Although prox-regular functions in general are nonconvex, they possess properties that one would expect to find in convex or lowerC2  functions. The class of prox-regular functions covers all convex functions, lower C2  functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal subdifferential. Then, the definition of prox-regula...

The human neurofilament (H) promoter contains multiple binding sites for nuclear proteins including a Proximal (Prox) site centered around the sequence GGTTGGACC and an adjacent pyrimidine (Pyr) tract site centered around the sequence CCCTCCTCCCC. Surprisingly binding to a probe containing the Prox/Pyr region of the NF(H) promoter was competed in gel shifts by an oligonucleotide containing only...

Prox 1 is a vertebrate homeobox gene which is homologous to the Drosophila transcription factor, prospero. We have isolated a prox 1 cDNA from zebrafish, which encodes a protein that has 82%, 84% and 83% amino acid identity with chicken, mouse and human Prox 1, respectively. Antibodies raised against human Prox 1 cross-react with zebrafish Prox 1 and are used here to determine the expression pa...

Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Gradient Descent (prox-SGD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform sampling can guarantee that the sampled stochastic quantity is an unbiased estimate of the corresponding true quantity, the resulting estimator may have a ra...

This paper studies, for a differential variational inequality involving a locally prox-regular set, a regularization process with a family of classical differential equations whose solutions converge to the solution of the differential variational inequality. The concept of local prox-regularity will be termed in a quantified way, as (r, α)-prox-regularity.

Since the prox-mapping of stochastic mirror descent is intractable when directly being applied to the optimization problem (1), we propose the -inexact prox-mapping within the stochastic mirror descent framework in Section 3. Instead of solving the prox-mapping exactly, we approximate the solution with error. In this section, we will show as long as the approximation error is tolerate, the stoc...

Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Mirror Descent (prox-SMD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform sampling can guarantee that the sampled stochastic quantity is an unbiased estimate of the corresponding true quantity, the resulting estimator may have a rath...

Like other tissues and organs in vertebrates, multipotential stem cells serve as the origin of diverse cell types during genesis of the mammalian central nervous system (CNS). During early development, stem cells self-renew and increase their total cell numbers without overt differentiation. At later stages, the cells withdraw from this self-renewal mode, and are fated to differentiate into neu...

The study of lymphatic vessels and lymphatic tumors has been hampered with difficulty due to the overlapping morphological features between blood and lymphatic endothelial cells, as well as to the lack of specific lymphatic endothelial markers. Over the last few years, lymphatic vessels and lymphangiogenesis have received great attention owing to their putative implications in terms of metastat...