Analyzing three-player quantum games in an EPR type setup

We use the formalism of Clifford Geometric Algebra (GA) to develop an analysis of quantum versions of three-player non-cooperative games. The quantum games we explore are played in an Einstein-Podolsky-Rosen (EPR) type setting. In this setting, the players' strategy sets remain identical to the ones in the mixed-strategy version of the classical game that is obtained as a proper subset of the corresponding quantum game. Using GA we investigate the outcome of a realization of the game by players sharing GHZ state, W state, and a mixture of GHZ and W states. As a specific example, we study the game of three-player Prisoners' Dilemma.Comment: 21 pages, 3 figure

On Social Statement Spaces

logic space, logic statement space, logistic statement space, logistic regression, finite fields, vector spaces over code theory, algebraic geometric codes, entropy change, analysis of dichotomous data,

On the transposition anti-involution in real Clifford algebras I: the transposition map

A particular orthogonal map on a finite dimensional real quadratic vector space (V,Q) with a non-degenerate quadratic form Q of any signature (p,q) is considered. It can be viewed as a correlation of the vector space that leads to a dual Clifford algebra CL(V^*,Q) of linear functionals (multiforms) acting on the universal Clifford algebra CL(V,Q). The map results in a unique involutive automorphism and a unique involutive anti-automorphism of CL(V,Q). The anti-involution reduces to reversion (resp. conjugation) for any Euclidean (resp. anti-Euclidean) signature. When applied to a general element of the algebra, it results in transposition of the element matrix in the left regular representation of CL(V,Q). We give also an example for real spinor spaces. The general setting for spinor representations will be treated in part II of this work [...II: Spabilizer groups of primitive idempotents].Comment: 28 page

The Origin and Evolution of Complex Enough Systems in Biology

Recent criticisms of Neo-Darwinism are considered and disputed within the setting of recent advances in chemical physics. A related query, viz., the ontological thesis, that everything is physical, confronts a crucial test on the validity of reductionism as a fundamental approach to science.  While traditional ‘physicalism’ interprets evolution as a sequence of physical accidents governed by the second law of thermodynamics, the concepts of biology concern processes that owe their goal-directedness to the influence of an evolved program. This disagreement is met by unifying basic aspects of chemistry and physics, formulating the Correlated Dissipative Ensemble, CDE, as a characterization of a ‘complex enough systems’, CES, in biology. The latter entreats dissipative dynamics; non-Hermitian quantum mechanics together with modern quantum statistics thereby establish a precise spatio-temporal order of significance for living systems. The CDE grants a unitary transformation structure that comprises communication protocols of embedded Poisson statistics for molecular recognition and cellular differentiation, providing cell-hierarchies in the organism. The present conception of evolution, founded on communication with a built-in self-referential order, offers a valid argument in favour of Neo-Darwinism, providing an altogether solid response and answer to the criticisms voiced above