Elastic Embedding Research Articles

Personalized Elastic Embedding Learning for On-Device Recommendation

Personalized Elastic Embedding Learning for On-Device Recommendation

On the boundary conditions for a thin circular plate conjugated to a massive body

The problem of deformation under the action of uniform pressure of a circular plate coupled with a massive base is considered, while the condition for the coupling of the plate with the base is modeled using boundary conditions of the generalized elastic embedding type, i.e. the relationship between the bending moment and forces at the edge of the plate with displacements and rotation angles through the compliance matrix. The main goal of the work is to study the influence of the elasticity of the embedding on the elastic response of the plate. The solution to the problem was obtained in the formulation of the linear theory of plates, the theory of membranes in the approximation of homogeneity of longitudinal forces, and the Foppl — von Karman theory, also in the approximation of the assumption of homogeneity of longitudinal forces. The values of the coefficients of the compliance matrix were obtained using the finite element method for the auxiliary problem and compared with the values of the coefficients obtained for related problems by analytical methods. Numerical results were obtained for an aluminum wafer on a silicon base. The obtained solution was compared with the solution obtained for the rigid embedment condition for all three models used. It is shown that in the case of large deflections (several plate thicknesses), taking into account the compliance of the embedment becomes essential.

Unsupervised domain adaptation via feature transfer learning based on elastic embedding

Unsupervised domain adaptation via feature transfer learning based on elastic embedding

The elasto-plastic nano- and microscale compressive behaviour of rehydrated mineralised collagen fibres.

The hierarchical design of bio-based nanostructured materials such as bone enables them to combine unique structure-mechanical properties. As one of its main components, water plays an important role in bone's material multiscale mechanical interplay. However, its influence has not been quantified at the length-scale of a mineralised collagen fibre. Here, we couple in situ micropillar compression, and simultaneous synchrotron small angle X-ray scattering (SAXS) and X-ray diffraction (XRD) with a statistical constitutive model. Since the synchrotron data contain statistical information on the nanostructure, we establish a direct connection between experiment and model to identify the rehydrated elasto-plastic micro- and nanomechanical fibre behaviour. Rehydration led to a decrease of 65%-75% in fibre yield stress and compressive strength, and 70% in stiffness with a 3x higher effect on stresses than strains. While in agreement with bone extracellular matrix, the decrease is 1.5-3x higher compared to micro-indentation and macro-compression. Hydration influences mineral more than fibril strain with the highest difference to the macroscale when comparing mineral and tissue levels. The effect of hydration seems to be strongly mediated by ultrastructural interfaces while results provide insights towards mechanical consequences of reported water-mediated structuring of bone apatite. The missing reinforcing capacity of surrounding tissue for an excised fibril array is more pronounced in wet than dry conditions, mainly related to fibril swelling. Differences leading to higher compressive strength between mineralised tissues seem not to depend on rehydration while the lack of kink bands supports the role of water as an elastic embedding influencing energy-absorption mechanisms. STATEMENT OF SIGNIFICANCE: Characterising structure-property-function relationships in hierarchical biological materials helps us to elucidate mechanisms that enable their unique properties. Experimental and computational methods can advance our understanding of their complex behaviour with the potential to inform bio-inspired material development. In this study, we close a gap for bone's fundamental mechanical building block at micro- and nanometre length scales. We establish a direct connection between experiments and simulations by coupling in situ synchrotron tests with a statistical model and quantify the behaviour of rehydrated single mineralised collagen fibres. Results suggest a high influence of hydration on structural interfaces, and the role of water as an elastic embedding by outlining important differences between wet and dry elasto-plastic properties of mineral nanocrystals, fibrils and fibres.

Impact of Creep Effect on Hydraulic Fracture Long-Term Conductivity in Deep Shale Reservoirs

Abstract The main factor contributing to the decline in effective fracture width and conductivity is proppant embedding into the fracture surface. In the deep shale's high-temperature, high-pressure, and high-stress environment, the rheological properties of rock cause proppant embedding to be deeper. Additionally, the effect of hydraulic fracture is difficult to maintain after fracturing, which causes a sharp decline in cumulative production. In this paper, the Hertz contact theory is used to establish a long-term fracture conductivity model that incorporates the two embedding behaviors of proppant elastic deformation and reservoir creep deformation. Through time integration, the variation of long-term fracture conductivity is obtained. The experimental data and the theoretical model agree well. The results show that long-term fracture conductivity gradually decreases as the proppant progresses from the elastic embedding stage to the creep embedding stage. The elastic modulus, viscoelastic coefficient, and particle size significantly impact on the fracture width. The rock's elastic modulus and viscoelastic coefficient have a negligible impact on the long-term fracture conductivity, which is positively correlated with sand concentration, proppant particle size, and elastic modulus. In this research, an accurate and effective analysis model is proposed to quantify the long-term fracture conductivity, reveal the hydraulic fracture closure mechanism of deep shale under high temperature and high stress, and provide technological solutions for long-term maintenance of high conductivity fracture channels, which is useful to increase deep shale production efficiency, lower the production decline rate, and extend the stable production cycle.

Advances and challenges in hydraulic fracturing of tight reservoirs: A critical review

The hydraulic fracturing technology has been widely utilized to extract tight resources. Hydraulic fracturing involves rock failures, complex fracture generation, proppant transport and fracture closure. All these behaviors affect the productivity of fractured wells. In this work, the advances and challenges in hydraulic fracturing development of tight reservoirs are summarized from following aspects: the hydraulic fracture propagation, the proppant transport and distribution in hydraulic fractures, the calculation of hydraulic fracture conductivity, and productivity and/or pressure analysis model of multi-stages fractured horizontal wells. Current fracture propagation simulation methods generate only limited propagation paths and cannot truly reflect the complexity of the propagation. The current proppant migration and distribution research is mainly focused on indoor experimental studies of proppant migration in a single fracture or branched fracture, and simulation studies on proppant migration and distribution in a small-scale single slab fracture. Whereas fractures formed after hydraulic fracturing in tight reservoirs are generally complicated. There is a lack of models for calculating complex fracture conductivity that take into consideration the effect of proppant placement and proppant distribution in fractures, fracture surface roughness and dissolution, diffusion, deposition, elastic embedding, and creep caused by stress. The productivity models of fractured horizontal wells are mostly conducted based on the original reservoir fluid saturation and pressure distribution. Most of the studies are focused only on one aspect of the fracturing process. Predications of well performance after fracturing based on these studies are often inconsistent with actual field data. The paper also discusses the future research directions of fracturing in tight reservoirs and the results may be used to promote the development of tight reservoirs.

Elastic Embedding through Graph Convolution-based Regression for Semi-supervised Classification

This article introduces a scheme for semi-supervised learning by estimating a flexible non-linear data representation that exploits Spectral Graph Convolutions structure. Structured data are exploited in order to determine non-linear and linear models. The introduced scheme takes advantage of data-driven graphs at two levels. First, it incorporates manifold smoothness that is naturally encoded by the graph itself. Second, the regression model is built on the convolved data samples that are derived from the data and their associated graph. The proposed semi-supervised embedding can tackle the problem of over-fitting on neighborhood structures for image data. The proposed Graph Convolution-based Semi-supervised Embedding paves the way to new theoretical and application perspectives related to the non-linear embedding. Indeed, building flexible models that adopt convolved data samples can enhance both the data representation and the final performance of the learning system. Several experiments are conducted on six image datasets for comparing the introduced scheme with some state-of-the-art semi-supervised approaches. This empirical evaluation shows the effectiveness of the proposed embedding scheme.

D-EE: Distributed software for visualizing intrinsic structure of large-scale single-cell data.

BackgroundDimensionality reduction and visualization play vital roles in single-cell RNA sequencing (scRNA-seq) data analysis. While they have been extensively studied, state-of-the-art dimensionality reduction algorithms are often unable to preserve the global structures underlying data. Elastic embedding (EE), a nonlinear dimensionality reduction method, has shown promise in revealing low-dimensional intrinsic local and global data structure. However, the current implementation of the EE algorithm lacks scalability to large-scale scRNA-seq data.ResultsWe present a distributed optimization implementation of the EE algorithm, termed distributed elastic embedding (D-EE). D-EE reveals the low-dimensional intrinsic structures of data with accuracy equal to that of elastic embedding, and it is scalable to large-scale scRNA-seq data. It leverages distributed storage and distributed computation, achieving memory efficiency and high-performance computing simultaneously. In addition, an extended version of D-EE, termed distributed optimization implementation of time-series elastic embedding (D-TSEE), enables the user to visualize large-scale time-series scRNA-seq data by incorporating experimentally temporal information. Results with large-scale scRNA-seq data indicate that D-TSEE can uncover oscillatory gene expression patterns by using experimentally temporal information.ConclusionsD-EE is a distributed dimensionality reduction and visualization tool. Its distributed storage and distributed computation technique allow us to efficiently analyze large-scale single-cell data at the cost of constant time speedup. The source code for D-EE algorithm based on C and MPI tailored to a high-performance computing cluster is available at https://github.com/ShaokunAn/D-EE.

NeuralEE: A GPU-Accelerated Elastic Embedding Dimensionality Reduction Method for Visualizing Large-Scale scRNA-Seq Data.

The dramatic increase in amount and size of single-cell RNA sequencing data calls for more efficient and scalable dimensional reduction and visualization tools. Here, we design a GPU-accelerated method, NeuralEE, which aggregates the advantages of elastic embedding and neural network. We show that NeuralEE is both scalable and generalizable in dimensional reduction and visualization of large-scale scRNA-seq data. In addition, the GPU-based implementation of NeuralEE makes it applicable to limited computational resources while maintains high performance, as it takes only half an hour to visualize 1.3 million mice brain cells, and NeuralEE has generalizability for integrating newly generated data.

Elastic Graph-based Semi-supervised Embedding with Adaptive Loss Regression

Fast track article for IS&T International Symposium on Electronic Imaging 2020: Image Processing: Algorithms and Systems proceedings.

TSEE: an elastic embedding method to visualize the dynamic gene expression patterns of time series single-cell RNA sequencing data

BackgroundTime series single-cell RNA sequencing (scRNA-seq) data are emerging. However, the analysis of time series scRNA-seq data could be compromised by 1) distortion created by assorted sources of data collection and generation across time samples and 2) inheritance of cell-to-cell variations by stochastic dynamic patterns of gene expression. This calls for the development of an algorithm able to visualize time series scRNA-seq data in order to reveal latent structures and uncover dynamic transition processes.ResultsIn this study, we propose an algorithm, termed time series elastic embedding (TSEE), by incorporating experimental temporal information into the elastic embedding (EE) method, in order to visualize time series scRNA-seq data. TSEE extends the EE algorithm by penalizing the proximal placement of latent points that correspond to data points otherwise separated by experimental time intervals. TSEE is herein used to visualize time series scRNA-seq datasets of embryonic developmental processed in human and zebrafish. We demonstrate that TSEE outperforms existing methods (e.g. PCA, tSNE and EE) in preserving local and global structures as well as enhancing the temporal resolution of samples. Meanwhile, TSEE reveals the dynamic oscillation patterns of gene expression waves during zebrafish embryogenesis.ConclusionsTSEE can efficiently visualize time series scRNA-seq data by diluting the distortions of assorted sources of data variation across time stages and achieve the temporal resolution enhancement by preserving temporal order and structure. TSEE uncovers the subtle dynamic structures of gene expression patterns, facilitating further downstream dynamic modeling and analysis of gene expression processes. The computational framework of TSEE is generalizable by allowing the incorporation of other sources of information.

A Flexible 5-In-1 Microsensor for Internal Microscopic Diagnosis of Vanadium Redox Flow Battery Charging Process.

Multiple important physical parameters in the vanadium redox flow battery are difficult to measure accurately, and the multiple important physical parameters (e.g., temperature, flow, voltage, current, pressure, and electrolyte concentration) are correlated with each other; all of them have a critical influence on the performance and life of vanadium redox flow battery. In terms of the feed of fuel to vanadium redox flow battery, the pump conveys electrolytes from the outside to inside for reaction. As the performance of vanadium redox flow battery can be tested only by an external machine—after which, the speed of pump is adjusted to control the flow velocity of electrolyte—the optimum performance cannot be obtained. There is a demand for internal real-time microscopic diagnosis of vanadium redox flow batteries, and this study uses micro-electro-mechanical systems (MEMS) technology to develop a flexible five-in-one (temperature, flow, voltage, current, and pressure) microsensor, which is embedded in vanadium redox flow battery, for real-time sensing. Its advantages include: (1) Small size and the simultaneous measurement of five important physical quantities; (2) elastic measurement position and accurate embedding; and (3) high accuracy, sensitivity, and quick response time. The flexible five-in-one microsensor embedded in the vanadium redox flow battery can instantly monitor the changes in different physical quantities in the vanadium redox flow battery during charging; as such, optimum operating parameters can be found out so that performance and life can be enhancec.

DensityPath: an algorithm to visualize and reconstruct cell state-transition path on density landscape for single-cell RNA sequencing data.

Visualizing and reconstructing cell developmental trajectories intrinsically embedded in high-dimensional expression profiles of single-cell RNA sequencing (scRNA-seq) snapshot data are computationally intriguing, but challenging. We propose DensityPath, an algorithm allowing (i) visualization of the intrinsic structure of scRNA-seq data on an embedded 2-d space and (ii) reconstruction of an optimal cell state-transition path on the density landscape. DensityPath powerfully handles high dimensionality and heterogeneity of scRNA-seq data by (i) revealing the intrinsic structures of data, while adopting a non-linear dimension reduction algorithm, termed elastic embedding, which can preserve both local and global structures of the data; and (ii) extracting the topological features of high-density, level-set clusters from a single-cell multimodal density landscape of transcriptional heterogeneity, as the representative cell states. DensityPath reconstructs the optimal cell state-transition path by finding the geodesic minimum spanning tree of representative cell states on the density landscape, establishing a least action path with the minimum-transition-energy of cell fate decisions. We demonstrate that DensityPath can ably reconstruct complex trajectories of cell development, e.g. those with multiple bifurcating and trifurcating branches, while maintaining computational efficiency. Moreover, DensityPath has high accuracy for pseudotime calculation and branch assignment on real scRNA-seq, as well as simulated datasets. DensityPath is robust to parameter choices, as well as permutations of data. DensityPath software is available at https://github.com/ucasdp/DensityPath. Supplementary data are available at Bioinformatics online.

Kernel-based discriminative elastic embedding algorithm

A nonlinear version of discriminative elastic embedding (DEE) algorithm is presented, called kernel discriminative elastic embedding (KDEE). In this paper, we concretely fulfill the following works: (1) class labels and linear projection matrix are integrated into the kernel-based objective function; (2) two different strategies are adopted for optimizing the objective function of KDEE, and accordingly the final algorithms are termed as KDEE1 and KDEE2 respectively; (3) a deliberately selected Laplacian search direction is adopted in KDEE1 for faster convergence. Experimental results on several publicly available databases demonstrate that the proposed algorithm achieves powerful pattern revealing capability for complex manifold data.

Dimensionality reduction by supervised neighbor embedding using laplacian search.

Dimensionality reduction is an important issue for numerous applications including biomedical images analysis and living system analysis. Neighbor embedding, those representing the global and local structure as well as dealing with multiple manifolds, such as the elastic embedding techniques, can go beyond traditional dimensionality reduction methods and find better optima. Nevertheless, existing neighbor embedding algorithms can not be directly applied in classification as suffering from several problems: (1) high computational complexity, (2) nonparametric mappings, and (3) lack of class labels information. We propose a supervised neighbor embedding called discriminative elastic embedding (DEE) which integrates linear projection matrix and class labels into the final objective function. In addition, we present the Laplacian search direction for fast convergence. DEE is evaluated in three aspects: embedding visualization, training efficiency, and classification performance. Experimental results on several benchmark databases present that the proposed DEE exhibits a supervised dimensionality reduction approach which not only has strong pattern revealing capability, but also brings computational advantages over standard gradient based methods.

LF-EME: Local features with elastic manifold embedding for human action recognition

Human action recognition has been an active topic in computer vision. Currently, most of the approaches to this problem can be categorized into two classes. One is based on local features, and the other is based on global features. Meanwhile, manifold learning has become successful in many problems in computer vision, but because of the high variability of human body, the application of manifold learning to human action recognition is limited. We propose a framework based on Elastic Manifold Embedding (EME), a new sparse manifold learning algorithm, together with local interest point features to handle human action recognition. The result of the new framework is very promising in comparison with state-of-the-art methods.

Finite element-based force/moment-driven simulation of orthodontic tooth movement

The objectives of this study were to develop a numerically controlled experimental set-up to predict the movement caused by the force systems of orthodontic devices and to experimentally verify this system. The presented experimental set-up incorporated an artificial tooth fixed via a 3D force/moment sensor to a parallel kinematics robot. An algorithm determining the initial movement of the tooth in its elastic embedding controlled the set-up. The initial tooth movement was described by constant compliances. The constants were obtained prior to the experiment in a parameterised finite element (FE) study on the basis of a validated FE model of a human molar. The long-term tooth movement was assembled by adding up a multiple of incremental steps of initial tooth movements. A pure translational movement of the tooth of about 8 mm resulted for a moment to force ratio of − 8.85 mm, corresponding to the distance between the bracket and the centre of resistance. The correct behaviour of this linear elastic model in its symmetry plane allows for simulating single tooth movement induced by orthodontic devices.

A uniqueness theorem for the time-domain elastic-wave scattering in inhomogeneous, anisotropic solids with relaxation

A uniqueness theorem for the (analytic or computational) time-domain modeling of the elastic wave motion in a scattering configuration that consists of inhomogeneous, anisotropic solids with arbitrary relaxation properties, occupying a bounded subdomain in an unbounded homogeneous, isotropic, perfectly elastic embedding, is presented. No direct time-domain uniqueness proof seems to exist for this kind of configuration. As an intermediate step, the one-to-one correspondence between the causal time-domain wavefield components and the constitutive material response functions on the one hand, and their time Laplace-transform counterparts for (a sequence of) real, positive values of the transform parameter on the other hand, seems a necessary tool. It is shown that such an approach leads to simple, explicit, sufficiency conditions on the inertial loss and compliance relaxation tensors describing the solid’s constitutive behavior for uniqueness to hold. In it, the property of causality plays an essential role. In Christensen [Theory of Viscoelasticity—An Introduction (Academic, New York, 1971)] a similar approach is applied to the problem of uniqueness of the elastodynamic initial-/boundary-value problem associated with a viscoelastic object of bounded extent, the surface of which is subject to an admissible set of explicit boundary values. In the scattering configuration of unbounded extent, no explicit boundary values occur and the far-field compressional and shear wave radiation characteristics at “infinity” in the embedding play a key role in the proof.

A minmax relationship between embeddable and rigid graphs

Weighted graphs that can be embedded in Euclidean space in such a way as to preserve the weight of an edge as the distance between its two end points are of interest in a variety of applications. The concept of elastic embeddability, introduced in [1], is designed to deal with distances subject to error. Elastic graphs are related to, but distinct from, generically rigid graphs known in structural engineering. Whereas rigidity is defined via the possible motions of vertices that leave edge lengths invariant, elasticity deals with the behavior of embeddings as edge lengths are perturbed. Although these two classes are nearly disjoint, we prove that they meet at a common boundary: a graph is maximal with respect to elastic embedding if and only if it is minimal with respect to infinitesimal rigidity.

Kinematics of finite elastoplastic deformation

A model in which plastic deformation occurs as a result of crystallographic slip is used to derive a formula for decomposing a deformation gradient into parts attributable to elastic and plastic deformation processes. The dislocation kinematics are those in long use, for example by Rice (1971, J. Mech. Phys. Solids 19, 433) and by Hill and Havner (1982, J. Mech. Phys. Solids 30, 5). The analysis presented here differs from that given by these authors in that it concerns total deformation (and its elastic and plastic parts) rather than incremental deformation. The decomposition obtained is inherent in the physics of the deformation process, arising naturally when the spatial discreteness of the active slip planes is taken into account. Expressions for the decomposition components are obtained by means of volumetric averaging of contributions of elastic deformation and slip to the total deformation. The decomposition captures the effects of isoclinic orientation central to Mandel's (1973, Int. J. Solids Struct. 9, 725) theory, but without introduction of the intermediate configuration that arises when the deformation is assumed to be expressible as though the plastic and elastic deformations occurred sequentially. Because no intermediate configuration arises, the established objectivity principle applies without modification and the concept of elastic embedding that is essential to proper selection of temporal rates is implemented quite naturally. Although the new decomposition is motivated by dislocation-mechanical considerations, the result is a continuum-mechanical expression that can be used in other contexts in which the sites of inelastic deformation are spatially separated in the material.