Broken Symmetry

Bleg for Information about Management Accounting of Changes in Frequency

Any readers have experience or knowledge here?

A time series of journal entries records sales and costs of sales. Later these are summarized into income statement, balance sheet, and cash flows. Lost in these financial statements is the information about how often each unit of sales and costs of sales was earned or incurred, respectively. But obviously the company has to keep track of the rate or frequency of sales and costs to keep profits increasing. The two have to stay synchronized to keep profits increasing.

How is this done now?

Bleg: Geometry of Algorithms?

On a walk with a mathematician friend today we fell to talking about the value that geometric insights have had in solving difficult problems. The general thought is that great analysis is useful in solving difficult problems in well-understood systems. But geometric understanding has often been necessary to setting up the analysis properly in the first place. When I think of great physics, for example, an extraordinary ability to visualize geometry seems to run as a common thread through the best theory.

The other topic of conversation was algorithmic theory. We've been putting together algorithms for a long time -- every mathematical proof (whether true, false, or undecidable) -- is an algorithm. Algorithms are more general than equations.

So naturally we were talking about how one might go about setting up a geometry of algorithms. The connection between geometry and analysis (both real and complex) would be a subset of a more general geometry of algorithms -- viz., the subset in which real and complex functions are associated with a geometric manifold.

But let's say I wanted to start visualizing algorithms in two or three dimensions. Is there a theory for this? I remember from years ago that there are many different sorting algorithms, with quicksort being one of the fastest. Is there a systematic way to represent these algorithms in two or three dimensions and bring geometric intuition to bear on their similarities and differences?

The naive method that we talked about would involve taking a turing tape of 0s and 1s, breaking it into finite segments (of, say, 16 bits), and then mapping each segment into a two dimensional discrete grid of 256 points. An algorithm, then, would be a trajectory through that discrete space. This is unlikely to produce geometrical insights, however.

My friend insists that this is what graph theory is all about. I need to learn more graph theory. But if there are any readers that can point me towards a web page, paper, or book that provides an introduction to this type of theory, I'd be much obliged.

Bleg: Where to find the best online discussion of accounting rules?

I've been searching for a good blog or online forum for discussing the current GAAP and IFRS accounting rules, but so far have been disappointed by what I've found.

Anybody have any suggestions?  Please post a comment so that others can take advantage too.  But email if you must.

Bleg for Information about Liquidity

Lately, I've been particularly interested in two different measurements of liquidity:

(1) The bid-ask spread in volume (i.e., the absolute value of the difference in volume between the current bid and the current ask).

(2) The marginal increase in time it takes to complete a transactions given a marginal increase in volume

Could any readers tell me where I might be able to find statistics on these measures of liquidity?

Also, is there a terminological convention for describing these quantities that I haven't discovered yet?

What are the Existing Best Models for Business Cycles?

Readers:

Can anybody tell me what models academic economists right now consider the best for explaining business cycles?