A new Lagrangian dual global optimization algorithm for solving bilinear matrix inequalities

A new global optimization algorithm for solving bilinear matrix inequalities (BMI) problems is developed. It is based on a dual Lagrange formulation for computing lower bounds that are used in a branching procedure to eliminate partition sets in the space of complicating variables. The advantage of the proposed method is twofold. First, the lower bound computations reduce to solving easily tractable linear matrix inequality (LMI) problems. Secondly, the lower bounding procedure guarantees global convergence of the algorithm when combined with an exhaustive partitioning of the space of complicating variables. A rigorous proof of this fact is provided. Another important feature is that the branching phase takes place in the space of complicating variables only, hence limiting the overall cost of the algorithm. Also, an important point in the method is that separated LMI constraints are encapsulated into an augmented BMI for improving the lower bound computations. Applications of the algorithm to robust structure/controller design are considered. Copyright © 2000 John Wiley & Sons, Ltd.     

Self-Folding Graphene-Based Interface for Brain-Like Modular 3D Tissue (Adv. Funct. Mater. 37/2023)

Electrophysiology of 3D neuronal cultures is of rapidly growing importance for revealing cellular communications associated with neurodevelopment and neurological diseases in their brain-like 3D environment. Despite that the brain also exhibits an inherent modular architecture that is essential for cortical processing, it remains challenging to interface a modular network consisting of multiple 3D neuronal tissues. Here, a self-folding graphene-based electrode array is proposed that enables to reconstruct modular 3D neuronal tissue and investigate firing dynamics among moduli. A graphene-sandwiched parylene-C film self-folds into a cylindrical structure within which living cells can be encapsulated. Culture of encapsulated cells inside the folded graphene enables to spontaneously construct 3D cell aggregates and ensure firm contact between the graphene surface and encapsulated cells. As the inner graphene surface can be utilized as an electrode, the reliable cell–electrode contact allows for long-term electrical recording from multiple 3D aggregates. Additionally, the modular network consisting of multiple 3D aggregates exhibits richer firing patterns than a conventional homogenous 2D network, which demonstrates that the approach enables measurements of firing dynamics in complex 3D neuronal networks. The deformable graphene electrode will be a powerful platform for investigating complex cellular communications in brain-like 3D cultures.     

In situ Raman spectroscopy analysis of local structure in dry gel for zeolite beta synthesis

To investigate faster crystallization of zeolite beta by the dry-gel conversion method, the local structure of the dry gel before synthesis was quantitatively evaluated using in situ Raman spectroscopy during the drying process. The dry gel prepared from Si and Al sources, and tetraethylammonium hydroxide solution was crystallized after several hours by the dry-gel conversion method. The conformational change of TEA⁺ cations was observed during the drying process by the deconvolution of the spectrum, and the conformational change was larger than that during the synthesis process. The rate of conformational change was increased with the drying temperature, and the apparent activation energy was estimated to be 68.2 kJ/mol. The generation and transformation of double three-membered silicate rings (D3Rs) and 4-2 type secondary building units (SBUs), which are essential for the crystallization of zeolite beta, were observed during the drying process. The transformation from D3R to 4-2 SBU in the dry gel during drying process could be confirmed quantitatively by the difference of the time variation for the amounts of these silicate building units estimated by in situ observation.     

Fracture toughness evaluation of silicon nitride from microstructures via convolutional neural network

The fracture toughness of silicon nitride (Si₃N₄) ceramics was evaluated directly from their microstructures via deep learning using convolutional neural network models. Totally 156 data sets containing microstructural images and relative densities were prepared from 45 types of Si₃N₄ samples as input feature quantities (IFQs) and were correlated to the fracture toughness as an objective variable. The data sets were divided into two groups. One was used for training, resulting in the creation of regression models for two kinds of IFQs: the microstructures only and a combination of the microstructures and the relative densities. The other group was used for testing the validity of the created models. As a result, the determination coefficient was approximately 0.8 even when using only the microstructures as the IFQs and was further improved when adding the relative densities. It was revealed that the fracture toughness of Si₃N₄ ceramics was well evaluated from their microstructures.     

Effects of nitridation temperature on properties of sintered reaction-bonded silicon nitride

We prepared sintered reaction-bonded silicon nitride ceramics by using yttria and magnesia as sintering additives and evaluated effects of the nitridation temperature on their microstructure, bending strength, fracture toughness, and thermal conductivity. The effects of the nitridation temperature were large, but different depending on the property. The ratio of β-phase in the nitrided compacts significantly increased with increasing the nitridation temperature, whereas their microstructures had no clear difference. Although the bending strength varied, it maintains a high value of 800 MPa. Fracture toughness was almost constant regardless the temperature. The thermal conductivity improved as the β-phase in the nitrided compact increases. This resulted in a decrease of the lattice oxygen content and increase of the thermal conductivity. Therefore, elevating the nitridation temperature and consequently the β-phase ratio should be a promising strategy for achieving compatibly high strength and high thermal conductivity, which are generally known to be in a trade-off relationship.     

Identification and Analysis of the Biosynthetic Gene Cluster for the Indolizidine Alkaloid Iminimycin in Streptomyces griseus

Indolizidine alkaloids, which have versatile bioactivities, are produced by various organisms. Although the biosynthesis of some indolizidine alkaloids has been studied, the enzymatic machinery for their biosynthesis in Streptomyces remains elusive. Here, we report the identification and analysis of the biosynthetic gene cluster for iminimycin, an indolizidine alkaloid with a 6-5-3 tricyclic system containing an iminium cation from Streptomyces griseus. The gene cluster has 22 genes, including four genes encoding polyketide synthases (PKSs), which consist of eight modules in total. In vitro analysis of the first module revealed that its acyltransferase domain selects malonyl-CoA, although predicted to select methylmalonyl-CoA. Inactivation of seven tailoring enzyme-encoding genes and structural elucidation of four compounds accumulated in mutants provided important insights into iminimycin biosynthesis, although some of these compounds appeared to be shunt products. This study expands our knowledge of the biosynthetic machinery of indolizidine alkaloids and the enzymatic chemistry of PKS.     

Effects of nitrogen pressure on properties of sintered reaction-bonded silicon nitride

We prepared sintered reaction-bonded silicon nitride ceramics by using yttria and magnesia as sintering additives and evaluated the effects of nitrogen pressure (0.1–1.0 MPa) on their microstructure, bending strength, fracture toughness, and thermal conductivity. The ratio of β phase in the nitrided compacts varied with the pressure and increased with increasing it. Since many β grains in the nitrided compacts were formed and interlocked each other with a stable three-dimensional structure which restricted the shrinkage during the sintering procedure, many pores remained in the sintered body. Under the middle pressure (0.3–0.5 MPa), the grains grew large because the number of formed nuclei was small. On the other hand, under the high pressures (0.8–1.0 MPa), the grains were relatively fine and uniform because of a large number of nuclei. Since the porosity and grain length depended on the nitridation mechanism, which was affected by the nitrogen pressure, the properties largely varied accordingly. The nitridation at 0.1 MPa gave the best properties in this study.     

Improvement of steady-state performance for discrete-valued input control with an integrator utilizing feedback control of integrated value of input

In this study, we considered the regulator problem for discrete-valued input control with an integrator. In some cases, the state does not converge to the origin in the discrete-valued input control when the plant possesses an integrator. Therefore, a method that adds minor feedback control to the integrated value of the input was proposed. However, the effect of the feedback control of the integrated value of the input was not theoretically interpreted, and the feedback gain for the state of the integrated value of the input was designed with trial and error. Herein, we clarify the effect of feedback control on the integrated value of the input. Furthermore, we reveal that the trade-off between the steady-state and transient performances is controlled by one parameter, that is, the feedback gain for the integrated value of the input.