Switching to nonhyperbolic cycles from codim 2 bifurcations of equilibria in ODEs

The paper provides full algorithmic details on switching to the continuation of all possible codim 1 cycle bifurcations from generic codim 2 equilibrium bifurcation points in n-dimensional ODEs. We discuss the implementation and the performance of the algorithm in several examples, including an extended Lorenz-84 model and a laser system.Comment: 17 pages, 7 figures, submitted to Physica

Phylogeny of Cyperaceae Based on DNA Sequence Data–a New rbcL Analysis

Since the Monocots II meeting in 1998, significant new data have been published that enhance our systematic knowledge of Cyperaceae. Phylogenetic studies in the family have also progressed steadily. For this study, a parsimony analysis was carried out using all rbcL sequences currently available for Cyperaceae, including data for two new genera. One of the four subfamilies (Caricoideae) and seven of the 14 tribes (Bisboeckelereae, Cariceae, Cryptangieae, Dulichieae, Eleocharideae, Sclerieae, Trilepideae) are monophyletic. Subfamily Mapanioideae and tribe Chrysitricheae are monophyletic if, as the evidence suggests, Hellmuthia is considered a member of Cypereae. Some other features of our analysis include: well-supported Trilepideae and Sclerieae–Bisboeckelereae clades; a possible close relationship between Cryptangieae and Schoeneae; polyphyletic tribes Schoeneae and Scirpeae; the occurrence of Cariceae within the Dulichieae–Scirpeae clade, and a strongly supported clade, representing Cyperus and allied genera in Cypereae, sister to a poorly supported Ficinia–Hellmuthia– Isolepis–Scirpoides clade. Such patterns are consistent with other studies based on DNA sequence data. One outcome may be that only two subfamilies, Mapanioideae and Cyperoideae, are recognized. Much further work is needed, with efforts carefully coordinated among researchers. The work should focus on obtaining morphological and molecular data for all genera in the family

Mechanisms explaining transitions between tonic and phasic firing in neuronal populations as predicted by a low dimensional firing rate model

Several firing patterns experimentally observed in neural populations have been successfully correlated to animal behavior. Population bursting, hereby regarded as a period of high firing rate followed by a period of quiescence, is typically observed in groups of neurons during behavior. Biophysical membrane-potential models of single cell bursting involve at least three equations. Extending such models to study the collective behavior of neural populations involves thousands of equations and can be very expensive computationally. For this reason, low dimensional population models that capture biophysical aspects of networks are needed. \noindent The present paper uses a firing-rate model to study mechanisms that trigger and stop transitions between tonic and phasic population firing. These mechanisms are captured through a two-dimensional system, which can potentially be extended to include interactions between different areas of the nervous system with a small number of equations. The typical behavior of midbrain dopaminergic neurons in the rodent is used as an example to illustrate and interpret our results. \noindent The model presented here can be used as a building block to study interactions between networks of neurons. This theoretical approach may help contextualize and understand the factors involved in regulating burst firing in populations and how it may modulate distinct aspects of behavior.Comment: 25 pages (including references and appendices); 12 figures uploaded as separate file

Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues

Inverse bifurcation analysis: application to simple gene systems

BACKGROUND: Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional forward problem of determining the mapping from parameter space to the space of model behavior, the inverse problem of determining model parameters to result in certain desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems. These include understanding how the robustness of qualitative behavior arises from system design as well as providing a way to engineer biological networks with qualitative properties. RESULTS: We demonstrate that certain inverse bifurcation problems of biological interest may be cast as optimization problems involving minimal distances of reference parameter sets to bifurcation manifolds. This formulation allows for an iterative solution procedure based on performing a sequence of eigen-system computations and one-parameter continuations of solutions, the latter being a standard capability in existing numerical bifurcation software. As applications of the proposed method, we show that the problem of maximizing regions of a given qualitative behavior as well as the reverse engineering of bistable gene switches can be modelled and efficiently solved

Modelling Cell Polarization Driven by Synthetic Spatially Graded Rac Activation

The small GTPase Rac is known to be an important regulator of cell polarization, cytoskeletal reorganization, and motility of mammalian cells. In recent microfluidic experiments, HeLa cells endowed with appropriate constructs were subjected to gradients of the small molecule rapamycin leading to synthetic membrane recruitment of a Rac activator and direct graded activation of membrane-associated Rac. Rac activation could thus be triggered independent of upstream signaling mechanisms otherwise responsible for transducing activating gradient signals. The response of the cells to such stimulation depended on exceeding a threshold of activated Rac. Here we develop a minimal reaction-diffusion model for the GTPase network alone and for GTPase-phosphoinositide crosstalk that is consistent with experimental observations for the polarization of the cells. The modeling suggests that mutual inhibition is a more likely mode of cell polarization than positive feedback of Rac onto its own activation. We use a new analytical tool, Local Perturbation Analysis, to approximate the partial differential equations by ordinary differential equations for local and global variables. This method helps to analyze the parameter space and behaviour of the proposed models. The models and experiments suggest that (1) spatially uniform stimulation serves to sensitize a cell to applied gradients. (2) Feedback between phosphoinositides and Rho GTPases sensitizes a cell. (3) Cell lengthening/flattening accompanying polarization can increase the sensitivity of a cell and stabilize an otherwise unstable polarization

Pollutant effects on genotoxic parameters and tumor-associated protein levels in adults: a cross sectional study

<p>Abstract</p> <p>Background</p> <p>This study intended to investigate whether residence in areas polluted by heavy industry, waste incineration, a high density of traffic and housing or intensive use of pesticides, could contribute to the high incidence of cancer observed in Flanders.</p> <p>Methods</p> <p>Subjects were 1583 residents aged 50–65 from 9 areas with different types of pollution. Cadmium, lead, p,p'-DDE, hexachlorobenzene, PCBs and dioxin-like activity (Calux test) were measured in blood, and cadmium, t,t'-muconic acid and 1-hydroxypyrene in urine. Effect biomarkers were prostate specific antigen, carcinoembryonic antigen and p53 protein serum levels, number of micronuclei per 1000 binucleated peripheral blood cells, DNA damage (comet assay) in peripheral blood cells and 8-hydroxy-deoxyguanosine in urine. Confounding factors were taken into account.</p> <p>Results</p> <p>Overall significant differences between areas were found for carcinoembryonic antigen, micronuclei, 8-hydroxy-deoxyguanosine and DNA damage. Compared to a rural area with mainly fruit production, effect biomarkers were often significantly elevated around waste incinerators, in the cities of Antwerp and Ghent, in industrial areas and also in other rural areas. Within an industrial area DNA strand break levels were almost three times higher close to industrial installations than 5 kilometres upwind of the main industrial installations (p < 0.0001). Positive exposure-effect relationships were found for carcinoembryonic antigen (urinary cadmium, t,t'-muconic acid, 1-hydroxypyrene and blood lead), micronuclei (PCB118), DNA damage (PCB118) and 8-hydroxy-deoxyguanosine (t,t'-muconic acid, 1-hydroxypyrene). Also, we found significant associations between values of PSA above the p90 and higher values of urinary cadmium, between values of p53 above the p90 and higher serum levels of p,p'-DDE, hexachlorobenzene and marker PCBs (PCB 138, 153 and 180) and between serum levels of p,p'-DDE above the p90 and higher serum values of carcinoembryonic antigen. Significant associations were also found between effect biomarkers and occupational or lifestyle parameters.</p> <p>Conclusion</p> <p>Levels of internal exposure, and residence near waste incinerators, in cities, or close to important industries, but not in areas with intensive use of pesticides, showed positive correlations with biomarkers associated with carcinogenesis and thus probably contribute to risk of cancer. In some rural areas, the levels of these biomarkers were not lower than in the rest of Flanders.</p