Limit behaviour of upper and lower expected time averages in discrete-time imprecise Markov chains

We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now represented by sets of ‘plausible’ transition probabilities. Our main result is a necessary and sufficient condition under which these upper and lower bounds, called upper and lower expected time averages, will converge as time progresses towards infinity to limit values that do not depend on the process’ initial state. Remarkably, our condition is considerably weaker than those needed to establish similar results for so-called limit—or steady state—upper and lower expectations, which are often used to provide approximate information about the limit behaviour of time averages as well. We show that such an approximation is sub-optimal and that it can be significantly improved by directly using upper and lower expected time averages

Influence of Intra-granular Ferrite on the Tensile Behavior of Intercritically Annealed 12 pct Mn TWIP plus TRIP Steel

The influence of intra-granular ferrite islands, fully embedded in austenite matrix grains, on the tensile behavior of intercritically annealed Fe-12 pct Mn-0.3 pctC-3 pctAl TWIP+TRIP steel was investigated. The presence of intra-granular ferrite, which nucleated at twin boundaries during annealing, resulted in an increased yield strength by the Orowan dislocation looping mechanism and the generation of geometrically necessary dislocations at the ferrite particle/austenite matrix interface. The intra-granular ferrite also induced the formation of secondary twin variants. The resulting twin-twin intersections nucleated additional alpha'-martensite, thereby leading to an enhanced TRIP effect. (C) The Minerals, Metals & Materials Society and ASM International 2014open1155sciescopu

Observation of the TWIP plus TRIP Plasticity-Enhancement Mechanism in Al-Added 6 Wt Pct Medium Mn Steel

The intercritically annealed Fe-0.15 pctC-6.0 pctMn-1.5 pctSi-3.0 pctAl and Fe-0.30 pctC-6.0 pctMn-1.5 pctSi-3.0 pctAl medium Mn steels were found to have improved mechanical properties due to the TWIP and TRIP plasticity-enhancing mechanisms being activated in succession during tensile deformation. The increase of the C content from 0.15 to 0.30 pct resulted in ultra-high strength properties and a strength-ductility balance of approximately 65,000 MPa-pct, i.e., equivalent to the strength-ductility balance of high Mn TWIP steel with a fully austenitic microstructure.open112223sciescopu

Stability and convergence in discrete convex monotone dynamical systems

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is weaker than Lyapunov stability. Among others we show that the set of tangentially stable fixed points is isomorphic to a convex inf-semilattice, and a criterion is given for the existence of a unique tangentially stable fixed point. We also show that periods of tangentially stable periodic points are orders of permutations on $n$ letters, where $n$ is the dimension of the underlying space, and a sufficient condition for global convergence to periodic orbits is presented.Comment: 36 pages, 1 fugur

On Intercausal Interactions in Probabilistic Relational Models

Probabilistic relational models (PRMs) extend Bayesian networks beyond propositional expressiveness by allowing the representation of multiple interacting classes. For a specific instance of sets of concrete objects per class, a ground Bayesian network is composed by replicating parts of the PRM. The interactions between the objects that are thereby induced, are not always obvious from the PRM. We demonstrate in this paper that the replicative structure of the ground network in fact constrains the space of possible probability distributions and thereby the possible patterns of intercausal interactio

UNIFYING PRACTICAL UNCERTAINTY REPRESENTATIONS: I. GENERALIZED P-BOXES

Pre-print of final version.International audienceThere exist several simple representations of uncertainty that are easier to handle than more general ones. Among them are random sets, possibility distributions, probability intervals, and more recently Ferson's p-boxes and Neumaier's clouds. Both for theoretical and practical considerations, it is very useful to know whether one representation is equivalent to or can be approximated by other ones. In this paper, we define a generalized form of usual p-boxes. These generalized p-boxes have interesting connections with other previously known representations. In particular, we show that they are equivalent to pairs of possibility distributions, and that they are special kinds of random sets. They are also the missing link between p-boxes and clouds, which are the topic of the second part of this study