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In multi-modal learning tasks such as video understanding, the most important operations are feature extraction, feature enhancement for single modality and feature aggregation between modalities. In this paper, we present two attention based algorithms, the Position-embedding Non-local (PE-NL) Network and the Multi-modal Attention (MA) feature aggregation method. Inspired by Non-local Neural Networks and Transformers, our PE-NL is a self-attention liked feature enhancement operation and it can capture long-range dependencies and model relative positions. The MA aggregation method merges visual and audio modals while reduces feature dimension and the number of parameters without losing too much accuracy. Both of PE-NL and MA blocks can be plugged into many multi-modal learning architectures. Our Gated PE-NL-MA network achieves competitive results on Youtube-8M dataset. [ABSTRACT FROM AUTHOR]

In this study, Dual Horizon Peridynamics formulation is presented for thermal diffusion analysis. Lagrangian formalism is utilized to derive the governing equations. The proposed formulation allows utilization of variable discretization and horizon sizes inside the solution domain which can result in significant benefits in terms of computational time. To demonstrate the capability of the Dual Horizon Peridynamics formulation, three different example problems are considered including a square plate with temperature and no flux boundary conditions, a square plate under thermal shock loading, and a square plate with an insulated crack. For all problems that are considered good agreement is obtained between peridynamics (PD) predictions and finite element method (FEM) results. [ABSTRACT FROM AUTHOR]

Non-local patch-based methods were until recently the state of the art for image denoising but are now outperformed by CNNs. In video denoising, however, they are still competitive with CNNs, as they can effectively exploit the video temporal redundancy, which is a key factor to attain high denoising performance. The problem is that CNN architectures are not compatible with the search for self-similarities. In this work, we propose a simple, yet efficient way to feed video self-similarities to a CNN. The non-locality is incorporated into the network via a first non-trainable layer which finds for each patch in the input image its most similar patches in a search region. The central values of these patches are then gathered in a feature vector which is assigned to each image pixel. This information is presented to a CNN which is trained to predict the clean image. We apply the proposed method to image and video denoising. In the case of video, the patches are searched for in a 3D spatiotemporal volume. The proposed method achieves state-of-the-art results. [ABSTRACT FROM AUTHOR]

Epilepsy is a prevalent neurological disorder that threatens human health in the world. The most commonly used method to detect epilepsy is using the electroencephalogram (EEG). However, epilepsy detection from the EEG is time-consuming and error-prone work because of the varying levels of experience we find in physicians. To tackle this challenge, in this paper, we propose a multi-scale non-local (MNL) network to achieve automatic EEG signal detection. Our MNL-Network is based on 1D convolution neural network involving two specific layers to improve the classification performance. One layer is named the signal pooling layer which incorporates three different sizes of 1D max-pooling layers to learn the multi-scale features from the EEG signal. The other one is called a multi-scale non-local layer, which calculates the correlation of different multi-scale extracted features and outputs the correlative encoded features to further enhance the classification performance. To evaluate the effectiveness of our model, we conduct experiments on the Bonn dataset. The experimental results demonstrate that our MNL-Network could achieve competitive results in the EEG classification task. [ABSTRACT FROM AUTHOR]

We study the Γ -convergence of a family of non-local, non-convex functionals in L p (I) for p ≥ 1 , where I is an open interval. We show that the limit is a multiple of the W 1 , p (I) semi-norm to the power p when p > 1 (respectively, the B V (I) semi-norm when p = 1). In dimension one, this extends earlier results which required a monotonicity condition. [ABSTRACT FROM AUTHOR]

In this paper, we consider the nonlinear-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of solutions. The acquired results are extended to the nonlocal-Hilfer impulsive fractional differential equation. We gave an applications to the outcomes we obtained. Further, examples are provided in support of the results we got. [ABSTRACT FROM AUTHOR]

Single-image dehazing is an ill-posed problem. Most previous methods focused on estimating intermediate parameters for input hazy images. In this paper, we propose a novel end-to-end Simplified Non-locally Dense Network (SNDN) which does not rely on intermediate parameters. To capture long-range dependencies, we propose a Simplified Non-local Dense Block (SNDB) which is lightweight and outperforms traditional non-local method. Our SNDB will be embedded into a densely connected encoder–decoder network. To avoid gradients vanishing problem, we propose a simple branch network which only have five convolution layers. The effectiveness of our proposed network is proved through ablation experiment. In addition, we enhanced our training set by synthesizing colored hazy images, which helps restore the original color of the hazy image. The experimental results demonstrate that our network have better performance than most of the pervious state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The main aim of the current work is the study of the conditions under which (finite-time) blow-up of a non-local stochastic parabolic problem occurs. We first establish the existence and uniqueness of the local-in-time weak solution for such problem. The first part of the manuscript deals with the investigation of the conditions which guarantee the occurrence of noise-induced blow-up. In the second part we first prove the C 1 -spatial regularity of the solution. Then, based on this regularity result, and using a strong positivity result we derive, for first in the literature of SPDEs, a Hopf's type boundary value point lemma. The preceding results together with Kaplan's eigenfunction method are then employed to provide a (non-local) drift term induced blow-up result. In the last part of the paper, we present a method which provides an upper bound of the probability of (non-local) drift term induced blow-up. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel end-to-end deep neural network for the problem of video super-resolution. In contrast to most previous methods where frames need to wrap for temporal alignment based on the estimated optical flow, we propose short-temporal and bidirectional long-temporal blocks to exploit the spatial-temporal dependencies existing in inter-frames. It can effectively model the sudden and smooth varying motions of videos and overcome the limitations of explicit motion estimation. In addition, by introducing dense feature concatenation, it provides an effective way to combine the low-level and high-level features for boosting the reconstruction of mid/high-frequency information as shown in our analysis and experiment. Furthermore, we present a region-level non-local feature enhancing structure, which captures the spatial-temporal correlations of any two positions and makes use of long-distance relevant information. Extensive evaluations and comparisons with the current state-of-the-art approaches demonstrate the effectiveness of the proposed framework. [ABSTRACT FROM AUTHOR]

This paper proposed a novel stereo matching method of the mobile robot based on segment tree to improve the speed and accuracy of depth recovery at the low texture, repeated texture and reflective environment. Firstly, it preprocessed the images for the mobile robot environment to reduce the influence of the light changes. In addition, this paper used the minimum spanning tree to weight the image pixels,and segmented the image by the segment tree. Then,it restored the depth of the occlusion area and the edge area that did not provide depth, and improved the accuracy of depth recovery. Finally, it carried out the comparison experiments. In indoor scenes, the calculation speed of this paper method was 187.140% faster than the ST-2 method, and semantic information could be provided for the mobile robot. On the Middlebury datasets, the calculation speed of this method was 157.500% faster than the ST-2 method, while the matching accuracy was improved 66. 547%. [ABSTRACT FROM AUTHOR]

Given a video containing a person, the video-based person re-identification (Re-ID) task aims to identify the same person from videos captured under different cameras. How to embed spatial-temporal information of a video into its feature representation is a crucial challenge. Most existing methods have failed to make full use of the relationship between frames during feature extraction. In this work, we propose a plug-and-play non-local attention module (NLAM) for frame-level feature extraction. NLAM, based on global spatial attention and channel attention, helps the network to determine the location of the person in each frame. Besides, we propose a non-local temporal pooling (NLTP) method used for temporal features' aggregation, which can effectively capture long-range and global dependencies among the frames of the video. Our model obtained impressive results on different datasets compared to the state-of-the-art methods. In particular, it achieved the rank-1 accuracy of 86.3% on the MARS (Motion Analysis and Re-identification Set) dataset without re-ranking, which is 1.4% higher than the state-of-the-art way. On the DukeMTMC-VideoReID (Duke Multi-Target Multi-Camera Video Reidentification) dataset, our method also had an excellent performance of 95% rank-1 accuracy and 94.5% mAP (mean Average Precision). [ABSTRACT FROM AUTHOR]

Existing neural networks proposed for low-level image processing tasks are usually implemented by stacking convolution layers with limited kernel size. Every convolution layer merely involves in context information from a small local neighborhood. More contextual features can be explored as more convolution layers are adopted. However it is difficult and costly to take full advantage of long-range dependencies. We propose a novel non-local module, Pyramid Non-local Block, to build up connection between every pixel and all remain pixels. The proposed module is capable of efficiently exploiting pairwise dependencies between different scales of low-level structures. The target is fulfilled through first learning a query feature map with full resolution and a pyramid of reference feature maps with downscaled resolutions. Then correlations with multi-scale reference features are exploited for enhancing pixel-level feature representation. The calculation procedure is economical considering memory consumption and computational cost. Based on the proposed module, we devise a Pyramid Non-local Enhanced Networks for edge-preserving image smoothing which achieves state-of-the-art performance in imitating three classical image smoothing algorithms. Additionally, the pyramid non-local block can be directly incorporated into convolution neural networks for other image restoration tasks. We integrate it into two existing methods for image denoising and single image super-resolution, achieving consistently improved performance. [ABSTRACT FROM AUTHOR]

In this study, a new peridynamic Mindlin plate formulation is presented which is suitable for the analysis of functionally graded materials. The governing equations of peridynamic formulation are obtained by using Euler-Lagrange equations in conjunction with Taylor’s expansion. To validate the new formulation, three different numerical benchmark problems are considered for a Mindlin plate subjected to simply supported, fully clamped and mixed (clamped-simply supported) boundary conditions. Peridynamic results are compared against results from finite element analysis and a good agreement is observed between the two methods. [ABSTRACT FROM AUTHOR]

Embryonic exposure to the teratogen nicotine results in brain defects, by disrupting endogenous spatial pre patterns necessary for normal brain size and patterning. Extending prior work in Xenopus laevis that showed that misexpression of ion channels can rescue morphogenesis, we demonstrate and characterize a novel aspect of developmental bioelectricity: channel-dependent repair signals propagate long-range across the embryo. We show that distal HCN2 channel misexpression and distal transplants of HCN2-expressing tissue, non-cell-autonomously reverse profound defects, rescuing brain anatomy, gene expression, and learning. Moreover, such rescue can be induced by small-molecule HCN2 channel activators, even with delayed treatment initiation. We present a simple, versatile computational model of bioelectrical signaling upstream of key patterning genes such as OTX2 and XBF1 , which predicts long-range repair induced by ion channel activity, and experimentally validate the predictions of this model. Our results and quantitative model identify a powerful morphogenetic control mechanism that could be targeted by future regenerative medicine exploiting ion channel modulating drugs approved for human use. [ABSTRACT FROM AUTHOR]

In recent years, there has been rapid progress on peridynamics. It has been applied to many different material systems, used for coupled field analysis and is suitable for multi-scale analysis. This study mainly focuses on peridynamic analysis for plate-type structures. For this purpose, a new peridynamic Kirchhoff plate is developed. The new formulation is computationally efficient by having only one degree of freedom for each material point. Moreover, it is based on the state-based peridynamic formulation, which does not impose any limitation on material constants. After presenting how to impose simply supported and clamped boundary conditions in this new formulation, several numerical studies are considered to demonstrate the accuracy and capability of the proposed formulation. [ABSTRACT FROM AUTHOR]

Convolutional Neural Networks (CNNs) have been widely employed for image Super-Resolution (SR) in recent years. Various techniques enhance SR performance by altering CNN structures or incorporating improved self-attention mechanisms. Interestingly, these advancements share a common trait. Instead of explicitly learning high-frequency details, they learn an implicit feature processing mode that utilizes weighted sums of a feature map's own elements for reconstruction, akin to convolution and non-local. In contrast, early dictionary-based approaches learn feature decompositions explicitly to match and rebuild Low-Resolution (LR) features. Building on this analysis, we introduce Trainable Feature Matching (TFM) to amalgamate this explicit feature learning into CNNs, augmenting their representation capabilities. Within TFM, trainable feature sets are integrated to explicitly learn features from training images through feature matching. Furthermore, we integrate non-local and channel attention into our proposed Trainable Feature Matching Attention Network (TFMAN) to further enhance SR performance. To alleviate the computational demands of non-local operations, we propose a streamlined variant called Same-size-divided Region-level Non-Local (SRNL). SRNL conducts non-local computations in parallel on blocks uniformly divided from the input feature map. The efficacy of TFM and SRNL is validated through ablation studies and module explorations. We employ a recurrent convolutional network as the backbone of our TFMAN to optimize parameter utilization. Comprehensive experiments on benchmark datasets demonstrate that TFMAN achieves superior results in most comparisons while using fewer parameters. The code is available at https://github.com/qizhou000/tfman. • A novel Trainable Feature Matching (TFM) module for super-resolution is proposed. • An lightweight improvement for Non-Local (self-attention) is proposed. • Comprehensive experiments is conducted with BI, BD and DN degradation models. • Our method achieves best super-resolution results on multiple benchmarks. [ABSTRACT FROM AUTHOR]

Thoroughly mixing immiscible fluids creates droplets of one phase dispersed in a continuum of the other phase. In such emulsions, the individual droplets have rather mundane mechanical behavior. However, densely confining these suspended droplets generates a packing of particles with a spectacular diversity of mechanical behavior whose origins we are only beginning to understand. This mini review serves to survey a non-exhaustive range of experimental dense slow flow emulsion work. To embed these works in the context of the flow behavior of other structured fluids, we also discuss briefly the related non-local flow modeling attempts as one of the approaches that has been used successfully in describing emulsion flow properties and other materials.

This paper reviews the emergence of non-local flow phenomena in granular materials and discusses a range of models that have been proposed to integrate an intrinsic length-scale into granular rheology. The frameworks discussed include micro-polar modeling, kinetic theory, three particular order-parameter-based models, and strongly non-local integral-based models. An extensive commentary is included discussing the current capabilities of these existing models as well as their implementational ease, physical motivation, and breadth of predictive ability.

Cross-modality person re-identification is the study of images of people matching under different modalities (RGB modality, IR modality). Given one RGB image of a pedestrian collected under visible light in the daytime, cross-modality person re-identification aims to determine whether the same pedestrian appears in infrared images (IR images) collected by infrared cameras at night, and vice versa. Cross-modality person re-identification can solve the task of pedestrian recognition in low light or at night. This paper aims to improve the degree of similarity for the same pedestrian in two modalities by improving the feature expression ability of the network and designing appropriate loss functions. To implement our approach, we introduce a deep neural network structure combining heterogeneous center loss (HC loss) and a non-local mechanism. On the one hand, this can heighten the performance of feature representation of the feature learning module, and, on the other hand, it can improve the similarity of cross-modality within the class. Experimental data show that the network achieves excellent performance on SYSU-MM01 datasets.

Copyright of Sociologija: Mintis ir Veiksmas is the property of Vilnius University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

• A model for banded vegetation patterns is analysed that includes non-local seed dispersal. • Numerical continuation and bifurcation analysis is applied to map the stability of patterns. • Non-local seed dispersal can increase the ecological resilience of banded patterns. • Coping strategies for critically low levels of rainfall are oscillating band densities and non-migrating patterns. Landscape-scale vegetation stripes (tiger bush) observed on the gentle slopes of semi-arid regions are useful indicators of future ecosystem degradation and catastrophic shifts towards desert. Mathematical models like the Klausmeier model—a set of coupled partial differential equations describing vegetation and water densities in space and time—are central to understanding their formation and development. One assumption made for mathematical simplicity is the local dispersal of seeds via a diffusion term. In fact, a large amount of work focuses on fitting dispersal 'kernels', probability density functions for seed dispersal distance, to empirical data of different species and modes of dispersal. In this paper, we address this discrepancy by analysing an extended Klausmeier model that includes long-distance seed dispersal via a non-local convolution term in place of diffusion, and assessing its effect on the resilience of striped patterns. Many authors report a slow uphill migration of stripes; but others report no detectable migration speed. We show that long-distance seed dispersal permits the formation of patterns with a very slow (possibly undetectable) migration speed, and even stationary patterns which could explain the inconsistencies in the empirical data. In general, we show that the resilience of patterns to reduced rainfall may vary significantly depending on the rate of seed dispersal and the width of the dispersal kernel, and compare a selection of ecologically relevant kernels to examine the variation in pattern resilience. [ABSTRACT FROM AUTHOR]

Copyright of DYNA - Ingeniería e Industria is the property of Publicaciones Dyna SL and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract Color transfer methods usually suffer from spatial color coherency problem. In order to address this problem, this paper develops a fused color transfer method for image colorization. Our idea is to design a local student's t-test to screen the incoherent colors in the preliminary colorization results obtained by a simple color transfer method with DFT and variance features. Furthermore, we propose a variational fusion model to inpaint these incoherent colors and fuse the other useful colors together. We also present an efficient algorithm for solving the fusion model numerically, and show the convergence of the algorithm. Finally, experimental results are reported to demonstrate the effectiveness of the proposed method, and its performance is competitive with those of the other testing methods. [ABSTRACT FROM AUTHOR]

Abstract A considerable fluid load can cause local damages on the offshore structures, which may be a risk in the field of ocean engineering. Therefore, an accurate fluid motion prediction is a crucial issue in predicting the offshore structure motion. In this study, a non-local Lagrangian model is developed for Newtonian fluid low Reynold's number laminar flow. Based on the peridynamic theory, a peridynamic differential operator is recently proposed for directly converting the partial differential into its integral form. Therefore, the peridynamic differential operator is applied to convert the classical Navier-Stokes equations into their integral forms. The numerical algorithms are developed both in total and updated Lagrangian description. Finally, several benchmark fluid flow problems such as Couette flow, Poiseuille flow, Taylor Green vortex, shear-driven cavity problem and dam collapse problems are numerically solved. The simulation results are compared with the ones available in the published literature. The good agreements validate of the capability of the proposed non-local model for Newtonian fluid low Reynold's number laminar flow simulation. Highlights • A non-local model is developed for Newtonian fluid laminar low Reynolds number flow. • The peridynamic differential operator is used to develop the non-local model. • Numerical algorithms both in total and updated Lagrangian descriptions are provided. • Classical fluid flow problems are numerically simulated with the newly developed model. [ABSTRACT FROM AUTHOR]

A brief analysis of boundary value problem of Caputo fractional differential equations with non-local integral strip boundary conditions has been done. The investigation depends on the Banach fixed point theorem and Leray-Schauder alternative theorem. Example illustrating the main results are also constructed. [ABSTRACT FROM AUTHOR]

Abstract Partial differential equations (PDEs) have emerged as a useful tool for recovering structures when solving image inpainting problems. In the research presented in this paper, we extend structure tensor (ST)-based PDE to fine-grained texture inpainting by improving the ST with three modifications to enhance its suitability to more accurately process fine-grained textures of which the small-scale patterns repeat non-locally. These modifications are then inserted into an anisotropic PDE to recover damaged textures. The result is a subtly-conducted anisotropic diffusion inpainting algorithm free of detail-blurring artifacts produced by the classic tensor diffusion model and dislocation deficiencies affecting patch-based completion approaches. This is made possible by the following strategies: (1) construct a fractional ST (FST 1 1 Fractional structure tensor.) composed of the inner product of the fractional derivative vector and its transposition to more effectively address complex fractal-like texture details because of the characteristics of the fractional differential; (2) because FST is composed of the inner product of two vectors, it is necessary to represent the tensor at a higher resolution than for the original image to avoid spectrum aliasing, which is automatically implemented by the calculation of the twofold oversampling fractional derivative (i.e., double-sampling FST, DFST 2 2 Double-sampling fractional structure tensor.); (3) apply a non-local regularizing method to all four channels of the resulting DFST based on the repeatability of textures, which integrates non-local geometric characteristics to effectively infer how damaged textures extend. Finally, we insert the modified non-locally regularized DFST (NDFST 3 3 Nonlocally-regularized double-sampling fractional structure tensor.) into an anisotropic PDE to effectively guide the diffusion process and design its numerical implementation scheme. The experimental results show that, for fine-grained texture images, the proposed NDFST is equipped to accurately detect subtle and complex texture features, and the resulting NDFST-based PDE is particularly effective not only for recovering non-homogeneous structures, but also for the restitution of fine-grained textures. Highlights • An effective inpainting method for restoring damaged texture images is presented. • Our method extends structure-tensor-based partial differential equations (PDEs). • The algorithm is based on a fractional structure tensor with double-sampling (DFST). • Non-locally regularized DFST (NDFST) was then inserted into an anisotropic PDE. • The resulting method recovers non-homogeneous structures and fine-grained textures. [ABSTRACT FROM AUTHOR]

For delayed non-local reaction-diffusion equations arising from population biology, selection mechanisms of the speed sign for the bistable travelling wavefront have not been found. In this paper, based on the theory of asymptotic speeds of spread for monotone semiflows, we firstly provide an interval of values of wave speed and a novel general condition for determining the speed sign by applying the comparison principle and the globally asymptotic stability of the bistable travelling wave. Moreover, through constructing novel upper/lower solutions, we give explicit conditions for the speed sign to be positive or negative. The obtained results are efficiently applied to three classical forms of the kernel functions. [ABSTRACT FROM AUTHOR]

Highlights • Governing equations of Timoshenko beam were developed based on peridynamic theory. • A standard FEM formulation was constructed for peridynamic beam element. • Effects of different peridynamic (non-local) characteristics on the numerical convergence were studied in detail. • Influences of several parameters on the static and vibrational behavior of the beam were studied. Abstract In this paper, combination of classical and peridynamic theories is implemented to study static and free vibrational behavior of a Timoshenko beam. Employing Hamilton's principle, the governing integro-differential equations are developed. Due to problematic analytical solution, FEM formulations are constructed and necessary computer codes are developed. Static and vibrational problems are numerically studied to reveal influential parameters. Mesh sensitivity analysis and comparison with relevant results reported in the open literature are done for verification of the methodology and ensuring reliable results. Effects of peridynamic parameters, boundary conditions, and the beam size are studied. Regarding each influencing factor, relevant illustration is presented and the results are discussed from the physical point of view. [ABSTRACT FROM AUTHOR]

Given a video containing a person, the video-based person re-identification (Re-ID) task aims to identify the same person from videos captured under different cameras. How to embed spatial-temporal information of a video into its feature representation is a crucial challenge. Most existing methods have failed to make full use of the relationship between frames during feature extraction. In this work, we propose a plug-and-play non-local attention module (NLAM) for frame-level feature extraction. NLAM, based on global spatial attention and channel attention, helps the network to determine the location of the person in each frame. Besides, we propose a non-local temporal pooling (NLTP) method used for temporal features’ aggregation, which can effectively capture long-range and global dependencies among the frames of the video. Our model obtained impressive results on different datasets compared to the state-of-the-art methods. In particular, it achieved the rank-1 accuracy of 86.3% on the MARS (Motion Analysis and Re-identification Set) dataset without re-ranking, which is 1.4% higher than the state-of-the-art way. On the DukeMTMC-VideoReID (Duke Multi-Target Multi-Camera Video Reidentification) dataset, our method also had an excellent performance of 95% rank-1 accuracy and 94.5% mAP (mean Average Precision).

Due to the influence of equipment instability and surveying environment, scattering echoes and other factors, it is sometimes difficult to obtain high-quality sub-bottom profile (SBP) images by traditional denoising methods. In this paper, a novel SBP image denoising method is developed for obtaining underlying clean images based on a non-local low-rank framework. Firstly, to take advantage of the inherent layering structures of the SBP image, a direction image is obtained and used as a guidance image. Secondly, the robust guidance weight for accurately selecting the similar patches is given. A novel denoising method combining the weight and a non-local low-rank filtering framework is proposed. Thirdly, after discussing the filtering parameter settings, the proposed method is tested in actual measurements of sub-bottom, both in deep water and shallow water. Experimental results validate the excellent performance of the proposed method. Finally, the proposed method is verified and compared with other methods quantificationally based on the synthetic images and has achieved the total average peak signal-to-noise ratio (PSNR) of 21.77 and structural similarity index (SSIM) of 0.573, which is far better than other methods.

Every object in the world has a three-dimensional geometrical shape and it is usually possible to model structures in a three-dimensional fashion, although this approach can be computationally expensive. In order to reduce computational time, the three-dimensional geometry can be simplified as a beam, plate or shell type of structure depending on the geometry and loading. This simplification should also be accurately reflected in the formulation that is used for the analysis. In this study, such an approach is presented by developing an Euler–Bernoulli beam formulation within ordinary state-based peridynamic framework. The equation of motion is obtained by utilizing Euler–Lagrange equations. The accuracy of the formulation is validated by considering various benchmark problems subjected to different loading and displacement/rotation boundary conditions. [ABSTRACT FROM AUTHOR]

Abstract The main goal of this work is to prove the existence of three different solutions (one positive, one negative and one with nonconstant sign) for the equation (− Δ p) s u = | u | p s ⁎ − 2 u + λ f (x , u) in a bounded domain with Dirichlet condition, where (− Δ p) s is the well known p -fractional Laplacian and p s ⁎ = n p n − s p is the critical Sobolev exponent for the non local case. The proof follows the ideas of [28] and is based in the extension of the Concentration Compactness Principle for the p -fractional Laplacian [20] and Ekeland's variational Principle [7]. [ABSTRACT FROM AUTHOR]

Abstract Recently, real-time and robust infrared target identification methodshave become critical for many applications in almost all kinds of modern weapon systems, including infrared search and tracking systems,surveillance systems and so on. However, at the long distance noises contaminated infrared imaging which the targets only occupied several pixels and the lowest entropy of information to obscure recognition the targets with digital image processing approaches effectively. To address these issues, a robust and scalable method for infrared target identification was proposed. With non-local and dynamic pattern recognition, the template matching accuracy between template and target improved significantly. It demonstrated that more than 80% accurate prediction rate of the proposed method in the practicing applications. [ABSTRACT FROM AUTHOR]

Highlights • A multi-degree of freedom, non-local, geometrically non-linear model, based on the transverse displacement and on Airy's stress function is derived for graphene sheets. • The modes of vibration of graphene sheets are studied taking into account geometrical non-linearity and non-local effects. • The influence that non-local effects have on the non-linear modes of vibration of graphene sheets is verified by analysing backbone curves (frequency versus amplitude of vibration), time and phase plots. • It is found that the non-local effects influence very significantly the frequencies and vibration amplitudes at which graphene sheets experience bifurcations; they can even eliminate bifurcations. Abstract Single-layer graphene sheets (SLGSs) with dimensions of the order of a few nanometres are relatively new, but expected to have several applications. When SLGSs experience displacements that are large in comparison with their extremely small thickness, the membrane forces that develop lead to non-linear behaviour. Knowing the modes of vibration of SLSGs is important, because these modes provide a picture of what one may expect not only in free, but also in forced vibrations. In this paper, the non-linear modes of vibration of flat single-layer graphene sheets are investigated. For that purpose, a Galerkin type formulation, based on classic plate theory with Von Kármán non-linear terms and resorting to Airy' s stress function, is implemented. The formulation takes into account non-local effects, which are thought to be important in very small structural elements. The ordinary differential equations of motion are transformed into algebraic equations of motion via the harmonic balance method (HBM), with several harmonics, and are subsequently solved by an arc-length continuation method. The combined importance of non-local effects and of the geometrical non-linearity on the non-linear modes of vibration is analysed. They result in alterations of the natural frequencies, variations in the degrees of hardening, changes in the frequency content of the free vibrations, and alterations in shapes assumed along a period of vibration. The main outcome of this work is the finding that the small scale has a major effect on interactions between the first and higher order modes, interactions which are induced by the geometrical non-linearities. It turns out to be possible, e.g., for non-local effects to considerably change the frequencies at which internal resonances occur, or even to eliminate those internal resonances. Graphical abstract Bifurcation diagram, representing non-dimensional amplitudes of first harmonic (W 1 / h) as function of non-dimensional natural frequency of vibration (ω/ω ℓ1) at central point of armchair and zigzag graphene sheets. First main branch. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Free vibration of a bimaterial circular nano-tube is investigated. The tube is formed by bonding together a Si3N4/SUS304 functionally graded upper semi tube and a ZrO2/Ti-6Al-4V functionally graded lower semi tube. The material properties of the tube are assumed to vary along the radius according to power law with the power index of upper semi tube differing from that of lower semi tube. Based on non-local elasticity theory and Hamilton's principle, a refined beam model considering the effect of transverse shear deformation is used to derive the governing equations, then analytical solution is obtained by using a two-steps perturbation method. Our results were compared with the existing ones. The effects on tube's linear and non-linear frequency are analyzed of the factors, including small scale parameter, temperature, the double volume fraction indexes, slenderness ratio and different types of beam model. A new approach is suggested in this article to change the natural frequency of the tubes by adjusting constituent materials. In contrast to conventional approach, the new one can result in more accurate frequency control in the same dimensionless size of tubes. [ABSTRACT FROM AUTHOR]

Abstract In the visual Internet of Things (VIoT), imaging sensors must achieve a balance between limited bandwidth and useful information when images contain heavy noise. In this paper, we address the problem of removing heavy noise and propose a novel hierarchical extreme learning machine-based image denoising network, which comprises a sparse auto-encoder and a supervised regression. Due to the fast training of a hierarchical extreme learning machine, an effective image denoising system that is robust for various noise levels can be trained more efficiently than other denoising methods, using a deep neural network. Our proposed framework also contains a non-local aggregation procedure that aims to fine-tune noise reduction according to structural similarity. Compared to the compression ratio in noisy images, the compression ratio of denoised images can be dramatically improved. Therefore, the method can achieve a low communication cost for data interactions in the VIoT. Experimental studies on images, including both hand-written digits and natural scenes, have demonstrated that the proposed technique achieves excellent performance in suppressing heavy noise. Further, it greatly reduces the training time, and outperforms other state-of-the-art approaches in terms of denoising indexes for the peak signal-to-noise ratio (PSNR) or the structural similarity index (SSIM). Highlights • We address the heavy noise removing problem faced in visual Internet of Things by using the hierarchical extreme learning machine. The proposed framework contains a sparse auto-encoder and a supervised regression and a non-local aggregation. • We provide an effective patch-to-patch image denoising networks which are robust for dealing with various noise levels in both clipped and unclipped noisy model. The key advantage of this denoising network is fast training. • Experimental studies on images including both hand-written digits and natural scenes have shown that our method achieves excellent performance both in quality and efficiency. The nice performance can improve the compression ratio for data interactions in the visual Internet of Things. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a reaction- diffusion SIR epidemic model with nonlinear incidence rate and non-local delay effect in a continuous bounded spatial domain. We introduce the basic reproduction number R0 of the model by the idea of next generation operator. By means of the theory of dynamical systems and uniform persistence, we investigate the global dynamics of the model in terms of R0. Finally, we implement numerical simulations to show the feasibility of our results and explore some epidemiological insights. [ABSTRACT FROM AUTHOR]

Abstract The primary phenomenon responsible for rock failure called damage is described as the nucleation and evolution of voids in the rock matrix. The damage of rocks especially under the extreme conditions of High Pressure and High Temperature (HPHT) is studied. Rocks demonstrate ductile behavior in HPHT conditions, which is attributed to high confining pressure due to which fragments are held together and a continuum flow is possible. A new 3D non-local macroscopic continuum ductile-damage model is developed for realistic modeling of behavior of rocks under HPHT conditions. The model uses a damage variable, which is a volumetric quantity, called the void-volume fraction. It is assumed that damage is initiated and then driven by the onset of plasticity in a coupled non-local system. The numerical model is applied to a uniaxial compression and the dynamic indentation problems respectively. The dynamic indentation problem is of particular interest to rock drilling at ultra deep depths. Numerically, indentation introduces high stress concentrations and strain localizations, which are generally very hard to handle, owing to issues like loss of hyperbolicity, material length scale and shear deformation bands, using classical methods. The selected problems are solved by local and non-local approaches respectively. The uniaxial compression problem demonstrates the large difference in failure strains of rocks under normal pressure and temperature conditions and HPHT conditions. Results obtained from the dynamic indentation problem show that the damage is incurred in a rock body under the action of an indentor in the form of damage-zones of varying degrees of damage. The results also indicate the importance of non-locality that provides stability and convergence to the numerical solution. Highlights • A nonlocal continuum ductile damage model is developed for rocks under High Pressure and High Temperature (HPHT). • The damage variable introduced is a volumetric quantity called the voidvolume fraction and is represented as a balance law. • The model consists of coupled governing equations; the balance of linear momentum and the void-volume fraction equations. • The model is applied to the dynamic indentation problem, which is complimentary to mechanical evacuation of rocks. ◦ Model performance for local and non-local numerical settings is demonstrated ◦ Non-local model damage results showing different damage zones are qualitatively compared to the experimental observations [ABSTRACT FROM AUTHOR]

In this paper, we propose a rigorous and accurate non-local (in the oversampled region) upscaling framework based on some recently developed multiscale methods [10] . Our proposed method consists of identifying multi-continua parameters via local basis functions and constructing non-local (in the oversampled region) transfer and effective properties. To achieve this, we significantly modify our recent work proposed within Generalized Multiscale Finite Element Method (GMsFEM) in [10] and derive appropriate local problems in oversampled regions once we identify important modes representing each continuum. We use piecewise constant functions in each fracture network and in the matrix to write an upscaled equation. Thus, the resulting upscaled equation is of minimal size and the unknowns are average pressures in the fractures and the matrix. Note that the use of non-local upscaled model for porous media flows is not new, e.g., in [14] , the authors derive non-local approach. Our main contribution is identifying appropriate local problems together with local spectral modes to represent each continuum. The model problem for fractures assumes that one can identify fracture networks. The resulting non-local equation (restricted to the oversampling region, which is several times larger compared to the target coarse block) has the same form as [14] with much smaller local regions. We present numerical results, which show that the proposed approach can provide good accuracy. [ABSTRACT FROM AUTHOR]