Set Of Mapping Functions Research Articles

Performance analysis and optimisation of spatially-varying infill microstructure within CAD geometries

The article is aimed to provide an effective digital solution in support of the infill microstructural design within objectives generated from normal computer aided design (CAD) systems. The key here is to deploy the microstructure and to analyse the performance of the resulting multiscale objective in the parameter domain, from which a CAD objective is mapped, usually by means of Non-Uniform Rational B-Splines (NURBS) functions. In the regularly shaped domain defined in the parameter space, another set of mapping functions are defined for the description of spatially-varying microstructure (in the parameter space), and the actual multiscale CAD objective gets represented through composition of these mapping functions with the NURBS-based functions for CAD geometry generation. When the introduced mapping functions are also NURBS-based, the proposed representation strategy becomes more favoured by CAD systems, in the sense that the CAD geometry and its infill can be tuned simultaneously but independently with a same set of NURBS basis. Moreover, our computer-aided engineering (CAE) module is also installed over the parameter domain, based on a machine-learning-based homogenisation formulation for compliance and strength analysis. Thus the finite element meshes stay unchanged although the accommodating CAD geometry keeps varying. With the aforementioned treatments, a consecutive CAD-consistent scheme is proposed. Our numerical results show that each time as the control points are moved (by a CAD designer), one may choose to wait several seconds for two-dimensional cases and/or a few minutes for three-dimensional cases, to get a CAD geometry filled with microstructure bearing optimised compliance.

Effective multi-modal retrieval based on stacked auto-encoders

Multi-modal retrieval is emerging as a new search paradigm that enables seamless information retrieval from various types of media. For example, users can simply snap a movie poster to search relevant reviews and trailers. To solve the problem, a set of mapping functions are learned to project high-dimensional features extracted from data of different media types into a common low-dimensional space so that metric distance measures can be applied. In this paper, we propose an effective mapping mechanism based on deep learning (i.e., stacked auto-encoders) for multi-modal retrieval. Mapping functions are learned by optimizing a new objective function, which captures both intra-modal and inter-modal semantic relationships of data from heterogeneous sources effectively. Compared with previous works which require a substantial amount of prior knowledge such as similarity matrices of intra-modal data and ranking examples, our method requires little prior knowledge. Given a large training dataset, we split it into mini-batches and continually adjust the mapping functions for each batch of input. Hence, our method is memory efficient with respect to the data volume. Experiments on three real datasets illustrate that our proposed method achieves significant improvement in search accuracy over the state-of-the-art methods.

Profile-Based LC-MS Data Alignment - A Bayesian Approach

A Bayesian alignment model (BAM) is proposed for alignment of liquid chromatography-mass spectrometry (LC-MS) data. BAM belongs to the category of profile-based approaches, which are composed of two major components: a prototype function and a set of mapping functions. Appropriate estimation of these functions is crucial for good alignment results. BAM uses Markov chain Monte Carlo (MCMC) methods to draw inference on the model parameters and improves on existing MCMC-based alignment methods through 1) the implementation of an efficient MCMC sampler and 2) an adaptive selection of knots. A block Metropolis-Hastings algorithm that mitigates the problem of the MCMC sampler getting stuck at local modes of the posterior distribution is used for the update of the mapping function coefficients. In addition, a stochastic search variable selection (SSVS) methodology is used to determine the number and positions of knots. We applied BAM to a simulated data set, an LC-MS proteomic data set, and two LC-MS metabolomic data sets, and compared its performance with the Bayesian hierarchical curve registration (BHCR) model, the dynamic time-warping (DTW) model, and the continuous profile model (CPM). The advantage of applying appropriate profile-based retention time correction prior to performing a feature-based approach is also demonstrated through the metabolomic data sets.

Application of Predictive Oscillation-Based Test to a CMOS OpAmp

A predictive oscillation-based test (POBT) strategy, combined with supply current monitoring, is proposed as an alternative to the specification-based test of analog circuits. According to our simulation results, the combination of both techniques is excellent in predicting the main performance parameters of a CMOS operational amplifier (OpAmp) (dc gain, bandwidth, and slew rate) from test observables such as oscillation frequency and variations on the supply current. Considering tolerances in the fabrication process, a set of mapping functions has been found by circuit simulation, giving correlation coefficients higher than 0.999 and RMS prediction errors below 1.5%. A set of 19 fabricated circuits has been measured in both normal and test modes. The correlation between performance parameters and test observables, which are both measured, gives RMS errors of 0.65% for the dc gain, 11.30% for the bandwidth, and 4.12% for the slew rate.

A Discriminative Approach for Wavelet Denoising

This paper suggests a discriminative approach for wavelet denoising where a set of mapping functions (MFs) are applied to the transform coefficients in an attempt to produce a noise free image. As opposed to the descriptive approaches, modeling image or noise priors is not required here and the MFs are learned directly from an ensemble of example images using least-squares fitting. The suggested scheme generates a novel set of MFs that are essentially different from the traditional soft/hard thresholding in the over-complete case. These MFs are demonstrated to obtain comparable performance to the state-of-the-art denoising approaches. Additionally, this framework enables a seamless customization of the shrinkage operation to a new set of restoration problems that were not addressed previously with shrinkage techniques, such as deblurring, JPEG artifact removal, and various types of additive noise that are not necessarily Gaussian white noise.

Mapping correlation algorithm as interface between experimental optical technique and computer modeling for the study of mechanical structures

To create a hybrid system applied to mechanical structure analysis link to experimental optical techniques (EOTs) and computer modeling (CM), the correlation problem between Cm and EOT methods must be solved. A mapping correlation algorithm (MCA) is proposed as the interface between both techniques. Out-of-plane electronic speckle pattern interferometry (ESPI) as the experimental optical technique and a commercial finite element method (fEm) package are employed. The MCA proposed is based on a set of mapping functions, which are found by least-squares algorithms and enable the compensation of image distortions produced by the experimental optical setup. The algorithm was tested initially on a simple 2-D structure and two 3-D complex mechanical structures. Results are reported. Further, the MCA algorithm linking ESPI-FEM methods is applied to out-of-plane displacements over a rectangular plate under stress. Numerical and experimental results along with their error analysis are also presented.

Elimination of tropospheric path delays in GPS observations with the ECMWF numerical weather model

Recent comparisons have shown that zenith total delays (ZTD's) derived from Global Positioning System (GPS) observations and ZTD's calculated from analysis fields of numerical weather prediction (NWP) models agree within 1–2 cm (rms). Thus NWP models describe the tropospheric delay quite well, even though no GPS data are assimilated into the model. In this work we investigate how a NWP model can be used to calculate and eliminate the influence of the troposphere on GPS measurements. Using the European Centre for Medium-Range Weather Forecasts (ECMWF) global weather model we calculate the GPS path delays for each single GPS observation using a high precision 3D ray tracing procedure and subtract it from the GPS observations.We discuss two methods to process the corrected GPS observations. We find a reduction of the rms value of the phase residuals at low elevations, if the dry delay is eliminated and the wet delay is modeled in the adjustment. If the total delay is eliminated, tropospheric modeling of the remaining delay, whose correlation matrix will be determined, is still necessary. The analysis of the eigenvectors of the correlation matrix gives a set of mapping functions and weights which can be used to process the corrected GPS observations.

Parametric infinite element for seepage analysis

AbstractA set of mapping functions in the form of convergent series for an infinite element, which is capable to include the infinitely distanced constant head boundary condition from the area of disturbance (e.g. pumping), is proposed based on the asymptotic far‐field behaviour of typical seepage flow problems. The derived mapping functions have been successfully used in three‐dimensional point symmetric, two‐dimensional axi‐symmetric and one‐dimensional unidirectional flow for the fixed head boundary at infinite distance. The result shows excellent agreement with analytical solution. For the first time, the mapping function of an infinite element is presented in the form of a convergent series. The infinite elements are really capable of reducing the cost and efficiency of conventional finite element analysis. Finally, a figure is also proposed to indicate the required size of the near field to obtain accurate drawdown at specified locations based on some calculations for two‐dimensional radial flow case.

A backtracking method for constructing perfect hash functions from a set of mapping functions

This paper presents a backtracking method for constructing perfect hash functions from a given set of mapping functions. A hash indicator table is employed in the composition. By the nature of backtracking, the method can always find a perfect hash function when such a function does exist according to the composing scheme. Simulation results show that the probability of getting a perfect hash function by the backtracking method is much higher than by the single-pass and multipass methods previously proposed.