Simplicial quantum dynamics

Present-day quantum field theory can be regularized by a decomposition into quantum simplices. This replaces the infinite-dimensional Hilbert space by a high-dimensional spinor space and singular canonical Lie groups by regular spin groups. It radically changes the uncertainty principle for small distances. Gaugeons, including the gravitational, are represented as bound fermion-pairs, and space-time curvature as a singular organized limit of quantum non-commutativity. Keywords: Quantum logic, quantum set theory, quantum gravity, quantum topology, simplicial quantization.Comment: 25 pages. 1 table. Conference of the International Association for Relativistic Dynamics, Taiwan, 201

A framework for proving the self-organization of dynamic systems

This paper aims at providing a rigorous definition of self- organization, one of the most desired properties for dynamic systems (e.g., peer-to-peer systems, sensor networks, cooperative robotics, or ad-hoc networks). We characterize different classes of self-organization through liveness and safety properties that both capture information re- garding the system entropy. We illustrate these classes through study cases. The first ones are two representative P2P overlays (CAN and Pas- try) and the others are specific implementations of \Omega (the leader oracle) and one-shot query abstractions for dynamic settings. Our study aims at understanding the limits and respective power of existing self-organized protocols and lays the basis of designing robust algorithm for dynamic systems

Least-action perihelion precession

The precession of Mercury's perihelion is reinspected by the principle of least action. The anomalous advancement of the apside line that is customarily accounted by the theory of general relativity, is ascribed to the gravitational effect due to the entire Universe. When the least action is written in the Sun's frame of reference, the residual rotation is seen to stem from inertia due to all bodies in the Universe. Since mass corresponds to a bound form of energy, gravity, as any other force, can be described as an energy density difference between a system of bodies and its surrounding energy densities that are dispersed throughout the Universe. According to the principle of least action the Universe is expanding by combustion of mass to radiation in the quest of equilibrating the bound forms of energy with "zero-density surroundings" in least time. Keywords: cosmological principle; energy density; energy dispersal; evolution; gravity; the principle of least actionComment: 7 pages, 3 figure