute, 5 minutes and 10 minutes. Static shear stress (τs), dynamic shear stress (τd) and thixotropic index (β) were studied to analyze the thixotropic built of the slurries. The rheological parameters increase for all the mixes with decreasing w/c ratios and increasing resting times. However, for a w/c ratio greater than 0.60, all the mixes lose their plastic viscosity and the rheological parameters approach non-significant values. The τs and τd values for PPC and PSC pastes are higher than those of the OPC pastes because of the increase in cement fineness and increased rate of structuration and hydration. OPC 53 paste shows high β because of the large extent of reversible thixotropic built. The τs values obtained from the viscometrical tests were then compared the mini slump test values. Results show that the rheological parameters are more consistent than the flow values of the mini slump cone test.

Piezo-viscous micropolar fluid flow between two parallel annular disks

A theoretical analysis of the piezo-viscous dependence of micropolar fluid flow between parallel annular disks has been conducted. It is assumed that viscosity changes exponentially with pressure. Pressure is analytically approximated using a small perturbation method with the viscosity coefficient as the perturbation parameter. Squeeze film time, pressure, and load carrying capacity are calculated and graphically demonstrated across various viscosity–pressure characteristics. The study examines how an increase in cross-viscosity correlates with notable growth in pressure, response time, and bearing load. According to the results, micropolar fluid offers an increase in the load-bearing capacity and therefore lengthens the response time to prevent the contact of parallel annular disks. These observations are useful for bearings, seals, and lubrication systems, where controlling viscosity and pressure is crucial for smooth operation and productivity. As the limiting case of micro-polar fluid when the coupling number tends to zero or the couple stress parameter approaches infinity, without the annular ring, the present derivation agrees well with the Newtonian viscous case of parallel planar squeezing disks described by Bird et al. [Transport Phenomena (John Wiley & Sons, 2006)].

Optimization of ray-tracing simulations to confirm performance of the GP-SANS instrument at the High-Flux Isotope Reactor

The CG-2 beamline at the High Flux Isotope Reactor (HFIR) exhibits a notable discrepancy between observed count rates and the count rates we would expect based on a Monte-Carlo neutron ray-trace simulation. These simulations consistently predict count rates approximately five times greater than those observed in four separate experimental runs involving different instrument configurations. This discrepancy suggests that certain factors are causing losses in measurements that are not adequately accounted for in the simulation, in particular guide reflectivity or misalignment.To investigate these discrepancies, a high-dimensional simulation parameter approach is applied in order to understand the losses. Region of Interest (ROI) groups along the instrument are assigned to different surfaces of the guide components within the simulation. This allows the parameters of those guide components to be varied as a group to minimize the complexity of the search space. The result is an optimization of simulation parameters using an iterative scheme that aims to minimize the difference between experimentally measured count rates and simulated count rates across all tested collimator combinations.This proposed methodology holds the potential to reveal previously unrecognized sources of intensity loss in the CG-2 beamline at HFIR and improve the accuracy of simulations, leading to enhanced understanding and performance of the beamline for various scientific applications.

Data quality in laboratory convergent-beam X-ray total scattering

Measurement of laboratory atomic pair distribution function data has improved with contemporary X-ray sources, optics and detectors, with acquisition times of the order of minutes for ideal samples. This paper examines resolution effects in pair distribution function data obtained using a convergent-beam configuration and an Ag X-ray tube from standard silicon powder and from 10 nm BaTiO3 nanocubes. The elliptical multilayer X-ray mirror reflects a non-trivial X-ray spectrum and introduces resolution effects not commonly treated in ordinary parafocusing divergent-beam laboratory diffraction. These resolution effects are modeled using the fundamental parameters approach, and the influence this has on interpretation and modeling of the resulting reduced atomic pair distribution function data is demonstrated.

Weak dangling block reordering and multi-step block compression for efficiently computing and updating PageRank solutions

The PageRank model is a powerful tool for network analysis, utilized across various disciplines such as web information retrieval, bioinformatics, community detection, and graph neural network. Computing this model requires solving a large-dimensional linear system or eigenvector problem due to the ever-increasing scale of networks. Conventional preconditioners and iterative methods for general linear systems or eigenvector problems often exhibit unsatisfactory performance for such problems, particularly as the damping factor parameter approaches 1, necessitating the development of specialized methods that exploit the specific properties of the PageRank coefficient matrix. Additionally, in practical applications, the optimal settings of the hyperparameters are generally unknown in advance, and networks often evolve over time. Consequently, recomputation of the problem is necessary following minor modifications. In this scenario, highly efficient preconditioners that significantly accelerate the iterative solution at a low memory cost are desirable. In this paper, we present two techniques that leverage the sparsity structures and numerical properties of the PageRank system, as well as a preconditioner based on the computed matrix structure. Experiments demonstrate the positive performance of the proposed methods on realistic PageRank computations.

Numerical Simulation and Artificial Neural Network Modeling of Cavitation on 2D Tandem Hydrofoils Arrangement

Abstract In the current research, we used a parametric approach to investigate cavitation with tandem-arranged Clark Y-11.7% hydrofoils. We simulated the tandem-arranged hydrofoil system using ANSYS FLUENT with the Zwart cavitation model combined with the Transition SST turbulence model. To substantiate the accuracy and reliability of the numerical model, computations were performed for an individual Clark Y-11.7% hydrofoil and compared to experimental results. The following parameters were studied in tandem arrangement: cavitation number(σ), horizontal direction spacing ratio between two hydrofoils(x), vertical direction spacing ratio between two hydrofoils(y), angle of attack (AOA) of the upstream hydrofoil (α 1), and angle of the downstream hydrofoil relative to the upstream hydrofoil (α 2). The lift coefficient (C L) was used to estimate due to the acceptable error. An optimal artificial neural network (ANN) model was trained based on the five-parameter combination from numerical simulations. The model’s weights and biases were presented, providing a prediction method for hydrofoils in tandem arrangement with cavitation. A global sensitivity analysis based on the trained model is implemented, which reveals the AOA of the downstream hydrofoil (α 2), the horizontal spacing ratio (x), and the AOA of the upstream hydrofoil (α 1) have a main effect on the performance of the tandem arrangement.