A Formalization of Linkage Analysis

In this report a formalization of genetic linkage analysis is introduced. Linkage analysis is a computationally hard biomathematical method, which purpose is to locate genes on the human genome. It is rooted in the new area of bioinformatics and no formalization of the method has previously been established. Initially, the biological model is presented. On the basis of this biological model we establish a formalization that enables reasoning about algorithms used in linkage analysis. The formalization applies both for single and multi point linkage analysis. We illustrate the usage of the formalization in correctness proofs of central algorithms and optimisations for linkage analysis. A further use of the formalization is to reason about alternative methods for linkage analysis. We discuss the use of MTBDDs and PDGs in linkage analysis, since they have proven efficient for other computationally hard problems involving large state spaces. We conclude that none of the techniques discussed are directly applicable to linkage analysis, however further research is needed in order to investigated whether a modified version of one or more of these are applicable

A Formalization of Linkage Analysis

In this report a formalization of genetic linkage analysis is introduced. Linkage analysis is a computationally hard biomathematical method, which purpose is to locate genes on the human genome. It is rooted in the new area of bioinformatics and no formalization of the method has previously been established. Initially, the biological model is presented. On the basis of this biological model we establish a formalization that enables reasoning about algorithms used in linkage analysis. The formalization applies both for single and multi point linkage analysis. We illustrate the usage of the formalization in correctness proofs of central algorithms and optimisations for linkage analysis. A further use of the formalization is to reason about alternative methods for linkage analysis. We discuss the use of MTBDDs and PDGs in linkage analysis, since they have proven efficient for other computationally hard problems involving large state spaces. We conclude that none of the techniques discussed are directly applicable to linkage analysis, however further research is needed in order to investigated whether a modified version of one or more of these are applicable

Optimal Reachability for Multi-Priced Timed Automata

AbstractIn this paper, we prove the decidability of the minimal and maximal reachability problems for multi-priced timed automata, an extension of timed automata with multiple cost variables evolving according to given rates for each location. More precisely, we consider the problems of synthesizing the minimal and maximal costs of reaching a given target location. These problems generalize conditional optimal reachability, i.e., the problem of minimizing one primary cost under individual upper bound constraints on the remaining, secondary, costs, and the problem of maximizing the primary cost under individual lower bound constraints on the secondary costs. Furthermore, under the liveness constraint that all traces eventually reach the goal location, we can synthesize all costs combinations that can reach the goal.The decidability of the minimal reachability problem is proven by constructing a zone-based algorithm that always terminates while synthesizing the optimal cost tuples. For the corresponding maximization problem, we construct two zone-based algorithms, one with and one without the above liveness constraint. All algorithms are presented in the setting of two cost variables and then lifted to an arbitrary number of cost variables

Almost Optimal Strategies in One Clock Priced Timed Automata

International audienceWe consider timed games extended with cost information, and prove computability of the optimal cost and of $\epsilon$-optimal memoryless strategies in timed games with one~clock. In~contrast, this problem has recently been proved undecidable for timed games with three clocks