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Checking the fit between a prosthetic socket and a residual limb is important for functional prostheses. Designing a prosthetic socket using a CAD system and checking the above mentioned fit by analyzing the deformation and stress under the weight of an amputee requires a three-dimensional model of the residual limb that includes not only the surface, but also the fat, muscle and bone. An ultrasonic measurement system, including a probe that three-dimensionally measures the external surface shape and the shapes of internal tissues simultaneously was developed. The system uses wavelet analysis to define the positions of the boundaries between each tissue. A cone-shaped aluminum test object was measured using the system, which was shown to be capable of measuring radius with an error of 0.6mm and slope with an error of 6%. In addition, the lower legs were measured, and the surface, muscles and bone boundaries were defined by wavelet analysis. The results of these measurements were compared to MRI cross sectional data, and the average error for the leg surface, muscles and tibia were 1.7mm, 2.4mm and 1.9mm, respectively, for boundaries that were determined correctly.Coefficient of variation
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In this article, we take one step toward understanding the learning behavior of deep residual networks, and supporting the observation that deep residual networks behave like ensembles. We propose a new convolutional neural network architecture which builds upon the success of residual networks by explicitly exploiting the interpretation of very deep networks as an ensemble. The proposed multi-residual network increases the number of residual functions in the residual blocks. Our architecture generates models that are wider, rather than deeper, which significantly improves accuracy. We show that our model achieves an error rate of 3.73% and 19.45% on CIFAR-10 and CIFAR-100 respectively, that outperforms almost all of the existing models. We also demonstrate that our model outperforms very deep residual networks by 0.22% (top-1 error) on the full ImageNet 2012 classification dataset. Additionally, inspired by the parallel structure of multi-residual networks, a model parallelism technique has been investigated. The model parallelism method distributes the computation of residual blocks among the processors, yielding up to 15% computational complexity improvement.
Residual neural network
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In this article, we take one step toward understanding the learning behavior of deep residual networks, and supporting the hypothesis that deep residual networks are exponential ensembles by construction. We examine the effective range of ensembles by introducing multi-residual networks that significantly improve classification accuracy of residual networks. The multi-residual networks increase the number of residual functions in the residual blocks. This is shown to improve the accuracy of the residual network when the network is deeper than a threshold. Based on a series of empirical studies on CIFAR-10 and CIFAR-100 datasets, the proposed multi-residual network yield $6\%$ and $10\%$ improvement with respect to the residual networks with identity mappings. Comparing with other state-of-the-art models, the proposed multi-residual network obtains a test error rate of $3.92\%$ on CIFAR-10 that outperforms all existing models.
Residual neural network
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A residual-networks family with hundreds or even thousands of layers dominates major image recognition tasks, but building a network by simply stacking residual blocks inevitably limits its optimization ability. This paper proposes a novel residual-network architecture, Residual networks of Residual networks (RoR), to dig the optimization ability of residual networks. RoR substitutes optimizing residual mapping of residual mapping for optimizing original residual mapping. In particular, RoR adds level-wise shortcut connections upon original residual networks to promote the learning capability of residual networks. More importantly, RoR can be applied to various kinds of residual networks (ResNets, Pre-ResNets and WRN) and significantly boost their performance. Our experiments demonstrate the effectiveness and versatility of RoR, where it achieves the best performance in all residual-network-like structures. Our RoR-3-WRN58-4+SD models achieve new state-of-the-art results on CIFAR-10, CIFAR-100 and SVHN, with test errors 3.77%, 19.73% and 1.59%, respectively. RoR-3 models also achieve state-of-the-art results compared to ResNets on ImageNet data set.
Residual neural network
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Residual Neural Networks [1] won first place in all five main tracks of the ImageNet and COCO 2015 competitions. This kind of network involves the creation of pluggable modules such that the output contains a residual from the input. The residual in that paper is the identity function. We propose to include residuals from all lower layers, suitably normalized, to create the residual. This way, all previous layers contribute equally to the output of a layer. We show that our approach is an improvement on [1] for the CIFAR-10 dataset.
Deep Neural Networks
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Abstract This study demonstrates a successful application of Wavelet Analysis to fracturing pressure data across various conventional and unconventional formations to evaluate post treatment data and enhance future stimulation practices. This methodology was compared to the proven Moving Reference Point (MRP) technique developed by Pirayesh et al (2013), to improve the understanding of wavelet analysis. As a fracturing diagnostic tool, the wavelet analysis technique can also be used as companion diagnostic tool alongside previously published methods (such as MRP etc.) Wavelet analysis of a signal is the mathematical decomposition of that signal into orthogonal wavelet components. The level of decomposition is chosen to discern high and low-resolution parts of the signal. The process represents the signal as a sum of translations and scalings of the chosen wavelet to obtain coefficients of each wavelet. Fracturing treatment pressure signals occur at various frequencies with finite durations that makes it possible to divide the pressure signals into many components and analyze them individually by wavelet transformation. Discrete Wavelet Transformation by Daubechie wavelets was implemented on fracture propagation pressure to various resolution levels to reveal necessary information within the data. The detail coefficients were analyzed by examining the anomalies at various resolution levels. Wavelet analysis was performed on various shale and conventional fracturing data. Some interesting patterns are readily discernable from the wavelet detail coefficients. For instance, during the injection of proppants, there is an amplitude change in the detail coefficients at the exact moment when the proppant contacts the formation surface. This is expected because wavelet analysis is sensitive to any discontinuity in the system. Furthermore, such amplitude changes are also observed in the analyzed pressure data corresponding to tip screen-out and near wellbore sand-out events. Comparing such events along-side the MRP method paves the way for early detection of screen-out events. A comparison with the MRP technique is also provided in this study. This method reduces the uncertainty in analysis of Nolte-Smith and MRP method by providing an independent estimate of fracture propagation characteristics. There have been publications discussing wavelet transformations of various formation and reservoir parameters (permeability, reservoir pressure, etc.), and discussing the application of wavelets for noise reduction and data smoothing. However, this is the first study mainly about wavelet analysis of fracture injection pressure data to understand and detect anomalies during various completion treatments. Ultimately, this technique helps to improve treatment designs and efficiency by analyzing fracture and formation behavior of the treatment and enhance decision making during execution, by providing early screen-out detections.
SIGNAL (programming language)
Second-generation wavelet transform
Lifting Scheme
Stationary wavelet transform
Cascade algorithm
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From the development of the problem,developments the super-wavelets in theory mathematics and their achievements are discussed.The characters of extending a normalized tight frame wavelet to a super-wavelet and the construction methods of super-wavelets by using affine structure are introduced.Lastly,a few open problems are listed and some new possible directions of research one pointed out.The super-wavelet is a signal analysis method based on wavelet analysis.There are some important results on extending a normalized tight frame wavelet to a super-wavelet,but there are some open problems on finding a sufficient and necessary condition for a normalized tight frame wavelet to be extended to a super-wavelet and the important aspects of the MRA super-wavelets also open.
Gabor wavelet
Cascade algorithm
Lifting Scheme
Legendre wavelet
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Generalizing the result of Bownik and Speegle [Approximation Theory X: Wavelets, Splines and Applications, Vanderbilt University Press, pp. 63–85, 2002], we provide plenty of non-MSF A-wavelets with the help of a given A-wavelet set. Further, by showing that the dimension function of the non-MSF A-wavelet constructed through an A-wavelet set W coincides with the dimension function of W, we conclude that the non-MSF A-wavelet and the A-wavelet set through which it is constructed possess the same nature as far as the multiresolution analysis is concerned. Some examples of non-MSF d-wavelets and non-MSF A-wavelets are also provided. As an illustration we exhibit a pathwise connected class of non-MSF non-MRA wavelets sharing the same wavelet dimension function.
Legendre wavelet
Gabor wavelet
Multiresolution analysis
Cascade algorithm
Lifting Scheme
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Wavelets are mathematical functions which are used as a basis for writing down other complex functions in an easy way. These cut up data into its frequency components and so that we can study each and every part with more preciseness as it is scaled for our convenience. We may also term wavelets as a tool to decompose signals and trend as a function of time. Wavelets are certainly used in place of the applications of Fourier Analysis as wavelets give more freedom to work on. In this paper, a basic idea of wavelet is provided to a person who is unknown with the idea of function approximation. Apart from pure mathematics areas, wavelets are highly useful tool in analyzing a time series. Wavelets are used for removing noise from a statistical data which is one of the most important job in data analysis. The applications of wavelets not only bars here, but they are also used in quantum physics, artificial intelligence and visual recognition. An important aspect of wavelets, image processing is covered in brief in this paper which will give a thin-air idea of how digital images are stored.
Gabor wavelet
Legendre wavelet
Fast wavelet transform
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