106 research outputs found
Strong, Weak and Branching Bisimulation for Transition Systems and Markov Reward Chains: A Unifying Matrix Approach
We first study labeled transition systems with explicit successful
termination. We establish the notions of strong, weak, and branching
bisimulation in terms of boolean matrix theory, introducing thus a novel and
powerful algebraic apparatus. Next we consider Markov reward chains which are
standardly presented in real matrix theory. By interpreting the obtained matrix
conditions for bisimulations in this setting, we automatically obtain the
definitions of strong, weak, and branching bisimulation for Markov reward
chains. The obtained strong and weak bisimulations are shown to coincide with
some existing notions, while the obtained branching bisimulation is new, but
its usefulness is questionable
Mutation-selection models of sequence evolution in population genetics
The equilibrium properties of a number of deterministic mutation- selection models of sequence evolution are investigated. Both two- and four-state sequences are considered, the mutation model is a single-step mutation model. Two types of fitness functions are studied, namely permutation-invariant fitness functions, where the fitness of a sequence depends only on the number of mutations, not on their location within the sequence, and Hopfield-type fitness functions, where the fitness of a sequence is determined by its similarity to a number of predefined patterns. Maximum principles to determine the population mean fitness in equilibrium are derived, where the maximiser gives also the ancestral mean genotype. These maximum principles are used to investigate the error threshold phenomenon, i.e., the phenomenon that for certain fitness functions the population changes at a critical mutation rate from a well localised to a delocalised distribution in sequence space. The error threshold phenomenon is investigated for a four-state model with permutation-invariant fitness functions and for a two-state model with Hopfield-type fitness functions. Both models yield ordered and disordered as well as partially ordered phases
Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems
Development of robust dynamical systems and networks such as autonomous
aircraft systems capable of accomplishing complex missions faces challenges due
to the dynamically evolving uncertainties coming from model uncertainties,
necessity to operate in a hostile cluttered urban environment, and the
distributed and dynamic nature of the communication and computation resources.
Model-based robust design is difficult because of the complexity of the hybrid
dynamic models including continuous vehicle dynamics, the discrete models of
computations and communications, and the size of the problem. We will overview
recent advances in methodology and tools to model, analyze, and design robust
autonomous aerospace systems operating in uncertain environment, with stress on
efficient uncertainty quantification and robust design using the case studies
of the mission including model-based target tracking and search, and trajectory
planning in uncertain urban environment. To show that the methodology is
generally applicable to uncertain dynamical systems, we will also show examples
of application of the new methods to efficient uncertainty quantification of
energy usage in buildings, and stability assessment of interconnected power
networks
A uniform framework for modelling nondeterministic, probabilistic, stochastic, or mixed processes and their behavioral equivalences
Labeled transition systems are typically used as behavioral models of concurrent processes, and the labeled transitions define the a one-step state-to-state reachability relation. This model can be made generalized by modifying the transition relation to associate a state reachability distribution, rather than a single target state, with any pair of source state and transition label. The state reachability distribution becomes a function mapping each possible target state to a value that expresses the degree of one-step reachability of that state. Values are taken from a preordered set equipped with a minimum that denotes unreachability. By selecting suitable preordered sets, the resulting model, called ULTraS from Uniform Labeled Transition System, can be specialized to capture well-known models of fully nondeterministic processes (LTS), fully
probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and of nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. These can be defined on ULTraS by relying on appropriate measure functions that expresses the degree of reachability of a set of states when performing
single-step or multi-step computations. It is shown that the specializations of bisimulation, trace, and testing
equivalences for the different classes of ULTraS coincide with the behavioral equivalences defined in the literature over traditional models
Methodologies synthesis
This deliverable deals with the modelling and analysis of interdependencies between critical infrastructures, focussing attention on two interdependent infrastructures studied in the context of CRUTIAL: the electric power infrastructure and the information infrastructures
supporting management, control and maintenance functionality. The main objectives are: 1) investigate the main challenges to be addressed for the analysis and modelling of interdependencies, 2) review the modelling methodologies and tools that can be used to address these challenges and support the evaluation of the impact of interdependencies on the dependability and resilience of the service delivered to the users, and 3) present the preliminary directions investigated so far by the CRUTIAL consortium for describing and modelling interdependencies
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