Gradient Approximation Research Articles

Coordinate-Independent 3-D Ultrasound Principal Stretch and Direction Imaging.

In clinical ultrasound, current 2-D strain imaging faces challenges in quantifying three orthogonal normal strain components. This requires separate image acquisitions based on the pixel-dependent cardiac coordinate system, leading to additional computations and estimation discrepancies due to probe orientation. Most systems lack shear strain information, as displaying all components is challenging to interpret. This paper presents a 3-D high-spatial-resolution, coordinate-independent strain imaging approach based on principal stretch and axis estimation. All strain components are transformed into three principal stretches along three normal principal axes, enabling direct visualization of the primary deformation. We devised an efficient 3-D speckle tracking method with tilt filtering, incorporating randomized searching in a two-pass tracking framework and rotating the phase of the 3-D correlation function for robust filtering. The proposed speckle tracking approach significantly improves estimates of displacement gradients related to the axial displacement component. Non-axial displacement gradient estimates are enhanced using a correlation-weighted least-squares method constrained by tissue incompressibility. Simulated and in vivo canine cardiac datasets were evaluated to estimate Lagrangian strains from end-diastole to end-systole. The proposed speckle tracking method improves displacement estimation by a factor of 4.3 to 10.5 over conventional 1-pass processing. Maximum principal axis/direction imaging enables better detection of local disease regions than conventional strain imaging. Coordinate-independent tracking can identify myocardial abnormalities with high accuracy. This study offers enhanced accuracy and robustness in strain imaging compared to current methods.

Predictive slope stability early warning model based on CatBoost

A model for predicting slope stability is developed using Categorical Boosting (CatBoost), which incorporates 6 slope features to characterize the state of slope stability. The model is trained using a symmetric tree as the base model, utilizing ordered boosting to replace gradient estimation, which enhances prediction accuracy. Comparative models including Support Vector Machine (SVM), Light Gradient Boosting Machine (LGBM), Random Forest (RF), and Logistic Regression (LR) were introduced. Five performance evaluation metrics are utilized to assess the predictive capabilities of the CatBoost model. Based on CatBoost model, the predicted probability of slope instability is calculated, and the early warning model of slope instability is further established. The results suggest that the CatBoost model demonstrates a 6.25% disparity in accuracy between the training and testing sets, achieving a precision of 100% and an Area Under Curve (AUC) value of 0.95. This indicates a high level of predictive accuracy and robust ordering capabilities, effectively mitigating the problem of overfitting. The slope instability warning model offers reasonable classifications for warning levels, providing valuable insights for both research and practical applications in the prediction of slope stability and instability warning.

Theoretical aspects of structure, electronic, optical and elastic properties of Ca(1-x)CxSe mixed alloys in binary and ternary phases

The structural, optoelectronic, and elastic properties of Carbon doped Calcium Selenide binary and ternary semiconductor alloys with the general form of Ca(1-x)CxSe, 0 ≤ x ≤ 1 in B1 and B3 phases have been scrutinized adopting augmented plane wave plus local orbital methods within density functional theory applying different approximations like the Local density approximation (LDA), Wu-Cohen-Generalized Gradients Approximation (WC-GGA) and modified Becke-Johnson (mBJ). Structural properties summarize the crystal structure, relevant atomic positions, lattice constant, Bulk modulus B0, minimum energy E0, and minimum volume V0. Elastic constants confirm the structure stability of the B1 and B3 phases. The band gap was modified from a wider for appropriate optoelectronic devices application to narrow that enhanced the range of applicability of these binary and ternary semiconductor compounds for optoelectronic device applications. Whereas optical properties which include the study of zero frequency limit of static dielectric constant ε0(ω) with its real and imaginary parts, static refractive index n(0), optical reflectivity R(ω), optical absorption coefficient α(ω), optical conductivity σ(ω), and loss function L(ω) studied comprehensively to get real electrical and optical properties of these materials and give semiconductor market best alternative candidate which shows its effectiveness in the visible, ultraviolet and infrared region of the electromagnetic spectrum. Obtained results compared together and with the available experimental along with theoretical work on these binary and ternary Carbon-doped Alkaline earth Selenide.

Optimal error bounds for the two-point flux approximation finite volume scheme

We consider a finite volume scheme with two-point flux approximation (TPFA) to approximate a Laplace problem when the solution exhibits no more regularity than belonging to H 0 1 ( Ω ) H^1_0(\Omega ) . We define an error between the approximate solution and the exact one, involving their difference and the difference of normal gradients to the faces of the mesh. We prove that this error behaves as the sum of an interpolation error and a conformity error. As a consequence, some error bounds, depending on the regularity of the continuous solution, can be obtained for both the approximate solution and an approximate gradient post-processed from this approximate solution. A numerical example illustrates the error estimate in the context of a solution with minimal regularity. This result is extended to evolution problems discretized via the implicit Euler scheme in an appendix.

A THEORETICAL STUDY OF THE PHYSICAL PROPERTIES OF HEXAGONAL GALLIUM NITRATE USING DENSITY FUNCTIONAL THEORY

First-principles calculations based on density functional theory (DFT) have been used to investigate structural, electronic, optical and thermodynamic aspects of the α-GaN crystal. Based on local density approximations (LDA), Generalized gradient approximation (GGA) and meta-generalized gradient approximation (m-GGA) functional methods, the band gap energies of α-GaN crystals have been estimated as 1.962 eV, 2.069 eV and 2.354 eV. The band gap energies that are presented in these studies are in accordance with the ones from the other experimental and theoretical studies. Besides, our findings give us knowledge about the electronic and optical properties of α-GaN crystal. The band gap energies in the α-GaN crystal are the key factors that define its electrical and optical characteristics. They are the energy range in which the electrons can be exited from the valence band to the conduction band, which in turn affects the material's conductivity and the ability of the material to absorb and emit light. The approximate of our results with the previous researches indicates the reliability of our findings and thus increases our knowledge of α-GaN's electronic and optical phenomena. The orbital characteristics of the Ga and N atoms were found by simulating the density of state and the partial density of state for α-GaN. Besides the analysis of the band structure, density of states and optical properties of the compound we also included. The results show that α-GaN has a direct bandgap, which is at the G point in the Brillouin zone. This is the reason for its great potential for the development of optoelectronic devices. Also, we use the three approximations that are given earlier to find the optical characteristics (the absorption coefficient) of the compound. In addition to that, the thermodynamic properties that can be calculated like Debye temperature, enthalpy, free energy, entropy and heat capacity enable us to understand the thermal behavior of the compound better. The heat capacity of α-GaN is detected to be 17.3 Jmole-1K-1, with a Debye temperature of 824.6K. This research will offer a detailed interpretation of α- G-N, covering all its basic properties and the possible applications in optoelectronic and electronic devices. The results of this study are very important and the new technologies that will be developed based on the α-GaN research will be very beneficial.

DFT Analysis of Transition Metal (TM) Substitutions on Cu‐Based Chalcogenides: Structural, Electronic, and Thermophysical Properties for Interface Thermal Performance and Energy

ABSTRACTThe current investigation employs first‐principles DFT (density functional theory) calculations to examine the influence of transition metal replacements on the structural, thermodynamic, and thermoelectric properties of Cu‐based chalcogenides TMCu3Se4 (TM = Nb/Ta/V). The PBE‐generalized gradient approximation (GGA) model is utilized to compute the fundamental properties of Cu‐based chalcogenides under study. A thorough examination of the energy band structures indicates that these chalcogenides are semiconductor compounds with indirect energy bandgaps. We can infer from the calculated energy band structures that the bandgap values are 1.67, 1.77, and 1.05 eV for NbCu3Se4, TaCu3Se4, and VCu3Se4, respectively. The values for NbCu3Se4, TaCu3Se4, and VCu3Se4 are 0.661, 0.998, and 0.996, respectively. These values make them highly appropriate for usage in thermoelectric (TE) devices. The thermoelectric characteristics of pyrochlore oxides TMCu3Se4 (TM = Nb/Ta/V) suggest that these materials have promising potential for energy‐related applications. The analyzed thermodynamic properties demonstrate that the Cu0based chalcogenide materials TMCu3Se4 (TM = Nb/Ta/V) exhibit a notable level of thermal stability.

Comparison of Echocardiographically-Calculated Fontan Fenestration Gradient and Catheter-Based Measurement.

Patients born with single ventricle anatomy typically undergo surgical palliation in three stages, culminating in the Fontan procedure. Assessment of flow across a Fontan fenestration by Doppler ultrasound theoretically allows for non-invasive estimation of the transpulmonary gradient (TPG). Our objective was to determine the relationship between Doppler-derived mean fenestration gradient (mFG) and direct catheter-based measurements of TPG in patients with fenestrated Fontans. We performed a single-center retrospective cohort study of 59 patients with fenestrated Fontans completed between 2000 and 2022. The primary outcome was catheter-based measurement of TPG and the primary predictor was mFG from echo performed within 6 months of the catheterization. Linear regression and R2 were used to determine the relationship between predictors and outcomes. Catheter-based measurements of TPG and mFG were weakly correlated (R2 = 0.382, p < 0.001); the regression coefficient was 0.550, with a standard error of 0.09 for every increase in mFG (Cath TPG = 0.55 [mFG] + 1.92). mFG had a slightly better predictive relationship with cath-derived TPG in patients with systemic left ventricles with R2 of 0.47, p < 0.004. mFG accounts for approximately 38% of the variance in catheter-derived TPG. Although mFG is non-invasive and intuitive, mFG in Fontan patients should be interpreted with caution and direct measurement by cardiac catheterization should be considered.

Li-Yau type estimation of a semilinear parabolic system along geometric flow

This article provides a Li–Yau-type gradient estimate for a semilinear weighted parabolic system of semilinear equations along an abstract geometric flow on a smooth measure space. A Harnack-type inequality on the system is also derived at the end.

Integrating Kalman filter noise residue into U-Net for robust image denoising: the KU-Net model

In low-level image processing, where the main goal is to reconstruct a clean image from a noise-corrupted version, image denoising continues to be a critical challenge. Although recent developments have led to the introduction of complex architectures to improve denoising performance, these models frequently have more parameters and higher computational demands. Here, we propose a new, simplified architecture called KU-Net, which is intended to achieve better denoising performance while requiring less complexity. KU-Net is an extension of the basic U-Net architecture that incorporates gradient information and noise residue from a Kalman filter. The network’s ability to learn is improved by this deliberate incorporation, which also helps it better preserve minute details in the denoised images. Without using Image augmentation, the proposed model is trained on a limited dataset to show its resilience in restricted training settings. Three essential inputs are processed by the architecture: gradient estimations, the predicted noisy image, and the original noisy grey image. These inputs work together to steer the U-Net’s encoding and decoding stages to generate high-quality denoised outputs. According to our experimental results, KU-Net performs better than traditional models, as demonstrated by its superiority on common metrics like the Structural Similarity Index (SSIM) and Peak Signal-to-Noise Ratio (PSNR). KU-Net notably attains a PSNR of 26.60 dB at a noise level of 50, highlighting its efficacy and potential for more widespread use in image denoising.

Sharp Trace and Korn Inequalities for Differential Operators

AbstractWe establish sharp trace and Korn-type inequalities that involve vectorial differential operators, the focus being on situations where global singular integral estimates are not available. Starting from a novel approach to sharp Besov boundary traces by Riesz potentials and oscillations that equally applies to $$p=1$$ p = 1 , a case difficult to be handled by harmonic analysis techniques, we then classify boundary trace- and Korn-type inequalities. For $$p=1$$ p = 1 and so despite the failure of the Calderón-Zygmund theory, we prove that sharp trace estimates can be systematically reduced to full k-th order gradient estimates. Moreover, for $$1&lt;p&lt;\infty $$ 1 &lt; p &lt; ∞ , where sharp trace estimates yield Korn-type inequalities on smooth domains, we show for the basically optimal class of John domains that Korn-type inequalities persist – even though the reduction to global Calderón-Zygmund estimates by extension operators might not be possible.

Gradient estimates for unbounded Laplacians with ellipticity condition on graphs

In this article, we prove various gradient estimates for unbounded graph Laplacians which satisfy the ellipticity condition. Unlike common assumptions for unbounded Laplacians, i.e. completeness and non-degenerate measure, the ellipticity condition is purely local that is easy to verify on a graph. First, we establish an equivalent semigroup property, namely the gradient estimate of exponential curvature-dimension inequality, which is a modification of the curvature-dimension inequality and can be viewed as a notion of curvature on graphs. Additionally, we use the semigroup method to prove the Li-Yau inequalities and the Hamilton inequality for unbounded Laplacians on graphs with the ellipticity condition.

Agreement of echocardiographic and catheterization-based methods of transpulmonary pressure gradient measurement in dogs

Introduction/ObjectivesDoppler echocardiographic estimation of transpulmonary pressure gradient (PG) is widely used to determine severity of pulmonary valve stenosis and indication for transcatheter intervention. The objective of this study was to describe agreement between Doppler echocardiographic methods of transpulmonary PG estimation and direct peak-to-peak pressure gradient at catheterization (PGcath) in dogs. We hypothesized that with reference to PGcath, mean echocardiographic PG (PGecho-mean) would have less bias than peak modal instantaneous echocardiographic PG (PGecho-peak). AnimalsClient-owned dogs with congenital pulmonary valve stenosis that underwent balloon pulmonary valvuloplasty at one of two veterinary teaching hospitals between June 2012 and May 2022 were included in this study. Materials and MethodsCases that underwent transthoracic echocardiography and subsequent balloon pulmonary valvuloplasty separated by 30 or fewer days were retrospectively identified. For each echocardiogram, average PGecho-mean (mmHg) and average PGecho-peak (mmHg) were calculated from stored spectral Doppler recordings. Peak right ventricular-to-peak pulmonary artery PG data (mmHg) were obtained from catheterization reports. Bland–Altman analysis was used to assess agreement between echocardiographic and catheterization data. ResultsData from 209 dogs (n = 215 instances) were evaluated. Proportional bias, greater at higher gradients, was observed for PGecho-mean versus PGcath (P<0.001). A constant bias of −38.12 mmHg was observed for PGecho-peak versus PGcath (P=0.62). Bias for both echocardiographic variables had wide limits of agreement that increased with PG. ConclusionsPGecho-mean and PGecho-peak underestimated and overestimated PGcath, respectively, preventing their interchangeability with PGcath.

Generalized likelihood ratio method for stochastic models with uniform random numbers as inputs

We propose a new unbiased stochastic gradient estimator for a family of stochastic models driven by uniform random numbers as inputs. Dropping the requirement that the tails of the density of the input random variables decay smoothly, the estimator extends the applicability of the generalized likelihood ratio (GLR) method. We demonstrate the new estimator for several general classes of input random variates, including independent inverse transform random variates and dependent input random variables governed by an Archimedean copula. We show how the new estimator works in settings such as density estimation, and we illustrate applications to credit risk derivatives. Numerical experiments substantiate broad applicability and flexibility in dealing with discontinuities in the sample performance.

Lipschitz regularity for Poisson equations involving measures supported on C 1,Dini interfaces

We prove optimal Lipschitz regularity of solutions to Poisson’s equation with measure data supported on a C 1 , Dini interface and with C 0 , Dini density. We achieve this by deriving pointwise gradient estimates on the interface, further showing the piecewise differentiability of solutions up to this surface. Our approach relies on perturbation arguments and estimates for the Green’s function of the Laplacian. Additionally, we provide sharp counterexamples highlighting the minimality of our assumptions.

An optimization-based equilibrium measure describes fixed points of non-equilibrium dynamics: application to edge of chaos

Abstract Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient of a potential. These features make analytic studies very challenging. The common tool is the path integral approach or dynamical mean-field theory, but the drawback is that one has to solve the integro-differential or dynamical mean-field equations, which is computationally expensive and has no closed form solutions in general. From the aspect of associated Fokker-Planck equation, the steady state solution is generally unknown. Here, we treat searching for the steady states as an optimization problem, and construct an approximate potential related to the speed of the dynamics, and find that searching for the ground state of this potential is equivalent to running an approximate stochastic gradient dynamics or Langevin dynamics. Only in the zero temperature limit, the distribution of the original steady states can be achieved. The resultant stationary state of the dynamics follows exactly the canonical Boltzmann measure. Within this framework, the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method, which leads naturally to order parameters for the non-equilibrium steady states. Our theory reproduces the well-known result of edge-of-chaos, and further the order parameters characterizing the continuous transition are derived, and the order parameters are explained as fluctuations and responses of the steady states. Our method thus opens the door to analytically study the steady state landscape of the deterministic or stochastic high dimensional dynamics.

Geophysical modeling of the middle Bogotá River Basin with support from interpretation of electrical resistivity, gravity, seismic and borehole data to evaluate potential deep aquifers

The main objective of this research was to develop a geological and geophysical modeling to infer the geometry and thickness in the sedimentary sequence of the middle basin of the Bogotá River with emphasis on the Guadalupe Group, reconstructing the stratigraphic sequence, structural setting, hydrogeological modeling, and potential geothermal uses. Various geophysical methods were applied, including vertical electrical soundings (VES), and magneto telluric soundings (MT-VES), whose results were complemented with the interpretation of seismic lines, regional and local gravity anomaly maps, and borehole data, among others, which allowed to model the subsurface from the surface to depths beyond 3000 meters, with emphasis on the interval between 500m to 1000m depth. Integrated models were developed from interpretations of electrical resistivity data, gravity and magnetic data, reflection seismic and borehole data. Based on the results, potential deep aquifers have been proposed to be confirmed by drilling. These deep aquifers can contribute to satisfy the need for water, which historically has been explored and overexploited from shallower aquifers in this sector of the basin. A recommendation was also made to consider the potential of low enthalpy thermal energy for agro-industrial purposes associated with groundwater’s temperature at the depth of this research. As a result, the modeled sedimentary sequence is characterized by a thick quaternary overburden overlying an intensively folded and faulted Neogene, Paleogene, and upper Cretaceous formations, mainly composed of siltstone, sandstones, and shale sequences of fluvial and marine environment, including facies of marine regressions and transgressions near the coastline. The penetration obtained allows establishing a high hydrogeological potential in the first 2000m depth, especially associated with the Guadalupe group, where the Labor and Tierna and Arenisca Dura formations have the highest hydrogeological potential. In addition, the preliminary estimation of thermal gradients suggest that low enthalpy geothermal energy potential is feasible to be used for the agro-industrial demand of energy of the study area.

Analysis of harmonic functions under lower bounds of N-weighted Ricci curvature with ε-range

The behavior of harmonic functions on Riemannian manifolds under lower bounds of the Ricci curvature has been studied from both analytic and geometric viewpoints. For example, some Liouville type theorems are obtained under lower bounds of the Ricci curvature. Recently, those results are generalized under lower bounds of the N-weighted Ricci curvature RicψN with N∈[n,∞]. In this paper, we present a Liouville type theorem for harmonic functions of sublinear growth and a gradient estimate of harmonic functions on weighted Riemannian manifolds under weaker lower bounds of RicψN with N<0. We also prove an Lp-Liouville theorem under lower bounds of RicψN with N∈[n,∞] in a different way from previous studies. Our results are obtained as a consequence of an argument under lower bounds of RicψN with ε-range, which is a unification of constant and variable curvature bounds. Among various methods considered for the analysis of harmonic functions, this paper focuses on methods using the Moser's iteration procedure.

Random Learning Leads to Faster Convergence in ‘Model‐Free’ ILC: With Application to MIMO Feedforward in Industrial Printing

ABSTRACTModel‐free iterative learning control (ILC) can lead to high performance by attenuating repeating disturbances completely, using dedicated experiments on the real system to replace the traditional model. The aim of this paper is to develop a fast data‐driven method for MIMO ILC that uses random learning in the form of efficient unbiased gradient estimates. This is achieved by developing a stochastic conjugate gradient algorithm, in which the search direction and optimal step size are generated using dedicated experiments. The approach is applied to MIMO automated feedforward tuning. Simulation and experimental results show that the method is superior to earlier stochastic and deterministic methods.

Gradient Estimates for Δpu + Δqu + a|u|s−1u + b|u|l−1u = 0 on a Complete Riemannian Manifold and Applications

Gradient Estimates for Δpu + Δqu + a|u|s−1u + b|u|l−1u = 0 on a Complete Riemannian Manifold and Applications

Rectified Binary Network for Single-Image Super-Resolution.

Binary neural network (BNN) is an effective approach to reduce the memory usage and the computational complexity of full-precision convolutional neural networks (CNNs), which has been widely used in the field of deep learning. However, there are different properties between BNNs and real-valued models, making it difficult to draw on the experience of CNN composition to develop BNN. In this article, we study the application of binary network to the single-image super-resolution (SISR) task in which the network is trained for restoring original high-resolution (HR) images. Generally, the distribution of features in the network for SISR is more complex than those in recognition models for preserving the abundant image information, e.g., texture, color, and details. To enhance the representation ability of BNN, we explore a novel activation-rectified inference (ARI) module that achieves a more complete representation of features by combining observations from different quantitative perspectives. The activations are divided into several parts with different quantification intervals and are inferred independently. This allows the binary activations to retain more image detail and yield finer inference. In addition, we further propose an adaptive approximation estimator (AAE) for gradually learning the accurate gradient estimation interval in each layer to alleviate the optimization difficulty. Experiments conducted on several benchmarks show that our approach is able to learn a binary SISR model with superior performance over the state-of-the-art methods. The code will be released at https://github.com/jwxintt/Rectified-BSR.