Volume 7, Issue 4

In a power grid system, utility is a measure of the satisfaction of users’ electricity consumption; cost is a monetary value of electricity generated by the supplier. The utility and cost functions represent the satisfaction of different users and the supplier. Quadratic utility, logarithmic utility, and quadratic cost functions are widely used in social welfare maximization models of real-time pricing. These functions are not universal; they have to be discussed in detail for individual models. To overcome this problem, a piece-wise linear utility function and a piece-wise linear cost function with general properties are proposed in this paper. By smoothing the piece-wise linear utility and cost functions, a social welfare maximization model can be transformed into a differentiable convex optimization problem. A dual optimization method is used to solve the smoothed model. Through mathematical deduction and numerical simulations, the rationality of the model and the validity of the algorithm are verified as long as the elastic and cost coefficients take appropriate values. Thus, different user types and the supplier can be determined by selecting different elastic and cost coefficients.

A classical portfolio theory deals with finding the optimal proportion in which an agent invests a wealth in a risk-free asset and a probabilistic risky asset. Formulating and solving the problem depend on how the risk is represented and how, combined with the utility function defines a notion of expected utility. In this paper the risk is a fuzzy variable and the notion of expected utility is defined in the setting of Liu’s credibility theory. Thus, the portfolio choice problem is formulated as an optimization problem in which the objective function is a credibilistic expected utility. Different approximation calculation formulas for the optimal allocation of the credibilistic risky asset are proved. These formulas contain two types of parameters: Various credibilistic moments associated with fuzzy variables (expected value, variance, skewness and kurtosis) and the risk aversion, prudence and temperance indicators of the utility function.

This paper applies bootstrap methods to LM tests (including LM-lag test and LM-error test) for spatial dependence in panel data models with fixed effects, and removes fixed effects based on orthogonal transformation method proposed by Lee and Yu (2010). The consistencies of LM tests and their bootstrap versions are proved, and then some asymptotic refinements of bootstrap LM tests are obtained. It shows that the convergence rate of bootstrap LM tests is O (( NT ) −2 ) and that of fast double bootstrap LM tests is O (( NT ) −5/2 ). Extensive Monte Carlo experiments suggest that, compared to aysmptotic LM tests, the size of bootstrap LM tests gets closer to the nominal level of signifiance, and the power of bootstrap LM tests is higher, especially in the cases with small spatial correlation. Moreover, when the error is not normal or with heteroskedastic, asymptotic LM tests suffer from severe size distortion, but the size of bootstrap LM tests is close to the nominal significance level. Bootstrap LM tests are superior to aysmptotic LM tests in terms of size and power.

This paper deals with the effort problem under multiple risks in bivariate utility setting. We identify preference conditions to insure positive or negative effect of a background variable uncertainty on effort in the presence of other risks. We allow for the simultaneous presence of wealth and background variable uncertainties. We investigate the joint effect of two-source uncertainties on effort when two risks are either small or positive quadrant dependent. Our work extends the previous model of effort to bivariate utility framework and presents new insights into the issue of optimal effort under uncertainty.

Air transportation systems are often subject to failures or attacks induced by unexpected abominable weather or temporal airspace occupation, while complex networks have been springing up as a convenient yet efficient tool to represent and analyze various realistic complex systems such as realistic airline system. In terms of Chinese airline network formed during the spring festival timespan, structural empirical research and invulnerability simulation analysis against various deliberate attack strategies were made using complex network theory, where nodes and edges denotes domestic airports and direct flights between them respectively. The analysis results indicate: The presented airline network is a small net-work with scale-free characteristics, and correlation shows remarkable hierarchical structure and obvious assortative characteristics; The network shows obvious invulnerability under deliberate node attack, while shows partly robustness under edge attack even with obvious attack effects against various attack strategies.

Information flow retains a critical role in decision making among investors. In this paper, we employ a diffusion model based on epidemiology theory to study the rumor spreading process within investors. The paper introduce the feedback mechanism of classical control theory into the model, which helps to reflect the interaction between rumor spreaders and information supervision. Further we apply a time delay factor to give investors access to transparent information and change their behavior. Subsequently, the stability of the rumor disappearance equilibrium and the rumor existence equilibrium are analyzed and the condition for the system undergoes a Hopf-bifurcation is given. The mathematical arguments are subjected to numerical simulations to present the ideal case scenarios. The results suggest that, increase the general strength of information supervision and the proportion coefficient associated with the infected population in the short-term delay are conducive to better control.

In the current real life, systems theory is an abstract background of systems thinking, which is a part of systemic behavior. The systemic behavior is the alternative to the currently prevailing one-sidedness that puts all of humankind in danger of self-destruction due to the crucial over-sights (all the way to world wars) that unavoidably result from the current over-specialization (along with crucial, but partial insights), if the specialists fail to practice creative interdisciplinary cooperation. This contribution is a next phase of research after the contributions by Matjaz̆ Mulej, Zdenka Z̆enko and Viktor Z̆akelj (2017) and by Matjaz̆ Mulej, et al. (2013). Although the abstract background and thinking that the systemic behavior applies, are very necessary, theory and thinking are no longer enough for systems science to be a relevant science and practice helping humankind find the way out from the current blind alley and survive as a healthy civilization with a healthy social and natural environment. The suggestion in this contribution therefore reads: Let us systems and cybernetics scientists make/enable the transition to systemic behavior, which applies all the many theories, which are components in the background of systemic behavior in practice, next to each other and/or in synergy. Analysis, i.e., studying per isolated parts is too overlooking and one-sided to be enough. So is teaching on a single one out of several systems theories. Reality is too complex. Teaching is a part of this necessary effort, which must lead to a global peace and survival of humankind of today instead of the current hating the human descendants.