Functional Form Research Articles

Conformal symmetries in Vaidya geometry and collapse

In this paper, we perform a comprehensive analysis of conformal symmetries in the generalized Vaidya spacetime and establish several new results. First, a proper conformal Killing vector is shown to exist in the radial direction and interestingly the generalized Vaidya spacetimes with this symmetry are shown to be the subclass of those, which are embeddable in five-dimensional Euclidean space. The general form of the mass function that enables the proper and planar conformal symmetry in the [Formula: see text]–[Formula: see text] plane is also determined. This treatment also includes earlier results. We also consider the gravitational collapse of these spacetimes with proper planar conformal symmetry in the context of cosmic censorship conjecture. We obtain an interesting and novel result that censorship is always obeyed for these spacetimes, and no locally naked central singularity forms as the end state of the continual collapse.

Morris–Thorne-type wormholes with global monopole charge and the energy conditions

In this paper, we investigate Morris–Thorne-type wormholes with global monopole charge using various shape function forms known in the literature. We solve the Einstein field equations incorporating an anisotropic energy–momentum tensor and obtain different physical quantities associated with the matter-content. A crucial aspect of this study is the non-exotic matter distribution, examined through the evaluation of energy conditions, and exploring how different shape functions impact these conditions. Additionally, the anisotropy parameter is calculated to quantify the extent of attractive or repulsive behavior. Our study demonstrates that for different types of shape function forms, the energy conditions are influenced by the global monopole parameter. Our findings provide valuable insights for further theoretical explorations of these fascinating hypothetical structures in the realm of general relativity and beyond.

Using JADES NIRCam photometry to investigate the dependence of stellar mass inferences on the IMF in the early universe

The detection of numerous and relatively bright galaxies at redshifts z > 9 has prompted new investigations into the star-forming properties of high-redshift galaxies. Using local forms of the initial mass function (IMF) to estimate stellar masses of these galaxies from their light output leads to galaxy masses that are at the limit allowed for the state of the Lambda Cold Dark Matter (ΛCDM) Universe at their redshift. We explore how varying the IMF assumed in studies of galaxies in the early universe changes the inferred values for the stellar masses of these galaxies. We infer galaxy properties with the spectral energy distribution (SED) fitting code Prospector using varying IMF parameterizations for a sample of 102 galaxies with photometry from the James Webb Space Telescope, JWST Advanced Deep Extragalactic Survey that are spectroscopically confirmed to be at [Formula: see text], with additional photometry from the JWST Extragalactic Medium Band Survey for twenty-one of the galaxies. We demonstrate that models with stellar masses reduced by a factor of three or more do not affect the modeled SED.

Differentiating the Structural and Functional Instability of the Craniocervical Junction.

This paper presents the anatomical and biomechanical aspects of chronic instability of the craniocervical junction (CCJ) with a discussion on clinical diagnostics based on mobility tests and provocative tests related to ligamentous system injuries, as well as radiological criteria for CCJ instability. In addition to the structural instability of the CCJ, the hypothesis of its functional form resulting from cervical proprioceptive system (CPS) damage is discussed. Clinical and neurophysiological studies have shown that functional disorders or organic changes in the CPS cause symptoms similar to those of vestibular system diseases: dizziness, nystagmus, and balance disorders. The underlying cause of the functional form of CCJ instability may be the increased activity of mechanoreceptors, leading to "informational noise" which causes vestibular system disorientation. Due to the disharmony of mutual stimulation and the inhibition of impulses between the centers controlling eye movements, the cerebellum, spinal motoneurons, and the vestibular system, inadequate vestibulospinal and vestibulo-ocular reactions occur, manifesting as postural instability, dizziness, and nystagmus. The hyperactivity of craniocervical mechanoreceptors also leads to disturbances in the reflex regulation of postural muscle tone, manifesting as "general instability". Understanding this form of CCJ instability as a distinct clinical entity is important both diagnostically and therapeutically as it requires different management strategies compared to true instability. Chronic CCJ instability significantly impacts the quality of life (QOL) of affected patients, contributing to chronic pain, psychological distress, and functional impairments. Addressing both structural and functional instability is essential for improving patient outcomes and enhancing their overall QOL.

Domain growth kinetics in active binary mixtures.

We study motility-induced phase separation in symmetric and asymmetric active binary mixtures. We start with the coarse-grained run-and-tumble bacterial model that provides evolution equations for the density fields ρi(r⃗,t). Next, we study the phase separation dynamics by solving the evolution equations using the Euler discretization technique. We characterize the morphology of domains by calculating the equal-time correlation function C(r, t) and the structure factor S(k, t), both of which show dynamical scaling. The form of the scaling functions depends on the mixture composition and the relative activity of the species, Δ. For k → ∞, S(k, t) follows Porod's law: S(k, t) ∼ k-(d+1) and the average domain size L(t) shows a diffusive growth as L(t) ∼ t1/3 for all mixtures.

Joint modeling of zero-inflated longitudinal measurements and time-to-event outcomes with applications to dynamic prediction.

In this article, we present a joint modeling approach for zero-inflated longitudinal count measurements and time-to-event outcomes. For the longitudinal sub-model, a mixed effects Hurdle model is utilized, incorporating various distributional assumptions such as zero-inflated Poisson, zero-inflated negative binomial, or zero-inflated generalized Poisson. For the time-to-event sub-model, a Cox proportional hazard model is applied. For the functional form linking the longitudinal outcome history to the hazard of the event, a linear combination is used. This combination is derived from the current values of the linear predictors of Hurdle mixed effects. Some other forms are also considered, including a linear combination of the current slopes of the linear predictors of Hurdle mixed effects as well as the shared random effects. A Markov chain Monte Carlo method is implemented for Bayesian parameter estimation. Dynamic prediction using joint modeling is highly valuable in personalized medicine, as discussed here for joint modeling of zero-inflated longitudinal count measurements and time-to-event outcomes. We assess and demonstrate the effectiveness of the proposed joint models through extensive simulation studies, with a specific emphasis on parameter estimation and dynamic predictions for both over-dispersed and under-dispersed data. We finally apply the joint model to longitudinal microbiome pregnancy and HIV data sets.

Predicting and analysis of urban wastewater quantity to be treated by using Neural Network and ODE model: A case study

Wastewater data, including Population of the Municipality Served by the Wastewater Treatment Plants (WWTPs), Capacity, Number of WWTPs, Amount of Daily Wastewater Discharged per Person and Wastewater Treated in WWTPs (y(t)) obtained from Turkish Statistical Institute (TUIK) for Kayseri province for 2003-2020 were mathematically modelled and analysed with Artificial Neural Network (ANN) and Differential equations. Firstly, the data were augmented through ARIMA since TUIK data numbers are insufficient to ANN training and later the data were normalized. The augmented normalized data was trained with ANN twice, thus the effect of other variables on the y(t) variable was shown and mathematical ANN activation functions in the form of a tangent hyperbolic function was proposed for this variable. Then, arbitrary parameters used for a linear system consisting of differential equations representing the five variables mentioned above were estimated using normalized original data and thus the ODE (ordinary differential equation) model was proposed. Two ANN models and ODE model were evaluated on normalized real TUIK data and the performances of these three models were compared. Among these mathematical models, the model that gave the minimum MSE (mean squared error) has been determined as the ODE model. Finally, future predictions were made for the y(t) variable with the ODE model.

Energy landscape and flow dynamics measurements of driven-dissipative systems

Many experimental techniques aim at determining the energy landscape of a system given and compare it to a model Hamiltonian. This landscape governs the system's evolution in the absence of dissipation. Here, we theoretically propose and experimentally demonstrate a method to measure the energy landscape of a system without knowing its functional form. A crucial ingredient for our method is the presence of dissipation, which enables sampling of the landscape over a large area of phase space through ringdown-type measurements, overcoming the main limitation of previous techniques. We apply the method to a driven-dissipative system–a parametric oscillator–observed in a rotating frame. We first measure the phase-space flow dynamics of the system via ringdown measurements, unveiling its attractors and separatrices. With these measurements, we reconstruct the (quasi-)energy landscape of the system. Furthermore, we demonstrate that our method provides direct experimental access to the so-called symplectic norm of the stationary states of the system, which is tied to the particle- or holelike nature of excitations of these states. In this way, we establish a method to identify qualitative differences between the fluctuations around stabilized minima and maxima of the nonlinear out-of-equilibrium stationary states. Our method constitutes a versatile approach to characterize a wide class of driven-dissipative systems. Published by the American Physical Society 2024

A stable model order reduction scheme for an acoustic finite element model with perfectly matched layers

Perfectly matched layers (PMLs) are often used in an exterior acoustic finite element model to simulate the Sommerfeld radiation condition. However, the time-domain model is often too large to efficiently handle the transient simulation due to the frequency-dependent stretching function and the number of elements needed per wavelength. Krylov subspace-based model order reduction can alleviate this problem by only matching the important moments of the original model. However, stability-preservation is not guaranteed, which is the key to perform time-domain simulation. This work proposes a stability-preserving model order reduction scheme for the time-domain PMLs. By assessing the stability conditions of time-domain PMLs, a two-step strategy is applied. Firstly, a one-sided split basis is used to preserve the form of Lyapunov function of the original model such that a stable intermediate reduced order model (ROM) results. Secondly, an unsplit basis is applied on the modal transformation of this intermediate ROM to reduce the size further. The proposed method is verified by numerical simulations.

Comparative Analysis and Optimal Selection of Calibration Functions in Pure Rotational Raman Lidar Technique

The pure rotational Raman (PRR) lidar technique relies on calibration functions (CFs) to extract temperature information from raw detection data. The choice of CF significantly impacts the accuracy of the retrieved temperature. In this study, we propose a method that combines multiple Monte Carlo simulation experiments with a statistical analysis, and we first conduct simulated comparisons of the calibration effects of different CFs while considering the impact of noise. We categorized ten common CFs into four groups based on their functional form and the number of calibration coefficients. Based on functional form, specifically, we defined 1/T = f(lnQ) as a forward calibration function (FCF) and lnQ = g(1/T) as a backward calibration function (BCF). Here, T denotes temperature, and Q denotes the signal intensity ratio. Their performance within and outside the calibration interval is compared across different integration times, smoothing methods, and reference temperature ranges. The results indicate that CFs of the same category exhibit similar calibration effects, while those of different categories exhibit notable differences. Within the calibration interval, the FCF performs better, especially with more coefficients. However, outside the calibration interval, the linear calibration function (which can be considered a two-coefficient FCF) has an obvious advantage. Conclusions based on the simulation results are validated with actual data, and the factors influencing calibration errors are discussed. Utilizing these findings to guide CF selection can enhance the accuracy and stability of PRR lidar detection.

Grain boundary solute segregation across the 5D space of crystallographic character

Solute segregation in materials with grain boundaries (GBs) has emerged as a popular method to thermodynamically stabilize nanocrystalline structures. However, the impact of varied GB crystallographic character on solute segregation has never been thoroughly examined. This work examines Co solute segregation in a dataset of 7272 Al bicrystal GBs that span the 5D space of GB crystallographic character. Considerable attention is paid to verification of the calculations in the diverse and large set of GBs. In addition, the results of this work are favorably validated against similar bicrystal and polycrystal simulations. As with other work, we show that Co atoms exhibit strong segregation to sites in Al GBs and that segregation correlates strongly with GB energy and GB excess volume. Segregation varies smoothly in the 5D crystallographic space but has a complex landscape without an obvious functional form.

How to achieve model-robust inference in stepped wedge trials with model-based methods?

A stepped wedge design is an unidirectional crossover design where clusters are randomized to distinct treatment sequences. While model-based analysis of stepped wedge designs is a standard practice to evaluate treatment effects accounting for clustering and adjusting for covariates, their properties under misspecification have not been systematically explored. In this article, we focus on model-based methods, including linear mixed models and generalized estimating equationswith an independence, simple exchangeable, or nested exchangeable working correlation structure. We study when a potentially misspecified working model can offer consistent estimation of the marginal treatment effect estimands, which are defined nonparametrically with potential outcomes and may be functions of calendar time and/or exposure time. We prove a central result that consistency for nonparametric estimands usually requires a correctly specified treatment effect structure, but generally not the remaining aspects of the working model (functional form of covariates, random effects, and error distribution), and valid inference is obtained via the sandwich variance estimator. Furthermore, an additional g-computation step is required to achieve model-robust inference under non-identity link functions or for ratio estimands. The theoretical results are illustrated via several simulation experiments and re-analysis of a completed stepped wedge cluster randomized trial.

Improving resbos for the precision needs of the LHC

The resummation calculation (esos) is a widely used tool for the simulation of single vector boson production at colliders. In this work, we develop a significant improvement over the esos code by increasing the accuracy from NNLL+NLO to N3LL+NNLO and release the esos v2.0 code. Furthermore, we propose a new nonperturbative function that includes information about the rapidity of the system (IFY). The IFY functional form was fitted to data from fixed target experiments, the Tevatron, and the LHC. We find that the nonperturbative function has mild rapidity dependence based on the results of the fit. Published by the American Physical Society 2024

Relationship between Family Support and Quality of Life in Stroke Patients

Stroke is a disease of the brain in the form of impaired local nerve function that appears suddenly, progressively, and quickly. Family support is very influential on stroke patients, because family support is very instrumental in a form of assistance provided by family members to provide physical and psychological comfort when someone experiences illness and provides social support. This article review aims to determine the relationship between family support and quality of life in stroke patients. This study used the literature review method with the Preferred Reporting Items for Systematic Reviews & Meta-Analyses (PRISMA) protocol. Scientific articles or journals were downloaded from PubMed, Garuda Portal, and Google Scholar with SINTA IV and V standards within 2020-2024. In this literature, it was found that family support is an aspect that plays an important role in the quality of life of stroke patients. Family support itself includes emotional support, appreciation support, instrumental support and information support. The family is the closest person who always interacts with post-stroke patients, so the role of the family is very important in an effort to provide various supports that create a sense of security for patients.

Comparison and Optimization of Light Use Efficiency-Based Gross Primary Productivity Models in an Agroforestry Orchard

The light-use efficiency-based gross primary productivity (LUE-GPP) model is widely utilized for simulating terrestrial ecosystem carbon exchanges owing to its perceived simplicity and reliability. Variations in cloud cover and aerosol concentrations can affect ecosystem LUE, thereby influencing the performance of the LUE-GPP model, particularly in humid regions. In this study, the performance of six big-leaf LUE-GPP models and one two-leaf LUE-GPP model were evaluated in a humid agroforestry ecosystem from 2018–2020. All big-leaf LUE-GPP models yielded GPP values consistent with that derived from the eddy covariance system (GPPEC), with R2 ranging from 0.66–0.73 and RMSE ranging from 1.81–3.04 g C m−2 d−1. Differences in model performance were attributed to the differences in the quantification of temperature (Ts) and moisture constraints (Ws) and their combination forms in the models. The Ts and Ws algorithms in the eddy covariance-light-use efficiency (EF-LUE) model well characterized the environmental constraints on LUE. Simulation accuracy under the common limitation of Ts and Ws (Ts × Ws) was higher than the maximum limitation of Ts or Ws (Min (Ts, Ws)), and the combination of the Ts algorithm in the Carnegie–Ames–Stanford Approach (CASA) and the Ws algorithm in the EF-LUE model was optimized in combination forms, thereby constraining LUE for GPP estimates (GPPBLO, R2 = 0.76). Various big-leaf LUE-GPP models overestimated or underestimated GPP on sunny or cloudy days, respectively, while the two-leaf LUE-GPP model, which considered the transmission of diffuse radiation and the difference in photosynthetic capacity of canopy leaves, performed well (R2 = 0.72, p < 0.01). Nevertheless, the underestimation/overestimation for shaded/sunlit leaves remained under different weather conditions. Then, the clearness index (Kt) was introduced to calculate the dynamic LUE in the big-leaf and two-leaf LUE-GPP models in the form of exponential or power functions, resulting in consistent performance even in different weather conditions and an overall higher simulation accuracy. This study confirmed the potential applicability of different LUE-GPP models and emphasized the importance of dynamic LUE on model performance.

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.

Predefined-time controller design for a multiple space transportation robots system based on Lp-Norm-Normalized Sign Function

This paper presents a predefined-time controller for Multiple Space transportation Robots System (MSRS), which can be applied in on-orbit assembly tasks to transport modules to pre-assembly configuration quickly. Firstly, to simplify the analysis and design of predefined-time controller, a Predefined-time Stability Criterion is proposed in the form of Composite Lyapunov Function (CLF-PSC). Besides simplicity, the CLF-PSC also has the advantage of less conservativeness due to utilization of initial state information. Secondly, a concept of Lp-Norm-Normalized Sign Function (LPNNSF) is proposed based on the CLF-PSC. Different from traditional norm-normalized sign function, the Lp-norm of LPNNSF can be selected arbitrarily according to practical control task requirements, which means that the proposed LPNNSF is more generalized and more convenient for calculation. Thirdly, a predefined-time disturbance observer and predefined-time controller are designed based on the LPNNSF. The observer has the property of predefined-time convergence to achieve quicker and more accurate estimation of the lumped disturbance. The controller has less control input and chattering phenomenon than traditional predefined-time controller. In addition, by introducing the observer into the controller, the closed-loop system enjoys high precision and strong robustness. Finally, the effectiveness of the proposed controller is verified by numerical simulations. By employing the controller, the MSRS can carry assembly modules to the desired pre-assembly configuration accurately within predefined time.

Simulating Brown Dwarf Observations for Various Mass Functions, Birthrates, and Low-mass Cutoffs

After decades of brown dwarf discovery and follow-up, we can now infer the functional form of the mass distribution within 20 pc, which serves as a constraint on star formation theory at the lowest masses. Unlike objects on the main sequence that have a clear luminosity-to-mass correlation, brown dwarfs lack a correlation between an observable parameter (luminosity, spectral type, or color) and mass. A measurement of the brown dwarf mass function must therefore be procured through proxy measurements and theoretical models. We utilize various assumed forms of the mass function, together with a variety of birthrate functions, low-mass cutoffs, and theoretical evolutionary models, to build predicted forms of the effective temperature distribution. We then determine the best fit of the observed effective temperature distribution to these predictions, which in turn reveals the most likely mass function. We find that a simple power law ( dN/dM∝M−α ) with α ≈ 0.5 is optimal. Additionally, we conclude that the low-mass cutoff for star formation is ≲0.005 M ⊙. We corroborate the findings of Burgasser, which state that the birthrate has a far lesser impact than the mass function on the form of the temperature distribution, but we note that our alternate birthrates tend to favor slightly smaller values of α than the constant birthrate. Our code for simulating these distributions is publicly available. As another use case for this code, we present findings on the width and location of the subdwarf temperature gap by simulating distributions of very old (8–10 Gyr) brown dwarfs.

A dictionary-based Bayesian approach to optimizing left-turn restriction locations in grid networks

Left-turn movements at signalized intersections pose significant safety risks for the drivers and efficiency concerns for the traffic operations in urban networks. Restricting left-turn movements at selected locations has been shown to be effective at improving operational efficiency and mitigating safety concerns. However, determining optimal locations to restrict left-turns is a complex combinatorial optimization problem that is compounded by the lack of analytical forms for the objective function and constraints, as well as potential interdependencies between the decision variables. Following the common solution paradigm for this type of optimization problems, this paper presents a novel Bayesian approach that utilizes dictionary-based embeddings and is tailored for high-dimensional combinatorial (or even mixed) spaces. Simulation studies conducted using the Aimsun software under perfect or imperfect grid networks demonstrate that the presented method can consistently find promising left-turn restriction configurations that outperform the all-or-nothing strategies (to restrict all or none left-turn movements at all intersections), as well as the population based incremental learning algorithm. In addition, the presented method often does so with less simulation cost, thus showcasing its potential for efficient solution of more general traffic optimization problems.

Absolute Zeta functions and periodicity of quantum walks on cycles

The quantum walk is a quantum counterpart of the classical random walk. On the other hand, absolute zeta functions can be considered as zeta functions over $\mathbf{F}_1$. This study presents a connection between quantum walks and absolute zeta functions. In this paper, we focus on Hadamard walks and $3$-state Grover walks on cycle graphs. The Hadamard walks and the Grover walks are typical models of the quantum walks. We consider the periods and zeta functions of such quantum walks. Moreover, we derive the explicit forms of the absolute zeta functions of corresponding zeta functions. Also, it is shown that our zeta functions of quantum walks are absolute automorphic forms.