﻿ یک مدل ریاضی جدید برای مساله استنباط هاپلوتایپ‌ها از ژنوتایپ‌ها با معیار پارسیمونی

# یک مدل ریاضی جدید برای مساله استنباط هاپلوتایپ‌ها از ژنوتایپ‌ها با معیار پارسیمونی

نویسندگان

• باقریان, مهری گروه ریاضی کاربردی، دانشکده علوم ریاضی، دانشگاه گیلان، رشت
• فیض آبادی, رضا گروه ریاضی کاربردی، دانشکده علوم ریاضی، دانشگاه گیلان، رشت

چکیده

The haplotype inference is one of the most important issues in the field of bioinformatics. It is because of its various applications in the diagnosis and treatment of inherited diseases such as diabetes, Alzheimer's and heart disease, which has provided a competition for researchers in presentation of mathematical models and design of algorithms to solve this problem. Despite the existence of a robust literature, a need is still felt for providing new or improved methods because of the NP-hard nature of the problem. Haplotype inference is expressed by different criteria. Parsimony is one of the most important criteria here, and the problem in this study is examined with this criterion. Haplotype inference by parsimony criterion solving methods are divided into two categories: exact and approximate. The exact methods often formulate this problem as an integer programming model. Recently, in an article an exact model, HI Base- 10, for haplotype inference has been proposed, which first corresponds a number to each haplotype and genotype, and then forms the model based on these numbers. As a result of this action, it does not impose any variable and constraint corresponding to heterozygous sites in the model. In this paper, we correspond numbers to the genotype in a different approach and form a mixed binary model based on these numbers. As a result of this conversion, the new model has fewer variables than the HI Base- 10, and it doesn’t have integer variable. In addition, in the new model, there is no variable and constraint corresponding to homozygous sites, and they are assigned to heterozygous sites. In addition, the value of the model is determined considering the large number of homozygous sites compared with heterozygous sites.

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