Approximate Common Knowledge Based on Uncertain Measure

This paper studies that how an uncertain event can be outlined as an approximate common knowledge. By replacing “know” with “know with certainty α” in standard definitions of common knowledge, approximate common knowledge with some certainty, defined iteratively and mutually, iteratively known and mutually known with some certainty, are explored. Examples are constructed to show that an event which is not common knowledge can be analyzed as an approximate common knowledge with some certainty. An application in the principal-agent model is investigated to show that approximate common knowledge based on uncertain measure can be applied to improve the behavior of an economic model

A Birandom Job Search Problem with Risk Tolerance

This paper considers a novel class of birandom job search problem, in which the job offers are sampled by the job searcher from a finite job set with equivalent probability and their wages are characterized as independent but maybe not identically nonnegative random variables. The job searcher knows the job offer's wage distribution when he samples the job offer. Since the offered wage is a random variable and the reservation wage is a deterministic number, it is meaningless to make comparison directly. In order to rank the random wage and the reservation wage and provide decision support, a risk tolerance criterion is designed, and the job searcher then accepts or rejects the sampled job offer depending on whether the risk tolerance criterion is met or not. Since the offered wages are random variables and the search process is random, it's impossible to obtain the job searcher's real return; in this case, its expected value can be calculated via birandom theory. Simultaneously, some propositions on the expected return as well as the average search times are also studied which may provide some valuable suggestions to the job searcher. Numerical examples are given to illustrate the decision process of the risk tolerance-based birandom job search problem

Equilibrium search with heterogeneous firms, workers and endogenous human capital

This article shows how the endogenous human capital affects the labor market equilibrium when jobs provided by firms can be either unskilled or skilled and workers differ in their education level which can be either low-educated or high-educated. We develop an equilibrium search model in which the high-educated workers are assumed to be able to accept either the unskilled jobs or the skilled jobs, while the low-educated workers can only accept the unskilled jobs. The market equilibrium is characterized by deriving the unemployment rate and the human capital distributions when the growth rate of the human capital is an endogenous variable. The results demonstrate that the structure proportion of the offered jobs affects the equilibrium which shows there is a threshold that can distinguish whether the equilibrium is separating or cross-skill. In addition, the cross-skill equilibrium solution implies the high-educated workers are more likely to own higher pay rates than the low-educated workers with same tenure. It also yields a new insight on the effect of the structure proportion of workers on the profits, which implies the profits of the firms decrease with the increasing number of the low-educated workers. Moreover, the profit of the firms offering the skilled jobs is greater than those offering the unskilled jobs until there is only very few high-educated workers

Equilibrium search with heterogeneous firms, workers and endogenous human capital

This article shows how the endogenous human capital affects the labor market equilibrium when jobs provided by firms can be either unskilled or skilled and workers differ in their education level which can be either low-educated or high-educated. We develop an equilibrium search model in which the high-educated workers are assumed to be able to accept either the unskilled jobs or the skilled jobs, while the low-educated workers can only accept the unskilled jobs. The market equilibrium is characterized by deriving the unemployment rate and the human capital distributions when the growth rate of the human capital is an endogenous variable. The results demonstrate that the structure proportion of the offered jobs affects the equilibrium which shows there is a threshold that can distinguish whether the equilibrium is separating or cross-skill. In addition, the cross-skill equilibrium solution implies the high-educated workers are more likely to own higher pay rates than the low-educated workers with same tenure. It also yields a new insight on the effect of the structure proportion of workers on the profits, which implies the profits of the firms decrease with the increasing number of the low-educated workers. Moreover, the profit of the firms offering the skilled jobs is greater than those offering the unskilled jobs until there is only very few high-educated workers

The SPB-Box Transcription Factor AaSPL2 Positively Regulates Artemisinin Biosynthesis in Artemisia annua L.

Artemisinin, an important compound produced by Artemisia annua, is the active ingredient in the treatment of malaria. Jasmonic acid, one of the phytohormones, is an important elicitor of artemisinin biosynthesis by enhancing transcription levels of transcription factors. SPL transcription factors are plant-specific transcription factors of plant growth, development, and secondary metabolism regulation. However, to date, the SPL transcription factors that regulate artemisinin biosynthesis is currently unclear. Here, we show that an SPL transcription factor can positively regulate artemisinin biosynthesis by binding to the promoter of artemisinin biosynthetic pathway genes. We screened AaSPL2 by gene expression profiles analysis in 14 SPL transcription factors. We demonstrated that AaSPL2 can activate the promoter of DBR2 by dual-LUC assy. Moreover, in the AaSPL2 overexpression plants, the artemisinin content was increased by 33–86%, and in the AaSPL2 -RNAi transgenic plants, artemisinin content was decreased by 33–65%. These data suggest that AaSPL2 and DBR2 interact with a “GTAC” cis-element in the DBR2 promoter, mediating the transcriptional activation of DBR2 in response to JA and resulting in the improvement on artemisinin content

Optimal Control for a Class of Chaotic Systems

This paper proposes the optimal control methods for a class of chaotic systems via state feedback. By converting the chaotic systems to the form of uncertain piecewise linear systems, we can obtain the optimal controller minimizing the upper bound on cost function by virtue of the robust optimal control method of piecewise linear systems, which is cast as an optimization problem under constraints of bilinear matrix inequalities (BMIs). In addition, the lower bound on cost function can be achieved by solving a semidefinite programming (SDP). Finally, numerical examples are given to illustrate the results