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This article investigates the fault-tolerant control problem for stochastic switched interval type-2 (IT2) fuzzy time-delayed uncertain systems based on unknown input observer synthesis, which can avoid uneasy measurement on the time derivative of output, and estimate unavailable or partially measurable states, including sensor and actuator faults accurately. First, a desired fuzzy observer is designed to ensure the observer-based dynamic error system mean-square exponentially stable with sufficient condition of a strict (l,ℏ,℘)-℧-dissipative performance, which is a unified framework of passivity, and H∞ provides results with less conservativeness. Then, we concentrate on stability analyses on dissipativity-based switched IT2 fuzzy systems with stochastic perturbation through linear matrix inequalities, Lyapunov function, free-weighting matrices, and average dwell time, discussing it according to different values of disturbance. Finally, simulation examples are listed to account for availability and effectiveness of the research methodology.

Chromic oxide (Cr2O3) monolayer is a promising alternative hydrogen evolution reaction (HER) catalyst compared with expensive platinum (Pt) due to its advantages such as low cost, large specific surface area, high reserves, and designability. In this study, the two practical strategies, strain engineering and transition metal (TM) doping (Mn, Fe, Zn, etc.), are proposed to activate the catalytic sites of Cr2O3 monolayer for the HER. The density functional theory (DFT) calculations demonstrate that the strained Cr2O3 monolayer can stimulate the HER activity with the Gibbs free energy of hydrogen adsorption (ΔGH∗) close to 0.09eV, which can be considered as a performable strategy to tune the HER catalytic behavior of Cr2O3 monolayer. For the TM doping, it also plays a role in the performance adjustment. These results provide a guideline to optimize the HER performance of Cr2O3 monolayer.

In medical image analysis (MIA) and computer-assisted surgery (CAS), aligning two multiple point sets (PSs) together is an essential but also a challenging problem. For example, rigidly aligning multiple point sets into one common coordinate frame is a prerequisite for statistical shape modelling (SSM). Accurately aligning the pre-operative space with the intra-operative space in CAS is very crucial to successful interventions. In this article, we formally formulate the multiple generalized point set registration problem (MGPSR) in a probabilistic manner, where both the positional and the normal vectors are used. The six-dimensional vectors consisting of both positional and normal vectors are called as generalized points. In the formulated model, all the generalized PSs to be registered are considered to be the realizations of underlying unknown hybrid mixture models (HMMs). By assuming the independence of the positional and orientational vectors (i.e., the normal vectors), the probability density function (PDF) of an observed generalized point is computed as the product of Gaussian and Fisher distributions. Furthermore, to consider the anisotropic noise in surgical navigation, the positional error is assumed to obey a multi-variate Gaussian distribution. Finally, registering PSs is formulated as a maximum likelihood (ML) problem, and solved under the expectation maximization (EM) technique. By using more enriched information (i.e., the normal vectors), our algorithm is more robust to outliers. By treating all PSs equally, our algorithm does not bias towards any PS. To validate the proposed approach, extensive experiments have been conducted on surface points extracted from CT images of (i) a human femur bone model; (ii) a human pelvis bone model. Results demonstrate our algorithm's high accuracy, robustness to noise and outliers.

This note proposes an adaptive second-order sliding mode (ASOSM) controller design by means of the Lyapunov method. The notable feature of the proposed algorithm is that it only needs boundedness of the uncertainties, while boundedness of the derivatives of uncertainties is not demanded. Under the proposed ASOSM control scheme, the gain can be dynamically tuned, which avoids gain overestimation. The finite-time stability of the closed-loop ASOSM dynamics is proved via the Lyapunov theory. Finally, the simulation results are shown to validate the theoretical analysis.

The eternal vertex cover problem is a variant of the classical vertex cover problem defined in terms of an infinite attacker–defender game played on a graph. In each round of the game, the defender reconfigures guards from one vertex cover to another in response to a move by the attacker. The minimum number of guards required in any winning strategy of the defender when this game is played on a graph G is the eternal vertex cover number of G , denoted by evc ( G ) . It is known that given a graph G and an integer k , checking whether evc ( G ) ≤ k is NP-hard. Further, it is known that for any graph G , mvc ( G ) ≤ evc ( G ) ≤ 2 mvc ( G ) , where mvc ( G ) is the vertex cover number of G . Though a characterization is known for graphs for which evc ( G ) = 2 mvc ( G ) , a characterization of graphs for which evc ( G ) = mvc ( G ) remained as an open problem, since 2009. We achieve such a characterization for a class of graphs that includes chordal graphs and internally triangulated planar graphs. For biconnected chordal graphs, our characterization leads to a polynomial time algorithm for precisely determining evc ( G ) and an algorithm for determining a safe strategy for guard movement in each round of the game using only evc ( G ) guards. Though the eternal vertex cover problem is only known to be in PSPACE in general, it follows from our new characterization that the problem is in NP for locally connected graphs, a graph class which includes all biconnected internally triangulated planar graphs. We also provide reductions establishing NP-completeness of the problem for biconnected internally triangulated planar graphs. As far as we know, this is the first NP-completeness result known for the problem for any graph class.

This article addresses the spherical formation tracking control problem of nonlinear second-order vehicles moving in flowfields under both undirected networks and directed, strongly connected networks. Different from the previous adaptive estimate of the time-invariant parameters of flowfields, the flowfields under our consideration are spatial and absolutely unknown dynamics. Adaptive neural networks (ANNs) with the novel cooperative adaptive algorithms are proposed to approximate the flowfield acting on the channel of each vehicle's velocity (i.e., the mismatched flowfield) and the flowfield pushing the acceleration (i.e., the matched flowfield), respectively. For the purpose of avoiding the complex derivation derived from backstepping, the novel first-order filters are generated by dynamic surface based on barrier functions and relative positions of neighbors. The proposed control algorithms and adaptive upgrade law are fully distributed without using any global information of the graph. The uniform boundedness is analyzed in the Lyapunov sense. Simulation results are given to verify the theoretical analysis.

Mobile edge computing (MEC) is an emerging architecture for accommodating latency sensitive virtualized services (VSs). Many of these VSs are expected to be safety critical, and will have some form of reliability requirements. In order to support provisioning reliability to such VSs in MEC in an efficient and confidentiality preserving manner, in this paper we consider the joint resource dimensioning and placement problem for VSs with diverse reliability requirements, with the objective of minimizing the energy consumption. We formulate the problem as an integer programming problem, and prove that it is NP-hard. We propose a two-step approximation algorithm with bounded approximation ratio based on Lagrangian relaxation. We benchmark our algorithm against two greedy algorithms in realistic scenarios. The results show that the proposed solution is computationally efficient, scalable and can provide up to 30% reduction in energy consumption compared to greedy algorithms.

In this paper, we study the Cartesian product of signed graphs as defined by Germina, Hameed and Zaslavsky (2011). Here we focus on its algebraic properties and look at the chromatic number of some Cartesian products. One of our main results is the unicity of the prime factor decomposition of signed graphs. This leads us to present an algorithm to compute this decomposition in linear time based on a decomposition algorithm for oriented graphs by Imrich and Peterin (2018). We also study the chromatic number of a signed graph, that is the minimum order of a signed graph to which the input signed graph admits a homomorphism, of graphs with underlying graph of the form P n □ P m , of Cartesian products of signed paths, of Cartesian products of signed complete graphs and of Cartesian products of signed cycles.

The Gaussian-Bernoulli restricted Boltzmann machine (GB-RBM) is a useful generative model that captures meaningful features from the given n -dimensional continuous data. The difficulties associated with learning GB-RBM are reported extensively in earlier studies. They indicate that the training of the GB-RBM using the current standard algorithms, namely contrastive divergence (CD) and persistent contrastive divergence (PCD), needs a carefully chosen small learning rate to avoid divergence which, in turn, results in slow learning. In this work, we alleviate such difficulties by showing that the negative log-likelihood for a GB-RBM can be expressed as a difference of convex functions if we keep the variance of the conditional distribution of visible units (given hidden unit states) and the biases of the visible units, constant. Using this, we propose a stochastic difference of convex (DC) functions programming (S-DCP) algorithm for learning the GB-RBM. We present extensive empirical studies on several benchmark data sets to validate the performance of this S-DCP algorithm. It is seen that S-DCP is better than the CD and PCD algorithms in terms of speed of learning and the quality of the generative model learned.

For multimodal representation learning, traditional black-box approaches often fall short of extracting interpretable multilayer hidden structures, which contribute to visualize the connections between different modalities at multiple semantic levels. To extract interpretable multimodal latent representations and visualize the hierarchial semantic relationships between different modalities, based on deep topic models, we develop a novel multimodal Poisson gamma belief network (mPGBN) that tightly couples the observations of different modalities via imposing sparse connections between their modality-specific hidden layers. To alleviate the time-consuming Gibbs sampler adopted by traditional topic models in the testing stage, we construct a Weibull-based variational inference network (encoder) to directly map the observations to their latent representations, and further combine it with the mPGBN (decoder), resulting in a novel multimodal Weibull variational autoencoder (MWVAE), which is fast in out-of-sample prediction and can handle large-scale multimodal datasets. Qualitative evaluations on bimodal data consisting of image-text pairs show that the developed MWVAE can successfully extract expressive multimodal latent representations for downstream tasks like missing modality imputation and multimodal retrieval. Further extensive quantitative results demonstrate that both MWVAE and its supervised extension sMWVAE achieve state-of-the-art performance on various multimodal benchmarks.

Sequential recommendation aims to identify and recommend the next few items for a user that the user is most likely to purchase/review, given the user's purchase/rating trajectories. It becomes an effective tool to help users select favorite items from a variety of options. In this manuscript, we developed hybrid associations models (HAM) to generate sequential recommendations using three factors: 1) users long-term preferences, 2) sequential, high-order and low-order association patterns in the users most recent purchases/ratings, and 3) synergies among those items. HAM uses simplistic pooling to represent a set of items in the associations, and element-wise product to represent item synergies of arbitrary orders. We compared HAM models with the most recent, state-of-the-art methods on six public benchmark datasets in three different experimental settings. Our experimental results demonstrate that HAM models significantly outperform the state of the art in all the experimental settings, with an improvement as much as 46.6%. In addition, our run-time performance comparison in testing demonstrates that HAM models are much more efficient than the state-of-the-art methods, and are able to achieve significant speedup as much as 139.7 folds.

This article concentrates on the event-based collaborative design for strict-feedback systems with uncertain nonlinearities. The controller is designed based on neural network (NN) weights adaptive law. The controller and NN weights adaptive law are only updated at the triggering instants determined by a novel composite triggering threshold. Considering the conservativeness of event condition, the state-model error is integrated into constructing the composite condition and NN weights adaptive law. In the context of the proposed mechanism, the requirements of system information and the allowable range of event-triggering error are relaxed. The number of triggering instants is greatly reduced without deteriorating the system performance. Moreover, the stability of the closed-loop is proved by the Lyapunov method following time-interval and sampling instants. Simulation results show the effectiveness of the scheme proposed in this article.

This paper reveals the power and frequency oscillation mechanism of the islanded cascaded-type virtual synchronous generators (VSGs), and proposes a decentralized mutual damping suppression method. In the proposed scheme, the mutual damping term is constructed via the decentralized manner with transmission line current. It contributes to increasing damping and accelerating the frequency convergence of cascaded-type VSGs in the dynamic process. As a result, the power and frequency oscillations are restrained, and the system dynamic performance is improved. Further, the system stability based on the Lyapunov energy function method is proved. Finally, the effectiveness of the proposed decentralized mutual damping control is verified by simulations and experimental results.

This paper proposes a sliding fractional order (SFO) control strategy to provide robustness feature for integrating a multilevel converter into power grid under the system parameter uncertainties, nonlinear load alterations and grid voltage sag. All dynamics achieved from the input capacitors and output inductances of the multilevel converter are utilized to design the proposed sliding fractional surfaces (SFSs) such that a robust operation of the grid-tied converter-based system is achieved. Then, a SFS-based Lyapunov function is brought forward to assess the proposed controller stability. A thorough analysis of the Lyapunov function is carried out for distinguishing suitable boundaries of the controller coefficients when the error components of the system state variables are changed, accordingly. Using the derivative of Lyapunov function and SFS, a comprehensive evaluation is executed to detail regulation procedure for the robustness and fractional PI controller coefficients. Finally, a closed-loop system using the converter current dynamics aims to discern the differences between different values of fractional order (FO). Experimental tests using dSPACE-1202 along with MATLAB/Simulink simulations are employed to verify the effectiveness of the proposed control technique for providing proper harmonic compensation, enhanced power quality, unity power factor, voltage sag tolerance, and very low THD grid current.

Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive-to-evaluate. To tackle this challenge, Bayesian optimization, which conducts sequential design via a posterior distribution over the objective function, is a critical method used to find the global optimum of black-box functions. Kernel functions play an important role in shaping the posterior distribution of the estimated function. The widely used kernel function, e.g., radial basis function (RBF), is very vulnerable and susceptible to outliers; the existence of outliers is causing its Gaussian process surrogate model to be sporadic. In this paper, we propose a robust kernel function, Asymmetric Elastic Net Radial Basis Function (AEN-RBF). Its validity as a kernel function and computational complexity are evaluated. When compared to the baseline RBF kernel, we prove theoretically that AEN-RBF can realize smaller mean squared prediction error under mild conditions. The proposed AEN-RBF kernel function can also realize faster convergence to the global optimum. We also show that the AEN-RBF kernel function is less sensitive to outliers, and hence improves the robustness of the corresponding Bayesian optimization with Gaussian processes. Through extensive evaluations carried out on synthetic and real-world optimization problems, we show that AEN-RBF outperforms existing benchmark kernel functions.

Traditional target detection methods assume that the background spectrum is subject to the Gaussian distribution, which may only perform well under certain conditions. In addition, traditional target detection methods suffer from the problem of the unbalanced number of target and background samples. To solve these problems, this study presents a novel target detection method based on asymmetric weighted logistic metric learning (AWLML). We first construct a logistic metric-learning approach as an objective function with a positive semidefinite constraint to learn the metric matrix from a set of labeled samples. Then, an asymmetric weighted strategy is provided to emphasize the unbalance between the number of target and background samples. Finally, an accelerated proximal gradient method is applied to identify the global minimum value. Extensive experiments on three challenging hyperspectral datasets demonstrate that the proposed AWLML algorithm improves the state-of-the-art target detection performance.

In this article, the event-triggered resilient L∞ control problem is concerned for the Markov jump systems in the presence of denial-of-service (DoS) jamming attacks. First, a fixed lower bound-based event-triggering scheme (ETS) is presented in order to avoid the Zeno problem caused by exogenous disturbance. Second, when DoS jamming attacks are involved, the transmitted data are blocked and the old control input is kept by using the zero-order holder (ZOH). On the basis of this process, the effect of DoS attacks on ETS is further discussed. Next, by utilizing the state-feedback controller and multiple Lyapunov functions method, some criteria incorporating the restriction of DoS jamming attacks are proposed to guarantee the L∞ control performance of the event-triggered Markov closed-loop jump system. In particular, the bounded transition rates rather than the exact ones are taken into account. That is appropriate for the practical environment in which transition rates of the Markov process are difficult to measure accurately. Correspondingly, some criteria are proposed to obtain state-feedback gains and event-triggering parameters simultaneously. Finally, we provide two examples to show the effectiveness of the proposed method.

This article demonstrates the realization of angle tracking and deformation suppression by developing two boundary controllers for a flexible variable-length rotary crane arm with extraneous disturbances and asymmetric input-output constraints. The dynamic model description of this kind of crane arm system is several partial differential equations integrated into few ordinary differential equations. The S-curve acceleration and deceleration scheme is utilized to adjust the elongation rate of the arm. A kind of novel observer is put forward to tackle unknown extraneous disturbances. Auxiliary systems and barrier Lyapunov functions are introduced to meet the asymmetric input-output constraints. With the help of Lyapunov's theory, the global exponential stability and uniform boundedness are analyzed. The numerical simulations are finally provided to illuminate its availability of the designed control schemes.

The security and economy of multienergy systems (MESs) are directly threatened by the potential cyberattacks. It is of great importance to investigate the effects of cyberattacks, e.g., denial of service (DoS) attacks, on distributed energy management algorithms. To this end, this article focuses on exploring how the frequency and the time of duration of DoS attacks influence the behavior of Newton-Raphson-based distributed energy management (NRBDEM) algorithm for MES and in which condition the optimal operations can still be obtained. First, a switched NRBDEM algorithm is presented, which is composed of the normal operation mode and the attack mode. In the attack mode, the attackers are able to change the communication structure at will and make it unconnected to destroy the convergence of the switched NRBDEM algorithm. Then, by making use of automatons to generate the hybrid time domain, the switched NRBDEM algorithm is further modeled and formulated as a hybrid dynamical system, which provides a mathematical model for the subsequent convergence analysis. Therein, the generated hybrid time domain satisfies the average dwell-time constraint and time-ratio constraint to limit the persistent attacks. Furthermore, we analyze the restrained conditions for persistent attacks, under which the optimality and convergence of the switched NRBDEM algorithm can be guaranteed still. Finally, simulation results demonstrate the effectiveness of the proposed method.

Despite having plethora of works, wind speed time-series forecasting capabilities are prone to errors due to its intermittent and non-stationary nature as well as the limited generalization capabilities of forecasting methods for non-Gaussian distributed data. In this paper, a hybrid method that consists of elastic variational mode decomposition (eVMD) and forecasting random convolution nodes (fRCN) is proposed to forecast the Gaussian heteroscedastic wind speed time-series. The proposed eVMD algorithm gauges the non-stationary characteristics (complexity) of the wind speed signal and thereafter decomposes the signal into its intrinsic components (ICs) accordingly. The fRCN method rely on local receptive fields (LRF) to extract features that contribute to the local variations and the global trend in each IC. These features are subsequently learned using extreme learning machines (ELM) theories. An ensemble unit is employed to learn appropriate weightages for each forecasted IC before yielding the final forecasting values. Suitability of the proposed hybrid method for wind speed forecasting is evaluated via an actual wind speed dataset and comparing against various existing hybrid methods.

The state-of-the-art quadratic program-based control Lyapunov-barrier function (QP-CLBF) is a powerful control approach to balance safety and stability in an optimal fashion. However, under this approach, modeling inaccuracies may degrade the performance of closed-loop systems and cause violation or restriction of safety-critical constraints. This paper presents an adaptive QP-CLBF approach for a class of nonlinear systems in the presence of parameter uncertainties with an unknown control coefficient. We begin by presenting a filtering-based concurrent learning (FCL) adaptive technique to guarantee simultaneous exponential convergence of system parameters and control coefficient. The proposed FCL extends and encompasses the baseline CL technique, which was developed to achieve exponential convergence of either system parameters exclusively or control coefficient while relying on the estimation of state derivatives using numerical smoothing. The proposed FCL adaptive method is then unified with a modified version of QP-CLBF to achieve exponential convergence of system parameters, control coefficient, and control Lyapunov and control barrier functions while establishing

In the paper, the exponential stability of impulsive control systems with time delay is studied. By using the average impulsive interval method, some sufficient Lyapunov-based conditions are established for the stability of impulsive time-delay systems, and the impacts of delay on the stability analysis method are further revealed. It is interesting to show that some unstable impulsive time-delay systems may be stabilized by increasing the time delay in continuous dynamics. More interestingly, it is proved that along with the increase of the delay within a certain range, the convergence rate of such impulsive timedelay systems also increases correspondingly. Further, a strict comparison principle for impulsive control systems with delay is established. Then by utilizing this comparison principle, it can be shown that for some stable impulsive systems with delay, under certain conditions, the stability is robust against any large but bounded delay. Compared with the previous results on delay-free impulsive systems, some potential impacts of delay on the stability are investigated. Particularly, the obtained results are extended to the case of impulsive control systems with hybrid im

Traditional searchable encryption schemes based on the Term Frequency-Inverse Document Frequency (TF-IDF) model adopt the presence of keywords to measure the relevance of documents to queries, which ignores the latent semantic meanings that are concealed in the context. Latent Dirichlet Allocation (LDA) topic model can be utilized for modeling the semantics among texts to achieve semantic-aware multi-keyword search. However, the LDA topic model treats queries and documents from the perspective of topics, and the keywords information is ignored. In this paper, we propose a privacy-preserving searchable encryption scheme based on the LDA topic model and the query likelihood model. We extract the feature keywords from the document using the LDA-based Information Gain (IG) and Topic Frequency-Inverse Topic Frequency (TF-ITF) model. With feature keyword extraction and the query likelihood model, our scheme can achieve a more accurate semantic-aware keyword search. A special index tree is used to enhance search efficiency. The secure inner product operation is utilized to implement the privacy-preserving ranked search. The experiments on real-world datasets demonstrate the effectiveness of our scheme.

Restricted star colouring is a variant of star colouring introduced to design heuristic algorithms to estimate sparse Hessian matrices. For k ∈ N , a k -restricted star colouring ( k -rs colouring) of a graph G is a function f : V ( G ) → { 0 , 1 , … , k − 1 } such that (i) f ( x ) ≠ f ( y ) for every edge x y of G , and (ii) there is no bicoloured 3-vertex path ( P 3 ) in G with the higher colour on its middle vertex. We show that for k ≥ 3 , it is NP-complete to test whether a given planar bipartite graph of maximum degree k and arbitrarily large girth admits a k -rs colouring, and thereby answer a problem posed by Shalu and Sandhya (2016). In addition, it is NP-complete to test whether a 3-star colourable graph admits a 3-rs colouring. We also prove that for all ϵ > 0 , the optimization problem of restricted star colouring a 2-degenerate bipartite graph with the minimum number of colours is NP-hard to approximate within n 1 3 − ϵ . On the positive side, we design (i) a linear-time algorithm to test 3-rs colourability of trees, and (ii) an O ( n 3 ) -time algorithm to test 3-rs colourability of chordal graphs.

In the brief, delayed impulsive control is investigated for the synchronization of chaotic neural networks. In order to overcome the difficulty that the delays in impulsive control input can be flexible, we utilize the concept of average impulsive delay (AID). To be specific, we relax the restriction on the upper/lower bound of such delays, which is not well addressed in most existing results. Then, by using the methods of average impulsive interval (AII) and AID, we establish a Lyapunov-based relaxed condition for the synchronization of chaotic neural networks. It is shown that the time delay in impulsive control input may bring a synchronizing effect to the chaos synchronization. Furthermore, we use the method of linear matrix inequality (LMI) for designing average-delay impulsive control, in which the delays satisfy the AID condition. Finally, an illustrative example is given to show the validity of the derived results.

Given a graph G , we call a partition ( V 1 , V 2 , … , V k ) of its vertex set an induced star partition of G if each set in the partition induces a star. In this paper, we consider the problem of finding an induced star partition of a graph of minimum size and its decision versions. This problem may be viewed as an amalgamation of the well-known dominating set and coloring problems. We obtain the following main results: (1) Deciding whether a graph can be partitioned into k induced stars is NP-complete for each fixed k ≥ 3 and has a polynomial time algorithm for each k ≤ 2 . (2) It is NP-hard to approximate the minimum induced star partition size within n 1 2 − ϵ for all ϵ > 0 . (3) The decision version of the induced star partition problem is NP-complete for subcubic bipartite planar graphs, line graphs (a subclass of K 1 , r -free graphs, r ≥ 3 ), K 1 , 5 -free split graphs and co-tripartite graphs. (4) The minimum induced star partition problem has an r 2 -approximation algorithm for K 1 , r -free graphs ( r ≥ 2 ) and a 2-approximation algorithms for split graphs. We also identify some fixed parameter tractable and exact exponential time algorithms that follow from the literature.

The unified criteria are analyzed on the global dissipativity and stability for the delayed fractional-order systems of multidimension-valued memristive neural networks (FSMVMNNs) in this article. First, based on the comprehensive knowledge about multidimensional algebra, fractional derivatives, and nonsmooth analysis, we establish the unified model for the studied FSMVMNNs in order to propose a more uniform method to analyze the dynamic behaviors of multidimensional neural networks. Then, by mainly applying the Lyapunov method, employing several new lemmas, and solving some mathematical difficulties, without any separation, we acquire the unified and concise criteria. The derived criteria have many advantages in a smaller calculation, lower conservatism, more diversity, and higher flexibility. Finally, we provide two numerical examples to express the availability and improvements of the theoretical results.

The problem of computing induced subgraphs that satisfy some specified restrictions arises in various applications of graph algorithms and has been well studied. In this paper, we consider the following Balanced Connected Subgraph (shortly, BCS) problem. The input is a graph $G=(V,E)$, with each vertex in the set $V$ having an assigned color, "red" or "blue". We seek a maximum-cardinality subset $V'\subseteq V$ of vertices that is color-balanced (having exactly $|V'|/2$ red nodes and $|V'|/2$ blue nodes), such that the subgraph induced by the vertex set $V'$ in $G$ is connected. We show that the BCS problem is NP-hard, even for bipartite graphs $G$ (with red/blue color assignment not necessarily being a proper 2-coloring). Further, we consider this problem for various classes of the input graph $G$, including, e.g., planar graphs, chordal graphs, trees, split graphs, bipartite graphs with a proper red/blue $2$-coloring, and graphs with diameter $2$. For each of these classes either we prove NP-hardness or design a polynomial time algorithm., 15 pages, 3 figures

The present work aimed to investigate the electrochemical properties of ITO substrates in propylene carbonate (PC) with 0.5 mol/L lithium perchlorate (LiClO4) medium in the presence of elaborated thin films of cerium dioxide pure and doped with manganese at varying percentages Ce1–xMnxO2 (x=0 wt%, 2 wt%, 4 wt% and 6 wt%) were successfully deposited by the spray pyrolysis (SP) technique on the glass substrate and ITO at 450 °C.The effects of manganese (Mn) doping thin films Ce1–xMnxO2 were studied and investigated by using different analyses namely X-ray diffraction (XRD) analysis, Raman spectroscopy method, UV-Vis spectrophotometer technique, atomic force microscopy (AFM) analysis and electrochemical properties. XRD data obtained present a polycrystalline with a face-centred cubic structure of fluorite type. Raman results of thin films undoped and Mn doped show two peaks at 465 and 600 cm–1, this letter due to the formation of extrinsic oxygen vacancies by the incorporation of Mn rate into Ce1–xMnxO2 matrix. Energy dispersive spectroscopy (EDS) data show the presence of Ce, O, and Mn elements in the elaborated films. The AFM results reveal that the surface roughness decreases with increasing Mn rate. Further, band gap energy of thin films decreases with increasing in Mn rate due to the formation of defect state between valence and conduction band. The storage capacity of the elaborated (Ce1–xMnxO2/ITO/PC+LiClO4) electrode reaches a maximum of 1.997 mF in the presence of 6% of Mn.

This article studies the tracking control problem with a large-scale group of agents. Unlike traditional control techniques used in multiagent systems (MASs), a new type of intelligent design is needed to handle the intractable ``Curse of Dimensionality" caused by the extremely large number of agents. To address this challenge, the mean field game (MFG) theory has been embedded into reinforcement learning to advance intelligent tracking control with large-scale MAS. Specifically, MFG-based control can calculate the optimal strategy based on one unified fix-dimension probability density function (pdf) instead of high-dimensional large-scale MAS information collected from individual agents. Moreover, the approximate dynamic programming technique is adopted to generate a new type of MFG-based algorithm. Each agent has three neural networks (NNs) to approximate the solution of the mean field type control. In addition to the algorithm development, the performance of the NNs is also analyzed using the Lyapunov method. Finally, the linear and nonlinear tracking control simulations are given to evaluate the algorithm's performance.

It has been proved that the determination of independent components (ICs) in the independent component analysis (ICA) can be attributed to calculating the eigenpairs of high-order statistical tensors of the data. However, previous works can only obtain approximate solutions, which may affect the accuracy of the ICs. In addition, the number of ICs would need to be set manually. Recently, an algorithm based on semidefinite programming (SDP) has been proposed, which utilizes the first-order gradient information of the Lagrangian function and can obtain all the accurate real eigenpairs. In this article, for the first time, we introduce this into the ICA field, which tends to further improve the accuracy of the ICs. Note that the number of eigenpairs of symmetric tensors is usually larger than the number of ICs, indicating that the results directly obtained by SDP are redundant. Thus, in practice, it is necessary to introduce second-order derivative information to identify local extremum solutions. Therefore, originating from the SDP method, we present a new modified version, called modified SDP (MSDP), which incorporates the concept of the projected Hessian matrix into SDP and, thus, can intellectually exclude redundant ICs and select true ICs. Some cases that have been tested in the experiments demonstrate its effectiveness. Experiments on the image/sound blind separation and real multi/hyperspectral image also show its superiority in improving the accuracy of ICs and automatically determining the number of ICs. In addition, the results on hyperspectral simulation and real data also demonstrate that MSDP is also capable of dealing with cases, where the number of features is less than the number of ICs.

We investigate a novel anytime algorithm for wireless networked control with random dropouts. The controller computes sequences of tentative future control commands using time-varying (Markovian) computation resources. The sensor-controller and controller-actuator channel states are spatial- and time-correlated and are modeled as a multi-state Markov process. We develop a novel cycle-cost-based approach to obtain stability conditions on the nonlinear plant, controller, network and computation resources.

In this paper, the finite-time and fixed-time attractiveness problems are investigated for nonlinear impulsive systems. The aim of the proposed problems is to establish some general Lyapunov theorems and settling-time estimates for finite-time and fixed-time attractiveness of nonlinear impulsive systems by analysis technics. Moreover, some comparisons with the existing results are also given. The classical finite-time and fixed-time convergence theorems for nonlinear impulse-free systems are well extended to nonlinear impulsive systems by our results. Furthermore, the existing results of finite-time and fixed-time attractiveness for nonlinear impulsive systems are well improved. Finally, some simulations are utilized to illustrate the usefulness of the theoretical analysis.

Raman spectroscopy is commonly used to estimate peak temperatures in rocks containing organic carbon. In geological settings such as fold-thrust belts, temperature constraints are particularly important as complex burial and exhumation histories cannot easily be modelled. Many authors have developed equations to determine peak tempertaures from Raman spectral parameters, most recently to temperatures as low as 75 °C. However, recent work has shown that Raman spectra can be affected by strain as well as temperature. Fold-thrust systems are often highly deformed on multiple scales, with deformation characterised by faults and shear zones, and therefore temperatures derived from Raman spectra in these settings may be erroneous. In this study, we investigate how the four most common Raman spectral parameters and ratios change through a thrust-stacked carbonate sequence. By comparing samples from relatively low-strain localities to those on thrust planes and in shear zones, we show maximum differences of 0.16 for I[d]/I[g] and 0.11 for R2, while FWHM[d] and Raman Band Separation show no significant change between low and high strained samples. Plausible frictional heating temperatures of faulted samples suggest that the observed changes in Raman spectra are not the result of frictional heating. We apply three equations used to derive the peak temperatures from Raman spectra to our data to investigate the implications on predicted temperatures between strained and unstrained samples. All three equations produce different temperature gradients with depth in unstrained samples. We observe that individual equations exhibit apparently varying sensitivities to strain, but calculated temperatures can be up to 140 °C different for adjacent strained and unstrained samples using the same temperature equation. These results have implications for how temperatures are determined in strained rock samples from Raman spectra.

This paper proposes a Bayesian multifactor spatio-temporal model with a dynamic spatial autoregressive coefficient to estimate time-varying network interdependence with time-series cross-sectional data. To correct biases caused by unobserved time-varying homophily and common shocks with heterogeneous impact, we adopt the multifactor method to control for latent confounders and tackle the classic ``reflection problem." We use Bayesian shrinkage techniques to select latent factors. Monte Carlo studies and two empirical examples demonstrate that the multifactor specification reduces biases and improves the identification of network interdependence, and that falsely assuming a time-invariant network effect not only misses the variation of interdependence but also mis-estimates its central tendency. The proposed model is robust to misspecifcation and can accommodate various types of social networks.

In this paper, we consider the following Schrödinger equation (0.1) − Δ u − μ u | x | 2 + V ( x ) u = K ( x ) | u | 2 ∗ − 2 u + f ( x , u ) , x ∈ R N , u ∈ H 1 ( R N ) , where N ⩾ 4, 0 ⩽ μ < μ ‾, μ ‾ = ( N − 2 ) 2 4 , V is periodic in x, K and f are asymptotically periodic in x, we take advantage of the generalized Nehari manifold approach developed by Szulkin and Weth to look for the ground state solution of (0.1).

This paper presents the optimality of decay estimate of solutions to the initial value problem of 1D Schrödinger equations containing a long-range dissipative nonlinearity, i.e., λ | u | 2 u. Our aim is to obtain the two results. One asserts that, if the L 2 -norm of a global solution, with an initial datum in the weighted Sobolev space, decays at the rate more rapid than ( log t ) − 1 / 2 , then it must be a trivial solution. The other asserts that there exists a solution decaying just at the rate of ( log t ) − 1 / 2 in L 2 .

We establish short-time asymptotics with rates of convergence for the Laplace Dirichlet heat kernel in a ball. So far, such results were only known in simple cases where explicit formulae are available, i.e., for sets as half-line, interval and their products. Presented asymptotics may be considered as a complement or a generalization of the famous “principle of not feeling the boundary” in case of a ball. Following the metaphor, the principle reveals when the process does not feel the boundary, while we describe what happens when it starts feeling the boundary.

This paper studies the fuzzy adaptive output feedback control design problem for non-strict feedback multi-input multi-output (MIMO) nonlinear systems with full-states prescribed performance in finite-time. Fuzzy logic systems (FLSs) are introduced to solve the problem of unknown nonlinear dynamics. And on this basis, a fuzzy-based state observer is designed to observe the unmeasurable state. Further, by combining adaptive back-stepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which not only solves the computational complexity explosion the problem inherent in the back-stepping control algorithm, but also improves the control performance, in contrast to traditional DSC methods with linear filters. Besides, to further improve the tracking performance under the structure of full states prescribed performance, a new Lyapunov function is designed considering the transform error constraint. Based on Lyapunov theory, the stability of the closed-loop system is analyzed to ensure that all signals of the closed-loop system are semi-global practical finite-time stability (SGPFS). Finally, to elaborate on the feasibility and effectiveness of the proposed control method, a simulation example is provided.

In this second part of our work, we study the steady state of the population and the social utility for the three dynamics SSD, NBRD and NRPM; which were introduced in the first part. We provide sufficient conditions on the network based on a maximum payoff density parameter of each node under which there exists a unique Nash equilibrium. We then utilize positive correlation properties of the dynamics to reduce the flow graph in order to provide an upper bound on the steady state social utility. Finally we extend the idea behind the sufficient condition for the existence of a unique Nash equilibrium to partition the graph appropriately in order to provide a lower bound on the steady state social utility. We also illustrate interesting cases as well as our results using simulations.

A novel sliding mode control strategy is proposed to solve the trajectory tracking control problem of an offshore antenna platform, which uses a Stewart-type parallel mechanism and has a large orientation workspace. To obtain comprehensive posture parameters of the offshore antenna platform, a posture compensation algorithm using the information of azimuth and elevation is proposed. Considering known limb lengths, a state observer which based on a super-twisting algorithm is presented to obtain limb velocities. To solve the trajectory-tracking control problem of the platform, a modified nonsingular terminal integral sliding mode controller is proposed. To reduce chattering, the sliding mode controller is equipped with a higher order super-twisting algorithm. The Lyapunov theory was used to prove its stability. Simulation results on a large-orientation workspace offshore antenna platform demonstrate its superiority over three other controllers. Compared with the traditional sliding mode controller with super-twisting algorithm, the integral of the squared error of the proposed control strategy is 49.49% lower.

This article investigates the fixed-time synchronization problem of a class of delayed complex-valued inertial neural networks (CVINNs). The analysis does not rely on the traditional reduced-order transformation, but constructing Lyapunov functions directly focused on the original system. Based on the direct method and the separation method, different control strategies are proposed, under which the addressed CVINNs can achieve synchronization perfectly in a fixed time. The corresponding synchronization criteria in terms of matrix inequalities are derived, which are more concise and easier to verify than algebraic inequalities conditions, and the estimation of the settling times. The direct method makes full use of some innovative inequalities in the complex field; the exponential parameters in the designed controllers are independent. Finally, in order to fully support the theoretical results, based on two typical activation functions, the proposed theoretical results are numerically validated and compared.

We develop a theory of modular forms on the groups SO ( 3 , n + 1 ) , n ≥ 3 . This is very similar to, but simpler, than the notion of modular forms on quaternionic exceptional groups, which was initiated by Gross-Wallach and Gan-Gross-Savin. We prove the results analogous to those of earlier papers of the author on modular forms on exceptional groups, except now in the familiar setting of classical groups. Moreover, in the setting of SO ( 3 , n + 1 ) , there is a family of absolutely convergent Eisenstein series, which are modular forms. We prove that these Eisenstein series have algebraic Fourier coefficients, like the classical holomorphic Eisenstein series on SO ( 2 , n ) . As an application, using a local result of Savin, we prove that the so-called “next-to-minimal” modular form on quaternionic E 8 has rational Fourier expansion.

To realize the three-dimensional stabilization control of fixed-wing unmanned aerial vehicles (UAVs), we analyze the nonholonomic characteristics, constraint non-integrability, and controllability of UAVs. To simplify the trigonometric function term in the dynamics of the UAV and avoid the singularity problem of the Euler angle in describing attitude, we use the quaternion theory to transform the dynamics of the UAV to avoid the complex trigonometric function derivation, which makes the dynamic matrix more concise. Based on this, a continuous periodic time-varying controller (CPTVC) is designed, and the effectiveness of the controller is proved using the homogeneous method. Finally, the results of the hardware in a loop simulation indicated that the exponential stability provided by the feedback controller can realize the three-dimensional stabilization of any initial position.

A large number of experiments have proved that the ring structure is a common phenomenon in neural networks. Nevertheless, a few works have been devoted to studying the neurodynamics of networks with only one ring. Little is known about the dynamics of neural networks with multiple rings. Consequently, the study of neural networks with multiring structure is of more practical significance. In this article, a class of high-dimensional neural networks with three rings and multiple delays is proposed. Such network has an asymmetric structure, which entails that each ring has a different number of neurons. Simultaneously, three rings share a common node. Selecting the time delay as the bifurcation parameter, the stability switches are ascertained and the sufficient condition of Hopf bifurcation is derived. It is further revealed that both the number of neurons in the ring and the total number of neurons have obvious influences on the stability and bifurcation of the neural network. Ultimately, some numerical simulations are given to illustrate our qualitative results and to underpin the discussion.

Nonconvex Stochastic Optimization Nonconvex stochastic optimization problems arise in many machine learning problems, including deep learning. The stochastic gradient Hamiltonian Monte Carlo (SGHMC) is a variant of stochastic gradients with a momentum method in which a controlled and properly scaled Gaussian noise is added to the stochastic gradients to steer the iterates toward a global minimum. SGHMC has shown empirical success in practice for solving nonconvex stochastic optimization problems. In “Global convergence of stochastic gradient Hamiltonian Monte Carlo for nonconvex stochastic optimization: Nonasymptotic performance bounds and momentum-based acceleration,” Gao, Gürbüzbalaban, and Zhu provide, for the first time, the finite-time performance bounds for the global convergence of SGHMC in the context of both population and empirical risk minimization problems and show that acceleration with momentum is possible in the context of global nonconvex stochastic optimization.

Inferring gene co-expression networks from high-throughput gene expression data is an important task in bioinformatics. Many gene networks often exhibit modular structures. Even though several Gaussian graphical model-based methods have been developed to estimate gene co-expression networks by incorporating the modular structural prior, none of them takes into account the modular structures captured by the prior networks (e.g., protein interaction networks). In this study, we propose a novel prior network-dependent gene network inference (pGNI) method to estimate gene co-expression networks by integrating gene expression data and prior protein interaction network data. The underlying modular structure is learned from both sets of data. Through simulation studies, we demonstrate the feasibility and effectiveness of our method. We also apply our method to two real datasets. The modular structures in the networks estimated by our method are biological significant.

In this article, the stabilization problem of discrete-time power systems subject to random abrupt changes is studied via asynchronous control. In this regard, the transient faults in the power lines, and subsequent switching of associated circuit breakers are modeled as a Markov chain. Based on this, the power systems are described as discrete-time Markov jump systems. The focus is mainly to design the control for Markov jump-based power systems (MJPSs) when modes of the control asynchronously run with the modes of power systems. To do this, a hidden Markov model technique is used to characterize the nonsynchronization between the control and system. By constructing the mode-dependent stochastic Lyapunov function, the sufficient conditions are acquired in the form of linear matrix inequalities (LMIs), which ensure not only the stochastic stability of the resulting hidden MJPSs but also the existence of the desired control. Finally, the simulation example reveals the efficiency of the designed control law.