The rate of convergence of Euler approximations for solutions of stochastic differential equations driven by fractional Brownian motion

The paper focuses on discrete-type approximations of solutions to non-homogeneous stochastic differential equations (SDEs) involving fractional Brownian motion (fBm). We prove that the rate of convergence for Euler approximations of solutions of pathwise SDEs driven by fBm with Hurst index $H>1/2$ can be estimated by $O(\delta^{2H-1})$ ($\delta$ is the diameter of partition). For discrete-time approximations of Skorohod-type quasilinear equation driven by fBm we prove that the rate of convergence is $O(\delta^H)$.Comment: 21 pages, (incorrect) weak convergence result removed, to appear in Stochastic

Stochastic evolution equations driven by Liouville fractional Brownian motion

Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of L(H,E)-valued functions with respect to H-cylindrical Liouville fractional Brownian motions (fBm) with arbitrary Hurst parameter in the interval (0,1). For Hurst parameters in (0,1/2) we show that a function F:(0,T)\to L(H,E) is stochastically integrable with respect to an H-cylindrical Liouville fBm if and only if it is stochastically integrable with respect to an H-cylindrical fBm with the same Hurst parameter. As an application we show that second-order parabolic SPDEs on bounded domains in \mathbb{R}^d, driven by space-time noise which is white in space and Liouville fractional in time with Hurst parameter in (d/4,1) admit mild solution which are H\"older continuous both and space.Comment: To appear in Czech. Math.

Alteration in the plasma concentration of a DAAO inhibitor, 3-methylpyrazole-5-carboxylic acid, in the ketamine-treated rats and the influence on the pharmacokinetics of plasma d-tryptophan

A determination method for 3-methylpyrazole-5-carboxylic acid (MPC), an inhibitor of d-amino acid oxidase (DAAO), in rat plasma was developed by using high-performance liquid chromatography-mass spectrometry (LC-MS). The structural isomer of MPC, 3-methylpyrazole-4-carboxylic acid, was used as an internal standard, and the intra- and inter-day accuracies and precisions were satisfactory for the determination of plasma MPC

Regularity of the Solutions to SPDEs in Metric Measure Spaces

In this paper we study the regularity of non-linear parabolic PDEs and stochastic PDEs on metric measure spaces admitting heat kernel estimates. In particular we consider mild function solutions to abstract Cauchy problems and show that the unique solution is Hölder continuous in time with values in a suitable fractional Sobolev space. As this analysis is done via a-priori estimates, we can apply this result to stochastic PDEs on metric measure spaces and solve the equation in a pathwise sense for almost all paths. The main example of noise term is of fractional Brownian type and the metric measure spaces can be classical as well as given by various fractal structures. The whole approach is low dimensional and works for spectral dimensions less than 4

Pharmacological Alterations of Anxious Behaviour in Mice Depending on Both Strain and the Behavioural Situation

A previous study comparing non-emotive mice from the strain C57BL/6/ByJ with ABP/Le mice showed ABP/Le to be more anxious in an open-field situation. In the present study, several compounds affecting anxiety were assayed on ABP/Le and C57BL/6/ByJ mice using three behavioural models of anxiety: the elevated plus-maze, the light-dark discrimination test and the free exploratory paradigm. The compounds used were the full benzodiazepine receptor agonist, chlordiazepoxide, and the antagonist, flumazenil, the GABAA antagonist, bicuculline, the full 5-HT1A agonist 8-OH-DPAT, and the mixed 5-HT1A/5-HT1B agonist, RU 24969. Results showed the effect of the compounds to be dependent on both the strain and the behavioural task. Several compounds found to be anxiolytic in ABP/Le mice had an anxiogenic effect on C57BL/6/ByJ mice. More behavioural changes were observed for ABP/Le in the elevated plus-maze, but the clearest findings for C57BL/6/ByJ mice were observed in the light-dark discrimination apparatus. These data demonstrate that anxious behaviour is a complex phenomenon which cannot be described by a single behavioural task nor by the action of a single compound

Improved Learning and Memory in Aged Mice Deficient in Amyloid β-Degrading Neutral Endopeptidase

BACKGROUND: Neutral endopeptidase, also known as neprilysin and abbreviated NEP, is considered to be one of the key enzymes in initial human amyloid-beta (Abeta) degradation. The aim of our study was to explore the impact of NEP deficiency on the initial development of dementia-like symptoms in mice. METHODOLOGY/PRINCIPAL FINDINGS: We found that while endogenous Abeta concentrations were elevated in the brains of NEP-knockout mice at all investigated age groups, immunohistochemical analysis using monoclonal antibodies did not detect any Abeta deposits even in old NEP knockout mice. Surprisingly, tests of learning and memory revealed that the ability to learn was not reduced in old NEP-deficient mice but instead had significantly improved, and sustained learning and memory in the aged mice was congruent with improved long-term potentiation (LTP) in brain slices of the hippocampus and lateral amygdala. Our data suggests a beneficial effect of pharmacological inhibition of cerebral NEP on learning and memory in mice due to the accumulation of peptides other than Abeta degradable by NEP. By conducting degradation studies and peptide measurements in the brain of both genotypes, we identified two neuropeptide candidates, glucagon-like peptide 1 and galanin, as first potential candidates to be involved in the improved learning in aged NEP-deficient mice. CONCLUSIONS/SIGNIFICANCE: Thus, the existence of peptides targeted by NEP that improve learning and memory in older individuals may represent a promising avenue for the treatment of neurodegenerative diseases

Schizophrenia: do all roads lead to dopamine or is this where they start? Evidence from two epidemiologically informed developmental rodent models

The idea that there is some sort of abnormality in dopamine (DA) signalling is one of the more enduring hypotheses in schizophrenia research. Opinion leaders have published recent perspectives on the aetiology of this disorder with provocative titles such as ‘Risk factors for schizophrenia—all roads lead to dopamine' or ‘The dopamine hypothesis of schizophrenia—the final common pathway'. Perhaps, the other most enduring idea about schizophrenia is that it is a neurodevelopmental disorder. Those of us that model schizophrenia developmental risk-factor epidemiology in animals in an attempt to understand how this may translate to abnormal brain function have consistently shown that as adults these animals display behavioural, cognitive and pharmacological abnormalities consistent with aberrant DA signalling. The burning question remains how can in utero exposure to specific (environmental) insults induce persistent abnormalities in DA signalling in the adult? In this review, we summarize convergent evidence from two well-described developmental animal models, namely maternal immune activation and developmental vitamin D deficiency that begin to address this question. The adult offspring resulting from these two models consistently reveal locomotor abnormalities in response to DA-releasing or -blocking drugs. Additionally, as adults these animals have DA-related attentional and/or sensorimotor gating deficits. These findings are consistent with many other developmental animal models. However, the authors of this perspective have recently refocused their attention on very early aspects of DA ontogeny and describe reductions in genes that induce or specify dopaminergic phenotype in the embryonic brain and early changes in DA turnover suggesting that the origins of these behavioural abnormalities in adults may be traced to early alterations in DA ontogeny. Whether the convergent findings from these two models can be extended to other developmental animal models for this disease is at present unknown as such early brain alterations are rarely examined. Although it is premature to conclude that such mechanisms could be operating in other developmental animal models for schizophrenia, our convergent data have led us to propose that rather than all roads leading to DA, perhaps, this may be where they start