Problem-based Learning Combining Seminar Teaching Method for the Practice of Mathematical Modeling Course's Teaching Reform for Computer Discipline

Mathematical modeling course has been one of the fast development courses in China since 1992,which mainly trains students’innovation ability.However,the teaching of mathematical modeling course is quite difficult since it requires students to have a strong mathematical foundation,good ability to design algorithms,and programming skills.Besides,limited class hours and lack of interest in learning are the other reasons.To address these problems,according to the outcome-based education,we adopt the problem-based learning combined with a seminar mode in teaching.We customize cases related to computer and software engineering,start from simple problems in daily life,step by step deepen the difficulty,and finally refer to the professional application in computer and software engineering.Also,we focus on ability training rather than mathematical theory or programming language learning.Initially,we prepare the problem,related mathematic theory,and core code for students.Furtherly,we train them how to find the problem,and how to search the related mathematic theory and software tools by references for modeling and analysis.Moreover,we solve the problem of limited class hours by constructing an online resource learning library.After a semester of practical teaching,it has been shown that the interest and learning effectiveness of students have been increased and our reform plan has achieved good results.

Regional spatiotemporal variations of a nondipole magnetic field over the Chinese mainland and neighboring regions in millennial scale

Spatiotemporal variations of the nondipole （ND） magnetic field over the Chinese mainland and neighboring regions from 10000 BC to 1990 AD were analyzed using the latest global geomagnetic models CALS10K.1b, CALS3K.4, and IGRF 11. Moreover, for field sources, we investigated 2 n （n = 2 -10） pole ND fields and their energies. The results suggest that the study period can be divided into three. The intensity of the ND field has been mainly positive since 10000 BC and lasted almost 7500 years, then gradually decreased to negative in 2500 BC to 1500 AD, and finally sharply increased to positive. The anomaly areas of the ND field in East Asia took shape for n - 3, when the anomaly areas in East Asia were shaped into closed circles in the mainland. This suggests that the first three harmonic degrees account for most of the ND field. The energy of the ND field rapidly attenuates at the core mantle boundary and is stable at the surface.

Modeling of CHAMP satellite data according to the 3D surface spline model of geomagnetic fi elds

Surface observations and CHAMP measurement data are employed to develop a three-dimensional surface spline(3DSS)model of China's Mainland.The magnetic field distribution at the satellite level is then demonstrated using the model obtained.The results of this model are compared and verifi ed by deriving the corresponding two(2DTY)and threedimensional(3DTY)Taylor polynomial models.Issues such as the removal of disruptive geomagnetic fi elds,the data gap between the surface and satellite levels,and boundary eff ects are carefully considered during modeling.We then focus on evaluating the modeling eff ect of the satellite data.Ten satellite points not involved in the modeling procedure are selected,and the residuals,absolute change rates,and RMSEs of these points are calculated.Results show that the distribution of the magnetic fi eld determined by the 3DSS model is highly consistent with that obtained from the IGRF12 model.Expect for component Y,the absolute change rates of other components are less than 0.5%.Specifi cally,the RMSE of Y of 3DSS is nearly 60%lower than those of 3DTY and 2DTY;the RMSE of other components of the former are also over 90%lower than those of the latter.This fi nding implies that the 3DSS model has good performance for modeling satellite data and its results are reliable.Moreover,the modeling eff ect of 3DTY is better than that of 2DTY.

On the Convergence of Monotone Lattice Matrices

Since lattice matrices are useful tools in various domains like automata theory, design of switching circuits, logic of binary relations, medical diagnosis, markov chains, computer network, traffic control and so on, the study of the properties of lattice matrices is valuable. A lattice matrix A is called monotone if A is transitive or A is monotone increasing. In this paper, the convergence of monotone matrices is studied. The results obtained here develop the corresponding ones on lattice matrices shown in the references.

A Game Theoretic Approach for a Minimal Secure Dominating Set

The secure dominating set(SDS),a variant of the dominating set,is an important combinatorial structure used in wireless networks.In this paper,we apply algorithmic game theory to study the minimum secure dominating set(Min SDS) problem in a multi-agent system.We design a game framework for SDS and show that every Nash equilibrium(NE) is a minimal SDS,which is also a Pareto-optimal solution.We prove that the proposed game is an exact potential game,and thus NE exists,and design a polynomial-time distributed local algorithm which converges to an NE in O(n) rounds of interactions.Extensive experiments are done to test the performance of our algorithm,and some interesting phenomena are witnessed.

Spherical cap harmonic analysis of regional magnetic anomalies based on CHAMP satellite data

We used CHAMP satellite vector data and the latest IGRF12 model to investigate the regional magnetic anomalies over China's Mainland. We assumed satellite points on the same surface （307.69 km） and constructed a spherical cap harmonic model of the satellite magnetic anomalies for elements X, Y, Z, and F over Chinese mainland for 2010.0 （SCH2010） based on selected 498 points. We removed the external field by using the CM4 model. The pole of the spherical cap is 36N° and 104°E, and its half-angle is 30°. After checking and comparing the root mean square （RMS） error of AX, AY, and AZ and X, Y, and Z, we established the truncation level at Kmax = 9. The results suggest that the created China Geomagnetic Referenced Field at the satellite level （CGRF2010） is consistent with the CM4 model. We compared the SCH2010 with other models and found that the intensities and distributions are consistent. In view of the variation off at different altitudes, the SCH2010 model results obey the basics of the geomagnetic field. Moreover, the change rate of X, Y, and Z for SCH2010 and CM4 are consistent. The proposed model can successfully reproduce the geomagnetic data, as other data-fitting models, but the inherent sources of error have to be considered as well.

Global Synchronization of Stochastically Disturbed Memristive Neurodynamics via Discontinuous Control Laws

This paper presents the theoretical results on the master-slave (or driving-response) synchronization of two memristive neural networks in the presence of additive noise. First, a control law with a linear time-delay feedback term and a discontinuous feedback term is introduced. By utilizing the stability theory of stochastic differential equations, sufficient conditions are derived for ascertaining global synchronization in mean square using this control law. Second, an adaptive control law consisting of a linear feedback term and a discontinuous feedback term is designed to achieve global synchronization in mean square, and it does not need prior information of network parameters or random disturbances. Finally, simulation results are presented to substantiate the theoretical results. © 2014 Chinese Association of Automation.

Geomagnetic jerk extraction based on the covariance matrix

We normalize data from 43 Chinese observatories and select data from ten Chinese observatories with most continuous records to assess the secular variations(SVs)and geomagnetic jerks by calculating the deviations between annual observed and CHAOS-6 model monthly means.The variations in the north,east,and vertical eigendirections are studied by using the covariance matrix of the residuals,and we find that the vertical direction is strongly affected by magnetospheric ring currents.To obtain noise-free data,we rely on the covariance matrix of the residuals to remove the noise contributions from the largest eigenvalue or vectors owing to ring currents.Finally,we compare the data from the ten Chinese observatories to seven European observatories.Clearly,the covariance matrix method can simulate the SVs of Dst,the jerk of the northward component in 2014 and that of the eastward component in 2003.5 in China are highly agree with that of Vertically downward component in Europe,compare to CHAOS-6,covariance matrix method can show more details of SVs.

Improved Collaborative Filtering Recommendation Based on Classification and User Trust

When dealing with the ratings from users,traditional collaborative filtering algorithms do not consider the credibility of rating data,which affects the accuracy of similarity.To address this issue,the paper proposes an improved algorithm based on classification and user trust.It firstly classifies all the ratings by the categories of items.And then,for each category,it evaluates the trustworthy degree of each user on the category and imposes the degree on the ratings of the user.Finally,the algorithm explores the similarities between users,finds the nearest neighbors,and makes recommendations within each category.Simulations show that the improved algorithm outperforms the traditional collaborative filtering algorithms and enhances the accuracy of recommendation.

The Totally Non-positive Matrix Completion Problem

In this paper, the totally non-positive matrix is introduced. The totally non-positive completion asks which partial totally non-positive matrices have a completion to a totally non-positive matrix. This problem has. in general, a negative answer. Therefore, our question is for what kind of labeled graphs G each partial totally non-positive matrix whose associated graph is G has a totally non-positive completion? If G is not a monotonically labeled graph or monotonically labeled cycle, we give necessary and sufficient conditions that guarantee the existence of the desired completion.

Optimizing Polynomial-Time Solutions to a Network Weighted Vertex Cover Game

Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted networks.We first model the WVC problem as a general game on weighted networks.Under the framework of a game,we newly define several cover states to describe the WVC problem.Moreover,we reveal the relationship among these cover states of the weighted network and the strict Nash equilibriums(SNEs)of the game.Then,we propose a game-based asynchronous algorithm(GAA),which can theoretically guarantee that all cover states of vertices converging in an SNE with polynomial time.Subsequently,we improve the GAA by adding 2-hop and 3-hop adjustment mechanisms,termed the improved game-based asynchronous algorithm(IGAA),in which we prove that it can obtain a better solution to the WVC problem than using a the GAA.Finally,numerical simulations demonstrate that the proposed IGAA can obtain a better approximate solution in promising computation time compared with the existing representative algorithms.

General Lyapunov Stability and Its Application to Time-Varying Convex Optimization

In this article, a general Lyapunov stability theory of nonlinear systems is put forward and it contains asymptotic/finite-time/fast finite-time/fixed-time stability. Especially, a more accurate estimate of the settling-time function is exhibited for fixedtime stability, and it is still extraneous to the initial conditions.This can be applied to obtain less conservative convergence time of the practical systems without the information of the initial conditions. As an application, the given fixed-time stability theorem is used to resolve time-varying(TV) convex optimization problem.By the Newton's method, two classes of new dynamical systems are constructed to guarantee that the solution of the dynamic system can track to the optimal trajectory of the unconstrained and equality constrained TV convex optimization problems in fixed time, respectively. Without the exact knowledge of the time derivative of the cost function gradient, a fixed-time dynamical non-smooth system is established to overcome the issue of robust TV convex optimization. Two examples are provided to illustrate the effectiveness of the proposed TV convex optimization algorithms. Subsequently, the fixed-time stability theory is extended to the theories of predefined-time/practical predefined-time stability whose bound of convergence time can be arbitrarily given in advance, without tuning the system parameters. Under which, TV convex optimization problem is solved. The previous two examples are used to demonstrate the validity of the predefined-time TV convex optimization algorithms.

Network Representation Based on the Joint Learning of Three Feature Views

Network representation learning plays an important role in the field of network data mining. By embedding network structures and other features into the representation vector space of low dimensions, network representation learning algorithms can provide high-quality feature input for subsequent tasks, such as network link prediction, network vertex classification, and network visualization. The existing network representation learning algorithms can be trained based on the structural features, vertex texts, vertex tags, community information, etc.However, there exists a lack of algorithm of using the future evolution results of the networks to guide the network representation learning. Therefore, this paper aims at modeling the future network evolution results of the networks based on the link prediction algorithm, introducing the future link probabilities between vertices without edges into the network representation learning tasks. In order to make the network representation vectors contain more feature factors, the text features of the vertices are also embedded into the network representation vectors. Based on the above two optimization approaches, we propose a novel network representation learning algorithm, Network Representation learning algorithm based on the joint optimization of Three Features(TFNR). Based on Inductive Matrix Completion(IMC), TFNR algorithm introduces the future probabilities between vertices without edges and text features into the procedure of modeling network structures, which can avoid the problem of the network structure sparse. Experimental results show that the proposed TFNR algorithm performs well in network vertex classification and visualization tasks on three real citation network datasets.

MEROMORPHIC FUNCTIONS THAT SHARE FOUR VALUES

The uniqueness of meromorphic functions that share four values is investigated. A necessary condition to the case is acquired, and some partial results for question '1CM+3IM=4CM' are obtained.

Sliding Mode Control to Stabilization of an ODE-Schrdinger Cascade Systems Subject to Boundary Control Matched Disturbance

This paper is concerned with the boundary feedback stabilization of a coupled ODE- Schrodinger system cascades with the external disturbance flowing the control end. The author uses the sliding mode control （SMC） to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the ＂reaching condition＂ is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the dosed-loop system. Some numerical simulations is presented to illustrate the effectiveness of the proposed control.

Commutator of Hypersingular Integral with Rough Kernels on Sobolev Spaces

In this paper, the authors give the boundedness of the commutator of hypersingular integral T γ from the homogeneous Sobolev space Lpγ （Rn） to the Lebesgue space Lp（Rn） for 1

Commutators of Marcinkiewicz Integral with Rough Kernels on Sobolev Spaces

In this paper, the authors give the boundedness of the commutator [b,μΩ,γ] from the homogeneous Sobolev space LP（R^n） to the Lebesgue space L^p（R^n） for 1 〈 p 〈 ∞, where μΩ,γ denotes the Marcinkiewicz integral with rough hypersingular kernel defined by μΩ,γf（x）=（∫0^∞｜∫｜x-y｜≤tΩ（x-y）/｜x-y｜^n-1f（y）dy｜^2dt/t^3＋2γ）^1/2,with Ω∈L^1（S^n-1）for 0〈γ〈min（n/2,n/p）or Ω∈L（log＋L）^β（S^n-1）for｜1-2/p｜〈β〈1（0〈γ〈n/2）,respectively.

Graph Convolutional Network Combined with Semantic Feature Guidance for Deep Clustering

The performances of semisupervised clustering for unlabeled data are often superior to those of unsupervised learning,which indicates that semantic information attached to clusters can significantly improve feature representation capability.In a graph convolutional network(GCN),each node contains information about itself and its neighbors that is beneficial to common and unique features among samples.Combining these findings,we propose a deep clustering method based on GCN and semantic feature guidance(GFDC) in which a deep convolutional network is used as a feature generator,and a GCN with a softmax layer performs clustering assignment.First,the diversity and amount of input information are enhanced to generate highly useful representations for downstream tasks.Subsequently,the topological graph is constructed to express the spatial relationship of features.For a pair of datasets,feature correspondence constraints are used to regularize clustering loss,and clustering outputs are iteratively optimized.Three external evaluation indicators,i.e.,clustering accuracy,normalized mutual information,and the adjusted Rand index,and an internal indicator,i.e., the Davidson-Bouldin index(DBI),are employed to evaluate clustering performances.Experimental results on eight public datasets show that the GFDC algorithm is significantly better than the majority of competitive clustering methods,i.e.,its clustering accuracy is20% higher than the best clustering method on the United States Postal Service dataset.The GFDC algorithm also has the highest accuracy on the smaller Amazon and Caltech datasets.Moreover,DBI indicates the dispersion of cluster distribution and compactness within the cluster.

Online Internet Traffic Monitoring System Using Spark Streaming

Owing to the explosive growth of Internet traffic, network operators must be able to monitor the entire network situation and efficiently manage their network resources. Traditional network analysis methods that usually work on a single machine are no longer suitable for huge traffic data owing to their poor processing ability. Big data frameworks, such as Hadoop and Spark, can handle such analysis jobs even for a large amount of network traffic.However, Hadoop and Spark are inherently designed for offline data analysis. To cope with streaming data, various stream-processing-based frameworks have been proposed, such as Storm, Flink, and Spark Streaming. In this study, we propose an online Internet traffic monitoring system based on Spark Streaming. The system comprises three parts, namely, the collector, messaging system, and stream processor. We considered the TCP performance monitoring as a special use case of showing how network monitoring can be performed with our proposed system.We conducted typical experiments with a cluster in standalone mode, which showed that our system performs well for large Internet traffic measurement and monitoring.