Systemic Indicators for Rural Communities in Developing Economies: Bringing the Shared Vision into Being

Community indicators have been a frequent focus of the scholarly literature. There has been little exploration, however, in relation to rural communities, especially in developing countries. This reflects the special challenges associated with the complexity of rural systems, and the difficulties involved in developing appropriate and systemic indicators for rural communities. Identifying indicators that help the community to monitor progress towards sustainable outcomes requires a framework that is both practical and holistic. This paper introduces a participatory systemic framework for identifying community indicators, which respects the principles of complexity and honours the sense of ownership present in the communities. This framework is an iterative, sharing, co-learning engagement process that extends from creating a shared vision and extracting its core messages, to identifying indicators of progress and determining what actions to try. Importantly, this framework enables us to rank the indicators identified by communities with reference to ‘leverage points’, the best places to intervene in the social-environmental system for transformational change. This framework provides a potential pathway for sustainable rural development and perhaps also for organisations and urban communities.     

Adaptive Event-Based Consensus of Multi-Agent Systems with General Linear Dynamics

In this paper, adaptive event-based consensus of multi-agent systems with general linear dynamics is considered. A novel adaptive event-based controller and a state-dependent triggering function are proposed for each agent. The consensus can be achieved without the assumption that (A,B) is stabilizable. Furthermore, the Zeno-behavior of the concerned closed-loop system is also excluded under certain conditions. Finally, a numerical simulation example is presented to show the effectiveness of the theoretical results.     

An M/M/1 Queueing-Inventory System with Geometric Batch Demands and Lost Sales

This paper studies an M/M/1 queueing-inventory system with batch demands. Customers arrive in the system according to a compound Poisson process, where the size of the batch demands for each arrival is a random variable that follows a geometric distribution. The inventory is replenished according to the standard (s,S) policy. The replenishment time follows an exponential distribution. Two models are considered. In the first model, if the on-hand inventory is less than the size of the batch demands of an arrived customer, the customer takes away all the items in the inventory, and a part of the customer’s batch demands is lost. In the second model, if the on-hand inventory is less than the size of the batch demands of an arrived customer, the customer leaves without taking any item from the inventory, and all of the customer’s batch demands are lost. For these two models, the authors derive the stationary conditions of the system. Then, the authors derive the stationary distributions of the product-form of the joint queue length and the on-hand inventory process. Besides this, the authors obtain some important performance measures and the average cost functions by using these stationary distributions. The results are illustrated by numerical examples.     

Sequential Fair Stackelberg Equilibria of Linear Strategies in Risk-Seeking Insider Trading

This paper develops a sequential fair Stackelberg auction model in which each of the two risk-seeking insiders has an equal chance to be a leader or follower at each auction stage. The authors establish the existence, uniqueness of sequential fair Stackelberg equilibria (in short, FSE) when both insiders adopt linear strategies, and find that at the sequential equilibria such two insiders compete aggressively that cause the liquidity of market to drop, the information to be revealed and the profit to go down very rapidly while the trading intensity goes substantially high. Furthermore, the authors also give continuous versions of corresponding parameters in the sequential FSE in closed forms, as the time interval between auctions approaches to zero. It shows that such parameters go down or up approximately exponentially and all of the liquidity of market, information and profit become zero while the trading intensity goes to infinity. Some numerical simulations about the sequential FSE are also illustrated.     

Control and Stabilization of the Rosenau Equation Posed on a Periodic Domain

This paper considers the Rosenau equation with a moving control?t u + ?_t?_x~4 u + ?_xu + u?x u = a(x + ct)h(x, t), c = 0, x ∈ T = R/(2πZ), t 0.The authors prove that the Rosenau equation with a moving control is locally exact controllable in Hs(T) with s ≥ 0 and globally exponential stable in H~s(T) with s ≥ 2. The two results nontrivially extend the work of(Rosier L and Zhang B Y, 2013) from the BBM equation to the Rosenau equation.     

Non-Monomial Permutations with Differential Uniformity Six

In this paper, a family of non-monomial permutations over the finite field \({F_{{2^n}}}\) with differential uniformity at most 6 is proposed, where n is a positive integer. The algebraic degree of these functions is also determined.     

Component ACD Model and Its Application in Studying the Price-Related Feedback Effect in Investor Trading Behaviors in Chinese Stock Market

This paper explores the investors’ feedback to the price change by modelling the price-related dynamics of trading intensity. A component decomposition duration modeling approach, called the component autoregressive conditional duration (CACD) model, is proposed to capture the variation of trading intensity across time intervals between price change events. Based on the CACD model, an empirical analysis is carried out on the Chinese stock market that covers different market statuses. The empirical results suggest that the CACD model can capture the price-related dynamics of trading intensity, which supports the existence of the feedback effect and is robust across different market statuses. The authors also study how the investors react to the price change by examining the driven factors of the price-related dynamics of trading intensity. The authors find that the trading can be triggered by the fast rise in the price level and the high trading volume. Besides, investors are more sensitive to the price change direction in the sideways market than in the upward or downward markets.     

An FE-Inexact Heterogeneous ADMM for Elliptic Optimal Control Problems with <Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-Control Cost

Elliptic PDE-constrained optimal control problems with L¹-control cost (L¹-EOCP) are considered. To solve L¹-EOCP, the primal-dual active set (PDAS) method, which is a special semismooth Newton (SSN) method, used to be a priority. However, in general solving Newton equations is expensive. Motivated by the success of alternating direction method of multipliers (ADMM), we consider extending the ADMM to L¹-EOCP. To discretize L¹-EOCP, the piecewise linear finite element (FE) is considered. However, different from the finite dimensional l1-norm, the discretized L¹-norm does not have a decoupled form. To overcome this difficulty, an effective approach is utilizing nodal quadrature formulas to approximately discretize the L¹-norm and L²-norm. It is proved that these approximation steps will not change the order of error estimates. To solve the discretized problem, an inexact heterogeneous ADMM (ihADMM) is proposed. Different from the classical ADMM, the ihADMM adopts two different weighted inner products to define the augmented Lagrangian function in two subproblems, respectively. Benefiting from such different weighted techniques, two subproblems of ihADMM can be efficiently implemented. Furthermore, theoretical results on the global convergence as well as the iteration complexity results o(1/k) for ihADMM are given. In order to obtain more accurate solution, a two-phase strategy is also presented, in which the primal-dual active set (PDAS) method is used as a postprocessor of the ihADMM. Numerical results not only confirm error estimates, but also show that the ihADMM and the two-phase strategy are highly efficient.     

Influence of strategy continuity on cooperation in spatial prisoner’s dilemma games with migrating players

The phenomenon of cooperation is prevalent in both nature and human society. In this paper a simulative model is developed to examine how the strategy continuity influences cooperation in the spatial prisoner’s games in which the players migrate through the success-driven migration mechanism. Numerical simulations illustrate that the strategy continuity promotes cooperation at a low rate of migration, while impeding cooperation when the migration rate is higher. The influence of strategy continuity is also dependent on the game types. Through a more dynamic analysis, the different effects of the strategy continuity at low and high rates of migration are explained by the formation, expansion, and extinction of the self-assembled clusters of “partial- cooperators” within the gaming population.