Linearized Asymptotic Stability for Fractional Differential Equations

We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector \{\lambda \in \C : |\arg \lambda| > \frac{\alpha \pi}{2}\} where $\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable

Aspergillus nidulans Septa Are Indispensable for Surviving Cell Wall Stress

Septation in filamentous fungi is a normal part of development, which involves the formation of cross-hyphal bulkheads, typically containing pores, allowing cytoplasmic streaming between compartments. Based on previous findings regarding septa and cell wall stress, we hypothesized that septa are critical for survival during cell wall stress. To test this hypothesis, we used known Aspergillus nidulans septation-deficient mutants (ΔsepH, Δbud3, Δbud4, and Δrho4) and six antifungal compounds. Three of these compounds (micafungin, Congo red, and calcofluor white) are known cell wall stressors which activate the cell wall integrity signaling pathway (CWIS), while the three others (cycloheximide, miconazole, and 2,3-butanedione monoxime) perturb specific cellular processes not explicitly related to the cell wall. Our results show that deficiencies in septation lead to fungi which are more susceptible to cell wall-perturbing compounds but are no more susceptible to other antifungal compounds than a control. This implies that septa play a critical role in surviving cell wall stress

LNK (SH2B3): paradoxical effects in ovarian cancer.

LNK (SH2B3) is an adaptor protein studied extensively in normal and malignant hematopoietic cells. In these cells, it downregulates activated tyrosine kinases at the cell surface resulting in an antiproliferative effect. To date, no studies have examined activities of LNK in solid tumors. In this study, we found by in silico analysis and staining tissue arrays that the levels of LNK expression were elevated in high-grade ovarian cancer. To test the functional importance of this observation, LNK was either overexpressed or silenced in several ovarian cancer cell lines. Remarkably, overexpression of LNK rendered the cells resistant to death induced by either serum starvation or nutrient deprivation, and generated larger tumors using a murine xenograft model. In contrast, silencing of LNK decreased ovarian cancer cell growth in vitro and in vivo. Western blot studies indicated that overexpression of LNK upregulated and extended the transduction of the mitogenic signal, whereas silencing of LNK produced the opposite effects. Furthermore, forced expression of LNK reduced cell size, inhibited cell migration and markedly enhanced cell adhesion. Liquid chromatography-mass spectroscopy identified 14-3-3 as one of the LNK-binding partners. Our results suggest that in contrast to the findings in hematologic malignancies, the adaptor protein LNK acts as a positive signal transduction modulator in ovarian cancers

Search for Fingerprints of Tetrahedral Symmetry in 156Gd^{156}Gd

Theoretical predictions suggest the presence of tetrahedral symmetry as an explanation for the vanishing intra-band E2-transitions at the bottom of the odd-spin negative parity band in $^{156}Gd$. The present study reports on experiment performed to address this phenomenon. It allowed to determine the intra-band E2 transitions and branching ratios B(E2)/B(E1) of two of the negative-parity bands in $^{156}Gd$.Comment: presented by Q.T. Doan at XLII Zakopane School of Physics: Breaking Frontiers: Submicron Structures in Physics and Biology, May 2008. 5 pages, minor corrections. To be published in the proceeding