Consider finite sequences $X_{[1,n]}=X_1dots X_n$ and $Y_{[1,n]}=Y_1dots Y_n$ of length $n$, consisting of i.i.d. samples of random letters from a finite alphabet, and let $S$ and $T$ be chosen i.i.d. randomly from the unit ball in the space of symme
tric scoring functions over this alphabet augmented by a gap symbol. We prove a probabilistic upper bound of linear order in $n^{0.75}$ for the deviation of the score relative to $T$ of optimal alignments with gaps of $X_{[1,n]}$ and $Y_{[1,n]}$ relative to $S$. It remains an open problem to prove a lower bound. Our result contributes to the understanding of the microstructure of optimal alignments relative to one given scoring function, extending a theory begun by the first two authors.
We discuss a method for predicting financial movements and finding pockets of predictability in the price-series, which is built around inferring the heterogeneity of trading strategies in a multi-agent trader population. This work explores extension
s to our previous framework (arXiv:physics/0506134). Here we allow for more intelligent agents possessing a richer strategy set, and we no longer constrain the estimate for the heterogeneity of the agents to a probability space. We also introduce a scheme which allows the incorporation of models with a wide variety of agent types, and discuss a mechanism for the removal of bias from relevant parameters.
