On properties not inherited by monoids from their Schützenberger groups

We give an example of a monoid with finitely many left and right ideals, all of whose Schützenberger groups are presentable by finite complete rewriting systems, and so each have finite derivation type, but such that the monoid itself does not have finite derivation type, and therefore does not admit a presentation by a finite complete rewriting system. The example also serves as a counterexample to several other natural questions regarding complete rewriting systems and finite derivation type. Specifically it allows us to construct two finitely generated monoids M and N with isometric Cayley graphs, where N has finite derivation type (respectively, admits a presentation by a finite complete rewriting system) but M does not. This contrasts with the case of finitely generated groups for which finite derivation type is known to be a quasi-isometry invariant. The same example is also used to show that neither of these two properties is preserved under finite Green index extensions.     

Model order reduction methods for coupled systems in the time domain using Laguerre polynomials

In this paper, based on Laguerre polynomials, we present new methods for model reduction of coupled systems in the time domain. By appropriately selected projection matrices, a reduced order system is produced to retain the topology structure of the original system. Meanwhile, it preserves a desired number of Laguerre coefficients of the system’s output, thereby providing good approximation accuracy. We also study the two-sided projection method in the time domain, as well as the stability of reduced order systems. Two numerical examples are used to illustrate the efficiency of the proposed methods.     

Iterative methods for solving extended general mixed variational inequalities

In this paper, we introduce and consider a new class of mixed variational inequalities involving four operators, which are called extended general mixed variational inequalities. Using the resolvent operator technique, we establish the equivalence between the extended general mixed variational inequalities and fixed point problems as well as resolvent equations. We use this alternative equivalent formulation to suggest and analyze some iterative methods for solving general mixed variational inequalities. We study the convergence criteria for the suggested iterative methods under suitable conditions. Our methods of proof are very simple as compared with other techniques. The results proved in this paper may be viewed as refinements and important generalizations of the previous known results.     

On the mathematical theory of living systems II: The interplay between mathematics and system biology

This paper aims at showing how the so-called mathematical kinetic theory for active particles can be properly developed to propose a new system biology approach. The investigation begins with an analysis of complexity in biological systems, continues with reviewing a general methodology to reduce complexity and furnishes the mathematical tools to describe the time evolution of such systems by capturing all their features.     

A framework for the collective movement of mobile robots based on distributed decisions

A novel framework for the control of the collective movement of mobile robots is presented and analyzed in this article. It allows a group of robots to move as a unique entity performing the following functions: obstacle avoidance at group level, speed control and modification of the inter-robot distance. Its flocking controller is distributed among the robots, allowing them to move in the desired common direction and maintain a desired inter-robot distance. The framework is made up of different modules that modify the behavior of the group thus allowing different functions. They are based on consensus algorithms that allow the robots to agree on different parameters, taking into account which robot has more relevant information. New modules can be easily designed and incorporated into the framework in order to augment its capabilities. It can be easily implemented on any mobile robot capable of measuring the relative positions of neighboring robots and communicating with them. It has been successfully tested using 8 real robots and in simulation with up to 40 robots, demonstrating experimentally its scalability with an increasing number of robots.     

A review of optimization methodologies in support vector machines

Support vector machines (SVMs) are theoretically well-justified machine learning techniques, which have also been successfully applied to many real-world domains. The use of optimization methodologies plays a central role in finding solutions of SVMs. This paper reviews representative and state-of-the-art techniques for optimizing the training of SVMs, especially SVMs for classification. The objective of this paper is to provide readers an overview of the basic elements and recent advances for training SVMs and enable them to develop and implement new optimization strategies for SVM-related research at their disposal.     

改进的证据理论在合作频谱感知中的应用

为了能够在认知无线电网络中有效、准确地检测出授权用户,提出了基于改进的证据理论的合作频谱感知方案设计方法.根据各个次用户对授权用户进行多次本地检测得出的时域DS融合结果,设计并改进融合顺序和融合结构,将多个时域DS融合结果送到融合中心进行空域DS融合,得到最终判决.在此基础上,给出了融合顺序、融合结构的改变对算法性能的...     

网络控制系统的预测补偿

针对网络控制系统中存在长时延和数据丢包的情况,通过在控制器节点前设置缓冲器,并设计预估控制产生器和时延补偿器,提出了一种预测补偿控制方案,有效地克服了长时延、数据丢包和时序错乱问题对实际网络控制系统稳定性所造成的影响．证明了采用上述控制方案时闭环网络控制系统的稳定性,最后提供的仿真实例验证了该控制方案的有效性．     

多星系统相对轨道的自适应协同控制

基于一致性理论,在无向拓扑结构上对多星系统相对轨道的协同控制问题进行了研究.本文考虑近地卫星相对轨道的非线性方程,首先设计控制律使得多星系统形成目标队形,并给出了速度阻尼和通信拓扑(相对速度间的拓扑关系)连通性之间的关系;其次,针对卫星质量具有不确定性的情形,设计了新的辅助变量,提出了自适应的协同控制律,这里要求传感(相对位置间的拓扑关系)和通信具有相同的拓扑结构.最后对4颗卫星的编队飞行进行了仿真分析,仿真结果表明本文设计的协同控制律是有效可行的.