Hypernormal form theory: foundations and algorithms

Foundations of Analog Algorithms

We propose a formalization of analog algorithms, extending the framework of abstract state machines to continuous-time models of computation. The machine to be described here, like almost every contrivance, apparatus, or machine in practical use, is based very largely upon what has been accomplished by others who previously labored in the same field. —Description of the U.S. Coast and Geodetic ...

Foundations of Geneti Algorithms

Solomon Feferman Categorical Foundations and Foundations of Category Theory*

This paper is divided'into two parts. Part I deals briefly with the thesis that category theory (or something like it) should provide the proper foundations of mathematics, in preference to current foundational schemes. An opposite view is argued here on the grounds that the notions of operation and collection are prior to all structural notions. However, no position is taken as to whether such...

Foundations of Portfolio Theory

When I studied microeconomics forty years ago, I was first taught how optimizing firms and consumers would behave, and then taught the nature of the economic equilibrium which would result from such behavior. Let me refer to this as part one and part two of my microeconomics course. My work on portfolio theory considers how an optimizing investor would behave, whereas the work by Sharpe and Lin...

Foundations of Information Theory

Information has become the most precious resource of society. At the same time, there is no consensus on the meaning of the term " information, " and many researchers have considered problems of information definition. This results in a quantity of contradictions, misconceptions, and paradoxes related to the world of information. To remedy the situation, a new approach in information theory, wh...