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For a general infinite system of convex inequalities in a Banach space, we study the basic constraint qualification and its relationship with other fundamental concepts, including various versions of conditions of Slater type, the Mangasarian–Fromovitz constraint qualification, as well as the Pshenichnyi–Levin–Valadier property introduced by Li, Nahak, and(More)
Histone modifications have critical roles in regulating the expression of developmental genes during embryo development in mammals. However, genome-wide analyses of histone modifications in pre-implantation embryos have been impeded by the scarcity of the required materials. Here, by using a small-scale chromatin immunoprecipitation followed by sequencing(More)
Autophagy degrades cytoplasmic proteins and organelles to recycle cellular components that are required for cell survival and tissue homeostasis. However, it is not clear how autophagy is regulated in mammalian cells. WASH (Wiskott-Aldrich syndrome protein (WASP) and SCAR homologue) plays an essential role in endosomal sorting through facilitating tubule(More)
We consider a (finite or infinite) family of closed convex sets with nonempty intersection in a normed space. A property relating their epigraphs with their intersection’s epigraph is studied, and its relations to other constraint qualifications (such as the linear regularity, the strong CHIP, and Jameson’s (G)-property) are established. With suitable(More)
The notions of Lipschitz conditions with L average are introduced to the study of convergence analysis of Gauss-Newton's method for singular systems of equations. Unified convergence criteria ensuring the convergence of Gauss-Newton's method for one kind of singular systems of equations with constant rank derivatives are established and unified estimates of(More)
We consider the optimization problem (P A) inf x∈X {f (x) + g(Ax)} where f and g are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y respectively, and A is a linear operator from X to Y. By using the properties of the epigraph of the conjugated functions, some sufficient and necessary conditions for the strong(More)
The famous Newton–Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton's method to a solution of an equation. Here we present a " Kantorovich type " convergence analysis for the Gauss–Newton's method which improves the result in [W.M. Häußler, A Kantorovich-type convergence analysis for the(More)
Hepatocellular carcinoma (HCC) is the most prevalent subtype of liver cancer, and it is characterized by a high rate of recurrence and heterogeneity. Liver cancer stem cells (CSCs) may well contribute to both of these pathological properties, but the mechanisms underlying their self-renewal and maintenance are poorly understood. Here, using transcriptome(More)
Histone modifications are fundamental epigenetic regulators that control many crucial cellular processes. However, whether these marks can be passed on from mammalian gametes to the next generation is a long-standing question that remains unanswered. Here, by developing a highly sensitive approach, STAR ChIP-seq, we provide a panoramic view of the landscape(More)
For an inequality system defined by an infinite family of proper convex functions, we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions and study relationships between these new constraint qualifications and other well known constraint qualifications including the basic constraint(More)