A note on nowhere-zero 3-flow and Z_3-connectivity

There are many major open problems in integer flow theory, such as Tutte's 3-flow conjecture that every 4-edge-connected graph admits a nowhere-zero 3-flow, Jaeger et al.'s conjecture that every 5-edge-connected graph is $Z_3$-connected and Kochol's conjecture that every bridgeless graph with at most three 3-edge-cuts admits a nowhere-zero 3-flow (an equivalent version of 3-flow conjecture). Thomassen proved that every 8-edge-connected graph is $Z_3$-connected and therefore admits a nowhere-zero 3-flow. Furthermore, Lov$\acute{a}$sz, Thomassen, Wu and Zhang improved Thomassen's result to 6-edge-connected graphs. In this paper, we prove that: (1) Every 4-edge-connected graph with at most seven 5-edge-cuts admits a nowhere-zero 3-flow. (2) Every bridgeless graph containing no 5-edge-cuts but at most three 3-edge-cuts admits a nowhere-zero 3-flow. (3) Every 5-edge-connected graph with at most five 5-edge-cuts is $Z_3$-connected. Our main theorems are partial results to Tutte's 3-flow conjecture, Kochol's conjecture and Jaeger et al.'s conjecture, respectively.Comment: 10 pages. Typos correcte

An Intelligent Complex Event Processing with D

Efficient matching of incoming mass events to persistent queries is fundamental to complex event processing systems. Event matching based on pattern rule is an important feature of complex event processing engine. However, the intrinsic uncertainty in pattern rules which are predecided by experts increases the difficulties of effective complex event processing. It inevitably involves various types of the intrinsic uncertainty, such as imprecision, fuzziness, and incompleteness, due to the inability of human beings subjective judgment. Nevertheless, D numbers is a new mathematic tool to model uncertainty, since it ignores the condition that elements on the frame must be mutually exclusive. To address the above issues, an intelligent complex event processing method with D numbers under fuzzy environment is proposed based on the Technique for Order Preferences by Similarity to an Ideal Solution (TOPSIS) method. The novel method can fully support decision making in complex event processing systems. Finally, a numerical example is provided to evaluate the efficiency of the proposed method

Characterization of acyl-ACP thioesterases for the purpose of diversifying fatty acid synthesis pathway

Acyl-ACP TE selectively hydrolyzes the thiol ester bonds of acyl-ACPs to release free fatty acids, and therefore plays an essential role in determining the output of fatty acid synthesis (FAS) pathway. Comprehensive understanding of acyl-ACP TE is demanded to tailor this biocatalyst for the application in metabolic engineering of FAS pathway. To explore the diversity of acyl-ACP TEs, a total of 31 TEs enzymes were sourced from a wide range of biological taxa, including plants and bacteria, and these were functionally characterized. The results demonstrate that acyl-ACP TEs have great functional diversity relative to the acyl chain length specificity as well as acyl chains that contain additional chemical functionalities. Multiple sequence alignment of plant and bacterial TEs, and structure modeling of CvFatB2 revealed that a previously proposed residue Cys348 is unlikely to be a catalytic residue. Instead, residues Asp309 and Glu347, in addition to previously proposed residues Asn311 and His313 (numbers are based on CvFatB2 sequence), were proposed to be involved in the catalysis of acyl-ACP TEs. In vivo activities of site-directed mutants proved this hypothesis, and a two-step catalytic mechanism for plant and bacterial acyl-ACP TEs is proposed. To identify the region(s) that determine the substrate specificity, two acyl-ACP TEs were used for a domain-shuffling study. Comparing the substrate specificities of the resulting chimeric TEs led to the identification of the most important region that determines the substrate specificity of acyl-ACP TE. Site-directed mutagenesis analysis proved that six residues play critical roles in determining the substrate specificity, including V194 in Fragment II, V217, N223, R226, and R227 in Fragment III, and I268 in Fragment IV. Another three residues, L257, I260, and L289, impact the catalytic activity of acyl-ACP TE, because they are in two proposed ACP binding motifs. A directed evolution approach was successfully developed to improve the fatty acid productivity of acyl-ACP TE. Screening a designed variant library resulted in recovery of TE variants with increased fatty acid productivity and more insight into the relationship between sequences and substrate specificities of acyl-ACP TE