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.

B-type supergiants in the Small Magellanic Cloud: rotational velocities and implications for evolutionary models

High-resolution spectra for 24 SMC and Galactic B-type supergiants have been analysed to estimate the contributions of both macroturbulence and rotation to the broadening of their metal lines. Two different methodologies are considered, viz. goodness-of-fit comparisons between observed and theoretical line profiles and identifying zeros in the Fourier transforms of the observed profiles. The advantages and limitations of the two methods are briefly discussed with the latter techniques being adopted for estimating projected rotational velocities ( v sin i) but the former being used to estimate macroturbulent velocities. The projected rotational velocity estimates range from approximately 20 to 60 kms(-1), apart from one SMC supergiant, Sk 191, with a v sin i similar or equal to 90 km s(-1). Apart from Sk 191, the distribution of projected rotational velocities as a function of spectral type are similar in both our Galactic and SMC samples with larger values being found at earlier spectral types. There is marginal evidence for the projected rotational velocities in the SMC being higher than those in the Galactic targets but any differences are only of the order of 5 - 10 km s(-1), whilst evolutionary models predict differences in this effective temperature range of typically 20 to 70 km s(-1). The combined sample is consistent with a linear variation of projected rotational velocity with effective temperature, which would imply rotational velocities for supergiants of 70 kms(-1) at an effective temperature of 28 000 K ( approximately B0 spectral type) decreasing to 32 km s(-1) at 12 000 K (B8 spectral type). For all targets, the macroturbulent broadening would appear to be consistent with a Gaussian distribution ( although other distributions cannot be discounted) with an 1/e half-width varying from approximately 20 km s(-1) at B8 to 60 km s(-1) at B0 spectral types.

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

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.

Interobserver agreement of the Gross Motor Function Classification System in an ambulant population of children with cerebral palsy

Gross Motor Function Classification System (GMFCS) level was reported by three independent assessors in a population of children with cerebral palsy (CP) aged between 4 and 18 years (n=184; 112 males, 72 females; mean age 10y 10mo [SD 3y 7mo]). A software algorithm also provided a computed GMFCS level from a regional CP registry. Participants had clinical diagnoses of unilateral (n=94) and bilateral (n=84) spastic CP, ataxia (n=4), dyskinesia (n=1), and hypotonia (n=1), and could walk independently with or without the use of an aid (GMFCS Levels I-IV). Research physiotherapist (n=184) and parent/guardian data (n=178) were collected in a research environment. Data from the child's community physiotherapist (n=143) were obtained by postal questionnaire. Results, using the kappa statistic with linear weighting (?1w), showed good agreement between the parent/guardian and research physiotherapist (?1w=0.75) with more moderate levels of agreement between the clinical physiotherapist and researcher (?1w=0.64) and the clinical physiotherapist and parent/guardian (?1w=0.57). Agreement was consistently better for older children (>2y). This study has shown that agreement with parent report increases with therapists'experience of the GMFCS and knowledge of the child at the time of grading. Substantial agreement between a computed GMFCS and an experienced therapist (?1w=0.74) also demonstrates the potential for extrapolation of GMFCS rating from an existing CP registry, providing the latter has sufficient data on locomotor ability.

Homocysteine and B-group vitamins in renal transplant patients

Increased plasma homocysteine is an independent risk factor for cardiovascular disease. We have investigated homocysteine and B-group vitamin levels in renal transplant patients. Fasting blood was collected from 55 renal transplant recipients with good renal function and 32 age/sex matched control subjects. Total homocysteine was increased in transplant recipients in comparison to controls (10.9+/-1.5 vs. 6.7+/-1.3 micromol/l, P < 0.001). There was no difference in homocysteine between patients receiving cyclosporin (n = 39, homocysteine 11.0+/-1.5 micromol/l) and patients receiving prednisolone + azathioprine (n = 16, 10.8+/-1.6 micromol/l, mean+/-S.D.), although there was a significant correlation between homocysteine and serum cyclosporin concentration in the sub-group of patients receiving that immunosuppressive regimen (r = 0.42, P < 0.05). Levels of B-group vitamins were similar in patients and controls. Plasma homocysteine is increased in renal transplant recipients even in the presence of minor degrees of renal impairment and normal levels of B-group vitamins.

The dermis contains langerin+ dendritic cells that develop and function independently of epidermal Langerhans cells.

Langerhans cells (LCs) constitute a subset of dendritic cells (DCs) that express the lectin langerin and that reside in their immature state in epidermis. Paradoxically, in mice permitting diphtheria toxin (DT)-mediated ablation of LCs, epidermal LCs reappeared with kinetics that lagged behind that of their putative progeny found in lymph nodes (LNs). Using bone marrow (BM) chimeras, we showed that a major fraction of the langerin(+), skin-derived DCs found in LNs originates from a developmental pathway that is independent from that of epidermal LCs. This pathway, the existence of which was unexpected, originates in the dermis and gives rise to langerin(+) dermal DCs (DDCs) that should not be confused with epidermal LCs en route to LNs. It explains that after DT treatment, some langerin(+), skin-derived DCs reappear in LNs long before LC-derived DCs. Using CD45 expression and BrdU-labeling kinetics, both LCs and langerin(+) DDCs were found to coexist in wild-type mice. Moreover, DT-mediated ablation of epidermal LCs opened otherwise filled niches and permitted repopulation of adult noninflammatory epidermis with BM-derived LCs. Our results stress that the langerin(+) DC network is more complex than originally thought and have implications for the development of transcutaneous vaccines and the improvement of humanized mouse models.

The Function of Intestinal Afferent Neurons in Regulating Satiety During Health and Obesity

Background and aim: Within the gastrointestinal tract, vagal afferents regulate satiety and food intake via chemical and mechanical mechanisms. Cysteinyl Leukotrienes (CysLTs) are lipid mediators that are believed to regulate food intake and body weight. However, the involvement of vagal afferents in this effect remains to be established. Conversely, Glucagon like peptide-1 (GLP-1) is a satiety and incretin peptide hormone. The effect of obesity on GLP-1 mediated gut-brain signaling has yet to be investigated. Since intestinal vagal afferents’ activity is reduced during obesity, it is intriguing to investigate their responses to GLP-1 in such conditions. Methods: Extracellular recordings were performed on intestinal afferents from normal C57Bl6, low fat fed (LFF), and high fat fed (HFF) mice. To examine the effect on neuronal calcium signaling, calcium-imaging experiments were performed on isolated nodose ganglion neurons. Food intake experiments were conducted using LFF and HFF mice. Oral glucose tolerance tests (OGTT) were carried out. Whole cell patch clamp recordings were performed on nodose ganglion neurons from A) normal C57Bl mice to test the effect of CysLTs on membrane excitability, B) LFF and HFF mice to examine GLP-1 effect on membrane excitability during obesity. c-Fos immunohistochemical techniques were performed to measure the level of neuronal activation in the brainstem of both LFF and HFF mice in response to Ex-4. Results: CysLTs increased intestinal afferent firing rate and mechanosensitivity. In single nodose neuron experiments, CysLTs increased excitability. The GLP-1 agonist Ex-4 significantly decreased food intake in LFF but not HFF mice. However, Ex-4 markedly attenuated the rise in blood glucose in both LFF and HFF mice. The observed increase in nerve firing and mechanosensitivity following the application of GLP-1 and Ex-4 was abolished in HFF mice. Cell membrane excitability was significantly increased by Ex-4 in nodose from LFF but not HFF mice. Ex-4 significantly increased the number of activated neurons in the NTS area of LFF mice but not in their HFF counterparts. Conclusion: The previous observations indicate that the role CysLTs play in regulating satiety is likely to be vagally mediated. Also that satiety, but not incretin, effects of GLP-1 are impaired during obesity.