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The biological mechanism that produces allergies can be modeled as a stochastic system, where the input signals consist of allergens and the output signals are the measurable quantities related to symptoms. Allergens, such as milk, pollen and mold, consist of proteins and combinations of proteins. In an effort to identify the system, it is proposed that the output signal be considered as a function of time and allergen atoms, which we define to be the independent units of allergens. To accomplish this representation, we refer to realizable system representations to guide us in proposing a definition and an ordering for the allergen axis.