A recent claim by Bassi and Ghirardi that the consistent (decoherent) histories approach cannot provide a realistic interpretation of quantum theory is shown to be based upon a misunderstanding of the single-framework rule: they have replaced the correct rule with a principle which directly contradicts it. It is their assumptions, not those of the consistent histories approach, which lead to a ...

The consistent histories approach to quantum mechanics is traditionally based on linearly ordered sequences of events. We extend the histories formalism to sets of events whose causal ordering is described by directed acyclic graphs. The need for a global time is eliminated and our construction reflects the causal structure faithfully.

In this paper we suggest a numerical implementation based on plain Monte Carlo simulation of the conditional expectations in the following Markovian setting: Suppose (X(i),Fi), 0 ≤ i ≤ k, is a possibly high-dimensional Markov process and the cashflow is of the form Z(i) = f(i,X(i)). Assume a consistent stopping family τ(i) depends on ω only through the path of X and that for each i the event {τ...

While there is an increasing amount of interest in evaluating and supporting longer “search sessions”, the majority of research has focused on analysing large volumes of logs and dividing sessions according to obvious gaps between entries. Although such approaches have produced interesting insights into some different types of longer sessions, this paper describes the early results of an invest...

For a given graph G and a positive integer r the r-path graph, Pr(G), has for vertices the set of all paths of length r in G. Two vertices are adjacent when the intersection of the corresponding paths forms a path of length r − 1, and their union forms either a cycle or a path of length k+1 in G. Let P k r (G) be the k-iteration of r-path graph operator on a connected graph G. Let H be a subgra...

We prove that for an open system, in the Markovian regime, it is always possible to construct an infinite number of non trivial sets of histories that exactly satisfy the probability sum rules. In spite of being perfectly consistent, these sets manifest a very non–classical behavior: they are quite unstable under the addition of an extra instant to the list of times defining the history. To eli...