This book series presents a new type of cellular automata for 2D pattern generation, characterized by a high reproduction rate, in combination with the application of a small-sized 2D modular square lattice. The presented patterns are in the spirit of mathematical minimalism, generated from rudimentary kernels and a minimal set of rules. In similarity with fractals, this new concept could provide for the generation of patterns and geometries with applications in areas such as, visual arts, logo design, architecture, and game design.
This paper introduces two new categories of players, an equalization player, with the goal to minimize the score gap between the opponents, and a variation enhancement player, with the goal to maximize the same. In addition, a complementary player type is added to the classic max-player game, called the min-player, along with a mathematical formalization of basic strategies, yielding a new algorithm based on Hypermax.
The multilayer feedforward neural network is presently one of the most popular computational methods in computer science. The current method for the evaluation of its weights is however performed by a relatively slow iterative method known as backpropagation. According to previous research, attempts to evaluate the weights analytically by the linear least square method, showed to accelerate the evaluation process significantly. The evaluated networks showed however to fail in robustness tests compared to well-trained networks by backpropagation, thus resembling overtrained networks. This paper presents the design and verification of a new method, that solves the robustness issues for a large-scale neural network with many hidden nodes, as an upgrade to the previously suggested analytic method.
This paper presents an N-person generalization of minimax aligned with the original definition. An efficient optimization method is further presented as a result of a straightforward mathematical extension of alpha-beta pruning to N-person games.
Bivalent or two-valued logic is presently the foundation of logic in mathematics and computer science, and a cornerstone of software development. To address a number of classical logical paradoxes, such as Russell’s, multi-valued logic, such as balanced ternary logic has shown to be useful. Current methods lead however to information loss. Thus, to theoretically improve the robustness of bivalent logic, this paper proposes the use of quantum states, followed by an example, where the proposed method is shown to be successful in the solution of a problem that is not directly solvable using contemporary methods.