A generalization of the integer linear infeasibility problem

Does a given system of linear equations with nonnegative constraints have an integer solution? This is a fundamental question in many areas. In statistics this problem arises in data security problems for contingency table data and also is closely related to non-squarefree elements of Markov bases for sampling contingency tables with given marginals. To study a family of systems with no integer solution, we focus on a commutative semigroup generated by a finite subset of $\Z^d$ and its saturation. An element in the difference of the semigroup and its saturation is called a ``hole''. We show the necessary and sufficient conditions for the finiteness of the set of holes. Also we define fundamental holes and saturation points of a commutative semigroup. Then, we show the simultaneous finiteness of the set of holes, the set of non-saturation points, and the set of generators for saturation points. We apply our results to some three- and four-way contingency tables. Then we will discuss the time complexities of our algorithms.Comment: This paper has been published in Discrete Optimization, Volume 5, Issue 1 (2008) p36-5

Statistical analysis on detecting recombination sites in DNA-beta satellites associated with the old world geminiviruses

Although an exchange of genetic information by recombination plays an important role in the evolution of viruses, it is not clear how it generates diversity. {\it Geminiviruses} are plant viruses which have ambisense single-stranded circular DNA genomes and one of the most economically important plant viruses in agricultural production. Small circular single-stranded DNA satellites, termed DNA-$\beta$, have recently been found associated with some geminivirus infections. In this paper we analyze a satellite molecule DNA-$\beta$ of geminiviruses for recombination events using phylogenetic and statistical analysis and we find that one strain from ToLCMaB has a recombination pattern and is possibly recombinant molecule between two strains from two species, PaLCuB-[IN:Chi:05] (major parent) and ToLCB-[IN:CP:04] (minor parent).Comment: 8 figures and 2 tables. To appear in Frontiers in Systems Biolog

Network Classification with Incomplete Information

NPS NRP Executive SummaryNetwork Classification with Incomplete InformationOffice of Naval Intelligence (ONI)This research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrpChief of Naval Operations (CNO)Approved for public release. Distribution is unlimited.