Collocation Framework Research Articles

Nonlinear Meshfree Collocation Method for Solving Double-Diffusive Natural Convection in a Porous Enclosure

A meshfree collocation method formulated by using reproducing kernel shape functions with Newton–Raphson method is presented with application to analyzing a three-phase coupling system in a porous enclosure. To tackle such a highly nonlinear phenomenon caused by double-diffusive natural convection, direct collocation using local approximation in conjunction with a two-step iteration solver is employed to stably and efficiently solve this problem. It has been shown that a determined and well-conditioned system is established under the collocation framework with reproducing kernel approximation. By conducting the parametric study, the numerical results have demonstrated the robustness of the proposed method in analyzing the porous enclosure by considering various geometry, boundary conditions, and governing parameters.

A Bayesian Collocation Integral Method for Parameter Estimation in Ordinary Differential Equations

Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on basis functions or Gaussian processes to approximate the ODE solution and its derivatives. Due to the sensitivity of the ODE solution to its derivatives, these methods can be hindered by estimation error, especially when only sparse time-course observations are available. We present a Bayesian collocation framework that operates on the integrated form of the ODEs and also avoids the expensive use of numerical solvers. Our methodology has the capability to handle general nonlinear ODE systems. We demonstrate the accuracy of the proposed method through simulation studies, where the estimated parameters and recovered system trajectories are compared with other recent methods. A real data example is also provided. Supplementary materials for this article are available online.

Verification of uncertainty estimates of autonomous field measurements of marine reflectance using simultaneous observations

The primary ocean color product is the spectrum of remote sensing reflectance RRS that allows the quantification of in-water optically significant constituents and all ocean color applications. The determination of its uncertainties is thus key to the creation of comprehensive uncertainty budgets for all derived ocean color products. The assessment of satellite RRS uncertainties has largely relied on corresponding field measurements but this process is solid only if these field measurements are in turn fully characterized. Uncertainty budgets have therefore been defined and reported for the radiometric measurements collected in the framework of the Ocean Color component of the Aerosol Robotic Network (AERONET-OC). The contemporaneous deployment of two autonomous systems for 5.5 years on the Acqua Alta Oceanographic Tower (AAOT) located in the northern Adriatic Sea led to the collection of 4,449 pairs of coincident observations (collected with a time difference lower than 10 min) distributed over 659 days of data acquisitions that can be used to verify reported uncertainty values. The comparison of matched pairs showed a good agreement for RRS (with differences of typically 2%–3% between 412 and 560 nm), as well as for the aerosol optical thickness τa (3%–6%). Differences between data from the two systems appear generally consistent with their stated uncertainties, indicating that they are metrologically compatible and that uncertainties reported for AERONET-OC data are usually trustworthy (with possible exceptions depending on the level of error correlation between measurements from the two systems). Using uncertainty cone diagrams, this result holds across the range of uncertainty values with few exceptions. Independent uncertainty estimates associated with non-systematic error contributions were obtained using a collocation framework allowing for error correlation between measurements from the two systems. The resulting uncertainties appeared comparable with the reported values for τa and RRS. The related mathematical development also showed that the centered root-mean-square difference between data collected by two systems is a conservative estimate of the uncertainty associated with these data (excluding systematic contributions) if these data show a good agreement (expressed by a slope of method II regression close to 1) and if their uncertainties can be assumed similar with errors moderately correlated (typically lower than 0.5).

Collocated Clothing Synthesis with GANs Aided by Textual Information: A Multi-Modal Framework

Synthesizing realistic images of fashion items which are compatible with given clothing images, as well as conditioning on multiple modalities, brings novel and exciting applications together with enormous economic potential. In this work, we propose a multi-modal collocation framework based on generative adversarial network (GAN) for synthesizing compatible clothing images. Given an input clothing item that consists of an image and a text description, our model works on synthesizing a clothing image which is compatible with the input clothing, as well as being guided by a given text description from the target domain. Specifically, a generator aims to synthesize realistic and collocated clothing images relying on image- and text-based latent representations learned from the source domain. An auxiliary text representation from the target domain is added for supervising the generation results. In addition, a multi-discriminator framework is carried out to determine compatibility between the generated clothing images and the input clothing images, as well as visual-semantic matching between the generated clothing images and the targeted textual information. Extensive quantitative and qualitative results demonstrate that our model substantially outperforms state-of-the-art methods in terms of authenticity, diversity, and visual-semantic similarity between image and text.

Volumetric parameterization with truncated hierarchical B-splines for isogeometric analysis

Constructing spline parameterizations for computational domains is one of the fundamental problems in isogeometric analysis. In this paper, we present an efficient method for parameterizing volumetric computational domains using truncated hierarchical B-splines (THB). To ensure the injectivity of the parameterization, we utilize a collocation-based framework where the foldovers are eliminated on an increasing collocation set until the injectivity can be verified. A local–global solver is employed to eliminate any foldover effectively by projecting the mapping onto a bounded conformal distortion space. Local refinement of THB splines is also performed to enlarge the injectivity space. Various sufficient conditions are proposed to check the injectivity of the mapping efficiently. The quality of the bijective mapping is further improved by optimizing a geometrical energy, which is also embedded in the collocation framework to ensure injectivity. A coarse-to-fine variant of our method, which is more robust, is also presented. THB splines not only reduce the number of degrees of freedom in the parametric representation, but also increase the possibility of producing a bijective parameterization by local refinement. Some examples are provided to demonstrate the efficiency, effectiveness and robustness of our method.

Meshfree Collocation Framework for Multi-Phase Coupling Nonlinear Dynamic System in a Porous Enclosure

This study is aimed at establishing an effective incremental-iterative framework, for the first time, using reproducing kernel collocation method for solving multi-phase dynamic coupling problems in a porous enclosure. The central difference method is utilized in the temporal discretization while direct collocation with reproducing kernel approximation is adopted in the spatial discretization, in particular, with Newton–Raphson method for nonlinear iteration. Under the proposed numerical framework, a determined and well-conditioned nonlinear system is ensured during nonlinear iteration. In addition to the traditional mesh-based weak-form methods, it is shown that the present study provides an alternative effective approach to solve unsteady-state double-diffusive convection problems.

A direct collocation framework for optimal control simulation of pedaling using OpenSim.

The direct collocation (DC) method has shown low computational costs in solving optimization problems in human movements, but it has rarely been used for solving optimal control pedaling problems. Thus, the aim of this study was to develop a DC framework for optimal control simulation of human pedaling within the OpenSim modeling environment. A planar bicycle-rider model was developed in OpenSim. The DC method was formulated in MATLAB to solve an optimal control pedaling problem using a data tracking approach. Using the developed DC framework, the optimal control pedaling problem was successfully solved in 24 minutes to ten hours with different objective function weightings and number of nodes from two different initial conditions. The optimal solutions for equal objective function weightings were successful in terms of tracking, with the model simulated pedal angles and pedal forces within ±1 standard deviation of the experimental data. With these weightings, muscle tendon unit (MTU) excitation patterns generally matched with burst timings and shapes observed in the experimental EMG data. Tracking quality and MTU excitation patterns were changed little by selection of node density above 31, and the optimal solution quality was not affected by initial guess used. The proposed DC framework could easily be turned into a predictive simulation with other objective functions such as fastest pedaling rate. This flexible and computationally efficient framework should facilitate the use of optimal control methods to study the biomechanics, energetics, and control of human pedaling.

Wavelet-based adaptive wall-modeled large eddy simulation method for compressible turbulent flows

We develop a wavelet-based adaptive wall-modeled large eddy simulation (WA-WMLES) method to overcome the stringent restriction on step size for time integration, caused by mesh resolution requirement to resolve inner viscous sublayer, which becomes computationally expensive as the Reynolds number increases. This approach uses a wavelet-based adaptive large eddy simulation, incorporated into the anisotropic-adaptive wavelet collocation framework, to resolve the outer region of turbulent boundary layer, while the inner part is approximated by the wall-shear-stress model, and extends the application of the wavelet-based adaptive methods to a realistic wall-bounded turbulent flow configuration at a relatively high (order of a million) Reynolds number.

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A collocation framework to retrieve tropospheric delays from a combination of GNSS and InSAR

High spatio-temporal variability of atmospheric water vapor affects microwave signals of Global Navigation Satellite Systems (GNSS) and Interferometric Synthetic Aperture Radar (InSAR). A better knowledge of the distribution of water vapor improves both GNSS- and InSAR-derived data products. In this work, we present a collocation framework to combine and retrieve zenith and (relative) slant tropospheric delays. GNSS and InSAR meteorological products are combined aiming at a better retrieval of the atmospheric water vapor. We investigate the combination approach with synthetic and real data acquired in the Alpine region of Switzerland. Based on a closed-loop validation with simulated delays, a few mm accuracy is achieved for the GNSS-InSAR combination in terms of retrieved ZTDs. Furthermore, when real delays are collocated, the combination results are more congruent with InSAR computed products. This research is a contribution to improve the spatio-temporal mapping of tropospheric delays by combining GNSS-derived and InSAR-derived delays.

Learning Diverse Fashion Collocation by Neural Graph Filtering

Fashion recommendation systems are highly desired by customers to find visually-collocated fashion items, such as clothes, shoes, bags, etc. While existing methods demonstrate promising results, they remain lacking in flexibility and diversity, e.g. assuming a fixed number of items or favoring safe but boring recommendations. In this paper, we propose a novel fashion collocation framework, <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Neural Graph Filtering</b> , that models a flexible set of fashion items via a graph neural network. Specifically, we consider the visual embeddings of each garment as a node in the graph, and describe the inter-garment relationship as the edge between nodes. By applying symmetric operations on the edge vectors, this framework allows varying numbers of inputs/outputs and is invariant to their ordering. We further include a style classifier augmented with focal loss to enable the collocation of significantly diverse styles, which are inherently imbalanced in the training set. To facilitate a comprehensive study on diverse fashion collocation, we reorganize Amazon Fashion dataset with carefully designed evaluation protocols. We evaluate the proposed approach on three popular benchmarks, the Polyvore dataset, the Polyvore-D dataset, and our reorganized Amazon Fashion dataset. Extensive experimental results show that our approach significantly outperforms the state-of-the-art methods with over 10% improvements on the standard AUC metric. More importantly, 82.5% of the users prefer our diverse-style recommendations over other alternatives in a real-world perception study.

High-order maximum-entropy collocation methods

This paper considers the approximation of partial differential equations with a point collocation framework based on high-order local maximum-entropy schemes (HOLMES). In this approach, smooth basis functions are computed through an optimization procedure and the strong form of the problem is directly imposed at the collocation points, reducing significantly the computational times with respect to the Galerkin formulation. Furthermore, such a method is truly meshfree, since no background integration grid is necessary. The validity of HOLMES collocation is verified with supportive numerical examples, where the expected convergence rates are obtained. This includes the approximation of PDEs on domains bounded by implicit and explicit (NURBS) curves, illustrating a direct integration between geometric modeling and numerical analysis.

Reduced Hessian based parameter selection and estimation with simultaneous collocation approach

AbstractParameter estimation is a critical step in the building of process models. Given the nonlinear structure and limited measurements, it is often difficult to correctly estimate all the parameters involved in the model. Linear dependence and low correlation among the parameters are the main problems to be handled in parameter estimation. The common approach is to estimate a subset of the parameters by fixing the others at reasonable values. However, it is a challenge to determine which parameters can be properly estimated. In this work, the ratio between standard deviation and estimated parameter value is introduced for evaluating the estimability. A Gauss‐Jordan elimination based approach is proposed for parameter estimability ranking. Combined with the proposed ranking approach and approximate ratio criterion, a reduced Hessian based approach is proposed for parameter selection and estimation under a simultaneous collocation framework. The proposed approach is at least as effective and more efficient than competing approaches based on multiple eigenvalue decompositions or orthogonalizations for larger problems. Three case studies with increasing complexity are presented to demonstrate the performance of the proposed approach.

Near Synonymy Analysis of the Descriptive Adjective Pale in English and Bled, -a, -o in Serbian

Within the extensive scientific research on descriptive adjectives and their near synonyms, we noticed the prevailing idiomatic meaning of the adjectives analyzed here. In this paper, we will apply contrastive analysis of the descriptive adjective bled, -a, -o in Serbian and descriptive adjective pale as well as their near synonyms in English and Serbian in order to prove the presence of the aforementioned descriptive adjectives’ prevailing idiomatic meaning in both languages. The results of the analysis indicate that the semantic (and grammatical) aspects of words are reflected onto and within their collocational framework. Furthermore, it is expected that the collocational framework of the adjective bled, -a, -o in Serbian will change depending upon the grammatical gender implied (masculine, feminine, neuter), as well as on the sequence of its near synonyms. The same changes are not expected to occur in English due to its lack of grammatical gender. The methodology of the research comprises the frequency of the primary and idiomatic meaning analyses of the descriptive adjective bled, -a, -o, and its near synonyms based on the framework of the Contemporary Serbian language electronic corpus (Faculty of Mathematics, University of Belgrade), and the descriptive adjective pale and its near synonyms analyzed on the British National Corpus data (BNC) and the Words Bank: English database.

Generalized reproducing kernel peridynamics: unification of local and non-local meshfree methods, non-local derivative operations, and an arbitrary-order state-based peridynamic formulation

State-based peridynamics is a non-local reformulation of solid mechanics that replaces the force density of the divergence of stress with an integral of the action of force states on bonds local to a given position, which precludes differentiation with the aim to model strong discontinuities effortlessly. A popular implementation is a meshfree formulation where the integral is discretized by quadrature points, which results in a series of unknowns at the points under the strong-form collocation framework. In this work, the meshfree discretization of state-based peridynamics under the correspondence principle is examined and compared to traditional meshfree methods based on the classical local formulation of solid mechanics. It is first shown that the way in which the peridynamic formulation approximates differentiation can be unified with the implicit gradient approximation, and this is termed the reproducing kernel peridynamic approximation. This allows the construction of non-local deformation gradients with arbitrary-order accuracy, as well as non-local approximations of higher-order derivatives. A high-order accurate non-local divergence of stress is then proposed to replace the force density in the original state-based peridynamics, in order to obtain global arbitrary-order accuracy in the numerical solution. These two operators used in conjunction with one another is termed the reproducing kernel peridynamic method. The strong-form collocation version of the method is tested against benchmark solutions to examine and verify the high-order accuracy and convergence properties of the method. The method is shown to exhibit superconvergent behavior in the nodal collocation setting.

Reduced Collocation Method for Time-Dependent Parametrized Partial Differential Equations

Reduced basis methods (RBMs) in the collocation framework provide both high accuracy approximate solution and efficient error estimate to parametrized partial differential equations (PDEs). Reduced collocation method (RCM) has so far been applied for steady problems (Chen and Gottlieb in J Sci Comput 55(3):718–737, 2013). In this paper, we extend this methodology to time-dependent parametrized PDEs, so the novelty of this paper is the consideration of time in the presentation of formulas and solution of the problem. RBMs idea in collocation method is attractive for theirsimplicity of implementation and efficient result, especially for time-dependentproblems. For such case, we combine the proper orthogonal decomposition (POD)technique in time with greedy algorithm in parameter for producing optimal reduced basis (RB) space. Numerical results for time-dependent convection–diffusion problem and Burgers’ equation illustrate the highly accurate and efficiency of the presented method.

A Corpus-Driven Analysis of Collocational Framework the * of in the Legal Text: A Case Study of The Criminal Law of the PRC

Collocational framework is a critical part of the studies of phraseology. With the rapid development of corpus linguistics, the study of collocational frameworks gradually overcomes the limitation of statistics and becomes more persuasive than ever before. Under this background, this paper attempts to analyze the typical collocational framework the * of in the legal text based on a self-complied corpus of The Criminal Law of the PRC, hoping to revealing the features and functions of the collocational framework the * of in the legal text.

Mixed isogeometric collocation methods for the simulation of poromechanics problems in 1D

Isogeometric collocation is for the first time considered as a simulation tool for fluid-saturated porous media. Accordingly, with a focus on one-dimensional problems, a mixed collocation approach is proposed and tested in demanding situations, on both quasi-static and dynamic benchmarks. The developed method is proven to be very effective in terms of both stability and accuracy. In fact, the peculiar properties of the spline shape functions typical of isogeometric methods, along with the ease of implementation and low computational cost guaranteed by the collocation framework, make the proposed approach very attractive as a viable alternative to Galerkin-based approaches classically adopted in computational poromechanics.

Bridging boundaries across genre traditions

Abstract This study explores the benefits of a synergy between ESP research on genre and theoretical dimensions of Systemic Functional Linguistics (SFL). It models genre on SFL dimensions and employs this model to analyse 200 biodata written by Applied Linguistics scholars, 100 each from research articles and seminar posters. Data were analysed from contextual, logico-semantic and lexicogrammatical perspectives. The findings reveal five generic stages in biodata. The frequency distribution of these stages and the phases that realise them shows variation between research article bios and seminar bios. The most frequent logico-semantic (or rhetorical) relations identified among stages and phases are of the expansion type, namely addition and elaboration, Further, collocational frameworks are used in organising some generic phases into waves of meaning and in construing different identities. Finally, evaluative resources, in the form of lexical bundles, modification and circumstantial elements in the clause, are employed by writers to boost their professional achievements and promote themselves. These findings contribute to theoretical discussions on genre and the scholarship on the interface between identity construction and academic writing, and also motivate further research.

Interpreting Phraseological Units in Contracts: The Case of Extended Term–Embedding Collocation

Extended units of meaning (Sinclair 2004) have been scarcely investigated thus far in legal phraseology with the exception of research into lexical bundles (Goźdź–Roszkowski 2006, 2011 ; Kopaczyk 2013 ; Breeze 2013 ; Tomankova 2016 ; Biel 2017). This paper is therefore an attempt to show that the Sinclairian wider– context– perspective may prove to be especially useful for the study of phraseological units in legal genre since it helps us to reveal their collocational framework, allowing both grammatical and phraseological patterns to emerge. The paper focuses on extended ‘term– embedding collocations’ (Biel 2014b) extracted from the English and Croatian comparable corpora of contracts by means of WordsmithTools 6.0 (Scott 2012). It highlights some of the most striking examples supporting the above hypothesis and it accounts for their interpretation by means of analysing the extralinguistic context of phraseological units in contracts. It may be suggested that this study represents an attempt to fill a gap in research on legal phraseology due to the fact that private legal documents tend to be largely underrepresented in this specialized phraseology. It may also be suggested that by focusing on extended units of meaning in legal Croatian the paper attempts to fill yet another gap in corpus– based studies of legal language, which tend to be largely Anglocentric. Finally, the paper may, apart from revealing the stability of legal phrasemes, also represent a useful resource for translator training since it offers the wider context of a term or an expression in contract language.