Data-Driven Leader-Follower Output Synchronization for Networked Non-Linear Multi-Agent Systems with Switching Topology and Time-Varying Delays

This paper studies the output synchronization problem for a class of networked non-linear multi-agent systems with switching topology and time-varying delays. To synchronize the outputs, a leader is introduced whose connectivity to the followers varies with time, and a novel data-driven consensus protocol based on model free adaptive control is proposed, where the reference input of each follower is designed to be the time-varying average of the neighboring agents’ outputs. Both the case when the leader is with a prescribed reference input and the case otherwise are considered. The proposed protocol allows for time-varying delays, switching topology, and does not use the agent structure or the dynamics information implicitly or explicitly. Sufficient conditions are derived to guarantee the closed-loop stability, and conditions for consensus convergence are obtained, where only a joint spanning tree is required. Numerical simulations and practical experiments are conducted to demonstrate the effectiveness of the proposed protocol.     

Contours and Tight Clusters

Nested clusters arise independently in graph partitioning and in the study of contours. We take a step toward unifying these two instances of nested clusters. We show that the graph theoretical tight clusters introduced by Dress, Steel, Moulton and Wu in 2010 are a special case of nested clusters associated to contours.     

An empirical investigation on the risk-return relationship of carbon future market

This paper examines the risk-return relationship for the carbon future market during Phases I, II and III of the European Union Emission Trading Scheme (EU ETS). The risk factors derived from the newly developed LSW model, are embedded into a GARCH framework. This new specification is compared with several GARCH-M type models analyzing the risk-return relationship in the carbon market. The results show that the new specification consistently achieves a good fit and possesses superior explanatory power for the European Union Allowance (EUA) data. Some policy suggestions regarding market efficiency are also provided.     

Systemic Design for Applying the Combined Use of SSM and CDA to Social Practices

In this paper, we propose a framework for applying the combined use of soft systems methodology (SSM) and critical discourse analysis (CDA) based on social semiotic systemic functional linguistics to social practices. In the social practice, ‘participation’ mode of Checkland’s SSM is used for ‘problem-solving’ whilst CDA is used to problematize ‘problem-solving’ processes within the practice. During the meta-process of problematization of our research, we used Churchman’s systems approach and its theory of ‘boundary critique’ in order to explore issues such as governance, inequality of power, and social values within the organization examined for this study. In other words, the process-oriented methodology proposed in this paper consists of two processes: that of ‘problem-solving’ based on SSM and of problematization of naturalized discourse from the perspective of CDA and two phases of boundary critique in social practice. A detailed account of a case study of Korean social enterprise is given to demonstrate how our proposed framework of the combined use of SSM and CDA is applied into practice. Reflecting the outcome of the case study, this paper argues that critical social research from systemic inquiry using what we call ‘process-oriented methodology’ is useful to address some of the social and complex issues related to understanding dynamic relation between power and discourse amongst participants in the social enterprise in Korean contexts.     

On implementing the symbolic preprocessing function over Boolean polynomial rings in Gröbner basis algorithms using linear algebra

Some techniques using linear algebra was introduced by Faugère in F4 to speed up the reduction process during Gr?bner basis computations.These techniques can also be used in fast implementations of F5 and some other signature-based Gr?bner basis algorithms.When these techniques are applied,a very important step is constructing matrices from critical pairs and existing polynomials by the Symbolic Preprocessing function(given in F4).Since multiplications of monomials and polynomials are involved in the Symbolic Preprocessing function,this step can be very costly when the number of involved polynomials/monomials is huge.In this paper,multiplications of monomials and polynomials for a Boolean polynomial ring are investigated and a specific method of implementing the Symbolic Preprocessing function over Boolean polynomial rings is reported.Many examples have been tested by using this method,and the experimental data shows that the new method is very efficient.     

Comments on a Paper on Alleged Misconceptions Regarding the History of Analysis: Who Has Misconceptions?

This comment is analysing the last section of a paper by Piotr Blaszczyk, Mikhail G. Katz, and David Sherry on alleged misconceptions committed by historians of mathematics regarding the history of analysis, published in this journal in the first issue of 2013. Since this section abounds of wrong attributions and denouncing statements regarding my research and a key publication, the comment serves to rectify them and to recall some minimal methodological requirements for historical research.     

An M-Objective Penalty Function Algorithm Under Big Penalty Parameters

Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software, which makes them impossible to find out an optimal solution to constrained optimization problems. In this paper, a novel penalty function (called M-objective penalty function) with one penalty parameter added to both objective and constrained functions of inequality constrained optimization problems is proposed. Based on the M-objective penalty function, an algorithm is developed to solve an optimal solution to the inequality constrained optimization problems, with its convergence proved under some conditions. Furthermore, numerical results show that the proposed algorithm has a much better convergence than the classical penalty function algorithms under big penalty parameters, and is efficient in choosing a penalty parameter in a large range in Matlab software.