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

Sensing low concentrations of CO using flame-spray-made Pt/SnO2 nanoparticles

Tin dioxide nanoparticles of different sizes and platinum doping contents were synthesized in one step using the flame spray pyrolysis (FSP) technique. The particles were used to fabricate semiconducting gas sensors for low level CO detection, i.e. with a CO gas concentration as low as 5ppm in the absence and presence of water. Post treatment of the SnO2 nanoparticles was not needed enabling the investigation of the metal oxide particle size effect. Gas sensors based on tin dioxide with a primary particle size of 10nm showed signals one order of magnitude higher than the ones corresponding to the primary particle size of 330nm. In situ platinum functionalization of the SnO2 during FSP synthesis resulted in higher sensor responses for the 0.2wt% Pt-content than for the 2.0wt% Pt. The effect is mainly attributed to catalytic consumption of CO and to the associated reduced sensor response. Pure and functionalized tin dioxide nanoparticles have been characterized by Brunauer, Emmett and Teller (BET) surface area determination, X-ray diffraction (XRD), high resolution transmission electron microscopy (HRTEM) and scanning transmission electron microscopy (STEM) while the platinum oxidation state and dispersion have been investigated by X-ray photoelectron spectroscopy (XPS) and extended X-ray absorption fine structure (EXAFS). The sensors showed high stability (up to 20days) and are suitable for low level CO detection: <10ppm according to European and 50ppm according to US legislation, respectivel

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

Extent of hypoattenuation on CT angiography source images in Basilar Artery occlusion: prognostic value in the Basilar Artery International Cooperation Study

&lt;p&gt;&lt;b&gt;Background and Purpose:&lt;/b&gt; The posterior circulation Acute Stroke Prognosis Early CT Score (pc-ASPECTS) quantifies the extent of early ischemic changes in the posterior circulation with a 10-point grading system. We hypothesized that pc-ASPECTS applied to CT angiography source images predicts functional outcome of patients in the Basilar Artery International Cooperation Study (BASICS).&lt;/p&gt; &lt;p&gt;&lt;b&gt;Methods:&lt;/b&gt; BASICS was a prospective, observational registry of consecutive patients with acute symptomatic basilar artery occlusion. Functional outcome was assessed at 1 month. We applied pc-ASPECTS to CT angiography source images of patients with CT angiography for confirmation of basilar artery occlusion. We calculated unadjusted and adjusted risk ratios (RRs) of pc-ASPECTS dichotomized at &#8805;8 versus &#60;8. Primary outcome measure was favorable outcome (modified Rankin Scale scores 0–3). Secondary outcome measures were mortality and functional independence (modified Rankin Scale scores 0–2).&lt;/p&gt; &lt;p&gt;&lt;b&gt;Results:&lt;/b&gt; Of 158 patients included, 78 patients had a CT angiography source images pc-ASPECTS ≥8. Patients with a pc-ASPECTS ≥8 more often had a favorable outcome than patients with a pc-ASPECTS &#60;8 (crude RR, 1.7; 95% CI, 0.98–3.0). After adjustment for age, baseline National Institutes of Health Stroke Scale score, and thrombolysis, pc-ASPECTS &#8805;8 was not related to favorable outcome (RR, 1.3; 95% CI, 0.8–2.2), but it was related to reduced mortality (RR, 0.7; 95% CI, 0.5–0.98) and functional independence (RR, 2.0; 95% CI, 1.1–3.8). In post hoc analysis, pc-ASPECTS dichotomized at &#8805;6 versus &#60;6 predicted a favorable outcome (adjusted RR, 3.1; 95% CI, 1.2–7.5).&lt;/p&gt; &lt;p&gt;&lt;b&gt;Conclusions:&lt;/b&gt; pc-ASPECTS on CT angiography source images independently predicted death and functional independence at 1 month in the CT angiography subgroup of patients in the BASICS registry.&lt;/p&gt

Galilei invariant theories. I. Constructions of indecomposable finite-dimensional representations of the homogeneous Galilei group: directly and via contractions

All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations are also obtained via contractions of the corresponding representations of the Lorentz group. Finally the obtained representations are used to derive a general Pauli anomalous interaction term and Darwin and spin-orbit couplings of a Galilean particle interacting with an external electric field.Comment: 23 pages, 2 table

Contractions of Low-Dimensional Lie Algebras

Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of requisite invariant and semi-invariant quantities are calculated for wide classes of Lie algebras including all low-dimensional Lie algebras. An algorithm that allows one to handle one-parametric contractions is presented and applied to low-dimensional Lie algebras. As a result, all one-parametric continuous contractions for the both complex and real Lie algebras of dimensions not greater than four are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases. Levels and co-levels of low-dimensional Lie algebras are discussed in detail. Properties of multi-parametric and repeated contractions are also investigated.Comment: 47 pages, 4 figures, revised versio

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

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

Integrating modes of policy analysis and strategic management practice : requisite elements and dilemmas

There is a need to bring methods to bear on public problems that are inclusive, analytic, and quick. This paper describes the efforts of three pairs of academics working from three different though complementary theoretical foundations and intervention backgrounds (i.e., ways of working) who set out together to meet this challenge. Each of the three pairs had conducted dozens of interventions that had been regarded as successful or very successful by the client groups in dealing with complex policy and strategic problems. One approach focused on leadership issues and stakeholders, another on negotiating competitive strategic intent with attention to stakeholder responses, and the third on analysis of feedback ramifications in developing policies. This paper describes the 10 year longitudinal research project designed to address the above challenge. The important outcomes are reported: the requisite elements of a general integrated approach and the enduring puzzles and tensions that arose from seeking to design a wide-ranging multi-method approach

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