Showing papers on "Parametrization published in 2007"

Tracking Deforming Objects Using Particle Filtering for Geometric Active Contours

Abstract: Tracking deforming objects involves estimating the global motion of the object and its local deformations as a function of time. Tracking algorithms using Kalman filters or particle filters have been proposed for finite dimensional representations of shape, but these are dependent on the chosen parametrization and cannot handle changes in curve topology. Geometric active contours provide a framework which is parametrization independent and allow for changes in topology, in the present work, we formulate a particle filtering algorithm in the geometric active contour framework that can be used for tracking moving and deforming objects. To the best of our knowledge, this is the first attempt to implement an approximate particle filtering algorithm for tracking on a (theoretically) infinite dimensional state space.

Algebraic methods in mechanism analysis and synthesis

Abstract: Algebraic methods in connection with classical multidimensional geometry have proven to be very efficient in the computation of direct and inverse kinematics of mechanisms as well as the explanation of strange, pathological behavior. In this paper, we give an overview of the results achieved within the last few years using the algebraic geometric method, geometric preprocessing, and numerical analysis. We provide the mathematical and geometrical background, like Study's parametrization of the Euclidean motion group, the ideals belonging to mechanism constraints, and methods to solve polynomial equations. The methods are explained with different examples from mechanism analysis and synthesis.

Estimating the subgrid variance of saturation, and its parametrization for use in a gcm cloud scheme

Abstract: The prediction of cloud fraction and condensate in the unified weather forecasting/climate prediction model of the UK Meteorological Office, and many other general-circulation models, depends upon a probability distribution of a saturation variable in a grid box. A method of estimating the width of the probability distribution of the saturation variable on the scales of one grid box of the climate configuration (2.5° latitude × 3.75° longitude) has been created, using analyses from the global weather forecasting configuration (0.55° latitude × 0.833° longitude). This width was found to be potentially very variable in time at many locations, therefore the use of climatological values was inappropriate. A parametrization was created to predict the width of the probability distribution of the saturation variable for use in the climate model. the concept of this empirical parametrization was based upon a scaling relationship often observed, and which is present in the global analyses. This new statistically based parametrization replaced the standard approximation used in the Hadley Centre climate model, and significantly reduced the model's biases concerning water vapour, temperature and cloud amount in the upper troposphere.

Scaling and parametrization of clear-sky solar radiation over complex topography

Abstract: [1] Solar radiation at the land surface is influenced by slope, aspect, shadows, and obstruction of the sky, all of which vary over a wide range of length scales in regions of complex topography, with important consequences for the surface energy balance. Atmospheric models, however, generally assume the surface to be flat on subgrid scales. For four areas in North America, ranging in latitude from 39°N to 69°N and in topography from rolling to mountainous, we simulate spatial patterns of clear-sky incoming solar radiation. It is found that distributions of slope components and variations in shaded area with solar elevation can be approximated by simple functions that scale to each of the areas studied. From these results, parametrizations are developed for averages, standard deviations, and distributions of direct-beam and diffuse solar radiation. Results from these parametrizations, and from a modified form of a simpler parametrization presented previously, compare well with statistics from the spatial simulations. The only topographic input required by the parametrizations is the standard deviation of slope components; this parameter is again found to have simple scaling relationships with the resolution and extent of the underlying elevation grid and with the standard deviation of elevation.

Role of land-surface temperature feedback on model performance for the stable boundary layer

Abstract: At present a variety of boundary-layer schemes is in use in numerical models and often a large variation of model results is found. This is clear from model intercomparisons, such as organized within the GEWEX Atmospheric Boundary Layer Study (GABLS). In this paper we analyze how the specification of the land-surface temperature affects the results of a boundary-layer scheme, in particular for stable conditions. As such we use a well established column model of the boundary layer and we vary relevant parameters in the turbulence scheme for stable conditions. By doing so, we can reproduce the outcome for a variety of boundary-layer models. This is illustrated with the original set-up of the second GABLS intercomparison study using prescribed geostrophic winds and land-surface temperatures as inspired by (but not identical to) observations of CASES-99 for a period of more than two diurnal cycles. The model runs are repeated using a surface temperature that is calculated with a simple land-surface scheme. In the latter case, it is found that the range of model results in stable conditions is reduced for the sensible heat fluxes, and the profiles of potential temperature and wind speed. However, in the latter case the modelled surface temperatures are rather different than with the original set-up, which also impacts on near-surface air temperature and wind speed. As such it appears that the model results in stable conditions are strongly influenced by non-linear feedbacks in which the magnitude of the geostrophic wind speed and the related land-surface temperature play an important role.

Testing a cumulus parametrization with a cumulus ensemble model in weak-temperature-gradient mode

Abstract: This paper prototypes a method for calibrating a cumulus parametrization against a cumulus ensemble model The key to this technique is to run the cumulus model and the parametrization in identical ‘test cells’ that provide forcing typical of that seen over tropical oceans In particular, the mean temperature profile is relaxed to a reference profile that is assumed to be characteristic of the environment of the convection This is done by calculating the mean vertical velocity needed to balance heating due to convection, latent-heat release, and radiation with adiabatic cooling This ‘weak-temperature-gradient’ vertical-velocity profile is then used to advect moisture vertically and, via mass continuity, through the sides of the test cell, entraining reference-profile air as needed As an example, a toy cumulus parametrization used previously is altered to reproduce the dependence of rainfall rate on surface wind speed shown by the cumulus ensemble model This alteration greatly changes the behaviour of simulated large-scale disturbances in an aquaplanet equatorial beta-plane model In particular, increasing the slope of the curve of rainfall rate against wind speed results in the development of much greater synoptic-scale variance Copyright © 2007 Royal Meteorological Society

Solving general shallow wave equations on surfaces

Abstract: We propose a new framework for solving General Shallow Wave Equations (GSWE) in order to efficiently simulate water flows on solid surfaces under shallow wave assumptions. Within this framework, we develop implicit schemes for solving the external forces applied to water, including gravity and surface tension. We also present a two-way coupling method to model interactions between fluid and floating rigid objects. Water flows in this system can be simulated not only on planar surfaces by using regular grids, but also on curved surfaces directly without surface parametrization. The experiments show that our system is fast, stable, physically sound, and straightforward to implement on both CPUs and GPUs. It is capable of simulating a variety of water effects including: shallow waves, water drops, rivulets, capillary events and fluid/floating rigid body coupling. Because the system is fast, we can also achieve real-time water drop control and shape design.

Parametric approach to variational two-electron reduced-density-matrix theory

Abstract: Two general variational paradigms for computing ground-state energies and properties of molecular quantum systems are (i) the parametrization of the $N$-particle wave function, as in truncated configuration interaction, which yields an upper bound on the energy in a given basis set and (ii) the constraint of the two-electron reduced-density matrix (2-RDM) by necessary $N$-representability conditions (without using the wave function) which yields a lower bound on the energy in a given basis set [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. In this paper we synthesize these two directions in a class of techniques which we call parametric variational 2-RDM methods. The 2-RDM in these methods is parametrized to be size consistent while approximately satisfying the $N$-representability conditions. We extend an energy functional of Kollmar [C. Kollmar, J. Chem. Phys. 125, 084108 (2006)], which modifies configuration interaction with double excitations to be size consistent, by including not only double but also single excitations explicitly. Using the 2-RDM parametrization, we calculate ground-state energies at both equilibrium and nonequilibrium geometries in correlation-consistent polarized valance double-zeta (cc-pVDZ) basis sets. Energies as well as properties from the parametric variational 2-RDM method, particularly at nonequilibrium geometries, are better in accuracy than those obtained from coupled cluster with single and double excitations. The present work shows clearly that, except in the dissociation of ${\text{N}}_{2}$, the deviation of the 2-RDM from the well-known $N$-representability conditions, such as the $D$, $Q$, and $G$ conditions, is negligible. Furthermore, calculations with helium atoms demonstrate the size consistency of the method. The computational results on $N$ representability and size consistency are especially important because they legitimatize the selected parametrization of the 2-RDM.

Nonlinear and Adaptive Observers for Perspective Dynamic Systems

Abstract: Estimation of 3D structure and motion from 2D images in computer vision systems can be performed using a dynamic system, often referred to as a perspective dynamic system. This paper presents a novel parametrization of the nonlinear perspective dynamic system, from which different estimators for rigid body structure as well as motion can be derived in a straightforward manner. The parametrization allows a structure estimator to be formulated as a nonlinear observer which estimates 3D position, assuming knowledge of angular and linear velocities. The observer performance is demonstrated using simulation examples, where it is also shown how a time scaling parameter can be used to tune the transient response. The parametrization also allows a motion estimator to be formulated as an adaptive observer, estimating angular velocity and 3D position assuming knowledge of the linear velocity. This is demonstrated by deriving an estimator and illustrating its performance in a simulation example. The presented investigations and simulations indicate that the parametrization has a potential for future development of estimators for structure as well as motion in perspective dynamic systems, and for the investigation of similarities and differences in comparison to discrete, projective geometry based, methods.

Towards a new hybrid cumulus parametrization scheme for use in non-hydrostatic weather prediction models

Abstract: Classical mass flux parametrization schemes for cumulus convection generally transport heat and moisture only but do not include a net mass transport. This is well justified for large grid spacings comprising the whole convective circulation in the local grid column, such that all convective mass fluxes locally cancel out. A conceptual problem arises for finer grid spacings as used in contemporary numerical weather prediction (NWP) models, when convection becomes partially resolvable. This problem can be overcome by the hybrid approach presented here. Only updraft and downdraft are parametrized with a net mass transport; the environmental subsidence is treated by the grid-scale equations. The total mass flux in the continuity equation is split into a grid-scale and a subgrid-scale contribution. This parametrization scheme is designed for use in any nonlinear, non-hydrostatic and fully compressible NWP model. We here have chosen the Lokal–Modell (LM) of Deutscher Wetterdienst. Idealized dry mass lifting experiments (without convective heat transport) demonstrate the feasibility of the hybrid approach. Entrainment causes grid-scale convergence and the detrained air, if set to the environmental temperature, spreads mainly horizontally on the grid. Gravity waves are generated when convection starts and ends. Whereas their amplitude depends on the details of the switching on and off of convection, the stationary state (after about 30 minutes) does not. Four model runs with different grid spacings (3.5 km to 28 km) confirm that the mass exchange between the model grid and the parametrization scheme is independent of the chosen grid spacing. Total mass in a convective circulation cell is conserved to better than 0.1%, but only if the damping layer at the upper boundary of the LM is shifted to above 20 km. For moist convection (with convective heat transport), a simple cloud model for an updraft has been set up. As the detrained air at the cloud top is colder than the environment, it moves down by about 1 km but then mainly spreads horizontally again over several tens of kilometres as in the dry case without convective heat transport. The hybrid mass flux approach with both a grid-scale and a subgrid-scale contribution may fill the gap between coarse-grid models (grid spacing > 50 km) with classical parametrization schemes, and very highly resolved explicit convection modelling (with a grid spacing of the order of 100 m). Copyright © 2007 Royal Meteorological Society

Padé approximation of the S-matrix as a way of locating quantum resonances and bound states

Abstract: It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the S-matrix along the real positive energy axis. No calculations of the S-matrix at complex energies or a complex rotation are necessary. The proposed method is therefore universal in that it is applicable to any potential (local, non-local, discontinuous, etc) provided that there is a way of obtaining the S-matrix (or scattering phase shifts) at real collision energies. Besides this, combined with any method that extracts the phase shifts from the scattering data, the proposed rational parametrization technique would be able to do the spectral analysis using the experimental data.

The second COMPARE exercise: A model intercomparison using a case of a typical mesoscale orographic flow, the PYREX IOP3

Abstract: SUMMARY Fifteen models have been evaluated for their ability to simulate the various phenomena of a mesoscale orographic flow sampled during the PyrCnQs experiment (PYREX). A pure forecast exercise has been conducted and model performances were assessed using numerous observations. fio additional experiments were also performed in order to discriminate between small-scale errors and large-scale induced errors, and to discuss an optimal specification of model terrain height and roughness for use with envelope orography and effective roughness length parametrizations. The comparison results reveal systematic errors for all the models: the local winds are too weak, the mountain-wave amplitude is too large and the lee vortices are poorly represented. Since forcing by analyses did not correct the errors, they can be therefore mainly attributed to the model representation of orography. The blocking created by the model topography at low level is under-represented and the model topography does not sufficiently slow the flow. A positive consequence of the effective roughness length parametrization is to reduce the mountain-wave amplitude. Negligible benefit occurs from the use of an envelope orography parametrization. Although it favours the appearance of the lee vortices, the latter appear too early, the local winds remain too weak, and the mountainwave amplitude is enhanced. The comparison of the computed pressure drag with the observed one is reasonably good for most of the models but the pressure drag is found to be more correlated to the lee vorticity than to the mountain wave.

On the parametrization of multivariate garch models

Abstract: This paper deals with issues of structure and parametrization of VECH models proposed in Bollerslev, Engle, and Wooldridge (1988) and Baba, Engle, Kraft, and Kroner (BEKK) models. Both general models and also restricted versions such as the widely used diagonal VECH (DVECH) and factor generalized autoregressive conditional heteroskedastic (F-GARCH) models are discussed. A simple algorithm is presented that checks whether a given VECH model may be cast as a BEKK model. It is shown that in the bivariate case BEKK models are as general as VECH models. In higher dimensional cases however, VECH models allow for more flexibility. In addition, a parametrization for a generic, i.e., open and dense, class of BEKK models is given, and the frequently cited parametrization by Engle and Kroner (1995, Econometric Theory 11, 122–150) is analyzed. Two shortcomings of the latter are pointed out. Finally, parametrizations for BEKK(p,q,K) models with K ≤ n, including DVECH, F-GARCH, and a generalization of the latter, are discussed.This research was supported by the project P17065 “Identification of multivariate dynamic systems with a focus on dimension reduction” of the Austrian Science Foundation (FWF).

A General Framework for the Parametrization of Hierarchical Models

Abstract: In this paper, we describe centering and noncentering methodology as complementary techniques for use in parametrization of broad classes of hierarchical models, with a view to the construction of effective MCMC algorithms for exploring posterior distributions from these models. We give a clear qualitative understanding as to when centering and noncentering work well, and introduce theory concerning the convergence time complexity of Gibbs samplers using centered and noncentered parametrizations. We give general recipes for the construction of noncentered parametrizations, including an auxiliary variable technique called the state-space expansion technique. We also describe partially noncentered methods, and demonstrate their use in constructing robust Gibbs sampler algorithms whose convergence properties are not overly sensitive to the data.

Implicitization and parametrization of quadratic and cubic surfaces by μ -bases

Abstract: Parametric and implicit forms are two common representations of geometric objects. It is important to be able to pass back and forth between the two representations, two processes called parameterization and implicitization, respectively. In this paper, we study the parametrization and implicitization of quadrics (quadratic parametric surfaces with two base points) and cubic surfaces (cubic parametric surfaces with six base points) with the help of μ-bases – a newly developed tool which connects the parametric form and the implicit form of a surface. For both cases, we show that the minimal μ-bases are all linear in the parametric variables, and based on this observation, very efficient algorithms are devised to compute the minimal μ-bases either from the parametric equation or the implicit equation. The conversion between the parametric equation and the implicit equation can be easily accomplished from the minimal μ-bases.

Analytic Parametrization of Three-Dimensional Bodies of Constant Width

Abstract: We present a complete analytic parametrization of constant three-dimensional width bodies based on the median surface: more precisely, we define a bijection between spaces of functions and constant width bodies. We compute simple geometrical quantities like the volume and the surface area in terms of those functions. As a corollary we give a new algebraic proof of Blaschke’s formula. Finally, we derive weak optimality conditions for convex bodies which minimize the volume among constant width bodies.

Parametrization of orographic effects on surface radiation in HIRLAM

Abstract: A parametrization scheme for orographic effects on surface radiation was introduced in the High Resolution Limited Area Model. One-kilometre resolution digital elevation data were used to derive the needed orographic parameters. The scheme is applicable within a model setup of any resolution, but is shown to significantly affect the local near-surface temperatures only when the horizontal resolution is less than a few kilometres. Then, typical maximum local differences due to the new parametrizations are 50–100W m −2 in the net radiation fluxes and 1°–3° in the screen-level temperature. Interactions between clouds and radiation were detected both in the single-column and three-dimensional sensitivity experiments.

Reconstruction of interacting dark energy models from parametrizations

Abstract: Models with interacting dark energy can alleviate the cosmic coincidence problem by allowing dark matter and dark energy to evolve in a similar fashion. At a fundamental level, these models are specified by choosing a functional form for the scalar potential and for the interaction term. However, in order to compare to observational data it is usually more convenient to use parametrizations of the dark energy equation of state and the evolution of the dark matter energy density. Once the relevant parameters are fitted, it is important to obtain the shape of the fundamental functions. In this paper I show how to reconstruct the scalar potential and the scalar interaction with dark matter from general parametrizations. I give a few examples and show that it is possible for the effective equation of state for the scalar field to cross the phantom barrier when interactions are allowed. I analyze the uncertainties in the reconstructed potential arising from foreseen errors in the estimation of fit parameters and point out that a Yukawa-like linear interaction results from a simple parametrization of the coupling.

Implicitization of bihomogeneous parametrizations of algebraic surfaces via linear syzygies

Abstract: We show that the implicit equation of a surface in 3-dimensional projective space parametrized by bi-homogeneous polynomials of bi-degree (d,d)for a given integer d ≥1 can be represented and computed from the linear syzygies of its parametrization if the base points are isolated and form locally a complete intersection.

An improvement of parametrization of short-wave radiation at the sea surface on the basis of direct measurements in the Atlantic

Abstract: Based on the data of recent high-accuracy measurements of the incoming fluxes of short-wave radiation in 2004–2006 in the Atlantic, errors of existing short-wave radiation parametrizations are estimated. It is shown that the largest errors occur under large cloud amount. A parametrization scheme is proposed that takes into account not only total cloudiness, but also morphological types of clouds. The scheme improves parametrization under large cloud amount.

Joint estimation of mutual coupling, element factor, and phase center in antenna arrays

Abstract: A novel method is proposed for estimation of the mutual coupling matrix of an antenna array. The method extends previous work by incorporating an unknown phase center and the element factor (antenna radiation pattern) in the model, and treating them as nuisance parameters during the estimation of coupling. To facilitate this, a parametrization of the element factor based on a truncated Fourier series is proposed. The performance of the proposed estimator is illustrated and compared to other methods using data from simulations and measurements, respectively. The Cramer-Rao bound (CRB) for the estimation problem is derived and used to analyze how the required amount of measurement data increases when introducing additional degrees of freedom in the element factor model. We find that the penalty in SNR is 2.5 dB when introducing a model with two degrees of freedom relative to having zero degrees of freedom. Finally, the tradeoff between the number of degrees of freedom and the accuracy of the estimate is studied. A linear array is treated in more detail and the analysis provides a specific design tradeoff.

Computing general geometric structures on surfaces using Ricci flow

Abstract: Systematically generalizing planar geometric algorithms to manifold domains is of fundamental importance in computer aided design field. This paper proposes a novel theoretic framework, geometric structure, to conquer this problem. In order to discover the intrinsic geometric structures of general surfaces, we developed a theoretic rigorous and practical efficient method, Discrete Variational Ricci flow. Different geometries study the invariants under the corresponding transformation groups. The same geometry can be defined on various manifolds, whereas the same manifold allows different geometries. Geometric structures allow different geometries to be defined on various manifolds, therefore algorithms based on the corresponding geometric invariants can be applied on the manifold domains directly. Surfaces have natural geometric structures, such as spherical structure, affine structure, projective structure, hyperbolic structure and conformal structure. Therefore planar algorithms based on these geometries can be defined on surfaces straightforwardly. Computing the general geometric structures on surfaces has been a long lasting open problem. We solve the problem by introducing a novel method based on discrete variational Ricci flow. We thoroughly explain both theoretical and practical aspects of the computational methodology for geometric structures based on Ricci flow, and demonstrate several important applications of geometric structures: generalizing Voronoi diagram algorithms to surfaces via Euclidean structure, cross global parametrization between high genus surfaces via hyperbolic structure, generalizing planar splines to manifolds via affine structure. The experimental results show that our method is rigorous and efficient and the framework of geometric structures is general and powerful.

Dimension and natural parametrization for SLE curves

Abstract: Some possible definitions for the natural parametrization of SLE (Schramm-Loewner evolution) paths are proposed in terms of various limits. One of the definitions is used to give a new proof of the Hausdorff dimension of SLE paths.

The length of an SLE-Monte Carlo studies

Abstract: The scaling limits of a variety of critical two-dimensional lattice models are equal to the Schramm–Loewner evolution (SLE) for a suitable value of the parameter κ. These lattice models have a natural parametrization of their random curves given by the length of the curve. This parametrization (with suitable scaling) should provide a natural parametrization for the curves in the scaling limit. We conjecture that this parametrization is also given by a type of fractal variation along the curve, and present Monte Carlo simulations to support this conjecture. Then we show by simulations that if this fractal variation is used to parametrize the SLE, then the parametrized curves have the same distribution as the curves in the scaling limit of the lattice models with their natural parametrization.

Parametrization of the deuteron wave function obtained within a dispersion approach

Abstract: We present a convenient analytical parametrization of the deuteron wave function obtained previously within a certain dispersion technique. We fit the numerical results with a discrete superposition of Yukawa-type functions in both configuration and momentum spaces.

Implicitization of rational ruled surfaces with $\mu$-bases

Abstract: Chen, Sederberg, and Zheng introduced the notion of a $\mu$-basis for a rational ruled surface in Chen et al. (2001) and showed that its resultant is the implicit equation of the surface, if the parametrization is generically injective. We generalize this result to the case of an arbitrary parametrization. We also give a new proof for the corresponding theorem in the curve case and treat the reparametrization problem for curves and ruled surfaces.

A note on the parametric maximum flow problem and some related reoptimization issues

Abstract: In this paper, we will extend the results about the parametric maximum flow problem to networks in which the parametrization of the arc capacities can involve both the source and the sink, as in Gallo, Grigoriadis, and Tarjan (1989), and also an additional node. We will show that the minimum cuts of the investigated networks satisfy a relaxed form of the generalized nesting property (Arai, Ueno, and Kajitani, 1993). A consequence is that the corresponding parametric maximum flow value function has at most n −1 breakpoints. All the minimum cut capacities can therefore be computed by O(1) maximum flow computations.