On a refinement of Wilf-equivalence for permutations

Recently, Dokos et al. conjectured that for all $k, m\geq 1$, the patterns $12\ldots k(k+m+1)\ldots (k+2)(k+1)$ and $(m+1)(m+2)\ldots (k+m+1)m\ldots 21$ are $maj$-Wilf-equivalent. In this paper, we confirm this conjecture for all $k\geq 1$ and $m=1$. In fact, we construct a descent set preserving bijection between $12\ldots k (k-1)$-avoiding permutations and $23\ldots k1$-avoiding permutations for all $k\geq 3$. As a corollary, our bijection enables us to settle a conjecture of Gowravaram and Jagadeesan concerning the Wilf-equivalence for permutations with given descent sets

The Functional Variant in the 3'UTR of IGF1 with the Risk of Gastric Cancer in a Chinese Population

Background/Aims: IGF-1 can act as an endocrine hormone and its signaling server as essential roles in regulating tumorigenesis. Polymorphisms in IGF-1 have been reported associated bad prognosis of with human cancer, but their association with the risk of human gastric cancer (GC) has not been found so far. In this study rs6218 located in the 3'UTR of IGF-1 was selected to evaluate its relationship with the risk of GC among Chinese population. Methods: Questionnaire, SNaPshot genotype assay, real time PCR assay, cell transfection and the dual luciferase reporter assay were used in our study. Results: SNP rs6218 in IGF-1 3'-UTR was involved in the occurrence of GC by acting as a tumor promotion factor while rs6128 acting as a risk factor. SNP rs6128 was also could be regulated by miR-603 which caused an up-regulation of IGF-1 in patients with UC and CC genotype. Furthermore, the carriers of UC and CC genotype presented a big tumor size as well as the high probability of metastasis. Conclusion: In conclusion, our findings have shown that the SNP rs6218 in IGF-1 3'-UTR, through disrupting the regulatory role of miR-603 in IGF-1 expression, rs16128 in IGF-1 might act as a promotion factor in the pathogenesis of GC

Hetero-Element-Doped Molybdenum Oxide Materials for Energy Storage Systems

In order to meet the growing demand for the electronics market, many new materials have been studied to replace traditional electrode materials for energy storage systems. Molybdenum oxide materials are electrode materials with higher theoretical capacity than graphene, which was originally used as anode electrodes for lithium-ion batteries. In subsequent studies, they have a wider application in the field of energy storage, such as being used as cathodes or anodes for other ion batteries (sodium-ion batteries, potassium-ion batteries, etc.), and electrode materials for supercapacitors. However, molybdenum oxide materials have serious volume expansion concerns and irreversible capacity dropping during the cycles. To solve these problems, doping with different elements has become a suitable option, being an effective method that can change the crystal structure of the materials and improve the performances. Therefore, there are many research studies on metal element doping or non-metal doping molybdenum oxides. This paper summarizes the recent research on the application of hetero-element-doped molybdenum oxides in the field of energy storage, and it also provides some brief analysis and insights

Interfractional Variations of Tumor Centroid Position and Tumor Regression during Stereotactic Body Radiotherapy for Lung Tumor

Purpose. To determine interfractional changes of lung tumor centroid position and tumor regression during stereotactic body radiation therapy (SBRT). Methods and Materials. 34 patients were treated by SBRT in 4-5 fractions to a median dose of 50 Gy. The CT scans acquired for verification were registered with simulation CT scans. The gross target volume (GTV) was contoured on all verification CT scans and compared to the initial GTV in treatment plan system. Results. The mean (±standard deviation, SD) three-dimension vector shift was 5.2±3.1 mm. The mean (±SD) interfractional variations of tumor centroid position were -0.7±4.5 mm in anterior-posterior (AP) direction, 0.2±3.1 mm in superior-inferior (SI) direction, and 0.4±2.4 mm in right-left (RL) direction. Large interfractional variations (≥5 mm) were observed in 5 fractions (3.3%) in RL direction, 16 fractions (10.5%) in SI direction, and 36 fractions (23.5%) in AP direction. Tumor volume did not decrease significantly during lung SBRT. Conclusions. Small but insignificant tumor volume regression was observed during lung SBRT. While the mean interfractional variations of tumor centroid position were minimal in three directions, variations more than 5 mm account for approximately a third of all, indicating additional margin for PTV, especially in AP direction

Interfractional Variations of Tumor Centroid Position and Tumor Regression during Stereotactic Body Radiotherapy for Lung Tumor

Purpose. To determine interfractional changes of lung tumor centroid position and tumor regression during stereotactic body radiation therapy (SBRT). Methods and Materials. 34 patients were treated by SBRT in 4-5 fractions to a median dose of 50 Gy. The CT scans acquired for verification were registered with simulation CT scans. The gross target volume (GTV) was contoured on all verification CT scans and compared to the initial GTV in treatment plan system. Results. The mean (±standard deviation, SD) three-dimension vector shift was 5.2±3.1 mm. The mean (±SD) interfractional variations of tumor centroid position were -0.7±4.5 mm in anterior-posterior (AP) direction, 0.2±3.1 mm in superior-inferior (SI) direction, and 0.4±2.4 mm in right-left (RL) direction. Large interfractional variations (≥5 mm) were observed in 5 fractions (3.3%) in RL direction, 16 fractions (10.5%) in SI direction, and 36 fractions (23.5%) in AP direction. Tumor volume did not decrease significantly during lung SBRT. Conclusions. Small but insignificant tumor volume regression was observed during lung SBRT. While the mean interfractional variations of tumor centroid position were minimal in three directions, variations more than 5 mm account for approximately a third of all, indicating additional margin for PTV, especially in AP direction