Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

The Effects of Delta–9–Tetrahydrocannabinol, the primary psychoactive cannabinoid in marijuana, on human sperm function in vitro.

Objective: to investigate the effects of tetrahydrocannabinol; THC on human sperm function in vitro. Design: laboratory analysis of sperm motility with and without exposure to THC using computer assisted semen analysis (CASA) and acrosome reaction by fluoroscein isothiocyanate labelled peanut agglutinin (FITC-PNA) staining. Setting: An ART unit in a tertiary medical centre. Patients: semen was obtained from 78 men attending the Regional Fertility Centre, Belfast. Interventions: Sperm were divided into 90% (the best fertilizing potential used in assisted conception) and 45% (the poorer subpopulation) fractions by density centrifugation and incubated with, or without (controls), tetrahydrocannabinol (THC) at concentrations equivalent to therapeutic (0.032�?�¯?�?�­M) and recreational (4.8 and 0.32�?�¯?�?�­M) plasma levels, at 37�?�¯?�?�°C for 3 hours. Main outcome measures: Sperm motility, spontaneous and induced acrosome reactions Results: There was a dose-dependent decrease in percentage progressive motility (-21% at 4.8�??�?�µM, p0.05) in the 90% fraction. The 45% fraction showed a greater decrease in percentage progressive motility (-56% at 4.8�??�?�µM, p=0.011; -23% at 0.32�??�?�µM, p= 0.039; and -28% at 0.032�??�?�µM, p=0.004). A decrease in the straight line velocity; VSL (-10%) and the average path velocity; VAP (-10%) were also observed in the 90% fraction. A significant inhibition (-15% at 4.8�??�?�µM, p=0.04) in spontaneous acrosome reaction was observed in the 90% fraction. The 45% fraction showed a more marked inhibition [-35% (p

Eye movements and neurocognitive function in treatment resistant schizophrenia: a pilot study.

Objectives: It is increasingly important to develop predictors of treatment response and outcome in schizophrenia. Neuropsychological impairments, particularly those reflecting frontal lobe function, appear to predict poor outcome. Eye movement abnormalities probably also reflect frontal lobe deficits. We wished to see if these two aspects of schizophrenia were correlated and whether they could distinguish a treatment resistant from a treatment responsive group. Methods: Ten treatment resistant schizophrenic patients were compared with ten treatment responsive patients on three eye movement paradigms (reflexive saccades, antisaccades and smooth pursuit), clinical psychopathology (BPRS, SANS and CGI) and a neuropsychological test battery designed to detect frontal lobe dysfunction. Ten aged-matched controls also carried out the eye movement tasks. Results: Both treatment responsive (p = 0.038) and treatment resistant (p = 0.007) patients differed significantly from controls on the antisaccade task. The treatment resistant group had a higher error rate than the treatment responsive group, but the difference was not statistically significant. Similar poor neuropsychological test performance was found in both groups. Conclusions: To demonstrate the biological differences characteristic of treatment resistance, larger sample sizes and wider differences in outcome between the two groups are necessary.

Insulin Dependant Diabetes Mellitus: Implications for Male Reproductive Function.

BACKGROUND Diabetes mellitus (DM) is increasing in men of reproductive age. Despite this, the prevalence of diabetes in men attending fertility clinics is largely unknown. Furthermore, studies examining the effects of DM on sperm fertility potential have been limited to conventional semen analysis. METHODS Conventional semen analysis (semen volume, sperm count, motility and morphology) was performed for 27 diabetic (mean age 34 +/- 2 years) and 29 non-diabetic subjects (control group, men undergoing routine infertility investigations, mean age 33 +/- 1 years). Nuclear DNA (nDNA) fragmentation was assessed using the alkaline Comet assay and mitochondrial DNA (mtDNA) deletions by Long-PCR. RESULTS Other than a small, but significant, reduction in semen volume in diabetic men (2.6 versus 3.3 ml; P <0.05), conventional semen parameters did not differ significantly from control subjects. Diabetic subjects had significantly higher mean nDNA fragmentation (53 versus 32%; P <0.0001) and median number of mtDNA deletions (4 versus 3; P <0.05) compared with control subjects. CONCLUSIONS Diabetes is associated with increased sperm nuclear and mtDNA damage that may impair the reproductive capability of these men.

Fasciola hepatica cathepsin L-like proteases: biology, function and potential in the development of first generation liver fluke vaccines.

Fasciola hepatica secretes cathepsin L proteases that facilitate the penetration of the parasite through the tissues of its host, and also participate in functions such as feeding and immune evasion. The major proteases, cathepsin L1 (FheCL1) and cathepsin L2 (FheCL2) are members of a lineage that gave rise to the human cathepsin Ls, Ks and Ss, but while they exhibit similarities in their substrate specificities to these enzymes they differ in having a wider pH range for activity and an enhanced stability at neutral pH. There are presently 13 Fasciola cathepsin L cDNAs deposited in the public databases representing a gene family of at least seven distinct members, although the temporal and spatial expression of each of these members in the developmental stage of F. hepatica remains unclear. Immunolocalisation and in situ hybridisation studies, using antibody and DNA probes, respectively, show that the vast majority of cathepsin L gene expression is carried out in the epithelial cells lining the parasite gut. Within these cells the enzyme is packaged into secretory vesicles that release their contents into the gut lumen for the purpose of degrading ingested host tissue and blood. Liver flukes also express a novel multi-domain cystatin that may be involved in the regulation of cathepsin L activity. Vaccine trials in both sheep and cattle with purified native FheCL1 and FheCL2 have shown that these enzymes can induce protection, ranging from 33 to 79%, to experimental challenge with metacercariae of F. hepatica, and very potent anti-embryonation/hatch rate effects that would block parasite transmission. In this article we review the vaccine trials carried out over the past 8 years, the role of antibody and T cell responses in mediating protection and discuss the prospects of the cathepsin Ls in the development of first generation recombinant liver fluke vaccines. Author Keywords: Helminths; Trematodes; Parasites; Cathepsins; Proteases; Vaccines; Immunology; Biochemistry