Estimation Of Function Research Articles

Optimization-derived blood input function using a kernel method and its evaluation with total-body PET for brain parametric imaging

Dynamic PET allows quantification of physiological parameters through tracer kinetic modeling. For dynamic imaging of brain or head and neck cancer on conventional PET scanners with a short axial field of view, the image-derived input function (ID-IF) from intracranial blood vessels such as the carotid artery (CA) suffers from severe partial volume effects. Alternatively, optimization-derived input function (OD-IF) by the simultaneous estimation (SIME) method does not rely on an ID-IF but derives the input function directly from the data. However, the optimization problem is often highly ill-posed. We proposed a new method that combines the ideas of OD-IF and ID-IF together through a kernel framework. While evaluation of such a method is challenging in human subjects, we used the uEXPLORER total-body PET system that covers major blood pools to provide a reference for validation. MethodsThe conventional SIME approach estimates an input function using a joint estimation together with kinetic parameters by fitting time activity curves from multiple regions of interests (ROIs). The input function is commonly parameterized with a highly nonlinear model which is difficult to estimate. The proposed kernel SIME method exploits the CA ID-IF as a priori information via a kernel representation to stabilize the SIME approach. The unknown parameters are linear and thus easier to estimate. The proposed method was evaluated using 18F-fluorodeoxyglucose studies with both computer simulations and 20 human-subject scans acquired on the uEXPLORER scanner. The effect of the number of ROIs on kernel SIME was also explored. ResultsThe estimated OD-IF by kernel SIME showed a good match with the reference input function and provided more accurate estimation of kinetic parameters for both simulation and human-subject data. The kernel SIME led to the highest correlation coefficient (R = 0.97) and the lowest mean absolute error (MAE = 10.5 %) compared to using the CA ID-IF (R = 0.86, MAE = 108.2 %) and conventional SIME (R = 0.57, MAE = 78.7 %) in the human-subject evaluation. Adding more ROIs improved the overall performance of the kernel SIME method. ConclusionThe proposed kernel SIME method shows promise to provide an accurate estimation of the blood input function and kinetic parameters for brain PET parametric imaging.

Age-specific prevalence of the different clinical presentations of AD and FTD in young-onset dementia

BackgroundStudies have shown that the prevalence of all-variants Alzheimer’s disease (AD) and frontotemporal dementia (FTD) both increase with age, even before the age of 65. However, it is not known whether their different clinical presentations all increase in prevalence with age in the same way.MethodsWe studied the prevalence of the different clinical presentations of young-onset AD and FTD by 5-year age groups in a population-based study identifying all dementia patients with a diagnosis of AD and FTD and symptoms onset before age 65 in the Modena province, Italy. By using regression models of cumulative occurrences, we also estimated age-specific prevalence and compared the growth curves of the clinical presentations.ResultsThe prevalence of all-variants AD increased with age, from 18/1,000,000 in the 40–44 age group to 1411/1,000,000 in the 60–64 age group. The prevalence of all-variants FTD also increased with age, from 18/1,000,000 to 866/1,000,000. An estimation of age-specific prevalence functions of each clinical presentation showed that atypical non-amnestic AD and aphasic FTD grew the most in early ages, followed by the behavioural variant of FTD (bvFTD). Then, around the age of 60, amnestic AD took over and its age-specific prevalence continued to increase disproportionally compared to all the other clinical variants of AD and FTD, which, instead, started to decrease in prevalence.ConclusionsAmnestic AD is the clinical presentation that increases the most with advancing age, followed by bvFTD, suggesting that there is a differential vulnerability to the effect of ageing within the same neurodegenerative disease.

Stock market prices and Dividends in the US: Bubbles or Long-run equilibria relationships?

This paper presents a novel approach to identifying potential bubbles in the US stock market by employing alternative time series methods based on long memory, including fractional integration and cointegration, as well as duration dependence non-parametric models. To test for duration dependence, the paper employs a unique non-parametric hazard function estimation method, using monotonic P-splines, which enables the estimation of a coherent and sophisticated Bayesian confidence interval for the function. By analyzing historical data of real US stock index from January 1871 to November 2022, the results reveal strong evidence of bubbles in the US stock market. It is worth noting that this is the first time a fractional integration approach and a novel non-parametric hazard function have been utilized to test for rational speculative bubbles in the US stock market, making this paper a significant contribution to the field.

Group Selection and Shrinkage: Structured Sparsity for Semiparametric Additive Models

Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection. This work introduces structured sparse estimators that combine group subset selection with shrinkage. To accommodate sophisticated structures, our estimators allow for arbitrary overlap between groups. We develop an optimization framework for fitting the nonconvex regularization surface and present finite-sample error bounds for estimation of the regression function. As an application requiring structure, we study sparse semiparametric additive modeling, a procedure that allows the effect of each predictor to be zero, linear, or nonlinear. For this task, the new estimators improve across several metrics on synthetic data compared to alternatives. Finally, we demonstrate their efficacy in modeling supermarket foot traffic and economic recessions using many predictors. These demonstrations suggest sparse semiparametric additive models, fit using the new estimators, are an excellent compromise between fully linear and fully nonparametric alternatives. All of our algorithms are made available in the scalable implementation grpsel. Supplementary materials for this article are available online.

Exact Estimates of Functions in Sobolev Spaces with Uniform Norm

Exact Estimates of Functions in Sobolev Spaces with Uniform Norm

Interpolation problems for random fields on Sierpinski’s carpet

The prediction of stochastic processes and the estimation of random fields of different natures is becoming an increasingly common field of research among scientists of various specialties. However, an analysis of papers across different estimating problems shows that a dynamic approach over an iterative and recursive interpolation of random fields on fractal is still an open area of investigation. There are many papers related to the interpolation problems of stationary sequences, estimation of random fields, even on the perforated planes, but all of this still provides a place for an investigation of a more complicated structure like a fractal, which might be more beneficial in appliances of certain industry fields. For example, there has been a development of mobile phone and WiFi fractal antennas based on a first few iterations of the Sierpinski carpet. In this paper, we introduce an estimation for random fields on the Sierpinski carpet, based on the usage of the known spectral density, and calculation of the spectral characteristic that allows an estimation of the optimal linear functional of the omitted points in the field. We give coverage of an idea of stationary sequence estimating that is necessary to provide a basic understanding of the approach of the interpolation of one or a set of omitted values. After that, the expansion to random fields allows us to deduce a dynamic approach on the iteration steps of the Sierpinski carpet. We describe the numerical results of the initial iteration steps and demonstrate a recurring pattern in both the matrix of Fourier series coefficients of the spectral density and the result of the optimal linear functional estimation. So that it provides a dependency between formulas of the different initial sizes of the field as well as a possible generalizing of the solution for N-steps in the Sierpinski carpet. We expect that further evaluation of the mean squared error of this estimation can be used to identify the possible iteration step when further estimation becomes irrelevant, hence allowing us to reduce the cost of calculations and make the process viable.

On the behavior of the Lynden-Bell estimator in widely orthant-dependent model

. This article is devoted to investigating some asymptotic properties of the Lynden-Bell and the cumulative risk function estimators when the survival and the truncated times form widely orthant-dependent sequences. As main results, we establish strong uniform consistency rates for the proposed estimators. Then, as an application, we derive a strong uniform consistency rate for the hazard rate function estimator. The performances of the proposed estimators are illustrated via some simulations.

Estimating high-dimensional Hawkes process with time-dependent covariates

The Hawkes process models have been recently become a popular tool for modeling and analysis of neural spike train data. Despite this popularity, existing methodological and theoretical work has mainly focused on models without assumption of time-varying covariates, such as stimulus drive. In this article, motivated by neuronal spike trains study in the presence of stimuli, we propose a new Hawkes process model, where covariates are included in the intensity function. We consider the problem of simultaneous variable selection and estimation for the Hawkes process in the high-dimensional regime. Estimation of the intensity function of the high-dimensional point process is considered within a nonparametric framework, applying B-splines and the SCAD penalty for matters of sparsity. We apply the Doob-Kolmogorov inequality to establish the consistency of the resulting estimators. Finally, we illustrate the performance of our proposal through simulation and demonstrate its utility by applying it to the neuron spike train data set.

An experimental investigation on the fluid–structure coupling in horizontal pipes conveying two-phase intermittent flow

Two-phase flow is typically found in several industrial applications, such as in the production and transportation of oil and gas in the petrochemical industry, in the catalytic cracking and microreactors in the chemical industry, and in nuclear reactor cooling pumps. Measurement of two-phase flow features is usually necessary and has been done in several ways, including pressure probes, resistive sensors, gamma-ray, wire-mesh sensor and many others. However, these are either intrusive or invasive techniques, which might be of challenging application in industrial environments, or rely on a hazardous radioactive source. Vibration-based measurement of two-phase flow in pipes stands out as a non-invasive/non-intrusive approach and, consequently, multiphase-flow induced vibration in pipes has receiving increasing attention in recent years. In this work, the dynamic behaviour of a horizontal tube conveying an intermittent two-phase gas-liquid flow is investigated based on indirect approaches. The phenomenon of fluid–structure coupling is investigated using acceleration and pressure measurement. Moreover, the bubble size distribution is estimated from high-speed camera images and a deep learning model for image segmentation, along with its spectral content and time modulation. Focus is given at frequency bands around the cut-on frequencies of the circumferential wave modes of the pipe. An approach based on the estimation of frequency response function of the pressure and vibration at the liquid slug and elongated bubble is proposed, such that the coherence function can be used as quantitative measure of the coupling. Two experimental conditions with intermittent flow are investigated as representative cases. It is shown that there is a great vibration amplification at the cut-on frequencies of circumferential wave modes in pipes due to the corresponding structural wave and pressure coupling. Consequently, the frequency of passage of bubble can be estimated from the demodulation of vibration response filtered at the cut-on modes. The experimental results pave the way for innovative vibration-based measurement approaches.

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