This paper firstly analyzes the Brexit’s impact on the US stock market using a novel interval methodology. The interval-valued dummy variables are proposed to measure the direction and magnitudes of the changes in the inter-day trend and the intra-day volatility of S&P500 returns simultaneously. It is found that both the trend and the volatility of S&P500 returns increased before the Brexit. Besides, the Brexit negatively affected S&P500 returns’ trend in the short term after the event, while its impact on market volatility was positive, which slowly decayed across time. Furthermore, a new interesting finding is that there are both short-term momentum effects (i.e., positive autocorrelation of trends) and volatility clustering in stock markets.

This paper constructs a new non-uniform Doo-Sabin subdivision scheme via eigen polygon. The authors proved that the limit surface is always convergent and is G1 continuous for any valence and any positive knot intervals under a minor assumption, that λ is the second and third eigenvalues of the subdivision matrix. And then, a million of numerical experiments are tested with randomly selecting positive knot intervals, which verify that our new subdivision scheme satisfies the assumption. However this is not true for the other two existing non-uniform Doo-Sabin schemes in Sederberg, et al. (1998), Huang and Wang (2013). In additional, numerical experiments indicate that the quality of the new limit surface can be improved.

De Casteljau algorithm and degree elevation of B´ezier and NURBS curves/surfaces are two important techniques in computer aided geometric design. This paper presents the de Casteljau algorithm and degree elevation of toric surface patches, which include tensor product and triangular rational B´ezier surfaces as special cases. Some representative examples of toric surface patches with common shapes are illustrated to verify these two algorithms. Moreover, the authors also apply the degree elevation of toric surface patches to isogeometric analysis. And two more examples show the effectiveness of proposed method.

This paper presents an adaptive collocation method with weighted extended PHT-splines. The authors modify the classification rules for basis functions based on the relation between the basis vertices and the computational domain. The Gaussian points are chosen to be collocation points since PHT-splines are C1 continuous. The authors also provide relocation techniques to resolve the mismatch problem between the number of basis functions and the number of interpolation conditions. Compared to the traditional Greville collocation method, the new approach has improved accuracy with fewer oscillations. Several numerical examples are also provided to test our the proposed approach.

This paper proposes a two-stage point cloud super resolution framework that combines local interpolation and deep neural network based readjustment. For the first stage, the authors apply a local interpolation method to increase the density and uniformity of the target point cloud. For the second stage, the authors employ an outer-product neural network to readjust the position of points that are inserted at the first stage. Comparison examples are given to demonstrate that the proposed framework achieves a better accuracy than existing state-of-art approaches, such as PU-Net, PointNet and DGCNN (Source code is available at https://github.com/qwerty1319/PC-SR).

Tool path generation is a fundamental problem in 5-axis CNC machining, which consists of tool orientation planning and cutter-contact (CC) point planning. The planning strategy highly depends on the type of tool cutters. For ball-end cutters, the tool orientation and CC point location can be planned separately; while for flat end cutters, the two are highly dependent on each other. This paper generates a smooth tool path of workpiece surfaces for flat end mills from two stages: Computing smooth tool orientations on the surface without gouging and collisions and then designing the CC point path. By solving the tool posture optimization problem the authors achieve both the path smoothness and the machining efficiency. Experimental results are provided to show the effectiveness of the method.

In 2014, Chen and Singer solved the summability problem of bivariate rational functions. Later an algorithmic proof was presented by Hou and the author. In this paper, the algorithm will be simplified and adapted to the q-case.

This paper extends a method, called bilinear neural network method (BNNM), to solve exact solutions to nonlinear partial differential equation. New, test functions are constructed by using this method. These test functions are composed of specific activation functions of single-layer model, specific activation functions of “2-2” model and arbitrary functions of “2-2-3” model. By means of the BNNM, nineteen sets of exact analytical solutions and twenty-four arbitrary function solutions of the dimensionally reduced p-gBKP equation are obtained via symbolic computation with the help of Maple. The fractal solitons waves are obtained by choosing appropriate values and the self-similar characteristics of these waves are observed by reducing the observation range and amplifying the partial picture. By giving a specific activation function in the single layer neural network model, exact periodic waves and breathers are obtained. Via various three-dimensional plots, contour plots and density plots, the evolution characteristic of these waves are exhibited.

In the classical theory of self-tuning regulators, it always requires that the conditional variances of the systems noises are bounded. However, such a requirement may not be satisfied when modeling many practical systems, and one significant example is the well-known ARCH (autoregressive conditional heteroscedasticity) model in econometrics. The aim of this paper is to consider self-tuning regulators of linear stochastic systems with both unknown parameters and conditional heteroscedastic noises, where the adaptive controller will be designed based on both the weighted least-squares algorithm and the certainty equivalence principle. The authors will show that under some natural conditions on the system structure and the noises with unbounded conditional variances, the closed-loop adaptive control system will be globally stable and the tracking error will be asymptotically optimal. Thus, this paper provides a significant extension of the classical theory on self-tuning regulators with expanded applicability.

The formation of public opinion on the network is a hot issue in the field of complex network research, and some classical dynamic models are used to solve this problem. The signed network is a particular form of the complex network, which can adequately describe the amicable and hostile relationships in complex real-world systems. However, the methods for studying the dynamic process of public opinion propagation on signed networks still require to be further discussed. In this paper, the authors pay attention to the influence of negative edges in order to design a two-state public opinion propagation mechanism suitable for signed networks. The authors first set the interaction rules between nodes and the transition rules of node states and then apply the model to synthetic and real-world signed networks. The simulation results show that there is a critical value of the negative edge ratio. When the negative edge ratio exceeds this critical value, the evolutionary result of public opinion will change from a consistent state to a split state. This conclusion is also consistent with the distribution result of opinions within communities in the signed network. Besides, the research on the network structural balance shows that the model makes the network evolve in a more balanced direction.

Networked control systems (NCSs) are facing a great challenge from the limitation of network communication resources. Event-triggered control (ETC) is often used to reduce the amount of communication while still keeping a satisfactory performance of the system, by transmitting the measurements only when an event-triggered condition is satisfied. However, some network-induced problems would happen inevitably, such as communication delay and packet loss, which can degrade the control performance significantly and can even lead to instability. In this paper, a periodic eventtriggered NCS considering both time-varying delay and packet loss is studied. The system is discretized into a piecewise linear system with uncertainty. Then the model is handled by a polytopic overapproximation method to be more suitable for stability analysis. Finally, stability conditions are obtained and presented in terms of linear matrix inequalities (LMIs). The result is illustrated by a numerical example.