Opposing transcriptional programs of KLF5 and AR emerge during therapy for advanced prostate cancer.

Endocrine therapies for prostate cancer inhibit the androgen receptor (AR) transcription factor. In most cases, AR activity resumes during therapy and drives progression to castration-resistant prostate cancer (CRPC). However, therapy can also promote lineage plasticity and select for AR-independent phenotypes that are uniformly lethal. Here, we demonstrate the stem cell transcription factor Krüppel-like factor 5 (KLF5) is low or absent in prostate cancers prior to endocrine therapy, but induced in a subset of CRPC, including CRPC displaying lineage plasticity. KLF5 and AR physically interact on chromatin and drive opposing transcriptional programs, with KLF5 promoting cellular migration, anchorage-independent growth, and basal epithelial cell phenotypes. We identify ERBB2 as a point of transcriptional convergence displaying activation by KLF5 and repression by AR. ERBB2 inhibitors preferentially block KLF5-driven oncogenic phenotypes. These findings implicate KLF5 as an oncogene that can be upregulated in CRPC to oppose AR activities and promote lineage plasticity

A Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem

Based on the smoothing function of penalized Fischer-Burmeister NCP-function, we propose a new smoothing inexact Newton algorithm with non-monotone line search for solving the generalized nonlinear complementarity problem. We view the smoothing parameter as an independent variable. Under suitable conditions, we show that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem. We also establish the local superlinear (quadratic) convergence of the proposed algorithm under the BD-regular assumption. Preliminary numerical experiments indicate the feasibility and efficiency of the proposed algorithm

A Simultaneous Iteration Algorithm for Solving Extended Split Equality Fixed Point Problem

We study a kind of split equality fixed point problem which is an extension of split equality problem. We propose a kind of simultaneous iterative algorithm with a way of selecting the step length which does not need any a priori information about the operator norms and prove that the sequences generated by the iterative method converge weakly to the solution of this problem. Some numerical results are shown to confirm the feasibility and efficiency of the proposed methods

The Conjugate Gradient Viscosity Approximation Algorithm for Split Generalized Equilibrium and Variational Inequality Problems

In this paper, we study a kind of conjugate gradient viscosity approximation algorithm for finding a common solution of split generalized equilibrium problem and variational inequality problem. Under mild conditions, we prove that the sequence generated by the proposed iterative algorithm converges strongly to the common solution. The conclusion presented in this paper is the generalization, extension, and supplement of the previously known results in the corresponding references. Some numerical results are illustrated to show the feasibility and efficiency of the proposed algorithm

Convergence Theorems for Equilibrium Problems and Fixed-Point Problems of an Infinite Family of ki-Strictly Pseudocontractive Mapping in Hilbert Spaces

We first extend the definition of Wn from an infinite family of nonexpansive mappings to an infinite family of strictly pseudocontractive mappings, and then propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an infinite family of ki-strictly pseudocontractive mappings in Hilbert spaces. The results obtained in this paper extend and improve the recent ones announced by many others. Furthermore, a numerical example is presented to illustrate the effectiveness of the proposed scheme

A Simultaneous Iteration Algorithm for Solving Extended Split Equality Fixed Point Problem

We study a kind of split equality fixed point problem which is an extension of split equality problem. We propose a kind of simultaneous iterative algorithm with a way of selecting the step length which does not need any a priori information about the operator norms and prove that the sequences generated by the iterative method converge weakly to the solution of this problem. Some numerical results are shown to confirm the feasibility and efficiency of the proposed methods