Symplectic structures on right-angled Artin groups: between the mapping class group and the symplectic group

We define a family of groups that include the mapping class group of a genus g surface with one boundary component and the integral symplectic group Sp(2g,Z). We then prove that these groups are finitely generated. These groups, which we call mapping class groups over graphs, are indexed over labeled simplicial graphs with 2g vertices. The mapping class group over the graph Gamma is defined to be a subgroup of the automorphism group of the right-angled Artin group A_Gamma of Gamma. We also prove that the kernel of the map Aut A_Gamma to Aut H_1(A_Gamma) is finitely generated, generalizing a theorem of Magnus.Comment: 45 page

One-relator Kaehler groups

We prove that a one-relator group $G$ is K\"ahler if and only if either $G$ is finite cyclic or $G$ is isomorphic to the fundamental group of a compact orbifold Riemann surface of genus $g > 0$ with at most one cone point of order $n$: $$< a_1\, b_1\, \,...\, a_g\, b_g\, \mid\, (\prod_{i=1}^g [a_i\, b_i])^n>\, .$$Comment: v2: 9pgs. no figs. Final version, to appear in "Geometry and Topology

Limit groups and groups acting freely on R^n-trees

We give a simple proof of the finite presentation of Sela's limit groups by using free actions on R^n-trees. We first prove that Sela's limit groups do have a free action on an R^n-tree. We then prove that a finitely generated group having a free action on an R^n-tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic groups. As a corollary, such a group is finitely presented, has a finite classifying space, its abelian subgroups are finitely generated and contains only finitely many conjugacy classes of non-cyclic maximal abelian subgroups.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper39.abs.htm

Integrating Schedulability Analysis with UML-RT

The use of object oriented techniques and methodologies for the design of real-time control systems appear to be necessary in order to deal with the increasing complexity of such systems. Recently many object-oriented methods have been used for the modeling and design of real-time control systems. We believe that an approach that integrates the advancements in both object modeling and design methods, and real-time scheduling theory is the key to successful use of object oriented technology for real-time software. However, past approaches to integrate the two either restrict the object models, or do not allow sophisticated schedulability analysis techniques. In this paper we show how schedulability analysis can be integrated with object-oriented design; we develop the schedulability and feasibility analysis method for the external messages that may suffer release jitter due to being dispatched by a tick driven scheduler in real-time control system, and we also develop the scheduliability method for sporadic activities, where message arrive sporadically then execute periodically for some bounded time. This method can be used to cope with timing constraints in complex real-time control systems

UML Extensions for Real-Time Control Systems

The use of object oriented techniques and methodologies for the design of real-time control systems appears to be necessary in order to deal with the increasing complexity of such systems. Recently many object-oriented methods have been used for the modeling and design of real-time control systems. We believe that an approach that integrates the advancements in both object modeling and design methods, and real-time scheduling theory is the key to successful use of object oriented technology for real-time software. Surprisingly several past approaches to integrate the two either restrict the object models, or do not allow sophisticated schedulability analysis techniques. In this paper we show how schedulability analysis can be integrated with object-oriented design. More specifically, we develop the schedulability and feasibility analysis method for the external messages that may suffer release jitter due to being dispatched by a tick driven scheduler in real-time control system, and we also develop the scheduliability method for sporadic activities, where message arrive sporadically then execute periodically for some bounded time. This method can be used to cope with timing constraints in realistic and complex real-time control systems. Using this method, a designer can quickly evaluate the impact of various implementation decisions on schedulability. In conjunction with automatic code-generation, we believe that this will greatly streamline the design and development of real-time control system software

Extending UML-RT for Control System Modelling

There is a growing interest in adopting object technologies for the development of real-time control systems. Several commercial tools, currently available, provide object-oriented modeling and design support for real-time control systems. While these products provide many useful facilities, such as visualization tools and automatic code generation, they are all weak in addressing the central characteristic of real-time control systems design, i.e., providing support for a designer to reason about timeliness properties. We believe an approach that integrates the advancements in both object modeling and design methods and real-time scheduling theory is the key to successful use of object technology for real-time software. Surprisingly several past approaches to integrate the two either restrict the object models, or do not allow sophisticated schedulability analysis techniques. This study shows how schedulability analysis can be integrated with UML for Real-Time (UML-RT) to deal with timing properties in real time control systems. More specifically, we develop the schedulability and feasibility analysis modeling for the external messages that may suffer release jitter due to being dispatched by a tick driven scheduler in real-time control system and we also develop the scheduliablity modeling for sporadic activities, where messages arrive sporadically then execute periodically for some bounded time. This method can be used to cope with timing constraints in realistic and complex real-time control systems. Using this method, a designer can quickly evaluate the impact of various implementation decisions on schedulability. In conjunction with automatic code-generation, we believe that this will greatly streamline the design and development of real-time control systems software