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RISS 인기검색어
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- 저자 : Yujun He (검색결과 2 건)
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Topological entropy of a sequence of monotone maps on circles
Yujun Zhu,Jinlian Zhang,Lianfa He 대한수학회 2006 대한수학회지 Vol.43 No.2
In this paper, we prove that the topological entropy of a sequence of equi-continuous monotone maps $f_{1,\infty}=\{f_i\}_{i=1}^{\infty}\;$ on circles is $\;h(f_{1,\infty})=\limsup\limits_{n\rightarrow\infty}\frac{1}{n}\log\prod\limits_ {i=1}^{n}|\deg f_{i}|.$ As applications, we give the estimation of the entropies for some skew products on annular and torus. We also show that a diffeomorphism $f$ on a smooth $2$-dimensional closed manifold and its extension on the unit tangent bundle have the same entropy.
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Shuai Hao,Wuguo Tian,Jianjie Zhao,Yi Chen,Xiaohua Zhang,Bo Gao,Yujun He,Donglin Luo 한국유방암학회 2020 Journal of breast cancer Vol.23 No.4
Purpose: Real-time detection and intervention can be used as potential measures to markedly decrease breast cancer mortality. Assessment of circulating tumor DNA (ctDNA) may offer great benefits for the management of breast cancer over time. However, the use of ctDNA to predict the effectiveness of neoadjuvant treatment and recurrence of breast cancer has rarely been studied. Methods: We prospectively recruited 31 breast cancer patients with 4 subtypes. Three time points were set in this study, including before any therapy (C1), during surgery (T), and six months after surgery (C2). We collected peripheral blood samples from all 31 patients at C1, tumor tissue from all 31 patients at T, and peripheral blood samples from 25 patients at C2. Targeted 727-gene panel sequencing was performed on ctDNA from all blood samples and tissue DNA from all tissue samples. Somatic mutations were detected and analyzed using a reference standard pipeline. Statistical analysis was performed to identify possible associations between ctDNA profiles and clinical outcomes. Results: In total, we detected 159, 271, and 70 somatic mutations in 30 C1 samples, 31 T samples, and 12 C2 samples, respectively. We identified specific genes, such as PIK3CA, TP53, and KMT2C, which were highly mutated in the tissue samples. Furthermore, mutated KMT2C observed in ctDNA of the C2 samples may be an indicator of breast cancer recurrence. Conclusion: Our study highlights the potential of ctDNA analysis at different timepoints for assessing tumor progression and treatment effectiveness, as well as prediction of breast cancer recurrence.
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