Genetic testing for breast cancer susceptibility became a reality after two cancer predisposition genes, BRCA1 and BRCA2, were identified. Mutations in these two genes were predicted to account for 85% to 90% of hereditary breast and ovarian cancer syndromes. We present results of mutation analysis of the coding sequence of these two genes in 110 consecutive non-Jewish breast cancer patients with a positive family history of breast and/or ovarian cancer. The individuals were identified in various cancer risk evaluation centers in the country. Twenty-two (20%) mutations in the BRCA1 gene and 8 mutations (7%) in the BRCA2 gene were detected. We also analyzed 52 Ashkenazi Jewish breast cancer patients for mutations in the BRCA1 and BRCA2 genes. Eleven Jewish individuals (21%) carried either one of the two common mutations, 185delAG and 5382InsC, in the BRCA1 gene and 4 individuals (8%) had the 6174delT mutation in the BRCA2 gene. The frequency of mutations in BRCA genes in affected people in this ethnic group was not significantly different from the non-Jewish population. On further analysis, the data demonstrate that neither age of onset nor phenotype of the disease had any significant predictive value for the frequency of mutations in these genes. These data confirm the lower prevalence of mutations in either of the BRCA genes in clinical families when compared to high-risk families used for obtaining linkage data in a research setting.
International audienceA novel approach is described for the combination of unification algorithms for two equational theories E 1 and E 2 which share function symbols. We are able to identify a set of restrictions and a combination method such that if the restrictions are satisfied the method produces a unification algorithm for the union of non-disjoint equational theories. Furthermore, we identify a class of theories satisfying the restrictions. The critical characteristics of the class is the hierarchical organization and the shared symbols being restricted to "inner constructors"
We investigate the unification problem in theories defined by rewrite systems which are both convergent and forward-closed. These theories are also known in the context of protocol analysis as theories with the finite variant property and admit a variant-based unification algorithm. In this paper, we present a new rule-based unification algorithm which can be seen as an alternative to the variant-based approach. In addition, we define forward-closed combination to capture the union of a forward-closed convergent rewrite system with another theory, such as the Associativity-Commutativity, whose function symbols may occur in right-hand sides of the rewrite system. Finally, we present a combination algorithm for this particular class of non-disjoint unions of theories.
We prove that the Tiden and Arnborg algorithm for equational unification modulo one-sided distributivity is not polynomial time bounded as previously thought. A set of counterexamples is developed that demonstrates that the algorithm goes through exponentially many steps
The equational unification problem, where the underlying equational theory may be given as the union of component equational theories, appears often in practice in many fields such as automated reasoning, logic programming, declarative programming, and the formal analysis of security protocols. In this paper, we investigate the unification problem in the non-disjoint union of equational theories via the combination of hierarchical unification procedures. In this context, a unification algorithm known for a base theory is extended with some additional inference rules to take into account the rest of the theory. We present a simple form of hierarchical unification procedure. The approach is particularly well-suited for any theory where a unification procedure can be obtained in a syntactic way using transformation rules to process the axioms of the theory. Hierarchical unification procedures are exemplified with various theories used in protocol analysis. Next, we look at modularity methods for combining theories already using a hierarchical approach. In addition, we consider a new complexity measure that allows us to obtain terminating (combined) hierarchical unification procedures.
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