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Automated Fiber Placement (AFP) plays a significant role in advanced manufacturing, particularly in the aerospace and automotive industries. AFP technology is of benefit as it enables us to generate layups, based on optimum designs by fiber steering. The primary benefit of AFP is the lower cost through scrap reduction and improved production cycle time as opposed to hand layup methods. However, just as hand layup, AFP also suffers from inherent unintended imperfections. These imperfections could be due to multiple reasons, often the layup imperfections such as gaps and overlaps are studied but enough emphasis is not provided on the defects due to consolidation/curing. Optimized cure cycles are utilized to minimize residual stresses developed during curing, which could affect the mechanical performance of the composites. A continuum-based damage model called the “smeared crack approach” is used to conduct a progressive damage analysis on AFP fabricated coupons where the layup imperfections and consolidation defects are considered simultaneously. 

We explore using LLMs, GPT-4 specifically, to generate draft sentence-level Chinese Uniform Meaning Representations (UMRs) that human annotators can revise to speed up the UMR annotation process. In this study, we use few-shot learning and Think-Aloud prompting to guide GPT-4 to generate sentence-level graphs of UMR. Our experimental results show that compared with annotating UMRs from scratch, using LLMs as a preprocessing step reduces the annotation time by two thirds on average. This indicates that there is great potential for integrating LLMs into the pipeline for complicated semantic annotation tasks. 

We explore using LLMs, GPT-4 specifically, to generate draft sentence-level Chinese Uniform Meaning Representations (UMRs) that human annotators can revise to speed up the UMR annotation process. In this study, we use few-shot learning and Think-Aloud prompting to guide GPT-4 to generate sentence-level graphs of UMR. Our experimental results show that compared with annotating UMRs from scratch, using LLMs as a preprocessing step reduces the annotation time by two thirds on average. This indicates that there is great potential for integrating LLMs into the pipeline for complicated semantic annotation tasks. 

Two new efficient algorithms for computing greatest common divisors (gcds) of parametric multivariate polynomials over k[U][X]are presented. The key idea of the first algorithm is that the gcd of two non-parametric multivariate polynomials can be obtained by dividing their product by the generator of the intersection of two principal ideals generated by the polynomials. The second algorithm is based on another simple insight that the gcd can be extracted using the generator of the ideal quotient of a polynomial with respect to the second polynomial. Since the ideal intersection and ideal quotient in these cases are also principal ideals, their generators can be obtained by computing minimal Gröbner bases of the ideal intersection and ideal quotient, respectively. To avoid introducing new variables which can adversely affect the efficiency, minimal Gröbner bases computations are performed on modules. Both of these constructions generalize to the parametric case as shown in the paper. Comprehensive Gröbner system constructions are used for the parametric ideal intersection and ideal quotient using the Kapur-Sun-Wang’s algorithm. It is proved that whether in a minimal comprehensive Gröbner system of a parametric ideal 20intersection or in that of a parametric ideal quotient, each branch of the specializations corresponds to a principal parametric ideal with a single generator. Using this generator, the parametric gcd of that branch is obtained by division. For the case of more than two parametric polynomials, we can use the above two algorithms to compute gcds recursively, and get an extended algorithm by generalizing the idea of the second algorithm. Algorithms do not suffer from having to apply expensive steps such as ensuring whether parametric polynomials are primitive w.r.t. the main variable as used in both the algorithms proposed by Nagasaka (ISSAC, 2017). The resulting algorithms are not only conceptually simple to understand but are more efficient in practice. The proposed algorithms and both of Nagasaka’s algorithms have been implemented in Singular, and their performance is compared on a number of examples.