The common structure of the space of pure states P of a classical or a quantum mechanical system is that of a Poisson space with a transition probability. This is a topological space equipped with a Poisson structure, as well as with a function p : P×P → [0, 1], with certain properties. The Poisson structure is connected with the transition probabilities through unitarity (in a specific formula...

Chemical reactions can be modeled via diffusion processes conditioned to make a transition between specified molecular configurations representing the state of the system before and after the chemical reaction. In particular the model of Brownian dynamics— gradient flow subject to additive noise—is frequently used. If the chemical reaction is specified to take place on a given time interval, th...

This paper describes a compression algorithm for probability transition matrices. The compressed matrix is itself a probability transition matrix. In general the compression is not error-free, but the error appears to be small even for high levels of compression.

Transition Probability (fidelity) for pairs of density operators can be defined as a “functor” in the hierarchy of “all” quantum systems and also within any quantum system. The Introduction of “amplitudes” for density operators allows for a more intuitive treatment of these quantities, also pointing to a natural parallel transport. The latter is governed by a remarkable gauge theory with strong...

, the estimate of a linear approximation supported by a rough measurement of the value of "a" for the load in question may be far more useful than having no model at all. Acknowledgments. Akira Sekino developed a hierarchical strategy for system modeling which exposed the usefulness of a model of the mean headway between missing pages [15]. Professor F.J. Corbat6 suggested that a linear model w...

We examine the transition to, and survival in, self-employment among a sample of British workers. We find evidence of capital constrains, with wealthier individuals being more likely to transit ceteris paribus. Windfall gains raise the probability of transition at a decreasing rate – gains or more than £20000–£22000 reduce the probability of transition – and larger gains reduce the probability ...

Drought is one of the most important weather-induced phenomena which may have severe impacts on different areas such as agriculture, economy, energy production, and society. A number of drought indices have been introduced and used in various countries to date. In the current study, four meteorological drought indices including Percent of Normal Precipitation Index (PNPI), Standard Index of Ann...

Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical  Bayes estimators  for the transition probability  matrix of a finite nonstationary  Markov chain. The data are assumed to be of  a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...