In §9 we propose an abstract mathematical definition of, and practical way to measure, “intelligence.” Before that is much motivating discussion and arguments why it is a good definition, and after it we deduce several important consequences – fundamental theorems about intelligence. The most important (theorem 5 of §12) is our construction of an algorithm that implements an “asymptotically uni...

The aim of this paper is to define synthetic emergence in a domain independent fashion. The mathematical definition of the first kind of synthetic emergence will be given by the consideration of closed and open subsets of the limit of design systems. A brief sketch of design systems will be also given by using the concept of information flow from Barwise and Seligman.

“Life” and its “evolution” are fundamental concepts that have not yet been formulated in precise mathematical terms, although some efforts in this direction have been made. We suggest a possible point of departure for a mathematical definition of “life.” This definition is based on the computer and is closely related to recent analyses of “inductive inference” and “randomness.” A living being i...

Since the early work of [7], Large Eddy Simulation (LES) has become over the years an increasingly popular method, as evidenced by the vast amount of publications on the subject in the literature, and is now considered a tool of choice for simulating three-dimensional incompressible viscous flows at large Reynolds numbers. Heuristically speaking, Large Eddy models are obtained by applying a low...

The paper provides a mathematical yet simple model for the full programming language Prolog, as apparently intended by the ISO draft standard proposal. The model includes all control constructs, database operations, solution collecting predicates and error handling facilities, typically ignored by previous theoretical treatments of the language. We add to this the ubiquitous box-model debugger....

In discussions of the nature of life, the terms “complexity,” “organism,” and “information content,” are sometimes used in ways remarkably analogous to the approach of algorithmic information theory, a mathematical discipline which studies the amount of information necessary for computations. We submit that this is not a coincidence and that it is useful in discussions of the nature of life to ...

A Multi-objective optimization procedure has been developed to determine some kinetic parameters of free radical polymerization of vinyl acetate based on genetic algorithm. For this purpose, mathematical modeling of free radical polymerization of vinyl acetate is carried out first and then selected kinetic parameters are optimized by minimizing objective functions defined from comparing exp...

We introduce an inductive definition for two classes of orders. By simple proofs, we show that one corresponds to the interval orders class and that the other is exactly the semiorders class. To conclude we consider most of the known equivalence theorems on interval orders and on semiorders, and we give simple and direct inductive proofs of these equivalences with ours characterizations.

Definition of Artificial Neural Networks (ANNs) is made by computer scientists, artificial intelligence experts and mathematicians in various dimensions. Many of the definitions explain ANN by referring to graphics instead of giving well explained mathematical definitions; therefore, misleading weighted graphs (as in minimum cost flow problem networks) fit the definition of ANN. This study aims...