In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a b...In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a block design. This paper shows that a circular block design neighbor-balanced at distances up toγ≤k - 1, where k is the block size, is universally optimal for total effects under the linear models containing the neighbor effects at distances up toγamong the class of all circular binary block designs. Some combinatorial approaches to constructing these circular block designs neighbor-balanced at distances up to k - 1 are provided.展开更多
In agriculture experiments, the response on a given plot may be affected by the treatments on neighboring plots as well as by the treatments applied to that plot. In this paper we consider such type of situations and ...In agriculture experiments, the response on a given plot may be affected by the treatments on neighboring plots as well as by the treatments applied to that plot. In this paper we consider such type of situations and construct circular neighbor-balanced designs (CNBDs) by the method of cyclic shifts or sets of shifts. An important feature of this method is that the properties of a design can be easily obtained from the sets of shifts instead of constructing the actual blocks of the design. That is, the off-diagonal elements of the concurrence matrix can be easily obtained from the sets of shifts. Since the suggested designs are circular, balanced and binary, so they are universally optimal.展开更多
Most traditional artificial intelligence(AI)systems of the past decades are either very limited,or based on heuristics,or both.The new millennium,however,has brought substantial progress in the field of theoretically ...Most traditional artificial intelligence(AI)systems of the past decades are either very limited,or based on heuristics,or both.The new millennium,however,has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction,search,inductive inference based on Occam’s razor,problem solving,decision making,and reinforcement learning in environments of a very general type.Since inductive inference is at the heart of all inductive sciences,some of the results are relevant not only for AI and computer science but also for physics,provoking nontraditional predictions based on Zuse’s thesis of the computer-generated universe.We first briefly review the history of AI since Godel’s 1931 paper,then discuss recent post-2000 approaches that are currently transforming general AI research into a formal science.展开更多
基金This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10671007,10471127)Zhejiang Provincial Natural Science Foundation of China (Grant No. R604001)the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China and a CERG grant from Research Grants Council of Hong Kong
文摘In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a block design. This paper shows that a circular block design neighbor-balanced at distances up toγ≤k - 1, where k is the block size, is universally optimal for total effects under the linear models containing the neighbor effects at distances up toγamong the class of all circular binary block designs. Some combinatorial approaches to constructing these circular block designs neighbor-balanced at distances up to k - 1 are provided.
文摘In agriculture experiments, the response on a given plot may be affected by the treatments on neighboring plots as well as by the treatments applied to that plot. In this paper we consider such type of situations and construct circular neighbor-balanced designs (CNBDs) by the method of cyclic shifts or sets of shifts. An important feature of this method is that the properties of a design can be easily obtained from the sets of shifts instead of constructing the actual blocks of the design. That is, the off-diagonal elements of the concurrence matrix can be easily obtained from the sets of shifts. Since the suggested designs are circular, balanced and binary, so they are universally optimal.
文摘Most traditional artificial intelligence(AI)systems of the past decades are either very limited,or based on heuristics,or both.The new millennium,however,has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction,search,inductive inference based on Occam’s razor,problem solving,decision making,and reinforcement learning in environments of a very general type.Since inductive inference is at the heart of all inductive sciences,some of the results are relevant not only for AI and computer science but also for physics,provoking nontraditional predictions based on Zuse’s thesis of the computer-generated universe.We first briefly review the history of AI since Godel’s 1931 paper,then discuss recent post-2000 approaches that are currently transforming general AI research into a formal science.
