The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Transdentinal protective role of sodium ascorbate against the cytopathic effects of H(2)O(2) released from bleaching agents

Objectives. The objectives of this study were to evaluate the transdentinal cytotoxicity of 10% and 16% carbamide peroxide gel (CP), as well as the ability of the antioxidant, 10% sodium ascorbate (SA), to protect the odontoblasts in culture. Study design. Human dentin discs of 0.5-mm thickness were obtained and were placed into artificial pulp chambers. MDPC-23 odontoblastlike cells were seeded on pulp surface of the discs and the following groups were established: G1-No Treatment (control), G2-10% SA/6hs, G3-10%/CP6hs, G4-10%SA/6hs+10%CP/6hs, G5-16%CP/6hs, and G6-10%SA/6hs+16%CP/6hs. The cell viability was measured by the MTT assay. Results. In groups where 16% CP was used, decreased cell viability was observed. Conversely, the application of 10% SA on the dentin discs, before the use of the CP, reduced the cytotoxic effects of these products on cells. Conclusions. The 16% CP cause a significant decrease in MDPC-23 cell viability and 10% SA was able to partially prevent the toxic effects of CP. (Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2010; 109: e70-e76)

Rat forming incisor requires a rigorous ECM remodeling modulated by MMP/RECK balance

Reversion-inducing-cysteine-rich protein with Kazal motifs (RECK) is a single membrane-anchored MMP-regulator and regulates matrix metalloproteinases (MMP) 2, 9 and 14. In turn, MMPs are endopeptidases that play a pivotal role in remodeling ECM. In this work, we decided to evaluate expression pattern of RECK in growing rat incisor during, specifically focusing out amelogenesis process. Based on different kinds of ameloblasts, our results showed that RECK expression was conducted by secretory and post-secretory ameloblasts. At the secretory phase, RECK was localized in the infra-nuclear region of the ameloblast, outer epithelium, near blood vessels, and in the stellate reticulum. From the transition to the maturation phases, RECK was strongly expressed by non-epithelial immuno-competent cells (macrophages and/or dendritic-like cells) in the papillary layer. From the transition to the maturation stage, RECK expression was increased. RECK mRNA was amplified by RT-PCR from whole enamel organ. Here, we verified the presence of RECK mRNA during all stages of amelogenesis. These events were governed by ameloblasts and by non-epithelial cells residents in the enamel organ. Concluding, we found differential expression of MMPs-2, -9 and RECK in the different phases of amelogenesis, suggesting that the tissue remodeling is rigorously controlled during dental mineralization.

Ascorbate-induced osteoblast differentiation recruits distinct MMP-inhibitors: RECK and TIMP-2

The bone formation executed by osteoblasts represents an interesting research field both for basic and applied investigations. The goal of this work was to evaluate the molecular mechanisms involved during osteoblast differentiation in vitro. Accordingly, we demonstrated that, during the osteoblastic differentiation, TIMP-2 and RECK presented differential expressions, where RECK expression was downregulated from the 14th day in contrast with an increase in TIMP-2. Concomitantly, our results showed a temporal regulation of two major signaling cascades during osteoblast differentiation: proliferation cascades in which RECK, PI3 K, and GSK-3 beta play a pivotal role and latter, differentiation cascades with participation of Ras, Rho, Rac-1, PKC alpha/beta, and TIMP-2. Furthermore, we observed that phosphorylation level of paxillin was downregulated while FAK(125) remained unchangeable, but active during extracellular matrix (ECM) remodeling. Concluding, our results provide evidences that RECK and TIMP-2 are involved in the control of ECM remodeling in distinct phases of osteoblast differentiation by modulating MMP activities and a multitude of signaling proteins governs these events.

Role of the spinal cord heme oxygenase-carbon monoxide-cGMP pathway in the nociceptive response of rats

The aim of the present study was to investigate the role of the spinal cord heme oxygenase (HO)-carbon monoxide (CO)-soluble guanylate cyclase (sGC)-cGMP pathway in nociceptive response of rats to the formalin experimental nociceptive model. Animals were handled and adapted to the experimental environment for a few days before the formalin test was applied. For the formalin test 50 mu l of a 1% formalin solution was injected subcutaneously in the dorsal surface of the right hind paw. Following injections, animals were observed for I h and flinching behavior was measured as the nociceptive response. Thirty min before the test, rats were pretreated with intrathecal injections with the HO inhibitor, zinc deuteroporphyrin 2,4-bis glycol (ZnDPBG) or heme-lysinate, which is known to induce the HO pathway. Control animals were treated with vehicles. We observed a significant increase in nociceptive response of rats treated with ZnDPBG, and a drastic reduction of flinching nociceptive behavioral response in the heme-lysinate treated animals. Furthermore, the HO pathway seems to act via cGMP, since methylene blue (a sGC inhibitor) prevented the reduction of flinching nociceptive behavioral response caused by heme-lysinate. These findings strongly indicate that the HO pathway plays a spinal antinociceptive role during the formalin test, acting via cGMP. (C) 2007 Elsevier B.V. All rights reserved.

Prolactin differentially modulates the macrophage activity of lactating rats: possible role of reproductive experience

Reproductive experience (i.e., pregnancy and lactation) induces physiological changes in mammals. We recently showed that a previous reproductive experience can modulate the activity of dopaminergic hypothalamic systems while decreasing serum prolactin (PRL) levels and oxidative burst activity in peritoneal macrophages. Dopamine receptor antagonists increase serum PRL levels, and both PRL and dopamine receptors might be involved in the modulation of macrophage activity, providing a means of communication between the nervous and immune systems. The present study evaluated the in vitro effects of PRL and the dopamine receptor 02 antagonist domperidone (DOMP) on the peritoneal activity of macrophages from primiparous and multiparous female rats during lactation. Oxidative bursts and phagocytosis in peritoneal macrophages were evaluated by flow cytometry. Primiparous and multiparous Wistar rats, during the period of lactation (i.e., days 5-7 after parturition) were used. Samples of peritoneal fluid from these rats were first incubated with PRL (10 and 100 nM) for different periods of time. The same procedure was repeated to evaluate the effects of DOMP (10 and 100 nM). Our results showed that macrophages from multiparous rats respond more effectively to in vitro incubation with PRL, especially with regard to oxidative bursts and the percentage of phagocytosis. Additionally, these effects were more pronounced after 30 min of incubation. These data suggest that reproductive experience is associated with a reduction in serum PRL levels, and cells in experienced female animals, including their macrophages, become more sensitive to the effects of PRL (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Propyretic role of the locus coeruleus nitric oxide pathway

Nitric oxide has been reported to modulate fever in the brain. However, the sites where NO exerts this modulation remain somewhat unclear. Locus coeruleus (LC) neurons express not only nitric oxide synthase (NOS) but also soluble guanylyl cyclase (sGC). In the present study, we evaluated in vivo and ex vivo the putative role of the LC NO-cGMP pathway in fever. To this end, deep body temperature was measured before and after pharmacological modulations of the pathway. Moreover, nitrite/nitrate (NOx) and cGMP levels in the LC were assessed. Conscious rats were microinjected within the LC with a non-selective NOS inhibitor (NG-monomethyl-l-arginine acetate), a NO donor (NOC12), a sGC inhibitor (1H-[1,2,4]oxadiazolo[4,3-a]quinoxalin-1-one) or a cGMP analogue (8-bromo-cGMP) and injected intraperitoneally with endotoxin. Inhibition of NOS or sGC before endotoxin injection significantly increased the latency to the onset of fever. During the course of fever, inhibition of NOS or sGC attenuated the febrile response, whereas microinjection of NOC12 or 8-bromo-cGMP increased the response. These findings indicate that the LC NO-cGMP pathway plays a propyretic role. Furthermore, we observed a significant increase in NOx and cGMP levels, indicating that the febrile response to endotoxin is accompanied by stimulation of the NO-cGMP pathway in the LC.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Role of preoptic opioid receptors in the body temperature reduction during hypoxia

Evidence indicates that endogenous opioids play a role in body temperature (Tb) regulation in mammals but no data exist about the involvement of the specific opioid receptors, mu, kappa and delta, in the reduction of Tb induced by hypoxia. Thus, we investigated the participation of these opioid receptors in the anteroventral preoptic region (AVPO) in hypoxic decrease of Th. To this end, Th of unanesthetized Wistar rats was monitored by temperature data loggers before and after intra-AVPO microinjection of the selective kappa-opioid receptor antagonist nor-binaltorphimine dihydrochloride (nor-BNI; 0.1 and 1.0 mu g/100 nL/animal), the selective mu-opioid receptor antagonist D-Phe-Cys-Tyr-D-Trp-Arg-Thr-Pen-Thr-NH(2) cyclic (CTAP; 0.1 and 1.0 mu g/100 nL/animal), and the selective delta-opioid receptor antagonist Naltrindole (0.06 and 0.6 mu g/100 nL/animal) or saline (vehicle, 100 nu animal), during normoxia and hypoxia (7% inspired O(2)). Under normoxia, no effect of opioid antagonists on Th was observed. Hypoxia induced Th to reduce in vehicle group, a response that was inhibited by the microinjection intra-AVPO of nor-BNI. In contrast, CTAP and Naltrindole did not change Th during hypoxia but caused a longer latency for the return of Th to the normoxic values just after low O(2) exposure. Our results indicate the kappa-opioid receptor in the AVPO is important for the reduction of Th during hypoxia while the mu and delta receptors are involved in the increase of Th during normoxia post-hypoxia. (C) 2009 Elsevier B.V. All rights reserved.

Long-term effects of developmental exposure to di-n-butyl-phthalate (DBP) on rat prostate: Proliferative and inflammatory disorders and a possible role of androgens

In the present study we evaluated the toxic effects on the male adult rat prostate of DBP exposure during fetal and lactational periods, because although many studies have addressed the influence of phthalates on the male reproductive system, only a few have discussed their possible effects on prostate development. Pregnant females were distributed into two experimental groups: Control (C) and Treated (T). The females of the T group received DBP (100 mg/kg, by gavage) from gestation day 12 to postnatal day 21, while C rats received the vehicle (corn oil). In adulthood (90 days old), the animals were euthanized. The serum and testicular testosterone levels were measured. Ventral prostate was removed and weighed. Distal segment fragments of the ventral prostate were fixed and processed for histochemistry and immunohistochemistry to detect androgen receptor (AR) and Ki67 antigens. Protein extraction from ventral prostate fragments was performed for AR immunoblotting and Gelatin zymography for MMP-2 and MMP-9 (MMP, metalloproteinase). Stereological and histopathological analyses were also performed. Serum and testicular testosterone levels and prostate weight were comparable between groups. In the T group the relative proportions (%) of epithelial (C=32.86; T=42.04*) and stromal (C=21.61; T=27.88*) compartments were increased, while the luminal compartment was decreased (C=45.54; T=30.08*), *p < 0.05. In T, disseminated inflammatory infiltrate in the stroma, associated or not with epithelial dysplasia and PIN (Prostatic Intraepithelial Neoplasia), was observed. Increases in AR expression, proliferation index and metalloproteinase 9 (MMP-9) activity were noted in T animals. In some T animals, collagen fibrils accumulated adjacent to the epithelium. As far as we are aware, this is the first report in the literature showing that phthalates could play a role in proliferative and inflammatory disorders of the rat prostate. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

Modulatory role of locus coeruleus and estradiol on the stress response of female rats

The activity of the hypothalamic-pituitary-adrenal axis is modulated by the norepinephrinergic system and, in females, also by the ovarian hormones. We investigated the role of ovarian steroids and the locus coeruleus (LC) on stress-induced corticosterone secretion in female rats. Ovariectomized rats without hormonal replacement (OVX) or treated with estradiol (OVE) or estradiol plus progesterone (OVEP) were subjected to jugular cannulation. Immediately after that, each hormonal treatment group was subjected to LC lesion or sham surgery or no brain surgery. After 24 h, blood samples of all 9 groups were collected before and after ether inhalation. Other four groups (OVX control, sham and lesioned, and OVE) were perfused for glucocorticoid receptor (GR) immunocytochemistry in hippocampal CA1 neurons and paraventricular nucleus (PVN). Estradiol replacement decreased while LC lesions increased stress-induced corticosterone secretion. The effect of LC lesion was potentiated with the removal of ovarian steroids. Since GR expression of lesioned animals decreased in the hippocampus, but not in PVN, we suggest that the effect of LC lesion on corticosterone secretion could be due to a reduction in the efficiency of the negative feedback system in the CA1 neurons. However, this mechanism is not involved in the estradiol modulation on corticosteroid secretion, as no change in GR expression was observed in estradiol-treated animals.