Fitting Function Research Articles

Mploying Virial Coefficients for Optimal Solutions in Variational Calculations

In this study, virial coefficients for one and two-electron hydrogen and helium-like quantum dot structures confined in an infinite potential well were calculated. The virial coefficients were determined based on the dot radius using the Quantum Genetic Algorithm (QGA) method. Calculations were performed using Fernandez's expression; however, due to calculation errors in confined systems, this equivalent expression was found unsuitable as a direct stopping criterion. Instead, virial coefficients were calculated using the ⟨T⟩/⟨V⟩ relationship, and the results were plotted. The fitting function obtained for the virial coefficients is proposed as an effective cutoff criterion for electronic structure calculations of quantum dot systems.

An Investigation on the Thermal Degradation Kinetics of Wood-Polymer Composites Used in Interior Automobile Panels via Non-Isothermal Thermogravimetry

Wood plastic composites (WPCs) offer a promising alternative for various automotive components, combining the benefits of wood and polymers such as lightness, strength, and sustainability. However, determining decomposition kinetics is challenging due to the intricate composition of WPCs. Therefore, this research work focused to analyze the relationship between the thermal degradation of WPCs, the degradation atmosphere, and the kinetics. The kinetic parameters were evaluated by Coats and Redfern method based on a set of TGA experiments under variable atmospheres (inert and oxidative) using 10 ℃/min heating rate. Thermograms demonstrated significant differences in the thermal properties of WPC when subjected to oxidative and inert atmospheres, despite two conditions having the same number of thermal degradation zones. It has been suggested that the process of thermal decomposition of WPC contains three weight loss segments under inert and oxidative atmosphere according to the Gaussian multi-peak fitting function. The Coats-Redfern method showed multi-step chemical kinetics and more accurately characterizes the decomposition behavior of WPC, attributing to its multi-compositional properties. Proposed reaction schemes had regression coefficients higher than 0.9809 to obtain reaction order, activation energy and pre-exponential factor.

Optimal knots for smoothing splines and adaptive smoothing splines in generalized linear models: Design approach

Smoothing splines play a crucial role as a prevalent tool for estimating unknown functions in non parametric regression. In fitting functions with varying roughness, adaptive smoothing splines provide the flexibility to adjust the smoothing parameter adaptively with the changes over the predictor variable within specific intervals, facilitating accommodation for changing roughness. Despite its intuitive appeal and high flexibility, the implementation of this estimator poses challenges, especially in the absence of specified knot numbers, knot locations, and certain simplifying assumptions on the smoothing parameter. D-optimal designs are considered to specify the knot locations in this models. The prior information from data as the prior curvature knowledge can be useful for this optimization problem. For this purpose, the smoothing parameter in this optimization problem can be considered as a function based on the prior curvature. We apply this method to responses from the exponential family of distributions. The mathematical expression of the estimator of the curve in a generalized linear mixed model enables us to derive an information matrix. The derived information matrix and hence the optimum design will depend on the values of the model’s unknown parameters. In such situations, numerical techniques should be considered for evaluating and optimizing this criterion.

Multicomponent training: the effect of a strenght training program on physical and functional fitness in older women

Ageing is a natural, irreversible and progressive phenomenon. It is strongly associated with decreased physical abilities and motor skills, thus facilitating the appearance of degenerative diseases, being aggravated by factors such as a sedentary lifestyle. Multicomponent training applied in to the Third Age, namely, physically active elderly women, could constitute a valid mechanism in the development of anthropometric parameters and motor abilities. The objective of the present study was to evaluate the effect of a multicomponent training program on the anthropometric parameters and physical and functional fitness in elderly women. The study was conducted with fifteen volunteer elderly women, ages sixty-five and ninety-four, who performed daily living activities independently and autonomously. We used the Functional Physical Fitness Protocol Test Battery developed by Rikli & Jones (1999) (Pre and post-test). For the statistical data analysis, we used SPSS software version 25.0, for Windows. For comparison, between the study groups, at the two moments of evaluation, we used the t-test for paired samples. For the association between the variables under study, at the second moment of evaluation, we used Spearman's correlation coefficient (r). The level of significance was set at p ≤ 0.05. We concluded that multicomponent training provided benefits in functional physical fitness and body composition of the elderly women under study. It seems fundamental to include physical exercise for the development of motor skills, in its entirety, through multicomponent training exercises, to promote performance capacity in daily life activities, as well as in tasks with a higher level of demand.

Theoretical Study of Ion Pairing in Protic Ionic Liquids of ΔpKa range 6 to 18

Studies on “poor” protic ionic liquids, having proton-transfer strength ΔpKa = 0-6, have shown the need to make corrections to the Fuoss equation for prediction of ΔGioniz and Kioniz for ion-pairing equilibria in these systems. Recent work built empirical functions to replace the Fuoss equation for this ΔpKa region, based on ab initio ion-pairing energies, but the functions did not perform well at the higher end of this range. Here, we extend the study to the range ΔpKa = 6-18, examining hypothetical mixtures of trimethylamine (TEA) with acids from weak (CH3COOH) to quite strong (CF3SO3H). Ab initio pairing energies were obtained for these systems, followed by refitting. Preliminary comparisons with experimental ionicities appear to show inaccuracies in the ab initio dataset, not in the fitting function form. Future work is planned to include dataset shifts, empirical or theoretical, to allow the goal of a predictive function for ionicity as a function of ΔpKa and acid:base mixing ratio.

A Preliminary Comparative Study on the Centering Algorithms for Cassini-ISS NAC Images

Obtaining high precision is an important consideration for astrometric studies using images from the Narrow Angle Camera (NAC) of the Cassini Imaging Science Subsystem (ISS). Selecting the best centering algorithm is key to enhancing astrometric accuracy. In this study, we compared the accuracy of five centering algorithms: Gaussian fitting, the modified moments method, and three point-spread function (PSF) fitting methods (effective PSF (ePSF), PSFEx, and extended PSF (xPSF) from the Cassini Imaging Central Laboratory for Operations (CICLOPS)). We assessed these algorithms using 70 ISS NAC star field images taken with CL1 and CL2 filters across different stellar magnitudes. The ePSF method consistently demonstrated the highest accuracy, achieving precision below 0.03 pixels for stars of magnitude 8–9. Compared to the previously considered best, the modified moments method, the ePSF method improved overall accuracy by about 10% and 21% in the sample and line directions, respectively. Surprisingly, the xPSF model provided by CICLOPS had lower precision than the ePSF. Conversely, the ePSF exhibits an improvement in measurement precision of 23% and 17% in the sample and line directions, respectively, over the xPSF. This discrepancy might be attributed to the xPSF focusing on photometry rather than astrometry. These findings highlight the necessity of constructing PSF models specifically tailored for astrometric purposes in NAC images and provide guidance for enhancing astrometric measurements using these ISS NAC images.

MIRD Pamphlet No. 30: MIRDfit-A Tool for Fitting of Biodistribution Time-Activity Data for Internal Dosimetry.

In nuclear medicine, estimating the number of radioactive decays that occur in a source organ per unit administered activity of a radiopharmaceutical (i.e., the time-integrated activity coefficient [TIAC]) is an essential task within the internal dosimetry workflow. TIAC estimation is commonly derived by least-squares fitting of various exponential models to organ time-activity data (radiopharmaceutical biodistribution). Rarely, however, are methods used to objectively determine the model that best characterizes the data. Additionally, the uncertainty associated with the resultant TIAC is generally not evaluated. As part of the MIRDsoft initiative, MIRDfit has been developed to offer a biodistribution fitting software solution that provides the following essential features and advantages for internal dose assessment: nuclear medicine-appropriate fit functions; objective metrics for guiding best-fit selection; TIAC uncertainty calculation; quality control and data archiving; integration with MIRDcalc software for dose calculation; and a user-friendly Excel-based interface. For demonstration and comparative validation of MIRDfit's performance, TIACs were derived from serial imaging studies involving 18F-FDG and 177Lu-DOTATATE using MIRDfit. These TIACs were then compared with TIAC estimates obtained using other software. In most cases, the TIACs agreed within approximately 10% between MIRDfit and the other software. MIRDfit has been endorsed by the MIRD Committee of the Society of Nuclear Medicine and Molecular Imaging and has been integrated into the MIRDsoft suite of free dosimetry software; it is available for download at no user cost (https://mirdsoft.org/).

Effects of a 12-week training program in outdoor gym equipment in morphological and functional parameters, quality of life, and physical activity levels in older adults.

This study aimed to investigate the effectiveness of a supervised physical training program with controlled cadence on functional fitness parameters, quality of life perception, and physical activity level in older adults. Sixty physically independent older adults were randomly divided into three groups: Supervised Training (ST, n = 20), Unsupervised Training (UT, n = 20), and a Control Group (C, n = 20). The ST and UT groups participated in a 12-week program, performing exercises three times a week for 30 min. The ST group had structured weekly sessions consisting of a 5-minute warm-up (walking at 60% of max heart rate), 20 sets of 30 s at a moderate pace controlled by a metronome with 30 s of passive recovery, and a 5-minute cool-down on non-consecutive days. The UT group trained spontaneously using senior gym equipment, including elliptical machines, rowing machines, air skiers, and leg press machines. The control group maintained their usual daily routines throughout the study. Parameters evaluated included body mass, body mass index (BMI), muscle thickness (biceps brachii, triceps brachii, and vastus lateralis), and functional capacity tests (walking 10 m [W10 m], rising from a sitting position [RSP], rising from the prone position [RVDP], sitting and rising from a chair and moving around the house [SRCW]). Quality of life was assessed across physical, psychological, environmental, and social domains, and physical activity levels were also measured. No significant changes (p > 0.05) in body mass, BMI, or muscle thickness were observed between groups before and after the intervention. However, significant time effects in functional fitness tests were found only in the ST group for W10 m (p = 0.0469), RVDP (p < 0.0004), RSP (p < 0.0001), and SRCW (p < 0.0001). Quality of life improved significantly over time in the ST and UT groups across all domains (p < 0.0001). Both ST and UT groups also showed significant increases in weekly physical activity time (p > 0.0001). 12 weeks of training improved quality of life perception and physical activity levels in older adults.

Validation of finite-element-simulated orthodontic forces produced by thermoplastic aligners: Effect of aligner geometry and creep

PurposeFinite element (FE) models for determining the orthodontic forces delivered by clear aligners often lack validation. The aim of this study was to develop and validate accurate FE models for clear aligners, considering the small but important geometrical variations from the thermoforming process and the creep behavior of the aligner material. Methods and materialsThe tooth misalignment considered was a 2.4° torque aberration (rotation about the mesial-distal axis at the level of the center of resistance) of the maxillary left central incisor. FE models were created from Micro-CT scans of a model dental arch and five nominally identical aligners with the aforementioned misfit. Fitting of the aligners onto the dental arch was simulated using Abaqus's Interference Fit function, followed by surface-to-surface frictional interaction. Stress relaxation of the aligner material was measured using double-cantilever beam bending and modeled with a Prony series. The assembled FE models were validated by comparing the predicted forces and moments delivered to the maxillary left central incisor with experimental data, obtained with a custom-built but fully calibrated apparatus. ResultsGood agreement between prediction and measurement was obtained for both the short- and long-term forces and moments. In the short-term, i.e., after 30 s, the dominant force in the labial-lingual direction had a maximum difference of 2.9% between experiment and simulation, and the dominant moment about the mesial-distal axis had a maximum difference of 8.3%. In the long-term, i.e., after 4 h, the experimental and numerical forces had a maximum difference of 8.4%. There were statistically significant differences in the forces delivered among the nominally identical aligners, which were predicted by the geometrically accurate FE models and attributed to the variations in the points of contact between the aligners and the dental arch. The decay in force applied was affected by both the viscoelastic material behavior and friction between the aligner and arch. ConclusionFor accurate prediction of the forces and moments delivered by thermoplastic aligners, FE models that can accurately capture the point contacts between the aligners and the underlying teeth are essential. Stress relaxation of the aligners could be adequately modeled using the Prony series to represent the temporal changes of their elastic modulus.

Towards robust visual understanding: A paradigm shift in computer vision from recognition to reasoning

AbstractModels that learn from data are widely and rapidly being deployed today for real‐world use, but they suffer from unforeseen failures that limit their reliability. These failures often have several causes such as distribution shift; adversarial attacks; calibration errors; scarcity of data and/or ground‐truth labels; noisy, corrupted, or partial data; and limitations of evaluation metrics. But many failures also occur because many modern AI tasks require reasoning beyond pattern matching and such reasoning abilities are difficult to formulate as data‐based input–output function fitting. The reliability problem has become increasingly important under the new paradigm of semantic “multimodal” learning. In this article, I will discuss findings from our work to provide avenues for the development of robust and reliable computer vision systems, particularly by leveraging the interactions between vision and language. This article expands upon the invited talk at AAAI 2024 and covers three thematic areas: robustness of visual recognition systems, open‐domain reliability for visual reasoning, and challenges and opportunities associated with generative models in vision.

Promoting precision health using fitness wearable and apps among breast cancer survivors: Protocols of a smart health management trial

BackgroundAnnually, approximately 1.7 million women are diagnosed with breast cancer worldwide. Engaging in regular physical activity (PA) post-diagnosis brings significant health benefits, enhancing breast cancer survivors' (BCS) prognosis and overall health-related quality of life (HRQoL). Despite these benefits, a low percentage of Chinese BCS adhere to the recommended moderate-to-vigorous PA levels. This highlights the need for innovative PA interventions tailored for BCS management. eHealth technology, such as fitness wearables and apps, presents an opportunity to improve BCS healthcare by offering personalized exercise programs. MethodsThis study focuses on developing a precision eHealth PA program for 200 Chinese BCS in Guangdong Province, using a custom micro-application and a smart band for a 12-month trial. All participants will receive a Huawei Smart Band and be divided into 1) a personalized intervention group, receiving daily PA tracking and feedback, and 2) a control group receiving standard care. The primary outcome is PA and secondary outcomes include biomarkers, weight and body composition, functional fitness, HRQoL, and individual beliefs. Outcomes will be assessed at baseline, 6 months, and 12 months (endpoint). Successful outcomes could revolutionize PA programs for Chinese BCS, providing a model for future eHealth interventions.

An effective drift-diffusion model for pandemic propagation and uncertainty prediction

Predicting pandemic evolution involves complex modeling challenges, typically involving detailed discrete mathematics executed on large volumes of epidemiological data. Making them physics based provides added intuition as well as predictive value. Differential equations have the advantage of offering smooth, well-behaved solutions that try to capture overall predictive trends and averages. In this paper, the canonical susceptible-infected-recovered model is simplified, in the process generating quasi-analytical solutions and fitting functions that agree well with the numerics, as well as infection data across multiple countries. The equations provide an elegant way to visualize the evolution of the pandemic spread, by drawing equivalents with the similar dynamics of a particle, whose location over time represents the growing fraction of the population that is infected. This particle slides down a potential whose shape is set by model epidemiological parameters such as reproduction rate. Potential sources of errors and their growth over time are identified, and the uncertainties are mapped into a diffusive jitter that tends to push the particle away from its minimum. The combined physical understanding and analytical expressions offered by such an intuitive drift-diffusion model sets the foundation for their eventual extension to a multi-patch model while offering practical error bounds and could thus be useful in making policy decisions going forward.

Simulation and experimental study of tool passivation based on magnetic elastic abrasive particles

The presence of micro-cracks and serrations on the tool often leads to its premature failure. However, these microscopic defects can be mitigated through passivation treatment of the tool. Magnetoelastic abrasive particles are new composite particles formed by using abrasive phase particles, magnetic media phase particles and polymer matrix according to a certain ratio, the abrasive particles have both viscoelasticity and magnetic conductivity. The introduction of magnetoelastic abrasive grains into the dual-disk tool passivation equipment can effectively improve the surface quality of the tool and increase the passivation efficiency. At the outset, a model for tool passivation was crafted employing the ABAQUS simulation software. This model aimed to evaluate the effects of diverse passivation variables on the stress levels, the shape of the impact, and the depth of the impact experienced by the tool. Subsequently, by applying statistical theory combined with fitting function techniques, a mathematical model was constructed to determine the passivation volume of the tool subjected to multiple magnetic elastic abrasive particles. This model was then used to examine the impact count and passivation volume associated with each passivation factor. Finally, a tool passivation experiment was conducted using a dual-disk magnetic tool passivation device. The results showed that the smaller the impact velocity of magnetic elastic abrasive particles, the stress and impact depth of the cutting tool are decreasing, and the deformation of the cutting edge is caused by compressive stress. The error of impact depth calculated by simulation and mathematical model is within 20 %, which proves that the mathematical model can better calculate the impact depth of magnetic elastic abrasive particles on the cutting edge of the tool.

Effect of Differentiated Approach to Physical Activity Dosing on Mental Performance of Adolescents

Introduction. The article deals with an innovative approach to the dosing of physical activity taking into account the functional capabilities of adolescents and its impact on the mental performance of students. The aim of the study is to identify the impact of physical activity associated with the manifestation of general endurance on the mental performance of middle school students under different conditions of its dosing. Methodology. The study compares the effect of the load on general endurance without taking into account the physical capabilities of the organism of schoolchildren of grades 5–8 and in accordance with their functional fitness on the indicators of various properties of attention, semantic memory, and logical thinking. Results. The obtained data reflect the percentage ratio of adolescents with improvement, deterioration of mental performance indicators, as well as those in whom no changes were revealed taking into account individual intellectual development. It was revealed that after the differentiated approach, in contrast to the undifferentiated one, the majority of adolescents improved the indicators of attention span, the rate of intellectual tasks performance in the absence of mental efficiency exhaustion, also the number of memorized pairs of words increased, the number of errors in establishing semantic relations in judgments decreased. Conclusion. Differentiated approach to dosing of physical load in comparison with undifferentiated more often promotes improvement of stability and volume of attention, semantic memory and logical thinking of adolescents.

Dimuons from neutrino-nucleus collisions in the semi-inclusive DIS approach

We present a next-to-leading order perturbative QCD calculation of dimuon production in neutrino-nucleus collisions. This process is typically calculated by assuming it to be proportional to inclusive charm production, which requires an effective acceptance correction to take the experimental cuts on the decay-muon kinematics into account. Here, we instead compute the dimuon production cross section directly as a convolution of semi-inclusive deep inelastic scattering to produce charmed hadrons, and a decay function fitted to e+e− data to produce a muon from the charmed hadrons. The presented approach is in a good agreement with available experimental data and will serve as a starting point for higher-order QCD calculations without an external acceptance correction. The uncertainties arising from the decay function and scale dependence are sizeably smaller than those from the nuclear parton distribution functions. We also calculate the effective acceptances within our approach and compare them to those usually used in global fits of parton distribution functions, finding differences of the order of 10 %, depending on the kinematics, perturbative order, and applied parton distributions.

Functional fitness and physical independence in later years: cut-off values and validation

BackgroundTo establish and validate the criterion-referenced standards of functional fitness in predicting physical independence in 80 + years.MethodsA group of 2,749 older community dwellers (60–84 years) were recruited, and 2,050 were identified with moderate-to-high independent living ability according to the proposed minimum composite physical function score. The Senior Fitness Test battery was applied to measure functional fitness at five-year intervals. The declining rate for each fitness dimension was calculated based on the differences between any two adjacent age groups and was adjusted according to the reported degradation rate differences between the cross-sectional and longitudinal studies.ResultsThe age-and-sex-specific criterion-referenced standards were identified for muscle strength, cardiovascular endurance, and dynamic balance that older adults should possess at 60–79 to maintain independent living abilities. Moderate to high consistency (k = 0.622–0.650) and associations (φ = 0.641–0.694) were found between the predicted physical independence by criterion-referenced standards of functional fitness and the results from the composite physical function scale. Moreover, the predicted independent living abilities in later years from the criterion-referenced standards of functional fitness showed high test-retest reliability (Pa = 0.90–0.96).ConclusionThe criterion-referenced standards for functional fitness are valid and reliable to predict independent living abilities in later years, and provide the threshold to identify the limitations in physical fitness and detect the risks of functional disabilities among older adults in an early stage.

Comparison of curvilinear coordinates within vibrational structure calculations based on automatically generated potential energy surfaces.

For floppy molecules showing internal rotations and/or large amplitude motions, curvilinear internal coordinates are known to be superior to rectilinear normal coordinates within vibrational structure calculations. Due to the myriad definitions of internal coordinates, automated and efficient potential energy surface generators necessitate a high degree of flexibility, supporting the properties arising from these coordinates. Within this work, an approach to deal with these challenges is presented, including key elements, such as the selection of appropriate fit functions, the exploitation of symmetry, the positioning of grid points, or elongation limits for different coordinates. These elements are tested for five definitions of curvilinear coordinates, with three of them being generated in an automated manner. Calculations for semi-rigid molecules, namely H2O, H2CO, CH2F2, and H2CNH, demonstrate the general functionality of the implemented algorithms. Additional calculations for the HOPO molecule highlight the benefits of these curvilinear coordinates for systems with large amplitude motions. This new implementation allowed us to compare the performance of these different coordinate systems with respect to the convergence of the underlying expansion of the potential energy surface and subsequent vibrational configuration interaction calculations.

Construction and Application of Dynamic Threshold Model for Agricultural Drought Grades Based on Near-Infrared and Short-Wave Infrared Bands for Spring Maize

Maize (Zea mays L.) is one of the most important grain crops in the world. Drought caused by climate change in recent years may greatly threaten water supply and crop production, even if the drought only lasts for a few days or weeks. Therefore, effective daily drought monitoring for maize is crucial for ensuring food security. A pivotal challenge in current related research may be the selection of data collection and the methodologies in the construction of these indices. Therefore, orthorectified reflectance in the short-wave infrared (SWIR) band, which is highly sensitive to variations in vegetation water content, was daily obtained from the MODIS MCD43A4 product. Normalized Difference Water Index (NDWI) calculated using the NIR and SWIR bands and days after planting (DAP) were normalized to obtain the Vegetation Water Index (VWI) and normalized days after planting (NDAP), respectively. The daily dynamic threshold model for different agricultural drought grades was constructed based on the VWI and NDAP with double-logistic fitting functions during the maize growing season, and its specific threshold was determined with historical drought records. Verification results indicated that the VWI had a good effect on the daily agricultural drought monitoring of spring maize in the “Golden Maize Belt” in northeast China. Drought grades produced by the VWI were completely consistent with historical records for 84.6% of the validation records, and 96.2% of the validation records differed by only one grade level or less. The VWI can not only daily identify the occurrence and development process of drought, but also well reflect the impact of drought on the yield of maize. Moreover, the VWI could be used to monitor the spatial evolution of drought processes at both regional and precise pixel scales. These results contribute to providing theoretical guidance for the daily dynamic monitoring and evaluation of spring maize drought in the “Golden Maize Belt” of China.

Web apps for profile fitting and power balance analysis at Wendelstein 7-X.

Two novel web apps for W7-X are introduced: Profile Cooker and Power House. They are designed to streamline the workflow of profile fitting and power balance analysis while offering a graphical user interface that works in any common browser. This allows us to compile a comprehensive database of experimental power balance results. All fitting functions available in Profile Cooker are presented and compared on the basis of example profiles. The power balance equation assumed in Power House is established and its individual terms are discussed. The main focus of the power balance analysis is on the turbulent transport coefficients. A model for quick calculation of neutral beam power deposition based on experimental profiles is presented. Neoclassical root transition poses an issue for power balance analysis due to the uncertainty of the radial electric field. A global, neoclassical simulation with the code EUTERPE is performed for a set of experimental profiles to gain an understanding of the neoclassical root transition.

Optical Variability Properties of Southern TESS Blazars

We present a study of high-cadence, high-precision optical light curves from the TESS satellite of 67 blazars in the southern sky. We provide descriptive flux statistics, power spectral density (PSD) model parameters, and characteristic variability timescales. We find that only 15 BL Lacertae objects (BLLs) and 18 flat spectrum radio quasars (FSRQs) from the initial 26 and 41, respectively, exhibit statistically significant variability. We employ an adapted power spectral response method to test the goodness of fit for the PSD function to three power-law variant models. From our best-fitting description of the PSD, we extract the high-frequency power-spectral slopes, and if present, determine the significant bend or break in the model to identify characteristic timescales. We find no significant difference in the excess variance or rms scatter between blazar subpopulations. We identify a linear rms–flux relation in ∼69% of our sample, in which ∼20% show a strong correlation. We find that both subpopulations of blazars show power spectral slopes of α ∼ 2 in which a broken power-law best fits five BLLs and six FSRQs and a bending power-law best fits one BLL and five FSRQs. The shortest timescales of variability in each light-curve range widely from minutes to weeks. Additionally, these objects’ characteristic timescales range from ∼0.8 to 8 days, consistent with optical variability originating in the jet.