Local Estimates Research Articles

Local error estimates and post processing for the Galerkin BEM on polygons

In this paper we give local error estimates in Sobolev norms for the Galerkin method applied to strongly elliptic pseudodifferential equations on a polygon. By using the K-operator, an operator which averages the values of the Galerkin solution, we construct improved approximations.

Local Hamilton Type Gradient Estimates for Nonlinear Parabolic Equations on Riemannian Manifolds

In this paper, we present a new proof and attain some new local Hamilton type gradient estimates for positive solutions to the parabolic equation ut=ΔVup+aulogu+buon a complete noncompact Riemannian manifold with k-Bakry-Émery Ricci curvature bounded from below, where p, a and b are some given constants. As applications, related local Hamilton type gradient estimates, some parabolic type Liouville theorems and Harnack inequalities for porous media type equation and fast diffusion type equation are established. Some known results were generalized by our results.

Interacting Dark Energy after DESI Baryon Acoustic Oscillation Measurements

We investigate the implications of the baryon acoustic oscillations measurement released by the Dark Energy Spectroscopic Instrument for interacting dark energy (IDE) models characterized by an energy-momentum flow from dark matter to dark energy. By combining Planck-2018 and Dark Energy Spectroscopic Instrument data, we observe a preference for interactions, leading to a nonvanishing interaction rate ξ=−0.32−0.14+0.18, which results in a present-day expansion rate H0=70.8−1.7+1.4 km/s/Mpc, reducing the tension with the value provided by the SH0ES Collaboration to less than ∼1.3σ. The preference for interactions remains robust when including measurements of the expansion rate H(z) obtained from the relative ages of massive, early-time, and passively evolving galaxies, as well as when considering distance moduli measurements from Type Ia supernovae sourced from the Pantheon-plus catalog using the SH0ES Cepheid host distances as calibrators. Overall, the IDE framework provides an equally good, or better, explanation of both high- and low-redshift observations compared to the lambda cold dark matter model, while also yielding higher H0 values that align more closely with the local distance ladder estimates. However, a limitation of the IDE model is that it predicts lower Ωm and higher σ8 values, which may not be fully consistent with large-scale structure data at the level. Published by the American Physical Society 2024

Sequential fusion estimation for nonlinear systems under deceptive attacks

AbstractThis article deals with sequential fusion estimation for nonlinear systems under deceptive attacks, which may happen during transmissions of measurements and system states over communication networks. The estimator is developed by incorporating measurement fusion and local estimate fusion with attack detection. Moreover, a compensation strategy is designed to mitigate the impact of deceptive attacks on performance degradation. The proposed method may preserve the data integrity for accurate state estimation with deceptive attacks. Numerical simulation with the target tracking systems verifies the effectiveness of the proposed method.

On the calibration of multiscale geographically and temporally weighted regression models

Spatiotemporal analysis and modeling have long been key foci of geographical information science. In a recent paper, Wu et al. expanded the local spatial modeling technique of multiscale geographically weighted regression (MGWR) to incorporate a temporal component. This new model is named multiscale geographically and temporally weighted regression (MGTWR). Despite the utility of expanding MGWR to incorporate a temporal weighting function in addition to the existing spatial one, the approach developed by Wu et al. has two limitations: the bandwidth selection algorithm cannot guarantee an optimal result and no formulation for the effective number of parameters (ENPs) in the model is given. To address these issues, this paper describes a procedure to derive an optimal temporal and an optimal spatial bandwidth for MGTWR and also develops a formula for the ENPs in the model. The former ensures the reliability of the model outputs while the latter is essential for making reliable inferences from the local parameter estimates generated in the calibration of models by MGTWR. These advances in the MGTWR framework are demonstrated through applications to simulated and real-world data.

Interferometric Distributed Fiber Optic Vibration Sensor With Branching Sensing Optical Path Based on Time Delay Estimation for Disturbance Localization

Interferometric Distributed Fiber Optic Vibration Sensor With Branching Sensing Optical Path Based on Time Delay Estimation for Disturbance Localization

Comprehensive assessment of nonuniform image quality: Application to imaging near metal.

Comprehensive assessment of image quality requires accounting for spatial variations in (i) intensity artifact, (ii) geometric distortion, (iii) signal-to-noise ratio (SNR), and (iv) spatial resolution, among other factors. This work presents an ensemble of methods to meet this need, from phantom design to image analysis, and applies it to the scenario of imaging near metal. A modular phantom design employing a gyroid lattice is developed to enable the co-registered volumetric quantitation of image quality near a metallic hip implant. A method for measuring spatial resolution by means of local point spread function (PSF) estimation is presented and the relative fitness of gyroid and cubic lattices is examined. Intensity artifact, geometric distortion, and SNR maps are also computed. Results are demonstrated with 2D-FSE and MAVRIC-SL scan protocols on a 3T MRI scanner. The spatial resolution method demonstrates a worst-case error of 0.17 pixels for measuring in-plane blurring up to 3 pixels (full width at half maximum). The gyroid outperforms a cubic lattice design for the local PSF estimation task. The phantom supports four configurations toggling the presence/absence of both metal and structure with good spatial correspondence for co-registered analysis of the four quality factors. The marginal scan time to evaluate one scan protocol amounts to five repetitions. The phantom design can be fabricated in 2 days at negligible material cost. The phantom and associated analysis methods can elucidate complex image quality trade-offs involving intensity artifact, geometric distortion, SNR, and spatial resolution. The ensemble of methods is suitable for benchmarking imaging performance near metal.

Relating Rainfall Retrieval Parameters to Network and Environmental Features to Improve Rainfall Estimates from Commercial Microwave Links in the Tropics

Abstract Potentially, the greatest benefit of commercial microwave links (CMLs) as opportunistic rainfall sensors lies in regions that lack dedicated rainfall sensors, most notably low- and middle-income countries. However, current CML rainfall retrieval algorithms are predominantly tuned and applied to (European) CML networks in temperate or Mediterranean climates. This study investigates whether local quantitative precipitation estimates from CMLs in a tropical region, specifically Sri Lanka, can be improved by optimizing two dominant parameters in the rainfall retrieval algorithm RAINLINK, namely, the wet antenna attenuation correction factor Aa and the relative contribution of minimum and maximum received signal levels α. Using a grid search, based on 10 months of CML data from 22 link–gauge clusters consisting of 105 sublinks that lie within 1 km of a daily rain gauge, the optimal values of Aa and α are first derived for the entire country and compared to the default RAINLINK values. Subsequently, the CMLs are grouped by link length, frequency, climate zone, and daily rainfall depth classes, and Aa and α are derived for each of these classes. Calibrating parameters on all clusters across the country only leads to minor improvements. The actual optimal Aa and α values depend on the performance metric favored. Calibrating on network properties, particularly short link length and high-frequency classes, does significantly improve rainfall estimates. By relating the optimal Aa and α values to known network metadata, the results from this study are potentially applicable to other tropical CML networks that lack nearby reference rainfall data. Significance Statement The purpose of this study is to improve rainfall estimates from commercial microwave links in Sri Lanka by optimizing two important rainfall retrieval algorithm parameters. Our results show that relating the optimal parameter values to operating frequency and pathlength improves rainfall estimates more than applying a single optimal parameter set to the entire network. By relating the optimal parameter values to readily known network properties, we aim to make these results applicable to other tropical countries, particularly low- and middle-income countries, that lack adequate reference rainfall data to calibrate rainfall estimates from commercial microwave links on.

Magmatic processes associated with the 2020 eruption of Taal Volcano, Philippines, revealed by local seismic source estimates

Magmatic processes associated with the 2020 eruption of Taal Volcano, Philippines, revealed by local seismic source estimates

Improving Visual Place Recognition Based Robot Navigation by Verifying Localization Estimates

Improving Visual Place Recognition Based Robot Navigation by Verifying Localization Estimates

Metabolic Status Modulates Global and Local Brain Age Estimates in Overweight and Obese Adults

BackgroundAs people live longer, maintaining brain health becomes essential for extending healthspan and preserving independence. Brain degeneration and cognitive decline are major contributors to disability. This study investigates how metabolic health influences brain-age-gap-estimate (brainAGE), which measures the difference between neuroimaging-predicted brain age and chronological age. MethodsK-means clustering was applied to fasting metabolic markers including insulin, glucose, leptin, cortisol, triglycerides, high-density lipoprotein cholesterol and low-density lipoprotein cholesterol, steady-state-plasma glucose and of body mass index of 114 physically and cognitively healthy adults. The Homeostatic Model Assessment for Insulin Resistance served as a reference. T1-weighted brain MRIs were used to calculate voxel-level and global (G-brainAGE). Longitudinal data were available for 53 participants over a 3-year interval. ResultsK-mean clustering divided the sample into two groups: those with favorable (N=56) and suboptimal metabolic health (N=58). The suboptimal group showed signs of insulin resistance and dyslipidemia (PFDR<0.05) and had older G-brainAGE and L-brainAGE, with deviations most prominent in cerebellar, ventromedial prefrontal, and medial temporal regions (PFWE<0.05). Longitudinal analysis revealed group differences but no significant time or interaction effects on brainAGE measures. ConclusionsSuboptimal metabolic status is linked to accelerated brain aging, particularly in brain regions rich in insulin receptors. These findings highlight the importance of metabolic health in maintaining brain function and suggest that promoting metabolic well-being may help extend healthspan.

The Support Behavior of the Solution to the Cauchy Problem for Higher Order Weighted Parabolic Equations

In this paper we study the finite speed of propagation property to the Cauchy problem for weighted higher order degenerate parabolic equations. We prove that if initial data is compactly support in some fixed ball, then so does the solution for all time. Because we are considering exponentially growing weights, the size of the support should expand more slowly over time than in the non-weighted case. We prove that for a large time the support of the solution expand with logarithmic rate. That estimate of support meets with known estimate for second order parabolic equations. The main tool of the proof is based on local energy estimates on annuli which allows us to consider even nonpower character of weights. It works even in cases when the weighted Gagliardo-Nirenberg inequality does not occur. Early that approach was utilized by D. Andreucci and by author for equations in domains with noncomact boundaries and for higher order parabolic equations including the thin film equation.

Deep neural network-based feature selection with local false discovery rate estimation

Deep neural network-based feature selection with local false discovery rate estimation

EHFusion: an efficient heterogeneous fusion model for group-based 3D human pose estimation

AbstractStimulated by its important applications in animation, gaming, virtual reality, augmented reality, and healthcare, 3D human pose estimation has received considerable attention in recent years. To improve the accuracy of 3D human pose estimation, most approaches have converted this challenging task into a local pose estimation problem by dividing the body joints of the human body into different groups based on the human body topology. The body joint features of different groups are then fused to predict the overall pose of the whole body, which requires a joint feature fusion scheme. Nevertheless, the joint feature fusion schemes adopted in existing methods involve the learning of extensive parameters and hence are computationally very expensive. This paper reports a new topology-based grouped method ‘EHFusion’ for 3D human pose estimation, which involves a heterogeneous feature fusion (HFF) module that integrates grouped pose features. The HFF module reduces the computational complexity of the model while achieving promising accuracy. Moreover, we introduce motion amplitude information and a camera intrinsic embedding module to provide better global information and 2D-to-3D conversion knowledge, thereby improving the overall robustness and accuracy of the method. In contrast to previous methods, the proposed new network can be trained end-to-end in one single stage. Experimental results not only demonstrate the advantageous trade-offs between estimation accuracy and computational complexity achieved by our method but also showcase the competitive performance in comparison with various existing state-of-the-art methods (e.g., transformer-based) when evaluated on two public datasets, Human3.6M and HumanEva. The data and code are available at doi:10.5281/zenodo.11113132

Fast and Globally Consistent Normal Orientation based on the Winding Number Normal Consistency

Estimating consistently oriented normals for point clouds enables a number of important applications in computer graphics such as surface reconstruction. While local normal estimation is possible with simple techniques like principal component analysis (PCA), orienting these normals to be globally consistent has been a notoriously difficult problem. Some recent methods exploit various properties of the winding number formula to achieve global consistency with state-of-the-art performance. Despite their exciting progress, these algorithms either have high space/time complexity, or do not produce accurate and consistently oriented normals for imperfect data. In this paper, we propose a novel property from the winding number formula, termed Winding Number Normal Consistency (WNNC ), to tackle this problem. The derived property is based on the simple observation that the normals (negative gradients) sampled from the winding number field should be codirectional to the normals used to compute the winding number field. Since the WNNC property itself does not resolve the inside/outside orientation ambiguity, we further propose to incorporate an objective function from Parametric Gauss Reconstruction (PGR). We propose to iteratively update normals by alternating between WNNC-based normal updates and PGR-based gradient descents, which leads to an embarrassingly simple yet effective iterative algorithm that allows fast and high-quality convergence to a globally consistent normal vector field. Furthermore, our proposed algorithm only involves repeatedly evaluating the winding number formula and its derivatives, which can be accelerated and parallelized using a treecode-based approximation algorithm due to their special structures. Exploiting this fact, we implement a GPU-accelerated treecode-based solver. Our GPU (and even CPU) implementation can be significantly faster than the recent state-of-the-art methods for normal orientation from raw points. Our code is integrated with the popular PyTorch framework to facilitate further research into winding numbers, and is publicly available at https://jsnln.github.io/wnnc/index.html.

Signed integer-valued autoregressive model with time-varying coefficients

An integer time series is a sequence of discrete integers arranged chronologically to represent a specific event or phenomenon. It may include negative integers, and its behavior can be influenced by variations in covariates. To address these complexities, this paper introduces a p-order signed integer-valued autoregressive model with time-varying coefficients. Considering the presence of zero-inflated phenomena, we specifically employ the zero-inflated Skellam distribution. To estimate the unknown parameters and nonparametric functions in our proposed model, we adopt a two-step iterative process that combines local linear estimation with either conditional least squares or conditional maximum likelihood. Through a comprehensive simulation study, we evaluate the performance of our estimation method and demonstrate the usefulness of the proposed model using a real-life dataset.

GRADIENT ESTIMATES FOR POSITIVE EIGENFUNCTIONS OF THE $\mathcal {L}$ -OPERATOR ON CONFORMAL SOLITONS AND THEIR APPLICATIONS

Abstract We prove a local gradient estimate for positive eigenfunctions of the $\mathcal {L}$ -operator on conformal solitons given by a general conformal vector field. As an application, we obtain a Liouville type theorem for $\mathcal {L} u=0$ , which improves the one of Li and Sun [‘Gradient estimate for the positive solutions of $\mathcal Lu = 0$ and $\mathcal Lu ={\partial u}/{\partial t}$ on conformal solitons’, Acta Math. Sin. (Engl. Ser.)37(11) (2021), 1768–1782]. We also consider applications where manifolds are special conformal solitons and obtain a better Liouville type theorem in the case of self-shrinkers.

Does economic policy uncertainty matter to corporate default probability? findings from theoretic analyses and China’s listed firms

This paper conducts a theoretical–empirical study to investigate the nexus between economic policy uncertainty (EPU) and corporate default probability (CDP) and documents a significant and positive impact of EPU on CDP, which is validated through rigorous robustness tests and local project estimations. The study also reports that the increasing term structure of bond maturity aggravates the impact of EPU on CDP systematically. Our findings pronounce that EPU brings about the erosion of firm financing capacity, management quality deterioration, lowered stock liquidity, and corporate sentimental depression, providing an effective conducting mechanism to breed an increase in CDP. Additionally, state ownership, high technology, and internationalization curtail the CDP-increasing effect of EPU, and the same in the manufacturing sector. Whereas, this effect is intensified in non-state-owned, low-tech, service, and non-internationalized enterprises. We also highlight that EPU can robustly predict in the subsequent 2 years. This study suggests that the corporate financial position well reflects EPU and the relevant stakeholders, both governments and firms, may improve financial risk management by considering EPU and the attribute of its impacting CDP.

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.