Multidimensional Grid Research Articles

A Parametrically Constrained Optimization Method for Fitting Sedimentation Velocity Experiments

A method for fitting sedimentation velocity experiments using whole boundary Lamm equation solutions is presented. The method, termed parametrically constrained spectrum analysis (PCSA), provides an optimized approach for simultaneously modeling heterogeneity in size and anisotropy of macromolecular mixtures. The solutions produced by PCSA are particularly useful for modeling polymerizing systems, where a single-valued relationship exists between the molar mass of the growing polymer chain and its corresponding anisotropy. The PCSA uses functional constraints to identify this relationship, and unlike other multidimensional grid methods, assures that only a single molar mass can be associated with a given anisotropy measurement. A description of the PCSA algorithm is presented, as well as several experimental and simulated examples that illustrate its utility and capabilities. The performance advantages of the PCSA method in comparison to other methods are documented. The method has been added to the UltraScan-III software suite, which is available for free download from http://www.ultrascan.uthscsa.edu.

Discrete Tomography determination of bounded sets in [formula omitted

This paper deals with the uniqueness problem for bounded sets in Discrete Tomography, namely to decide when an unknown finite subset of points in a multidimensional grid is uniquely determined by its X-rays corresponding to a given set of lattice directions.In Brunetti et al. (2013) the authors completely settled the problem in dimension two, by proving that whole families of suitable sets of four directions can be found, for which they provided a complete characterization.In this paper we examine the problem in higher dimensions. We show that d+1 represents the minimal number of directions we need in Zn (n≥d≥3) to distinguish all the subsets of a finite grid by their X-rays in these directions, under the requirement that such directions span a d-dimensional subspace of Zn. It turns out that the situation differs from the planar case, where less than four directions are never sufficient for uniqueness. Moreover we characterize the minimal sets of directions of uniqueness by providing a necessary and sufficient condition. As a consequence, results in Brunetti et al. (2013) can be easily extended to the n-dimensional case.

Numerical approaches for multidimensional simulations of stellar explosions

We introduce numerical algorithms for initializing multidimensional simulations of stellar explosions with 1D stellar evolution models. The initial mapping from 1D profiles onto multidimensional grids can generate severe numerical artifacts, one of the most severe of which is the violation of conservation laws for physical quantities. We introduce a numerical scheme for mapping 1D spherically-symmetric data onto multidimensional meshes so that these physical quantities are conserved. We verify our scheme by porting a realistic 1D Lagrangian stellar profile to the new multidimensional Eulerian hydro code CASTRO. Our results show that all important features in the profiles are reproduced on the new grid and that conservation laws are enforced at all resolutions after mapping. We also introduce a numerical scheme for initializing multidimensional supernova simulations with realistic perturbations predicted by 1D stellar evolution models. Instead of seeding 3D stellar profiles with random perturbations, we imprint them with velocity perturbations that reproduce the Kolmogorov energy spectrum expected for highly turbulent convective regions in stars. Our models return Kolmogorov energy spectra and vortex structures like those in turbulent flows before the modes become nonlinear. Finally, we describe approaches to determining the resolution for simulations required to capture fluid instabilities and nuclear burning. Our algorithms are applicable to multidimensional simulations besides stellar explosions that range from astrophysics to cosmology.

Electrical Conductivity Imaging of Active Layer and Permafrost in an Arctic Ecosystem, through Advanced Inversion of Electromagnetic Induction Data

Characterizing the spatial variability of active layer and permafrost properties is critical for parameterizing process‐rich models that simulate feedbacks from Arctic ecosystem to a changing climate. Because of the sensitivity of electrical conductivity (EC) measurements to moisture content, salinity, and freeze state and the ease of collecting electromagnetic induction (EMI) data with portable tools (e.g., EM38, GEM2, or DUALEM) over large regions, EMI surveys hold great potential for Arctic ecosystem characterization. However, estimation of subsurface EC distribution from such data is challenging because of the insufficient amount of information such data provide towards finding a unique solution. The non‐uniqueness problem is often approached by fixing inversion constraints and initial models without a clear understanding of their possible effects on the obtained results. Here we developed a direct search method, which involves a grid‐based evaluation of one‐dimensional layered model parameters, to estimate EC distribution from EMI data and evaluate the influence of prior constraints, data information content, and solution non‐uniqueness. We applied the new method to EMI data acquired in Barrow, AK, as part of the Department of Energy Next‐Generation Ecosystem Experiments (DOE NGEE–Arctic). Results demonstrate the success of the developed approach for estimating models that reproduce recorded data within a specified range of uncertainty at each measurement location, as well as the value of different types of constraints. Importantly, the method can be used to quickly investigate the need for and effects of different priors at numerous measurement locations, since the time‐consuming simulation of the EMI signals from the multidimensional search grid is performed only once.

Parabolized Navier–Stokes model for study the interaction between roughness structures and concentrated vortices

We perform a combined analytical-numerical study of hydrodynamic sensitivity of a concentrated vortex in collision with a roughness wall. Models of the hydrodynamic instability and wall-bounded flow sensitivity are provided analytically by means of parabolization of the Navier-Stokes equations. The differential quadrature method was originally applied as a numerical technique to solve sets of linear algebraic equations by use of a uniform grid. We extend this technique to multidimensional clustered grids and we develop a two-level differential quadrature algorithm to compute the fluctuating flow and the sensitivity field. Extensive numerical results are presented for a two-dimensional Lamb–Oseen problem and both the solution accuracy and convergence rate are assessed. A variational flow control method is also investigated, that proved to be useful for mitigating the flow instabilities by setting the base flow to optimal parameters.

Multi-Dimensional Model Version Management System Based on Model Cloud Technology

Due to the poor openness between grid models at different levels in existing dispatching centers, theres lack of unified device naming conventions, data exchange standards and interface specifications, making it difficult to easily implement the exchange and sharing of network model parameters and data. In this article, a multi-dimensional grid model version management system is promoted based on model cloud technology with centralized and integrated deployment. Taking advantage of model cloud storage and service technology, unified maintenance and management technology, model subscribing and extracting technology as well as its releasing methods and standardized access technology, the system can construct a cloud service unified in the whole grid, covering all dispatch services with the integration of the grid model information, therefore realizing the unified management, maintenance, generation, release and subscriptions.

Quantum dynamics with sparse grids: A combination of Smolyak scheme and cubature. Application to methanol in full dimensionality

Quantum dynamical approaches based on product-grids are limited to the studies of molecular systems with few degrees of freedom, typically less than ten. Recently, Avila et al. [G. Avila, T. Carrington, J. Chem. Phys., 131 (2009) 174103] have introduced the Smolyak scheme [S.A. Smolyak, Sov. Math. Dokl., 4 (1963) 240], which considerably reduces the size of the grids. This approach has pushed back the present calculation limits on the vibrational spectra of polyatomic molecules.In the present study, we have developed an extension of the standard Smolyak scheme in which this scheme is combined with multidimensional grids, such as cubatures, to obtain new sparse grids.This scheme has been applied to the study of the torsional energy levels of methanol in full dimensionality (12D).

A note on a simplified and general approach to simulating from multivariate copula functions

Copulas have become an important analytic tool for characterizing multivariate distributions and dependence. One is often interested in simulating data from copula estimates. The process can be analytically and computationally complex and usually involves steps that are unique to a given parametric copula. We describe an alternative approach that uses ‘Probability-Proportional-to-Size’ random sampling with weights formed from the copula likelihood function. The method is flexible and can be applied to parametric and nonparametric marginal density estimates. The precision of the simulation can be calibrated by adjusting the density of the multidimensional grid used in the simulation process. The approach is fully transparent to any copula function with continuous random variables. An example evaluates a number of goodness-of-fit criteria and provides strong support for the validity and practicality of the method.

Streamline upwind/Petrov–Galerkin‐based stabilization of proper generalized decompositions for high‐dimensional advection–diffusion equations

SUMMARYThis work is a first attempt to address efficient stabilizations of high dimensional advection–diffusion models encountered in computational physics. When addressing multidimensional models, the use of mesh‐based discretization fails because the exponential increase of the number of degrees of freedom related to a multidimensional mesh or grid, and alternative discretization strategies are needed. Separated representations involved in the so‐called proper generalized decomposition method are an efficient alternative as proven in our former works; however, the issue related to efficient stabilizations of multidimensional advection–diffusion equations has never been addressed to our knowledge. Thus, this work is aimed at extending some well‐experienced stabilization strategies widely used in the solution of 1D, 2D, or 3D advection–diffusion models to models defined in high‐dimensional spaces, sometimes involving tens of coordinates.Copyright © 2013 John Wiley & Sons, Ltd.

Data reduction and calibration for LAMOST survey

AbstractThere are three data pipelines for LAMOST survey. The raw data is reduced to one dimension spectra by the data reduction pipeline(2D pipeline), the extracted spectra are classified and measured by the spectral analysis pipeline(1D pipeline), while stellar parameters are measured by LASP pipeline.(a) The data reduction pipeline. The main tasks of the data reduction pipeline include bias calibration, flat field, spectra extraction, sky subtraction, wavelength calibration, exposure merging and wavelength band connection.(b) The spectra analysis pipeline. This pipeline is designed to classify and identify objects from the extracted spectra and to measure their redshift (or radial velocity). The PCAZ (Glazebrooket al. 1998) method is applied to do the classification and redshift measurement.(c) Stellar parameters LASP. Stellar parameters pipeline (LASP) is to estimate stellar atmospheric parameters, e.g. effective temperature Teff, surface gravity log g, and metallicity [Fe/H], for F, G and K type stars. To effectively determine those fundamental stellar measurements, three steps with different methods are employed. The first step utilizes the line indices to approximately define the effective temperature range of the analyzed star. Secondly, a set of the initial approximate values of the three parameters are given based on template fitting method. Finally, we exploit ULySS (Kolevaet al. 2009) to give the final values of parameters through minimizing the χ2value between the observed spectrum and a multidimensional grid of model spectra which is generated by an interpolating of ELODIE library. There are two other classification for A type star and M type star. For A type star, standard MK system is employed (Grayet al. 2009) to give each object temperature class and luminosity type. For M type star, they are classified into subclasses by an improved Hammer method, and metallicity of each objects is also given.During the pilot survey, algorithms were improved and the pipelines were tested. The products of LAMOST survey will include extracted and calibrated spectra in FITS format, a catalog of FGK stars with stellar parameters, a catalog of M dwarf with subclass and metallicity, and a catalog of A type star with MK classification. A part of the pilot survey data, including about 319 000 high quality spectra with SNR > 10, a catalog of stellar parameters of FGK stars and another catalog of a subclass of M type stars have been released to the public in August 2012 (Luoet al. 2012). The general survey started from October 2012, and completed the first year survey. The formal data release one (DR1) is being prepared, which will include both pilot survey and first year general survey, and planed to be released under the LAMOST data policy.

Analysis of efficiency of detecting extended signals on multidimensional grids

The paper is devoted to the problems of detecting extended space-time signals. An algorithm is proposed that enables one to calculate the variance of filtering with lower computational costs than those of the methods based on solving the Wiener-Hopf equations. Based on the proposed algorithms for detecting extended signals, relatively simple quasi-optimal resolving rules using only a fraction of existing observations can be constructed. A comparative analysis is given of the efficiency of detection and potentialities of real systems.

Gränser för kulturvetenskaplig kunskapsbildning?

Some findings from the project “The contents and organization of cross boundary learning” are reported and made relevant to the question of how to think the future of learning and pedagogy in cultural studies. In the project, the focus was on “boundary work” in interdisciplinary undergraduate programmes at two Swedish universities. The following three questions are addressed: Are concepts and other language practices of curricular change of any importance? How can we identify interdisciplinarity in a multidimensional grid? Are the limits and boundaries in higher education only those that derives from the inside of the academic world, or also those from the outside?

Energy-efficient distributed wireless sensor network scheme for cluster detection

Detection of an environmental phenomenon, e.g. air pollution and oil spills, occurs when a group of sensors continuously produces similar readings (i.e. data streams) over a period of time. Thus, detection of environmental phenomena is basically a process of clustering the sensors' data streams, which commonly involves the processing of hundreds and maybe thousands of data streams in real time. Since the sensor network environment is wireless, energy conservation of the sensors would be the main concern. Thus in this paper, we propose an efficient and energy friendly distributed scheme to detect phenomena in a wireless sensor network (WSN). To achieve fast response, the proposed algorithms reduce the dimensionality of the streams. Then, each stream is represented by a point in a multi-dimensional grid. The algorithm uses a grid-based clustering technique to detect clusters of similar stream values. The processing of the algorithm is distributed among different elements of the WSN in a hierarchical topology for more energy efficiency. The paper shows the feasibility of the proposed fully distributed scheme by comparing it with three other WSN schemes in terms of clustering accuracy and energy consumption.

Nonlinear Robust and Optimal Control via Proper Orthogonal Decomposition

In this paper, a methodology based on proper orthogonal decomposition (POD) for computing approximate closed-loop optimal or robust control laws for finite-dimensional nonlinear systems is proposed. The solution can be obtained on any arbitrary domain of the state space represented by a multidimensional grid. The method only requires the computation of a limited number of well-conditioned two-point boundary value problems and a simple backwards integration of a reduced model of the Hamilton-Jacobi-Bellman or Hamilton-Jacobi-Isaacs equation associated to the control problem. Two illustrative examples demonstrate the effectiveness of the approach.

Estimating Correlation Dimension Using Multi Layered Grid and Damped Window Model Over Data Streams

A fractal dataset is known by its characteristic of being self-similar and they are described by a non-integer dimension. Fractals are generally self-similar and independent of scale and is a measure of the complexity of a self-similar object .In a rough sense, it measures number of points lying in a given set which are self-similar. This paper presents a multi-dimensional grid based algorithm to estimate the correlation dimension of the points in a data stream which stores only statistics of the data. Each cell in every layer stores the statistics of the data which can be summed up to obtain the statistics of the upper layers. A sliding window of data points is considered to handle the continuous in flow of data. Hence, authors propose a linear, faster and accurate method to determine correlation dimension, which completes in a single pass over data stream. Experimental results on synthetic and real world data sets demonstrate the effectiveness of the proposed algorithm

A Maximum Likelihood Time Delay Estimator in a Multipath Environment Using Importance Sampling

In this paper, we present a new implementation of the maximum likelihood criterion for the estimation of the time delays in a multipath environment and then extend it to the estimation of the time difference of arrival when the transmitted signal is unknown. The new technique implements the concept of importance sampling (IS) to find the global maximum of the compressed likelihood function in a modest computational manner. It thereby avoids traditional complex multidimensional grid search or initialization-dependent iterative methods. Indeed, one of the most interesting features is that it transforms the multi-dimensional search inherent to multipath propagation into a much simpler one-dimensional optimization problem in the delays dimension. Moreover, it guarantees convergence to the global maximum, contrarily to the popular iterative implementation of the maximum likelihood criterion by the well known expectation maximization (EM) algorithm. Comparisons with some other methods such as the EM algorithm, MUSIC and accelerated random search (ARS) demonstrates the superiority of the proposed IS-based multipath delay estimator in terms of estimation performance and complexity.

Conservative Initial Mapping For Multidimensional Simulations of Stellar Explosions

Mapping one-dimensional stellar profiles onto multidimensional grids as initial conditions for hydrodynamics calculations can lead to numerical artifacts, one of the most severe of which is the violation of conservation laws for physical quantities such as energy and mass. Here we introduce a numerical scheme for mapping one-dimensional spherically-symmetric data onto multidimensional meshes so that these physical quantities are conserved. We validate our scheme by porting a realistic 1D Lagrangian stellar profile to the new multidimensional Eulerian hydro code CASTRO. Our results show that all important features in the profiles are reproduced on the new grid and that conservation laws are enforced at all resolutions after mapping.

Decomposed multidimensional control grid interpolation for common consumer electronic image processing applications

Interpolation is an essential and broadly employed function of signal processing. Accordingly, considerable development has focused on advancing interpolation algorithms toward optimal accuracy. Such development has motivated a clear shift in the state-of-the art from classical interpolation to more intelligent and resourceful approaches, registration-based interpolation for example. As a natural result, many of the most accurate current algorithms are highly complex, specific, and computationally demanding. However, the diverse hardware destinations for interpolation algorithms present unique constraints that often preclude use of the most accurate available options. For example, while computationally demanding interpolators may be suitable for highly equipped image processing platforms (e.g., computer workstations and clusters), only more efficient interpolators may be practical for less well equipped platforms (e.g., smartphones and tablet computers). The latter examples of consumer electronics present a design tradeoff in this regard: high accuracy interpolation benefits the consumer experience but computing capabilities are limited. It follows that interpolators with favorable combinations of accuracy and efficiency are of great practical value to the consumer electronics industry. We address multidimensional interpolation-based image processing problems that are common to consumer electronic devices through a decomposition approach. The multidimensional problems are first broken down into multiple, independent, one-dimensional (1-D) interpolation steps that are then executed with a newly modified registration-based one-dimensional control grid interpolator. The proposed approach, decomposed multidimensional control grid interpolation (DMCGI), combines the accuracy of registration-based interpolation with the simplicity, flexibility, and computational efficiency of a 1-D interpolation framework. Results demonstrate that DMCGI provides improved interpolation accuracy (and other benefits) in image resizing, color sample demosaicing, and video deinterlacing applications, at a computational cost that is manageable or reduced in comparison to popular alternatives.

Ground filtering and vegetation mapping using multi-return terrestrial laser scanning

Discriminating laser scanner data points belonging to ground from points above-ground (vegetation or buildings) is a key issue in research. Methods for filtering points into ground and non-ground classes have been widely studied mostly on datasets derived from airborne laser scanners, less so for terrestrial laser scanners. Recent developments in terrestrial laser sensors (longer ranges, faster acquisition and multiple return echoes) has aroused greater interest for surface modelling applications. The downside of TLS is that a typical dataset has high variability in point density, with evident side-effects on processing methods and CPU-time. In this work we use a scan dataset from a sensor which returns multiple target echoes, in this case providing more than 70million points on our study site. The area presents low, medium and high vegetation, undergrowth with varying density, as well as bare ground with varying morphology (i.e. very steep slopes as well as flat areas). We test an integrated work-flow for defining a terrain and surface model (DTM and DSM) and successively for extracting information on vegetation density and height distribution on such a complex environment. Attention was given to efficiency and speed of processing. The method consists on a first step which subsets the original points to define ground candidates by taking into account the ordinal return number and the amplitude. A custom progressive morphological filter (opening operation) is applied next, on ground candidate points using a multidimensional grid to account for the fallout in point density as a function of distance from scanner. Vegetation density mapping over the area is then estimated using a weighted ratio of point counts in the tri-dimensional space over each cell. The overall result is a pipeline for processing TLS points clouds with minimal user interaction, producing a Digital Terrain Model (DTM), a Digital Surface Model (DSM), a vegetation density map and a derived Canopy Height Model (CHM). These products are of high importance for many applications ranging from forestry to hydrology and geomorphology.

Intimate Partner Violence and Child Custody Evaluation, Part I: Theoretical Framework, Forensic Model, and Assessment Issues

An integrative conceptual framework and forensic evaluation model are presented for custody evaluators when the issue of Intimate Partner Violence is salient in a child custody case (IPV-CC). A revised typology of IPV combines previously proposed categories with a violence risk assessment approach to reflect both the descriptive and predictive functions for evaluators. It is a research-based forensic model. Continuous and categorical variable approaches to the analysis of IPV in custody cases are presented and contrasted. Ten behavioral dimensions of IPV-CC are described to serve as a multidimensional behavioral grid approach to the assessment of IPV. The integrated framework and perspective allows for greater behavioral specificity in the analysis. It avoids problems inherent in forensic assessment by subtype labeling. The court will be better informed by a multidimensional and continuous variable approach that provides behavioral versus categorical differentiation. This approach allows for more accurate and efficient risk communications to the court and translation to parenting plan recommendations. Issues involved with the forensic assessment of IPV in the custody context and making predictions/ recommendations about future parenting, co-parenting, and child adjustment are discussed.