Discontinuous Galerkin Methods for an Elliptic Optimal Control Problem with a General State Equation and Pointwise State Constraints

We investigate discontinuous Galerkin methods for an elliptic optimal control problem with a general state equation and pointwise state constraints on general polygonal domains. We show that discontinuous Galerkin methods for general second-order elliptic boundary value problems can be used to solve the elliptic optimal control problems with pointwise state constraints. We establish concrete error estimates and numerical experiments are shown to support the theoretical results

A cubic C\u3csup\u3e0\u3c/sup\u3e interior penalty method for elliptic distributed optimal control problems with pointwise state and control constraints

We design and analyze a cubic C interior penalty method for linear–quadratic elliptic distributed optimal control problems with pointwise state and control constraints. Numerical results that corroborate the theoretical error estimates are also presented.

A convergent adaptive finite element method for elliptic Dirichlet boundary control problems

This paper concerns the adaptive finite element method for elliptic Dirichlet boundary control problems in the energy space. The contribution of this paper is twofold. First, we rigorously derive efficient and reliable a posteriori error estimates for finite element approximations of Dirichlet boundary control problems. As a by-product, a priori error estimates are derived in a simple way by introducing appropriate auxiliary problems and establishing certain norm equivalence. Secondly, for the coupled elliptic partial differential system that resulted from the first-order optimality system, we prove that the sequence of adaptively generated discrete solutions including the control, the state and the adjoint state, guided by our newly derived a posteriori error indicators, converges to the true solution along with the convergence of the error estimators. We give some numerical results to confirm our theoretical findings

Learning Accurate Entropy Model with Global Reference for Image Compression

In recent deep image compression neural networks, the entropy model plays a critical role in estimating the prior distribution of deep image encodings. Existing methods combine hyperprior with local context in the entropy estimation function. This greatly limits their performance due to the absence of a global vision. In this work, we propose a novel Global Reference Model for image compression to effectively leverage both the local and the global context information, leading to an enhanced compression rate. The proposed method scans decoded latents and then finds the most relevant latent to assist the distribution estimating of the current latent. A by-product of this work is the innovation of a mean-shifting GDN module that further improves the performance. Experimental results demonstrate that the proposed model outperforms the rate-distortion performance of most of the state-of-the-art methods in the industry

Hydrophilic microporous membranes for selective ion separation and flow-battery energy storage

Membranes with fast and selective ion transport are widely used for water purification and devices for energy conversion and storage including fuel cells, redox flow batteries and electrochemical reactors. However, it remains challenging to design cost-effective, easily processed ion-conductive membranes with well-defined pore architectures. Here, we report a new approach to designing membranes with narrow molecular-sized channels and hydrophilic functionality that enable fast transport of salt ions and high size-exclusion selectivity towards small organic molecules. These membranes, based on polymers of intrinsic microporosity containing Tröger’s base or amidoxime groups, demonstrate that exquisite control over subnanometre pore structure, the introduction of hydrophilic functional groups and thickness control all play important roles in achieving fast ion transport combined with high molecular selectivity. These membranes enable aqueous organic flow batteries with high energy efficiency and high capacity retention, suggesting their utility for a variety of energy-related devices and water purification processes

The oyster genome reveals stress adaptation and complexity of shell formation

The Pacific oyster Crassostrea gigas belongs to one of the most species-rich but genomically poorly explored phyla, the Mollusca. Here we report the sequencing and assembly of the oyster genome using short reads and a fosmid-pooling strategy, along with transcriptomes of development and stress response and the proteome of the shell. The oyster genome is highly polymorphic and rich in repetitive sequences, with some transposable elements still actively shaping variation. Transcriptome studies reveal an extensive set of genes responding to environmental stress. The expansion of genes coding for heat shock protein 70 and inhibitors of apoptosis is probably central to the oyster's adaptation to sessile life in the highly stressful intertidal zone. Our analyses also show that shell formation in molluscs is more complex than currently understood and involves extensive participation of cells and their exosomes. The oyster genome sequence fills a void in our understanding of the Lophotrochozoa. © 2012 Macmillan Publishers Limited. All rights reserved