Applications of the alternating direction method of multipliers to the semidefinite inverse quadratic eigenvalue problem with a partial eigenstructure

National Natural Science Foundation of China [11271308]; Natural Science Foundation of Fujian Province of China for Distinguished Young Scholars [2010J06002]; NCET; General Research Fund from Hong Kong Research Grants Council [203712]This paper shows that the alternating direction method of multipliers (ADMM) is efficient for solving the semidefinite inverse quadratic eigenvalue problem (SDIQEP) with a partial eigenstructure. We derive several ADMM-based iterative schemes for SDIQEP and demonstrate their efficiency for large-scale cases of SDIQEP numerically

Multi-contrast brain magnetic resonance image super-resolution using the local weight similarity

Abstract Background Low-resolution images may be acquired in magnetic resonance imaging (MRI) due to limited data acquisition time or other physical constraints, and their resolutions can be improved with super-resolution methods. Since MRI can offer images of an object with different contrasts, e.g., T1-weighted or T2-weighted, the shared information between inter-contrast images can be used to benefit super-resolution. Methods In this study, an MRI image super-resolution approach to enhance in-plane resolution is proposed by exploring the statistical information estimated from another contrast MRI image that shares similar anatomical structures. We assume some edge structures are shown both in T1-weighted and T2-weighted MRI brain images acquired of the same subject, and the proposed approach aims to recover such kind of structures to generate a high-resolution image from its low-resolution counterpart. Results The statistical information produces a local weight of image that are found to be nearly invariant to the image contrast and thus this weight can be used to transfer the shared information from one contrast to another. We analyze this property with comprehensive mathematics as well as numerical experiments. Conclusion Experimental results demonstrate that the image quality of low-resolution images can be remarkably improved with the proposed method if this weight is borrowed from a high resolution image with another contrast. Graphical Abstract Multi-contrast MRI Image Super-resolution with Contrast-invariant Regression Weight

Applications of the alternating direction method of multipliers to the semidefinite inverse quadratic eigenvalue problem with a partial eigenstructure

This paper shows that the alternating direction method of multipliers (ADMM) is efficient for solving the semidefinite inverse quadratic eigenvalue problem (SDIQEP) with a partial eigenstructure. We derive several ADMM-based iterative schemes for SDIQEP and demonstrate their efficiency for large-scale cases of SDIQEP numerically. © 2013 IOP Publishing Ltd.Link_to_subscribed_fulltex

On the alternating direction method of multipliers for nonnegative inverse eigenvalue problems with partial eigendata

We consider the nonnegative inverse eigenvalue problem with partial eigendata, which aims to find a nonnegative matrix such that it is nearest to a pre-estimated nonnegative matrix and satisfies the prescribed eigendata. In this paper, we propose several iterative schemes based on the alternating direction method of multipliers for solving the nonnegative inverse problem. We also extend our schemes to the symmetric case and the cases of prescribed lower bounds and of prescribed entries. Numerical tests (including a practical engineering application in vibrations) show the efficiency of the proposed iterative schemes. (C) 2012 Elsevier B.V. All rights reserved

One-pot assembling of hierarchical porous carbon/silica nanocomposites for cycloaddition reaction

Hierarchically structured porous materials are of great interest to catalysis, where an accurately controlled pore texture at different length scales is favorable to reduce or otherwise control transport limitations. With one-step assembly of silica and carbon by using varying amounts of tetraethoxysilane (TEOS) as silica source and resorcinol and formaldehyde (R–F) as carbon source, a series carbon and silica nanocomposite materials with hierarchical porous structure (abundant micropores and ordered mesopores) were synthesized. Due to the matching condensation and polymerization rate of TEOS and R–F, carbon/silica nanocomposites (CSNs) with spherical morphology and uniform distribution of carbon and silica can be obtained. However, once the equilibrium point of this condensation and polymerization is deviated, the pore structure and morphology of the materials will be changed. According to the results, in CSNs materials, silica acts as the main structure skeleton, while carbon mainly contributes to the construction of micropores. Furthermore, the resultant CSNs were used as a carrier for the catalyst to support the ionic liquid, thereby catalyzing the cycloaddition of CO2 with epoxide, in which the materials showed high catalytic activity and stability due to the special structure and compositions

Hollow Carbon Spheres with Abundant Micropores for Enhanced CO₂ Adsorption

The interest in the design and controllable fabrication of hollow carbon spheres (HCSs) emanates from their tremendous potential applications in adsorption, energy conversion and storage, and catalysis. However, the effective synthesis of uniform HCSs with high surface area and abundant micropores remains a challenge. In this work, HCSs with tunable microporous shells were rationally synthesized via the hard-template method using resorcinol (R) and formaldehyde (F) as a carbon precursor. HCSs with a very high surface area (1369 m²/g) and abundant micropores (0.53 cm³/g) can be obtained with the assistance of additional inorganic silanes (TEOS) simultaneously with the carbon source (RF). Interestingly, the extra-abundant micropores showed favorable adsorption for CO₂, resulting in a 1.5 times increase in the CO₂ adsorption capacity compared to that of normal HCSs under the same conditions. Meanwhile, these HCSs hold potential for use in the separation of gases such as CO₂ and N₂

Additional file 1: of Multi-contrast brain magnetic resonance image super-resolution using the local weight similarity

Detailed formula derivations, analysis of regression weight in completely opposite contrast images, and more super-resolved MRI images. (DOCX 1215 kb