Construction of an isotropic cellular automaton for a reaction-diffusion equation by means of a random walk

We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random walk of microscopic particles and a discrete vector field which defines the time evolution of the particles. The cellular automaton thus obtained can retain isotropy and therefore reproduces the patterns found in the numerical solutions of the reaction-diffusion equation. As a specific example, we apply the method to the Belousov-Zhabotinsky reaction in excitable media

Chiroptical studies on brevianamide B : vibrational and electronic circular dichroism confronted

Chiroptical spectroscopy, such as electronic circular dichroism (ECD) and vibrational circular dichroism (VCD) are highly sensitive techniques to probe molecular conformation, configuration, solvation and aggregation. Here we report the application of these techniques to study the fungal metabolite brevianamide B. Comparison of the experimental ECD and VCD spectra with the density functional theory (DFT) simulated counterparts establishes that VCD is the more reliable technique to assign absolute configuration due to the larger functional and dispersion dependence of computed ECD spectra. Despite a low amount of available material, and a relatively unusual example of using VCD carbonyl multiplets, the absolute configuration could be reliably predicted, strengthening the case for application of VCD in the study of complex natural products. Spectral and crystallographic evidence for or against the formation of a dimeric aggregate is discussed; in solution the VCD spectra strongly suggest only monomeric species are present

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

Quasi-classical Lie algebras and their contractions

After classifying indecomposable quasi-classical Lie algebras in low dimension, and showing the existence of non-reductive stable quasi-classical Lie algebras, we focus on the problem of obtaining sufficient conditions for a quasi-classical Lie algebras to be the contraction of another quasi-classical algebra. It is illustrated how this allows to recover the Yang-Mills equations of a contraction by a limiting process, and how the contractions of an algebra may generate a parameterized families of Lagrangians for pairwise non-isomorphic Lie algebras.Comment: 17 pages, 2 Table

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

Studying engaged learning in online communities

Workshop paper presented at the International Conference of the Learning Sciences, ICLS '06, Bloomington, IN. Retrieved July 18, 2007 from http://www.cis.drexel.edu/faculty/gerry/pub/icls2006eloc.pdf.In this interactive session, participants will think together about “live” issues in the study of online communities as environments in which engaged learning can take place. Specifically, (a) What can we learn from contrasting cases of engaged learning in online communities? (b) Given differing methods, questions, timescales, grain sizes, philosophical orientations, and site contexts, how might generalizability of findings be ensured? (c) What do researchers need in order to develop a coherent theory of learning

Contractions and deformations of quasi-classical Lie algebras preserving a non-degenerate quadratic Casimir operator

By means of contractions of Lie algebras, we obtain new classes of indecomposable quasi-classical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise naturally from non-compact real simple algebras with non-simple complexification, where we impose that a non-degenerate quadratic Casimir operator is preserved by the limiting process. We further consider the converse problem, and obtain sufficient conditions on integrable cocycles of quasi-classical Lie algebras in order to preserve non-degenerate quadratic Casimir operators by the associated linear deformations.Comment: 12 pages. LATEX with revtex4; Proceedings of the XII International Conference on Symmetry Methods in Physics, (Yerevan, 2006) eds. G.S. Pogosyan et al

LOng-term follow-up after liVE kidney donation (LOVE) study: A longitudinal comparison study protocol

Background: The benefits of live donor kidney transplantation must be balanced against the potential harm to the donor. Well-designed prospective studies are needed to study the long-term consequences of kidney donation. Methods: The "LOng-term follow-up after liVE kidney donation" (LOVE) study is a single center longitudinal cohort study on long-term consequences after living kidney donation. We will study individuals who have donated a kidney from 1981 through 2010 in the Erasmus University Medical Center in Rotterdam, The Netherlands. In this time period, 1092 individuals donated a kidney and contact information is available for all individuals. Each participating donor will be matched (1:4) to non-donors derived from the population-based cohort studies of the Rotterdam Study and the Study of Health in Pomerania. Matching will be based on baseline age, gender, BMI, ethnicity, kidney function, blood pressure, pre-existing co-morbidity, smoking, the use of alcohol and highest education degree. Follow-up data is collected on kidney function, kidney-related comorbidity, mortality, quality of life and psychological outcomes in all participants. Discussion: This study will provide evidence on the long-term consequences of live kidney donation for the donor compared to matched non-donors and evaluate the current donor eligibility criteria. Trial registration: Dutch Trial Register NTR3795

Long-term prognosis after kidney donation: a propensity score matched comparison of living donors and non-donors from two population cohorts

Background: Live donor nephrectomy is a safe procedure. However, long-term donor prognosis is debated, necessitating high-quality studies. Methods: A follow-up study of 761 living kidney donors was conducted, who visited the outpatient clinic and were propensity score matched and compared to 1522 non-donors from population-based cohort studies. Primary outcome was kidney function. Secondary outcomes were BMI (kg/m2), incidences of hypertension, diabetes, cardiovascular events, cardiovascular and overall mortality, and quality of life. Results: Median follow-up after donation was 8.0 years. Donors had an increase in serum creatinine of 26 μmol/l (95% CI 24–28), a decrease in eGFR of 27 ml/min/1.73 m2 (95% CI − 29 to − 26), and an eGFR decline of 32% (95% CI 30–33) as compared to non-donors. There was no difference in outcomes between the groups for ESRD, microalbuminuria, BMI, incidence of diabetes or cardiovascular events, and mortality. A lower risk of new-onset hypertension (OR 0.45, 95% CI 0.33–0.62) was found among donors. The EQ-5D health-related scores were higher among donors, whereas the SF-12 physical and mental component scores were lower. Conclusion: Loss of kidney mass after live donation does not translate into negative long-term outcomes in terms of morbidity and mortality compared to non-donors. Trial registration: Dutch Trial Register NTR3795