Error Graphs and the Reconstruction of Elements in Groups

Packing and covering problems for metric spaces, and graphs in particular, are of essential interest in combinatorics and coding theory. They are formulated in terms of metric balls of vertices. We consider a new problem in graph theory which is also based on the consideration of metric balls of vertices, but which is distinct from the traditional packing and covering problems. This problem is motivated by applications in information transmission when redundancy of messages is not sufficient for their exact reconstruction, and applications in computational biology when one wishes to restore an evolutionary process. It can be defined as the reconstruction, or identification, of an unknown vertex in a given graph from a minimal number of vertices (erroneous or distorted patterns) in a metric ball of a given radius r around the unknown vertex. For this problem it is required to find minimum restrictions for such a reconstruction to be possible and also to find efficient reconstruction algorithms under such minimal restrictions. In this paper we define error graphs and investigate their basic properties. A particular class of error graphs occurs when the vertices of the graph are the elements of a group, and when the path metric is determined by a suitable set of group elements. These are the undirected Cayley graphs. Of particular interest is the transposition Cayley graph on the symmetric group which occurs in connection with the analysis of transpositional mutations in molecular biology. We obtain a complete solution of the above problems for the transposition Cayley graph on the symmetric group.Comment: Journal of Combinatorial Theory A 200

Interpreting Sequence-Levenshtein distance for determining error type and frequency between two embedded sequences of equal length

Levenshtein distance is a commonly used edit distance metric, typically applied in language processing, and to a lesser extent, in molecular biology analysis. Biological nucleic acid sequences are often embedded in longer sequences and are subject to insertion and deletion errors that introduce frameshift during sequencing. These frameshift errors are due to string context and should not be counted as true biological errors. Sequence-Levenshtein distance is a modification to Levenshtein distance that is permissive of frameshift error without additional penalty. However, in a biological context Levenshtein distance needs to accommodate both frameshift and weighted errors, which Sequence-Levenshtein distance cannot do. Errors are weighted when they are associated with a numerical cost that corresponds to their frequency of appearance. Here, we describe a modification that allows the use of Levenshtein distance and Sequence-Levenshtein distance to appropriately accommodate penalty-free frameshift between embedded sequences and correctly weight specific error types.Comment: 10 pages, 8 figure

Reasoning about Social Semantic Web Applications using String Similarity and Frame Logic

Social semantic Web or Web 3.0 application gained major attention from academia and industry in recent times. Such applications try to take advantage of user supplied meta data, using ideas from the semantic Web initiative, in order to provide better services. An open problem is the formalization of such meta data, due to its complex and often inconsistent nature. A possible solution to inconsistencies are string similarity metrics which are explained and analyzed. A study of performance and applicability in a frame logic environment is conducted on the case of agent reasoning about multiple domains in TaOPis - a social semantic Web application for self-organizing communities. Results show that the NYSIIS metric yields surprisingly good results on Croatian words and phrases

Similarity Matching Techniques For Fault Diagnosis In Automotive Infotainment Electronics

Fault diagnosis has become a very important area of research during the last decade due to the advancement of mechanical and electrical systems in industries. The automobile is a crucial field where fault diagnosis is given a special attention. Due to the increasing complexity and newly added features in vehicles, a comprehensive study has to be performed in order to achieve an appropriate diagnosis model. A diagnosis system is capable of identifying the faults of a system by investigating the observable effects (or symptoms). The system categorizes the fault into a diagnosis class and identifies a probable cause based on the supplied fault symptoms. Fault categorization and identification are done using similarity matching techniques. The development of diagnosis classes is done by making use of previous experience, knowledge or information within an application area. The necessary information used may come from several sources of knowledge, such as from system analysis. In this paper similarity matching techniques for fault diagnosis in automotive infotainment applications are discussed