A Skyrme-like model with an exact BPS bound

We propose a new Skyrme-like model with fields taking values on the sphere S3 or, equivalently, on the group SU(2). The action of the model contains a quadratic kinetic term plus a quartic term which is the same as that of the Skyrme-Faddeev model. The novelty of the model is that it possess a first order Bogomolny type equation whose solutions automatically satisfy the second order Euler-Lagrange equations. It also possesses a lower bound on the static energy which is saturated by the Bogomolny solutions. Such Bogomolny equation is equivalent to the so-called force free equation used in plasma and solar Physics, and which possesses large classes of solutions. An old result due to Chandrasekhar prevents the existence of finite energy solutions for the force free equation on the entire three- dimensional space R3. We construct new exact finite energy solutions to the Bogomolny equations for the case where the space is the three-sphere S3, using toroidal like coordinates.

Local scale air quality model with several pollutant sources

[EN]This paper shows a finite element method for pollutant transport with several pollutant sources. An Eulerian convection–diffusion–reaction model to simulate the pollutant dispersion is used. The discretization of the different sources allows to impose the emissions as boundary conditions. The Eulerian description can deal with the coupling of several plumes. An adaptive stabilized finite element formulation, specifically Least-Squares, with a Crank-Nicolson temporal integration is proposed to solve the problem. An splitting scheme has been used to treat separately the transport and the reaction. A mass-consistent model has been used to compute the wind field of the problem…

The electron antineutrino angular correlation coefficient a in free neutron decay: Testing the standard model with the aSPECT-spectrometer

The beta-decay of free neutrons is a strongly over-determined process in the Standard Model (SM) of Particle Physics and is described by a multitude of observables. Some of those observables are sensitive to physics beyond the SM. For example, the correlation coefficients of the involved particles belong to them. The spectrometer aSPECT was designed to measure precisely the shape of the proton energy spectrum and to extract from it the electron anti-neutrino angular correlation coefficient "a". A first test period (2005/ 2006) showed the “proof-of-principles”. The limiting influence of uncontrollable background conditions in the spectrometer made it impossible to extract a reliable value for the coefficient "a" (publication: Baessler et al., 2008, Europhys. Journ. A, 38, p.17-26). A second measurement cycle (2007/ 2008) aimed to under-run the relative accuracy of previous experiments (Stratowa et al. (1978), Byrne et al. (2002)) da/a =5%. I performed the analysis of the data taken there which is the emphasis of this doctoral thesis. A central point are background studies. The systematic impact of background on a was reduced to da/a(syst.)=0.61 %. The statistical accuracy of the analyzed measurements is da/a(stat.)=1.4 %. Besides, saturation effects of the detector electronics were investigated which were initially observed. These turned out not to be correctable on a sufficient level. An applicable idea how to avoid the saturation effects will be discussed in the last chapter.

Periodicities in the Hodgkin-Huxley model and versions of this model with stochastic input

A field of computational neuroscience develops mathematical models to describe neuronal systems. The aim is to better understand the nervous system. Historically, the integrate-and-fire model, developed by Lapique in 1907, was the first model describing a neuron. In 1952 Hodgkin and Huxley [8] described the so called Hodgkin-Huxley model in the article “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve”. The Hodgkin-Huxley model is one of the most successful and widely-used biological neuron models. Based on experimental data from the squid giant axon, Hodgkin and Huxley developed their mathematical model as a four-dimensional system of first-order ordinary differential equations. One of these equations characterizes the membrane potential as a process in time, whereas the other three equations depict the opening and closing state of sodium and potassium ion channels. The membrane potential is proportional to the sum of ionic current flowing across the membrane and an externally applied current. For various types of external input the membrane potential behaves differently. This thesis considers the following three types of input: (i) Rinzel and Miller [15] calculated an interval of amplitudes for a constant applied current, where the membrane potential is repetitively spiking; (ii) Aihara, Matsumoto and Ikegaya [1] said that dependent on the amplitude and the frequency of a periodic applied current the membrane potential responds periodically; (iii) Izhikevich [12] stated that brief pulses of positive and negative current with different amplitudes and frequencies can lead to a periodic response of the membrane potential. In chapter 1 the Hodgkin-Huxley model is introduced according to Izhikevich [12]. Besides the definition of the model, several biological and physiological notes are made, and further concepts are described by examples. Moreover, the numerical methods to solve the equations of the Hodgkin-Huxley model are presented which were used for the computer simulations in chapter 2 and chapter 3. In chapter 2 the statements for the three different inputs (i), (ii) and (iii) will be verified, and periodic behavior for the inputs (ii) and (iii) will be investigated. In chapter 3 the inputs are embedded in an Ornstein-Uhlenbeck process to see the influence of noise on the results of chapter 2.

Quantum solitons in the XXZ model with staggered external magnetic field

The 1-D 1/2-spin XXZ model with staggered external magnetic field, when restricting to low field, can be mapped into the quantum sine-Gordon model through bosonization: this assures the presence of soliton, antisoliton and breather excitations in it. In particular, the action of the staggered field opens a gap so that these physical objects are stable against energetic fluctuations. In the present work, this model is studied both analytically and numerically. On the one hand, analytical calculations are made to solve exactly the model through Bethe ansatz: the solution for the XX + h staggered model is found first by means of Jordan-Wigner transformation and then through Bethe ansatz; after this stage, efforts are made to extend the latter approach to the XXZ + h staggered model (without finding its exact solution). On the other hand, the energies of the elementary soliton excitations are pinpointed through static DMRG (Density Matrix Renormalization Group) for different values of the parameters in the hamiltonian. Breathers are found to be in the antiferromagnetic region only, while solitons and antisolitons are present both in the ferromagnetic and antiferromagnetic region. Their single-site z-magnetization expectation values are also computed to see how they appear in real space, and time-dependent DMRG is employed to realize quenches on the hamiltonian parameters to monitor their time-evolution. The results obtained reveal the quantum nature of these objects and provide some information about their features. Further studies and a better understanding of their properties could bring to the realization of a two-level state through a soliton-antisoliton pair, in order to implement a qubit.

An in vitro triple cell co-culture model with primary cells mimicking the human alveolar epithelial barrier

A triple cell co-culture model was recently established by the authors, consisting of either A549 or 16HBE14o- epithelial cells, human blood monocyte-derived macrophages and dendritic cells, which offers the possibility to study the interaction of xenobiotics with those cells. The 16HBE14o- containing co-culture model mimics the airway epithelial barrier, whereas the A549 co-cultures mimic the alveolar type II-like epithelial barrier. The goal of the present work was to establish a new triple cell co-culture model composed of primary alveolar type I-like cells isolated from human lung biopsies (hAEpC) representing a more realistic alveolar epithelial barrier wall, since type I epithelial cells cover >93% of the alveolar surface. Monocultures of A549 and 16HBE14o- were morphologically and functionally compared with the hAEpC using laser scanning microscopy, as well as transmission electron microscopy, and by determining the epithelial integrity. The triple cell co-cultures were characterized using the same methods. It could be shown that the epithelial integrity of hAEpC (mean ± SD, 1180 ± 188 Ω cm(2)) was higher than in A549 (172 ± 59 Ω cm(2)) but similar to 16HBE14o- cells (1469 ± 156 Ω cm(2)). The triple cell co-culture model with hAEpC (1113 ± 30 Ω cm(2)) showed the highest integrity compared to the ones with A549 (93 ± 14 Ω cm(2)) and 16HBE14o- (558 ± 267 Ω cm(2)). The tight junction protein zonula occludens-1 in hAEpC and 16HBE14o- were more regularly expressed but not in A549. The epithelial alveolar model with hAEpC combined with two immune cells (i.e. macrophages and dendritic cells) will offer a novel and more realistic cell co-culture system to study possible cell interactions of inhaled xenobiotics and their toxic potential on the human alveolar type I epithelial wall.

Stocking of captive-bred fish can cause long-term population decline and gene pool replacement: predictions from a population dynamics model incorporating density-dependent mortality

Releasing captive-bred fish into natural environments (stocking) is common in fisheries worldwide. Although stocking is believed to have a positive effect on fish abundance over the short term, little is known about the long-term consequences of recurrent stocking and its influence on natural populations. In fact, there are growing concerns that genetically maladapted captive-bred fish can eventually reduce the abundance of natural population. In this study, we develop a simple model to quantitatively investigate the condition under which recurrent stocking has long-term effects on the natural population. Using a population dynamics model that takes into account a density-dependent recruitment, a gene responsible for the fitness difference between wild and captive-bred fish, and hybridization between them, we show that there is little or no contribution of recurrent stocking to the stock enhancement without a replacement of the wild gene pool by the captive-bred gene pool. The model further predicted that stocking of an intermediate level causes a reduction, rather than enhancement, of population size over the long term. The population decline due to stocking was attributed to the fitness disadvantage of captive-bred fish and strong overcompensation at recruitment stage. These results suggest that it would be difficult to simultaneously attain population size recovery and conservation of the local gene pool when captive-bred fish have fitness disadvantage in the wild, although caution is needed when applying the predictions from the simplified model to a specific species or population.

The Dual Ownership Structure: a Model to Connect the Cooperative Model With Financial Markets

In business literature, the conflicts among workers, shareholders and the management have been studied mostly in the frame of stakeholder theory. The stakeholder theory recognizes this issue as an agency problem, and tries to solve the problem by establishing a contractual relationship between the agent and principals. However, as Marcoux pointed out, the appropriateness of the contract as a medium to reduce the agency problem should be questioned. As an alternative, the cooperative model minimizes the agency costs by integrating the concept of workers, owners and management. Mondragon Corporation is a successful example of the cooperative model which grew into the sixth largest corporation in Spain. However, the cooperative model has long been ignored in discussions of corporate governance, mainly because the success of the cooperative model is extremely difficult to duplicate in reality. This thesis hopes to revitalize the scholarly examination of cooperatives by developing a new model that overcomes the fundamental problem in the cooperative model: the limited access to capital markets. By dividing the ownership interest into financial and control interest, the dual ownership structure allows cooperatives to issue stock in the capital market by making a financial product out of financial interest.

A Functional-Based Distribution Diagnostic for a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed modesl and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated marginal residual vector by the Cholesky decomposition of the inverse of the estimated marginal variance matrix. Linear functions or the resulting "rotated" residuals are used to construct an empirical cumulative distribution function (ECDF), whose stochastic limit is characterized. We describe a resampling technique that serves as a computationally efficient parametric bootstrap for generating representatives of the stochastic limit of the ECDF. Through functionals, such representatives are used to construct global tests for the hypothesis of normal margional errors. In addition, we demonstrate that the ECDF of the predicted random effects, as described by Lange and Ryan (1989), can be formulated as a special case of our approach. Thus, our method supports both omnibus and directed tests. Our method works well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series).

Cholesky Residuals for Assessing Normal Errors in a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting "rotated" residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and Ryan (1989), Pierce (1982), and Randles (1982). Our method appears to work well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series). Our methods can produce satisfactory results even for models that do not satisfy all of the technical conditions stated in our theory.

Posterior Simulation in the Generalized Linear Model with Semiparmetric Random Effects

Generalized linear mixed models with semiparametric random effects are useful in a wide variety of Bayesian applications. When the random effects arise from a mixture of Dirichlet process (MDP) model, normal base measures and Gibbs sampling procedures based on the Pólya urn scheme are often used to simulate posterior draws. These algorithms are applicable in the conjugate case when (for a normal base measure) the likelihood is normal. In the non-conjugate case, the algorithms proposed by MacEachern and Müller (1998) and Neal (2000) are often applied to generate posterior samples. Some common problems associated with simulation algorithms for non-conjugate MDP models include convergence and mixing difficulties. This paper proposes an algorithm based on the Pólya urn scheme that extends the Gibbs sampling algorithms to non-conjugate models with normal base measures and exponential family likelihoods. The algorithm proceeds by making Laplace approximations to the likelihood function, thereby reducing the procedure to that of conjugate normal MDP models. To ensure the validity of the stationary distribution in the non-conjugate case, the proposals are accepted or rejected by a Metropolis-Hastings step. In the special case where the data are normally distributed, the algorithm is identical to the Gibbs sampler.