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In inverse reinforcement learning (RL), there are two agents. An expert target agent has a performance cost function and exhibits control and state behaviors to a learner. The learner agent does not know the expert's performance cost function but seeks to reconstruct it by observing the expert's behaviors and tries to imitate these behaviors optimally by its own response. In this article, we formulate an imitation problem where the optimal performance intent of a discrete-time (DT) expert target agent is unknown to a DT Learner agent. Using only the observed expert's behavior trajectory, the learner seeks to determine a cost function that yields the same optimal feedback gain as the expert's, and thus, imitates the optimal response of the expert. We develop an inverse RL approach with a new scheme to solve the behavior imitation problem. The approach consists of a cost function update based on an extension of RL policy iteration and inverse optimal control, and a control policy update based on optimal control. Then, under this scheme, we develop an inverse reinforcement Q-learning algorithm, which is an extension of RL Q-learning. This algorithm does not require any knowledge of agent dynamics. Proofs of stability, convergence, and optimality are given. A key property about the nonunique solution is also shown. Finally, simulation experiments are presented to show the effectiveness of the new approach.

Spectral clustering is a well-known clustering algorithm for unsupervised learning, and its improved algorithms have been successfully adapted for many real-world applications. However, traditional spectral clustering algorithms are still facing many challenges to the task of unsupervised learning for large-scale datasets because of the complexity and cost of affinity matrix construction and the eigen-decomposition of the Laplacian matrix. From this perspective, we are looking forward to finding a more efficient and effective way by adaptive neighbor assignments for affinity matrix construction to address the above limitation of spectral clustering. It tries to learn an affinity matrix from the view of global data distribution. Meanwhile, we propose a deep learning framework with fully connected layers to learn a mapping function for the purpose of replacing the traditional eigen-decomposition of the Laplacian matrix. Extensive experimental results have illustrated the competitiveness of the proposed algorithm. It is significantly superior to the existing clustering algorithms in the experiments of both toy datasets and real-world datasets.

This article develops a novel cost function (performance index function) to overcome the obstacles in solving the optimal tracking control problem for a class of nonlinear systems with known system dynamics via adaptive dynamic programming (ADP) technique. For the traditional optimal control problems, the assumption that the controlled system has zero equilibrium is generally required to guarantee the finiteness of an infinite horizon cost function and a unique solution. In order to solve the optimal tracking control problem of nonlinear systems with nonzero equilibrium, a specific cost function related to tracking errors and their derivatives is designed in this article, in which the aforementioned assumption and related obstacles are removed and the controller design process is simplified. Finally, comparative simulations are conducted on an inverted pendulum system to illustrate the effectiveness and advantages of the proposed optimal tracking control strategy.

Remaining useful life (RUL) prediction of aircraft engine (AE) is of great importance to improve its reliability and availability, and reduce its maintenance costs. This article proposes a novel deep bidirectional recurrent neural networks (DBRNNs) ensemble method for the RUL prediction of the AEs. In this method, several kinds of DBRNNs with different neuron structures are built to extract hidden features from sensory data. A new customized loss function is designed to evaluate the performance of the DBRNNs, and a series of the RUL values is obtained. Then, these RUL values are reencapsulated into a predicted RUL domain. By updating the weights of elements in the domain, multiple regression decision tree (RDT) models are trained iteratively. These models integrate the predicted results of different DBRNNs to realize the final RUL prognostics with high accuracy. The proposed method is validated by using C-MAPSS datasets from NASA. The experimental results show that the proposed method has achieved more superior performance compared with other existing methods.

Several measurement models have been proposed for data from the continuous-reproduction paradigm for studying visual working memory: The original mixture model (Zhang & Luck, 2008) and its extension (Bays, Catalao, & Husain, 2009); the interference measurement model (Oberauer, Stoneking, Wabersich, & Lin, 2017), and the target confusability competition model (Schurgin, Wixted, & Brady, 2020). This article describes a space of possible measurement models in which all existing models can be placed. The space is defined by three dimensions: (1) The choice of a activation function (von-Mises or Laplace), the choice of a response-selection function (variants of Luce’s choice rule or of signal detection theory), and whether or not memory precision is assumed to be a constant over manipulations affecting memory. A factorial combination of these three variables generates all possible models in the model space. Fitting all models to eight data sets revealed a new model as empirically most adequate, which combines a von-Mises activation function with a signal-detection response-selection rule. The precision parameter can be treated as a constant across many experimental manipulations, though it might vary with manipulations not yet explored. All modelling code and the raw data modelled are available on the OSF: osf.io/zwprv

Decision models such as the drift-diffusion model (DDM) are widely used and broadly accepted for their ability to account remarkably well for binary choices between perceptual hypotheses about a stimulus or for preferential decisions between valued options (such as snacks or consumer products), and for their response time (RT) distributions, as a function of the stimulus or the option values. The DDM is built on an evidence accumulation to bound concept, where, in the value domain, a decision maker repeatedly samples the mental representations of the values of the options on offer until satisfied that there is enough evidence in favor of one option over the other. As the value signals that drive the DDM evidence are derived from value estimates that are not known to the decision maker with certainty, repeated sequential samples are necessary to average out noise. The classic DDM typically does not allow for different options to have different levels of variability in their value representations. However, recent value-based decision studies have shown that decision makers often report levels of certainty regarding value estimates that vary across choice options. There is therefore a need to extend the DDM to include an option-specific value certainty component. We present several such DDM extensions and validate them against empirical data from four previous studies. The data supports best a DDM version in which the drift of the accumulation is based on a sort of signal-to-noise ratio of value for each option (rather than a mere accumulation of samples from the corresponding value distributions). This DDM variant accounts for the positive impact of value certainty on choice consistency and for the negative impact of value certainty on RT.

Online users are typically active on multiple social media networks (SMNs), which constitute a multiplex social network. With improvements in cybersecurity awareness, users increasingly choose different usernames and provide different profiles on different SMNs. Thus, it is becoming increasingly challenging to determine whether given accounts on different SMNs belong to the same user; this can be expressed as an interlayer link prediction problem in a multiplex network. To address the challenge of predicting interlayer links, feature or structure information is leveraged. Existing methods that use network embedding techniques to address this problem focus on learning a mapping function to unify all nodes into a common latent representation space for prediction; positional relationships between unmatched nodes and their common matched neighbors (CMNs) are not utilized. Furthermore, the layers are often modeled as unweighted graphs, ignoring the strengths of the relationships between nodes. To address these limitations, we propose a framework based on multiple types of consistency between embedding vectors (MulCEVs). In MulCEV, the traditional embedding-based method is applied to obtain the degree of consistency between the vectors representing the unmatched nodes, and a proposed distance consistency index based on the positions of nodes in each latent space provides additional clues for prediction. By associating these two types of consistency, the effective information in the latent spaces is fully utilized. In addition, MulCEV models the layers as weighted graphs to obtain representation. In this way, the higher the strength of the relationship between nodes, the more similar their embedding vectors in the latent representation space will be. The results of our experiments on several real-world and synthetic datasets demonstrate that the proposed MulCEV framework markedly outperforms current embedding-based methods, especially when the number of training iterations is small.

The extrusion process of plastic transformation involves a series of variables and components which must be associated with the concept of reliability to achieve an expected performance in operational and quality terms. This paper describes the reliability framework of an extruder of a packaging company located in Brazil through the following mathematical representations: probability density function f(t), reliability curve R(t) and function rate of failure h(t). Through a statistical software the set of representations was able to develop the reliability framework of the machine, which can be used to support a FMEA analysis. Besides that, it was evidenced that in the current operating conditions of the machine, approximately 50% of the failure observations happen on the hour 100 of operating time. The main outcome is that it is recommended a systematic preventive maintenance based on 100h cycles. It is expected that this work may act as a guide for future implementation of improvement activities.

A principal wants to procure a discrete number of homogeneous units from a finite set of agents. Each agent has an increasing and convex cost function, whose exact shape is unknown to the principal. Utility is quasilinear in money. We characterize the set of mechanisms that are strategy-proof and robust to collusion. The latter is captured by reallocation-proofness (group strategy-proofness) if the colluding agents can (cannot) make side deals among each other. We show that in every reallocation-proof mechanism, the principal offers the agents a fixed price per unit. While group-strategy-proof mechanisms can be more complex, they cannot guarantee that the principal will receive exactly her desired quantity. We fully characterize the set of group-strategy-proof mechanisms with a uniform price.

In the last decade, deep neural networks (DNNs) have become dominant tools for various of supervised learning tasks, especially classification. However, it is demonstrated that they can easily overfit to training set biases, such as label noise and class imbalance. Example reweighting algorithms are simple and effective solutions against this issue, but most of them require manually specifying the weighting functions as well as additional hyperparameters. Recently, a meta-learning-based method Meta-Weight-Net (MW-Net) has been proposed to automatically learn the weighting function parameterized by an MLP via additional unbiased metadata, which significantly improves the robustness of prior arts. The method, however, is proposed in a deterministic manner, and short of intrinsic statistical support. In this work, we propose a probabilistic formulation for MW-Net, probabilistic MW-Net (PMW-Net) in short, which treats the weighting function in a probabilistic way, and can include the original MW-Net as a special case. By this probabilistic formulation, additional randomness is introduced while the flexibility of the weighting function can be further controlled during learning. Our experimental results on both synthetic and real datasets show that the proposed method improves the performance of the original MW-Net. Besides, the proposed PMW-Net can also be further extended to fully Bayesian models, to improve their robustness.

Recent advances in high-resolution microscopy have allowed scientists to better understand the underlying brain connectivity. However, due to the limitation that biological specimens can only be imaged at a single timepoint, studying changes to neural projections is limited to general observations using population analysis. In this paper, we introduce NeuRegenerate, a novel end-to-end framework for the prediction and visualization of changes in neural fiber morphology within a subject, for specified age-timepoints.To predict projections, we present neuReGANerator, a deep-learning network based on cycle-consistent generative adversarial network (cycleGAN) that translates features of neuronal structures in a region, across age-timepoints, for large brain microscopy volumes. We improve the reconstruction quality of neuronal structures by implementing a density multiplier and a new loss function, called the hallucination loss.Moreover, to alleviate artifacts that occur due to tiling of large input volumes, we introduce a spatial-consistency module in the training pipeline of neuReGANerator. We show that neuReGANerator has a reconstruction accuracy of 94% in predicting neuronal structures. Finally, to visualize the predicted change in projections, NeuRegenerate offers two modes: (1) neuroCompare to simultaneously visualize the difference in the structures of the neuronal projections, across the age timepoints, and (2) neuroMorph, a vesselness-based morphing technique to interactively visualize the transformation of the structures from one age-timepoint to the other. Our framework is designed specifically for volumes acquired using wide-field microscopy. We demonstrate our framework by visualizing the structural changes in neuronal fibers within the cholinergic system of the mouse brain between a young and old specimen., Comment: Accepted for publication in IEEE Transactions on Visualization and Computer Graphics

For general antiferromagnetic 2-spin systems, including the hardcore model and the antiferromagnetic Ising model, there is an $\mathsf{FPTAS}$ for the partition function on graphs of maximum degree $\Delta$ when the infinite regular tree lies in the uniqueness region by Li et al. (2013). Moreover, in the tree non-uniqueness region, Sly (2010) showed that there is no $\mathsf{FPRAS}$ to estimate the partition function unless $\mathsf{NP}=\mathsf{RP}$. The algorithmic results follow from the correlation decay approach due to Weitz (2006) or the polynomial interpolation approach developed by Barvinok (2016). However the running time is only polynomial for constant $\Delta$. For the hardcore model, recent work of Anari et al. (2020) establishes rapid mixing of the simple single-site Markov chain known as the Glauber dynamics in the tree uniqueness region. Our work simplifies their analysis of the Glauber dynamics by considering the total pairwise influence of a fixed vertex $v$ on other vertices, as opposed to the total influence on $v$, thereby extending their work to all 2-spin models and improving the mixing time. More importantly our proof ties together the three disparate algorithmic approaches: we show that contraction of the tree recursions with a suitable potential function, which is the primary technique for establishing efficiency of Weitz's correlation decay approach and Barvinok's polynomial interpolation approach, also establishes rapid mixing of the Glauber dynamics. We emphasize that this connection holds for all 2-spin models (both antiferromagnetic and ferromagnetic), and existing proofs for correlation decay or polynomial interpolation immediately imply rapid mixing of Glauber dynamics. Our proof utilizes that the graph partition function divides that of Weitz's self-avoiding walk trees, leading to new tools for analyzing influence of vertices., Comment: Section 7 and Appendix E are updated to fix a small error

We consider composition problems of the form , which are important for machine learning. Although gradient descent and stochastic gradient descent are straightforward solutions, the essential computation of in each single iteration is expensive, let alone for large m. In this article, we devise a stochastically controlled compositional gradient algorithm. Specifically, we introduce two variants of stochastically controlled technique to estimate the inner function G(x) and the gradient of the objective function, respectively. The computational cost is largely reduced. However, the natural needs of two stochastic subsets D1 and D2 form direct barriers to guarantee the convergence of the algorithm, especially the theoretical proof of the convergence. To this end, we present a general convergence analysis by proving and , through which the proposed method significantly improve composition algorithms under low target accuracy (i.e., 1/e≪ m or n) in both strongly convex and nonconvex settings. Comprehensive experiments demonstrate the superiority of the proposed method over existing methods.

This article investigates the problem of global neural network (NN) tracking control for uncertain nonlinear systems in output feedback form under disturbances with unknown bounds. Compared with the existing NN control method, the differences of the proposed scheme are as follows. The designed actual controller consists of an NN controller working in the approximate domain and a robust controller working outside the approximate domain, in addition, a new smooth switching function is designed to achieve the smooth switching between the two controllers, in order to ensure the globally uniformly ultimately bounded of all closed-loop signals. The Lyapunov analysis method is used to strictly prove the global stability under the combined action of unmeasured states and system uncertainties, and the output tracking error is guaranteed to converge to an arbitrarily small neighborhood through a reasonable selection of design parameters. A numerical example and a practical example were put forward to verify the effectiveness of the control strategy.

In this work, we design a distributed algorithm for time-varying convex optimization over networks with quantized communications. Each agent has its local time-varying objective function, while the agents need to cooperatively track the optimal solution trajectories of global time-varying functions. The distributed algorithm is motivated by the alternating direction method of multipliers, but the agents can only share quantization information through an undirected graph. To reduce the tracking error due to information loss in quantization, we apply the dynamic quantization scheme with a decaying scaling function. The tracking error is explicitly characterized with respect to the limit of the decaying scaling function in quantization. Furthermore, we are able to show that the algorithm could asymptotically track the optimal solution when time-varying functions converge, even with quantization information loss. Finally, the theoretical results are validated via numerical simulation.

We push a little further the study of two recent characterizations of almost perfect nonlinear (APN) functions. We state open problems about them, and we revisit in their perspective a well-known result from Dobbertin on APN exponents. This leads us to a new result about APN power functions and more general APN polynomials with coefficients in a subfield \begin{document}$ \mathbb{F}_{2^k} $\end{document} , which eases the research of such functions. It also allows to construct automatically many differentially uniform functions from them (this avoids calculations for proving their differential uniformity as done in a recent paper, which are tedious and specific to each APN function). In a second part, we give simple proofs of two important results on Boolean functions, one of which deserves to be better known but needed clarification, while the other needed correction.

In power systems, Economic Power dispatch Problem (EPP) is an influential optimization problem which is a highly non-convex and non-linear optimization problem. In the current study, a novel version of Differential Evolution (NDE) is used to solve this particular problem. NDE algorithm enhances local and global search capability along with efficient utilization of time and space by making use of two elite features: selfadaptive control parameter and single population structure. The combined effect of these concepts improves the performance of Differential Evolution (DE) without compromising on quality of the solution and balances the exploitation and exploration capabilities of DE. The efficiency of NDE is validated by evaluating on three benchmark cases of the power system problem having constraints such as power balance and power generation along with nonsmooth cost function and is compared with other optimization algorithms. The Numerical outcomes uncovered that NDE performed well for all the benchmark cases and maintained a trade-off between convergence rate and efficiency.

Graph Mining has gained importance due to its wide range of applications. As graph mining is a form of data mining where data is depicted in the form of graphs. The data when represented in the form of graphs helps to model the real scenario and relationship well. Discovery of interesting pattern from real relationship is of utmost beneficial. Frequent Subgraph Mining (FSM) is a significant area of graph mining. We accompany our approach in the field of FSM by adding a graph sampling function. This sampling function takes the single graph and a sampling percentage as input and produces a sampled graph which is similar in properties with original graph. This sampled graph is then taken as input while implementing the GraMi framework. Our sampling approach successfully mines the subgraphs with lower frequency threshold thus significantly improving the efficiency of the original GraMi framework.

Functional Encryption (FE) expands traditional public-key encryption in two different ways: it supports fine-grained access control and allows learning a function of the encrypted data. In this paper, we review all FE classes, describing their functionalities and main characteristics. In particular, we mention several schemes for each class, providing their security assumptions and comparing their properties. To our knowledge, this is the first survey that encompasses the entire FE family., To appear in Advances in Mathematics of Communications, https://www.aimsciences.org/article/doi/10.3934/amc.2021049

The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree distribution. The degree distribution can either be theoretical or extracted from a real-world network. The main idea is to invert the recurrence equation commonly used to compute the degree distribution in order to find a convenient attachment function for node connections - commonly chosen as linear. We compute this attachment function for some classical distributions, as the power-law, broken power-law, geometric and Poisson distributions. We also use the model on an undirected version of the Twitter network, for which the degree distribution has an unusual shape. We finally show that the divergence of chosen attachment functions is heavily links to the heavy-tailed property of the obtained degree distributions., Comment: 23 pages, 3 figures

The dynamic parameters of multiple projectiles that are fired using multi-barrel weapons in high-frequency continuous firing modes are important indicators to measure the performance of these weapons. The characteristics of multiple projectiles are high randomness and large numbers launched in a short period of time, making it very difficult to obtain the real dispersion parameters of the projectiles due to the occlusion or coincidence of multiple projectiles. Using six intersecting-screen testing system, in this paper, we propose an association recognition and matching algorithm of multiple projectiles using a temporal and spatial information constraint mechanism. We extract the output signal from each detection screen and then use the wavelet transform to process the output signal. We present a method to identify and extract the time values on which the projectiles pass through the detection screens using the wavelet transform modulus maximum theory. We then use the correlation of the output signals of three parallel detection screens to establish a correlation coefficient recognition constraint function for the multiple projectiles. Based on the premise of linear projectile motion, we establish a temporal and spatial constraint matching model using the projectile's position coordinates in each detection screen and the projectile's time constraints within the multiple intersecting-screen geometry. We then determine the time values of the multiple projectiles in each detection screen using an iterative search cycle registration, and finally obtain the flight parameters for the multiple projectiles in the presence of uncertainty. The proposed method and algorithm were verified experimentally and can solve the problem of uncertainty in projectiles flight parameter under different multiple projectile firing states.

Symmetric Searchable Encryption (SSE) schemes facilitate searching over encrypted data, and have been extensively explored to improve function, efficiency or security. There are, however, additional functions that we need to consider in a real-world setting. For example, forward and backward privacy are required to adequately secure newly added documents and deleted documents in Dynamic SSE (DSSE) schemes, and support boolean search (that allows users to search over encrypted data using basic boolean operations) to achieve improved efficiency and retrieval accuracy. Therefore, in this paper we first construct the Verifiable Boolean Search over encrypted data (VBS), and then improve VBS to achieve Forward and Backward privacy (VBS-FB). Finally, we formally prove the security of our proposed schemes, and evaluate their performance using real-world datasets.

Good generalization performance is the fundamental goal of any machine learning algorithm. Using the uniform stability concept, this article theoretically proves that the choice of loss function impacts the generalization performance of a trained deep neural network (DNN). The adopted stability-based framework provides an effective tool for comparing the generalization error bound with respect to the utilized loss function. The main result of our analysis is that using an effective loss function makes stochastic gradient descent more stable which consequently leads to the tighter generalization error bound, and so better generalization performance. To validate our analysis, we study learning problems in which the classes are semantically correlated. To capture this semantic similarity of neighboring classes, we adopt the well-known semantics-preserving learning framework, namely label distribution learning (LDL). We propose two novel loss functions for the LDL framework and theoretically show that they provide stronger stability than the other widely used loss functions adopted for training DNNs. The experimental results on three applications with semantically correlated classes, including facial age estimation, head pose estimation, and image esthetic assessment, validate the theoretical insights gained by our analysis and demonstrate the usefulness of the proposed loss functions in practical applications.

A Boolean function in \begin{document}$ n $\end{document} variables is 2-rotation symmetric if it is invariant under even powers of \begin{document}$ \rho(x_1, \ldots, x_n) = (x_2, \ldots, x_n, x_1) $\end{document} , but not under the first power (ordinary rotation symmetry); we call such a function a 2-function. A 2-function is called monomial rotation symmetric (MRS) if it is generated by applying powers of \begin{document}$ \rho^2 $\end{document} to a single monomial. If the quartic MRS 2-function in \begin{document}$ 2n $\end{document} variables has a monomial \begin{document}$ x_1 x_q x_r x_s $\end{document} , then we use the notation \begin{document}$ {2-}(1,q,r,s)_{2n} $\end{document} for the function. A detailed theory of equivalence of quartic MRS 2-functions in \begin{document}$ 2n $\end{document} variables was given in a \begin{document}$ 2020 $\end{document} paper by Cusick, Cheon and Dougan. This theory divides naturally into two classes, called \begin{document}$ mf1 $\end{document} and \begin{document}$ mf2 $\end{document} in the paper. After describing the equivalence classes, the second major problem is giving details of the linear recursions that the Hamming weights for any sequence of functions \begin{document}$ {2-}(1,q,r,s)_{2n} $\end{document} (with \begin{document}$ q say), \begin{document}$ n = s, s+1, \ldots $\end{document} can be shown to satisfy. This problem was solved for the \begin{document}$ mf1 $\end{document} case only in the \begin{document}$ 2020 $\end{document} paper. Using new ideas about "short" functions, Cusick and Cheon found formulas for the \begin{document}$ mf2 $\end{document} weights in a \begin{document}$ 2021 $\end{document} sequel to the \begin{document}$ 2020 $\end{document} paper. In this paper the actual recursions for the weights in the \begin{document}$ mf2 $\end{document} case are determined.

In this paper, we define and introduce some new concepts of the higher order strongly general biconvex functions involving the arbitrary bifunction and a function. Some new relationships among various concepts of higher order strongly general biconvex functions have been established. It is shown that the new parallelogram laws for Banach spaces can be obtained as applications of higher order strongly affine general biconvex functions, which is itself an novel application. It is proved that the optimality conditions of the higher order strongly general biconvex functions are characterized by a class of variational inequalities, which is called the higher order strongly general bivariational inequality. Auxiliary principle technique is used to suggest an implicit method for solving strongly general bivariational inequalities. Convergence analysis of the proposed method is investigated using the pseudo-monotonicity of the operator. Some special cases also discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results.

Newton-step approximations to pseudo maximum likelihood estimates of spatial autoregressive models with a large number of parameters are examined, in the sense that the parameter space grows slowly as a function of sample size. These have the same asymptotic efficiency properties as maximum likelihood under Gaussianity but are of closed form. Hence they are computationally simple and free from compactness assumptions, thereby avoiding two notorious pitfalls of implicitly defined estimates of large spatial autoregressions. For an initial least squares estimate, the Newton step can also lead to weaker regularity conditions for a central limit theorem than those extant in the literature. A simulation study demonstrates excellent finite sample gains from Newton iterations, especially in large multiparameter models for which grid search is costly. A small empirical illustration shows improvements in estimation precision with real data., 36 pages

In this paper, we model the trajectory of the cumulative confirmed cases and deaths of COVID-19 (in log scale) via a piecewise linear trend model. The model naturally captures the phase transitions of the epidemic growth rate via change-points and further enjoys great interpretability due to its semiparametric nature. On the methodological front, we advance the nascent self-normalization (SN) technique (Shao, 2010) to testing and estimation of a single change-point in the linear trend of a nonstationary time series. We further combine the SN-based change-point test with the NOT algorithm (Baranowski et al., 2019) to achieve multiple change-point estimation. Using the proposed method, we analyze the trajectory of the cumulative COVID-19 cases and deaths for 30 major countries and discover interesting patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. Furthermore, based on the change-point detection algorithm and a flexible extrapolation function, we design a simple two-stage forecasting scheme for COVID-19 and demonstrate its promising performance in predicting cumulative deaths in the U.S.

In this article, a combined gradient descent-Barzilai Borwein (GD-BB) algorithm and radial basis function neural network (RBFNN) output tracking control strategy was proposed for a family of nonlinear systems with unknown drift function and control input gain function. In such a method, a neural network (NN) is used to approximate the controller directly. The main merits of the proposed strategy are given as follows: first, not only the NN parameters, such as weights, centers, and widths but also the learning rates of NN parameter updating laws are updated online via the proposed learning algorithm based on Barzilai-Borwein technique; and second, the controller design process can be further simplified, the controller parameters that should be tuned can be greatly reduced. Theoretical analysis about the stability of the closed-loop system is manifested. In addition, simulations were conducted on a numerical discrete time system and an inverted pendulum system to validate the presented control strategy.

Top-k recommendation is a fundamental task in recommendation systems that is generally learned by comparing positive and negative pairs. The contrastive loss (CL) is the key in contrastive learning that has recently received more attention, and we find that it is well suited for top-k recommendations. However, CL is problematic because it treats the importance of the positive and negative samples the same . On the one hand, CL faces the imbalance problem of one positive sample and many negative samples. On the other hand, there are so few positive items in sparser datasets that their importance should be emphasized. Moreover, the other important issue is that the sparse positive items are still not sufficiently utilized in recommendations. Consequently, we propose a new data augmentation method by using multiple positive items (or samples) simultaneously with the CL loss function. Therefore, we propose a multisample-based contrastive loss (MSCL) function that solves the two problems by balancing the importance of positive and negative samples and data augmentation. Based on the graph convolution network (GCN) method, experimental results demonstrate the state-of-the-art of MSCL. The proposed MSCL is simple and can be applied in many methods. Our code is available at https://github.com/haotangxjtu/MSCL.

Recent works have shown that neural networks are promising parameter-free limiters for a variety of numerical schemes (Morgan et al. in A machine learning approach for detecting shocks with high-order hydrodynamic methods. https://doi.org/10.2514/6.2020-2024 ; Ray et al. in J Comput Phys 367: 166–191. https://doi.org/10.1016/j.jcp.2018.04.029 , 2018; Veiga et al. in European Conference on Computational Mechanics and VII European Conference on Computational Fluid Dynamics, vol. 1, pp. 2525–2550. ECCM. https://doi.org/10.5167/uzh-168538 , 2018). Following this trend, we train a neural network to serve as a shock-indicator function using simulation data from a Runge-Kutta discontinuous Galerkin (RKDG) method and a modal high-order limiter (Krivodonova in J Comput Phys 226: 879–896. https://doi.org/10.1016/j.jcp.2007.05.011 , 2007). With this methodology, we obtain one- and two-dimensional black-box shock-indicators which are then coupled to a standard limiter. Furthermore, we describe a strategy to transfer the shock-indicator to a residual distribution (RD) scheme without the need for a full training cycle and large dataset, by finding a mapping between the solution feature spaces from an RD scheme to an RKDG scheme, both in one- and two-dimensional problems, and on Cartesian and unstructured meshes. We report on the quality of the numerical solutions when using the neural network shock-indicator coupled to a limiter, comparing its performance to traditional limiters, for both RKDG and RD schemes.

Region-based methods are currently achieving state-of-the-art performance for monocular 3D object tracking. However, they are still prone to fail in cases of partial occlusions and ambiguous colors. We propose a novel region-based method to tackle these problems. The key idea is to derive a pixel-wise weighted region-based cost function using contour constraints. Firstly, we propose a novel region-based cost function using search lines around the object contour, which is more efficient than previous region-based cost functions using signed distance transform, and in the meantime can deal with partial occlusions and ambiguous colors more effectively. Secondly, we propose an optimal searching strategy to search the object contour points in cluttered scenes, and then use the object contour points to detect partial occlusions and ambiguous colors. Thirdly, we propose a pixel-wise weight function based on color and distance constraints of the object contour points, and integrate it into the proposed region-based cost function to reduce the negative impact of partial occlusions and ambiguous colors. We verify the effectiveness and efficiency of our method on challenging public datasets. Experiments demonstrate that our method outperforms the recent state-of-the-art region-based methods in complex scenarios, especially in the presence of partial occlusions and ambiguous colors.

Humans routinely sit or lean against supporting surfaces and it is important to shape these surfaces to be comfortable and ergonomic. We give a method to design the geometric shape of rigid supporting surfaces to maximize the ergonomics of physically based contact between the surface and a deformable human. We model the soft deformable human using a layer of FEM deformable tissue surrounding a rigid core, with measured realistic elastic material properties, and large-deformation nonlinear analysis. We define a novel cost function to measure the ergonomics of contact between the human and the supporting surface. We give a stable and computationally efficient contact model that is differentiable with respect to the supporting surface shape. This makes it possible to optimize our ergonomic cost function using gradient-based optimizers. Our optimizer produces supporting surfaces superior to prior work on ergonomic shape design. Our examples include furniture, apparel and tools. We also validate our results by scanning a real human subject's foot and optimizing a shoe sole shape to maximize foot contact ergonomics. We 3D-print the optimized shoe sole, measure contact pressure using pressure sensors, and demonstrate that the real unoptimized and optimized pressure distributions qualitatively match those predicted by our simulation.

The system considered in this paper operates with a feedback that is characterized by a gain and a desired final state (DFS), which is the main parameter of interest in the present study. The system is, however, subjected intermittently to stochastic inputs according to a Markov process. Since the system operates in two modes | under the feedback to the DFS and under a stochastic input|the Interacting Multiple Model (IMM) estimator is used. Two approaches are considered: (i) the DFS is a discrete-valued random variable | one of a finite number of possible states | with an a priori probability mass function (pmf), and (ii) the DFS is a continuous-valued random variable with an a priori probability density function (pdf). For Approach (i), we use a multiple IMM estimator (MIMM) that features one IMM for each one of the possible DFS. The a posteriori probability of the model for each IMM, i.e., of each DFS, will be computed based on the likelihood function (LF) of the corresponding IMM. For Approach (ii), we design a single IMM to handle the unknown DFS to be estimated (mode M1), and the random inputs (mode M2). Simulation results explore several scenarios and investigate the degree of observability of this stochastic problem.

Surrogate-assisted multi-objective evolutionary algorithms have advanced the field of computationally expensive optimization, but their progress is often restricted to low-dimensional problems. This manuscript presents a multiple classifiers-assisted evolutionary algorithm based on decomposition, which is adapted for high-dimensional expensive problems in terms of the following two insights. Compared to approximation-based surrogates, the accuracy of classification-based surrogates is robust for few high-dimensional training samples. Further, multiple local classifiers can hedge the risk of over-fitting issues. Accordingly, the proposed algorithm builds multiple classifiers with support vector machines on a decomposition-based multi-objective algorithm, wherein each local classifier is trained for a corresponding scalarization function. Experimental results statistically confirm that the proposed algorithm is competitive to the state-of-the-art algorithms and computationally efficient as well.

Elastic Riemannian metrics have been used successfully in the past for statistical treatments of functional and curve shape data. However, this usage has suffered from an important restriction: the function boundaries are assumed fixed and matched. Functional data exhibiting unmatched boundaries typically arise from dynamical systems with variable evolution rates such as COVID-19 infection rate curves associated with different geographical regions. In this case, it is more natural to model such data with sliding boundaries and use partial matching, i.e., only a part of a function is matched to another function. Here, we develop a comprehensive Riemannian framework that allows for partial matching, comparing, and clustering of functions under both phase variability and uncertain boundaries. We extend past work by: (1) Forming a joint action of the time-warping and time-scaling groups; (2) Introducing a metric that is invariant to this joint action, allowing for a gradient-based approach to elastic partial matching; and (3) Presenting a modification that, while losing the metric property, allows one to control relative influence of the two groups. This framework is illustrated for registering and clustering shapes of COVID-19 rate curves, identifying essential patterns, minimizing mismatch errors, and reducing variability within clusters compared to previous methods., Submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence

The microgrid with the high proportion of renewable sources has become the trend of the future. However, the negative features, such as renewable energy perturbation, nonlinear counterpart, and so on, are prone to causing the low-power quality of the ac microgrid. To deal with these problems, this article proposes an event-triggered consensus control approach. First, the nonlinear state-space function regarding the ac microgrid is built, which is further transformed into the standard linear multiagent model by using the singular perturbation method. It provides indispensable preprocessing for the direct application of advanced linear control approaches. Then, based on this standard linear multiagent model, the secondary consensus approach with the leader is designed to compensate for the output voltage deviation and achieve accurate power sharing. In order to decrease the communication among various distributed generators, the event-triggered communication method is further proposed. Meanwhile, the Zeno behavior is avoided through the theoretical proof. Finally, simulation results are presented to demonstrate the effectiveness of the proposed approach.

Network Utility Maximization (NUM) studies the problems of allocating traffic rates to network users in order to maximize the users' total utility subject to network resource constraints. In this paper, we propose a new NUM framework, Learning-NUM, where the users' utility functions are unknown apriori and the utility function values of the traffic rates can be observed only after the corresponding traffic is delivered to the destination, which means that the utility feedback experiences \textit{queueing delay}. The goal is to design a policy that gradually learns the utility functions and makes rate allocation and network scheduling/routing decisions so as to maximize the total utility obtained over a finite time horizon $T$. In addition to unknown utility functions and stochastic constraints, a central challenge of our problem lies in the queueing delay of the observations, which may be unbounded and depends on the decisions of the policy. We first show that the expected total utility obtained by the best dynamic policy is upper bounded by the solution to a static optimization problem. Without the presence of feedback delay, we design an algorithm based on the ideas of gradient estimation and Max-Weight scheduling. To handle the feedback delay, we embed the algorithm in a parallel-instance paradigm to form a policy that achieves $\tilde{O}(T^{3/4})$-regret, i.e., the difference between the expected utility obtained by the best dynamic policy and our policy is in $\tilde{O}(T^{3/4})$. Finally, to demonstrate the practical applicability of the Learning-NUM framework, we apply it to three application scenarios including database query, job scheduling and video streaming. We further conduct simulations on the job scheduling application to evaluate the empirical performance of our policy.

Recent learning-based intrinsic image decomposition methods have achieved remarkable progress. However, they usually require massive ground truth intrinsic images for supervised learning, which limits their applicability on real-world images since obtaining ground truth intrinsic decomposition for natural images is very challenging. In this paper, we present an unsupervised framework that is able to learn the decomposition effectively from a single natural image by training solely with the image itself. Our approach is built upon the observations that the reflectance of a natural image typically has high internal self-similarity of patches, and a convolutional generation network tends to boost the self-similarity of an image when trained for image reconstruction. Based on the observations, an unsupervised intrinsic decomposition network (UIDNet) consisting of two fully convolutional encoder-decoder sub-networks, i.e., reflectance prediction network (RPN) and shading prediction network (SPN), is devised to decompose an image into reflectance and shading by promoting the internal self-similarity of the reflectance component, in a way that jointly trains RPN and SPN to reproduce the given image. A novel loss function is also designed to make effective the training for intrinsic decomposition. Experimental results on three benchmark real-world datasets demonstrate the superiority of the proposed method.

In this article, a rapid sensor fault diagnosis (SFD) method is presented for a class of nonlinear systems. First, by exploiting the linear adaptive observer technology and the deterministic learning method (DLM), an adaptive neural network (NN) observer is constructed to capture the information of the unknown sensor fault function. Second, when the NN input orbit is a period or recurrent one, the partial persistent excitation (PE) condition of the NNs can be guaranteed through the DLM. Based on the partial PE condition and the uniformly completely observable property of a linear time-varying system, the accurate state estimation and the sensor fault identification can be achieved by properly choosing the observer gain. Third, a bank of dynamical observers utilizing the experiential knowledge is constructed to achieve rapid SFD and data recovery. The attractions of the proposed approach are that accurate approximations of sensor faults can be achieved through the DLM, and the data that are destroyed by the sensor faults can be recovered by using the learning results. Simulation studies of a robot system are utilized to show the effectiveness of the proposed method.

A mixed-integer programming (MIP) problem contains both constraints and integer restrictions. Integer restrictions divide the feasible region defined by constraints into multiple discontinuous feasible parts. In particular, the number of discontinuous feasible parts will drastically increase with the increase of the number of integer decision variables and/or the size of the candidate set of each integer decision variable. Due to the fact that the optimal solution is located in one of the discontinuous feasible parts, it is a challenging task to solve a MIP problem. This article presents a cutting and repulsion-based evolutionary framework (called CaR) to solve MIP problems. CaR includes two main strategies: 1) the cutting strategy and 2) the repulsion strategy. In the cutting strategy, an additional constraint is constructed based on the objective function value of the best individual found so far, the aim of which is to continuously cut unpromising discontinuous feasible parts. As a result, the probability of the population entering a wrong discontinuous feasible part can be decreased. In addition, in the repulsion strategy, once it has been detected that the population has converged to a discontinuous feasible part, the population will be reinitialized. Moreover, a repulsion function is designed to repulse the previously explored discontinuous feasible parts. Overall, the cutting strategy can significantly reduce the number of discontinuous feasible parts and the repulsion strategy can probe the remaining discontinuous feasible parts. Sixteen test problems developed in this article and two real-world cases are used to verify the effectiveness of CaR. The results demonstrate that CaR performs well in solving MIP problems.

In this article we investigates the practical fixed-time consensus tracking problem for multiple Euler–Lagrange systems, which is subject to, concurrently, stochastic packet losses in directed communication networks (DCNs) and input/output constraints. In practice, the packet losses in the communication network may lead to communication failure and control accuracy degradation. To address this impact, a novel fully distributed observer is established to estimate the leader’s states within fixed time. Subsequently, the state constraint function is introduced so that the designed adaptive control protocol can be used in a uniform structure with unconstrained or asymmetric/symmetric output constraints without changing the adaptive structure. Combining the backstepping technique with fuzzy-logic systems, an adaptive fixed-time local control protocol is constructed to drive each agent to track the leader’s states estimated by the observer. Besides, a novel auxiliary system is introduced to solve the constraint problem of the control input. Furthermore, through rigorous theoretical analysis, it is verified that all signals converge to the compact set close to zero with guaranteed fixed-time convergence rate. At last, a representative simulation is carried out to demonstrate the practicability of the proposed method.

This article proposes a mathematical model to optimally locate a set of detectors in such a way that the expected number of casualties in a given threat area can be minimized. The reliability of a detector is often a function of the duration that the threat remains within the effective radius. To accurately detect any threat event and to avoid any false alarm, in this article, two sets of detectors, primary and secondary, are utilized; the primary detectors rely on the secondary set as reinforcement to confirm or deny that a threat is present. The problem is formulated as a nonlinear binary integer programming model and then solved as a linearized branch and bound algorithm. A number of sensitivity analyses are performed to illustrate the robustness of the model and to draw key managerial insights. Experimental results reveal that a two-layer detection system will significantly minimize the expected number of casualties in a given threat area as opposed to a one-layer detection system.

We study the list decodability of different ensembles of codes over the real alphabet under the assumption of an omniscient adversary. It is a well-known result that when the source and the adversary have power constraints $ P $ and $ N $ respectively, the list decoding capacity is equal to $ \frac{1}{2}\log\frac{P}{N} $. Random spherical codes achieve constant list sizes, and the goal of the present paper is to obtain a better understanding of the smallest achievable list size as a function of the gap to capacity. We show a reduction from arbitrary codes to spherical codes, and derive a lower bound on the list size of typical random spherical codes. We also give an upper bound on the list size achievable using nested Construction-A lattices and infinite Construction-A lattices. We then define and study a class of infinite constellations that generalize Construction-A lattices and prove upper and lower bounds for the same. Other goodness properties such as packing goodness and AWGN goodness of infinite constellations are proved along the way. Finally, we consider random lattices sampled from the Haar distribution and show that if a certain number-theoretic conjecture is true, then the list size grows as a polynomial function of the gap-to-capacity., Comment: Significantly revised

A revision of the mechanism of mechanical-to-vibrational energy transfer in crystals of energetic materials undergone impact loading is proposed. The new approach takes into account previous inaccuracies of normalization of the number of couplings between phonon overtones and conformational vibrational fundamentals (ζ), which is critical for comparison of molecules that differ greatly in the number of atoms. Moreover, it introduces two very important damping factors, namely a and b. The a factor allows differentiation of the phonon overtones by their coupling strength; the lower the overtone interacts, the stronger the coupling is. Meanwhile, the b factor is aimed to distinguish the coupling strength itself. This factor is the denominator in the exponent of a Gaussian-type function and determines the rate at which the coupling strength decays with the rise of difference between the interacting phonon overtones and conformational vibrational fundamentals. After a careful regression analysis of ζ against impact sensitivities (h50) of 30 common nitroexplosives, we have determined the numerical values of these damping factors as a = 2.5 and b = 40 cm–1. The proposed approach is extrapolated on the vibrational spectra of 21 crystalline energetic materials with Z' ≥ 1 and a general applicability along with limitations of the method are discussed for the family of nitroexplosives and nitrogen-rich (cyclo-pentazolate and 5,5′-bitetrazole) energetic salts as an example.

The output gap, the difference between potential and actual output, has a direct impact on policy decisions, e.g., monetary policy. Estimating this gap and its further analysis remain the subject of controversial debates due to methodological problems. We propose a local polynomial regression combined with a Self-Exciting Threshold AutoRegressive (SETAR) model and its forecasting extension for a systematic output gap estimation. Furthermore, local polynomial regression is proposed for the (multivariate) OECD production function approach and its reliability is demonstrated in forecasting output growth. A comparison of the proposed gap to the Hodrick–Prescott filter as well as to estimations by experts from the FED and OECD shows a higher correlation of our output gap with those from those economic institutions. Furthermore, sometimes gaps with different magnitude and different positions above or below the trend are observed between different methods. This may cause competing policy implications which can be improved with our results.

The present study focuses on designing the memory-based sampled data control approach to achieve the desired performance from switched-type of neural networks. The overall contribution of the study can be viewed from two directions. The first part is to derive the theoretical-based sufficient stability conditions that ensure the synchronization of uncontrolled and controlled systems. The idea behind the synchronization analysis is because of time complexity and computational cost. Once, we derive the closed-loop system then user can employ them in any practical application without interruptions. The existence of time-delays during the information transmission is inevitable, and in a practical sense, the delays, which are a function of time are well-effective. Besides, the sufficient conditions are derived in terms of solvable linear matrix inequalities (LMIs), which can be solved to ensure the global asymptotical stability of the error system, derived from uncontrolled–controlled systems. Technically, the work integrates with the new type of discontinuous Lyapunov–Krasovskii functional candidate with integral terms, several delay-dependent stability conditions, and Wirtinger-based integral inequality. The second part works on utilizing the controlled system into a real-life application, say, encryption/decryption process. To an evident, the proposed controlled system is considered as crypto-system in the encryption/decryption process.

This paper presents a design method of cylindrical uniform field coil based on quasi-elliptic function fitting (EFF method with multiple optimizations. EFF method is a type of discrete wire techniques aiming at simplifying the coil structure. Combing with particle swarm optimization (PSO algorithm, the optimized parameters of EFF coil are obtained for high uniform magnetic field. And to further improve the uniformity of magnetic field in the central space, a new regional points selection optimization method is proposed. The calculation results show that after PSO optimization the absolute maximum relative error in the target region is optimized to 0.098% by EFF coil comparing with modified single saddle coil (3.08%, nest coil (2.4% and target field method (TFM coil (0.11% . And after regional points selection optimization, the volume proportion of absolute magnetic field relative error less than 110-4 increases from 35.24% to 54.38% by EFF coil comparing with TFM coil. In addition, the simple EFF coil structure is verified to be easy to process and keep high performance through experiments. As the EFF coil's high uniformity and simple structure, the new method has important significance for miniaturization of atomic sensors.

Due to wide distribution and high energy-saving potential of industrial robots, energy optimization techniques of industrial robots attract increasing attention. Dynamic time-scaling methods can optimize the energy consumption of robots only by stretching or shrinking reference trajectories in time dimension, and the dynamic time-scaling methods shows advantages over other energy-saving techniques for time-scaling methods can achieve energy-saving without hardware investment. To obtain the optimal solution, traditional dynamic time-scaling methods need to search the possible state transitions from the initial configuration to the final configuration, and the integration of robot transient power has to be carried out for each possible state transition, which directly leads to intensive computation. Therefore, a computation efficient method for robot trajectory optimization is proposed in this paper. Based on parameter separation, an energy characteristic parameter model based on dynamic time-scaling is developed, which describes the energy consumption during the state transition as a function of the scaling parameters. Based on the energy characteristic parameter model, DP algorithm can replaces the integral operation of transient power with the substitution calculation, which avoid intensive computation. Experimental results show the proposed method can achieve 33.7% less energy consumption, and the computation time can be reduced by nearly 99%.

This article addresses an adaptive neural network (NN) constraint control scheme for a class of fractional-order uncertain nonlinear nonstrict-feedback systems with full-state constraints and input saturation. The radial basis function (RBF) NNs are used to deal with the algebraic loop problem from the nonstrict-feedback formation based on the approximation structure. In order to overcome the problem of input saturation nonlinearity, a smooth nonaffine function is applied to approach the saturation function. To arrest the violation of full-state constraints, the barrier Lyapunov function (BLF) is introduced in each step of the backstepping procedure. By using the fractional-order Lyapunov stability theory and the given conditions, it proves that all the states remain in their constraint bounds, the tracking error converges to a bounded compact set containing the origin, and all signals in the closed-loop system are ensured to be bounded. Finally, the effectiveness of the proposed control scheme is verified by two simulation examples.