Properly Quantized History Dependent Parrondo Games, Markov Processes, and Multiplexing Circuits

In the context of quantum information theory, "quantization" of various mathematical and computational constructions is said to occur upon the replacement, at various points in the construction, of the classical randomization notion of probability distribution with higher order randomization notions from quantum mechanics such as quantum superposition with measurement. For this to be done "properly", a faithful copy of the original construction is required to exist within the new "quantum" one, just as is required when a function is extended to a larger domain. Here procedures for extending history dependent Parrondo games, Markov processes and multiplexing circuits to their "quantum" versions are analyzed from a game theoretic viewpoint, and from this viewpoint, proper quantizations developed

Octonionization of three player, two strategy maximally entangled quantum games

We develop an octonionic representation of the payoff function for three player, two strategy, maximally entangled quantum games in order to obtain computationally friendly version of this function. This computational capability is then exploited to analyze and potentially classify the Nash equilibria in the quantum games

Lens spaces and dehn surgery

GThe question of when a lens space arises by Dehn surgery is discussed with a characterization given for satellite knots. The lens space L(2, 1), i.e. real projective 3-space, is shown to be unobtainable by surgery on a symmetric knot. © 1989 American Mathematical Society

ON TWO-GENERATOR SATELLITE KNOTS

Abstract. Techniques are introduced which determine the geometric structure of non-simple two-generator 3-manifolds from purely algebraic data. As an application, the satellite knots in the 3-sphere with a two-generator presentation in which at least one generator is represented by a meridian for the knot are classified. 1

Automorphisms of surfaces after Nielsen and Thurston

This book, which grew out of Steven Bleiler's lecture notes from a course given by Andrew Casson at the University of Texas, is designed to serve as an introduction to the applications of hyperbolic geometry to low dimensional topology. In particula