A profile hidden Markov model (PHMM) is widely used in assigning protein sequences to protein families. In this model, the hidden states only depend on the previous hidden state and observations are independent given hidden states. In other words, in the PHMM, only the information of the left side of a hidden state is considered. However, it makes sense that considering the information of the b...

Message Sequence Charts (MSCs) are an attractive visual formalism used during the early stages of design in domains such as telecommunication software. A popular mechanism for generating a collection of MSCs is a Hierarchical Message Sequence Chart (HMSC). However, not all HMSCs describe collections of MSCs that can be “realized” as a finite-state device. Our main goal is to pin down this notio...

We study linear estimators for the weighted integral of a stochastic process. The process may only be observed on a nite sampling design. The error is deened in mean square sense, and the process is assumed to satisfy Sacks-Ylvisaker regularity conditions of order r 2 N 0. We show that sampling at the quantiles of a particular density already yields asymptotically optimal estimators. Hereby we ...

Imposing constraints in the form of a finite automaton or a regular expression is an effective way to incorporate additional a priori knowledge into sequence alignment procedures. With this motivation, the Regular Expression Constrained Sequence Alignment Problem was introduced, which proposed an O(n²t⁴) time and O(n²t²) space algorithm for solving it, where n is the length of the input strings...

“Regular expressions”, also known as “RegExps” or sometimes as “grep patterns”, are a way of specifying patterns of characters within a text file or longer string of characters. Regular expressions can contain various “wild cards” or sets of alternatives, which can be used to include ambiguity in the pattern to be matched. One common use is to perform sophisticated find-and-replace operations.

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

We associate in a canonical way a substitution to any abstract numeration system built on a regular language. In relationship with the growth order of the letters, we define the notion of two independent substitutions. Our main result is the following. If a sequence x is generated by two independent substitutions — at least one being of exponential growth. Then the factors of x appearing infini...