Validation and Calibration of Models for Reaction-Diffusion Systems

Space and time scales are not independent in diffusion. In fact, numerical simulations show that different patterns are obtained when space and time steps ($\Delta x$ and $\Delta t$) are varied independently. On the other hand, anisotropy effects due to the symmetries of the discretization lattice prevent the quantitative calibration of models. We introduce a new class of explicit difference methods for numerical integration of diffusion and reaction-diffusion equations, where the dependence on space and time scales occurs naturally. Numerical solutions approach the exact solution of the continuous diffusion equation for finite $\Delta x$ and $\Delta t$, if the parameter $\gamma_N=D \Delta t/(\Delta x)^2$ assumes a fixed constant value, where $N$ is an odd positive integer parametrizing the alghorithm. The error between the solutions of the discrete and the continuous equations goes to zero as $(\Delta x)^{2(N+2)}$ and the values of $\gamma_N$ are dimension independent. With these new integration methods, anisotropy effects resulting from the finite differences are minimized, defining a standard for validation and calibration of numerical solutions of diffusion and reaction-diffusion equations. Comparison between numerical and analytical solutions of reaction-diffusion equations give global discretization errors of the order of $10^{-6}$ in the sup norm. Circular patterns of travelling waves have a maximum relative random deviation from the spherical symmetry of the order of 0.2%, and the standard deviation of the fluctuations around the mean circular wave front is of the order of $10^{-3}$.Comment: 33 pages, 8 figures, to appear in Int. J. Bifurcation and Chao

Endometrial stromal cells of women with recurrent miscarriage fail to discriminate between high- and low-quality human embryos

Background The aetiology of recurrent miscarriage (RM) remains largely unexplained. Women with RM have a shorter time to pregnancy interval than normally fertile women, which may be due to more frequent implantation of non-viable embryos. We hypothesized that human endometrial stromal cells (H-EnSCs) of women with RM discriminate less effectively between high-and low-quality human embryos and migrate more readily towards trophoblast spheroids than H-EnSCs of normally fertile women. Methodology/Principal Findings Monolayers of decidualized H-EnSCs were generated from endometrial biopsies of 6 women with RM and 6 fertile controls. Cell-free migration zones were created and the effect of the presence of a high-quality (day 5 blastocyst, n = 13), a low-quality (day 5 blastocyst with three pronuclei or underdeveloped embryo, n = 12) or AC-1M88 trophoblast cell line spheroid on H-ESC migratory activity was analyzed after 18 hours. In the absence of a spheroid or embryo, migration of H-EnSCs from fertile or RM women was similar. In the presence of a low-quality embryo in the zone, the migration of H-EnSCs of control women was inhibited compared to the basal migration in the absence of an embryo (P<0.05) and compared to the migration in the presence of high-quality embryo (p<0.01). Interestingly, the migratory response H-EnSCs of women with RM did not differ between high- and low-quality embryos. Furthermore, in the presence of a spheroid their migration was enhanced compared to the H-EnSCs of controls (p<0.001). Conclusions H-EnSCs of fertile women discriminate between high- and low-quality embryos whereas H-EnSCs of women with RM fail to do so. H-EnSCs of RM women have a higher migratory response to trophoblast spheroids. Future studies will focus on the mechanisms by which low-quality embryos inhibit the migration of H-EnSCs and how this is deregulated in women with RM

Control of human endometrial stromal cell motility by PDGF-BB, HB-EGF and trophoblast-secreted factors

Human implantation involves extensive tissue remodeling at the fetal-maternal interface. It is becoming increasingly evident that not only trophoblast, but also decidualizing endometrial stromal cells are inherently motile and invasive, and likely contribute to the highly dynamic processes at the implantation site. The present study was undertaken to further characterize the mechanisms involved in the regulation of endometrial stromal cell motility and to identify trophoblast-derived factors that modulate migration. Among local growth factors known to be present at the time of implantation, heparin-binding epidermal growth factor-like growth factor (HB-EGF) triggered chemotaxis (directed locomotion), whereas platelet-derived growth factor (PDGF)-BB elicited both chemotaxis and chemokinesis (non-directed locomotion) of endometrial stromal cells. Supernatants of the trophoblast cell line AC-1M88 and of first trimester villous explant cultures stimulated chemotaxis but not chemokinesis. Proteome profiling for cytokines and angiogenesis factors revealed neither PDGF-BB nor HB-EGF in conditioned media from trophoblast cells or villous explants, while placental growth factor, vascular endothelial growth factor and PDGF-AA were identified as prominent secretory products. Among these, only PDGF-AA triggered endometrial stromal cell chemotaxis. Neutralization of PDGF-AA in trophoblast conditioned media, however, did not diminish chemoattractant activity, suggesting the presence of additional trophoblast-derived chemotactic factors. Pathway inhibitor studies revealed ERK1/2, PI3 kinase/Akt and p38 signaling as relevant for chemotactic motility, whereas chemokinesis depended primarily on PI3 kinase/Akt activation. Both chemotaxis and chemokinesis were stimulated upon inhibition of Rho-associated, coiled-coil containing protein kinase. The chemotactic response to trophoblast secretions was not blunted by inhibition of isolated signaling cascades, indicating activation of overlapping pathways in trophoblast-endometrial communication. In conclusion, trophoblast signals attract endometrial stromal cells, while PDGF-BB and HB-EGF, although not identified as trophoblast-derived, are local growth factors that may serve to fine-tune directed and non-directed migration at the implantation site

An integrable discretization of the rational su(2) Gaudin model and related systems

The first part of the present paper is devoted to a systematic construction of continuous-time finite-dimensional integrable systems arising from the rational su(2) Gaudin model through certain contraction procedures. In the second part, we derive an explicit integrable Poisson map discretizing a particular Hamiltonian flow of the rational su(2) Gaudin model. Then, the contraction procedures enable us to construct explicit integrable discretizations of the continuous systems derived in the first part of the paper.Comment: 26 pages, 5 figure

Incidence of osteonecrosis after renal transplantation

The incidence of osteonecrosis was 24% in 248 patients who had received 262 kidney transplants 1971-1982. However, based only on patients at risk, i.e. alive with functioning transplants, the incidence at 1, 3 and 6 years was found to be 13, 27 and 36%; after six years no new cases were found. the relative increase in body-weight at 180 days was predictive as regards risk for osteonecrosis, while the cumulative dose of steroids was not. This suggests that individual sensitivity to steroids rather than the absolute cumulative dose is involved in the development of osteonecrosis

Long-term air pollution and traffic noise exposures and mild cognitive impairment in older adults : a cross-sectional analysis of the Heinz Nixdorf recall study

Background: Mild cognitive impairment (MCI) describes the intermediate state between normal cognitive aging and dementia. Adverse effects of air pollution (AP) on cognitive functions have been proposed, but investigations of simultaneous exposure to noise are scarce. Objectives: We analyzed the cross-sectional associations of long-term exposure to AP and traffic noise with overall MCI and amnestic (aMCI) and nonamnestic (naMCI) MCI. Methods: At the second examination of the population-based Heinz Nixdorf Recall study, cognitive assessment was completed in 4,086 participants who were 50–80 years old. Of these, 592 participants were diagnosed as having MCI (aMCI, n = 309; naMCI, n = 283) according to previously published criteria using five neuropsychological subtests. We assessed long-term residential concentrations for size-fractioned particulate matter (PM) and nitrogen oxides with land use regression, and for traffic noise [weighted 24-hr (LDEN) and night-time (LNIGHT) means]. Logistic regression models adjusted for individual risk factors were calculated to estimate the association of environmental exposures with MCI in single- and two-exposure models. Results: Most air pollutants and traffic noise were associated with overall MCI and aMCI. For example, an interquartile range increase in PM2.5 and a 10 A-weighted decibel [dB(A)] increase in LDEN were associated with overall MCI as follows [odds ratio (95% confidence interval)]: 1.16 (1.05, 1.27) and 1.40 (1.03, 1.91), respectively, and with aMCI as follows: 1.22 (1.08, 1.38) and 1.53 (1.05, 2.24), respectively. In two-exposure models, AP and noise associations were attenuated [e.g., for aMCI, PM2.5 1.13 (0.98, 1.30) and LDEN 1.46 (1.11, 1.92)]. Conclusions: Long-term exposures to air pollution and traffic noise were positively associated with MCI, mainly with the amnestic subtype

Uterine selection of human embryos at implantation

Human embryos frequently harbor large-scale complex chromosomal errors that impede normal development. Affected embryos may fail to implant although many first breach the endometrial epithelium and embed in the decidualizing stroma before being rejected via mechanisms that are poorly understood. Here we show that developmentally impaired human embryos elicit an endoplasmic stress response in human decidual cells. A stress response was also evident upon in vivo exposure of mouse uteri to culture medium conditioned by low-quality human embryos. By contrast, signals emanating from developmentally competent embryos activated a focused gene network enriched in metabolic enzymes and implantation factors. We further show that trypsin, a serine protease released by pre-implantation embryos, elicits Ca2+ signaling in endometrial epithelial cells. Competent human embryos triggered short-lived oscillatory Ca2+ fluxes whereas low-quality embryos caused a heightened and prolonged Ca2+ response. Thus, distinct positive and negative mechanisms contribute to active selection of human embryos at implantation

Extensions, expansions, Lie algebra cohomology and enlarged superspaces

After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.Comment: 9 pages. Invited talk delivered at the EU RTN Workshop, Copenhagen, Sep. 15-19 and at the Argonne Workshop on Branes and Generalized Dynamics, Oct. 20-24, 2003. Only change: wrong number of a reference correcte