Local Estimates Research Articles

Semiconvexity estimates for nonlinear integro‐differential equations

AbstractIn this paper we establish for the first time local semiconvexity estimates for fully nonlinear equations and for obstacle problems driven by integro‐differential operators with general kernels. Our proof is based on the Bernstein technique, which we develop for a natural class of nonlocal operators and consider to be of independent interest. In particular, we solve an open problem from Cabré‐Dipierro‐Valdinoci. As an application of our result, we establish optimal regularity estimates and smoothness of the free boundary near regular points for the nonlocal obstacle problem on domains. Finally, we also extend the Bernstein technique to parabolic equations and nonsymmetric operators.

Analysis of Spatial Effects of New Energy Vehicles Based on Semi-parametric Spatial Durbin Model

The global scientific and technological revolution and industrial change are developing rapidly, the integration of automotive technology with energy, transportation and information and communication fields is accelerating, and electrification, internet connectivity and intelligence have become the main trends. Therefore, studying the impact of digital development on the growth of new energy vehicle industry and consumer purchase intention is of great theoretical and practical significance for the digital transformation of automobile companies. In this paper, based on the provincial panel data of new energy vehicles in China from 2016 to 2023, we constructed the index system of digital economy and economic development, used the entropy method to calculate the level of development, and conducted spatial autocorrelation tests using global and local Moran indices. Considering the non-linear relationship between variables, a semi-parametric spatial Durbin model is established using local polynomial estimation to explore the impact of digital economy on new energy automobile industry. The results of the study show that the development of digital economy promotes the development of new energy automobile industry to a certain extent, but its development level may have a negative impact if it is too low or too high.

Application of Rasch analysis in nursing research: A methodological introduction.

The design and validation of tools constitutes a fundamental pillar of nursing research, where it is essential to incorporate the most current methodologies and analyses in order to guarantee validity and reliability in their clinical application. The aim of this paper is to describe the characteristics of the RASCH analysis and the methodology for its development as well as to discuss its relevance and applicability in nursing research, highlighting its potential contribution to the improvement of the quality and accuracy of measurement instruments in the discipline. Through a narrative synthesis, the theoretical foundations of RASCH analysis are described and the characteristics and assumptions that must be fulfilled to carry out this type of analysis are presented. Subsequently, the implementation methodology is presented in 11 steps: definition of objectives and preparation, instrument design, data collection, initial and unidimensionality analysis, goodness-of-fit assessment (infit-outfit, reliability and separation), item local independence assessment (Yen's Q3 coefficient), item calibration and estimation of skills, measurement invariance analysis (DIF analysis), review and modification of the instrument, final analysis and validation, interpretation of results. Examples of use are presented, as well as the advantages and limitations of the method. In conclusion, the RASCH analysis provides a valuable methodology for the evaluation of clinical competencies and skills, as well as for the development and validation of measurement instruments of great utility for research in care, although it would be necessary to promote training and standardization in its use.

Global Kato smoothing and Strichartz estimates for Schrödinger type equations with rough decay potentials

Let [Formula: see text] be a higher-order elliptic operator on [Formula: see text], where [Formula: see text] is a general bounded decaying potential. This paper focuses on the global Kato smoothing and Strichartz estimates for solutions to Schrödinger-type equation associated with [Formula: see text]. In particular, we first establish sharp global Kato smoothing estimates for [Formula: see text], based on uniform resolvent estimates of Kato–Yajima type for the absolutely continuous part of [Formula: see text]. As a consequence, we also obtain optimal local decay estimates. Using these local decay estimates, we then prove the full set of Strichartz estimates, including the endpoint case. Notably, we derive Strichartz estimates with sharp smoothing effects for higher-order cases with rough potentials, which are applicable to the study of nonlinear higher-order Schrödinger equations. Finally, we introduce new uniform Sobolev estimates of the Kenig–Ruiz–Sogge type, incorporating an additional derivative term, which are crucial for establishing the sharp Kato smoothing estimates.

Local linear estimators for reflected diffusions

In this paper, we investigate the nonparametric local linear estimator for the drift function of reflected stochastic differential equations based on the discretely observed process. Under certain regularity conditions, we prove the strong consistency and establish the asymptotic normality for our proposed estimator. We also propose the optimal bandwidth selector for the estimator and show that the estimator does not have a boundary effect. Simulation results demonstrate that our method is superior to the method proposed by Cholaquidis et al. [Stat. Sin. 2021, 31: 29–51]. We apply the EUR/USD currency exchange rate data to illustrate our theoretical results.

Forecasting economic growth by combining local linear and standard approaches

Today, developing economies are of major importance for global macroeconomic development. However, the empirical analysis and especially the forecasting of macroeconomic time series remain difficult due to a lack of sufficient data, data frequency, high volatility, and non-linear developments. These difficulties require more sophisticated approaches to obtain reliable forecasts. Therefore, we propose an improved forecasting method especially for growth data based on a data-driven local linear trend estimation with an extended iterative plug-in algorithm for determining the bandwidth endogenously. This approach allows a smooth trend estimation that takes care of temporary changes in trend processes. Further, the naïve random walk model is extended for forecasting by including a local linear, time-varying drift. We apply this method to GDP development for six developing and two advanced economies and compare different forecast combinations. The combinations that include the local linear approach and the random walk with a local linear trend improve forecasting accuracy and reduce variance.

Local genetic correlation via knockoffs reduces confounding due to cross-trait assortative mating.

Local genetic correlation analysis is an important tool for identifying genetic loci with shared biology across traits. Recently, Border etal. have shown that the results of these analyses are confounded by cross-trait assortative mating (xAM), leading to many false-positive findings. Here, we describe LAVA-Knock, a local genetic correlation method that builds off an existing genetic correlation method, LAVA, and augments it by generating synthetic data in a way that preserves local and long-range linkage disequilibrium (LD), allowing us to reduce the confounding induced by xAM. We show in simulations based on a realistic xAM model and in genome-wide association study (GWAS) applications for 630 trait pairs that LAVA-Knock can greatly reduce the bias due to xAM relative to LAVA. Furthermore, we show a significant positive correlation between the reduction in local genetic correlations and estimates in the literature of cross-mate phenotype correlations; in particular, pairs of traits that are known to have high cross-mate phenotype correlation values have a significantly higher reduction in the number of local genetic correlations compared with other trait pairs. A few representative examples include education and intelligence, education and alcohol consumption, and attention-deficit hyperactivity disorder and depression. These results suggest that LAVA-Knock can reduce confounding due to both short-range LD and long-range LD induced by xAM.

Modal volatility function

We in this article propose a novel non‐parametric estimator for the volatility function within a broad context that encompasses nonlinear time series models as a special case. The new estimator, built on the mode value, is designed to complement existing mean volatility measures to reveal distinct data features. We demonstrate that the suggested modal volatility estimator can be obtained asymptotically as well as if the conditional mean regression function were known, assuming observations are from a strictly stationary and absolutely regular process. Under mild regularity conditions, we establish that the asymptotic distributions of the resulting estimator align with those derived from independent observations, albeit with a slower convergence rate compared to non‐parametric mean regression. The theory and practice of bandwidth selection are discussed. Moreover, we put forward a variance reduction technique for the modal volatility estimator to attain asymptotic relative efficiency while maintaining the asymptotic bias unchanged. We numerically solve the modal regression model with the use of a modified modal‐expectation‐maximization algorithm. Monte Carlo simulations are conducted to assess the finite sample performance of the developed estimation procedure. Two real data analyses are presented to further illustrate the newly proposed model in practical applications. To potentially enhance the accuracy of the bias term, we in the end discuss the extension of the method to local exponential modal estimation. We showcase that the suggested exponential modal volatility estimator shares the same asymptotic variance as the non‐parametric modal volatility estimator but may exhibit a smaller bias.

Textual Analysis of CT and MR images in bladder cancer: The promise and pitfalls in systematic review

Introduction: Textual analysis is a new stage in the development and improvement of radiology. Textual analysis (TA) or radiomics is a method of in-depth study of medical images using specialized computer programs. It`s based on the quantification of invisible features and provides tools for researchers to gain deep insights into tumor morphology.A number of mathematically extracted texture features (TF) can be correlate with morphological, molecular and genotypic characteristics of the studied field of interest. Aim: Analysis of the literature and comparative evaluation of publications to perform challenges and possibilities of texture analysis in bladder cancer. Materials and methods: We searched for scientific publications in the PubMed and Google Scholar information and analytical systems for 2016-2024 by keywords: «bladder cancer», «bladder cancer radiomics», «mri bladder cancer»». As a result, 40 articles were selected for analysis. Results: Our review demonstrates the methodology, challenges, opportunities and prospects of TA CT and MP imagesin bladder cancer.Numerous studies have demonstrated high accuracy of radiomics in local staging and estimation of tumor morphology, as well as in prediction of clinical outcomes. Conclusion: TA in controversial clinical cases is a useful way of increasing theinformationobtainable frommedical images. Further validation of these methodis required however.

Coda-derived source properties estimated using local earthquakes in the Sea of Marmara, Türkiye

Abstract. Accurate estimates of the moment magnitude of earthquakes that physically measure the earthquake source energy are crucial for improving our understanding of seismic hazard in regions prone to tectonic activity. To address this demand, a method involving coda wave modelling was employed to estimate the moment magnitudes of earthquakes in the Sea of Marmara, northwestern Türkiye. This approach enabled us to model the source displacement spectrum of 303 local earthquakes efficiently recorded at 49 regional seismic stations between 2018 and 2020 in the region. The coda wave traces of individual events were inverted across 12 frequency ranges between 0.3 and 16 Hz. The resultant coda-derived moment magnitudes were found to be in good accordance with the conventional local magnitude estimates. However, the notable move-out between local magnitude and coda-derived moment magnitude estimates for smaller earthquakes less than a magnitude of 3.5 likely occurs due to potential biases arising from incorrect assumptions for anelastic attenuation and/or the finite sampling intervals of seismic recordings. Scaling relations between the total radiated energy and seismic moment imply a non-self-similar behaviour for the earthquakes in the Sea of Marmara. Our findings suggest that larger earthquakes in the study area exhibit distinct rupture dynamics compared to smaller ones, resulting in a more efficient release of seismic energy. Hence, we introduce an empirical relationship obtained from the scatter between local magnitude and coda-derived moment magnitude estimates.

Local wavenumber imaging in anisotropic structures

Local wavenumber imaging has been proven effective for damage detection in thin-walled structures. Such structures are, however, often inherently anisotropic, posing serious challenges to the known algorithms of local wavenumber mapping. The use of local wavenumber mapping algorithm designed for isotropic, rather than anisotropic, structures results in processing artifacts that may prohibit correct detection and characterization of defects. Therefore, in this work, we propose an improved implementation of the local wavenumber estimation algorithm for anisotropic media (ALWE). The working principle and efficiency of the proposed algorithm are illustrated on datasets coming from numerical simulations and experimental testing on anisotropic carbon fiber reinforced polymer (CFRP) laminates. We demonstrate that the proposed algorithm successfully compensates for the processing artifacts and enhances the overall quality of the wavenumber maps facilitating unequivocal damage detection.

Assessing volatility persistence in fractional Heston models with self-exciting jumps

We derive a new fractional Heston model with self-exciting jumps. We study volatility persistence and demonstrate that the quadratic variation necessarily exhibits less memory than the integrated variance, which preserves the degree of long-memory of the instantaneous volatility. Focusing on realized volatility measures, we find that traditional long-memory estimators are dramatically downward biased, in particular for low-frequency intraday sampling. Conveniently, our Monte Carlo experiments reveal that some noise-robust local Whittle-type estimators offer good finite sample properties. We apply our theoretical results in a risk forecasting study and show that our frequency-domain forecasting procedure outperforms the traditional benchmark models.

Economic Valuation of Ecosystem Services of Coastal Area of Kinondoni District, Tanzania

This study investigates the often overlooked economic values of ecosystem services in the coastal area of Kinondoni District, Tanzania, in the context of spatial and temporal changes in land use and land cover (LULC). The primary objectives were to assess how ecosystem services and functions have been affected by LULC changes over a 30-year period, from 1993 to 2023. The study employs a benefit transfer method, integrating local and global estimations of ecosystem service value (ESV) with field survey, remote sensing and GIS techniques. The findings reveal that the annual changes in ESV during the study period are estimated at US$ 0.024 million and US$ 0.034 million using local and global coefficients, respectively. Over the three decades, there has been a significant annual loss of US$ 0.72 million locally and US$ 2.11 million globally, primarily due to the degradation of mangrove forests and bushland. The decline in ecosystem functions is largely driven by reductions in regulating services, which account for 54.1% of the total decrease in local valuations and 31.6% in global valuations. Supporting services also experienced substantial declines, with reductions of 39.7% in local valuations and 55.8% in global valuations. The study underscores the urgent need to review and enhance management and conservation strategies to ensure the sustainability of the coastal ecosystems in Kinondoni District, Tanzania.

Credibility-based multi-sensor fusion for non-Gaussian conversion error mitigation

In a complex environment, a multi-sensor fusion algorithm can compensate for the limitations of a single sensor’s performance. In a distributed fusion algorithm, sensors need to transmit local estimates to a central coordinate system, and the existence of coordinate transformation uncertainty can undermine the performance of data transmission. Therefore, this paper proposes a multi-sensor distributed fusion method based on trustworthiness. Firstly, considering the presence of non-Gaussian conversion errors, a credibility-based multi-sensor fusion framework is constructed. Secondly, to address the difficulty in estimating conversion errors when measurement errors follow a non-Gaussian distribution, an optimization model is constructed based on actual measurement information to estimate the distribution of non-Gaussian conversion errors. Then, in response to the non-linear and non-Gaussian characteristics of the target optimization function, a particle swarm optimization algorithm based on trustworthiness adaptive weights is proposed to estimate the coordinate transformation errors. Finally, given the inconsistency in local estimates due to missing sensor measurements or significant errors in a non-Gaussian complex environment, a maximum correntropy consensus algorithm is proposed to avoid the trustworthiness calculation being affected by the current measurement errors, thereby improving the accuracy of the global estimation.

Existence and stability of almost finite energy weak solutions to the quantum Euler-Maxwell system

In this paper we prove the existence of global in time, finite energy weak solutions to the quantum magnetohydrodynamics (QMHD) system, for a large class of initial data that are slightly more regular than being of finite energy. No restriction is given on their size or the uniform positivity of the mass density. The QMHD system is a well-established model in superconductivity due to Feynman, and is intimately related to a nonlinear Maxwell-Schrödinger (NLMS) system via the Madelung transformations. The lack of global well-posedness (GWP) results for the NLMS system in the energy norm provides an obstruction to stability of its solutions, and consequently to the use of approximation arguments to make rigorous the Madelung approach. We implement here a new strategy, that derives weak solutions to QMHD starting from weak solutions to NLMS, by exploiting its Duhamel formulation. This derivation is rigorously justified by means of suitable dispersive/smoothing estimates for almost finite energy weak solutions to NLMS. The corresponding weak solutions to QMHD satisfy a generalized irrotationality condition, that allows for the presence of non-trivial vorticity (e.g., vortex filaments) concentrated in the vacuum region. This is in sharp contrast with the Euler-Maxwell system where the dispersion is not able to deal with the vorticity transport, therefore almost GWP (for regular solutions that are small perturbations of constant states) holds only in a lifespan, reciprocal of the size of the initial vorticity. Moreover, we also prove a stability property in the energy norm of the weak solutions constructed by our approach. This result follows from new local smoothing estimates for NLMS that are also of independent interest. As a byproduct, we also show the stability for the electromagnetic Lorentz force.

Social determinants of health and newer glucose-lowering drugs adoption among US Medicare beneficiaries with type 2 diabetes.

Two classes of newer glucose-lowering drugs (GLDs), sodium-glucose cotransporter-2 inhibitors and glucagon-like peptide-1 receptor agonists, improve cardiovascular and renal outcomes among patients with type 2 diabetes (T2D). However, racial and ethnic minority groups carry higher cardiovascular risks but have lower access to newer GLDs. Contextual-level social determinants of health (SDOH) may be the underlying factor associated with newer GLD adoption. To identify the association between contextual-level SDOH and real-world adoption of newer GLDs among Medicare beneficiaries and to examine the nonstationarity in the associations. Data were from 15% random samples of January 2017 to December 2018 nationwide Medicare beneficiaries. We identified patients with T2D who did not use newer GLDs in the year before the index date-January 1, 2018-and followed the cohort for 1 year to record their status of initiating a newer GLD. We used a geographically weighted multivariable Poisson regression model to determine to what extent the SDOH-newer GLD initiation association (β coefficient) varied geographically. We identified 795,469 eligible Medicare beneficiaries with T2D during the study period from our dataset. Of the study cohort, mean age was 73.1 (SD = 10.5) years, 424,312 (53.3%) were female, 562,994 (70.8%) were non-Hispanic White, 96,891 (12.2%) were non-Hispanic Black, 84,744 (10.6%) were Hispanic, and 29,645 (3.7%) were Asian/Pacific Islander. Newer GLD initiation was negatively associated with the percentage of the population reporting non-Hispanic Black race, Hispanic ethnicity, and unemployment, as revealed by nonspatial regression analyses. The county-level median household income was also associated with higher newer GLD initiation. The spatial analysis presented distinct distributions of local parameter estimates for each contextual-level SDOH. We identified key contextual-level SDOH associated with real-world adoption of newer GLDs and explored their geographic variation through spatially explicit, data-driven analytical approaches. Identifying areas of strong association between SDOH and newer GLD initiation is crucial for policymakers to allocate resources and develop interventions that address structural inequities.

P021 Three-dimensional local shear-wave viscoelastographic estimation by system identification for prostate cancer localization

P021 Three-dimensional local shear-wave viscoelastographic estimation by system identification for prostate cancer localization

Light-duty gasoline vehicle emission deterioration insights from large-scale inspection/maintenance data: The synergistic impact of usage characteristics

Accurately estimating vehicle emissions is crucial for effective air quality management. As key data for emission inventory construction, emission factors (EFs) are influenced by vehicle usage characteristics and experience deterioration. Current deterioration models often employ single-factor approaches based on vehicle age or accumulated mileage, which fail to capture the effects of varying usage intensities within the same mileage or age intervals. This study addressed this limitation by developing a novel emission deterioration model that incorporates multi-dimensional usage characteristics and that utilizes a large-scale inspection and maintenance (I/M) dataset for light-duty gasoline vehicles (LDGVs). The modeling results reveal distinct deterioration patterns for different pollutants and highlight the synergistic effects of the usage duration and intensity: natural aging significantly impacts HC and NOx emissions, while CO emissions are more strongly affected by intensive use. Specifically, China V LDGVs that were driven 4 × 104 km/yr exhibited HC, CO, and NOx deterioration rates per mile that were approximately 4.1 % lower, 10.3 % higher, and 1.1 % higher, respectively, than those of vehicles driven 2 × 104 km/yr as the mileage increased from 5 × 104 km to 10 × 104 km. By leveraging timely emission data and explicitly accounting for usage intensity, this study corrected biases in local emission estimates by 5–85 % with respect to estimates from commonly used models. This framework enables the development of more effective control strategies and refinements to policy evaluations in megacities with I/M programs.

Ten-Year Outcome After Supracricoid Partial Laryngectomy in cT3M0 Laryngeal Squamous Cell Carcinoma-A STROBE Analysis.

The aim of this study was to document 10-year outcomes after supracricoid partial laryngectomy (SCPL) in selected cT3M0 laryngeal squamous cell carcinoma (SCC) patients. This real-life retrospective observational study analyzed an inception cohort of 168 patients with isolated, untreated, selected cT3M0 laryngeal SCC, that were consecutively managed by SCPL during the period 1973-2013, and followed up until death or for a minimum of 10 years in 92% of cases at a single French academic and tertiary referral care center. Prior induction chemotherapy, arytenoid cartilage removal, level II-IV neck dissection, and postoperative radiation therapy were performed on 148, 77, 136, and 27 patients, respectively. The main objective was to determine 10-year actuarial local control and laryngeal preservation estimates. Secondary objectives included 10-year actuarial survival and cause-of-death analysis, and assessment of correlations between endpoints and clinical variables. The significance threshold was set at p < 0.005. Ten-year actuarial local control, laryngeal preservation, and survival estimates were 90%, 85%, and 52%, respectively. Salvage treatment resulted in an overall 99% local control rate. Metachronous second primary cancer, intercurrent disease without evidence of SCC, SCPL-related death, and uncontrolled local recurrence accounted for 31%, 26%, 7%, and 2% of causes of death. On univariate analysis, overall local recurrence and laryngeal preservation rates varied significantly, from 5% to 54% and 90% to 46% when resection margins were R0 and R1, respectively. The present study highlighted successful 10-year outcomes after SCPL, providing further evidence in favor of its integration into the conservative armamentarium for endolaryngeal cT3 SCC. 4 Laryngoscope, 134:4557-4563, 2024.

Prevalence of problematic drug use in Martinique in 2006: The NEMO study

ObjectivesSubstance use disorders are of worldwide public health interest. Local estimates of problematic drug use provide useful indicators to regional public health agencies in developing prevention and treatment programs. The purpose of the current study was to estimate the prevalence of problematic drug use in Martinique. MethodsThe capture-recapture method was applied to a multisource data collection (eight specialized drug and two law enforcement sources) to provide an estimate of drug use (opiates, cocaine hydrochloride, crack (cocaine base), stimulants and/or hallucinogens). Data collection was organized over a period of six consecutive months (September 2005 to March 2006) and concerned all persons residing in Martinique longer than three months and who had consumed at least one of the studied drugs in the month prior to the study. ResultsWe identified 287 cases (86% male; mean age 36.1±9.6 years), 98% of whom had used crack. Comorbid use of illicit drugs other than alcohol and cannabis was 4%. Our study showed that patients with problematic drug use in Martinique is estimated to be 1.936 [95% CI: 964,2907] in a total population of 380.863 (INSEE, 1999). Prevalence rates were 5.0 per thousand among the global population and 7.7 per thousand in the adult population aged 15–64 years. ConclusionsOur study is the first to provide relevant data on the extent of problematic drug use in Martinique for health policies and decision-makers.