Estimation Of Function Research Articles

Qualitative properties of solutions for dual parabolic equation involving uniformly elliptic nonlocal operator

In this research, we study certain characteristics of the solution for an equation involving uniformly elliptic nonlocal operator by establishing various maximum principles in bounded and unbounded regions. Additionally, we don't need the conditions that the narrow region principle's bound assumption and decay in the unbounded domain. In order to get the monotonicity of the solution, we use several maximum principles and averaging effects to overcome the challenges that generated by the uniformly elliptic nonlocal operator and fractional‐order variable . Of course, while investigating the qualitative characteristics of the equation, we also provide some estimates of auxiliary function. For the study of additional nonlocal operators, we believe the method of uniformly elliptic nonlocal operators will also be helpful.

The Quasar Catalogue for S-PLUS DR4 (QuCatS) and the estimation of photometric redshifts

ABSTRACT The advent of massive broad-band photometric surveys enabled photometric redshift estimates for unprecedented numbers of galaxies and quasars. These estimates can be improved using better algorithms or by obtaining complementary data such as narrow-band photometry, and broad-band photometry over an extended wavelength range. We investigate the impact of both approaches on photometric redshifts for quasars using data from Southern Photometric Local Universe Survey (S-PLUS) DR4, Galaxy Evolution Explorer (GALEX) DR6/7, and the unWISE catalog for the Wide-field Infrared Survey Explorer (WISE) in three machine learning methods: Random Forest, Flexible Conditional Density Estimation (FlexCoDE), and Bayesian Mixture Density Network (BMDN). Including narrow-band photometry improves the root-mean-square error by 11 per cent in comparison to a model trained with only broad-band photometry. Narrow-band information only provided an improvement of 3.8 per cent when GALEX and WISE colours were included. Thus, narrow bands play a more important role for objects that do not have GALEX or WISE counterparts, which respectively makes 92 per cent and 25 per cent of S-PLUS data considered here. Nevertheless, the inclusion of narrow-band information provided better estimates of the probability density functions obtained with FlexCoDE and BMDN. We publicly release a value-added catalogue of photometrically selected quasars with the photo-z predictions from all methods studied here. The catalogue provided with this work covers the S-PLUS DR4 area (∼3000 square degrees), containing 645 980, 244 912, 144 991 sources with the probability of being a quasar higher than, 80 per cent, 90 per cent, 95 per cent up to r < 21.3 and good photometry quality in the detection image. More quasar candidates can be retrieved from the S-PLUS data base by considering less restrictive selection criteria.

Efficient estimation of the reliability functions in a multicomponent stress‐strength set‐up for a generalized family of distributions under progressive type II censoring

AbstractIn this paper, we have introduced the concept of a new multicomponent reliability function Estimation procedures are developed for under progressive type II censoring scheme, which is subsequently used to develop the estimation procedures for the multicomponent stress‐strength reliability function . Herein, we consider a system having k statistically independent and identically distributed strength components, , say, which are exposed to a common random stress Y. Both strength and stress variables are independent and follow different scaled proportional hazard rate family of distributions with common scale parameter. The reliability functions and are estimated by using maximum likelihood and Bayesian methods of estimation. The performances of these estimators are studied on the basis of their mean squared errors through Monte Carlo simulation technique. Finally, the utility of the proposed estimators is examined and explained through two different real data sets.

Effects of a ketogenic diet on motor function and motor unit number estimation in aged C57BL/6 mice

ObjectivePathological, age-related loss of muscle function, commonly referred to as sarcopenia, contributes to loss of mobility, impaired independence, as well as increased risk of adverse health events. Sarcopenia has been attributed to changes in both neural and muscular integrity during aging. Current treatment options are primarily limited to exercise and dietary protein fortification, but the therapeutic impact of these approaches are often inadequate. Prior work has suggested that a ketogenic diet (KD) might improve healthspan and lifespan in aging mice. Thus, we sought to investigate the effects of a KD on neuromuscular indices of sarcopenia in aged C57BL/6 mice. DesignA randomized, controlled pre-clinical experiment consisting of longitudinal assessments performed starting at 22-months of age (baseline) as well as 2, 6 and 10 weeks after the start of a KD vs. regular chow intervention. SettingPreclinical laboratory study. Sample sizeThirty-six 22-month-old mice were randomized into 2 dietary groups: KD [n = 22 (13 female and 9 male)], and regular chow [n = 15 (7 female and 8 male)]. MeasurementsMeasures included body mass, hindlimb and all limb grip strength, rotarod for motor performance, plantarflexion muscle contractility, motor unit number estimations (MUNE), and repetitive nerve stimulation (RNS) as an index of neuromuscular junction transmission efficacy recorded from the gastrocnemius muscle. At end point, muscle wet weight and blood samples were collected to assess blood beta-hydroxybutyrate levels. Statistical analysisPrimary analyses were two-way mixed effects ANOVA (diet and time × diet) to determine the effect of a KD on indices of motor function (grip, rotarod) and indices of motor unit (MUNE) and muscle (contractility) function. ResultsBeta-hydroxybutyrate (BHB) was significantly higher at 10 weeks in mice on a KD vs control group (0.83 ± 0.44 mmol/l versus 0.42 ± 0.21 mmol/l, η2 = 0.265, unpaired t-test, p = 0.0060). Mice on the KD intervention demonstrated significantly increased hindlimb grip strength (diet, p = 0.0001; time × diet, p = 0.0030), all limb grip strength (diet, p = 0.0005; time × diet, p = 0.0523), and rotarod latency to fall (diet, p = 0.0126; time × diet, p = 0.0021). Mice treated with the KD intervention also demonstrated increased MUNE (diet, p = 0.0465; time × diet, p = 0.0064), but no difference in muscle contractility (diet, p = 0.5248; time × diet, p = 0.5836) or RNS (diet, p = 0.3562; time × diet, p = 0.9871). ConclusionKD intervention improved neuromuscular and motor function in aged mice. This pre-clinical work suggests that further research is needed to assess the efficacy and physiological effects of a KD on indices of sarcopenia.

Neuroimaging alterations and relapse in early-stage psychosis.

Recent reports have indicated that symptom exacerbation after a period of improvement, referred to as relapse, in early-stage psychosis could result in brain changes and poor disease outcomes. We hypothesized that substantial neuroimaging alterations may exist among patients who experience relapse in early-stage psychosis. We studied patients with psychosis within 2 years after the first psychotic event and healthy controls. We divided patients into 2 groups, namely those who did not experience relapse between disease onset and the magnetic resonance imaging (MRI) scan (no-relapse group) and those who did experience relapse between these 2 timings (relapse group). We analyzed 3003 functional connectivity estimates between 78 regions of interest (ROIs) derived from resting-state functional MRI data by adjusting for demographic and clinical confounding factors. We studied 85 patients, incuding 54 in the relapse group and 31 in the no-relapse group, along with 94 healthy controls. We observed significant differences in 47 functional connectivity estimates between the relapse and control groups after multiple comparison corrections, whereas no differences were found between the no-relapse and control groups. Most of these pathological signatures (64%) involved the thalamus. The Jonckheere-Terpstra test indicated that all 47 functional connectivity changes had a significant cross-group progression from controls to patients in the no-relapse group to patients in the relapse group. Longitudinal studies are needed to further validate the involvement and pathological importance of the thalamus in relapse. We observed pathological differences in neuronal connectivity associated with relapse in early-stage psychosis, which are more specifically associated with the thalamus. Our study implies the importance of considering neurobiological mechanisms associated with relapse in the trajectory of psychotic disorders.

Iteration complexity and finite-time efficiency of adaptive sampling trust-region methods for stochastic derivative-free optimization

ASTRO-DF is a prominent trust-region method using adaptive sampling for stochastic derivative-free optimization of nonconvex problems. Its salient feature is an easy-to-understand-and-implement concept of maintaining “just enough” replications when evaluating points throughout the search to guarantee almost-sure convergence to a first-order critical point. To reduce the dependence of ASTRO-DF on the problem dimension and boost its performance in finite time, we present two key refinements, namely: (i) local models with diagonal Hessians constructed on interpolation points based on a coordinate basis; and (ii) direct search using the interpolation points whenever possible. We demonstrate that the refinements in (i) and (ii) retain the convergence guarantees while matching existing results on iteration complexity. Uniquely, our iteration complexity results match the canonical rates without placing assumptions on iterative models’ quality and their independence from function estimates. Numerical experimentation on a testbed of problems and comparison against existing popular algorithms reveals the computational advantage of ASTRO-DF due to the proposed refinements.

Exploring gender differences in residential water demand

Residential water demand has been extensively studied, with the impact of various household characteristics on consumption well-documented. However, the specific effect of gender on household consumption remains insufficiently identified due to the predominant focus on mixed-gender households in previous research. In this paper, we aim to address this gap by examining gender differences in water consumption specifically within single-gender households. To accomplish this, we analyze data from 275 households equipped with individual meters in the city of Gijón, Spain, between 2017 and 2021. Our approach involves two main steps: first, the estimation of a Stone-Geary demand function for water consumption for both women and men single-gender households, and second, employ the Oaxaca-Blinder decomposition to examine gender differences based on the previous estimations. Our findings reveal that women's households consume significantly more water compared to men's households. Additionally, we observe that the demand for water is more inelastic among women, and their level of conditional use threshold is higher than that of men. Importantly, we find that these differences can be primarily attributed to distinct factors such as family composition, housing characteristics, and bill information between genders.

Online estimation of objective function for continuous-time deterministic systems

We developed two online data-driven methods for estimating an objective function in continuous-time linear and nonlinear deterministic systems. The primary focus addressed the challenge posed by unknown input dynamics (control mapping function) in the expert system, a critical element for an online solution of the problem. Our methods leverage both the learner’s and expert’s data for effective problem-solving. The first approach, which is model-free, estimates the expert’s policy and integrates it into the learner agent to approximate the objective function associated with the optimal policy. The second approach estimates the input dynamics from the learner’s data and combines it with the expert’s input-state observations to tackle the objective function estimation problem. Compared to other methods for deterministic systems that rely on both the learner’s and expert’s data, our approaches offer reduced complexity by eliminating the need to estimate an optimal policy after each objective function update. We conduct a convergence analysis of the estimation techniques using Lyapunov-based methods. Numerical experiments validate the effectiveness of our developed methods.

On integral theorems and their statistical properties

We introduce a class of integral theorems based on cyclic functions and Riemann sums approximating integrals. The Fourier integral theorem, derived as a combination of a transform and inverse transform, arises as a special case. The integral theorems provide natural estimators of density functions via Monte Carlo methods. Assessment of the quality of the density estimators can be used to obtain optimal cyclic functions, alternatives to the sin function, which minimize square integrals. Our proof techniques rely on a variational approach in ordinary differential equations and the Cauchy residue theorem in complex analysis.

The Law of the Iterated Logarithm for Lp-Norms of Kernel Estimators of Cumulative Distribution Functions

In this paper, we consider the strong convergence of Lp-norms (p≥1) of a kernel estimator of a cumulative distribution function (CDF). Under some mild conditions, the law of the iterated logarithm (LIL) for the Lp-norms of empirical processes is extended to the kernel estimator of the CDF.

Transfer learning for functional mean estimation: Phase transition and adaptive algorithms

Transfer learning for functional mean estimation: Phase transition and adaptive algorithms

Entirely Coupled Recurrent Neural Network-Based Backstepping Control for Global Stability of Power System Networks

In an interconnected power system network, global performance is affected by various unknown power system parameters subjected to system uncertainties. These unknown parameters in the control expression deteriorate the performance of the power system network. Therefore, these terms associated with the control expression must be estimated precisely. This paper proposes an adaptive backstepping scheme using an entirely coupled recurrent neural network (ECRNN) to estimate these control terms. Three continuous differentiable functions are used to design control input, virtual signals, and adaptive control laws to achieve global performance. The objective of ECRNN is to reduce the control complexity by estimating the associated nonlinear term in the control expression. It will facilitate the complex formulation of the controller and improve system performance. The robust functional estimation ability of ECRNN will make the system immune to uncertainties that may appear due to external disturbances. In ECRNN, feedback loops are added to each neuron layer to achieve additional estimation accuracy. The proposed adaptive law enhances the online weight update speed and accuracy. Verification of the proposed scheme is carried out in MATLAB/Simulink. It is also verified in the real-time digital simulator (RTDS) platform using the IEEE standard New England 39-bus, 10-machine power system model. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the existing limitations in the global performance of a multimachine power system network due to uncertainty in the system parameters. Uncertainties in the power system network primarily appeared due to penetration of renewable power sources, load uncertainty, or occurrence of an uncertain fault in the network. As power system networks are complex nonlinear interconnected systems, these perturbations in the generator states may cause economic losses, load demand uncertainty, or electric scarcity. Thus, a control scheme is required to address the global performance of such networks. This article proposes uniform ultimate bounded stability of synchronous generators in a multimachine power system network with a robust ECRNN-based backstepping control design. The other available technique has not adequately addressed the global performance under uncertainties. The efficacy of the proposed scheme is verified in a real-time environment via a real-time digital simulator which may be a feasible solution for designing excitation control for the synchronous machine in an extensive industrial network.

Performance Gap between Best-bet System of Rice Intensification and Farmers’ Practices in Zamfara State, Nigeria: An Additive-Multiplicative Translog Stochastic Frontier Profit Function

Inadequate information about the performance of a technology can hinder its uptake. The aim of this paper was to provide a thorough examination of the performance gap between the best bet system of rice intensification (BB-SRI) and farmers’ practices (FP) in Zamfara State, Nigeria. Using a multi-stage sampling technique, a sample of 300 rice farmers were selected from the Bakolori Irrigation Scheme, Zamfara State, among which 40 farmers (13%) used the BB-SRI while the remaining 260 farmers (87%) used FP. The data were analyzed using descriptive statistics, farm budget technique, additive-multiplicative stochastic frontier translog profit function and propensity score matching (PSM) estimator. The findings revealed that yield increased from 5,285 kg/ha with FP to 12,735 kg/ha with BB-SRI, an increase of 141%. Rice production was profitable under both FP and BB-SRI with return on investment (ROI) increasing from 2.64 using FP to 6.66 under BB-SRI, an increase of 152%. There was evidence of profit inefficiency in rice farming since the profit could still be raised by 7% and 21% using FP and BB-SRI, respectively. The yield, ROI and profit efficiency gaps between the BB-SRI and FP ranged from 7,452 kg/ha to 7,510 kg/ha, 4.02 to 4.05, and from 0.08 to 0.09, respectively. We recommend therefore that important investments and training in SRI should be considered as a top priority for the transformation and sustainability of the rice sector in order to ensure its successful promotion, uptake and diffusion across other rice producing States in Nigeria.

The Application of Truncated Spline Semiparametric Path Analysis on Determining Factors Influencing Cashless Society Development

Semiparametric path analysis is a combination of parametric and nonparametric path analysis. Semiparametric path analysis is used when there are partially nonlinear and unknown patterns of relationships. One approach to semiparametric pathways is truncated spline. Truncated spline approach tends to search for their own estimation of regression functions according to the data. This is because in the truncated spline there are knot points, which are intersection points that indicate changes in data behavior patterns. Truncated spline semiparametric path analysis will be applied to this study to determine the variables that have a significant effect on the development of the Cashless Society so that the result can be used as a reference for banks and the government in maximizing non-cash-based community development. The data used is the result of a questionnaire with 100 respondents of mobile banking users in Jakarta and will be analyzed using R Studio. Based on the results, it was found that the optimal knot point in the truncated spline function is 3 with many knots is 1, thus dividing the condition of digitizing electronic money into 2 regimes. It was concluded that the product and digitalization of electronic money had a significant effect on the development of cashless society where the modeling obtained could explain 83.87548% of the data. However, when electronic digitalization increases through the value of knot points, the development of cashless society tends to stagnate. This could be due to people who are not ready when the condition of digitizing electronic money is increasingly sophisticated because the available electronic money features are increasingly complex. Therefore, it is important for banks to pay attention to the sophistication of electronic money features provided to customers and adjust the target market so that customers are more accustomed and comfortable to use electronic money in the future.

Spectral density estimation for random processes with stationary increments

AbstractSpectral density analysis plays an important role in studying a stationary random process on a real line. In this paper, we extend this discussion for the random process with stationary increments. We investigate the properties of the method of moments structure function estimation, and propose a nonparametric spectral density function estimator. Our numerical results show that the proposed spectral density estimator performs comparable with the parametric counterpart when the underlying process is assumed to be band‐limited. Additionally, this method is applied to analyze US Housing Starts Data, where the hidden periodicities are detected, providing consistent conclusions with previous economic studies.

Integrated distance sampling models for simple point counts.

Point counts (PCs) are widely used in biodiversity surveys but, despite numerous advantages, simple PCs suffer from several problems: detectability, and therefore abundance, is unknown; systematic spatiotemporal variation in detectability yields biased inferences, and unknown survey area prevents formal density estimation and scaling-up to the landscape level. We introduce integrated distance sampling (IDS) models that combine distance sampling (DS) with simple PC or detection/nondetection (DND) data to capitalize on the strengths and mitigate the weaknesses of each data type. Key to IDS models is the view of simple PC and DND data as aggregations of latent DS surveys that observe the same underlying density process. This enables the estimation of separate detection functions, along with distinct covariate effects, for all data types. Additional information from repeat or time-removal surveys, or variable survey duration, enables the separate estimation of the availability and perceptibility components of detectability with DS and PC data. IDS models reconcile spatial and temporal mismatches among data sets and solve the above-mentioned problems of simple PC and DND data. To fit IDS models, we provide JAGS code and the new "IDS()" function in the R package unmarked. Extant citizen-science data generally lack the information necessary to adjust for detection biases, but IDS models address this shortcoming, thus greatly extending the utility and reach of these data. In addition, they enable formal density estimation in hybrid designs, which efficiently combine DS with distance-free, point-based PC or DND surveys. We believe that IDS models have considerable scope in ecology, management, and monitoring.

A Symmetric Kernel Smoothing Estimation of the Time-Varying Coefficient for Medical Costs

In longitudinal studies, subjects are repeatedly observed at a set of distinct time points until the terminal event time. The time-varying coefficient model extends the parametric method and captures the dynamic trajectories of time-dependent covariate effects, thus enabling it to describe the potential relationship between the longitudinal variable and the observed time points. In this study, we propose a novel approach to the estimation of medical costs using a symmetric kernel smoothing method in the time-varying coefficient joint model. A smooth function of medical costs is derived by weighting the values of longitudinal data at all distinct observed time points via the combination of the kernel method and the inverse probability weighting method. For the simulation study, we first set up the true functions of time-varying coefficients; we then generated random samples for covariates and censored survival times. Subsequently, the longitudinal data of response variables could be produced. Further, numerical simulation experiments were conducted by using the proposed method and applying R code to the generated data. The estimated results for the parameters and non-parametric functions were compared with different settings. The numerical results illustrate that as the sample size increases, the bias and model-based standard errors decrease, and the performance improves with larger sample sizes. The estimates of functions in the model almost coincide with the true functions, as shown in the figures of the simulation study. Furthermore, the consistency of the obtained estimator is demonstrated via theoretical analysis, and a numerical simulation is performed to illustrate the performance of the proposed estimators. The proposed model is applied to a real-world data set acquired from a multicenter automatic defibrillator implantation trial (MADIT).

On almost-prime k-tuples

Let [Formula: see text] denote the divisor function and [Formula: see text] be an admissible set. We prove that there are infinitely many [Formula: see text] for which the product [Formula: see text] is square-free and [Formula: see text], where [Formula: see text] is asymptotic to [Formula: see text]. It improves a previous result of Ram Murty and Vatwani, replacing [Formula: see text] by [Formula: see text]. The main ingredients in our proof are the higher rank Selberg sieve and Irving–Wu–Xi estimate for the divisor function in arithmetic progressions to smooth moduli.

On the growth of Sobolev norm for the cubic NLS on two dimensional product space

We obtain polynomial bounds on the growth in time of Sobolev norm of solutions to the cubic defocussing nonlinear Schrödinger equation on two dimensional product space. We also give the angular improved bilinear Strichartz estimates for frequency localized functions, which estimates are used for enhancement of a smoothing estimates. Such upper bounds for the growth of Sobolev norms measure the transfer of energy from low to high modes as time grows on.

The spillover effect of export on total factor productivity of enterprises: panel data approach in Vietnam

PurposeThis study addresses the empirical results of the spillover effect with export as the primary economic activity that enhances local businesses' total factor productivity (TFP). A learning mechanism is expected to be generated and used as the basis for the policy implication.Design/methodology/approachThis study adopted the Cobb–Douglas function and multiple estimation approaches, including the generalized method of moments, the Olley–Pakes and the Levinsohn–Petrin estimation techniques. The findings were estimated based on the panel data of a Vietnamese local businesses survey conducted by the General Statistics Office of Vietnam (GSO) from 2010 to 2019.FindingsThe results showed that the highest TFP belongs to the businesses in the Southeast region, the Mekong Delta region, the mining industry and the foreign-invested enterprises. The lowest impacted TFP are businesses in the Northwest region and agricultural, forestry and fishery sectors. In addition, the estimated results also show that the positive spillover effect on TFP is shown through forward and backward linkage. The negative spillover effect is expressed through the backward and horizontal channels.Research limitations/implicationsThis study offers original empirical evidence on the learning mechanisms via which exports contribute to productivity improvement in a developing Asian economy, so making a valuable contribution to the existing academic literature in this domain. The findings of this research make a valuable contribution to the advancement of understanding on the many ways via which spillover effects manifest such as horizontal, forward, backward and supplied-backward linkage.Practical implicationsThe study's findings indicate that it is advisable for governments to give priority to the development and improvement of forward and supply chain linkages between exporters and local suppliers. This approach is recommended in order to optimize the advantages derived from export spillovers. At the organizational level, it is imperative for enterprises to strengthen their technological and managerial skills in order to efficiently incorporate knowledge spillovers that originate from overseas partners and trade counterparts.Originality/valueThis study sheds new evidence on the export spillover effect on productivity in emerging economies, with Vietnam as the case study. The paper contributes to the research's originality by adopting novel methodological aspects to estimate local businesses' impact on total factor productivity.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/IJSE-05-2023-0373