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The proliferation of depth cameras and LiDAR sensors in actual industrial environments has fueled the pursuit of an effective and efficient 3D point cloud model that enables us to perceive and interact with the physical world. However, the intrinsic complexity of 3D semantic information poses significant challenges to model design, including spatial rotation invariance and irregular point cloud structure, which fundamentally impact the representation and behavior of 3D point cloud systems. Existing have either heavily relied on labeling information in a supervised learning setting or failed to effectively capture the inherent patterns of the 3D point clouds within a self-supervised learning framework, leading to poor performance in specific downstream tasks. To address these limitations, this paper introduces a self-supervised framework, D ual- C ross C ontrastive Neural N etwork (DCCN) for 3D point cloud self-supervised representation learning. DCCN leverages cross-view, cross-network, and domain-specific knowledge distillation to enhance the extraction of hidden features from point clouds and fully exploit the capabilities of the encoder. Our DCCN employs a pseudo-Siamese network consisting of an online network and a target network, facilitating knowledge interaction and distillation. The method extracts internal states from augmented 3D point cloud by learning cross-view relationships and optimizes model parameters through intra-modal cross-network learning. We incorporate a momentum-updating mechanism without shared weights in the Siamese network architecture to distill knowledge and enhance the role differentiation the online and target networks. Experimental results demonstrate that our approach outperforms a range of supervised and self-supervised learning methods across a series of downstream tasks consisting of four tasks in three representative datasets. Ablation studies validate the component-wise effectiveness of cross-view, cross-network, and moment-updating learning objectives in achieving superior point cloud representation. The overall findings establish our method, DCCN, as an effective solution for 3D point cloud representation learning in real-world applications. [ABSTRACT FROM AUTHOR]

Urban drainage system plays an important role in urban rainwater management. The design of urban drainage system is challenging for its complex constraints and expensive individual evaluation. A kind of multi-objective evolutionary algorithm driven by both structural and empirical knowledge, called structural and empirical knowledge driven multi-objective evolutionary algorithm, is proposed in this paper. A novel tree-template-based encoding schema is proposed to extract the structural knowledge of urban drainage system. The population initialization method and genetic operators (i.e., crossover and mutation) are customized to handle the constraints among decision variables caused by the structure restriction of the urban drainage system. The radial basis function (RBF) model is employed to learn the empirical knowledge from the previous evolution process, and the RBF-based approximate evaluation is used to partially replace the expensive individual evaluation to improve the efficiency of the algorithm. Besides, by combining the decomposition idea and the constrained dominance principle, the local constrained dominance principle is suggested to handle the constraints in decision space, which can effectively improve the defect that the constrained dominance principle is easy to fall into local optimum. Comprehensive experiments on two urban drainage system cases show the superiority of the proposed algorithm for the optimal urban drainage system design. [ABSTRACT FROM AUTHOR]

This paper proposes a prescribed intelligent elliptical pursuing algorithm driven by deep reinforcement learning (DRL) for Unmanned Aerial Vehicles (UAVs), aiming to achieve an optimal performance without violating appointed-time constraints. Specifically, an unknown system dynamics estimator (USDE) with merely one filtering coefficient is employed to counteract uncertainties effectively. Subsequently, an elliptical enclosing controller is devised for UAVs to achieve asymptotic convergence towards the target ellipse orbit. Particularly, a proximal policy optimization (PPO)-based optimal learning term is contrived to achieve control optimality related to consumption and efficiency, where a refined reward function is established to characterize the appointed-time constraints. The salient merit is that an efficient learning paradigm is formulated to fulfill a near optimal appointed-time enclosing free from prescribed performance control. Finally, a plenty of simulations substantiate the feasibility of developed algorithm. [ABSTRACT FROM AUTHOR]

Influence maximization in social networks aims to identify users with the highest influence in the network and leverage them as initial spreaders to maximize the revenue of influence. Recently, an increasing number of studies have drawn attention to the study of influence maximization in multi-entity social networks, achieving some degrees of success. However, most of them still have two major shortcomings. First, most of the previous work oversimplifies the correlation between the target entity and other entities, and overlooks the influence of user's interest preference on information propagation. Second, the majority of existing methods face a trade-off between operational efficiency and solution accuracy, making it difficult to be effectively applied to large social networks. To fill this gap, this paper proposes a Deep neural network model based on Historical Behavior Sequences, named DHBS. DHBS consists of two core components: a Deep neural network model Incorporating Multi-head Self-attention, named DIMS; and a Reverse Influence Sampling algorithm based on Historical Behavior Sequence, named RIS-HBS. Specifically, DIMS captures the dynamic interest changes of users through its attention mechanism, enabling more accurate modeling of entity correlation in multi-entity social networks. RIS-HBS efficiently identifies a set of high-influential users for the target entity by incorporating the concept of reverse influence sampling. Experimental results on four publicly available network datasets demonstrate that DHBS outperforms baseline methods in terms of prediction accuracy, expected spread, and scalability, and DIMS plays a key role on RIS-HBS in the DHBS model. • Influence maximization is studied by mining users' historical behavior sequences. • Analyze entity correlation by capturing users' interest changes. • A neural attentive influence maximization model named DHBS is proposed. [ABSTRACT FROM AUTHOR]

Recently, extensive research is showing that deep learning has enormous potential in image steganography. However, most steganography methods based on deep learning are not sufficiently invisible. In this paper, a novel end-to-end deep neural network for image steganography based on generative adversarial network (GAN) and discrete wavelet transformation (DWT) is proposed, which can greatly improve the invisibility of the method. Firstly, the cover image is transformed from the RGB domain to the DWT domain to embed information in frequency. Furthermore, a multi-scale attention convolution to fuse different scales of feature information is proposed, which can help the model to find a better location to embed the information. Finally, the fusion module is used to embed the information into the cover image at different modification intensities. In addition, a new Discriminator that compares cover images and stego images in a patch-to-patch way to improve the ability of the Discriminator. We analyze our algorithm from multiple aspects (e.g., security and invisibility) to verify the superior performance of the proposed method. To demonstrate generalization ability, experiments are conducted on three widely used datasets and show the superior performance of our method compared to other steganography methods based on deep learning. • End-to-end deep neural network based image steganography method. • An effective DWT based method to embed information in frequency. • A multi-scale attention convolution is used to find a better embedding location. • A fusion module is used to embed data at different modification intensities. • A new Discriminator that compares cover and stego in a patch-to-patch way. [ABSTRACT FROM AUTHOR]

The users' click prediction holds significant commercial value in online purchase platforms. Currently, some session-based interest extraction models overlook the impact of temporal interval factors on the distribution pattern of behaviors within a session. To address the above issue, this paper designs a module named session-based time-aware gated recurrent units (ST-GRU) to integrate the temporal interval factors into session sequence. The ST-GRU module utilizes a memory decay function, enabling the simulation process to identify the users' memory changes within each session. Subsequently, to account for the interdependence between different sessions, this paper introduces bi-directional gated recurrent units (Bi-GRU) with an attention mechanism to learn interaction relations of user interests. Additionally, for high-dimensional potential features, this paper integrates above modules and proposes a method called time interval aware deep session interest network (TIAE-DSIN) model. Correspondingly, comparative experiments are carried out on three public datasets, and the obtained results indicate that the AUC of TIAE-DSIN model is superior to other session interest extraction models. [ABSTRACT FROM AUTHOR]

In recent investigations concerning manipulated image localization, prevailing methodologies have relied on Convolutional Neural Networks (CNNs) to facilitate supervised learning predicated upon manipulated images and their corresponding ground-truth annotations. Nevertheless, these methods produce high false detection rates when detecting unaltered images due to the limited availability of authentic images. In this paper, we initiate our inquiry by scrutinizing the distribution characteristics of class activation maps within the context of image manipulation detection and the inherent patterns of alterations within this domain. We then introduce the novel concept of a tampering Edge-based Class Activation Map (EdgeCAM) tailored for detecting tampering within manipulated images. Leveraging EdgeCAM, we formulate a framework for localizing tampered regions in images through a weakly-supervised approach, relying solely on image-level annotations. Ultimately, we establish a fundamental benchmark for weakly-supervised image manipulation localization by utilizing genuine tampered images collected from real-world scenarios. The empirical results highlight the notable efficacy of our proposed method, outperforming current weakly-supervised methods for detecting image manipulation by a significant margin of 12.7% on the average combined F1 metrics across various generic datasets. This result also achieves performance comparable to supervised methods for image manipulation localization. • CNN models focus on tampered edges for image detection, emphasizing shallow features. • Proposed EdgeCAM rectifies imprecise shallow representation in CNN models. • Weakly-supervised framework using EdgeCAM enhances image localization accuracy. • Approach shows effectiveness on diverse datasets, comparable to supervised methods. • Novel weakly-supervised baseline for image manipulation uses PS-Battles dataset. [ABSTRACT FROM AUTHOR]

Visual features encompass visual information extracted from images or videos, serving as supplementary input to enhance the efficacy of neural machine translation (NMT) systems. By seamlessly integrating these visual features into the translation process, NMT models can tap into the expansive visual context, thereby making more precise predictions during translation. Nonetheless, limited efforts have been directed towards exploring the potential of learning target-side future context using visual features to augment NMT performance. To bridge this gap, this paper introduces the Vision-guided Target-side Future Context (VisTFC) learning framework for NMT. Our core objective is to refine translation quality by effectively harnessing and incorporating target-side future contextual insights derived from the visual modality. The VisTFC framework consists of three pivotal components. Firstly, a graph-based multimodal encoder–decoder is established, constructing a bipartite vision-source/target graph. This enables the acquisition of vision-fused textual representations, synthesizing both linguistic and visual attributes to enhance translation accuracy. Secondly, a target-side future context predictor, incorporating a dynamic routing mechanism, infers future context by synergizing visual information. This empowers the model to anticipate and assimilate contextual cues, ensuring more coherent and contextually coherent translations. Thirdly, a sigmoid update gate is introduced, facilitating controlled integration of predicted future context into the decoding process, enabling the decoder to flexibly adapt and utilize the inferred context. Moreover, the VisTFC framework is fortified with additional loss functions that enforce source/target-vision consistency, reinforcing its robustness and effectiveness. Our results demonstrate that our model can achieve substantial improvements, reaching up to 1.0/0.9/1.1 BLEU points beyond the performance of the most robust baselines. This superior performance is evident on both the Test2016 and Test2017 datasets, as well as on the MSCOCO test sets for English-French translation tasks. Furthermore, our experiments underscore the efficacy of VisTFC, even in scenarios with limited resources, such as the English-Hausa language pair. Here, the model achieves notable enhancements, with improvements of up to 1.8/1.9 BLEU points compared to the strongest text-only NMT models on E-Test and C-Test test sets. These findings provide strong evidence supporting our model's ability to effectively harness target-side future contextual information from the visual modality, resulting in substantial enhancements in machine translation quality. Further analysis and visualization suggest that VisTFC is capable of learning target-side future context from visual signals for better translation. We also have open-sourced our work in Github. 1 1 https://github.com/nlpdl/VsiTFC. • Exploring how to incorporate visual features into the translation process. • Adopting a dynamic routing mechanism to infer target-side future context. • Integrating a multimodal graph into encoder–decoder. [ABSTRACT FROM AUTHOR]

In this paper, we propose two numerical approaches for approximating the solution of the following kind of integral equation f (y) − μ ∫ − 1 1 f (x) k (x , y) w (x) d x = g (y) , y ∈ [ − 1 , 1 ] , where f is the unknown solution, μ ∈ R ∖ { 0 } , k , g are given functions not necessarily known in the analytical form, and w is a Jacobi weight. The proposed projection methods are based on the constrained mock-Chebyshev least squares polynomials, and starting from data known at equally spaced points, provide a fine approximation of the solution. Such peculiarity can be helpful in all cases we deal with experimental data, typically measured at equispaced points. We prove the introduced methods are stable and convergent in some Sobolev subspace of C [ − 1 , 1 ]. Several numerical tests confirm the theoretical estimates and numerical effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we solve a non-linear reaction–diffusion system with Dirichlet–Neumann mixed boundary conditions using a finite difference method (FDM) in space and the implicit midpoint method in time. This type of system appears, e.g., in the mathematical modeling of light-controlled drug delivery. One of the key results of this paper is the proof that the method has superconvergence second-order in space in a discrete H 1 -norm and optimal second-order convergence in time in a discrete L 2 -norm. Our result relies on the direct analysis of a suitable error equation, avoiding the classic construction of consistency plus stability implies convergence. One advantage of such an analysis technique is the establishment of the method's non-linear stability in an elegant way. Numerical examples support the theoretical convergence result. [ABSTRACT FROM AUTHOR]

In this paper we extend recent results obtained for the Navier–Stokes equations to propose and analyze a new fully mixed virtual element method (mixed-VEM) for the stationary two-dimensional Boussinesq equations appearing in non-isothermal flow phenomena. The model consists of a Navier–Stokes type system, modeling the velocity and the pressure of the fluid, coupled to an advection-diffusion equation for the temperature. The variational formulation is based on the introduction of the additional unknowns given by a modified pseudostress tensor, which depends on the pressure, and the diffusive and convective terms of the fluid, and the pseudoheat vector, which involves the temperature, its gradient, and the velocity. As a consequence of the former, the pressure is eliminated from the system, but computed afterwards via a post-processing formula. In turn, for the Galerkin approximation we follow the approach employed in a previous work introducing for the first time an L p spaces-based mixed-VEM for the Navier–Stokes equations, and couple it with a similar mixed-VEM for the convection–diffusion equation modeling the temperature. The solvability analysis of the resulting coupled discrete scheme is carried out by using appropriate fixed-point arguments, along with the discrete versions of the Babuška–Brezzi theory and the Banach-Nečas-Babuška theorem, both in subspaces of Banach spaces. The first Strang lemma is applied to derive the a priori error estimates for the virtual element solution as well as for the fully computable approximation of the pseudostress tensor, the pseudoheat vector, and the post-processed pressure. Finally, several numerical results, illustrating the performance of the mixed-VEM scheme and confirming the rates of convergence predicted by the theory, are reported. [ABSTRACT FROM AUTHOR]

In this paper, an accelerated spectral conjugate gradient projection algorithm is proposed for solving the constrained nonlinear pseudo-monotone equations. We set a restart procedure related to the conjugate parameter in the search direction of the spectral conjugate gradient method. We use an accelerated gradient descent scheme to generate the spectral parameter. Finally, we adopt the relaxed-inertial strategy to accelerated algorithm iteration process. Global convergence is proved under mild conditions without the Lipschitz continuity assumption. Numerical comparisons with other methods show the performances of our algorithm for solving large-scale equations. Our applications are on regularized decentralized logistic regression and image de-blurring problems. [ABSTRACT FROM AUTHOR]

This paper introduces the Neural Network for Non-linear Hawkes processes (NNNH), a non-parametric method based on neural networks to fit non-linear Hawkes processes. Our method is suitable for analysing large datasets in which events exhibit both mutually-exciting and inhibitive patterns. The NNNH approach models the individual kernels and the base intensity of the non-linear Hawkes process using feed forward neural networks and jointly calibrates the parameters of the networks by maximizing the log-likelihood function. We utilize Stochastic Gradient Descent to search for the optimal parameters and propose an unbiased estimator for the gradient, as well as an efficient computation method. We demonstrate the flexibility and accuracy of our method through numerical experiments on both simulated and real-world data, and compare it with state-of-the-art methods. Our results highlight the effectiveness of the NNNH method in accurately capturing the complexities of non-linear Hawkes processes. • Non-parametric estimation of non-linear Hawkes process using feed forward neural network. • Provides unbiased estimators for the gradient of the likelihood function. • Reveals causal relationship between events with in the node and across other nodes. • Modelling order arrivals for BTC-USD and ETH-USD cryptocurrency pairs. • Allows online learning of the Hawkes network parameters making the method suitable for large datasets. [ABSTRACT FROM AUTHOR]

The computation of the proximal operator of the ℓ p -norm (0 < p < 1) is critically important for non-convex optimization with the sparse-promoting ℓ p -regularization. Over the last decade, many exact and inexact numerical methods for simple and efficient computation of the proximal operator have been proposed in the literature. For this purpose, a Bisection method is given in the paper, which is based on the properties of the proximal operator. Numerical experiments illuminate the efficiency of the Bisection method. As a byproduct, the Bisection method is applied to calculate the proximal operator of the Schatten p -norm with 0 < p < 1. [ABSTRACT FROM AUTHOR]

Network traffic data is the pivot of input in many network tasks but its direct measurement can be insufferably costly. In this paper, we propose a network traffic recovery method which only requires the conveniently measurable link-load traffics. We arrange the traffic data as a third-order tensor and utilize the triple decomposition technique proposed very recently by Qi et al. (2021). The studied model is a differentialble unconstrained minimization problem, which can be efficiently solved by a Barzilai–Borwein (BB) gradient algorithm. We prove that the generated iteration sequence can globally converge to a certain stationary point of the objective function. The numerical simulations on three open-source traffic datasets demonstrate the superiority of our method in comparison with other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we derive exact series expressions for the conditional moments of a multivariate Cox-Ingersoll-Ross term structure model with a weak mean-reversion effect assumption. First, we construct the perturbation solution for the system of Riccati equations, which illustrates the conditional characteristic function of this term structure model. Second, we derive the power series expression for the perturbation solution. Via the power series solutions, we establish the exact series expressions for conditional moments. Furthermore, we demonstrate the error bounds for these perturbation approximations of the conditional moments. Numerical analysis indicates that our method is more efficient, accurate and superior to the Monte Carlo approach with the Euler scheme for computing the conditional moments. [ABSTRACT FROM AUTHOR]

In this paper, we study the stochastic differential equation with singular drift coefficient driven by fractional Brownian motion with Hurst parameter H ∈ (1 2 , 1). We obtain that the optimal convergence rate of the backward Euler method is 1.0. The constant elasticity of variance model and the Aït-Sahalia interest rate model are performed as numerical experiments to validate our theoretical results. [ABSTRACT FROM AUTHOR]

We describe an efficient method for the approximation of functions using radial basis functions (RBFs), and extend this to a solver for boundary value problems on irregular domains. The method is based on RBFs with centers on a regular grid defined on a bounding box, with some of the centers outside the computational domain. The equation is discretized using collocation with oversampling, with collocation points inside the domain only, resulting in a rectangular linear system to be solved in a least squares sense. The goal of this paper is the efficient solution of that rectangular system. We show that the least squares problem splits into a regular part, which can be expedited with the FFT, and a low rank perturbation, which is treated separately with a direct solver. The rank of the perturbation is influenced by the irregular shape of the domain and by the weak enforcement of boundary conditions at points along the boundary. The solver extends the AZ algorithm which was previously proposed for function approximation involving frames and other overcomplete sets. The solver has near optimal log-linear complexity for univariate problems, and loses optimality for higher-dimensional problems but remains faster than a direct solver. A Matlab implementation is available at https://gitlab.kuleuven.be/numa/public/2023-RBF-AZalgorithm. • We describe an efficient RBF-based algorithm, which is a variant of the AZ algorithm. • The algorithm has near-optimal computational complexity for 1D problems and quadratic complexity for 2D problems. • The methodology allows approximation on domains with arbitrary shape. • We show how to adapt the AZ algorithm to also solve boundary value problems using the Gaussian RBF. • In our approach, boundary value problems can be seen as a low-rank perburbation of the function approximation problem. [ABSTRACT FROM AUTHOR]

Recently Riehl and Verity have introduced ∞-cosmoi, which are certain simplicially enriched categories with additional structure. In this paper we investigate those ∞-cosmoi which are in fact 2-categories; we shall refer to these as 2-cosmoi. We show that each 2-category with flexible limits gives rise to a 2-cosmos whose distinguished class of isofibrations consists of the normal isofibrations. Many examples arise in this way, and we show that such 2-cosmoi are minimal as Cauchy-complete 2-cosmoi. Finally, we investigate accessible 2-cosmoi and develop a few aspects of their basic theory. [ABSTRACT FROM AUTHOR]

Mutation of torsion pairs is a generalization of mutation of cluster tilting subcategories. Torsion pairs and cluster tilting subcategories in Igusa-Todorov cluster categories of type A ∞ have been classified by Gratz-Holm-Jørgensen in [12]. In this paper we give a geometric realization of mutation of torsion pairs in discrete cluster categories of Dynkin type A ∞ by rotating some combinatorial models in S 1. This result generalizes a work of Zhou-Zhu for cluster category of type A ∞ [27]. [ABSTRACT FROM AUTHOR]

In this paper, we present a formula for the degree of the 3-secant variety of a nonsingular projective variety embedded by a 5-very ample line bundle. The formula is provided in terms of Segre classes of the tangent bundle of a given variety. We use the generalized version of the double point formula to reduce the calculation into the case of the 2-secant variety. As a resolution of the 2-secant variety, we use secant bundle and compute powers of desired algebraic cycles. [ABSTRACT FROM AUTHOR]

The construction of Arf rings and strictly closed rings has been studied widely; however, there has been no clear description of the structure of the strict closure R ⁎ when R ‾ is not a finitely generated R -module. In this paper, we investigate the construction and finite generation of the strict closure of rings. We determine its structure when R is a Cohen-Macaulay semi-local ring of dimension one, with dim ⁡ R M = 1 for every M ∈ Max R. Using this, a characterization of the finite generation of the strict closure is given. [ABSTRACT FROM AUTHOR]

The statement of Proposition 3.1 in the cited paper misses a condition that the initial index i j must be chosen with care. Subsequent Theorem 3.2 is also modified accordingly. [ABSTRACT FROM AUTHOR]

Condition (S +) , introduced in [17] , plays a key role in the study of Kloosterman and hypergeometric l -adic local systems in positive characteristic p. Prior results of [17] , [20] establish (S +) for primitive Kloosterman and hypergeometric sheaves, except possibly in ranks 4, 8, and 9. In this paper we study (S +) in these remaining ranks, and completely determine when (S +) does or does not hold. [ABSTRACT FROM AUTHOR]

This paper considers the joint estimation of the parameters of a first-order fractional autoregressive model. A one-step procedure is considered in order to obtain an asymptotically-efficient estimator with an initial guess estimator with convergence speed lower than n and singular asymptotic joint distribution. This estimator is computed faster than the maximum likelihood estimator or the Whittle estimator and therefore allows for faster inference on large samples. The paper also illustrates the performance of this method on finite-size samples via Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Ultrahigh-dimensional data analysis has been a popular topic in decades. In the framework of ultrahigh-dimensional setting, feature screening methods are key techniques to retain informative covariates and screen out non-informative ones when the dimension of covariates is extremely larger than the sample size. In the presence of incomplete data caused by censoring, several valid methods have also been developed to deal with ultrahigh-dimensional covariates for time-to-event data. However, little approach is available to handle feature screening for survival data subject to biased sample, which is usually induced by left-truncation. In this paper, we extend the C-index estimation proposed by Hartman et al. (2023) to develop a valid feature screening procedure to deal with left-truncated and right-censored survival data subject to ultrahigh-dimensional covariates. The sure screening property is also rigorously established to justify the proposed method. Numerical results also verify the validity of the proposed procedure. • This manuscript explores ultrahigh-dimensional survival data with biased and incomplete responses. • The C-index approach is applied and is robust regardless of regression models and truncation rates. • The sure screening property is established. • Numerical studies show the satisfactory performance of the method. [ABSTRACT FROM AUTHOR]

Detecting the correlation between two random variables is widely used in many empirical problems in economics. Among them, Pearson's correlation can be used to quantify the degree of dependence between variables. However, it cannot handle asymmetric correlations. To deal with this situation, we proposed a pair of widely applicable measures of conditional dependence (M C D s), which can not only account for the asymmetry but also the linear or nonlinear conditional dependencies in the presence of multiple variables. We give instances: when the paired measures are the same, resulting in symmetric correlation measures that are equivalent to the square of the Pearson coefficient; when no condition variables are given, M C D s are used to assess the relationship between two variables. Consequently, Pearson's correlation is a particular instance of M C D s. Theoretical attributes of M C D s show that they have wide applicability. In statistical inference, we develop the joint asymptotics of kernel-based estimators for M C D s , which can be applied to determine whether two randomly generated variables exhibit symmetric conditional dependence in the presence of confounding variables. In the simulation, we verify the efficacy of the proposed M C D s. Then we use real data to analyze the asymmetric impact of M C D s on stock market movements. • This paper proposes a pair of conditional dependence measures (MCDs). • We use the non-parametric method based on kernel estimation. • The effectiveness of the proposed method is verified by an example. [ABSTRACT FROM AUTHOR]

Step-stress is a special type of accelerated life-testing procedure that allows the experimenter to test the units of interest under various stress conditions changed (usually increased) at different intermediate time points. In this paper, we study the problem of testing hypothesis for the scale parameter of a simple step-stress model with exponential lifetimes and under Type-II censoring. We consider several modifications of the log-likelihood ratio statistic and eliminate the distributional dependence on the unknown lifetime parameters by exploiting the scale invariant properties of the normalized failure spacings. The presented results and the ratio statistic are further generalized to the multilevel step-stress case under the log-link assumption. We compare the power performance of the proposed tests via Monte Carlo simulations. As an illustration, the described procedures are applied to a real data example from the literature. • Step-stress model with exponential lifetimes under Type-II censoring is considered. • Scale invariant tests are proposed to test hypothesis for the lifetime parameters. • Normalized spacings are used to eliminate the dependence on the unknown parameters. • Generalization to the multilevel step-stress case under the log-link assumption. • The power of the suggested tests is exploited via Monte Carlo simulations. • Implementation on a real data example. [ABSTRACT FROM AUTHOR]

In this paper, we perform deep neural networks for learning stationary ψ -weakly dependent processes. Such weak-dependence property includes a class of weak dependence conditions such as mixing, association ⋯ and the setting considered here covers many commonly used situations such as: regression estimation, time series prediction, time series classification ⋯ The consistency of the empirical risk minimization algorithm in the class of deep neural networks predictors is established. We achieve the generalization bound and obtain an asymptotic learning rate, which is less than O (n − 1 / α) , for all α > 2. A bound of the excess risk, for a wide class of target functions, is also derived. Applications to binary time series classification and prediction in affine causal models with exogenous covariates are carried out. Some simulation results are provided, as well as an application to the US recession data. [ABSTRACT FROM AUTHOR]

Ordinary differential equations (ODEs) are widely used to model complex dynamics that arise in biology, chemistry, engineering, finance, physics, etc. Calibration of a complicated ODE system using noisy data is generally challenging. In this paper, we propose a two-stage nonparametric approach to address this problem. We first extract the de-noised data and their higher order derivatives using boundary kernel method, and then feed them into a sparsely connected deep neural network with rectified linear unit (ReLU) activation function. Our method is able to recover the ODE system without being subject to the curse of dimensionality and the complexity of the ODE structure. We have shown that our method is consistent if the ODE possesses a general modular structure with each modular component involving only a few input variables, and the network architecture is properly chosen. Theoretical properties are corroborated by an extensive simulation study that also demonstrates the effectiveness of the proposed method in finite samples. Finally, we use our method to simultaneously characterize the growth rate of COVID-19 cases from the 50 states of the United States. • ODEs are used for modeling complex dynamics in various fields. • Calibrating complex ODE models with noisy data is difficult. • A two-stage nonparametric approach is proposed based on deep learning. • The approach is proven to be consistent. [ABSTRACT FROM AUTHOR]

The modified Cholesky decomposition (MCD) method is commonly used in precision matrix estimation assuming that the random variables have a specified order. In this paper, we develop a permutation-based refitted cross validation (PRCV) estimation procedure for ultrahigh dimensional precision matrix based on the MCD, which does not rely on the order of variables. The consistency of the proposed estimator is established under the Frobenius norm without normal distribution assumption. Simulation studies present satisfactory performance of in various scenarios. The proposed method is also applied to analyze a real data. We provide the complete code at https://github.com/lwfwhunanhero/PRCV. • Propose an ultrahigh dimensional precision matrix estimation based on MCD. • Theoretical analysis does not need normal distribution assumption. • Provide the rate of convergence under the Frobenius norm. [ABSTRACT FROM AUTHOR]

In this paper, we study high-dimensional reduced rank regression and propose a doubly robust procedure, called D4R , meaning concurrent robustness to both outliers in predictors and heavy-tailed random noise. The proposed method uses the composite gradient descent based algorithm to solve the nonconvex optimization problem resulting from combining Tukey's biweight loss with spectral regularization. Both theoretical and numerical properties of D4R are investigated. We establish non-asymptotic estimation error bounds under both the Frobenius norm and the nuclear norm in the high-dimensional setting. Simulation studies and real example show that the performance of D4R is better than that of several existing estimation methods. • develop a doubly robust procedure for high-dimensional reduced rank regression; • propose a composite gradient descent based algorithm; • provide non-asymptotic estimation error bounds under the Frobenius and nuclear norms. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of kernel estimation of the Expected Shortfall (ES) risk measure for financial losses that satisfy the α -mixing conditions. First, we introduce a new non-parametric estimator for the ES measure using a kernel estimation. Given that the ES measure is the sum of the Value-at-Risk and the mean-excess function, we provide an estimation of the ES as a sum of the estimators of these two components. Our new estimator has a closed-form expression that depends on the choice of the kernel smoothing function, and we derive these expressions in the case of Gaussian, Uniform, and Epanechnikov kernel functions. We study the asymptotic properties of this new estimator and compare it to the Scaillet estimator. Capitalizing on the properties of these two estimators, we combine them to create a new estimator for the ES which reduces the bias and lowers the mean square error. The combined estimator shows better stability with respect to the choice of the kernel smoothing parameter. Our findings are illustrated through some numerical examples that help us to assess the small sample properties of the different estimators considered in this paper. • Introduction of the mean-excess-based (MEB) estimator for the expected shortfall (ES) risk measure. • Derivation of the asymptotic properties of this new MEB estimator. • Comparison of the performance of the MEB estimator and Scaillet's estimator. • Introduction of a bias-reduced estimator for the ES, which is defined as a combination of the MEB estimator and Scaillet's estimator. [ABSTRACT FROM AUTHOR]

Problems of large-scale multiple testing are often encountered in modern scientific research. Conventional multiple testing procedures usually suffer considerable loss of testing efficiency when correlations among tests are ignored. In fact, appropriate use of correlation information not only enhances the efficacy of the testing procedure, but also improves the interpretability of the results. Since the disease- or trait-related single nucleotide polymorphisms (SNPs) tend to be clustered and exhibit serial correlations, hidden Markov model (HMM) based multiple testing procedures have been successfully applied in genome-wide association studies (GWAS). However, modeling the entire chromosome using a single HMM is somewhat rough. To overcome this issue, this paper employs the hierarchical hidden Markov model (HHMM) to describe local correlations among tests, and develops a multiple testing procedure that can automatically divide different class of chromosome regions, while taking into account local correlations among tests. We first propose an oracle procedure that is shown theoretically to be valid, and in fact optimal in some sense. We then develop a date-driven procedure to mimic the oracle version. Extensive simulations and a real data example show that the novel multiple testing procedure outperforms its competitors. • Modeling the entire chromosome using a single HMM is somewhat rough. • This paper employs the hierarchical hidden Markov model to describe local correlations among tests. • The proposed multiple testing procedure can automatically divide different class of chromosome regions, while considering local correlations among tests. [ABSTRACT FROM AUTHOR]

High-dimensional additive quantile regression model via penalization provides a powerful tool for analyzing complex data in many contemporary applications. Despite the fast developments, how to combine the strengths of additive quantile regression with total variation penalty with theoretical guarantees still remains unexplored. In this paper, we propose a new methodology for sparse additive quantile regression model over bounded variation function classes via the empirical norm penalty and the total variation penalty for local adaptivity. Theoretically, we prove that the proposed method achieves the optimal convergence rate under mild assumptions. Moreover, an alternating direction method of multipliers (ADMM) based algorithm is developed. Both simulation results and real data analysis confirm the effectiveness of our method. • Establish convergence rate for high-dimensional additive quantile regression with TV penalty. • Matching lower bound is shown. • Numerical results demonstrated the favorable performance. [ABSTRACT FROM AUTHOR]

In this paper, we suggest an empirical likelihood-based test for the autoregressive coefficient of an integer-valued AR(1) model, i.e., INAR(1). We derive the limit distributions of the resulting test statistic under both null and alternative hypotheses. It turns out that regardless of whether the INAR process is stable or unstable, the statistic is always chi-squared distributed asymptotically under the null hypothesis, and as a result, it can offer unified inferences for the autoregressive coefficient. The performance of its finite sample is also demonstrated using simulations and an empirical example. • An empirical likelihood-based unified test for the coefficient of INAR(1) model. • The test statistic is always chi-squared distributed asymptotically. • The unified test is robust to the distribution of ϵ t. [ABSTRACT FROM AUTHOR]

Proactive identification and the management of disruption risks play a crucial role in the achievement of a global supply chain's aims. Given the velocity and volume by which such disruption events occur, it is impractical to expect supply chain managers to determine the occurrence of such events manually. Given the pressures facing global supply chains due to the COVID-19 crisis, it is important for supply chain managers to proactively identify disruption risks to their supply chains and manage them to either achieve the outcomes or develop plans by which resilience against them can be built. In this paper, we demonstrate how the integration of natural language processing and reinforcement learning, which are fundamental artificial intelligence methods, can be used to assist supply chain risk managers in the timely identification of such disruption events. We explain in detail our proposed approach, namely RL-SCRI and show its superiority over the current models in achieving its aim. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) heavily rely on sensors to perceive their environment, ensuring safe flight operations. However, sensor failures can occur unexpectedly, jeopardizing flight safety. To address this issue, we propose an innovative real-time solution for diagnosing and preventing sensor failures during autonomous flights. Our study is motivated by the lack of sensor failure datasets for UAVs. We contribute by generating the first comprehensive UAV sensor failures dataset, encompassing 70 autonomous flight data instances with over 7 h of flight time. Our Biomisa Arducopter Sensory Critique (BASiC) dataset includes various sensor failure scenarios, such as GPS, remote control, accelerometer, gyroscope, compass, and barometer. In this paper, we introduce an attention-based novel framework leveraging transformer neural network architecture for UAV sensor failure prediction and classification. The proposed framework analyzes our multivariate spatio-temporal BASiC dataset using transformers. We conducted ablation studies to evaluate transformer performance under different hyperparameter settings, demonstrating the effects of parameter tuning. Our framework achieved an average accuracy of 86% in predicting sensor failures, anticipating them 1 min and 2 s before occurrence - a 30-second improvement over the established LSTM-based (long short-term memory) approach. Additionally, our framework attained a 94% accuracy in classifying sensor failures. This performance evaluation highlights the potential of our optimized framework for integration in mission-critical UAVs, enabling real-time sensor failure prediction and classification. [Display omitted] • Real-time solution for preventing failures in mission-critical UAV flights. • First UAV sensors failures dataset with 70 flights and 7+ hours' flight time. • Novel application of transformer neural network for sensory failure prediction. • 86% failure prediction accuracy and 62-second early time-to-predict the failure. • 94% accuracy in classifying sensor failures with the novel framework. [ABSTRACT FROM AUTHOR]

Knowledge discovery from big datasets is one of the most important challenges in the pattern recognition field. More important than this is how much the extracted information and created models are reliable. Studies have shown that these models are usually highly dependent on the samples, features, data, and structure of the models. In general, the issue of stability is very important in creating models. This paper presents a method that not only considers the effect of different known classifiers but also tries to achieve a stable model for separating samples by combining different feature selection methods and considering the criterion of stability. Briefly, our contributions to the proposed method include 1) analyzing the ability of features in sample classification individually with different well-known classifiers, 2) estimating the probability of the features that could be selected in high-impact sets of features, and 3) applying the stability concept to increase the weight of the robust sets of the features. The proposed algorithm is used to select the high-impact genes of microarray datasets. Three high-dimensional gene expressions of cancerous tissues are used as benchmarks. The results obtained show relative superiority compared to other methods. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a finite collection of fuzzy sets that are used to represent a given linguistic variable in real-world problems. These fuzzy sets are usually represented as fuzzy singletons, fuzzy numbers, or fuzzy G-numbers. In many cases, there are significant interactions between elements of a given set, so it is useful to evaluate and rank elements while taking the degree of interactions into consideration. To find the degree of interaction, we develop a fuzzy equivalence relation based on a similarity function and a triangular norm operator. The compositions of the (max -(T -norm)) and (min -(S -norm)) cause the membership function to change from the minimum values (certainty version) to the maximum values (possibility version). These concepts are also useful for improving fuzzy data mining, rough fuzzy set theory, etc. Furthermore, two indices, α and β , are introduced to determine the degree of certainty (α -certainty) and degree of possibility (β -possibility). Examples are provided to compare the proposed method with the existing method. After comparing the experimental results, it can be concluded that the proposed approach is satisfactory for many situations. Finally, we apply the proposed methodology to evaluate the results of a hospital efficiency study conducted for the Office of Inspector General(OIG)-Eastern Virginia Department of Health and Human Services. • The degree of interaction of fuzzy sets are found by fuzzy equivalence relations. • Two indices α and β determine the degree of certainty and possibility. • Certainty and possibility versions are used to analyze fuzzy information systems. • The proposed method is used to evaluate and rank 38 hospitals selected by the OIG. [ABSTRACT FROM AUTHOR]

The time-variant Sylvester equation (TVSE) plays a highly crucial role in many areas of scientific research and engineering applications. Recently, zeroing neural network (ZNN) has been prevailed as an effective solution for time-variant problem. However, the majority of the existing ZNN solution schemes for TVSE are either only considered in noiseless environments or are unable to converge in a finite amount of time, and while there is a pressing need for effective and noise-resisting ZNNs to fulfill real-time applications' requirements in the actual world. For this reason, inspired by the advantages offered by super-twisting algorithm (STA), being a well-accepted second order sliding mode method, this paper introduces STA into ZNN and establishes a novel STZNN model for TVSE solving. Actually, the intrinsic properties of STA, such as finite-time convergence and anti-noise robustness, are perfectly in line with what an efficient and noise-resisting ZNN model desired to be. Hence, the STZNN model can realize a much quick convergence time and a much great resistance against noise. Moreover, rigorous theoretical analyses on the case of zero noise, constant noise and dynamic bounded noise are conducted, and the illustrative verification not only verifies the STZNN's convergence property, validates its superior ability in convergence time and noise resisting compared to the gradient-based neural network (GNN), the conventional ZNN (CZNN) model and the integration-enhanced ZNN (IEZNN) model, but also shows the STZNN model's capability in addressing moving localization problems based on angle of arrival (AoA) and time difference of arrival (TDOA). [ABSTRACT FROM AUTHOR]

Long-range dependence modeling has been demonstrated to be an effective technique for boosting the performance of channelwise attention. As a state-of-the-art attention mechanism and a lightweight model, coordinate attention (CA) captures long-range dependencies in its context modeling phase. However, its subsequent transformation phase can only capture interchannel dependencies. This leads to a linear receptive field in overall dependency modeling scenarios. To further expand the receptive field of CA, a novel attention mechanism called patch-enhanced attention (PEA) is proposed in this paper. To redesign the transformation phase, a group of unfolding and folding operations are embedded into the thin waist of the hourglass structure. In this way, the receptive field range for coordinate orientations is expanded from a line to a patch. Extensive experiments conducted on the ImageNet and Pascal VOC benchmarks validate the effectiveness of the proposed PEA mechanism. Compared with CA, PEA achieves state-of-the-art performance with fewer parameters. • For Coordinate Attention, expending the receptive field is more effective than lessening the reduction ratio on channels. • A more efficient lightweight attention mechanism than Coordinate Attention. • Consistent performance increase on various tasks and various backbones. • Visualization shows learned attention. [ABSTRACT FROM AUTHOR]

Prompt-tuning was proposed to bridge the gap between pretraining and downstream tasks, and it has achieved promising results in Relation Extraction (RE). Although the existing prompt-based RE methods have outperformed the methods based on fine-tuning paradigm, these methods require domain experts to design prompt templates, making them hard to be generalized. In this paper, we propose a G enerative context- A ware P rompt-tuning method (GAP) to address these limitations. Our method consists of three crucial modules: (1) a pretrained prompt generator module that extracts or generates the relation triggers from the context and embeds them into the prompt tokens, (2) an in-domain adaptive pretraining module that further trains the Pretrained Language Models (PLMs) to promote the adaptability of the model, and (3) a joint contrastive loss that prevents PLMs from generating unrelated content and optimizes our model more effectively. We observe that the context-enhanced prompt tokens generated by GAP can better guide PLMs to make more accurate predictions. And the in-domain pretraining can effectively inject domain knowledge to enhance the robustness of the model. We conduct experiments on four public RE datasets with supervised and few-shot settings. The experimental results have demonstrated the superiority of GAP over existing benchmark methods and GAP shows remarkable improvements in few-shot settings, with average F1 score enhancements of 3.5%, 2.7%, and 3.4% on the TACRED, TACREV, and Re-TACRED datasets, respectively. Furthermore, GAP still achieved state-of-the-art (SOTA) performance in supervised settings. • We introduced the prompt-tuning framework for relation extraction task. • We proposed a pre-extractor to enhance the stability of the model. • We designed a prompt generator to generate prompt tokens for RE. • We introduced a retrieval-based in-domain pretraining strategy. • We proposed Joint Contrastive Loss to optimize our model. [ABSTRACT FROM AUTHOR]

Scientific publications clustering has attracted much attention, and many different approaches have been proposed. One of the challenges in scientific documents clustering is how to combine citation and textual information to improve clustering quality. In this paper, we explore the use of the von Mises-Fisher distribution for scientific documents clustering. The von Mises-Fisher distribution is particularly well-suited for the analysis of directional data. More precisely, we propose a multi-view version of the mixture of von Mises-Fisher distributions in which one view corresponds to textual information and the other view corresponds to citation information. The hypothesis underlying our approach is that both text and citation data are directional. To estimate the parameters of the proposed model, we use the Expectation-Maximization algorithm along with deterministic annealing to escape poor local maxima solutions. Experiments on two real world datasets show that our algorithm outperforms baseline algorithms in terms of clustering accuracy. [ABSTRACT FROM AUTHOR]

The recommendation algorithm is an important means to alleviate the information explosion in the era of big data. There has been a great deal of research into the use of knowledge graphs as auxiliary information in recommender systems, which can be used to alleviate data sparsity and cold start problems. However, most knowledge graph-based recommendation methods only use rating data to capture the user's potential interest, and the rating is only a comprehensive evaluation of the item by the user, which cannot intuitively and accurately express the user's personalized preference. In addition, existing recommendation strategies that blend ratings and reviews cannot simultaneously model the aspect fine-grained sentiment preferences of users in reviews as well as the personalized characteristics of items from the user's perspective. To this end, in this paper, we propose Reviews Sentiment-Aware Knowledge Graph Convolutional Neural Network (RAKCR), a generic review and knowledge graph-based framework that provides better recommendations by fully mining the fine-grained personalization features in user reviews. In contrast to existing correlation recommendation methods, we designed a new reviews sentiment perception feature and knowledge graph alignment module to characterize user preferences for specific features of items in the knowledge graph. To better represent the personalized feature distribution of users and items, we use the proposed RAKCR to aggregate sentiment relationship weight-aware neighborhood information in the knowledge graph to capture personalized feature representations of both users and items, and to better learn user and item embeddings for more accurate personalized recommendations. Experimental results demonstrate that the proposed RAKCR model outperforms the benchmark model significantly in click-through rate prediction for recommendation scenarios. Across the three datasets, Movielens-20 m, Amazon-book, and Yelp, the AUC values show an average improvement of 6.4%, 6.0%, and 3.4%, respectively. Additionally, the F1 values exhibit an average improvement of 7.2%, 6.2%, and 4.1%, respectively, when compared to existing state-of-the-art methods. • Sentiment analysis of reviews to extract aspect features and sentiment polarity. • Aligning sentiment features with knowledge graphs to build sentiment dictionaries. • Knowledge graph convolutional networks incorporating sentiment weights. • Aggregate user fine-grained and item personalized feature representations. [ABSTRACT FROM AUTHOR]

• This paper studies the impact of oil shocks on systemic risk of G7 stock markets. • We construct a risk spillover network among G7 stock markets by TVP-VAR. • The results indicate that the impact of oil supply shock is insignificant. • Demand shock contributes the most to systematic risk in the short term. • G7 stock markets play a role as receiver and all oil structural shocks as emitter. In this paper, we delve into the critical role of oil shocks in influencing the systematic risk of G7 stock markets—a concern of paramount importance given the interconnectedness of global economies and the pivotal role of energy markets. We employ Delta Conditional Value at Risk (ΔCoVaR) and Marginal Expected Shortfall (MES) to measure the systematic risk of G7 stock markets due to volatility in the oil market. By decomposing oil price change into oil supply shocks, aggregate demand shocks, and oil-specific demand shocks using a structural vector autoregression model, we offer a more granular perspective to investigate the time-varying effects of oil price fluctuations on the systematic risk of G7 stock markets. The results indicate that the impact of oil supply shock is insignificant compared with aggregate demand shock and speculative demand shock. Speculative demand shock contributes the most to systematic risk in the short term, but their impact declines as the number of periods increases. In the long term, the biggest impact on systematic risk is aggregate demand shock. Additionally, we construct a network among G7 stock markets and oil structural shocks based on time-varying spillover and the empirical results show that G7 stock markets play a role as receiver and all oil structural shocks as emitter. Besides, Japan is the country in G7 countries most affected by oil shocks. [ABSTRACT FROM AUTHOR]

Augmented assembly provides intuitive assembly guidelines to the assembly operators. With assembly tasks developing toward diversification, the position of virtual components that are superimposed on the real environment may change frequently and virtual components have different length-diameter ratios and overlap each other. However, existing object detection methods are time consuming and hardly separate virtual components in dense for augmented assembly. Therefore, this paper proposes a rapid oriented detection method based on swift oriented detection region-based convolutional network (SODR-CNN) for virtual components in augmented assembly. Specifically, a dual channel selection (DCS) structure is designed to extract spatial features by reducing redundant computation and memory access. Further, the novel backbone network, rapid network (RapidNet), is proposed building upon the DCS, which can decrease the inference latency of SODR-CNN. Finally, the comprehensive experiments demonstrate that the RapidNet achieves lower inference latency than comparison backbone networks, which means that the SODR-CNN achieves superior inference latency and detection accuracy. Moreover, intuitive evaluation experiments are carried out, in which the effectiveness of the proposed method is further verified by searching for several virtual components in a real environment. [ABSTRACT FROM AUTHOR]

In various areas of real life, Multivariate Time Series Classification (MTSC) is widely used. It has been the focus of attention of many researchers, and a number of MTSC methods have been proposed in recent years. These methods tend to focus on the features in only a single domain. However, they have ignored the correlation and complementarity between the features in a space of multiple domains. In this paper, a novel MTSC method based on fusion features (MTSC_FF) is presented to address this problem. Firstly, MTSC_FF extracts the frequency domain features using an attention layer based on continuous wavelet transform. In parallel, MTSC_FF extracts long-range dependency features from the time domain, using a sparse self-attention layer. Simultaneously, MTSC_FF obtains spatial correlations between multivariate time series dimensions via Kendall coefficient. Then, a graph neural network is used to fuse all features. Finally, the fusion features are used to predict the classification labels by means of the fully connected layer. The experimental results obtained on the UEA datasets show that the proposed method can achieve high accuracy. In addition, the proposed method can visualize the classification-dependent features, which is an improvement in the interpretability of the results. • A multivariate time series classification method is proposed. • Kendall coefficients are used to represent the spatial correlation. • Extensive experiments demonstrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

The design of real-world engineering systems deals with high complexity at the system and subsystem levels, as well as the interaction between the subsystems involved. Multidisciplinary Design Optimization (MDO), which aims to integrate the optimization algorithms in both system and subsystem levels along with exploring mechanisms of synergistic action among subsystems, is a renowned methodology to design complex engineering systems. In Multi-Agent Systems (MASs), as a complex system, to achieve the best system performance, agents have to work their individual tasks in a coordinated manner and in cooperation with other agents. Given some architectural resemblance between MDO and MAS, especially in subsystems interaction (agents, in MAS case), this paper addresses proposing a multi-agent multidisciplinary system design optimization strategy. This strategy by taking advantage of the capabilities of MDO proposes a consolidated framework for the optimal design of real world engineering systems. This strategy is extendable to multi-agent systems in a diverse range of missions and tasks. In this regard to illustrating its application a distributed cooperative search and coverage (CSC) mission in uncertain environments is considered as a case study for designing a MAS. The proposed framework contributes to designing a MAS by applying the history data of previously completed missions and the normalized cross-correlating (NCC) algorithm as well. The effectiveness of the proposed framework is demonstrated via simulations and comparison. [ABSTRACT FROM AUTHOR]

• We predict the number of shares of fake news shares based on its content. • The propagation of fake and real news follows different patterns. • Fake news that conveys strongly negative emotions are more likely to be shared. • We use machine learning to detect early fake news that are potentially viral. Fake news about brands and companies can cause reputation and financial damage, but there exist preventive strategies that could be implemented if we were able to early predict the virality of fake news pieces. In this paper, we consider the early prediction of fake news virality using textual information (body and headlines). We show that the impact of content features on virality is different for true and fake news, and so the propagation of true and fake news is. Furthermore, we use machine learning nonparametric models to classify fake news according to its propagation level. We also discuss defensive response strategies. [ABSTRACT FROM AUTHOR]