Automatic computation of data-set definitions

Mathematical method for the construction of a computer program data set description from a computer program contains detailed declarative information. Cartesian products and disjoint-union operators are used to yield a series of recursive group equations

Kalman Filtering Over a Packet-Dropping Network: A Probabilistic Perspective

We consider the problem of state estimation of a discrete time process over a packet-dropping network. Previous work on Kalman filtering with intermittent observations is concerned with the asymptotic behavior of E[P_k], i.e., the expected value of the error covariance, for a given packet arrival rate. We consider a different performance metric, Pr[P_k ≤ M], i.e., the probability that P_k is bounded by a given M. We consider two scenarios in the paper. In the first scenario, when the sensor sends its measurement data to the remote estimator via a packet-dropping network, we derive lower and upper bounds on Pr[P_k ≤ M]. In the second scenario, when the sensor preprocesses the measurement data and sends its local state estimate to the estimator, we show that the previously derived lower and upper bounds are equal to each other, hence we are able to provide a closed form expression for Pr[P_k ≤ M]. We also recover the results in the literature when using Pr[P_k ≤ M] as a metric for scalar systems. Examples are provided to illustrate the theory developed in the paper

Deliverable JRA1.1: Evaluation of current network control and management planes for multi-domain network infrastructure

This deliverable includes a compilation and evaluation of available control and management architectures and protocols applicable to a multilayer infrastructure in a multi-domain Virtual Network environment.The scope of this deliverable is mainly focused on the virtualisation of the resources within a network and at processing nodes. The virtualization of the FEDERICA infrastructure allows the provisioning of its available resources to users by means of FEDERICA slices. A slice is seen by the user as a real physical network under his/her domain, however it maps to a logical partition (a virtual instance) of the physical FEDERICA resources. A slice is built to exhibit to the highest degree all the principles applicable to a physical network (isolation, reproducibility, manageability, ...). Currently, there are no standard definitions available for network virtualization or its associated architectures. Therefore, this deliverable proposes the Virtual Network layer architecture and evaluates a set of Management- and Control Planes that can be used for the partitioning and virtualization of the FEDERICA network resources. This evaluation has been performed taking into account an initial set of FEDERICA requirements; a possible extension of the selected tools will be evaluated in future deliverables. The studies described in this deliverable define the virtual architecture of the FEDERICA infrastructure. During this activity, the need has been recognised to establish a new set of basic definitions (taxonomy) for the building blocks that compose the so-called slice, i.e. the virtual network instantiation (which is virtual with regard to the abstracted view made of the building blocks of the FEDERICA infrastructure) and its architectural plane representation. These definitions will be established as a common nomenclature for the FEDERICA project. Other important aspects when defining a new architecture are the user requirements. It is crucial that the resulting architecture fits the demands that users may have. Since this deliverable has been produced at the same time as the contact process with users, made by the project activities related to the Use Case definitions, JRA1 has proposed a set of basic Use Cases to be considered as starting point for its internal studies. When researchers want to experiment with their developments, they need not only network resources on their slices, but also a slice of the processing resources. These processing slice resources are understood as virtual machine instances that users can use to make them behave as software routers or end nodes, on which to download the software protocols or applications they have produced and want to assess in a realistic environment. Hence, this deliverable also studies the APIs of several virtual machine management software products in order to identify which best suits FEDERICA’s needs.Postprint (published version

Model Creation and Equivalence Proofs of Cellular Automata and Artificial Neural Networks

Computational methods and mathematical models have invaded arguably every scientific discipline forming its own field of research called computational science. Mathematical models are the theoretical foundation of computational science. Since Newton's time, differential equations in mathematical models have been widely and successfully used to describe the macroscopic or global behaviour of systems. With spatially inhomogeneous, time-varying, local element-specific, and often non-linear interactions, the dynamics of complex systems is in contrast more efficiently described by local rules and thus in an algorithmic and local or microscopic manner. The theory of mathematical modelling taking into account these characteristics of complex systems has to be established still. We recently presented a so-called allagmatic method including a system metamodel to provide a framework for describing, modelling, simulating, and interpreting complex systems. Implementations of cellular automata and artificial neural networks were described and created with that method. Guidance from philosophy were helpful in these first studies focusing on programming and feasibility. A rigorous mathematical formalism, however, is still missing. This would not only more precisely describe and define the system metamodel, it would also further generalise it and with that extend its reach to formal treatment in applied mathematics and theoretical aspects of computational science as well as extend its applicability to other mathematical and computational models such as agent-based models. Here, a mathematical definition of the system metamodel is provided. Based on the presented formalism, model creation and equivalence of cellular automata and artificial neural networks are proved. It thus provides a formal approach for studying the creation of mathematical models as well as their structural and operational comparison.Comment: 13 pages, 1 tabl