With the development of intelligent technology, the problem of LiDAR-based localization has played an increasingly important role in the localization of robots in unmanned systems. Since the dense point clouds from the environment requires a large amount of memory, specific and stable structural features, such as pole-like objects in the environment, can serve as the ideal landmarks for localization in unmanned systems, which can effectively reduce the memory usage and mitigate the effects of dynamic environment changes. In this paper, we propose a pole-like objects extraction approach and then, it is applied into the localization system of mobile robots. Under the same experimental conditions, our method can extract more pole-like objects and achieve better long-term localization accuracy than some existing methods in different urban environmental datasets.

This paper investigates a new resource-allocation problem involving multi-resource operations, where completing an operation requires simultaneous use of multiple (renewable) resources, probably of different types. The goal of the study is to provide a solution method that minimizes the makespan. We formulate the problem into a novel mixed-integer linear program (MILP) model. To efficiently solve practical-sized instances, an exact Benders decomposition algorithm is developed. This algorithm divides the original problem into a master problem of allocating resources and a subproblem of calculating the makespan, and both are linked via Benders cuts. The convergence is sped up by improving the mathematical model and embedding the variable neighborhood search algorithm. Compared with CPLEX, a commonly used MILP solver, the computational results demonstrate that the proposed algorithm provides tighter upper and lower bounds in most instances. In particular, compared with CPLEX, the proposed method can on average improve the upper and lower bounds by 4.76% and 4.39%, respectively, in solving practical-sized instances.

In this article, we propose an adaptive Barrier-Lyapunov-Functions (BLFs) based control scheme for nonlinear pure-feedback systems with full state constraints. Due to the coexist of the non-affine structure and full state constraints, it is very difficult to construct a desired controller for the considered system. According to the mean value theorem, we transform the pure-feedback system into a system with strict-feedback structure, so that the well-known backstepping method can be applied. Then, in the backstepping design process, the BLFs are employed to avoid the violation of the state constraints, and neural networks (NNs) are directly used to online approximate the unknown packaged nonlinear terms. The presented controller ensures that all the signals in the closed-loop system are bounded and the tracking error asymptotically converges to zero. Meanwhile, it is shown that the constraint requirement on the system will not be violated during the operation. Finally, two simulation examples are provided to show the effectiveness of the proposed control scheme.

This paper designs an incentive Stackelberg strategy for the discrete-time stochastic systems with mean-field terms. Sufficient conditions for the existence of such a design are suggested. Moreover, the incentive strategy is obtained as a feedback form including the deviation of the state and its mathematical expectation. Also, the stability analysis is involved. It is found that the stability can be guaranteed by the follower. In addition, the specific algorithm is proposed and its effectiveness is checked by two examples.

In this paper, we consider the stabilization and blow up of the wave equation with infinite memory, logarithmic nonlinearity and acoustic boundary conditions. We discuss the existence of global solutions for the initial energy less than the depth of the potential well and investigate the energy decay estimates by introducing a Lyapunov function. Moreover, we establish the finite time blow up results of solutions and give the blow up time with upper bounded initial energy.

This paper focuses on linear-quadratic (LQ) optimal control for a class of systems governed by first-order hyperbolic partial differential equations (PDEs). Different from most of the previous works, an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems. The contributions of this paper consist of the following aspects: 1) The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method. 2) A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed. Meanwhile, the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations (FBPDEs). 3) The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented. It is shown that our results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case, but also support the existing operator results and give a more convenient form of computation.

In recent years, Kriging model has gained wide popularity in various fields such as space geology, econometrics, and computer experiments. As a result, research on this model has proliferated. In this paper, we propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method, with consideration for the model uncertainty. We present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method. First, the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction risk. Second, the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models. The effectiveness of the proposed method is verified through numerical analyses.

Negative binomial regression is a powerful technique for modeling count data, particularly when dealing with overdispersion. However, estimating the parameters for large-dimensional sparse models is challenging due to the complexity of optimizing the mean and variance parameters of the negative binomial distribution. To address this issue, we propose a novel approach that employs two iterations of the majorize-minimize (MM) algorithm, one for estimating the variance parameter and the other for estimating the mean parameters. These approaches improve the convergence speed and stability of the algorithm. We also use group penalty for variable selection, which enhances the accuracy and efficiency of the algorithm. Our method provides an explicit solution, simplifies the iteration process, and maintains good stability while ensuring algorithm convergence. Furthermore, we apply the proposed algorithm to the zero-inflated model and demonstrate its promising predictive performance on specific data sets. Our research has important implications for count data modeling and analysis in various fields, such as data mining, machine learning, and bioinformatics.

In this paper, the problem of identifying autoregressive-moving-average (ARMA) systems under random threshold binary-valued output measurements is considered. With the help of stochastic approximation algorithms with expanding truncations (SAAWET), we give the recursive estimates for the parameters of both the linear system and the binary sensor. Under reasonable conditions, all constructed estimates are proved to be convergent to the true values with probability one. A simulation example is provided to justify the theoretical results

In recent years, automatic search has been widely used to search differential characteristics and linear approximations with high probability/correlation in symmetric-key cryptanalyses. Among these methods, the automatic search with the Boolean Satisfiability Problem (SAT, in short) gradually becomes a powerful cryptanalysis tool. A key problem in the SAT-based automatic search method is how to fully characterize a set $S \subseteq \{0,1\}^n$ with as few Conjunctive Normal Form (CNF, in short) clauses as possible, which is called a full CNF characterization (FCC, in short) problem. In this work, we establish a complete theory to solve a best solution of a FCC problem. Specifically, we start from plain sets, which can be characterized by exactly one clause. By exploring mergeable sets, we give a sufficient and necessary condition for characterizing a plain set. Based on the properties of plain sets, we further provide an algorithm of solving a FCC problem for a given set $S$, which can generate all the minimal plain closures of $S$ and produce a best FCC theoretically. As application, we apply our algorithm to many common S-boxes used in block ciphers to characterize their differential distribution tables and linear approximation tables and get their FCCs, all of which are the best-known results at present.

This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model. A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectation under the null model. The proposed test statistic has an asymptotic standard normal distribution under the null hypothesis, and tends to infinity in probability under the alternative hypothesis, which implies the consistency of the test. Furthermore, it is proved that the test statistic converges to a normal distribution with nonzero mean under a local alternative hypothesis. Extensive simulations are reported, and the results show that the proposed test has proper sizes and is sensitive to the considered model discrepancies. The proposed methods are also applied to two real datasets.

Fully homomorphic encryption (FHE) can be used for privacy-preserving aggregation of medical data. In this typical application, the security against passive attacks has been well studied by Li and Micciancio (EUROCRYPT' 21). In this paper, we further consider a "nearly passive" kind of attack, where the attacker may behave like a passive attacker in the view of the third-party server. To capture the security against this hard-to-detect attack, we propose a new notion of IND-CPA$^{rD}$ security. We show that the standard LWE encryption and its related FHE schemes can not defend against IND-CPA$^{rD}$ attack, even under a stricter rule limiting the content and number of queries made by the attacker. To make the application of FHE schemes more secure, we discuss some possible modifications that may serve as countermeasures to IND-CPA$^{rD}$ attack.

In recent years, there has been a growing focus on high-reliability products in industrial and military fields. Storage plays a crucial role in these products, and as a result, research on storage reliability has gained more attention. This paper specifically targets a class of products with complex structures that require long-term storage, regular testing, and maintenance. Firstly, an expression method for system availability is provided based on the reliability structure of the system and the maintenance situation of the constituent equipment in storage. Since the expression of system availability is typically complex and difficult to compute, and the storage life of the system cannot be represented as an explicit function of the reliability indicators of the constituent equipment, it is challenging to evaluate the availability and storage life of repairable systems. To address this, the article proposes a comprehensive evaluation methodology for assessing the storage reliability of complex repairable systems based on Fiducial inference. This approach is employed to derive point estimates and determine the lower Fiducial limits for both system availability and storage life. Furthermore, simulation results demonstrate that this comprehensive evaluation method for storage reliability of complex repairable systems is not only convenient but also highly effective.

In this work, an $H_{\infty}$/passive-based secure synchronization control problem is investigated for continuous-time semi-Markov neural networks subject to hybrid attacks, in which hybrid attacks are the combinations of denial-of-service attacks and deception attacks, and they are described by two groups of independent Bernoulli distributions. On this foundation, via the Lyapunov stability theory and linear matrix inequality technology, the $H_{\infty}$/passive-based performance criteria for semi-Markov jump neural networks are obtained. Additionally, an activation function division approach for neural networks is adopted to further reduce the conservatism of the criteria. Finally, a simulation example is provided to verify the validity and feasibility of the proposed method.

This paper presents a new study on modeling and optimization of trajectory and posture for the super-giant (SG) slalom of alpine skiing. It is the first time that a Three-Rigid-Body-Particle model based on rigorous derivations and stability analysis is established to represent skiers’ trajectory and posture characteristics, as it is more accurate than the single-rigid-body model which is commonly used in existing studies. In addition, the Radau pseudospectral method is applied to solve the trajectory and posture optimization problem in order to obtain better skiing trajectory, skiing posture, and some key kinematic parameters of skiers. Moreover, this paper analyzes the effects of different body types, minimum turning radii, and flexor and extensor strength of knees and hip joint on skiing performance. Finally, based on the findings of the study, some advice about how to improve the performance of the SG slalom in view of science and technology is given to skiers and coaches for reference.

In the past two decades, model averaging, as a way to solve model uncertainty, has attracted more and more attention. In this paper, we propose a jackknife model averaging (JMA) method for the quantile single-index coefficient model, which is widely used in statistics. Under model misspecification, the model averaging estimator is proved to be asymptotically optimal in terms of minimizing out-ofsample quantile loss. Simulation experiments are conducted to compare the JMA method with several model selection and model averaging methods, and the results show that our method has a satisfactory performance. Our method is also applied to a real dataset.

This paper focuses on a Pareto cooperative differential game with a linear mean-field backward stochastic system and a quadratic form cost functional. Based on a weighted sum optimality method, the Pareto game is equivalently converted to an optimal control problem. In the first place, the feedback form of Pareto optimal strategy is derived by virtue of decoupling technology, which is represented by four Riccati equations, a mean-field forward stochastic differential equation (MF-FSDE), and a mean-field backward stochastic differential equation (MF-BSDE). In addition, the corresponding Pareto optimal solution is further obtained. Finally, we solve a problem in mathematical finance to illustrate the application of the theoretical results.

This paper is concerned with nonzero-sum discrete-time stochastic games in Borel state and action spaces under the expected discounted payoff criterion. The payoff function can be unbounded. The transition probability is a convex combination of finite probability measures that are dominated by a probability measure on the state space and depend on the state variable. Under suitable conditions, we establish the existence of stationary almost Markov ε-equilibria and give an approximation method via some stochastic games with bounded payoffs. Finally, a production game is introduced to illustrate the applications of the main result, which generalizes the bounded payoff case.

The scheduling problem in surgery is difficult because, in addition of the planning of the operating rooms which are the most expensive resources in hospitals, each surgery requires a combination of human and material resources. In this paper, we address a surgery scheduling problem which arises in operated health care facility. Moreover, we consider simultaneously materiel and human resources. This problem is a three-stages flow shop scheduling environment. The first stage (ward) contains a limited number of resources of the same type (beds); the second stage contains different resources with limited capacity (operating rooms, surgeons, nurses, anesthesiologists) and the third stage contains a limited number of recovery beds. There is also a limited number of transporters (porters) between the ward and the other stages. The objective of the problem is to minimize the completion time of the last patient (makespan). We formulate this NP-Hard problem in a mixed integer programming model and we conduct computational experiments to evaluate the performance of the proposed model.

Random sampling algorithm was proposed firstly by Schnorr in 2003 to find short lattice vectors, as an alternative to enumeration. The follow-up developments in random sampling were mainly proposed by Fukase and Kashiwabara in 2015 and Aono and Nguyen in 2017. Although they extended the sampling space compared to Schnorr’s work through the natural number representation, they did not show how to sample specifically in practice and what vectors should be sampled, in order to find short enough lattice vectors. In this paper, the authors firstly introduce a practical random sampling algorithm under some reasonable assumptions which can find short enough lattice vectors efficiently. Then, as an application of this new random sampling algorithm, the authors show that it can improve the performance of progressive BKZ algorithm in practice. Finally, the authors solve the Darmstadt’s Lattice Challenge and get a series of new records in the dimension from 500 to 825, using the improved progressive BKZ algorithm.

Surface/surface intersection is a fundamental problem in Compute Aided Design and Geometric Modeling since it is essential to solid modeling, numerically controlled machining, feature recognition, computer animation, etc. In this paper, a robust algorithm is proposed for computing the intersection curve segments of two trimmed quadrics based on the parametric representation of the intersection curves of two quadrics. Our algorithm guarantees correct topology and ensures that the approximation errors of the end points of the intersection curve segments are less than a given tolerance. The error control is based on an effective solution to a set of polynomial inequality system using the root isolation technique. Some examples are presented to validate the robustness and effectiveness of our algorithm.

This work investigates the input-to-state stability (ISS) problem for impulsive switched singular systems (ISSSs) with mismatched disturbances. In this paper, ‘disturbance’ is a general concept that includes model uncertainty, unknown system dynamic, external disturbance, etc. The modified uncertainty and disturbance estimator (UDE)-based control method is presented for singular systems and ISSSs, a virtual control is introduced to offset the effects of mismatched disturbances. On the basis of a discontinuous multiple Lyapunov functional and admissible edge-dependent average dwell time (AED-ADT) method, several sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained to ensure that the closed-loop systems are regular, impulse-free and ISS. Finally, two examples are given to demonstrate the effectiveness of the proposed results.

This study investigates the robust feedback set stabilization of switched logic control networks (SLCNs) with state-dependent uncertain switching and control constraints. First, based on the properties of the semi-tensor product of matrices and the vector representation of logic, an SLCN with state-dependent uncertain switching and control constraints is expressed in algebraic form. Second, an input transformation and a switching model are constructed to transfer the original SLCN into one with a free control input and arbitrary switching. The equivalence between the set stabilizability of the original SLCN and that of the resulting SLCN is established. Based on such equivalence, we propose a necessary and sufficient condition for robust feedback set stabilizability. Finally, an example is presented to demonstrate the application of the results obtained.

Accurately predicting stock returns is a conundrum in financial market. Solving this conundrum can bring huge economic benefits for investors and also attract the attention of all circles of people. In this paper we combine semi-varying coefficient model with technical analysis and statistical learning, and propose semi-varying coefficient panel data model with individual effects to explore the dynamic relations between the stock returns from five companies: CVX, DFS, EMN, LYB and MET and five technical indicators: CCI, EMV, MOM, ATR, RSI as well as closing price (CP), combine semiparametric fixed effect estimator, semi-parametric random effect estimator with the testing procedure to distinguish fixed effects (FE) from random effects (RE), and finally apply the estimated dynamic relations and the testing set to predict stock returns in December 2020 for the five companies. The proposed method can accommodate the varying relationship and the interactive relationship between the different technical indicators, and further enhance the prediction accuracy to stock returns.

Wan and Zhang have recently obtained a nontrivial lower bound for the number of zeros of complete symmetric polynomials over finite fields, and proposed a problem whether their bound can be improved. In this paper, we improve Wan-Zhang’s bound from three aspects. Our results are based on the estimates related to the number of certain permutations and the value sets of non-permutation polynomials associated to the complete symmetric polynomial. And we believe that there are still possibilities to improve our bounds and hence Wan-Zhang’s bound.

The semi-tensor product (STP) of matrices is generalized to multidimensional arrays, called the compound product of hypermatrices. The product is first defined for three-dimensional hypermatrices with compatible orders and then extended to general cases. Three different types of hyperdeterminants are introduced and certain properties are revealed. The Lie groups and Lie algebras corresponding to the hypermatrix products are constructed. Finally, these results are applied to dynamical systems.

Micro triadic structure is an important motif and is the building block of complex networks. In this paper, we define structure entropy for a social network and explain this concept by using the coded triads proposed by Holland and Leinhardt. The proposed structure entropy serves as a new macro-evolution index to measure the networks stability at a given timestamp. Empirical analysis of real-world network structure entropy discloses rich information on the mechanism that yields given triadic motifs frequency distribution. This paper illustrates the intrinsic link between the micro dyadic/triadic motifs and network structure entropy. Importantly, we find that the high proportion of reciprocity and transitivity results in the emergence of hierarchy, order, and cooperation of online social networks.

Existing research has shown that political crisis events can directly impact the tourism industry. However, the current methods suffer from potential changes of unobserved variables, which poses challenges for a reliable evaluation of the political crisis impacts. This paper proposes a panel counterfactual approach with Internet search index, which can quantitatively capture the change of crisis impacts across time and disentangle the effect of the event of interest from the rest. It also provides a tool to examine potential channels through which the crisis may affect tourist outflows. This research empirically applies the framework to analyzing the THAAD event on tourist flows from mainland China to South Korea. Findings highlight the strong and negative short-term impact of the political crisis on the tourists’ intentions to visit a place. This paper provides essential evidence to help decision-makers improve the management of the tourism crisis.

Influenced by the global economy, politics, energy and other factors, the price of carbon market fluctuates sharply. It is of great practical significance to explore a suitable measurement method of extreme risk of carbon market. Considering that the return series of carbon market has the characteristics of leptokurtosis, fat tail, skewness and multifractal, and there maybe many extreme risk values in the carbon market, this paper introduces the Skewed-t distribution which can describe the characteristics of leptokurtosis, fat tail and skewness of return series into MSM model which can describe multifractal characteristic of return series to model volatility of carbon market. On the basis, based on the extreme value theory, this paper constructs Skewed-t-MSM-EVT model to measure extreme risk of carbon market. This paper chooses EUA market as the object to study extreme risk of carbon market, and draws the following conclusions: Skewed-t-MSM-EVT model has significantly higher prediction accuracy for carbon market’s VaR than MSM-EVT models under other distributions (including normal distribution, t distribution, GED distribution); Skewed-t-MSM-EVT model is superior to traditional Skewed-t-FIGARCH-EVT and Skewed-t-GARCH-EVT models in predicting carbon market’s VaR. This research has important practical significance for accurately grasping the risk of carbon market and promoting energy conservation and emission reduction.

Given a $k\times n$ integer primitive matrix A (i.e., a matrix can be extended to an $n\times n$ unimodular matrix over the integers) with the maximal absolute value of entries ||A|| bounded by an integer $\lambda$ from above, we study the probability that the $m\times n$ matrix extended from A by appending other $m-k$ row vectors of dimension $n$ with entries chosen randomly and independently from the uniform distribution over $\{0,1,...,{\lambda-1}\}$ is still primitive. We present a complete and rigorous proof of a lower bound on the probability, which is at least a constant for fixed $m$ in the range $[k+1, n-4]$. As an application, we prove that there exists a fast Las Vegas algorithm that completes a $k\times n$ primitive matrix A to an $n\times n$ unimodular matrix within expected Õ(n^wlog ||A||) bit operations, where Õ is big-$O$ but without log factors, $\omega$ is the exponent on the arithmetic operations of matrix multiplication.

In this paper, we propose a frequentist model averaging method for composite quantile regression with diverging number of parameters. Different from the traditional model averaging for quantile regression which considers only a single quantile, our proposed model averaging estimator is based on multiple quantiles. The well-known delete-one cross-validation or jackknife approach is applied to estimate the model weights. The resultant jackknife model averaging estimator is shown to be asymptotically optimal in terms of minimizing the out-of-sample composite final prediction error. Simulation studies are conducted to demonstrate the finite sample performance of our new model averaging estimator. The proposed method is also applied to the analysis of the stock returns data and the wage data.

A cooperative game theoretical approach is taken to production and transportation coordinated scheduling problems of two-machine flow-shop (TFS-PTCS problems) with an interstage transporter. We assume that there is an initial scheduling order for processing jobs on the machines. The cooperative sequencing game models associated with TFS-PTCS problems are established with jobs as players and the maximal cost savings of a coalition as its value. The properties of cooperative games under two different types of admissible rearrangements are analysed. For TFS-PTCS problems with identical processing time, it is proved that, the corresponding games are σ₀-component additive and convex under one admissible rearrangement. The Shapley value gives a core allocation, and is provided in a computable form. Under the other admissible rearrangement, the games neither need to be σ₀-component additive nor convex, and an allocation rule of modified Shapley value is designed. The properties of the cooperative games are analysed by a counterexample for general problems.

Elliptic curve cryptography is an important part of nowaday's public key cryptosystem. Counting points of elliptic curves over finite fields is of great significance to the selection of safety curves. At present, there are many $p$-adic algorithms, such as SST algorithm, generalized AGM algorithm, Kedlaya algorithm, etc., which can deal with the situation of finite fields of small characteristics. In this paper, we generalize the MSST algorithm of characteristic 2 to general fields of odd characteristic, and propose the generalized MSST algorithm. The generalized MSST algorithm is achieved by combining the advantages of the SST algorithm and the generalized AGM algorithm. If the time complexity of the multiplication of two $n$-bit numbers is denoted as $O(n^{\mu})$, then} the time complexity of the generalized MSST algorithm is $O(n^{2\mu+\frac{1}{1+\mu}})$, which is the same as the improved SST algorithm. In practical experiments, the running time of the generalized MSST algorithm is less than that of the improved SST algorithm.

This paper focuses on the disturbance suppression issue of hidden semi-Markov jump systems leveraging composite control. The system consists of a semi-Markov layer and an observed mode sequence layer, and it is subject to a matched disturbance generated by an exogenous system and a mismatched disturbance that is norm bounded. The proposal is to design a composite controller based on a disturbance observer to counteract and attenuate the disturbances effectively. By constructing a special Lyapunov function comparison point, the exponential stability is analyzed with the stability criterion in the form of linear matrix inequality is established. Two simulation examples are provided to demonstrate the practical merits of the composite controller relative to the single H_∞ control.

The theory of uniform design has received increasing interest because of its wide application in the field of computer experiments. The generalized discrete discrepancy is proposed to evaluate the uniformity of the mixed-level factorial design. In this paper, we give a lower bound of the generalized discrete discrepancy and provide some construction methods of optimal mixed-level uniform designs which can achieve this lower bound. These methods are all deterministic construction methods which can avoid the complexity of stochastic algorithms. Both saturated mixed-level uniform designs and supersaturated mixed-level uniform designs can be obtained with these methods. Moreover, the resulting designs are also χ²-optimal and minimum moment aberration designs.

This paper is devoted to stabilizing the high-order uncertain nonlinear system in a fixed time by output feedback control. First, a novel settling time solution method is proposed by establishing an indirect double system and using the comparison principle. Then a fixed-time observer and a neural networked based adaptive law are constructed to estimate the state and the unknown disturbance for the high-order uncertain nonlinear system. Furthermore, a fixed-time output feedback controller is proposed via the homogeneity technique. The upper bound of the settling time is analyzed for the closed-loop system under the proposed output feedback control. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.

In our paper, a theoretical model is developed on the basis of systems theory, which structures the livelihood system of low-income households in a European country characterized by a semi-peripheral economy. Based on our model, the complex system of network connections and formal and informal financial transactions, which households use in their daily lives to cover their expenses, becomes graspable. Our theoretical model is analysed through simulations based on agentbased modelling (ABM) centred on empirical network data. Through the simulations, we explore the mechanisms of the market and ask what formal and informal credit transactions determine its operation, how these factors shape the local social structure and how resilient the market is to crises. Our results show that this dynamic, complex risk-sharing system has an inherent logic and it can mitigate the small liquidity shocks but it is not resistant to bigger financial shocks or overconsumptions.

This paper studies customer joining behavior and system regulation strategy in nonexhaustive visible M/M/m queues with synchronous vacations of a part of the servers. Once this part of the servers are idle, they take multiple vacations simultaneously (vacation period). Until there are customers waiting in the queue, they are reactivated and all servers are busy or idle (busy period). We call this part of the servers as “partial servers”. In view of the fully visible queue and the almost visible queue, we obtain customers’ equilibrium joining threshold strategies and their socially optimal joining threshold strategies, respectively, and observe that customer joining behavior in equilibrium generally makes the system overcrowded, which makes the equilibrium social welfare lower than the optimal social welfare. After regulation, interestingly, for optimizing social welfare, the system manager hopes not only customers arriving in vacation period pay attention to the number of partial servers, but also customers arriving in busy period should care about it rather than ignore. Moreover, arranging more servers for vacation does not necessarily lead to the decrease of social welfare on condition that the number of partial servers is close to m. As for the information advantage of the fully visible case, it is not obvious for increasing social welfare and even unfavorable to servers’ profit unless the number of partial servers is great enough. Furthermore, given the different composition of social welfare, there exists the optimal number of partial servers and the optimal arrival rate of customers for maximizing social welfare.

This paper studies the cluster consensus of multi-agent systems (MASs) with objective optimization on directed and detail balanced networks, in which the global optimization objective function is a linear combination of local objective functions of all agents. Firstly, a directed and detail balanced network is constructed that depends on the weights of the global objective function, and two kinds of novel continuous-time optimization algorithms are proposed based on time-invariant and timevarying objective functions. Secondly, by using fixed-time stability theory and convex optimization theory, some sufficient conditions are obtained to ensure that all agents’ states reach cluster consensus within a fixed-time, and asymptotically converge to the optimal solution of the global objective function. Finally, two examples are presented to show the efficacy of the theoretical results.

Curve interpolation with B-spline is widely used in various areas. This problem is classic and recently raised in application scenario with new requirements such as path planning following the tangential vector field under certified error in CNC machining. This paper proposes an algorithm framework to solve Hausdorff distance certified cubic B-spline interpolation problem with or without tangential direction constraints. The algorithm has two stages: the first stage is to find the initial cubic B-spine fitting curve which satisfies the Hausdorff distance constraint; the second stage is to set up and solve the optimization models with certain constraints. Especially, the sufficient conditions of the global Hausdorff distance control for any error bound are discussed, which can be expressed as a series of linear and quadratic constraints. A simple numerical algorithm to compute the Hausdorff distance between a polyline and its B-spline interpolation curve is proposed to reduce our computation. Experimental results are presented to show the advantages of our algorithms.