Mutually catalytic branching at infinite rate

The purpose of this doctoral thesis is to prove existence for a mutually catalytic random walk with infinite branching rate on countably many sites. The process is defined as a weak limit of an approximating family of processes. An approximating process is constructed by adding jumps to a deterministic migration on an equidistant time grid. As law of jumps we need to choose the invariant probability measure of the mutually catalytic random walk with a finite branching rate in the recurrent regime. This model was introduced by Dawson and Perkins (1998) and this thesis relies heavily on their work. Due to the properties of this invariant distribution, which is in fact the exit distribution of planar Brownian motion from the first quadrant, it is possible to establish a martingale problem for the weak limit of any convergent sequence of approximating processes. We can prove a duality relation for the solution to the mentioned martingale problem, which goes back to Mytnik (1996) in the case of finite rate branching, and this duality gives rise to weak uniqueness for the solution to the martingale problem. Using standard arguments we can show that this solution is in fact a Feller process and it has the strong Markov property. For the case of only one site we prove that the model we have constructed is the limit of finite rate mutually catalytic branching processes as the branching rate approaches infinity. Therefore, it seems naturalto refer to the above model as an infinite rate branching process. However, a result for convergence on infinitely many sites remains open.

Algorithmique et complexité des systèmes à compteurs

Réalisé en cotutelle avec l'École normale supérieure de Cachan – Université Paris-Saclay

Algorithmique et complexité des systèmes à compteurs

Réalisé en cotutelle avec l'École normale supérieure de Cachan – Université Paris-Saclay

On the Structure of Spatial Branching Processes

The paper is a contribution to the theory of branching processes with discrete time and a general phase space in the sense of [2]. We characterize the class of regular, i.e. in a sense sufficiently random, branching processes (Φk) k∈Z by almost sure properties of their realizations without making any assumptions about stationarity or existence of moments. This enables us to classify the clans of (Φk) into the regular part and the completely non-regular part. It turns out that the completely non-regular branching processes are built up from single-line processes, whereas the regular ones are mixtures of left-tail trivial processes with a Poisson family structure.

Unusual branching in the palm Euterpe edulis Mart

The unusual development of branches along the stem of Euterpe edulis is described for the first time. Branches originated at 2 to 190 cm from the ground. Ramified individuals and branches were able to produce reproductive structures and some branches produced roots. A plausible cause for the observed anomaly could be genetic problems due to small population sizes. The better agreement of this process can have a positive effect in the harvest of the heart of palm through the artificial induction of sprouts, what would prevent the death of the individual.

Electromagnetic energy within a magnetic infinite cylinder and scattering properties for oblique incidence

We analytically calculate the time-averaged electromagnetic energy stored inside a nondispersive magnetic isotropic cylinder that is obliquely irradiated by an electromagnetic plane wave. An expression for the optical-absorption efficiency in terms of the magnetic internal coefficients is also obtained. In the low absorption limit, we derive a relation between the normalized internal energy and the optical-absorption efficiency that is not affected by the magnetism and the incidence angle. This relation, indeed, seems to be independent of the shape of the scatterer. This universal aspect of the internal energy is connected to the transport velocity and consequently to the diffusion coefficient in the multiple scattering regime. Magnetism favors high internal energy for low size parameter cylinders, which leads to a low diffusion coefficient for electromagnetic propagation in 2D random media. (C) 2010 Optical Society of America

Analyzing static three-dimensional elastic domains with a new infinite boundary element formulation

A new two-dimensionally mapped infinite boundary element (IBE) is presented. The formulation is based on a triangular boundary element (BE) with linear shape functions instead of the quadrilateral IBEs usually found in the literature. The infinite solids analyzed are assumed to be three-dimensional, linear-elastic and isotropic, and Kelvin fundamental solutions are employed. One advantage of the proposed formulation over quadratic or higher order elements is that no additional degrees of freedom are added to the original BE mesh by the presence of the IBEs. Thus, the IBEs allow the mesh to be reduced without compromising the accuracy of the result. Two examples are presented, in which the numerical results show good agreement with authors using quadrilateral IBEs and analytical solutions. (C) 2010 Elsevier Ltd. All rights reserved.

Unsaturated Infinite Slope Stability Considering Surface Flux Conditions

A slope stability model is derived for an infinite slope subjected to unsaturated infiltration flow above a phreatic surface. Closed form steady state solutions are derived for the matric suction and degree of saturation profiles. Soil unit weight, consistent with the degree of saturation profile, is also directly calculated and introduced into the analyzes, resulting in closed-form solutions for typical soil parameters and an infinite series solution for arbitrary soil parameters. The solutions are coupled with the infinite slope stability equations to establish a fully realized safety factor function. In general, consideration of soil suction results in higher factor of safety. The increase in shear strength due to the inclusion of soil suction is analogous to making an addition to the cohesion, which, of course, increases the factor of safety against sliding. However, for cohesive soils, the results show lower safety factors for slip surfaces approaching the phreatic surface compared to those produced by common safety factor calculations. The lower factor of safety is due to the increased soil unit weight considered in the matric suction model but not usually accounted for in practice wherein the soil is treated as dry above the phreatic surface. The developed model is verified with a published case study, correctly predicting stability under dry conditions and correctly predicting failure for a particular storm.

Infinite horizon MPC with non-minimal state space feedback

In the MPC literature, stability is usually assured under the assumption that the state is measured. Since the closed-loop system may be nonlinear because of the constraints, it is not possible to apply the separation principle to prove global stability for the Output feedback case. It is well known that, a nonlinear closed-loop system with the state estimated via an exponentially converging observer combined with a state feedback controller can be unstable even when the controller is stable. One alternative to overcome the state estimation problem is to adopt a non-minimal state space model, in which the states are represented by measured past inputs and outputs [P.C. Young, M.A. Behzadi, C.L. Wang, A. Chotai, Direct digital and adaptative control by input-output, state variable feedback pole assignment, International journal of Control 46 (1987) 1867-1881; C. Wang, P.C. Young, Direct digital control by input-output, state variable feedback: theoretical background, International journal of Control 47 (1988) 97-109]. In this case, no observer is needed since the state variables can be directly measured. However, an important disadvantage of this approach is that the realigned model is not of minimal order, which makes the infinite horizon approach to obtain nominal stability difficult to apply. Here, we propose a method to properly formulate an infinite horizon MPC based on the output-realigned model, which avoids the use of an observer and guarantees the closed loop stability. The simulation results show that, besides providing closed-loop stability for systems with integrating and stable modes, the proposed controller may have a better performance than those MPC controllers that make use of an observer to estimate the current states. (C) 2008 Elsevier Ltd. All rights reserved.

Alterations in growth and branching of Neurospora crassa caused by sub-inhibitory concentrations of antifungal agents

Six antifungal agents at subinhibitory concentrations were used for investigating their ability to affect the growth and branching in Neurospora crassa. Among the antifungals herein used, the azole agent ketoconazole at 0.5 mu g/ml inhibited radial growth more than fluconazole at 5.0 mu g/ml while amphotericin B at 0.05 mu g/ml was more effective than nystatin at 0.05 mu g/ml. Morphological alterations in hyphae were observed in the presence of griseofulvin, ketoconazole and terbinafine at the established concentrations. The antifungal agents were more effective on vegetative growth than on conidial germination. Terbinafine markedly reduced growth unit length (GU) by 54.89%, and caused mycelia to become hyperbranched. In all cases, there was a high correlation between hyphal length and number of tips (r > 0.9). All our results showed highly significant differences by ANOVA, (p < 0.001, alpha = 0.05). Considering that the hyphal tip is the main interface between the fungus and its environment/through which enzymes and toxins are secreted and nutrients absorbed, it would not be desirable to obtain a hyperbranched mycelia with inefficient doses of antifungal drugs.

The collision branching process

We consider a branching model, which we call the collision branching process (CBP), that accounts for the effect of collisions, or interactions, between particles or individuals. We establish that there is a unique CBP, and derive necessary and sufficient conditions for it to be nonexplosive. We review results on extinction probabilities, and obtain explicit expressions for the probability of explosion and the expected hitting times. The upwardly skip-free case is studied in some detail.

Quasispin graded-fermion formalism and gl(m vertical bar n)down arrow osp(m vertical bar n) branching rules

The graded-fermion algebra and quasispin formalism are introduced and applied to obtain the gl(m\n)down arrow osp(m\n) branching rules for the two- column tensor irreducible representations of gl(m\n), for the case m less than or equal to n(n > 2). In the case m < n, all such irreducible representations of gl(m\n) are shown to be completely reducible as representations of osp(m\n). This is also shown to be true for the case m=n, except for the spin-singlet representations, which contain an indecomposable representation of osp(m\n) with composition length 3. These branching rules are given in fully explicit form. (C) 1999 American Institute of Physics. [S0022-2488(99)04410-2].

Long-distance signalling and a mutational analysis of branching in pea

Four ramosus mutants with increased branching at basal and aerial nodes have been used to investigate the genetic regulation of bud outgrowth in Pisum sativum L. (garden pea). Studies of long-distance signalling, xylem sap cytokinin concentrations, shoot auxin level, auxin transport and auxin response are discussed. A model of branching control is presented that encompasses two graft-transmissible signals in addition to auxin and cytokinin. Mutants rms1 through rms4 are not deficient in indole-3-acetic acid (IAA) or in the basipetal transport of this hormone. Three of the four mutants, rms1, rms3 and rms4, have very reduced cytokinin concentrations in xylem sap from roots. This reduction in xylem sap cytokinin concentration appears to be caused by a property of the shoot and may be part of a feedback mechanism induced by an aspect of bud outgrowth. The shoot-to-root feedback signal is unlikely to be auxin itself, as auxin levels and transport are not correlated with xylem sap cytokinin concentrations in various intact and grafted mutant and wild-type plants. Rms1 and Rms2 act in shoot and rootstock to regulate the level or transport of graft-transmissible signals. Various grafting studies and double mutant analyses have associated Rms2 with the regulation of the shoot-to-root feedback signal. Rms1 is associated with a second unknown graft-transmissible signal that is postulated to move in the direction of root-to-shoot. Exogenous auxin appears to interact with both of the signals regulated by Rms1 and Rms2 in the inhibition of branching after decapitation. The action of Rms3 and Rms4 is less apparent at this stage, although both appear to act largely in the shoot.

Scope for further analytical solutions for constant flux infiltration into a semi-infinite soil profile or redistribution in a finite soil profile

[1] We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.