Local non-negative initial data scalar characterization of the Kerr solution

For any vacuum initial data set, we define a local, non-negative scalar quantity which vanishes at every point of the data hypersurface if and only if the data are Kerr initial data. Our scalar quantity only depends on the quantities used to construct the vacuum initial data set which are the Riemannian metric defined on the initial data hypersurface and a symmetric tensor which plays the role of the second fundamental form of the embedded initial data hypersurface. The dependency is algorithmic in the sense that given the initial data one can compute the scalar quantity by algebraic and differential manipulations, being thus suitable for an implementation in a numerical code. The scalar could also be useful in studies of the non-linear stability of the Kerr solution because it serves to measure the deviation of a vacuum initial data set from the Kerr initial data in a local and algorithmic way.

A new approach to the initial value problem

5th Portuguese Conference on Automatic Control, September, 5-7, 2002, Aveiro, Portugal

Promotion carryover as a missing data problem

An important feature of agribusiness promotion programs is their lagged impact on consumption. Efficient investment in advertising requires reliable estimates of these lagged responses and it is desirable from both applied and theoretical standpoints to have a flexible method for estimating them. This note derives an alternative Bayesian methodology for estimating lagged responses when investments occur intermittently within a time series. The method exploits a latent-variable extension of the natural-conjugate, normal-linear model, Gibbs sampling and data augmentation. It is applied to a monthly time series on Turkish pasta consumption (1993:5-1998:3) and three, nonconsecutive promotion campaigns (1996:3, 1997:3, 1997:10). The results suggest that responses were greatest to the second campaign, which allocated its entire budget to television media; that its impact peaked in the sixth month following expenditure; and that the rate of return (measured in metric tons additional consumption per thousand dollars expended) was around a factor of 20.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

Initial-condition problem for a chiral Gross-Neveu system

A time-dependent projection technique is used to treat the initial-value problem for self-interacting fermionic fields. On the basis of the general dynamics of the fields, we derive formal equations of kinetic-type for the set of one-body dynamical variables. A nonperturbative mean-field expansion can be written for these equations. We treat this expansion in lowest order, which corresponds to the Gaussian mean-field approximation, for a uniform system described by the chiral Gross-Neveu Hamiltonian. Standard stationary features of the model, such as dynamical mass generation due to chiral symmetry breaking and a phenomenon analogous to dimensional transmutation, are reobtained in this context. The mean-field time evolution of nonequilibrium initial states is discussed.

Existence of solutions for the 3D-micropolar fluid system with initial data in Besov-Morrey spaces

In this paper, we show a local-in-time existence result for the 3D micropolar fluid system in the framework of Besov-Morrey spaces. The initial data class is larger than the previous ones and contains strongly singular functions and measures. © 2013 Springer Basel.

Geometric inequalities for initial data with symmetries

We consider a class of initial data sets (Σ,h,K) for the Einstein constraint equations which we define to be generalized Brill (GB) data. This class of data is simply connected, U(1)²-invariant, maximal, and four-dimensional with two asymptotic ends. We study the properties of GB data and in particular the topology of Σ. The GB initial data sets have applications in geometric inequalities in general relativity. We construct a mass functional M for GB initial data sets and we show:(i) the mass of any GB data is greater than or equals M, (ii) it is a non-negative functional for a broad subclass of GB data, (iii) it evaluates to the ADM mass of reduced t − φi symmetric data set, (iv) its critical points are stationary U(1)²-invariant vacuum solutions to the Einstein equations. Then we use this mass functional and prove two geometric inequalities: (1) a positive mass theorem for subclass of GB initial data which includes Myers-Perry black holes, (2) a class of local mass-angular momenta inequalities for U(1)²-invariant black holes. Finally, we construct a one-parameter family of initial data sets which we show can be seen as small deformations of the extreme Myers- Perry black hole which preserve the horizon geometry and angular momenta but have strictly greater energy.

Quenching phenomenon of singular parabolic problems with L1 initial data

We extend some previous existence results for quenching type parabolic problems involving a negative power of the unknown in the equation to the case of merely integrable initial data. We show that L1 Ω is the suitable framework to obtain the continuous dependence with respect to some norm of the initial datum; This way we answer to the question raised by several authors in the previous literature. We also show the complete quenching phenomena for such a L1-initial datum.

Mining protein structure data

The principal topic of this work is the application of data mining techniques, in particular of machine learning, to the discovery of knowledge in a protein database. In the first chapter a general background is presented. Namely, in section 1.1 we overview the methodology of a Data Mining project and its main algorithms. In section 1.2 an introduction to the proteins and its supporting file formats is outlined. This chapter is concluded with section 1.3 which defines that main problem we pretend to address with this work: determine if an amino acid is exposed or buried in a protein, in a discrete way (i.e.: not continuous), for five exposition levels: 2%, 10%, 20%, 25% and 30%. In the second chapter, following closely the CRISP-DM methodology, whole the process of construction the database that supported this work is presented. Namely, it is described the process of loading data from the Protein Data Bank, DSSP and SCOP. Then an initial data exploration is performed and a simple prediction model (baseline) of the relative solvent accessibility of an amino acid is introduced. It is also introduced the Data Mining Table Creator, a program developed to produce the data mining tables required for this problem. In the third chapter the results obtained are analyzed with statistical significance tests. Initially the several used classifiers (Neural Networks, C5.0, CART and Chaid) are compared and it is concluded that C5.0 is the most suitable for the problem at stake. It is also compared the influence of parameters like the amino acid information level, the amino acid window size and the SCOP class type in the accuracy of the predictive models. The fourth chapter starts with a brief revision of the literature about amino acid relative solvent accessibility. Then, we overview the main results achieved and finally discuss about possible future work. The fifth and last chapter consists of appendices. Appendix A has the schema of the database that supported this thesis. Appendix B has a set of tables with additional information. Appendix C describes the software provided in the DVD accompanying this thesis that allows the reconstruction of the present work.

Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

Modelling ecological values in heterogeneous and dynamic landscapes with geospatial data

Our surrounding landscape is in a constantly dynamic state, but recently the rate of changes and their effects on the environment have considerably increased. In terms of the impact on nature, this development has not been entirely positive, but has rather caused a decline in valuable species, habitats, and general biodiversity. Regardless of recognizing the problem and its high importance, plans and actions of how to stop the detrimental development are largely lacking. This partly originates from a lack of genuine will, but is also due to difficulties in detecting many valuable landscape components and their consequent neglect. To support knowledge extraction, various digital environmental data sources may be of substantial help, but only if all the relevant background factors are known and the data is processed in a suitable way. This dissertation concentrates on detecting ecologically valuable landscape components by using geospatial data sources, and applies this knowledge to support spatial planning and management activities. In other words, the focus is on observing regionally valuable species, habitats, and biotopes with GIS and remote sensing data, using suitable methods for their analysis. Primary emphasis is given to the hemiboreal vegetation zone and the drastic decline in its semi-natural grasslands, which were created by a long trajectory of traditional grazing and management activities. However, the applied perspective is largely methodological, and allows for the application of the obtained results in various contexts. Models based on statistical dependencies and correlations of multiple variables, which are able to extract desired properties from a large mass of initial data, are emphasized in the dissertation. In addition, the papers included combine several data sets from different sources and dates together, with the aim of detecting a wider range of environmental characteristics, as well as pointing out their temporal dynamics. The results of the dissertation emphasise the multidimensionality and dynamics of landscapes, which need to be understood in order to be able to recognise their ecologically valuable components. This not only requires knowledge about the emergence of these components and an understanding of the used data, but also the need to focus the observations on minute details that are able to indicate the existence of fragmented and partly overlapping landscape targets. In addition, this pinpoints the fact that most of the existing classifications are too generalised as such to provide all the required details, but they can be utilized at various steps along a longer processing chain. The dissertation also emphases the importance of landscape history as an important factor, which both creates and preserves ecological values, and which sets an essential standpoint for understanding the present landscape characteristics. The obtained results are significant both in terms of preserving semi-natural grasslands, as well as general methodological development, giving support to science-based framework in order to evaluate ecological values and guide spatial planning.

Data assimilation for state and parameter estimation: application to morphodynamic modelling

Data assimilation is predominantly used for state estimation; combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts we need good estimates of both the current system state and the model parameters. This paper presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three dimensional variational(3D-Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from SAR satellite imagery and a ship-borne survey is shown to significantly improve the predictive capability of the model over a 2 year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this paper considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D-Var data assimilation algorithm for joint state-parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation-based state-parameter estimation in coastal morphodynamic modelling.

Four-dimensional data assimilation

Numerical weather prediction can be regarded as an initial value problem whereby the governing atmospheric equations are integrated forward from fully determined initial values of the meteorological parameters. However, in spite of the considerable improvements of the observing systems in recent years, the initial values are known only incompletely and inaccurately and one of the major tasks of any forecasting centre is to determine the best possible initial state from available observations.