An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation

An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation

The aim of this book volume is to explain the importance of Markov state models to molecular simulation, how they work, and how they can be applied to a range of problems.

An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation

Fuzzy Probabilities New Approach and Applications

Fuzzy Probabilities New Approach and Applications

In probability and statistics we often have to estimate probabilities and parameters in probability distributions using a random sample. Instead of using a point estimate calculated from the data we propose using fuzzy numbers which are constructed from a set of confidence intervals. In probability calculations we apply constrained fuzzy arithmetic because probabilities must add to one. Fuzzy random variables have fuzzy distributions. A fuzzy normal random variable has the normal distribution with fuzzy number mean and variance. Applications are to queuing theory, Markov chains, inventory control, decision theory and reliability theory.

Fuzzy Probabilities New Approach and Applications