Reduction and Realization in Toda and Volterra

We construct a new symplectic, bi-hamiltonian realization of the KM-system by reducing the corresponding one for the Toda lattice. The bi-hamiltonian pair is constructed using a reduction theorem of Fernandes and Vanhaecke. In this paper we also review the important work of Moser on the Toda and KM-systems.Comment: 17 page

The last integrable case of kozlov-Treshchev Birkhoff integrable potentials

We establish the integrability of the last open case in the Kozlov-Treshchev classification of Birkhoff integrable Hamiltonian systems. The technique used is a modification of the so called quadratic Lax pair for $D_n$ Toda lattice combined with a method used by M. Ranada in proving the integrability of the Sklyanin case.Comment: 13 page

The Poisson bracket compatible with the classical reflection equation algebra

We introduce a family of compatible Poisson brackets on the space of $2\times 2$ polynomial matrices, which contains the reflection equation algebra bracket. Then we use it to derive a multi-Hamiltonian structure for a set of integrable systems that includes the $XXX$ Heisenberg magnet with boundary conditions, the generalized Toda lattices and the Kowalevski top.Comment: 13 pages, LaTeX with AmsFont

Reactive policies for the semantic web

Semantic Web policies are general statements defining the behavior of a system that acts on behalf of real users. These policies have various applications ranging from dynamic agent control to advanced access control policies. Although policies attracted a lot of research efforts in recent years, suitable representation and reasoning facilities allowing for reactive policies are not likewise developed. In this paper, we describe the concept of reactive Semantic Web policies. Reactive policies allow for the definition of events and actions, that is, they allow to define reactive behavior of a system acting on the Semantic Web. A reactive policy makes use of the tremendous amount of knowledge available on the Semantic Web in order to guide system behaviour while at the same time ensuring trusted and policy-compliant communication. We present a formal framework for expressing and enforcing such reactive policies in combination with advanced trust establishing techniques featuring an interplay between reactivity and agent negotiation. Finally, we explain how our approach was applied in a prototype which allows to define and enforce reactive Semantic Web policies on the Social Network and communication tool Skype

Rule-Based Policy Representations and Reasoning

Trust and policies are going to play a crucial role in enabling the potential of many web applications. Policies are a well-known approach to protecting security and privacy of users in the context of the Semantic Web: in the last years a number of policy languages were proposed to address different application scenarios. The first part of this chapter provides a broad overview of the research field by accounting for twelve relevant policy languages and comparing them on the strength of ten criteria which should be taken into account in designing every policy language. By comparing the choices designers made in addressing such criteria, useful conclusions can be drawn about strong points and weaknesses of each policy language. The second part of this chapter is devoted to the description of the Protune framework, a system for specifying and cooperatively enforcing security and privacy policies on the Semantic Web developed within the network of excellence REWERSE. We describe the framework’s functionalities, provide details about their implementation, and report the results of performance evaluation experiments