A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).

A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountains

An analytical model of orographic gravity wave drag due to sheared flow past elliptical mountains is developed. The model extends the domain of applicability of the well-known Phillips model to wind profiles that vary relatively slowly in the vertical, so that they may be treated using a WKB approximation. The model illustrates how linear processes associated with wind profile shear and curvature affect the drag force exerted by the airflow on mountains, and how it is crucial to extend the WKB approximation to second order in the small perturbation parameter for these effects to be taken into account. For the simplest wind profiles, the normalized drag depends only on the Richardson number, Ri, of the flow at the surface and on the aspect ratio, γ, of the mountain. For a linear wind profile, the drag decreases as Ri decreases, and this variation is faster when the wind is across the mountain than when it is along the mountain. For a wind that rotates with height maintaining its magnitude, the drag generally increases as Ri decreases, by an amount depending on γ and on the incidence angle. The results from WKB theory are compared with exact linear results and also with results from a non-hydrostatic nonlinear numerical model, showing in general encouraging agreement, down to values of Ri of order one.

The structure of the optimal income tax in the quasi-linear model

Existing numerical characterizations of the optimal income tax have been based on a limited number of model specifications. As a result, they do not reveal which properties are general. We determine the optimal tax in the quasi-linear model under weaker assumptions than have previously been used; in particular, we remove the assumption of a lower bound on the utility of zero consumption and the need to permit negative labor incomes. A Monte Carlo analysis is then conducted in which economies are selected at random and the optimal tax function constructed. The results show that in a significant proportion of economies the marginal tax rate rises at low skills and falls at high. The average tax rate is equally likely to rise or fall with skill at low skill levels, rises in the majority of cases in the centre of the skill range, and falls at high skills. These results are consistent across all the specifications we test. We then extend the analysis to show that these results also hold for Cobb-Douglas utility.

Improving power and accuracy of genome-wide association studies via a multi-locus mixed linear model methodology

Genome-wide association studies (GWAS) have been widely used in genetic dissection of complex traits. However, common methods are all based on a fixed-SNP-effect mixed linear model (MLM) and single marker analysis, such as efficient mixed model analysis (EMMA). These methods require Bonferroni correction for multiple tests, which often is too conservative when the number of markers is extremely large. To address this concern, we proposed a random-SNP-effect MLM (RMLM) and a multi-locus RMLM (MRMLM) for GWAS. The RMLM simply treats the SNP-effect as random, but it allows a modified Bonferroni correction to be used to calculate the threshold p value for significance tests. The MRMLM is a multi-locus model including markers selected from the RMLM method with a less stringent selection criterion. Due to the multi-locus nature, no multiple test correction is needed. Simulation studies show that the MRMLM is more powerful in QTN detection and more accurate in QTN effect estimation than the RMLM, which in turn is more powerful and accurate than the EMMA. To demonstrate the new methods, we analyzed six flowering time related traits in Arabidopsis thaliana and detected more genes than previous reported using the EMMA. Therefore, the MRMLM provides an alternative for multi-locus GWAS.

Mitochondrial sequence data and Dipsacales phylogeny: Mixed models, partitioned Bayesian analyses, and model selection

Phylogenetic analyses of chloroplast DNA sequences, morphology, and combined data have provided consistent support for many of the major branches within the angiosperm, clade Dipsacales. Here we use sequences from three mitochondrial loci to test the existing broad scale phylogeny and in an attempt to resolve several relationships that have remained uncertain. Parsimony, maximum likelihood, and Bayesian analyses of a combined mitochondrial data set recover trees broadly consistent with previous studies, although resolution and support are lower than in the largest chloroplast analyses. Combining chloroplast and mitochondrial data results in a generally well-resolved and very strongly supported topology but the previously recognized problem areas remain. To investigate why these relationships have been difficult to resolve we conducted a series of experiments using different data partitions and heterogeneous substitution models. Usually more complex modeling schemes are favored regardless of the partitions recognized but model choice had little effect on topology or support values. In contrast there are consistent but weakly supported differences in the topologies recovered from coding and non-coding matrices. These conflicts directly correspond to relationships that were poorly resolved in analyses of the full combined chloroplast-mitochondrial data set. We suggest incongruent signal has contributed to our inability to confidently resolve these problem areas. (c) 2007 Elsevier Inc. All rights reserved.

Hierarchical spherical model from a geometric point of view

A continuous version of the hierarchical spherical model at dimension d=4 is investigated. Two limit distributions of the block spin variable X(gamma), normalized with exponents gamma = d + 2 and gamma=d at and above the critical temperature, are established. These results are proven by solving certain evolution equations corresponding to the renormalization group (RG) transformation of the O(N) hierarchical spin model of block size L(d) in the limit L down arrow 1 and N ->infinity. Starting far away from the stationary Gaussian fixed point the trajectories of these dynamical system pass through two different regimes with distinguishable crossover behavior. An interpretation of this trajectories is given by the geometric theory of functions which describe precisely the motion of the Lee-Yang zeroes. The large-N limit of RG transformation with L(d) fixed equal to 2, at the criticality, has recently been investigated in both weak and strong (coupling) regimes by Watanabe (J. Stat. Phys. 115:1669-1713, 2004) . Although our analysis deals only with N = infinity case, it complements various aspects of that work.

Bayesian binary regression model: an application to in-hospital death after AMI prediction

Um modelo bayesiano de regressão binária é desenvolvido para predizer óbito hospitalar em pacientes acometidos por infarto agudo do miocárdio. Métodos de Monte Carlo via Cadeias de Markov (MCMC) são usados para fazer inferência e validação. Uma estratégia para construção de modelos, baseada no uso do fator de Bayes, é proposta e aspectos de validação são extensivamente discutidos neste artigo, incluindo a distribuição a posteriori para o índice de concordância e análise de resíduos. A determinação de fatores de risco, baseados em variáveis disponíveis na chegada do paciente ao hospital, é muito importante para a tomada de decisão sobre o curso do tratamento. O modelo identificado se revela fortemente confiável e acurado, com uma taxa de classificação correta de 88% e um índice de concordância de 83%.

Multiobjective linear model for pre-feasibility design of cogeneration systems

This article deals with some methodologies for economic and technical evaluations of cogeneration projects proposed by several authors. A discussion on design philosophy applied to thermal power plants leads to the decision problem of a conflicting, multiobjective formulation that includes the most important parameters. This model is formulated to help decision makers and designers in choosing compromise values for included parameters. (C) 1997 Elsevier B.V. Ltd.

A Multi-Stage Stochastic Non-Linear Model for Reactive Power Planning Under Contingencies

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-destructive linear model for leaf area estimation in Vernonia ferruginea Less

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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.