Different Approaches on Stochastic Reachability as an Optimal Stopping Problem

Reachability analysis is the core of model checking of time systems. For stochastic hybrid systems, this safety verification method is very little supported mainly because of complexity and difficulty of the associated mathematical problems. In this paper, we develop two main directions of studying stochastic reachability as an optimal stopping problem. The first approach studies the hypotheses for the dynamic programming corresponding with the optimal stopping problem for stochastic hybrid systems. In the second approach, we investigate the reachability problem considering approximations of stochastic hybrid systems. The main difficulty arises when we have to prove the convergence of the value functions of the approximating processes to the value function of the initial process. An original proof is provided

A statistical inference method for the stochastic reachability analysis.

The main contribution of this paper is the characterization of reachability problem associated to stochastic hybrid systems in terms of imprecise probabilities. This provides the connection between reachability problem and Bayesian statistics. Using generalised Bayesian statistical inference, a new concept of conditional reach set probabilities is defined. Then possible algorithms to compute the reach set probabilities are derived

Bisimulation, Logic and Reachability Analysis for Markovian Systems

In the recent years, there have been a large amount of investigations on safety verification of uncertain continuous systems. In engineering and applied mathematics, this verification is called stochastic reachability analysis, while in computer science this is called probabilistic model checking (PMC). In the context of this work, we consider the two terms interchangeable. It is worthy to note that PMC has been mostly considered for discrete systems. Therefore, there is an issue of improving the application of computer science techniques in the formal verification of continuous stochastic systems. We present a new probabilistic logic of model theoretic nature. The terms of this logic express reachability properties and the logic formulas express statistical properties of terms. Moreover, we show that this logic characterizes a bisimulation relation for continuous time continuous space Markov processes. For this logic we define a new semantics using state space symmetries. This is a recent concept that was successfully used in model checking. Using this semantics, we prove a full abstraction result. Furthermore, we prove a result that can be used in model checking, namely that the bisimulation preserves the probabilities of the reachable sets

Survival of the black hole's Cauchy horizon under non-compact perturbations

We study numerically the evolution of spactime, and in particular of a spacetime singularity, inside a black hole under a class of perturbations of non-compact support. We use a very simplified toy model of a spherical charged black hole which is perturbed nonlinearly by a self-gravitating, spherical scalar field. The latter grows logarithmically with advanced time along an outgoing characteristic hypersurface. We find that for that class of perturbations a portion of the Cauchy horizon survives as a non-central, null singularity.Comment: 5 pages, 4 figure

Analysis of nonlinear oscillators in the frequency domain using volterra series Part II : identifying and modelling jump Phenomenon

In this the second part of the paper, a common and severe nonlinear phenomenon called jump, a behaviour associated with the Duffing oscillator and the multi-valued properties of the response solution, is investigated. The new frequency domain criterion of establishing the upper limits of the nonlinear oscillators, developed in Part I of this paper, is applied to predict the onset point of the jump, and the Volterra time and frequency domain analysis of this phenomenon are carried out based on graphical and numerical techniques

Piecewise Volterra modelling of the Duffing oscillator in the frequency domain

When analysing the nonlinear Duffing oscillator, the weak nonlinearity is basically dependent on the amplitude range of the input excitation. The nonlinear differential equation models of such nonlinear oscillators, which can be transformed into the frequency domain, can generally only provide Volterra modelling and analysis in the frequency-domain over a fraction of the entire framework of weak nonlinearity. This paper discusses the problem of using a new non-parametric routine to extend the capability of Volterra analysis, in the frequency domain, to weakly nonlinear Duffing systems at a wider range of excitation amplitude range which the current underlying nonlinear differential equation models fail to address

Self-concept, emotions and consumer coping : smoking across Europe

Whereas much previous research focuses on the ways consumers strive to gain social approval, consumption that may result in social disapproval must be considered. In order to do so, the purpose of this paper is to explore consumers' self-concepts within a risky consumption context, namely smoking. Self-concept discrepancies and the resulting emotions and coping strategies are identified. A qualitative methodology based on 30 focus groups conducted across ten European countries is employed. Findings demonstrate self-concept discrepancies between both the actual self and ought/ideal guiding end states, as well as between the 'I' and social selves. Such discrepancies generate negative emotions and result in emotion-focused coping strategies. In addition, the accuracy of smokers' social self-concepts with reference to the actual perceptions of non-smokers is discussed. Important implications for the design of effective anti-smoking advertising are discussed, based on the findings. It is suggested that counter advertising should encourage dialogue between smokers and non-smokers and that message themes should centre on building the self-efficacy of smokers. The reason why the social context should be an integral part of consumer self-concept research is highlighted. Moreover, the importance of moving beyond merely understanding the existence of self-discrepancies, to focus on the emotions that are generated by these discrepancies and the consequent coping strategies employed to resolve them is identified. As such, the potential contributions that may arise by recognising the intersection between two bodies of literature that are often treated separately, namely, consumer coping and the self-concept, are highlighted

RRS "Charles Darwin" Cruise 169, 17 Feb-19 Mar 2005. Hydrothermal exploration of the southern Mid-Atlantic Ridge

The principal objective of this cruise was to identify the first site or sites of high temperature hydrothermal venting anywhere on the southern Mid-Atlantic Ridge, to characterize their geological setting, preliminary chemical nature and to identify, where possible, the nature of any vent-endemic species that might inhabit such vents to investigate whether this ridge system might represent a new biogeographic province. Initially we used the TOBI deep-tow sidescan system equipped with a CTD system and optical backscatter sensors, together with Miniature Autonomous Plume Recorders (MAPRs) to identify two new sites in which diagnostic chemically- and particle-laden plumes indicated the presence of high-temperature hydrothermal venting. Subsequently, we used the ABE autonomous underwater vehicle to (1) locate the core of one of these hydrothermal plumes, (2) obtain a detailed map of the underlying seafloor and (3) photograph three discrete hydrothermal sites (2 black-smoker systems, 1 diffuse-flow) and their associated ecosystems. A series of CTD stations were occupied for water column investigations and a number of rock-coring and dredging stations were also undertaken to provide groundtruthing of sidescan sonar images of the Mid-Atlantic Ridge seafloor

Analysis of a duffing oscillator that exhibits hysteresis with varying excitation frequency and amplitude

Hysteresis, or jump phenomenon, are a common and severe nonlinear behaviour associated with the Duffing oscillator and the multi-valued properties of the response solution. Jump phenomenon can be induced by either varying the amplitude or the frequency of excitation. In this paper a new time and frequency domain analysis is applied to this class of system based on the response curve and the response spectrum map

Analysis of nonlinear oscillators using volterra series in the frequency domain Part I : convergence limits

The Volterra series representation is a direct generalisation of the linear convolution integral and has been widely applied in the analysis and design of nonlinear systems, both in the time and the frequency domain. The Volterra series is associated with the so-called weakly nonlinear systems, but even within the framework of weak nonlinearity there is a convergence limit for the existence of a valid Volterra series representation for a given nonlinear differential equation. Barrett(1965) proposed a time domain criterion to prove that the Volterra series converges with a given region for a class of nonlinear systems with cubic stiffness nonlinearity. In this paper this time-domain criterion is extended to the frequency domain to accommodate the analysis of nonlinear oscillators subject to harmonic excitation