Effects of periodically modulated coupling on amplitude death in nonidentical oscillators

The effects of periodically modulated coupling on amplitude death in two coupled nonidentical oscillators are explored. The AD domain could be significantly influenced by tuning the modulation amplitude and the modulation frequency of the modulated coupling strength. There is an optimal value of modulation amplitude for the modulated coupling with which the largest AD domain is observed in the parameter space. The AD domain is enlarged with the decrease of the modulation frequency for a given small modulation amplitude, while is shrunk with decrease of the modulation frequency for a given large modulation amplitude. The mechanism of AD in the presence of periodic modulation in the coupling is investigated via the local condition Lyapunov exponent of the coupled system. The stability of AD state can be well characterized by conditional Lyapunov exponent. The coupled system experiencing from the oscillatory state to AD is clearly indicated by the observation that the conditional Lyapunov exponent transits from positive to negative. Our results are helpful to many potential applications for the research of neuroscience and dynamical control in engineering.Comment: 11 figures, 8 page

Epigenetic Regulation of Prostate Cancer

Prostate cancer is (PCa) the second leading cause of cancer death in males in the United State, with 174,650 new cases and 31,620 deaths estimated in 2019. It has been documented that epigenetic deregulation such as histone modification and DNA methylation contributes to PCa initiation and progression. EZH2 (enhancer of zeste homolog 2), the catalytic subunit of the Polycomb Repressive Complex (PRC2) responsible for H3K27me3 and gene repression, has been identified as a promising target in PCa. In addition, overexpression of other epigenetic regulators such as DNA methyltransferases (DNMT) is also observed in PCa. These epigenetic regulators undergo extensive post-translational modifications, in particular, phosphorylation. AKT, CDKs, PLK1, PKA, ATR and DNA-PK are the established kinases responsible for phosphorylation of various epigenetic regulators

Polo-like kinase 1 (Plk1): an Unexpected Player in DNA Replication

Regulation of cell cycle progression is important for the maintenance of genome integrity, and Polo-like kinases (Plks) have been identified as key regulators of this process. It is well established that Polo-like kinase 1 (Plk1) plays critical roles in mitosis but little is known about its functions at other stages of the cell cycle. Here we summarize the functions of Plk1 during DNA replication, focusing on the molecular events related to Origin Recognition Complex (ORC), the complex that is essential for the initiation of DNA replication. Within the context of Plk1 phosphorylation of Orc2, we also emphasize regulation of Orc2 in different organisms. This review is intended to provide some insight into how Plk1 coordinates DNA replication in S phase with chromosome segregation in mitosis, and orchestrates the cell cycle as a whole

An inexact regularized proximal Newton method for nonconvex and nonsmooth optimization

This paper focuses on the minimization of a sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. We propose an inexact regularized proximal Newton method by an approximation of the Hessian $\nabla^2\!f(x)$ involving the $\varrho$th power of the KKT residual. For $\varrho=0$, we demonstrate the global convergence of the iterate sequence for the KL objective function and its $R$-linear convergence rate for the KL objective function of exponent $1/2$. For $\varrho\in(0,1)$, we establish the global convergence of the iterate sequence and its superlinear convergence rate of order $q(1\!+\!\varrho)$ under an assumption that cluster points satisfy a local H\"{o}lderian local error bound of order $q\in(\max(\varrho,\frac{1}{1+\varrho}),1]$ on the strong stationary point set; and when cluster points satisfy a local error bound of order $q>1+\varrho$ on the common stationary point set, we also obtain the global convergence of the iterate sequence, and its superlinear convergence rate of order $\frac{(q-\varrho)^2}{q}$ if $q>\frac{2\varrho+1+\sqrt{4\varrho+1}}{2}$. A dual semismooth Newton augmented Lagrangian method is developed for seeking an inexact minimizer of subproblem. Numerical comparisons with two state-of-the-art methods on $\ell_1$-regularized Student's $t$-regression, group penalized Student's $t$-regression, and nonconvex image restoration confirm the efficiency of the proposed method