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Efficient strategies for precise genome editing in human-induced pluripotent cells (hiPSCs) will enable sophisticated genome engineering for research and clinical purposes. The development of programmable sequence-specific nucleases such as Transcription Activator-Like Effectors Nucleases (TALENs) and Cas9-gRNA allows genetic modifications to be made more(More)
Protein pathways are dynamic and highly coordinated spatially and temporally, capable of performing a diverse range of complex chemistries and enzymatic reactions with precision and at high efficiency. Biotechnology aims to harvest these natural systems to construct more advanced in vitro reactions, capable of new chemistries and operating at high yield.(More)
A k-container of G between u and v, C(u, v), is a set of k internally disjoint paths between u and v. A k-container C(u, v) of G is a k-container if it contains all vertices of G. A graph G is k-connected if there exists a k-container between any two distinct vertices. Thus, every 1-connected graph is Hamiltonian connected. Moreover, every 2-connected graph(More)
Let ~r = (ri) n i=1 be a sequence of real numbers of length n with sum s. Let s0 = 0 and si = r1 + . . . + ri for every i ∈ {1, 2, . . . , n}. Fluctuation theory is the name given to that part of probability theory which deals with the fluctuations of the partial sums si. Define p(~r) to be the number of positive sum si among s1, . . . , sn and m(~r) to be(More)
In 1999, the 512-bit number of 155 digits taken from the RSA Challenge list was first factored by the General Number Field Sieve. This work was done on a supercomputer and about 300 PCs or workstations by 17 experts all over the world. The calendar time for the factorization was over 6 months. Based on the open source GGNFS, we improved its algorithms and(More)
The conceptions of G-parking functions and G-multiparking functions were introduced in [15] and [12] respectively. In this paper, let G be a connected graph with vertex set {1, 2, . . . , n} and m ∈ V (G). We give the definition of (G,m)-multiparking function. This definition unifies the conceptions of G-parking function and G-multiparking function. We(More)