Discrete Dynamics in Nature and Society https://www.hindawi.com The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Numerical Feedback Stabilization with Applications to Networks Mon, 22 May 2017 10:05:13 +0000 http://www.hindawi.com/journals/ddns/2017/6896153/ The focus is on the numerical consideration of feedback boundary control problems for linear systems of conservation laws including source terms. We explain under which conditions the numerical discretization can be used to design feedback boundary values for network applications such as electric transmission lines or traffic flow systems. Several numerical examples illustrate the properties of the results for different types of networks. Simone Göttlich and Peter Schillen Copyright © 2017 Simone Göttlich and Peter Schillen. All rights reserved. A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991–2014 Mon, 22 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/5243287/ The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in observational data. In theory, both the allometric growth law and Zipf’s law are related to the hierarchical scaling laws associated with fractal structure. In this paper, the scaling laws of hierarchies with cascade structure are used to study Chinese cities, and the method of analysis is applied to analyzing the change trend of the allometric scaling exponents. The results show that the hierarchical scaling relations of Chinese cities became clearer and clearer from 1991 to 2014 year; the global allometric scaling exponent values fluctuated around 0.85, and the local scaling exponent approached 0.85. The Hurst exponent of the allometric parameter change is greater than 0.5, indicating persistence and a long-term memory of urban evolution. The main conclusions can be reached as follows: the allometric scaling law of cities represents an evolutionary order rather than an invariable rule, which emerges from self-organized process of urbanization, and the ideas from allometry and fractals can be combined to optimize spatial and hierarchical structure of urban systems in future city planning. Yanguang Chen and Jian Feng Copyright © 2017 Yanguang Chen and Jian Feng. All rights reserved. Simulation of Pedestrian Behavior in the Collision-Avoidance Process considering Their Moving Preferences Mon, 22 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/3678268/ Walking habits can affect the self-organizing movement in pedestrian flow. In China, pedestrians prefer to walk along the right-hand side in the collision-avoidance process, and the same is true for the left-hand preference that is followed in several countries. Through experiments with pedestrian flow, we find that the relative position between pedestrians can affect their moving preferences. We propose a kind of collision-avoidance force based on the social force model, which considers the predictions of potential conflict and the relative position between pedestrians. In the simulation, we use the improved model to explore the effect of moving preference on the collision-avoidance process and self-organizing pedestrian movement. We conclude that the improved model can bring the simulation closer to reality and that moving preference is conducive to the self-adjustment of counterflow. Zhilu Yuan, Hongfei Jia, Linfeng Zhang, and Lei Bian Copyright © 2017 Zhilu Yuan et al. All rights reserved. Myopic versus Far-Sighted Behaviors in Dynamic Supply Chain Coordination through Advertising with Reference Price Effect Thu, 18 May 2017 08:54:27 +0000 http://www.hindawi.com/journals/ddns/2017/9759561/ To better understand the different effects of the myopic and far-sighted behaviors on the advertising coordination in dynamic supply chain, this paper takes the reference price effect into consideration and formulates four differential game models for the two-level supply chain composed of a manufacturer and a retailer in the situation of Stackelberg game. In our models, the market demand is assumed to be affected by the goodwill, reference price, and the advertising investment, in which the advertising investment can promote the construction of goodwill and such goodwill can further enhance the reference price. The results show that the participating members in the supply chain should invest more in advertisement to improve the goodwill and the relative reference price reflected in the minds of consumers. A far-sighted manufacturer will invest more in the advertisement and charge a higher wholesale price regardless of the behavior choice of the retailer. However, such kind of ignorance leads to different results on the retail pricing strategies of the retailer. The numerical analyses are given in the end to verify the effectiveness of the conclusions which provide the theoretical support to the dynamic supply chain coordination in practice. Yafei Zu and Lianghua Chen Copyright © 2017 Yafei Zu and Lianghua Chen. All rights reserved. Assigning Passenger Flows on a Metro Network Based on Automatic Fare Collection Data and Timetable Tue, 16 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/4373871/ Assigning passenger flows on a metro network plays an important role in passenger flow analysis that is the foundation of metro operation. Traditional transit assignment models are becoming increasingly complex and inefficient. These models may even not be valid in case of sudden changes in the timetable or disruptions in the metro system. We propose a methodology for assigning passenger flows on a metro network based on automatic fare collection (AFC) data and realized timetable. We find that the routes connecting a given origin and destination (O-D) pair are related to their observed travel times (OTTs) especially their pure travel times (PTTs) abstracted from AFC data combined with the realized timetable. A novel clustering algorithm is used to cluster trips between a given O-D pair based on PTTs/OTTs and complete the assignment. An initial application to categorical O-D pairs on the Shanghai metro system, which is one of the largest systems in the world, shows that the proposed methodology works well. Accompanying the initial application, an interesting approach is also provided for determining the theoretical maximum accuracy of the new assignment model. Ling Hong, Wei Li, and Wei Zhu Copyright © 2017 Ling Hong et al. All rights reserved. Improved RIP Conditions for Compressed Sensing with Coherent Tight Frames Mon, 15 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/4372080/ This paper establishes new sufficient conditions on the restricted isometry property (RIP) for compressed sensing with coherent tight frames. One of our main results shows that the RIP (adapted to ) condition guarantees the stable recovery of all signals that are nearly -sparse in terms of a coherent tight frame via the -analysis method, which improves the existing ones in the literature. Yao Wang and Jianjun Wang Copyright © 2017 Yao Wang and Jianjun Wang. All rights reserved. Pricing Collar Options with Stochastic Volatility Sun, 14 May 2017 08:32:10 +0000 http://www.hindawi.com/journals/ddns/2017/9673630/ This paper studies collar options in a stochastic volatility economy. The underlying asset price is assumed to follow a continuous geometric Brownian motion with stochastic volatility driven by a mean-reverting process. The method of asymptotic analysis is employed to solve the PDE in the stochastic volatility model. An analytical approximation formula for the price of the collar option is derived. A numerical experiment is presented to demonstrate the results. Pengshi Li and Jianhui Yang Copyright © 2017 Pengshi Li and Jianhui Yang. All rights reserved. Predicting Social Unrest Events with Hidden Markov Models Using GDELT Wed, 10 May 2017 08:40:04 +0000 http://www.hindawi.com/journals/ddns/2017/8180272/ Proactive handling of social unrest events which are common happenings in both democracies and authoritarian regimes requires that the risk of upcoming social unrest event is continuously assessed. Most existing approaches comparatively pay little attention to considering the event development stages. In this paper, we use autocoded events dataset GDELT (Global Data on Events, Location, and Tone) to build a Hidden Markov Models (HMMs) based framework to predict indicators associated with country instability. The framework utilizes the temporal burst patterns in GDELT event streams to uncover the underlying event development mechanics and formulates the social unrest event prediction as a sequence classification problem based on Bayes decision. Extensive experiments with data from five countries in Southeast Asia demonstrate the effectiveness of this framework, which outperforms the logistic regression method by 7% to 27% and the baseline method 34% to 62% for various countries. Fengcai Qiao, Pei Li, Xin Zhang, Zhaoyun Ding, Jiajun Cheng, and Hui Wang Copyright © 2017 Fengcai Qiao et al. All rights reserved. The Patch-Levy-Based Bees Algorithm Applied to Dynamic Optimization Problems Wed, 10 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/5678393/ Many real-world optimization problems are actually of dynamic nature. These problems change over time in terms of the objective function, decision variables, constraints, and so forth. Therefore, it is very important to study the performance of a metaheuristic algorithm in dynamic environments to assess the robustness of the algorithm to deal with real-word problems. In addition, it is important to adapt the existing metaheuristic algorithms to perform well in dynamic environments. This paper investigates a recently proposed version of Bees Algorithm, which is called Patch-Levy-based Bees Algorithm (PLBA), on solving dynamic problems, and adapts it to deal with such problems. The performance of the PLBA is compared with other BA versions and other state-of-the-art algorithms on a set of dynamic multimodal benchmark problems of different degrees of difficulties. The results of the experiments show that PLBA achieves better results than the other BA variants. The obtained results also indicate that PLBA significantly outperforms some of the other state-of-the-art algorithms and is competitive with others. Wasim A. Hussein, Siti Norul Huda Sheikh Abdullah, and Shahnorbanun Sahran Copyright © 2017 Wasim A. Hussein et al. All rights reserved. Some New Existence and Uniqueness Results for an Integral Boundary Value Problem of Caputo Fractional Differential Equations Tue, 09 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/4087403/ In this work, we consider an integral boundary value problem of Caputo fractional differential equations. Based on a fixed-point theorem of generalized concave operators, we obtain the existence and uniqueness of positive solutions. As applications of main results, we give two examples in the end. Haixing Feng and Chengbo Zhai Copyright © 2017 Haixing Feng and Chengbo Zhai. All rights reserved. Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence Rate Tue, 09 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/2340549/ This paper is concerned with a delayed SEIS (Susceptible-Exposed-Infectious-Susceptible) epidemic model with a changing delitescence and nonlinear incidence rate. First of all, local stability of the endemic equilibrium and the existence of a Hopf bifurcation are studied by choosing the time delay as the bifurcation parameter. Directly afterwards, properties of the Hopf bifurcation are determined based on the normal form theory and the center manifold theorem. At last, numerical simulations are carried out to illustrate the obtained theoretical results. Juan Liu Copyright © 2017 Juan Liu. All rights reserved. Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics Mon, 08 May 2017 10:06:19 +0000 http://www.hindawi.com/journals/ddns/2017/5716015/ We depart from the well-known one-dimensional Fisher’s equation from population dynamics and consider an extension of this model using Riesz fractional derivatives in space. Positive and bounded initial-boundary data are imposed on a closed and bounded domain, and a fully discrete form of this fractional initial-boundary-value problem is provided next using fractional centered differences. The fully discrete population model is implicit and linear, so a convenient vector representation is readily derived. Under suitable conditions, the matrix representing the implicit problem is an inverse-positive matrix. Using this fact, we establish that the discrete population model is capable of preserving the positivity and the boundedness of the discrete initial-boundary conditions. Moreover, the computational solubility of the discrete model is tackled in the closing remarks. J. E. Macías-Díaz Copyright © 2017 J. E. Macías-Díaz. All rights reserved. Prophet: A Context-Aware Location Privacy-Preserving Scheme in Location Sharing Service Mon, 08 May 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/6814832/ Location sharing service has become an indispensable part in mobile social networks. However, location sharing may introduce a new class of privacy threats ranging from localizing an individual to profiling and identifying him based on the places he shared. Although users may avoid releasing geocontent in sensitive locations, it does not necessarily prevent the adversary from inferring users’ privacy through space-temporal correlations and historical information. In this paper, we design a Prophet framework, which provides an effective security scheme for users sharing their location information. First, we define fingerprint identification based on Markov chain and state classification to describe the users’ behavior patterns. Then, we propose a novel location anonymization mechanism, which adopts a -indistinguishability strategy to protect user’s sensitive location information published. Finally, experimental results are given to illustrate good performance and effectiveness of the proposed scheme. Jiaxing Qu, Guoyin Zhang, and Zhou Fang Copyright © 2017 Jiaxing Qu et al. All rights reserved. Global Dynamics of Rational Difference Equations and Wed, 03 May 2017 09:15:57 +0000 http://www.hindawi.com/journals/ddns/2017/1295089/ Global dynamics of a system of nonlinear difference equations was investigated, which had five kinds of equilibria including isolated points and a continuum of nonhyperbolic equilibria along the coordinate axes. The local stability of these equilibria was analyzed which led to nine regions in the parameters space. The solution of the system converged to the equilibria or the boundary point or in each region depending on nonnegative initial conditions. These results completely described the behavior of the system. Keying Liu, Peng Li, and Weizhou Zhong Copyright © 2017 Keying Liu et al. All rights reserved. On Subdirect Decompositions of Finite Distributive Lattices Thu, 27 Apr 2017 06:09:33 +0000 http://www.hindawi.com/journals/ddns/2017/6490903/ Subdirect decomposition of algebra is one of its quite general and important constructions. In this paper, some subdirect decompositions (including subdirect irreducible decompositions) of finite distributive lattices and finite chains are studied, and some general results are obtained. Yizhi Chen, Jing Tian, and Zhongzhu Liu Copyright © 2017 Yizhi Chen et al. All rights reserved. The Minimum Spectral Radius of an Edge-Removed Network: A Hypercube Perspective Wed, 19 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/1382980/ The spectral radius minimization problem (SRMP), which aims to minimize the spectral radius of a network by deleting a given number of edges, turns out to be crucial to containing the prevalence of an undesirable object on the network. As the SRMP is NP-hard, it is very unlikely that there is a polynomial-time algorithm for it. As a result, it is proper to focus on the development of effective and efficient heuristic algorithms for the SRMP. For that purpose, it is appropriate to gain insight into the pattern of an optimal solution to the SRMP by means of checking some regular networks. Hypercubes are a celebrated class of regular networks. This paper empirically studies the SRMP for hypercubes with two/three/four missing edges. First, for each of the three subproblems of the SRMP, a candidate for the optimal solution is presented. Second, it is shown that the candidate is optimal for small-sized hypercubes, and it is shown that the proposed candidate is likely to be optimal for medium-sized hypercubes. The edges in each candidate are evenly distributed over the network, which may be a common feature of all symmetric networks and hence is instructive in designing effective heuristic algorithms for the SRMP. Yingbo Wu, Tianrui Zhang, Shan Chen, and Tianhui Wang Copyright © 2017 Yingbo Wu et al. All rights reserved. Evaluating Operational Effects of Bus Lane with Intermittent Priority under Connected Vehicle Environments Wed, 19 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/1659176/ Bus lane with intermittent priority (BLIP) is an innovative method to improve the reliability of bus services while promoting efficient usage of road resources. Vehicle-to-vehicle (V2V) communication is an advanced technology that can greatly enhance the vehicle mobility, improve traffic safety, and alleviate traffic jams. To explore the benefits of BLIP operation under a connected environment, this study proposed a three-lane cellular automata (CA) model under opening boundary condition. In particular, a mandatory BLIP lane-changing rule is developed to analyze special asymmetric lane-changing behaviors. To improve the simulation accuracy, a smaller cell size is used in the CA model. Through massive numerical simulations, the benefits and influences of BLIP are explored in this paper. They include impacts on neighborhood lanes such as traffic density increasing and average speed decreasing, lane-changing behaviors, lane usage, and the impacts of bus departure interval and clear distance on the road capacity of BLIP. Analysis of traffic flow characteristics of BLIP reveals that there is a strong relationship among bus departure interval, clear distance, and road capacity. Furthermore, setting conditions for deployment of BLIP under the V2V environment such as reasonable departure interval, clear distance, and traffic density are obtained. Dingxin Wu, Wei Deng, Yan Song, Jian Wang, and Dewen Kong Copyright © 2017 Dingxin Wu et al. All rights reserved. An Analysis of Discrete Stage-Structured Prey and Prey-Predator Population Models Sun, 16 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/9475854/ Discrete stage-structured prey and prey-predator models are considered. Regarding the former, we prove that the models at hand are permanent (i.e., the population will neither go extinct nor exhibit explosive oscillations) and, moreover, that the transfer from stability to nonstationary behaviour always goes through a supercritical Neimark−Sacker bifurcation. The prey model covers species that possess a wide range of different life histories. Predation pressure may both stabilize and destabilize the prey dynamics but the strength of impact is closely related to life history. Indeed, if the prey possesses a precocious semelparous life history and exhibits chaotic oscillations, it is shown that increased predation may stabilize the dynamics and also, in case of large predation pressure, transfer the population to another chaotic regime. Arild Wikan Copyright © 2017 Arild Wikan. All rights reserved. Opportunity Loss Minimization and Newsvendor Behavior Thu, 13 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/3481869/ To study the decision bias in newsvendor behavior, this paper introduces an opportunity loss minimization criterion into the newsvendor model with backordering. We apply the Conditional Value-at-Risk (CVaR) measure to hedge against the potential risks from newsvendor’s order decision. We obtain the optimal order quantities for a newsvendor to minimize the expected opportunity loss and CVaR of opportunity loss. It is proven that the newsvendor’s optimal order quantity is related to the density function of market demand when the newsvendor exhibits risk-averse preference, which is inconsistent with the results in Schweitzer and Cachon (2000). The numerical example shows that the optimal order quantity that minimizes CVaR of opportunity loss is bigger than expected profit maximization (EPM) order quantity for high-profit products and smaller than EPM order quantity for low-profit products, which is different from the experimental results in Schweitzer and Cachon (2000). A sensitivity analysis of changing the operation parameters of the two optimal order quantities is discussed. Our results confirm that high return implies high risk, while low risk comes with low return. Based on the results, some managerial insights are suggested for the risk management of the newsvendor model with backordering. Xinsheng Xu, Hong Yan, and Chi Kin Chan Copyright © 2017 Xinsheng Xu et al. All rights reserved. Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model Mon, 10 Apr 2017 07:08:25 +0000 http://www.hindawi.com/journals/ddns/2017/6312964/ This work is related to dynamics of a discrete-time 3-dimensional plant-herbivore model. We investigate existence and uniqueness of positive equilibrium and parametric conditions for local asymptotic stability of positive equilibrium point of this model. Moreover, it is also proved that the system undergoes Neimark-Sacker bifurcation for positive equilibrium with the help of an explicit criterion for Neimark-Sacker bifurcation. The chaos control in the model is discussed through implementation of two feedback control strategies, that is, pole-placement technique and hybrid control methodology. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long-term behavior over a broad range of parameters. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behavior in the model. Qamar Din, A. A. Elsadany, and Hammad Khalil Copyright © 2017 Qamar Din et al. All rights reserved. The Effects of Abandonment Options on Investment Timing and Profit Sharing of FDI Sun, 09 Apr 2017 07:02:12 +0000 http://www.hindawi.com/journals/ddns/2017/5141975/ The paper incorporates cooperative game theory into a real option method in a foreign direct investment setting and examines the operational decisions of a multinational corporation in a cooperative framework, where the corporation is endowed with an abandonment option and shares its profit with the host country. In particular, we investigate how the abandonment options affect the optimal investment timing and the optimal profit share of a foreign direct investment using a real option game method. We show that the flexibility of the abandonment option induces the corporation to investment earlier, which indicates the negative effects on investment trigger. The result is consistent with intuition since the abandonment option provides insurance and thus reduces the overall risk of the project. We also find that the introduction of the abandonment option reduces the optimal profit share in a cooperative framework and in turn the lower profit share increases the investment trigger, thereby having a positive effect on the investment threshold to hinder the investment. By numerical analysis, we find that the overall effect of the abandonment options is inversely related to the investment trigger. These findings provide quantitative analysis about the decisions regarding cooperation in international investment extraction projects. Weiwei Zhang and Minggao Xue Copyright © 2017 Weiwei Zhang and Minggao Xue. All rights reserved. Electricity Demand Projection Using a Path-Coefficient Analysis and BAG-SA Approach: A Case Study of China Sun, 09 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/2379381/ Path-coefficient analysis is utilized to investigate the direct and indirect effects of economic growth, population growth, urbanization rate, industrialization level, and carbon intensity on electricity demand of China. To improve the projection accuracy of electricity demand, this study proposes a hybrid bat algorithm, Gaussian perturbations, and simulated annealing (BAG-SA) optimization method. The proposed BAG-SA algorithm not only inherits the simplicity and efficiency of the standard BA with a capability of searching for global optimality but also enhances local search ability and speeds up the global convergence rate. The BAG-SA algorithm is employed to optimize the coefficients of the multiple linear and quadratic forms of electricity demand estimation model. Results indicate that the proposed algorithm has higher precision and reliability than the coefficients optimized by other single-optimization methods, such as genetic algorithm, particle swarm optimization algorithm, or bat algorithm. And the quadratic form of BAG-SA electricity demand estimation model has better fitting ability compared with the multiple linear form of the model. Therefore, the quadratic form of the model is applied to estimate electricity demand of China from 2016 to 2030. The findings of this study demonstrate that China’s electricity demand will reach 14925200 million KWh in 2030. Qunli Wu and Chenyang Peng Copyright © 2017 Qunli Wu and Chenyang Peng. All rights reserved. Comment on “Unilateral Global Bifurcation from Intervals for Fourth-Order Problems and Its Applications” Wed, 05 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/1024950/ In the recent paper W. Shen and T. He and G. Dai and X. Han established unilateral global bifurcation result for a class of nonlinear fourth-order eigenvalue problems. They show the existence of two families of unbounded continua of nontrivial solutions of these problems bifurcating from the points and intervals of the line trivial solutions, corresponding to the positive or negative eigenvalues of the linear problem. As applications of this result, these authors study the existence of nodal solutions for a class of nonlinear fourth-order eigenvalue problems with sign-changing weight. Moreover, they also establish the Sturm type comparison theorem for fourth-order problems with sign-changing weight. In the present comment, we show that these papers of above authors contain serious errors and, therefore, unfortunately, the results of these works are not true. Note also that the authors used the results of the recent work by G. Dai which also contain gaps. Ziyatkhan Aliyev Copyright © 2017 Ziyatkhan Aliyev. All rights reserved. Periodic Solutions and -Asymptotically Periodic Solutions to Fractional Evolution Equations Mon, 03 Apr 2017 08:37:59 +0000 http://www.hindawi.com/journals/ddns/2017/1364532/ This paper deals with the existence and uniqueness of periodic solutions, -asymptotically periodic solutions, and other types of bounded solutions for some fractional evolution equations with the Weyl-Liouville fractional derivative defined for periodic functions. Applying Fourier transform we give reasonable definitions of mild solutions. Then we accurately estimate the spectral radius of resolvent operator and obtain some existence and uniqueness results. Jia Mu, Yong Zhou, and Li Peng Copyright © 2017 Jia Mu et al. All rights reserved. Evolution of Bounded Confidence Opinion in Social Networks Mon, 03 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/3173016/ We investigate opinion dynamics as a stochastic process in social networks. We introduce the stubborn agent in order to determine the impact of network structure on the emergence of consensus. Depending on the fraction of undirected long-range connections, we observe fascinatingly rich dynamical behavior and transitions from disordered to ordered states. In general, we find that the stubborn agent promotes the emergence of consensus due to the so-called “group effect” that facilitates coalescence between separated network components. Agents are also behaviorally constrained Shannon information entropy in networks. However, since agents want to evolve their opinion with Brownian motion, which may in turn impede full consensus, sufficiently frequent long-range links are in such situations crucial for the network to converge into an absorbing phase. Our experimental findings indicate that, for a large range of control parameters, our model yields stable and fluctuating polarized states. Hui Xie, Guangjian Li, Yongjie Yan, and Sihui Shu Copyright © 2017 Hui Xie et al. All rights reserved. Mining Important Nodes in Directed Weighted Complex Networks Thu, 30 Mar 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/9741824/ In complex networks, mining important nodes has been a matter of concern by scholars. In recent years, scholars have focused on mining important nodes in undirected unweighted complex networks. But most of the methods are not applicable to directed weighted complex networks. Therefore, this paper proposes a Two-Way-PageRank method based on PageRank for further discussion of mining important nodes in directed weighted complex networks. We have mainly considered the frequency of contact between nodes and the length of time of contact between nodes. We have considered the source of the nodes (in-degree) and the whereabouts of the nodes (out-degree) simultaneously. We have given node important performance indicators. Through numerical examples, we analyze the impact of variation of some parameters on node important performance indicators. Finally, the paper has verified the accuracy and validity of the method through empirical network data. Yunyun Yang, Gang Xie, and Jun Xie Copyright © 2017 Yunyun Yang et al. All rights reserved. Stochastic Control for Discrete-Time Singular Systems with State and Disturbance Dependent Noise Wed, 29 Mar 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/4173852/ This paper is concerned with the stochastic state feedback control problem for a class of discrete-time singular systems with state and disturbance dependent noise. Two stochastic bounded real lemmas (SBRLs) are proposed via strict linear matrix inequalities (LMIs). Based on the obtained SBRLs, a state feedback controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribed performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results. Yong Zhao, Xiushan Jiang, and Weihai Zhang Copyright © 2017 Yong Zhao et al. All rights reserved. Solutions for a Class of Nonperiodic Superquadratic Hamiltonian Elliptic Systems Involving Gradient Terms Tue, 28 Mar 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/9125486/ In the present paper, we consider the following Hamiltonian elliptic system : , A new existence result of nontrivial solutions is obtained for the system via variational methods for strongly indefinite problems, which generalizes some known results in the literatures. Shengzhong Duan and Xian Wu Copyright © 2017 Shengzhong Duan and Xian Wu. All rights reserved. Pricing Formula for Exotic Options with Assets Exposed to Counterparty Risk Mon, 27 Mar 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/5239808/ This paper gives analytical formulas for lookback and barrier options on underlying assets that are exposed to a counterparty risk. The counterparty risk induces a drop in the asset price, but the asset can still be traded after this default time. A novel technique is developed to valuate the lookback and barrier options by first conditioning on the predefault and the postdefault time and then obtain the unconditional analytic formulas for their prices. Li Yan Copyright © 2017 Li Yan. All rights reserved. A New Method for Solving Multiobjective Bilevel Programs Thu, 23 Mar 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/2870420/ We study a class of multiobjective bilevel programs with the weights of objectives being uncertain and assumed to belong to convex and compact set. To the best of our knowledge, there is no study about this class of problems. We use a worst-case weighted approach to solve this class of problems. Our “worst-case weighted multiobjective bilevel programs” model supposes that each player (leader or follower) has a set of weights to their objectives and wishes to minimize their maximum weighted sum objective where the maximization is with respect to the set of weights. This new model gives rise to a new Pareto optimum concept, which we call “robust-weighted Pareto optimum”; for the worst-case weighted multiobjective optimization with the weight set of each player given as a polytope, we show that a robust-weighted Pareto optimum can be obtained by solving mathematical programing with equilibrium constraints (MPEC). For an application, we illustrate the usefulness of the worst-case weighted multiobjective optimization to a supply chain risk management under demand uncertainty. By the comparison with the existing weighted approach, we show that our method is more robust and can be more efficiently applied to real-world problems. Ying Ji, Shaojian Qu, and Zhensheng Yu Copyright © 2017 Ying Ji et al. All rights reserved.