200,279 research outputs found
Equicontinuous factors, proximality and Ellis semigroup for Delone sets
We discuss the application of various concepts from the theory of topological
dynamical systems to Delone sets and tilings. We consider in particular, the
maximal equicontinuous factor of a Delone dynamical system, the proximality
relation and the enveloping semigroup of such systems.Comment: 65 page
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
Modeling fractal structure of city-size distributions using correlation function
Zipf's law is one the most conspicuous empirical facts for cities, however,
there is no convincing explanation for the scaling relation between rank and
size and its scaling exponent. Based on the idea from general fractals and
scaling, this paper proposes a dual competition hypothesis of city develop to
explain the value intervals and the special value, 1, of the power exponent.
Zipf's law and Pareto's law can be mathematically transformed into one another.
Based on the Pareto distribution, a frequency correlation function can be
constructed. By scaling analysis and multifractals spectrum, the parameter
interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf
distribution, a size correlation function can be built, and it is opposite to
the first one. By the second correlation function and multifractals notion, the
Pareto exponent interval is derived as [1, 2). Thus the process of urban
evolution falls into two effects: one is Pareto effect indicating city number
increase (external complexity), and the other Zipf effect indicating city size
growth (internal complexity). Because of struggle of the two effects, the
scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium
with each other, the scaling exponent approaches 1. A series of mathematical
experiments on hierarchical correlation are employed to verify the models and a
conclusion can be drawn that if cities in a given region follow Zipf's law, the
frequency and size correlations will follow the scaling law. This theory can be
generalized to interpret the inverse power-law distributions in various fields
of physical and social sciences.Comment: 18 pages, 3 figures, 3 table
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