Relentless reogranization

INTJ. That's my Meyers-Briggs personality type. And, as much as I'm wary about over-simplifying human behavior, I have to concede that the description of that type fits me rather well. One of the attributes is "relentless reorganizer".

And, yes, I'm going to re-frame part of my problem once again. This time, however, it's not of my own volition. My adviser felt that some more clarification could be made about what exactly we mean by a "query". That's obviously a fair thing to ask since the entire method hinges on it. I thought about giving a bunch of examples. I may still do that, but I think what would fly a lot better would be a rigorous mathematical definition. So, here's a first cut at that:

Let X = {X_i} be a set of financial measures and Y = {Y_i} be a set of attribute vectors describing each corresponding measure in X. Let I_Q: Y → {0, 1} be an indicator of whether a vector in Y should be included in a query. A query, Q: ℝⁿ ⨉ Y → ℝ, is a function such that Q(X,Y) = Σ X_i I_Q(Y_i).

I_Q is called the query condition. Typically, I_Q defines a rectangular subspace of the full attribute space. That is, each attribute is limited to a range of values independent of other attributes. However, our results do not rely on that assumption. Any subset of the attribute space is an acceptable query condition.

If using a multi-currency model, then one could further indicate how exchange rates factor in:

Let C be the set of currencies and T be the range of time values. An exchange rate is a function F: C² ⨉ T such that F(d, c, t) is the conversion factor from input currency c to display currency d at time t. Let Y_ci be the input currency for X_i (that is, the financial units of measure X_i) and Y_ti be the time attribute for X_i. Then, a query, Q: ℝⁿ ⨉ Y ⨉ C→ ℝ, is a function such that Q(X,Y,d) = Σ X_i I_Q(Y_i) F(d, Y_ci, Y_ti) where the result is expressed in units d. As we don't specifically deal with multi-currency in this paper, I'll leave that bit out. Might need it later, though.