4,707 research outputs found
Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction
Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov-Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn-Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn
Algebraic renormalization of supersymmetric gauge theories with dimensionful parameters
It is usually believed that there are no perturbative anomalies in
supersymmetric gauge theories beyond the well-known chiral anomaly. In this
paper we revisit this issue, because previously given arguments are incomplete.
Specifically, we rule out the existence of soft anomalies, i.e., quantum
violations of supersymmetric Ward identities proportional to a mass parameter
in a classically supersymmetric theory. We do this by combining a previously
proven theorem on the absence of hard anomalies with a spurion analysis, using
the methods of Algebraic Renormalization. We work in the on-shell component
formalism throughout. In order to deal with the nonlinearity of on-shell
supersymmetry transformations, we take the spurions to be dynamical, and show
how they nevertheless can be decoupled.Comment: Final version, typoes fixed. Revtex, 48 page
Off-Equilibrium Dynamics in Finite-Dimensional Spin Glass Models
The low temperature dynamics of the two- and three-dimensional Ising spin
glass model with Gaussian couplings is investigated via extensive Monte Carlo
simulations. We find an algebraic decay of the remanent magnetization. For the
autocorrelation function a typical
aging scenario with a scaling is established. Investigating spatial
correlations we find an algebraic growth law of
the average domain size. The spatial correlation function scales with . The sensitivity of the
correlations in the spin glass phase with respect to temperature changes is
examined by calculating a time dependent overlap length. In the two dimensional
model we examine domain growth with a new method: First we determine the exact
ground states of the various samples (of system sizes up to )
and then we calculate the correlations between this state and the states
generated during a Monte Carlo simulation.Comment: 38 pages, RevTeX, 14 postscript figure
A neo-Kaldorian approach to structural economic dynamics
Although the structural economic dynamic approach provides a simultaneous consideration of demand and supply sides of economic growth, it does not fully take into account the possible role played by demand in the generation of technical progress. From a neo-Kaldorian perspective, this paper seeks to establish the concepts of demand and productivity regimes in an open version of the pure labour Pasinettian model. In order to derive the demand regime, a disaggregated version of the static Harrod foreign multiplier is derived, while the productivity regime is built in terms of disaggregated Kaldor–Verdoorn laws. The upshot is a multi-sectoral growth model of structural change and cumulative causation, in which an open version of the Pasinettian model to foreign trade may be obtained as a particular case. Furthermore, we show that the evolution of demand patterns, while being affected by differential rates of productivity growth in different sectors of the economy, also play an important role in establishing the pace of technical progress
Algebraic Quantum Mechanics and Pregeometry
We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the algebra itself would carry the symmetries of translation, rotation, etc. Our suggestion is illustrated in a preliminary way by using a particular generalized Clifford algebra proposed originally by Weyl, which approaches the ordinary Heisenberg algebra a suitable limit. We thus obtain a certain insight into how quantum mechanics may be regarded as a purely algebraic theory, provided that we further introduce a new set of "neighbourhood operators", which remove an important kind of arbitrariness that has thus far been present in the attempt to treat quantum mechanics solely in terms of a Heisenberg algebra
- …