Estimation Of Function Research Articles

On the spectrum of the Sturm–Liouville problem with arithmetically self-similar weight

We consider the spectral asymptotics of the Sturm–Liouville problem with an arithmetically self-similar singular weight. In previous papers, A. A. Vladimirov and I. A. Sheĭpak, as well as the author, relied on the spectral periodicity property, which places major constraints on the self-similarity parameters of the weight. In this study, a different approach to estimation of the eigenvalue counting function is presented. As a result, a significantly wider class of self-similar measures can be considered. The obtained asymptotics are applied to the problem of small ball deviations for the Green Gaussian processes.

Data-driven Approximation of Cumulative Distribution Function Using Particle Swarm Optimization based Finite Mixtures of Logistic Distribution

This paper proposes a data-driven approximation of the Cumulative Distribution Function using the Finite Mixtures of the Cumulative Distribution Function of Logistic distribution. Since it is not possible to solve the logistic mixture model using the Maximum likelihood method, the mixture model is modeled to approximate the empirical cumulative distribution function using the computational intelligence algorithms. The Probability Density Function is obtained by differentiating the estimate of the Cumulative Distribution Function. The proposed technique estimates the Cumulative Distribution Function of different benchmark distributions. Also, the performance of the proposed technique is compared with the state-of-the-art kernel density estimator and the Gaussian Mixture Model. Experimental results on κ−μ distribution show that the proposed technique performs equally well in estimating the probability density function. In contrast, the proposed technique outperforms in estimating the cumulative distribution function. Also, it is evident from the experimental results that the proposed technique outperforms the state-of-the-art Gaussian Mixture model and kernel density estimation techniques with less training data.

Reliability Estimation of Scale Parameter in Type II Generalized Half-Logistic Distribution from Doubly Censored Samples Based on Monte Carlo Simulation

Objectives: This article deals with estimation of the reliability function for one-parameter Type II Generalized Half- Logistic distribution (Type II GHLD). Methods: The Maximum likelihood (ML) and Approximate Maximum likelihood (AML) methods provided by Jilani et.al. 1 . Findings: Comparisons between the estimators were made using Monte Carlo Simulation based on statistical indicter bias and mean squared error (MSE). We have generated 3000 random samples of size n=10(5)20 from a standard one-parameter Type II GHLD with = 0.5, 1.5 and 2.0. Each sample is then ordered and from this sample a doubly (including left and right) censored sample is considered, by censoring r smallest observations and s largest observations with all possible choices of r and s corresponding to this resultant sample we compute MLEs (using Newton-Raphson method), the LAMLE and unbiased LAMLE . Finally, the results are explained with tables. Novelty: This study has empirically proves that all the three reliability estimators have the same asymptotic variance. Hence, in this case, any one of the three estimators can be used but preferable estimator based unbiased estimator. Keywords: Maximum likelihood estimation, Approximate Maximum likelihood estimation, Bias, Mean squared error, Variances

Adaptive support vector machine for time-variant failure probability function estimation

Time variant reliability analysis introduces additional complexity due to the inclusion of time. When the time-variant failure probability function (TFPF) of the structure is of interest, it inherently involves sequential evaluations of the failure probabilities of series systems varied with time in discretized space, posing a challenge to reliability analysis. An efficient approach for the evaluation of the TFPF, called ‘Time-dependent Adaptive Support Vector Machine combined with Monte Carlo Simulation’ (TASVM-MCS), is presented to reduce the corresponding computational cost. Based on the samples from Monte Carlo simulation (MCS), an iterative strategy is proposed to actively extract the most valuable sample points from the sample pool and iteratively update the support vector machine (SVM) model. In particular, an active learning function is proposed to take into account the diversity of samples and time simultaneously. In this way, the built SVM will be more suitable for the evaluation of TFPF other than a point-wise failure probability. The proposed TASVM-MCS method is relatively less sensitive to the dimensionality of the input variables, making it a powerful and promising approach for time-variant reliability computations. Four representative examples are given to demonstrate the significant effectiveness and efficiency of the proposed method.

On the existence and estimates of inverse functions in the degenerate case

On the existence and estimates of inverse functions in the degenerate case

An adaptation of Random Forest to estimate convex non‐parametric production technologies: an empirical illustration of efficiency measurement in education

AbstractThis paper presents a novel approach to conduct non‐parametric estimations of production technologies that adhere to the basic assumptions of production theory axioms, including free disposability in inputs and outputs and convexity. The methodology is rooted in adapting the highly effective machine learning techniques associated with Random Forest and the use of splines. The new method features a piecewise linear estimator analogous to data envelopment analysis (DEA); however, it distinguishes itself by addressing DEA's overfitting and lack of robustness via randomization of data and input variables in the construction of the models. In this paper, the virtues of employing machine learning techniques for assessing the efficiency of public services, particularly in the realm of educational institutions, are underscored. The new approach has the capability to predict outputs based on inputs, even for units not included in the observed sample. Furthermore, it enables the identification of the most relevant inputs in relation to output production. To demonstrate the advantages of our method, an estimation of the educational production function is conducted for Spanish regions utilizing data sourced from the Program for International Student Assessment.

Interferometric Rayleigh Scattering for Flow Temperature and Velocity Analysis

A new processing method is developed to analyze images from a Fabry–Pérot interferometer in order to extract point measurements of temperature and velocity within a gas flow, using Rayleigh scattering. Two types of interferograms are generated from a Fabry–Pérot model combined with a simulated light source. The first type is obtained from a diffuse coherent light source, namely, a laser beam on a diffuser. The interferometer characteristics, defined by only two independent parameters, are retrieved within 0.1% accuracy. The knowledge of these parameters is mandatory to analyze interferograms from Rayleigh scattered light. The second type corresponds to Rayleigh scattered light from a small volume under flow conditions, lighted with a focused laser beam and captured with long exposure time. Several flow parameters are chosen to generate these interferograms. The relative errors on the temperature and velocity estimates are found to be weak. Noise is also added to assess the robustness of the processing method. The error induced by the estimates of the instrument function is found to be of second order compared to the error induced by the image analysis.

A Sequential Stein's Method for Faster Training of Additive Index Models.

The additive index models (AIMs) can be viewed as a kind of artificial neural networks based on nonparametric activation or so-called ridge functions. Recently, they are shown to achieve enhanced explainability after incorporating various interpretability constraints. However, the training of AIMs by either the backfitting algorithm or the joint stochastic optimization is known to be very slow for especially high dimensional inputs. In this article, we propose a novel sequential approach based on the celebrated Stein's lemma. The proposed SeqStein method can successfully decouple the training of AIMs into two separable steps, namely, the following: 1) Stein's estimation of the projection indices and 2) nonparametric estimation of ridge functions using the smoothing splines. We show through numerical experiments that the SeqStein algorithm is not only more efficient for training AIMs, but also inclined to produce more interpretable models that have smooth ridge functions with sparse and nearly orthogonal projection indices.

Photometric redshifts probability density estimation from recurrent neural networks in the DECam local volume exploration survey data release 2

Photometric wide-field surveys are imaging the sky in unprecedented detail. These surveys face a significant challenge in efficiently estimating galactic photometric redshifts while accurately quantifying associated uncertainties. In this work, we address this challenge by exploring the estimation of Probability Density Functions (PDFs) for the photometric redshifts of galaxies across a vast area of 17,000 square degrees, encompassing objects with a median 5σ point-source depth of g= 24.3, r=23.9, i= 23.5, and z= 22.8 mag. Our approach uses deep learning, specifically integrating a Recurrent Neural Network architecture with a Mixture Density Network, to leverage magnitudes and colors as input features for constructing photometric redshift PDFs across the whole DECam Local Volume Exploration (DELVE) survey sky footprint. Subsequently, we rigorously evaluate the reliability and robustness of our estimation methodology, gauging its performance against other well-established machine learning methods to ensure the quality of our redshift estimations. Our best results constrain photometric redshifts with the bias of −0.0013, a scatter of 0.0293, and an outlier fraction of 5.1%. These point estimates are accompanied by well-calibrated PDFs evaluated using diagnostic tools such as Probability Integral Transform and Odds distribution. We also address the problem of the accessibility of PDFs in terms of disk space storage and the time demand required to generate their corresponding parameters.We present a novel Autoencoder model that reduces the size of PDF parameter arrays to one-sixth of their original length, significantly decreasing the time required for PDF generation to one-eighth of the time needed when generating PDFs directly from the magnitudes.

Bayesian Optimization for Sparse Neural Networks With Trainable Activation Functions.

In the literature on deep neural networks, there is considerable interest in developing activation functions that can enhance neural network performance. In recent years, there has been renewed scientific interest in proposing activation functions that can be trained throughout the learning process, as they appear to improve network performance, especially by reducing overfitting. In this paper, we propose a trainable activation function whose parameters need to be estimated. A fully Bayesian model is developed to automatically estimate from the learning data both the model weights and activation function parameters. An MCMC-based optimization scheme is developed to build the inference. The proposed method aims to solve the aforementioned problems and improve convergence time by using an efficient sampling scheme that guarantees convergence to the global maximum. The proposed scheme has been tested across a diverse datasets, encompassing both classification and regression tasks, and implemented in various CNN architectures to demonstrate its versatility and effectiveness. Promising results demonstrate the usefulness of our proposed approach in improving models accuracy due to the proposed activation function and Bayesian estimation of the parameters.

Some Estimates of Functions of General Franklin System

Some Estimates of Functions of General Franklin System

Latent-Maximum-Entropy-Based Cognitive Radar Reward Function Estimation With Nonideal Observations

Latent-Maximum-Entropy-Based Cognitive Radar Reward Function Estimation With Nonideal Observations

Development of an ultrasound-based metric of muscle functional capacity for use in patients with neuromuscular disease.

Spinal muscular atrophy (SMA) and Duchenne muscular dystrophy (DMD) are progressive neuromuscular disorders characterized by severe muscle weakness and functional decline (Pillen et al., Muscle Nerve 2008; 37(6):679-693). With new therapeutics, objective methods with increased sensitivity are needed to assess muscle function. Ultrasound imaging is a promising approach for assessing muscle fat and fibrosis in neuromuscular disorders. This study builds on prior work by combining ultrasound-based measurements of muscle size, shape, and quality, relating these measures to muscle strength, and proposing a multivariable image-based estimate of muscle function. Maximum voluntary elbow flexion torque of 36 participants (SMA, DMD, and healthy controls) was measured by hand-held dynamometry and elbow flexor muscles were imaged using ultrasound. Muscle size (cross-sectional area, maximum Feret diameter or width, and thickness), quality (echogenicity, texture anisotropy index), and cross-sectional shape (diameter ratio) were measured. Multivariable regression was used to select ultrasound measurements that predict elbow flexion torque. Significant differences were observed in muscle size (decreased), shape (thinned), and quality (decreased) with increased disease severity and compared to healthy participants. CSA (brachioradialis R2 = 0.51), maximum Feret diameter (biceps R2 = 0.49, brachioradialis R2 = 0.58) and echogenicity (brachioradialis R2 = 0.61) were most correlated with torque production. Multivariable regression models identified that muscle size (CSA, maximum Feret diameter) and quality (echogenicity) were both essential to predict elbow flexion torque (R2 = 0.65). A multivariable approach combining muscle size and quality improves strength predictions over single variable approaches. These methods present a promising avenue for the development of sensitive and functionally relevant biomarkers of neuromuscular disease.

The Hybrid Odd Exponential-Exponential Distribution: Statistical Properties and Applications

In this paper, we study a new statistical distribution called the hybrid odd exponential-exponential distribution (HOE-E distribution for short) we the aim of applying it to real data sets. This new distribution appears as a sub-model of the larger HOEE-Φ family in (Mahdi et al., 2024). We explore many mathematical and statistical properties of this distribution such as the series expansion of the PDF, the quantile function, moments and their generating function, incomplete moments, the shape of the PDF, and the shape of the hazard rate function, order statistics, and parameter estimation using the maximum likelihood estimation. We use this distribution to model a plasma concentration data set. Moreover, this we show that the suggested HOE-E distribution outperformance many other distributions based on various statistical criteria like AIC, CAIC, BIC, HQIC, W, and A.

The Effect of Herbal Medicine for Chronic Kidney Disease: A Systematic Review and Meta-Analysis

Objectives: This study aimed to evaluate the effect of herbal medicine on patients with non-dialysis chronic kidney disease (CKD).Methods: Articles published from 2011 to February 17, 2024 were searched via PubMed, EMBASE, Cochrane Library, CNKI, CiNii, KISS, RISS, and OASIS. The quality of included articles was evaluated using a risk-of-bias tool. Meta-analyses considered the effects of herbal medicines on the total effective rate, renal function estimates (GFR, SCr, BUN, 24h-Upro), and other indicators (e.g., uric acid, hemoglobin, and bone density-related indicators).Results: A total of 13 RCTs were included in this study. The treatment group showed a significantly higher total effective rate (RR: 1.47, 95% CI: 1.33-1.62, P<0.00001) and GFR (MD: 9.28, 95% CI: 6.52-12.04, P<0.00001), together with improvements in other renal function indicators, except for 24h-Upro (p=0.05). There were no significant differences in uric acid, hemoglobin, and bone density-related indicators. Adverse events were minimal in both groups.Conclusion: For non-dialysis CKD, this study supports the effectiveness of nine herbal medicines, either alone or in combination with Western medicines. However, even the meta-analyses provide insufficient evidence to conclusively guarantee the safety and efficacy of all types of herbal medicines in treating CKD. Therefore, additional well-designed studies are necessary to enhance the clinical application of herbal medicines in CKD.

FARO-44 RICE PRODUCTION EFFICIENCY OF FADAMA III ADDITIONAL FINANCE II BENEFICIARIES IN TARABA STATE,

The study analysed the faro-44 rice production efficiency of fadama III additional finance II beneficiaries in Taraba State, Nigeria. A Multi-stage sampling procedure was used to select 250 respondents. Data were analyzed using descriptive and inferential statistics. The findings of the study revealed that The result of maximum likelihood estimates of the stochastic frontier production Function of dry season faro-44 rice farmers reveal that farm size (P<0.01), fertilizer (P<0.05), quantity of seed (kg) (P<0.01), herbicide (liter) (P<0.05), were positive and significant increasing output of the farmers. Similarly, the age (P<0.01) level of education (P<0.01), farming experience (P<0.05) and household size (P<0.05 were the socio-economic characteristics influencing the increase in technical efficiency of the farmers. Furthermore, the technical efficiency of the farmers is glaringly below 1, an indication that the farmers are operating below their production efficiency frontier. A reasonable proportion (41.20%) of the respondents were within 0.60-0.69 technical efficiency index range with highest value of 0.91 for the most efficient farmers and minimum of 0.50 for the least efficient or worst farmer. Consequently, farmers obtained mean technical efficiency of 0.76 which will improve their technical efficiency by 24%. The result further revealed that, the farmers attained an estimated mean allocative efficiency of 0.88. It was concluded that most of the farmers were unable to obtain technical efficiency level above 76% and farmers were 88% allocative efficient. The study recommended that farmers level of technical efficiency can be increased by 27% by building farmers’ capacity through training, workshops and seminars on postharvest loss management, processing techniques, farm record keeping in order to avoid wastages and sustain efficiency.

Drive force allocation control based on pump displacement optimization for hydraulic hybrid motor-assisted system

To achieve rational coordination of the front and rear axle torque of commercial vehicles equipped with hydraulic hybrid motor-assisted systems (HHMAS), and further enhance the vehicle’s fuel efficiency and traction capability. A hydraulic pump displacement control strategy based on energy-efficiency-orientation (EEO) is proposed for driving force distribution. Firstly, the efficiency is analyzed from the perspective of system energy flow. Then, considering the time-varying efficiency characteristics of the hydraulic variable pump and hydraulic motor, the stochastic dynamic optimization problem is modeled as a markov decision process, and a value function estimation method is introduced to approximate the optimal energy efficiency of the entire HHMAS. Finally, the results indicate that the EEO strategy can enhance the fuel economy of vehicles, with a fuel-saving rate of 6.3% compared to the wheel-speed-following-control (WSFC) strategy. In addition, the proposed strategy exhibits superior traction capacity and climbing ability compared to the traditional WSFC strategy.

Estimation of Chloride Channel Residual Function and Assessment of Targeted Drugs Efficiency in the Presence of a Complex Allele [L467F;F508del] in the CFTR Gene.

Complex alleles of the CFTR gene complicate the diagnosis of cystic fibrosis (CF), the classification of its pathogenic variants, affect the clinical picture of the disease and can affect the efficiency of targeted drugs. The total frequency of complex allele [L467F;F508del] in the Russian population of patients with CF is 0.74%, and in patients with the F508del/F508del genotype, its frequency reaches 8%. This article presents multi-faceted study of the complex allele [L467F;F508del] in a cohort of patients with genotypes [L467F;F508del]/class I (c.3532_3535dup, c.1766+2T>C, W1310X, 712-1G>T), and data for a unique patient with the genotype [L467F;F508del]/[L467F;F508del]. Using the intestinal current measurement method, it was demonstrated the absence of CFTR function for [L467F;F508del]/class I and [L467F;F508del]/[L467F;F508del] genotypes. In intestinal organoids, it was shown that [L467F;F508del] in combination with class I variants and in the homozygotes abolishes the efficacy of both two-component (ivacaftor+lumacaftor; ivacaftor+tezacaftor) and three-component (ivacaftor+tezacaftor+elexacaftor) targeted drugs. When prescribing ivacaftor+tezacaftor+elexacaftor to three patients, they did not have a clinical effect after 6-12 months.

Online functional connectivity analysis of large all-to-all networks in MNE Scan

Abstract The analysis of electroencephalography (EEG)/magnetoencephalography (MEG) functional connectivity has become an important tool in neuroscience. Especially the high time resolution of EEG/MEG enables important insight into the functioning of the human brain. To date, functional connectivity is commonly estimated offline, that is, after the conclusion of the experiment. However, online computation of functional connectivity has the potential to enable unique experimental paradigms. For example, changes of functional connectivity due to learning processes could be tracked in real time and the experiment be adjusted based on these observations. Furthermore, the connectivity estimates can be used for neurofeedback applications or the instantaneous inspection of measurement results. In this study, we present the implementation and evaluation of online sensor and source space functional connectivity estimation in the open-source software MNE Scan. Online capable implementations of several functional connectivity metrics were established in the Connectivity library within MNE-CPP and made available as a plugin in MNE Scan. Online capability was achieved by enforcing multithreading and high efficiency for all computations, so that repeated computations were avoided wherever possible, which allows for a major speed-up in the case of overlapping intervals. We present comprehensive performance evaluations of these implementations proving the online capability for the computation of large all-to-all functional connectivity networks. As a proof of principle, we demonstrate the feasibility of online functional connectivity estimation in the evaluation of somatosensory evoked brain activity

Extrapolation Framework and Characteristic Analysis of Load Spectrum for Agriculture General Power Machinery

As a crucial step in food production, tillage and land preparation play a pivotal role in achieving sustainable crop production and improving the soil environment. However, accurate assessment of the load that agricultural machinery implements during the operation process has always been a vexing problem that needs urgent solutions. In this paper, an extrapolation and reconstruction framework for the time-domain load is constructed based on the probability-weighted moments (PWM) estimation and the peaks-over-threshold function, and the load spectrum is obtained for agriculture general power machinery. Firstly, the load acquisition system was developed, the traction resistance and output torque of the tractor were measured, and the collected load signals were preprocessed. Next, the mean excess function and PWM estimation are introduced to select the optimal threshold and generalized Pareto distribution (GPD) fitting parameters and the extreme load distribution that exceeds the threshold range is fitted. The extreme points in the original data are replaced by generating new extreme points that follow the GPD distribution, and the extrapolation of the load spectrum is achieved. Finally, the real extrapolated load spectrum was validated based on statistical characteristics and rainflow counting analysis, and the correlation coefficient between the fitting data and the extreme load samples was greater than 0.99. It can retain the load sequence characteristics of the original load to a great extent, truly reflecting the load state during the operation of agricultural machinery. Meanwhile, the characteristics of the load spectrum can be accurately obtained, such as extreme, mean, and amplitude values, and the real load during deep loosening and rotary tillage are accurately described. The values provide more authentic and reliable data support for the subsequent selection of optimal operating parameters, reliability design of the power transmission system, and the life assessment of the agricultural implements.