Elements of a Theory of Simulation

Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However, simulation also qualifies as a separate species of system representation with its own motivations, characteristics, and implications. This work outlines how simulation can be rooted in mathematics and shows which properties some of the elements of such a mathematical framework has. The properties of simulation are described and analyzed in terms of properties of dynamical systems. It is shown how and why a simulation produces emergent behavior and why the analysis of the dynamics of the system being simulated always is an analysis of emergent phenomena. A notion of a universal simulator and the definition of simulatability is proposed. This allows a description of conditions under which simulations can distribute update functions over system components, thereby determining simulatability. The connection between the notion of simulatability and the notion of computability is defined and the concepts are distinguished. The basis of practical detection methods for determining effectively non-simulatable systems in practice is presented. The conceptual framework is illustrated through examples from molecular self-assembly end engineering.Comment: Also available via http://studguppy.tsasa.lanl.gov/research_team/ Keywords: simulatability, computability, dynamics, emergence, system representation, universal simulato

Sequence selection in an autocatalytic binary polymer model

An autocatalytic pattern matching polymer system is studied as an abstract model for chemical ecosystem evolution. Highly ordered populations with particular sequence patterns appear spontaneously out of a vast number of possible states. The interplay between the selected microscopic sequence patterns and the macroscopic cooperative structures is examined. Stability, fluctuations, and evolutionary selection mechanisms are investigated for the involved self-organizing processes

On the Growth Rate of Non-Enzymatic Molecular Replicators

It is well known that non-enzymatic template directed molecular replicators X + nO ---> 2X exhibit parabolic growth d[X]/dt = k [X]^{1/2}. Here, we analyze the dependence of the effective replication rate constant k on hybridization energies, temperature, strand length, and sequence composition. First we derive analytical criteria for the replication rate k based on simple thermodynamic arguments. Second we present a Brownian dynamics model for oligonucleotides that allows us to simulate their diffusion and hybridization behavior. The simulation is used to generate and analyze the effect of strand length, temperature, and to some extent sequence composition, on the hybridization rates and the resulting optimal overall rate constant k. Combining the two approaches allows us to semi-analytically depict a fitness landscape for template directed replicators. The results indicate a clear replication advantage for longer strands at low temperatures.Comment: Submitted to: Entrop

Quasi-Species and Aggregate Dynamics

At an early stage in pre-biotic evolution, groups of replicating molecules must coordinate their reproduction to form aggregated units of selection. Mechanisms that enable this to occur are currently not well understood. In this paper we introduce a deterministic model of primitive replicating aggregates, proto-organisms, that host populations of replicating information carrying molecules. Some of the molecules promote the reproduction of the proto-organism at the cost of their individual replication rate. A situation resembling that of group selection arises. We derive and analytically solve a partial differential equation that describes the system. We find that the relative prevalence of fast and slow replicators is determined by the relative strength of selection at the aggregate level to the selection strength at the molecular level. The analysis is concluded by a preliminary treatment of finite population size effects.Comment: 6 page

Dansk Idræts Forbund og forholdet til Tyskland 1940-45

Artikel om Dansk Idræts Forbund og forholdet til Tyskland i årene 1940-45

Dansk Idræts Forbund og forholdet til Tyskland 1940-45

Artikel om Dansk Idræts Forbund og forholdet til Tyskland i årene 1940-45