Phylogenetic mixture models can reduce node-density artifacts

We investigate the performance of phylogenetic mixture models in reducing a well-known and pervasive artifact of phylogenetic inference known as the node-density effect, comparing them to partitioned analyses of the same data. The node-density effect refers to the tendency for the amount of evolutionary change in longer branches of phylogenies to be underestimated compared to that in regions of the tree where there are more nodes and thus branches are typically shorter. Mixture models allow more than one model of sequence evolution to describe the sites in an alignment without prior knowledge of the evolutionary processes that characterize the data or how they correspond to different sites. If multiple evolutionary patterns are common in sequence evolution, mixture models may be capable of reducing node-density effects by characterizing the evolutionary processes more accurately. In gene-sequence alignments simulated to have heterogeneous patterns of evolution, we find that mixture models can reduce node-density effects to negligible levels or remove them altogether, performing as well as partitioned analyses based on the known simulated patterns. The mixture models achieve this without knowledge of the patterns that generated the data and even in some cases without specifying the full or true model of sequence evolution known to underlie the data. The latter result is especially important in real applications, as the true model of evolution is seldom known. We find the same patterns of results for two real data sets with evidence of complex patterns of sequence evolution: mixture models substantially reduced node-density effects and returned better likelihoods compared to partitioning models specifically fitted to these data. We suggest that the presence of more than one pattern of evolution in the data is a common source of error in phylogenetic inference and that mixture models can often detect these patterns even without prior knowledge of their presence in the data. Routine use of mixture models alongside other approaches to phylogenetic inference may often reveal hidden or unexpected patterns of sequence evolution and can improve phylogenetic inference.

Parallel Monte Carlo approach for integration of the rendering equation

This paper is addressed to the numerical solving of the rendering equation in realistic image creation. The rendering equation is integral equation describing the light propagation in a scene accordingly to a given illumination model. The used illumination model determines the kernel of the equation under consideration. Nowadays, widely used are the Monte Carlo methods for solving the rendering equation in order to create photorealistic images. In this work we consider the Monte Carlo solving of the rendering equation in the context of the parallel sampling scheme for hemisphere. Our aim is to apply this sampling scheme to stratified Monte Carlo integration method for parallel solving of the rendering equation. The domain for integration of the rendering equation is a hemisphere. We divide the hemispherical domain into a number of equal sub-domains of orthogonal spherical triangles. This domain partitioning allows to solve the rendering equation in parallel. It is known that the Neumann series represent the solution of the integral equation as a infinity sum of integrals. We approximate this sum with a desired truncation error (systematic error) receiving the fixed number of iteration. Then the rendering equation is solved iteratively using Monte Carlo approach. At each iteration we solve multi-dimensional integrals using uniform hemisphere partitioning scheme. An estimate of the rate of convergence is obtained using the stratified Monte Carlo method. This domain partitioning allows easy parallel realization and leads to convergence improvement of the Monte Carlo method. The high performance and Grid computing of the corresponding Monte Carlo scheme are discussed.

Nonlinear system identification using particle swarm optimisation tuned radial basis function models

A novel particle swarm optimisation (PSO) tuned radial basis function (RBF) network model is proposed for identification of non-linear systems. At each stage of orthogonal forward regression (OFR) model construction process, PSO is adopted to tune one RBF unit's centre vector and diagonal covariance matrix by minimising the leave-one-out (LOO) mean square error (MSE). This PSO aided OFR automatically determines how many tunable RBF nodes are sufficient for modelling. Compared with the-state-of-the-art local regularisation assisted orthogonal least squares algorithm based on the LOO MSE criterion for constructing fixed-node RBF network models, the PSO tuned RBF model construction produces more parsimonious RBF models with better generalisation performance and is often more efficient in model construction. The effectiveness of the proposed PSO aided OFR algorithm for constructing tunable node RBF models is demonstrated using three real data sets.

Wigner Transport models of the electron-phonon kinetics in quantum wires

Two quantum-kinetic models of ultrafast electron transport in quantum wires are derived from the generalized electron-phonon Wigner equation. The various assumptions and approximations allowing one to find closed equations for the reduced electron Wigner function are discussed with an emphasis on their physical relevance. The models correspond to the Levinson and Barker-Ferry equations, now generalized to account for a space-dependent evolution. They are applied to study the quantum effects in the dynamics of an initial packet of highly nonequilibrium carriers, locally generated in the wire. The properties of the two model equations are compared and analyzed.

Ocean acoustic models for low frequency propagation in 2D and 3D environments

In this paper we are mainly concerned with the development of efficient computer models capable of accurately predicting the propagation of low-to-middle frequency sound in the sea, in axially symmetric (2D) and in fully 3D environments. The major physical features of the problem, i.e. a variable bottom topography, elastic properties of the subbottom structure, volume attenuation and other range inhomogeneities are efficiently treated. The computer models presented are based on normal mode solutions of the Helmholtz equation on the one hand, and on various types of numerical schemes for parabolic approximations of the Helmholtz equation on the other. A new coupled mode code is introduced to model sound propagation in range-dependent ocean environments with variable bottom topography, where the effects of an elastic bottom, of volume attenuation, surface and bottom roughness are taken into account. New computer models based on finite difference and finite element techniques for the numerical solution of parabolic approximations are also presented. They include an efficient modeling of the bottom influence via impedance boundary conditions, they cover wide angle propagation, elastic bottom effects, variable bottom topography and reverberation effects. All the models are validated on several benchmark problems and versus experimental data. Results thus obtained were compared with analogous results from standard codes in the literature.

A note on the analysis error associated with 3D-FGAT

The analysis-error variance of a 3D-FGAT assimilation is examined analytically using a simple scalar equation. It is shown that the analysis-error variance may be greater than the error variances of the inputs. The results are illustrated numerically with a scalar example and a shallow-water model.

The International Urban Energy Balance Models Comparison Project: First Results from Phase 1

A large number of urban surface energy balance models now exist with different assumptions about the important features of the surface and exchange processes that need to be incorporated. To date, no com- parison of these models has been conducted; in contrast, models for natural surfaces have been compared extensively as part of the Project for Intercomparison of Land-surface Parameterization Schemes. Here, the methods and first results from an extensive international comparison of 33 models are presented. The aim of the comparison overall is to understand the complexity required to model energy and water exchanges in urban areas. The degree of complexity included in the models is outlined and impacts on model performance are discussed. During the comparison there have been significant developments in the models with resulting improvements in performance (root-mean-square error falling by up to two-thirds). Evaluation is based on a dataset containing net all-wave radiation, sensible heat, and latent heat flux observations for an industrial area in Vancouver, British Columbia, Canada. The aim of the comparison is twofold: to identify those modeling ap- proaches that minimize the errors in the simulated fluxes of the urban energy balance and to determine the degree of model complexity required for accurate simulations. There is evidence that some classes of models perform better for individual fluxes but no model performs best or worst for all fluxes. In general, the simpler models perform as well as the more complex models based on all statistical measures. Generally the schemes have best overall capability to model net all-wave radiation and least capability to model latent heat flux.

An improved digital deconvolution equation

This paper first points out the important fact that the rectangle formulas of continuous convolution discretization, which was widely used in conventional digital deconvolution algorithms, can result in zero-time error. Then, an improved digital deconvolution equation is suggested which is equivalent to the trapezoid formulas of continuous convolution discretization and can overcome the disadvantage of conventional equation satisfactorily. Finally, a simulation in computer is given, thus confirming the theoretical result.

Four-dimensional variational data assimilation for high resolution nested models

Four-dimensional variational data assimilation (4D-Var) is used in environmental prediction to estimate the state of a system from measurements. When 4D-Var is applied in the context of high resolution nested models, problems may arise in the representation of spatial scales longer than the domain of the model. In this paper we study how well 4D-Var is able to estimate the whole range of spatial scales present in one-way nested models. Using a model of the one-dimensional advection–diffusion equation we show that small spatial scales that are observed can be captured by a 4D-Var assimilation, but that information in the larger scales may be degraded. We propose a modification to 4D-Var which allows a better representation of these larger scales.

Linear-wavelet models for system identification

A model structure comprising a wavelet network and a linear term is proposed for nonlinear system identification. It is shown that under certain conditions wavelets are orthogonal to linear functions and, as a result, the two parts of the model can be identified separately. The linear-wavelet model is compared to a standard wavelet network using data from a simulated fermentation process. The results show that the linear-wavelet model yields a smaller modelling error when compared to a wavelet network using the same number of regressors.

Atmospheric blocking and mean biases in climate models

Models often underestimate blocking in the Atlantic and Pacific basins and this can lead to errors in both weather and climate predictions. Horizontal resolution is often cited as the main culprit for blocking errors due to poorly resolved small-scale variability, the upscale effects of which help to maintain blocks. Although these processes are important for blocking, the authors show that much of the blocking error diagnosed using common methods of analysis and current climate models is directly attributable to the climatological bias of the model. This explains a large proportion of diagnosed blocking error in models used in the recent Intergovernmental Panel for Climate Change report. Furthermore, greatly improved statistics are obtained by diagnosing blocking using climate model data corrected to account for mean model biases. To the extent that mean biases may be corrected in low-resolution models, this suggests that such models may be able to generate greatly improved levels of atmospheric blocking.

The influence of carbon surface oxygen groups on Dubinin–Astakhov equation parameters calculated from CO2 adsorption isotherm

We present the results of a systematic study of the influence of carbon surface oxidation on Dubinin–Astakhov isotherm parameters obtained from the fitting of CO2 adsorption data. Using GCMC simulations of adsorption on realistic VPC models differing in porosity and containing the most frequently occurring carbon surface functionalities (carboxyls, hydroxyls and carbonyls) and their mixtures, it is concluded that the maximum adsorption calculated from the DA model is not strongly affected by the presence of oxygen groups. Unfortunately, the same cannot be said of the remaining two parameters of this model i.e. the heterogeneity parameter (n) and the characteristic energy of adsorption (E0). Since from the latter the pore diameters of carbons are usually calculated, by inverse-type relationships, it is concluded that they are questionable for carbons containing surface oxides, especially carboxyls.

A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.

Hyper-parallel tempering Monte Carlo simulations of Ar adsorption in new models of microporous non-graphitizing activated carbon: effect of microporosity

The adsorption of gases on microporous carbons is still poorly understood, partly because the structure of these carbons is not well known. Here, a model of microporous carbons based on fullerene- like fragments is used as the basis for a theoretical study of Ar adsorption on carbon. First, a simulation box was constructed, containing a plausible arrangement of carbon fragments. Next, using a new Monte Carlo simulation algorithm, two types of carbon fragments were gradually placed into the initial structure to increase its microporosity. Thirty six different microporous carbon structures were generated in this way. Using the method proposed recently by Bhattacharya and Gubbins ( BG), the micropore size distributions of the obtained carbon models and the average micropore diameters were calculated. For ten chosen structures, Ar adsorption isotherms ( 87 K) were simulated via the hyper- parallel tempering Monte Carlo simulation method. The isotherms obtained in this way were described by widely applied methods of microporous carbon characterisation, i. e. Nguyen and Do, Horvath - Kawazoe, high- resolution alpha(a)s plots, adsorption potential distributions and the Dubinin - Astakhov ( DA) equation. From simulated isotherms described by the DA equation, the average micropore diameters were calculated using empirical relationships proposed by different authors and they were compared with those from the BG method.

Generic unified modelling process for developing semantically rich, dynamic and temporal models

Models play a vital role in supporting a range of activities in numerous domains. We rely on models to support the design, visualisation, analysis and representation of parts of the world around us, and as such significant research effort has been invested into numerous areas of modelling; including support for model semantics, dynamic states and behaviour, temporal data storage and visualisation. Whilst these efforts have increased our capabilities and allowed us to create increasingly powerful software-based models, the process of developing models, supporting tools and /or data structures remains difficult, expensive and error-prone. In this paper we define from literature the key factors in assessing a model’s quality and usefulness: semantic richness, support for dynamic states and object behaviour, temporal data storage and visualisation. We also identify a number of shortcomings in both existing modelling standards and model development processes and propose a unified generic process to guide users through the development of semantically rich, dynamic and temporal models.