Function approximation via the subsampled Poincaré inequality

Function approximation and recovery via some sampled data have long been studied in a wide array of applied mathematics and statistics fields. Analytic tools, such as the Poincaré inequality, have been handy for estimating the approximation errors in different scales. The purpose of this paper is to study a generalized Poincaré inequality, where the measurement function is of subsampled type, with a small but non-zero lengthscale that will be made precise. Our analysis identifies this inequality as a basic tool for function recovery problems. We discuss and demonstrate the optimality of the inequality concerning the subsampled lengthscale, connecting it to existing results in the literature. In application to function approximation problems, the approximation accuracy using different basis functions and under different regularity assumptions is established by using the subsampled Poincaré inequality. We observe that the error bound blows up as the subsampled lengthscale approaches zero, due to the fact that the underlying function is not regular enough to have well-defined pointwise values. A weighted version of the Poincaré inequality is proposed to address this problem; its optimality is also discussed

Function approximation via the subsampled Poincaré inequality

Function approximation and recovery via some sampled data have long been studied in a wide array of applied mathematics and statistics fields. Analytic tools, such as the Poincaré inequality, have been handy for estimating the approximation errors in different scales. The purpose of this paper is to study a generalized Poincaré inequality, where the measurement function is of subsampled type, with a small but non-zero lengthscale that will be made precise. Our analysis identifies this inequality as a basic tool for function recovery problems. We discuss and demonstrate the optimality of the inequality concerning the subsampled lengthscale, connecting it to existing results in the literature. In application to function approximation problems, the approximation accuracy using different basis functions and under different regularity assumptions is established by using the subsampled Poincaré inequality. We observe that the error bound blows up as the subsampled lengthscale approaches zero, due to the fact that the underlying function is not regular enough to have well-defined pointwise values. A weighted version of the Poincaré inequality is proposed to address this problem; its optimality is also discussed

Satellite image resolution enhancement using discrete wavelet transform and new edge-directed interpolation

An image resolution enhancement approach based on discrete wavelet transform (DWT) and new edge-directed interpolation (NEDI) for degraded satellite images by geometric distortion to correct the errors in image geometry and recover the edge details of directional high-frequency subbands is proposed. The observed image is decomposed into four frequency subbands through DWT, and then the three high-frequency subbands and the observed image are processed with NEDI. To better preserve the edges and remove potential noise in the estimated high-frequency subbands, an adaptive threshold is applied to process the estimated wavelet coefficients. Finally, the enhanced image is reconstructed by applying inverse DWT. Four criteria are introduced, aiming to better assess the overall performance of the proposed approach for different types of satellite images. A public satellite images data set is selected for the validation purpose. The visual and quantitative results show the superiority of the proposed approach over the conventional and state-of-the-art image resolution enhancement

Residual Stress State in Single-Edge Notched Tension Specimen Caused by the Local Compression Technique

Three-dimensional (3D) finite element analyses (FEA) are performed to simulate the local compression (LC) technique on the clamped single-edge notched tension (SE(T)) specimens. The analysis includes three types of indenters, which are single pair of cylinder indenters (SPCI), double pairs of cylinder indenters (DPCI) and single pair of ring indenters (SPRI). The distribution of the residual stress in the crack opening direction in the uncracked ligament of the specimen is evaluated. The outcome of this study can facilitate the use of LC technique on SE(T) specimens

Predictive coupled-cluster isomer orderings for some Sin{}_nCm{}_m (m,n≤12m, n\le 12) clusters; A pragmatic comparison between DFT and complete basis limit coupled-cluster benchmarks

The accurate determination of the preferred ${\rm Si}_{12}{\rm C}_{12}$ isomer is important to guide experimental efforts directed towards synthesizing SiC nano-wires and related polymer structures which are anticipated to be highly efficient exciton materials for opto-electronic devices. In order to definitively identify preferred isomeric structures for silicon carbon nano-clusters, highly accurate geometries, energies and harmonic zero point energies have been computed using coupled-cluster theory with systematic extrapolation to the complete basis limit for set of silicon carbon clusters ranging in size from SiC$_3$ to ${\rm Si}_{12}{\rm C}_{12}$. It is found that post-MBPT(2) correlation energy plays a significant role in obtaining converged relative isomer energies, suggesting that predictions using low rung density functional methods will not have adequate accuracy. Utilizing the best composite coupled-cluster energy that is still computationally feasible, entailing a 3-4 SCF and CCSD extrapolation with triple-$\zeta$ (T) correlation, the {\it closo} ${\rm Si}_{12}{\rm C}_{12}$ isomer is identified to be the preferred isomer in support of previous calculations [J. Chem. Phys. 2015, 142, 034303]. Additionally we have investigated more pragmatic approaches to obtaining accurate silicon carbide isomer energies, including the use of frozen natural orbital coupled-cluster theory and several rungs of standard and double-hybrid density functional theory. Frozen natural orbitals as a way to compute post MBPT(2) correlation energy is found to be an excellent balance between efficiency and accuracy

What about the partner? -factors associated with patient-perceived partner dyspareunia in men with Peyronie\u27s disease

Background: Limited data are available on how partners of men with Peyronie\u27s disease (PD) are affected by the disease. We sought to characterize PD patients whose curvatures result in pain for their partners during penetrative intercourse. Methods: We queried a database of all men undergoing initial evaluation for PD at a single clinic between March 2014 and June 2016. Patients were administered a questionnaire regarding sexual health concerns with domains including erectile dysfunction, ejaculatory dysfunction, libido, and penile curvature. In the penile curvature section, patients were specifically asked: Does the curvature cause your partner any pain during penetrative intercourse? (Y/N). Patients\u27 partners were not directly evaluated for conditions associated with dyspareunia. Additionally, patients interested in treatment for PD underwent objective curve assessment after intracavernosal injection of erectogenic medications along with penile duplex Doppler ultrasound. Statistical analysis was performed to identify differences in clinicopathologic variables and patient-responses to questionnaire prompts between patients who did and did not report partner pain with intercourse. Results: A total of 322 patients with information available on partner pain were included in the study. Patients who reported partner pain had significantly higher subjective erectile rigidity (mean 5.9/10 Conclusions: Men with superior erectile function, higher degrees of penile curvature and ventral curvatures were more likely to report partner pain during penetrative intercourse. These specific disease characteristics reported in this series may assist clinicians in identifying men who are more motivated to select more invasive therapies