Global dynamics of a parabolic type equation arising from the curvature flow

This paper studies a type of degenerate parabolic problem with nonlocal term \begin{equation*} \begin{cases} u_t=u^p(u_{xx}+u-\bar{u}) & 0<t<T_{{\max}},\ 0<x<a, u_x(0,t)=u_x(a,t)=0 & 0<t<T_{{\max}}, u(x,0)=u_0(x) & 0<x<a, \end{cases} \end{equation*} where $p>1$, $a>0$. In this paper, the classification of the finite-time blowup/global existence phenomena based on the associated energy functional and explicit expression of all nonnegative steady states are demonstrated. Moreover, we combine the applications of Lojasiewicz-Simon inequality and energy estimates to derive that any bounded solution with positive initial data converges to some steady state as $t\rightarrow +\infty$

A Counterexample for the Principal Eigenvalue of An Elliptic Operator with Large Advection

There are numerous studies focusing on the convergence of the principal eigenvalue $\lambda(s)$ as $s\to+\infty$ corresponding to the elliptic eigenvalue problem \begin{align*} -\Delta\varphi(x)-2s\mathbf{v}\cdot\nabla\varphi(x)+c(x)\varphi(x)=\lambda(s)\varphi(x),\quad x\in \Omega, \end{align*} where $\Omega$ is a bounded domain and the advection term $\mathbf{v}$ under some certain restrictions. In this paper, we construct an infinitely oscillating gradient advection term $\mathbf{v}=\nabla m(x)\in C^1(\Omega)$ such that the principal eigenvalue $\lambda(s)$ does not converge as $s\to+\infty$. As far as we know, this is the first result that guarantee the non-convergence of the principal eigenvalue

Finding the spectral radius of a nonnegative irreducible symmetric tensor via DC programming

The Perron-Frobenius theorem says that the spectral radius of an irreducible nonnegative tensor is the unique positive eigenvalue corresponding to a positive eigenvector. With this in mind, the purpose of this paper is to find the spectral radius and its corresponding positive eigenvector of an irreducible nonnegative symmetric tensor. By transferring the eigenvalue problem into an equivalent problem of minimizing a concave function on a closed convex set, which is typically a DC (difference of convex functions) programming, we derive a simpler and cheaper iterative method. The proposed method is well-defined. Furthermore, we show that both sequences of the eigenvalue estimates and the eigenvector evaluations generated by the method $Q$-linearly converge to the spectral radius and its corresponding eigenvector, respectively. To accelerate the method, we introduce a line search technique. The improved method retains the same convergence property as the original version. Preliminary numerical results show that the improved method performs quite well

A Semipersistent Plant Virus Differentially Manipulates Feeding Behaviors of Different Sexes and Biotypes of Its Whitefly Vector.

It is known that plant viruses can change the performance of their vectors. However, there have been no reports on whether or how a semipersistent plant virus manipulates the feeding behaviors of its whitefly vectors. Cucurbit chlorotic yellows virus (CCYV) (genus Crinivirus, family Closteroviridae) is an emergent plant virus in many Asian countries and is transmitted specifically by B and Q biotypes of tobacco whitefly, Bemisia tabaci (Gennadius), in a semipersistent manner. In the present study, we used electrical penetration graph (EPG) technique to investigate the effect of CCYV on the feeding behaviors of B. tabaci. The results showed that CCYV altered feeding behaviors of both biotypes and sexes of B. tabaci with different degrees. CCYV had stronger effects on feeding behaviors of Q biotype than those of B biotype, by increasing duration of phloem salivation and sap ingestion, and could differentially manipulate feeding behaviors of males and females in both biotype whiteflies, with more phloem ingestion in Q biotype males and more non-phloem probing in B biotype males than their respective females. With regard to feeding behaviors related to virus transmission, these results indicated that, when carrying CCYV, B. tabaci Q biotype plays more roles than B biotype, and males make greater contribution than females

Label-free trace detection of bio-molecules by liquid-interface assisted surface-enhanced Raman scattering using a microfluidic chip

Surface-enhanced Raman scattering (SERS), owing to its high sensitivity based on localized surface plasmon resonance of nanostructured metals, is recently attracting much attention to be used for biotechnology, such as cell imaging and tumor therapy. On the other hand, the trace detection of bio-molecules with large molecular weight is still challenging because the troublesome treatment of SERS substrate using coupling or cross-linking agents is required. In this paper, we apply liquid interface assisted SERS (LI-SERS) method, which provides unique features of collection and self-immobilization of analyte molecules on the SERS substrate, to realize the label-free trace detection of bio-molecules with detection limits of pM ~ fM. Specifically, deoxyribonucleic acid (DNA) discrimination and quantitative detection of β-Amyloid (Aβ) in trace-concentration are demonstrated to illustrate the ultrahigh sensitivity and versatility of the LI-SERS method. The results suggest LI-SERS is promising for the early-stage diagnosis of diseases such as virus infection and Alzheimer's disease

Serotonin promotes the proliferation of serum-deprived hepatocellular carcinoma cells via upregulation of FOXO3a

BACKGROUND: Peripheral serotonin is involved in tumorigenesis and induces a pro-proliferative effect in hepatocellular carcinoma (HCC) cells; however, the intracellular mechanisms by which serotonin exerts a mitogenic effect remain unclear. In this research, we examined whether FOXO3a, a transcription factor at the interface of crucial cellular processes, plays a role downstream of serotonin in HCC cells. RESULTS: The cell viability and expression of FOXO3a was assessed in three HCC cell lines (Huh7, HepG2 and Hep3B) during serum deprivation in the presence or absence of serotonin. Serum free media significantly inhibited HCC proliferation and led to reduced expression and nuclear accumulation of FOXO3a. Knockdown of FOXO3a enhanced the ability of serum deprivation to inhibit HCC cells proliferation. And overexpression of non-phosphorylated FOXO3a in HCC cells reversed serum-deprivation-induced growth inhibition. Serotonin reversed the serum-deprivation-induced inhibition of cell proliferation and upregulated FOXO3a in Huh7 cells; however, serotonin had no effect on the proliferation of serum-deprived HepG2 or Hep3B cells. In addition to proliferation, serotonin also induced phosphorylation of AKT and FOXO3a in serum-deprived Huh7 cells but not in HepG2 and Hep3B cells. However, the phosphorylation of FOXO3a induced by serotonin did not export FOXO3a from nucleus to cytoplasm in serum-deprived Huh7 cells. Consequently, we demonstrated that serotonin promoted the proliferation of Huh7 cells by increasing the expression of FOXO3a. We also provide preliminary evidence that different expression levels of the 5-HT2B receptor (5-HT(2B)R) may contribute to the distinct effects of serotonin in different serum-deprived HCC cells. CONCLUSIONS: This study demonstrates that FOXO3a functions as a growth factor in serum-deprived HCC cells and serotonin promotes the proliferation of serum-deprived HCC cells via upregulation of FOXO3a, in the presence of sufficient levels of the serotonin receptor 5-HT(2B)R. Drugs targeting the serotonin-5-HT(2B)R-FOXO3a pathway may provide a novel target for anticancer therapy