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Matthew effect or cumulative advantage (CA) is widely studied in all sorts of fields. It is considered as an important factor that causes inequality in labor wages, education and careers. This even greatly impacts the scientific activities including journal publication, grant application, peer recognition, promotion, etc. Numerous models are developed to analyze the CA process. However, we are not aware of any work on the analysis of CA issue encountered by young scientists at their early stage of careers in the form of tenure track. The CA process for this group has its unique characteristics and requires special treatment. Therefore, a modified CA model is constructed and its implications are also analyzed.