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The concept of microbial consortia is of great attractiveness in synthetic biology. Despite of all its benefits, however, there are still problems remaining for large-scaled multicellular gene circuits, for example, how to reliably design and distribute the circuits in microbial consortia with limited number of well-behaved genetic modules and wiring quorum-sensing molecules. To manage such problem, here we propose a formalized design process: (i) determine the basic logic units (AND, OR and NOT gates) based on mathematical and biological considerations; (ii) establish rules to search and distribute simplest logic design; (iii) assemble assigned basic logic units in each logic operating cell; and (iv) fine-tune the circuiting interface between logic operators. We in silico analyzed gene circuits with inputs ranging from two to four, comparing our method with the pre-existing ones. Results showed that this formalized design process is more feasible concerning numbers of cells required. Furthermore, as a proof of principle, an Escherichia coli consortium that performs XOR function, a typical complex computing operation, was designed. The construction and characterization of logic operators is independent of “wiring” and provides predictive information for fine-tuning. This formalized design process provides guidance for the design of microbial consortia that perform distributed biological computation.

This paper is concerned with the algebraic derivation for the production lot size problem with backlogging, random defective rate, and rework. Conventional approaches for solving optimal production lot size are by using the differential calculus on the productioninventory cost function with the need to prove optimality first. Recent articles proposed the algebraic approach to the solution of the classic economic order quantity (EOQ) and economic production quantity (EPQ) models without reference to the use of derivatives. This paper extends it to an EPQ model taking backlogging, random defective rate, and rework into consideration. This note demonstrates that optimal lot size for such an imperfect quality EPQ model can be derived without derivatives. The expected production-inventory costs can also be obtained immediately.

Capacitive touch panels (CTPs) with advantages of water-proof, stain-proof, scratch-proof, and fast response are widely used in various electronic products built in touch technology functions. It is a difficult inspection task when defects imbedded on surfaces of CTPs with structural textures. This research proposes a Fourier transform-based approach to inspect surface defects of CTPs. When a CTP image with four directional and periodic lines of texture is transformed to Fourier domain, four principal bands with high-energy frequency components crisscross at the center of Fourier spectrum. A multi-crisscross filter is designed to filter out the frequency components of the principal band regions. The filtered image is then transformed back to spatial domain. Finally, the restored image is segmented by a simple threshold method and defects are located. Experimental results show the proposed method achieves a high defect detection rate and a low false alarm rate on defect inspection of touch panels.

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