On the commutativity of discrete memoryless channels in cascade

The conditions are discussed under which two square discrete memoryless channels (DMCs) in cascade commute. Two different types of channel commutativity are considered: matrix commutativity, in which changing the order of two cascaded channels results in an identical overall channel, and capacity commutativity, in which the order of two cascaded channels results in an overall channel with the same capacity as the original cascade. A theorem is presented giving necessary and sufficient conditions for a pair of square DMCs to be matrix commutative and note its implications for a number of example channel cascades. Finally, it is shown that all pairs of r-ary symmetric channels are matrix commutative, regardless of their crossover probabilities.     

On convergence criteria for jarratt's method

Let f(χ) together with its first two derivatives be continuous in the domain D and additionally let χ_M?D be an extremum (or turning point) of this function. Also, let χ_n+1 = T (χ_n,χ_n-1,χ_n-2) be Jarratt's Method for computing the extremum (or turning point) of a function. Criteria are demonstrated which insure that, for any triple of initial assumptions (χ₁,χ₀,χ_-1)?D, Jarratt's Method, converges to the extremum of f(χ), and that from and after some n = N₀, the rate of convergence of this method increases steadily, finally becoming unbounded when the solution χ_M is attained.     

Fixed point properties of the binomial function

Fixed point properties of the binomial function

are developed. It is shown that for any 1 < L < N, T^L_Nhas a unique fixed point p? in (0, 1), and that for large N, the fixed point is L/N. This has application to signal detection schemes commonly used in communication systems. When detecting the presence or absence of a signal with an initial false alarm probability p_FAand an initial detection probability p_D, then T^L_N(p_FA) < p_FAand T^L_N(p_D) > p_Dif, and only if, p_FA < p? < p_D. When this condition is satisfied, as N → ∞, T^L_N(p_FA) → 0 and T^L_N(p_D → 1.     

Robust mixed H2/H∞ model predictive control for Markov jump systems with partially uncertain transition probabilities

This paper addresses the control problem for a class of discrete-time Markov jump linear systems with partially unknown transition probabilities using model predictive controller subject to external disturbances and input constraints. Our focus is on the design of a model predictive controller to stabilize the system with a given mixed H₂/H_∞ performance index. Sufficient conditions are derived in terms of a set of linear matrix inequalities. Examples are presented to demonstrate the effectiveness of the proposed controller design method.     

Finding the Graph with the Maximum Number of Spanning Trees

The problem is to determine the linear graph that has the maximum number of spanning trees, where only the number of nodes N and the number of branches B are prescribed. We deal with connected graphs G(N,B) obtained by deleting D branches from a complete graph K_N. Our solution is for D less than or equal to N     

Delay-dependent H∞ filtering for discrete singular Markov jump systems with Wiener process and partly unknown transition probabilities

This paper is devoted to the investigation of the delay-dependent H_∞ filtering problem for a class of discrete-time singular Markov jump systems with Wiener process and partly unknown transition probabilities. The class of stochastic singular model under consideration is more general and covers the stochastic singular Markov jump time-varying delay systems with completely known and completely unknown transition probabilities as two special cases. Firstly, based on a stochastic Lyapunov–Krasovskii candidate function and an auxiliary vector function, by employing some appropriate free-weighting matrices, the discretized Jensen inequality and combining them with the structural characteristics of the filtering error system, a set of delay-dependent sufficient conditions are established, which ensure that the filtering error system is stochastically admissible. And then, a singular filter is designed such that the filtering error system is not only regular, causal and stochastically stable, but also satisfy a prescribed H_∞ performance for all time-varying delays no larger than a given upper bound. Furthermore, the sufficient conditions for the solvability of the H_∞ filtering problem are obtained in terms of a new type of Lyapunov–Krasovskii candidate function and a set of linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness of the proposed method in the paper.     

Observer-based finite-time H∞ control for uncertain discrete-time nonhomogeneous Markov jump systems

The problem of observer-based finite-time H_∞ control for discrete-time Markov jump systems with time-varying transition probabilities and uncertainties is studied in this paper, in which time-varying transition probabilities are modelled as convex polyhedron, and the parameter uncertainty satisfies norm-bounded. First of all, a Luenberger observer is designed to measure the system state. Then, observer-based controller is constructed to ensure the stochastic finite-time boundedness of the resulting closed-loop system with an H_∞ performance. Furthermore, sufficient conditions are derived in light of linear matrix inequalities. In the end, the flexibility and applicability of the developed methods are demonstrated by two illustrative examples.     

Adaptive threshold to guarantee both detection and false alarm probabilities in multi-taper based spectrum sensing

The multi-taper spectrum (MTS) estimator enjoys a relatively low computational complexity and high estimation accuracy making it an attractive method for spectrum sensing in cognitive radio (CR) networks. However, it is difficult to guarantee both detection and false alarm probabilities when its design is based on fixed threshold, especially when the noise power fluctuates due to channel conditions. In this paper, a new adaptive threshold method to guarantee both detection and false alarm probabilities for MTS based spectrum sensing is proposed. By means of estimating noise power and signal power, the decision of adaptive threshold is able to adapt the noise fluctuation and achieve efficient trade-off between detection and false alarm probabilities. A closed form expression for the adaptive threshold is derived for both additive white Gaussian noise (AWGN) channel and multipath fading channel. Several metrics are employed to compare the performance of the proposed adaptive threshold method with that of the fixed threshold methods such as: error decision probability, detection probability, false alarm probability and throughput. The obtained results show that the proposed method achieves better spectrum efficiency and high throughput in comparison with the conventional fixed and adaptive threshold methods presented in the literature.     

Plan and generate: Explicit and implicit variational augmentation for multi-document summarization of scientific articles

Multi-Document Summarization of Scientific articles (MDSS) is a challenging task that aims to generate concise and informative summaries for multiple scientific articles on a particular topic. However, despite recent advances in abstractive models for MDSS, grammatical correctness and contextual coherence remain challenging issues. In this paper, we introduce EDITSum, a novel abstractive MDSS model that leverages sentence-level planning to guide summary generation. Our model incorporates neural topic model information as explicit guidance and sequential latent variables information as implicit guidance under a variational framework. We propose a hierarchical decoding strategy that generates the sentence-level planning by a sentence decoder and then generates the final summary conditioned on the planning by a word decoder. Experimental results show that our model outperforms previous state-of-the-art models by a significant margin on ROUGE-1 and ROUGE-L metrics. Ablation studies demonstrate the effectiveness of the individual modules proposed in our model, and human evaluations provide strong evidence that our model generates more coherent and error-free summaries. Our work highlights the importance of high-level planning in addressing intra-sentence errors and inter-sentence incoherence issues in MDSS.     

N-step off-line MPC design of nonhomogeneous Markov jump systems: A suboptimal case

This paper mainly concerns N-step off-line suboptimal predictive controller design for discrete nonhomogeneous Markov jump systems, in which the Markov chains are time-varying transition probabilities matrix modeled as a polytope. The design procedure is divided into N-step, more precisely, the first is to design the Nth step when the changes of Euclidean form of mode-dependent feedback law between the Nth and the (N+1)th asymptotically stable mode-dependent ellipsoids are less than the given accuracy. Then the N  th asymptotically stable mode-dependent invariant ellipsoid is defined. In the previous (N−1)$(N-1)$ steps, an off-line mode-dependent predictive controller is designed to drive the state to this small area including the origin. Compared with on-line MPC algorithm, the computation time is dramatically reduced while the dynamic performance of controller is comparable. One numerical example is presented to illustrate the validity of the developed results.     

On recursive averaging processes and Hilbert space extensions of the contraction mapping principle

If T maps a convex domain D_T into itself, and if {ω_n} is a real sequence with range in (0, 1] then the recursive averaging process,

$\text{X}{}_{\mathrm{n+1}}\text{=(1?omega;}{}_{\mathrm{n}}\text{)}\text{X}{}_{\mathrm{n}}\text{+ω}{}_{\mathrm{n}}\text{+ω}{}_{\mathrm{n}}\text{T}\text{x}{}_{\mathrm{n}}\text{,}\text{x}{}_0\text{=ξ?D}{}_{\mathrm{T}}$

generates a sequence {x?_n}; with range in D_T. Under suitable conditions on D_T, T and {ω_n} the sequence {x?_n} will converge in some sense to a fixed point of T. We prove that if D_T is a closed convex subset of a complex Hilbert space H, if Tω = (1 ? ω) I + ωT is a strict contraction for some ω ? (0, 1], and if {ω_n} satisfies the conditions,

$\text{ω}{}_{\mathrm{n}}\text{→ 0}$

and

$\text{∑}\text{n=0}\text{∞}\text{ω}{}_{\mathrm{n}}\text{=∞}$

then, for arbitrary ξ ? D_T, {x?_n} converges strongly to (the unique) fixed point of T. We also prove that if D_T and {ω_n} satisfy the foregoing conditions, if T has at least one fixed point, and if Tω is non-expansive for some ω ? (0, 1], then for all ξ ? D_T, {x?_n} converges at least weakly to some fixed point of T. Finally, we apply these results to linear equations involving bounded normal operators and obtain an extension of the classical Neumann operator series.     

gDART: Improving rumor verification in social media with Discrete Attention Representations

Due to the harmful impact of fabricated information on social media, many rumor verification techniques have been introduced in recent years. Advanced techniques like multi-task learning (MTL), shared-private models suffer from many strategic limitations that restrict their capability of veracity identification on social media. These models are often reliant on multiple tasks for the primary targeted objective. Even the most recent deep neural network (DNN) models like VRoC, Hierarchical-PSV, StA-HiTPLAN etc. based on VAE, GCN, Transformer respectively with improved modification are able to perform good on veracity identification task but with the help of additional auxiliary information, mostly. However, their rise is still not substantial with respect to the proposed model even though the proposed model is not using any additional information. To come up with an improved DNN model architecture, we introduce globally Discrete Attention Representations from Transformers (gDART). Discrete-Attention mechanism in gDART is capable of capturing multifarious correlations veiled among the sequence of words which existing DNN models including Transformer often overlook. Our proposed framework uses a Branch-CoRR Attention Network to extract highly informative features in branches, and employs Feature Fusion Network Component to identify deep embedded features and use them to make enhanced identification of veracity of an unverified claim. Moreover, to achieve its goal, gDART is not dependent on any costly auxiliary resource but on an unsupervised learning process. Extensive experiments reveal that gDART marks a considerable performance gain in veracity identification task over state-of-the-art models on two real world rumor datasets. gDART reports a gain of 36.76%, 40.85% on standard benchmark metrics.     

Reliable H∞ control on saturated linear Markov jump system with uncertain transition rates and asynchronous jumped actuator failure

This paper is concerned with reliable H_∞?control for saturated linear Markov jump systems with uncertain transition rates and asynchronous jumped actuator failure. The actuator failures are assumed to occur randomly under the Markov process with a different jumping mode from the system jumping mode. In considering the mixed-mode-dependent state feedback controller, both H_∞ stochastic stability analysis for closed-loop system with completely accessible transition rates and uncertain transition rates are investigated. Moreover, based on the obtained stability conditions, the H_∞?control problems are investigated, and the controller gains can be obtained by solving a convex optimization problem with minimizing H_∞ performance as objective and linear matrix inequalities (LMIs) as constraints. The problem of designing state feedback controllers such that the estimate of the domain of attraction is enlarged is also formulated and solved as an optimization problem with LMI constraints. Simulation results are presented to illustrate the effectiveness of the proposed results.     

Moving horizon estimation for ARMAX processes with additive output noise

Auto-Regressive-Moving-Average with eXogenous input (ARMAX) models play an important role in control engineering for describing practical systems. However, ARMAX models can be non-realistic in many practical contexts because they do not consider the measurement errors on the output of the process. Due to the auto-regressive nature of ARMAX processes, a measurement error may affect multiple data entries, making the estimation problem very challenging. This problem can be solved by enhancing the ARMAX model with additive error terms on the output, and this paper develops a moving horizon estimator for such an extended ARMAX model. In the proposed method, measurement errors are modeled as nuisance variables and estimated simultaneously with the states. Identifiability was achieved by regularizing the least-squares cost with the ?₂-norm of the nuisance variables, which leads to an optimization problem that has an analytical solution. For the proposed estimator, convergence results are established and unbiasedness properties are also proved. Insights on how to select the tuning parameter in the cost function are provided. Because of the explicit modeling of output noise, the impact of a measurement error on multiple data entries can be estimated and reduced. Examples are given to demonstrate the effectiveness of the proposed estimator in dealing with additive output noise as well as outliers.     

Backstepping-based decentralized bounded-H∞ adaptive neural control for a class of large-scale stochastic nonlinear systems

In this paper, a novel decentralized adaptive neural control approach based on the backstepping technique is proposed to design a decentralized H_∞ adaptive neural controller for a class of stochastic large-scale nonlinear systems with external disturbances and unknown nonlinear functions. RBF neural networks are utilized to approximate the packaged unknown nonlinearities. A novel concept with regard to bounded-H_∞ performance is proposed. It can be applied to solve an H_∞ control problem for a class of stochastic nonlinear systems. The constant terms appeared in stability analysis are dealt with by using Gronwall inequality, so that H_∞ performance criterion is satisfied. The assumption that the approximation errors of neural networks must be square-integrable in some literature can be eliminated. The design process for decentralized bounded-H_∞ controllers is given. The proposed control scheme guarantees that all the signals in the resulting closed-loop large-scale system are uniformly ultimately bounded in probability, and each subsystem possesses disturbance attenuation performance for external disturbances. Finally, the simulation results are provided to illustrate the effectiveness and feasibility of the proposed approach.     

Finite-time asynchronous state estimation for jump systems with partial transition probabilities via redundant channels: A co-design method

This paper addresses the $H_{\infty }$ finite-time asynchronous state estimation issue for Markov jump systems with partial transition probabilities. A hidden-Markov-chain-based redundant channel model (HMCb-RCM) is established to reflect a more practical situation. Based on the output of the HMCb-RCM, firstly an asynchronous full-order state estimator is devised for the jump system with partial transition probabilities. Then, new sufficient criteria are derived such that the state estimation error is $H_{\infty }$ stochastically finite-time bounded. The relationship between the partial transition probabilities and asynchronous modes is revealed as few attempts. The conditional transition probability matrix (CTPM) for the HMCb-RCM is not fixed but designable accordingly; a co-design strategy is newly developed to synthesize the CTPM and the state estimator simultaneously, which produces less conservatism than that with fixed CTPM. Finally, the theoretical results are applied to a one-link robotic manipulator to validate the proposed results.     

Spatio-temporal graph-based CNNs for anomaly detection in weakly-labeled videos

Abnormal event detection in videos plays an essential role for public security. However, most weakly supervised learning methods ignore the relationship between the complicated spatial correlations and the dynamical trends of temporal pattern in video data. In this paper, we provide a new perspective, i.e., spatial similarity and temporal consistency are adopted to construct Spatio-Temporal Graph-based CNNs (STGCNs). For the feature extraction, we use Inflated 3D (I3D) convolutional networks to extract features which can better capture appearance and motion dynamics in videos. For the spatio graph and temporal graph, each video segment is regarded as a vertex in the graph, and attention mechanism is introduced to allocate attention for each segment. For the spatial-temporal fusion graph, we propose a self-adapting weighting to fuse them. Finally, we build ranking loss and classification loss to improve the robustness of STGCNs. We evaluate the performance of STGCNs on UCF-Crime datasets (total 128 h) and ShanghaiTech datasets (total 317,398 frames) with the AUC score 84.2% and 92.3%, respectively. The experimental results also show the effectiveness and robustness with other evaluation metrics.     

Enhancing sequential recommendation with contrastive Generative Adversarial Network

Sequential recommendation models a user’s historical sequence to predict future items. Existing studies utilize deep learning methods and contrastive learning for data augmentation to alleviate data sparsity. However, these existing methods cannot learn accurate high-quality item representations while augmenting data. In addition, they usually ignore data noise and user cold-start issues. To solve the above issues, we investigate the possibility of Generative Adversarial Network (GAN) with contrastive learning for sequential recommendation to balance data sparsity and noise. Specifically, we propose a new framework, Enhanced Contrastive Learning with Generative Adversarial Network for Sequential Recommendation (ECGAN-Rec), which models the training process as a GAN and recommendation task as the main task of the discriminator. We design a sequence augmentation module and a contrastive GAN module to implement both data-level and model-level augmentations. In addition, the contrastive GAN learns more accurate high-quality item representations to alleviate data noise after data augmentation. Furthermore, we propose an enhanced Transformer recommender based on GAN to optimize the performance of the model. Experimental results on three open datasets validate the efficiency and effectiveness of the proposed model and the ability of the model to balance data noise and data sparsity. Specifically, the improvement of ECGAN-Rec in two evaluation metrics (HR@N and NDCG@N) compared to the state-of-the-art model performance on the Beauty, Sports and Yelp datasets are 34.95%, 36.68%, and 13.66%, respectively. Our implemented model is available via https://github.com/nishawn/ECGANRec-master.     

A new approach to the design of coupling networks

Mathematical results are derived, which enable one to find a vector of parameters k⁰ such that (P₁(s,k⁰)?H)∩(P₂(k⁰)=0), where P₁(s,k) is a polynomial in s and in the components of k,P₂(k) is a polynomial in the components of k, and H is the set of Hurwitz polynomials. The algorithm is based on an extension of the root locus technique to the multiparameter case. The design problem of coupling networks between a resistive generator and a passive load, under prescribed power gain characteristics, is translated into the above formulation. A numerical example is provided.     

Direct transformation of dinitrogen: synthesis of N-containing organic compounds via N−C bond formation

N-containing organic compounds are of vital importance to lives. Practical synthesis of valuable N-containing organic compounds directly from dinitrogen (N₂), not through ammonia (NH₃), is a holy-grail in chemistry and chemical industry. An essential step for this transformation is the functionalization of the activated N₂ units/ligands to generate N−C bonds. Pioneering works of transition metal-mediated direct conversion of N₂ into organic compounds via N−C bond formation at metal-dinitrogen [N₂-M] complexes have generated diversified coordination modes and laid the foundation of understanding for the N−C bond formation mechanism. This review summarizes those major achievements and is organized by the coordination modes of the [N₂-M] complexes (end-on, side-on, end-on-side-on, etc.) that are involved in the N−C bond formation steps, and each part is arranged in terms of reaction types (N-alkylation, N-acylation, cycloaddition, insertion, etc.) between [N₂-M] complexes and carbon-based substrates. Additionally, earlier works on one-pot synthesis of organic compounds from N₂ via ill-defined intermediates are also briefed. Although almost all of the syntheses of N-containing organic compounds via direct transformation of N₂ so far in the literature are realized in homogeneous stoichiometric thermochemical reaction systems and are discussed here in detail, the sporadically reported syntheses involving photochemical, electrochemical, heterogeneous thermo-catalytic reactions, if any, are also mentioned. This review aims to provide readers with an in-depth understanding of the state-of-the-art and perspectives of future research particularly in direct catalytic and efficient conversion of N₂ into N-containing organic compounds under mild conditions, and to stimulate more research efforts to tackle this long-standing and grand scientific challenge.