Most results on the polynomial-like iterative equation are given under the condition that the given function is monotone,while a work by L.Liu and X.Gong gets nonmonotone PM solutions with height 1 when the given func...Most results on the polynomial-like iterative equation are given under the condition that the given function is monotone,while a work by L.Liu and X.Gong gets nonmonotone PM solutions with height 1 when the given function is of the same case.Removing the condition on height for the given function,we first give a method to assert the nonexistence of C^(0)solutions,then present equivalent conditions for the existence of PM solutions with finite height.Finally,as an application of the equivalent conditions,we construct the PM solutions in the case that the given function has one fort.展开更多
In this paper we consider iteration of single-plateau functions,an important class of continuous functions with infinitely many forts,and investigate changes of number and length of plateaux under iteration.We use the...In this paper we consider iteration of single-plateau functions,an important class of continuous functions with infinitely many forts,and investigate changes of number and length of plateaux under iteration.We use the indices flatness,plateau limit and limit length to formulate those changes.Furthermore,we compute the flatness,plateau limit and limit length for all the nine types of single-plateau functions.展开更多
Transposable elements(TEs)have been shown to have important gene regulatory functions and their alteration could lead to disease phenotypes.Acute myeloid leukemia(AML)develops as a consequence of a series of genetic c...Transposable elements(TEs)have been shown to have important gene regulatory functions and their alteration could lead to disease phenotypes.Acute myeloid leukemia(AML)develops as a consequence of a series of genetic changes in hematopoietic precursor cells,including mutations in epigenetic factors.Here,we set out to study the gene regulatory role of TEs in AML.We first explored the epigenetic landscape of TEs in AML patients using ATAC-seq data.We show that a large number of TEs in general,and more specifically mammalian-wide interspersed repeats(MIRs),are more enriched in AML cells than in normal blood cells.We obtained a similar finding when analyzing histone modification data in AML patients.Gene Ontology enrichment analysis showed that genes near MIRs in open chromatin regions are involved in leukemogenesis.To functionally validate their regulatory role,we selected 19 MIR regions in AML cells,and tested them for enhancer activity in an AML cell line(Kasumi-1)and a chronic myeloid leukemia(CML)cell line(K562);the results revealed several MIRs to be functional enhancers.Taken together,our results suggest that TEs are potentially involved in myeloid leukemogenesis and highlight these sequences as potential candidates harboring AML-associated variation.展开更多
基金supported by the Natural Science Foundation of Shandong Province(ZR2017MA019)the Scientific Research Fund of Binzhou University(BZXYL1802)+2 种基金supported by the National Science Foundation of China(11501394)the Science Research Fund of Sichuan Provincial Education Department(15ZB0041)funding of School of Mathematical Sciences and V.C.&V.R.Key Lab of Sichuan Province。
文摘Most results on the polynomial-like iterative equation are given under the condition that the given function is monotone,while a work by L.Liu and X.Gong gets nonmonotone PM solutions with height 1 when the given function is of the same case.Removing the condition on height for the given function,we first give a method to assert the nonexistence of C^(0)solutions,then present equivalent conditions for the existence of PM solutions with finite height.Finally,as an application of the equivalent conditions,we construct the PM solutions in the case that the given function has one fort.
基金supported by National Natural Science Foundation of China(Grant Nos.11501394,11771307 and 11726623)Science Research Fund of Sichuan Provincial Education Department(Grant No.15ZB0041)China Scholarship Council。
文摘In this paper we consider iteration of single-plateau functions,an important class of continuous functions with infinitely many forts,and investigate changes of number and length of plateaux under iteration.We use the indices flatness,plateau limit and limit length to formulate those changes.Furthermore,we compute the flatness,plateau limit and limit length for all the nine types of single-plateau functions.
基金supported by grants from the National Natural Science Foundation of China(91749205,91329302,and 31210103916)Ministry of Science and Technology of China(2015CB964803 and 2016YFE0108700)+2 种基金a Max Planck fellowship to J.D.J.H.supported by the National Human Genome Research Institute(NHGRI)and the National Cancer Institute(1R01CA197139)NHGRI(1UM1HG009408)the National Health Lung and Blood Institute(1R01HL138424)。
文摘Transposable elements(TEs)have been shown to have important gene regulatory functions and their alteration could lead to disease phenotypes.Acute myeloid leukemia(AML)develops as a consequence of a series of genetic changes in hematopoietic precursor cells,including mutations in epigenetic factors.Here,we set out to study the gene regulatory role of TEs in AML.We first explored the epigenetic landscape of TEs in AML patients using ATAC-seq data.We show that a large number of TEs in general,and more specifically mammalian-wide interspersed repeats(MIRs),are more enriched in AML cells than in normal blood cells.We obtained a similar finding when analyzing histone modification data in AML patients.Gene Ontology enrichment analysis showed that genes near MIRs in open chromatin regions are involved in leukemogenesis.To functionally validate their regulatory role,we selected 19 MIR regions in AML cells,and tested them for enhancer activity in an AML cell line(Kasumi-1)and a chronic myeloid leukemia(CML)cell line(K562);the results revealed several MIRs to be functional enhancers.Taken together,our results suggest that TEs are potentially involved in myeloid leukemogenesis and highlight these sequences as potential candidates harboring AML-associated variation.
