Abstract
New techniques and probes are routinely emerging for detecting short-lived free radicals such as superoxide radical anion (O2*-), nitric oxide (*NO), and transient oxidants derived from ...peroxynitrite (ONOO-/ONOOH). Recently, we reported the profiles of oxidation products (2-hydroxyethidium, ethidium, and various dimeric products) of the fluorogenic probe hydroethidine (HE) in the *NO/O2*- system (Zielonka et al. 2012). In this study, we used HPLC analyses of HE oxidation products in combination with continuous wave electron paramagnetic resonance (CW-EPR) spin trapping with 5-tert-butoxycarbonyl-5-methyl-1-pyrroline N-oxide (BMPO) to define the identity of the oxidizing species formed in the *NO/O2*- system. EPR spin-trapping technique is still considered as the gold standard for characterization of free radicals and their intermediates. We monitored formation of BMPO-superoxide (BMPO-*OOH) and BMPO-hydroxyl (BMPO-*OH) radical adducts. Simultaneous analyses of results from EPR spin-trapping and HPLC measurements are helpful in the interpretation of the mechanism of formation of products of HE oxidation.
Recently, we have proved that Naimark-Sacker bifurcations occur in the Euler method applied to a delay differential equation 1. By slightly modifying the proof, it is verified that the same result ...holds, e.g., for another equation obtained from the equation by a change of the dependent variable. However, in computer experiments, the Euler method presents different behavior for the two equations: an invariant circle is observed in the former case; a stable periodic orbit is observed in the latter case.
We show that it is reasonable to consider the behavior in the latter case as a weak resonance in the Naimark-Sacker bifurcation. More specifically, we study a class of delay differential equations which includes the second equation, paying attention to special periodic solutions found by Kaplan and Yorke 2, and prove constructively that the Euler method applied to each equation of the class has at least two periodic orbits. Numerical experiments are presented which indicate that one orbit is stable and the other orbit is unstable, whose unstable manifold forms an invariant circle.
Stability of IMEX (implicit–explicit) Runge–Kutta methods applied to delay differential equations (DDEs) is studied on the basis of the scalar test equation
d
u
/
d
t
=
λ
u
(
t
)
+
μ
u
(
t
-
τ
)
, ...where
τ
is a constant delay and
λ
,
μ
are complex parameters. More specifically,
P-stability regions of the methods are defined and analyzed in the same way as in the case of the standard Runge–Kutta methods. A new IMEX method which possesses a superior stability property for DDEs is proposed. Some numerical examples which confirm the results of our analysis are presented.
The mechanisms underlying the hypoxia-induced disruption of the barrier function of neural vasculature were analyzed with reference to the expression of claudin-5, a component of tight junctions ...between neural endothelial cells. The movement of claudin-5 from the cytoplasm to the plasma membrane of cultured confluent brain-derived endothelial (bEND.3) cells was closely correlated with the increase in the transendothelial electrical resistance. Inhibition of the expression of claudin-5 by RNAi resulted in a reduction of transendothelial electrical resistance, indicating a critical role of claudin-5 in the barrier property. Hypoxia (1% O2 ) altered the location of claudin-5 in the plasma membrane and the level of claudin-5 protein in bEND.3 cells, and these changes were accompanied by a decrease in the transendothelial electrical resistance. In vivo the claudin-5 molecules were expressed under normoxia in the plasma membrane of retinal microvascular endothelial cells but were significantly reduced under hypoxic conditions. Tracer experiments revealed that the barrier function of hypoxic retinal vasculature with depressed claudin-5 expression was selectively disrupted against small molecules, which is very similar to the phenotype of claudin-5-deficient mice. These in vitro and in vivo data indicate that claudin-5 is a target molecule of hypoxia leading to the disruption of the barrier function of neural vasculature.
We study stability of Runge–Kutta (RK) methods for delay integro-differential equations with a constant delay on the basis of the linear equation
du
dt
=Lu(t)+Mu(t−τ)+K
∫
t−τ
t
u(θ)
dθ,
where
L,
M,
K ...are constant complex matrices. In particular, we show that the same result as in the case
K=0 (Koto, BIT 34 (1994) 262–267) holds for this test equation, i.e., every
A-stable RK method preserves the delay-independent stability of the exact solution whenever a step-size of the form
h=
τ/
m is used, where
m is a positive integer.
Recently Bellen, Jackiewicz and Zennaro have studied stability properties of Runge-Kutta (RK) methods for neutral delay differential equations using a scalar test equation. In particular, they have ...shown that everyA-stable collocation method isNP-stable, i.e., the method has an analogous stability property toA-stability with respect to the test equation. Consequently, the Gauss, Radau IIA and Lobatto IIIA methods areNP-stable.In this paper, we examine the stability of RK methods based on classical quadrature by a slightly different approach from theirs. As a result, we prove that the Radau IA and Lobatto IIIC methods equipped with suitable continuous extensions are alsoNP-stable by virtue of fundamental notions related to those methods such as simplifying conditions, algebraic stability, and theW-transformation.
The KOTO experiment at the J-PARC 30-GeV Main Ring is dedicated to search for the rare decay
. This mode directly breaks the CP symmetry and is highly suppressed in the Standard Model (SM). In ...addition, the theoretical uncertainties on the decay is only a few percent. Those features make this decay one of the best probes to search for new physics beyond the SM. We have been accumulating physics data since 2013 and we had finalized the analysis with the dataset taken in 2016–2018. In the analysis, we found charged kaons contained in the neutral beam could become a serious background source. Thus, we have installed a new counter to detect the charged kaons and resumed physics data taking. In this parper, we report the results of the 2016–2018 analysis and the status of recent data taking.
We consider a special type of numerical methods for delay differential equations (DDEs). By introducing a new independent variable, an initial value problem for DDEs is converted into an ...initial-boundary value problem for the convection equation. Thus, it is also possible to get an approximate solution to the DDE problem by solving the initial-boundary value problem with a suitable numerical method instead of solving the original problem.
In this paper, we study a family of method of lines (MOL) approximations to the problem, which is obtained by applying Runge-Kutta (RK) methods for space discretization, and prove their convergence under the assumption that the RK methods satisfy a condition, known as an algebraic characterization of
A-stability. The result is also confirmed by numerical experiments. Moreover, we show that the condition derives several stability properties of the MOL approximations.
Interleukin (IL)-6, a potent proinflammatory cytokine, is suggested to be a risk factor for choroidal neovascularization (CNV) because of its increased levels in the serum of patients with ...age-related macular degeneration; however, the role of IL-6 in CNV has not been defined. The present study reveals the critical contribution of IL-6 signaling and its downstream STAT3 pathway to the murine model of laser-induced CNV. CNV induction by laser treatment stimulated IL-6 expression in the retinal pigment epithelium-choroid complex, and antibody-based blockade of IL-6 receptor or genetic ablation of IL-6 led to significant suppression of CNV. CNV generation was accompanied by STAT3 activation in choroidal endothelial cells and macrophages, and IL-6 receptor blockade resulted in selectively inhibited phosphorylation of STAT3 but not extracellular signal-regulated kinase 1/2. Consistently, pharmacological blockade of STAT3 pathway also suppressed CNV. In addition, IL-6 receptor neutralization led to significant inhibition of the in vivo and in vitro expression of inflammation-related molecules including monocyte chemotactic protein, intercellular adhesion molecule-1, and vascular endothelial growth factor, and of macrophage infiltration into CNV. These results indicate the significant involvement of IL-6 receptor-mediated activation of STAT3 inflammatory pathway in CNV generation, suggesting the possibility of IL-6 receptor blockade as a therapeutic strategy to suppress CNV associated with age-related macular degeneration.
Stability of
θ-methods for delay integro-differential equations (DIDEs) is studied on the basis of the linear equation
du
dt
=λu(t)+μu(t−τ)+κ
∫
t−τ
t
u(σ)
dσ,
where
λ,
μ,
κ are complex numbers and
τ ...is a constant delay. It is shown that every
A-stable
θ-method possesses a similar stability property to
P-stability, i.e., the method preserves the delay-independent stability of the exact solution under the condition that
κ is real and
τ/
h is an integer, where
h is a step-size. It is also shown that the method does not possess the same property if
τ/
h is not an integer. As a result, no
θ-method can possess a similar stability property to
GP-stability with respect to DIDEs.
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