Elliptic Reconstruction and a Posteriori Error Estimates for Fully Discrete Semilinear Parabolic Optimal Control Problems

This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment is performed to illustrate the performance of the derived estimators.     

C-Shaped Cartilage Development Using Wharton's Jelly-Derived Hydrogels to Assemble a Highly Biomimetic Neotrachea for use in Circumferential Tracheal Reconstruction

A highly biomimetic neotrachea with C-shaped cartilage rings has promising clinical applications in the treatment of circumferential tracheal defects (CTDs) owing to its structure and physiological function. However, to date, most fabricated tracheal cartilages are O-shaped. In this study, finite element analysis demonstrates C-shaped cartilage rings that exhibit better compliance than O-shaped. Hydrogel is developed using methacryloyl-modified decellularized Wharton's jelly matrix (DWJMA) for the regeneration of C-shaped cartilage rings. This novel hydrogel possesses adjustable physicochemical properties and favorable cytocompatibility. When loaded with chondrocytes, DWJMA hydrogels support the optimal cartilage regeneration both in vitro and in vivo. More importantly, a highly biomimetic neotrachea simultaneously simulating the structural and physiological properties of the normal trachea is regenerated via modular assembly of several individual C-shaped cartilage rings. The results demonstrate the highly biomimetic neotrachea have better patency (88.6 ± 6.1% vs 74.4 ± 9.4%, p < 0.05), improve the survival rate, alleviate weight loss and mucoid impaction, than its O-shaped counterpart when used for the treatment of CTDs in a rabbit model. Therefore, this study proposes a novel hydrogel for the regeneration of C-shaped cartilage and provides new insights into the treatment of CTDs using a highly biomimetic neotrachea with C-shaped cartilage rings.     

DRBR-HDR: Dual-Branch recursive band reconstruction network for HDR with large motions

Ghosting artifacts due to misaligned imaging and missing content of the moving regions are major challenges of synthesizing high dynamic range (HDR) images from multiple low-dynamic range (LDR) with different exposures in dynamic scenes. Therefore, it hopes the HDR reconstruction model can align the LDRs’ features and restore the missing content without artifacts. In the paper, a new dual-branch recursive band reconstruction network for high dynamic range (DRBR-HDR) is proposed to generate credible result in missing content regions, which not only uses global features as supplementary information to help local features from different receptive fields for efficient feature alignment but also designs a series of coarse-to-fine band representation to better repair missing areas in the process of recursion. In addition, we introduce an interactive attention mechanism for local branches to alleviate ghosting artifacts. The experimental results demonstrate that DRBR-HDR achieves state-of-the-art performance compared with that of the prevailing HDR reconstruction methods in various challenging scenes.Index Terms—inverse tone mapping, band reconstruction, global features, high dynamic range images.     

Trigonometric wavelets for Hermite interpolation

The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval . Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions. Together with the corresponding dual functions, these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences. Consequently, this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment.

     

Characterization of Heterogeneous Catalysts by use of Test Reactions

The following report gives an overview on work done in the Catalysis Laboratory of the Department of Chemistry, National University of Singapore over the last 15 years (1989–2004). Much of this work can be described as “characterization of catalytically active surfaces through test reactions”. The methods, systems studied and the reactions that we evaluated will be described. The review will mostly concentrate on work from the authors’ laboratory, but other relevant work will also be cited.     

Component reconstruction in the primary space of spectra and concentrations. Alternating regression and related direct methods

A set of methods that extract the spectral components in a chromatographic run is considered. The methods do not need libraries of previously known spectra or retention times. The methods have been developed for two-dimensional spectra but they can also be used for chromatographic analyses with a single-channel detector. The methods are direct; they do not use principal components as the starting point. Alternating regression (AR) remains in the primary space of spectra and concentrations during the calculations. Random numbers are used as the starting spectra. Regression is used to solve first for the concentrations, then for the spectra. The method uses two kinds of constraints: all spectra and concentrations are forced to be positive; and all concentration profiles are forced to a unimodal shape with a single local maximum. It is assumed that all observations are a linear sum of components. Compact alternating regression (CAR) is a new variant of the basic AR. The idea is to replace multiplication of a large matrix by two multiplications of smaller matrices. This typically speeds up the iterations by a factor of ten. AR and CAR have been successfully used with combined techniques such as gas chromatography—mass spectrometry and liquid chromatography with UV—visible detection. The reliability of the solution is checked by repeatedly injecting noise and performing the analysis several times. This produces estimates of confidence intervals. AR and CAR have recently been extended to handle single-dimensional signals. Examples are single-channel detectors such as the flame ionization detector in gas or liquid chromatography with a fixed-wavelength UV detector. A batch of samples is used as the observation matrix. As a result, one obtains both the concentrations and the elution shapes of individual chromatographic peaks.     

First principle calculations study of AlN surface terminal structure evolution under different conditions

The surface structure and properties of aluminum nitride (AlN) play an important role in many applications. Using the first principle calculations method, we analyzed the surface terminal structure of AlN and its evolution under different conditions by determining the surface energy, adsorption energy, and evaporation energy of the Al and N terminals on the AlN(0001) surface. Our results show that the reason why the N terminal is less stable than the Al terminal is not only because of its high surface energy but also because its adsorption performance is extremely sensitive to the adsorption position. The surface N atoms combine to form N₂ molecules that escape during the evaporation process at high temperature. After surface N atoms escape, the AlN surface structure reconstitutes to form a hexagonal closest packing (HCP)–like structure, and the energy barrier for the reconstructing process is 3.2 eV. This shows that the structure and form of the AlN(0001) terminals depend on the environmental conditions.     

Fourier transform Raman spectral measurements of powdered quaternary mixtures of organic compounds: Exceptional pure component spectral reconstruction using band-target entropy minimization (BTEM)

Fourier transform Raman spectra of eight mixtures of four organic solids, namely dicyandiamide, melamine, acetamide and urea were measured. Matrices formed from these spectra were first subjected to singular value decomposition to obtain the right singular vectors. The right singular vectors were then subjected to blind source separation using band-target entropy minimization (BTEM), thus no a priori information (i.e. involving the nature of the components present, their spectra, nor their concentrations) was included in the analysis. The recovered pure component spectra are of exceptionally high quality and are consistent with pure reference spectra. Various empirical and statistical tests, such as the Euclidean norm and target transform factor analysis, were employed to assess the quality of the recovered spectra. The present results indicate the applicability of combined Raman and BTEM analysis for solid mixtures.     

双极场逆Radon变换的数值模拟

对双极场（DPF）的逆Radon变换进行了数值模拟。采用加法代数重建迭代算法（ART）对含有正负值的DPF进行重建，迭代了500次。结果发现，迭代一直收敛，重建场与原场相似，包括峰的位置、方向和形状，但各个峰的高度都较原场相应的峰矮，重建区域的边界出现了明显的波动现象。与相应单极场（SPF）的重建误差作比较，结果发现，DPF的3种模拟误差都大于SPF相应的误差，其中均方误差（MSE）大10^-4数量级，绝对平均误差（AVE）、峰值相对误差（PE）分别大10^-3、10^-2数量级，说明同样条件下DPF的重建精度比SPF的小。     

The polynomial reconstruction problem: The first 50 years

The problem of reconstructing the characteristic polynomial of a graph of order at least 3 from the collection of characteristic polynomials of its vertex-deleted subgraphs was posed by Cvetkovi? in 1973 as a spectral counter part to the well-known Ulam's reconstruction conjecture. Over the last 50 years, this problem has received notable attention, many positive results have been obtained, but in the general case the problem is still unresolved. In particular, no counter example is found in literature. In this expository paper we survey classical and some more recent results concerning the polynomial reconstruction problem, discuss some related problems, variations and generalizations.