This is the first in a series of papers which we study representations Brauer category and its allies. We define general notion triangular that abstracts key properties decomposition semisimple complex Lie algebra, develop highest weight theory for them. show category, partition number related diagram categories admit this structure.

MBD and breast cancer risk Elevated MBD is considered one of the strongest risk factors for breast cancer regardless of whether it is assessed as a categorical or quantitative measure.6 Women in the highest categories of breast density have a 4to 6-fold increased breast cancer risk compared with women in the lowest categories. MBD has been shown to be a stronger risk factor for breast cancer th...

0.1 Abstract ii 0.1 Abstract The project consists of two chapters and an appendix. In the rst chapter dene quasi-categories, and perform basic constructions with these, some of which are motivated by ordinary category theory. Among these, we shall build under-categories and colimits. Also we briey review some dierent notions of brations needed for the next chapter, and introduce a pair of adjoi...

The component’s reliability is a function of component age during a system’s operating life. Component aging is strongly affected by maintenance activities performed on the system.Two categories of maintenance activities are considered in this work: Corrective maintenance (CM) and preventive maintenance (PM). We expound a new method to integrate the effect of CM while planning for the preventiv...

This paper describes the use of validation methods in model building. We address issues associated with the increasing complexity of models that is in part a response to the growing popularity of Agent-Based Models (ABM), commonly used to study cognitive, natural, and social phenomena. The first section of this manuscript discusses model categories and attributes. The second section discusses t...