A Study of GD′- Implications, a New Hyper Class of Fuzzy Implications

In this paper, we introduce and study the GD′-operations, which are a hyper class of the known D′-operations. GD′-operations are in fact D′-operations, that are generated not only from the same fuzzy negation. Similar with D′-operations, they are not always fuzzy implications. Nevertheless, some sufficient, but not necessary conditions for a GD′-operation to be a fuzzy implication, will be proved. A study for the satisfaction, or the violation of the basic properties of fuzzy implications, such as the left neutrality property, the exchange principle, the identity principle and the ordering property will also be made. This study also completes the study of the basic properties of D′-implications. At the end, surprisingly an unexpected new result for the connection of the QL-operations and D-operations will be presented.

Looking Back to Move Forward: How Review Articles Could Boost Forensic Entomology

The Locard′s exchange principle (1930) holds that the perpetrator of a crime leaves traces behind that can later be sampled and used as forensic evidence [...]

A Method of Generating Fuzzy Implications from n Increasing Functions and n + 1 Negations

In this paper, we introduce a new construction method of a fuzzy implication from n increasing functions g i : [ 0 , 1 ] → [ 0 , ∞ ) , ( g ( 0 ) = 0 ) ( i = 1 , 2 , … , n , n ∈ ℕ ) and n + 1 fuzzy negations N i ( i = 1 , 2 , … , n + 1 , n ∈ ℕ ). Imagine that there are plenty of combinations between n increasing functions g i and n + 1 fuzzy negations N i in order to produce new fuzzy implications. This method allows us to use at least two fuzzy negations N i and one increasing function g in order to generate a new fuzzy implication. Choosing the appropriate negations, we can prove that some basic properties such as the exchange principle (EP), the ordering property (OP), and the law of contraposition with respect to N are satisfied. The worth of generating new implications is valuable in the sciences such as artificial intelligence and robotics. In this paper, we have found a novel method of generating families of implications. Therefore, we would like to believe that we have added to the literature one more source from which we could choose the most appropriate implication concerning a specific application. It should be emphasized that this production is based on a generalization of an important form of Yager’s implications.

An ultra-sensitive multiplexed enrichment of rare DNA variants via toehold exchange principle.

e13658 Background: As a major type of liquid biopsy, circulating tumor DNA (ctDNA) provides important somatic mutation information, but the feature of rare allele frequency of mutation in ctDNA hampers its wide application. Methodology with high sensitivity, cost effectiveness, and multiplexing capability is needed for analyzing ctDNA samples. Methods: We have developed a novel methodology, termed MTEA (Multiplexed Toehold Exchange Amplification), which selectively amplifies and enriches all sequence variants (including SNV and deletion) 1000-fold over the wild-type sequence within ~20-nucleotide window. The amplified products are detected by Sanger sequencing or next-generation sequencing (NGS). This novel approach takes advantage of toehold exchange principle in which PCR amplification of wild-type rather than mutants would be greatly reduced due to the formation of a duplex of wild-type sequence with a blocker targeting to the wild-type rather than the mutant alleles. Results: Using circulating cell-free DNA (cfDNA) reference standards, we demonstrated that the major driver mutations of lung adenocarcinomas, including EGFR L858R and exon 19 deletion, KRAS G12X, and BRAF V600E, were enriched and detected simultaneously with MTEA technology at abundance as low as 0.01-0.05%. The clinical implications of MTEA technology were further validated using ctDNA from liquid biopsy specimens of 29 non-small cell lung cancer patients, and results were compared with those collected from the NGS and ddPCR analysis. Consistent results were obtained from all of the three platforms, which indicated 100% accuracy. The MTEA method has advantages over ddPCR since the later lacks the multiplexing detection ability. The MTEA technology can also save cost compared with NGS method. Conclusions: MTEA technology can enrich ctDNA from cancer patients to detect ultra-low abundance of clinically relevant mutations. Upon validation using a larger cohort, the technology may have wide application in precision medicine and guide clinicians for therapeutic decisions.