The forward Fractional Advection Dispersion Equation (FADE) provides a useful model for non-Fickian transport in heterogeneous porous media. The space FADE captures the long leading tail, skewness, and fast spreading typically seen in concentration profiles from field data. This paper develops the corresponding backward FADE model, to identify source location and release time. The backward meth...

MOTIVATION Kinesin is a smart motor protein that steps processively forward and backward along microtubules (MTs). The mechanical kinetics of kinesin affecting its stepping behavior is not fully understood. Here, we propose a mathematical model to study the mechanical kinetics of forward and backward stepping of kinesin motor based on the four-state discrete stochastic model of the motor. RES...

We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then develop numerical algorithms to solve for escape probability and mean residence time, which are described by backward Fokker-Planck type partial differential equ...

Profile hidden Markov models (HMMs) based on classical HMMs have been widely applied for protein sequence identification. The formulation of the forward and backward variables in profile HMMs is made under statistical independence assumption of the probability theory. We propose a fuzzy profile HMM to overcome the limitations of that assumption and to achieve an improved alignment for protein s...

We say that the game is favorable if there is a gambling strategy such that almost. Only quite recently has the question of gambling systems optimal with respect.Optimal Gambling Systems for Favorable Games. Nonconstant sum red-and-black games with betdependent win probability functionIt is an easy problem to find, by backward induction, the betting system that maximizes. 1961 Optimal gambling ...

This is a report about Hidden Markov Models, a data structure used to model the probabilities of sequences, and the three algorithms associated with it. The algorithms are the forward algorithm and the Viterbi algorithm, both used to calculate the probability of a sequence, and the forward-backward algorithm, used to train a Hidden Markov Model on a set of sequences, raising the propabilites of...

Proper consistency is defined by the properties that each player takes all opponent strategies into account (is cautious) and deems one opponent strategy to be infinitely more likely than another if the opponent prefers the one to the other (respects preferences). When there is common certain belief of proper consistency, a most preferred strategy is properly rationalizable. Any strategy used w...