Elastic Kernel Research Articles

Implementation of the RESKR module in NJOY

The Blackshaw-Murray[1] elastic kernel represents the effect of neutron up-scattering caused by thermal motion of target nuclei and resonance elastic scattering on the multigroup scattering matrices. A first implementation of this model was proposed by Ouisloumen and Sanchez and made available in proprietary cross-sections libraries of the PARAGON and APOLLO lattice codes.[2] Later, the same technique was reimplemented as module RESK in the NECP-Atlas cross-section generating code by J. Xu, T. Zu and L. Cao.[3, 4] The proposed reskr module in NJOY-2012 and NJOY-2016 is based on the implementation of module RESK in the NECP-Atlas cross-section generating code.[5] The reskr module is released under the BSD Open-Source license.

Insights into the selection mechanism of Widmanstätten growth by phase-field calculations

We investigate the growth of Widmanstätten structures in metallic alloys with phase field calculations. We show that elastic energy anisotropy associated with shear dominated transformations is alone sufficient to give rise to plate or needle like precipitates with constant lengthening rates at constant supersaturations. We show that Ivantsov analytical solutions still provide good estimates of the diffusion flux around tips even when elasticity is accounted for. A careful analysis demonstrates that, for shear dominated transformations, (i) the lengthening direction lies in the habit plane determined by one of the minima of the elastic kernel; (ii) the tip shape and size are equilibrium features, driven by elastic forces, rather than dynamically determined as usually assumed; (iii) the tip size of acicular precipitates can be rationalized by the value of the elastic kernel in the lengthening direction.

Intelligent fault diagnosis of high-voltage circuit breakers using triangular global alignment kernel extreme learning machine

In recent years, vibration-based intelligent fault diagnosis of high-voltage circuit breakers (HVCBs) exhibits excellent performance. It requires a reliable machine learning method to develop an automatically diagnostic model to recognize the mechanical state from vibration signals. However, the traditional machine learning methods tend to produce unstable diagnostic results under the case of sampling asynchrony caused by the fluctuation of the control voltage. To address this problem, an improved kernel extreme learning machine (K-ELM) called triangular global alignment kernel (TGAK) extreme learning machine (TGAK-ELM) was presented in this study, which was developed by introducing TGAK into K-ELM. The TGAK is an elastic kernel which was designed by considering all the possible alignments between samples. Therefore, it provides a flexible similarity measure for samples, resulting in the improvement of the diagnostic performance. Experiments on the 35kV HVCB verified the effectiveness of the proposed method. Compared to other state-of-the-art machine learning methods, the proposed TGAK-ELM produced better diagnostic results. And further experiments on eight datasets picked from UCR repository suggested the applicability of TGAK-ELM in other fields.

Elastic Interfaces on Disordered Substrates: From Mean-Field Depinning to Yielding.

We consider a model of an elastic manifold driven on a disordered energy landscape, with generalized long range elasticity. Varying the form of the elastic kernel by progressively allowing for the existence of zero modes, the model interpolates smoothly between mean-field depinning and finite dimensional yielding. We find that the critical exponents of the model change smoothly in this process. Also, we show that in all cases the Herschel-Buckley exponent of the flow curve depends on the analytical form of the microscopic pinning potential. Within the present elastoplastic description, all this suggests that yielding in finite dimensions is a mean-field transition.

Estimating Road Segments Using Kernelized Averaging of GPS Trajectories

A method called iTEKA, which stands for iterative time elastic kernel averaging, was successfully used for averaging time series. In this paper, we adapt it to GPS trajectories. The key contribution is a denoising procedure that includes an over-sampling scheme, the detection and removal of outlier trajectories, a kernelized time elastic averaging method, and a down-sampling as post-processing. The experiment carried out on benchmark datasets showed that the proposed procedure is effective and outperforms straightforward methods based on medoid or Euclidean averaging approaches.

Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic Kernels

Abstract In the light of regularized dynamic time warping kernels, this paper re-considers the concept of a time elastic centroid for a set of time series. We derive a new algorithm based on a probabilistic interpretation of kernel alignment matrices. This algorithm expresses the averaging process in terms of stochastic alignment automata. It uses an iterative agglomerative heuristic method for averaging the aligned samples, while also averaging the times of their occurrence. By comparing classification accuracies for 45 heterogeneous time series data sets obtained by first nearest centroid/medoid classifiers, we show that (i) centroid-based approaches significantly outperform medoid-based ones, (ii) for the data sets considered, our algorithm, which combines averaging in the sample space and along the time axes, emerges as the most significantly robust model for time-elastic averaging with a promising noise reduction capability. We also demonstrate its benefit in an isolated gesture recognition experiment and its ability to significantly reduce the size of training instance sets. Finally, we highlight its denoising capability using demonstrative synthetic data. Specifically, we show that it is possible to retrieve, from few noisy instances, a signal whose components are scattered in a wide spectral band.

Tensor Multi-Elastic Kernel Self-Paced Learning for Time Series Clustering

Time series clustering has attracted growing attention due to the abundant data accessible and extensive value in various applications. The unique characteristics of time series, including high-dimension, warping, and the integration of multiple elastic measures, pose challenges for the present clustering algorithms, most of which take into account only part of these difficulties. In this paper, we make an effort to simultaneously address all aforementioned issues in time series clustering under a unified multiple kernels clustering (MKC) framework. Specifically, we first implicitly map the raw time series space into multiple kernel spaces via elastic distance measure functions. In such high-dimensional spaces, we resort to the tensor constraint based self-representation subspace clustering approach, which involves the self-paced learning paradigm, to explore the essential low-dimensional structure of the data, as well as the high-order complementary information from different elastic kernels. The proposed approach can be extended to more challenging multivariate time series clustering scenario in a direct but elegant way. Extensive experiments on 85 univariate and 10 multivariate time series datasets demonstrate the significant superiority of the proposed approach beyond the baseline and several state-of-the-art MKC methods.

A multiple attributes convolution kernel with reproducing property

Various kernel-based methods have been developed with great success in many fields, but very little research has been published that is concerned with a multiple attribute kernel in reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel elastic kernel called a multiple attribute convolution kernel with reproducing property (MACKRP) and present improved classification results over conventional approaches in the RKHS rather than the more commonly used Hilbert space. The MACKRP consists of two major steps. First, we find the basic solution of a generalized differential operator by the delta function, and then we design a convolution function using this solution. This convolution function is proven to be a specific reproducing kernel called a convolution reproducing kernel (CRK) in H3-space. Second, we prove that the CRK satisfies the condition of Mercer kernel. And the CRK is composed of three attributes (L1-norm, L2-norm and Laplace kernel), and each attribute can capture a different feature, with all attributes generating a novel kernel which we call an MACKRP. The experimental results demonstrate that the MACKRP possesses approximation and regularization performance and that classification results are consistently comparable or superior to a number of other state-of-the-art kernel functions.

On Recursive Edit Distance Kernels With Application to Time Series Classification

This paper proposes some extensions to the work on kernels dedicated to string or time series global alignment based on the aggregation of scores obtained by local alignments. The extensions that we propose allow us to construct, from classical recursive definition of elastic distances, recursive edit distance (or time-warp) kernels that are positive definite if some sufficient conditions are satisfied. The sufficient conditions we end up with are original and weaker than those proposed in earlier works, although a recursive regularizing term is required to get proof of the positive definiteness as a direct consequence of the Haussler's convolution theorem. Furthermore, the positive definiteness is maintained when a symmetric corridor is used to reduce the search space, and thus the algorithmic complexity, which is quadratic in the worst case. The classification experiment we conducted on three classical time-warp distances (two of which are metrics), using support vector machine classifier, leads to the conclusion that when the pairwise distance matrix obtained from the training data is far from definiteness, the positive definite recursive elastic kernels outperform in general the distance substituting kernels for several classical elastic distances we have tested.

Construction of multi-dimensional isotropic kernels for nonlocal elasticity based on phonon dispersion data

Kernels for non-local elasticity are in general obtained from phonon dispersion relations. However, non-local elastic kernels are in the form of three-dimensional (3D) functions, whereas the dispersion relations are always in the form of one-dimensional (1D) frequency versus wave number curves corresponding to a particular wave direction. In this paper, an approach to build 2D and 3D kernels from 1D phonon dispersion data is presented. Our particular focus is on isotropic media where we show that kernels can be obtained using Fourier–Bessel transform, yielding axisymmetric kernel profiles in reciprocal and real spaces. These kernel functions are designed to satisfy the necessary requirements for stable wave propagation, uniformity of nonlocal stress and stress regularization. The proposed concept is demonstrated by developing some physically meaningful 2D and 3D kernels that will find useful applications in nonlocal mechanics. Relative merits of the kernels obtained via proposed methods are explored by fitting 1D kernels to dispersion data for Argon and using the kernel to understand the size effect in non local energy as seen from molecular simulations. A comparison of proposed kernels is made based on their predictions of stress field around a crack tip singularity.

Improving GPGPU concurrency with elastic kernels

Each new generation of GPUs vastly increases the resources available to GPGPU programs. GPU programming models (like CUDA) were designed to scale to use these resources. However, we find that CUDA programs actually do not scale to utilize all available resources, with over 30% of resources going unused on average for programs of the Parboil2 suite that we used in our work. Current GPUs therefore allow concurrent execution of kernels to improve utilization. In this work, we study concurrent execution of GPU kernels using multiprogram workloads on current NVIDIA Fermi GPUs. On two-program workloads from the Parboil2 benchmark suite we find concurrent execution is often no better than serialized execution. We identify that the lack of control over resource allocation to kernels is a major serialization bottleneck. We propose transformations that convert CUDA kernels into elastic kernels which permit fine-grained control over their resource usage. We then propose several elastic-kernel aware concurrency policies that offer significantly better performance and concurrency compared to the current CUDA policy. We evaluate our proposals on real hardware using multiprogrammed workloads constructed from benchmarks in the Parboil 2 suite. On average, our proposals increase system throughput (STP) by 1.21x and improve the average normalized turnaround time (ANTT) by 3.73x for two-program workloads when compared to the current CUDA concurrency implementation.

Improving GPGPU concurrency with elastic kernels

Each new generation of GPUs vastly increases the resources available to GPGPU programs. GPU programming models (like CUDA) were designed to scale to use these resources. However, we find that CUDA programs actually do not scale to utilize all available resources, with over 30% of resources going unused on average for programs of the Parboil2 suite that we used in our work. Current GPUs therefore allow concurrent execution of kernels to improve utilization. In this work, we study concurrent execution of GPU kernels using multiprogram workloads on current NVIDIA Fermi GPUs. On two-program workloads from the Parboil2 benchmark suite we find concurrent execution is often no better than serialized execution. We identify that the lack of control over resource allocation to kernels is a major serialization bottleneck. We propose transformations that convert CUDA kernels into elastic kernels which permit fine-grained control over their resource usage. We then propose several elastic-kernel aware concurrency policies that offer significantly better performance and concurrency compared to the current CUDA policy. We evaluate our proposals on real hardware using multiprogrammed workloads constructed from benchmarks in the Parboil 2 suite. On average, our proposals increase system throughput (STP) by 1.21x and improve the average normalized turnaround time (ANTT) by 3.73x for two-program workloads when compared to the current CUDA concurrency implementation.

Discriminant Kernel Learning Using Hybrid Regularization

Kernel discriminant analysis (KDA) is one of the state-of-the-art kernel-based methods for pattern classification and dimensionality reduction. It performs linear discriminant analysis in the feature space via kernel function. However, the performance of KDA greatly depends on the selection of the optimal kernel for the learning task of interest. In this paper, we propose a novel algorithm termed as elastic multiple kernel discriminant analysis (EMKDA) by using hybrid regularization for automatically learning kernels over a linear combination of pre-specified kernel functions. EMKDA makes use of a mixing norm regularization function to compromise the sparsity and non-sparsity of the kernel weights. A semi-infinite program based algorithm is then proposed to solve EMKDA. Extensive experiments on synthetic datasets, UCI benchmark datasets, digit and terrain database are conducted to show the effectiveness of the proposed methods.

Research on Nonlocal Elastic Kernel Function under Ultrasonic Excitation of Ceramics Materials

Through considering the influence factors of ultrasonic excitation parameters, the nonlocal kernel parameter formula under ultrasonic excitation is established and the nonlocal elastic kernel function is also deduced. The attenuation characteristics and effects of the elastic kernel function are also studied in this paper. The nonlocal stress under ultrasonic vibration is calculated based on the nonlocal elastic kernel formula. It is concluded that stress decay phenomenon can explain through nonlocal kernel function attenuation in frequencies.

Elasticity of a contact-line and avalanche-size distribution at depinning

Motivated by recent experiments, we extend the Joanny-deGennes calculation of the elasticity of a contact line to an arbitrary contact angle and an arbitrary plate inclination in presence of gravity. This requires a diagonalization of the elastic modes around the nonlinear equilibrium profile, which is carried out exactly. We then make detailed predictions for the avalanche-size distribution at quasistatic depinning: we study how the universal (i.e., short-scale independent) rescaled size distribution and the ratio of moments of local to global avalanches depend on the precise form of the elastic kernel.

Line Creep in Paper Peeling

We have studied experimentally the dynamics of the separation of a sheet of paper into two halves in a peeling configuration. The experimental setup consists of a peeling device, where a fracture front is driven along the plane of the paper, with a constant force. The theoretical picture is how an elastic line interacts with a random landscape of fracture toughness. We compare the results with theoretical simulations in several aspects. One recent finding concerns the autocorrelation function of the average front position. The data from the experiments produces so-called cusps or singularities in the correlation function, as predicted by the functional renormalization group theory for elastic lines. Comparisons with simulations with either a short range or a long range elastic kernel demonstrate that the latter agrees with the experimental observations, as expected.

Depinning transition of dislocation assemblies: Pileups and low-angle grain boundaries

We investigate the depinning transition occurring in dislocation assemblies. In particular, we consider the cases of regularly spaced pileups and low-angle grain boundaries interacting with a disordered stress landscape provided by solute atoms, or by other immobile dislocations present in nonactive slip systems. Using linear elasticity, we compute the stress originated by small deformations of these assemblies and the corresponding energy cost in two and three dimensions. Contrary to the case of isolated dislocation lines, which are usually approximated as elastic strings with an effective line tension, the deformations of a dislocation assembly cannot be described by local elastic interactions with a constant tension or stiffness. A nonlocal elastic kernel results as a consequence of long-range interactions between dislocations. In light of this result, we revise statistical depinning theories of dislocation assemblies and compare the theoretical results with numerical simulations and experimental data.

Energy conservation property of MW-CRF deterministic particle method

A deterministic particle method for kinetic equation in several dimensions was presented by Motta and Wick some years ago. In the present paper, we formulate the method in general coordinates and apply this formulation to an elastic collision kernel. We show that the method preserves exactly the energy conservation property of the elastic kernel.

Calculation of Forces at Focal Adhesions from Elastic Substrate Data: The Effect of Localized Force and the Need for Regularization

Forces exerted by stationary cells have been investigated on the level of single focal adhesions by combining elastic substrates, fluorescence labeling of focal adhesions, and the assumption of localized force when solving the inverse problem of linear elasticity theory. Data simulation confirms that the inverse problem is ill-posed in the presence of noise and shows that in general a regularization scheme is needed to arrive at a reliable force estimate. Spatial and force resolution are restricted by the smoothing action of the elastic kernel, depend on the details of the force and displacement patterns, and are estimated by data simulation. Corrections arising from the spatial distribution of force and from finite substrate size are treated in the framework of a force multipolar expansion. Our method is computationally cheap and could be used to study mechanical activity of cells in real time.

Buckling and nonlocal elasticity of charged membranes.

The elastic behavior of an interacting, and, in specific, of a charged flexible membrane is considered. In the first part of this paper the effective nonlocal elastic energy of a membrane due to a pairwise and arbitrary intra-membrane interaction is derived. Nonlocal elasticity is included to all orders, this description, therefore, corresponds to an infinite resummation of the standard gradient expansion. In the second part, the pair interaction between segments of an (on average) neutral membrane consisting of mobile positive and negative charges is derived both field theoretically in the Gaussian approximation and using a simple ion-pairing approximation. This model might also apply to strongly charged membranes with strongly condensed counter ions. The resulting contribution to the elastic energy is negative and thus favors undulations of the membrane. The bending modulus is extracted from the large-scale or small-momentum behavior of the elastic kernel and found to be comparable to k(B)T for the case where ion pairing is dominant. The large-momentum elastic response exhibits a markedly different scaling than the small-momentum regime and sensitively depends on the small-distance cutoff and thus on molecular details.