A complex network approach to urban growth

The economic geography can be viewed as a large and growing network of interacting activities. This fundamental network structure and the large size of such systems makes complex networks an attractive model for its analysis. In this paper we propose the use of complex networks for geographical modeling and demonstrate how such an application can be combined with a cellular model to produce output that is consistent with large scale regularities such as power laws and fractality. Complex networks can provide a stringent framework for growth dynamic modeling where concepts from e.g. spatial interaction models and multiplicative growth models can be combined with the flexible representation of land and behavior found in cellular automata and agent-based models. In addition, there exists a large body of theory for the analysis of complex networks that have direct applications for urban geographic problems. The intended use of such models is twofold: i) to address the problem of how the empirically observed hierarchical structure of settlements can be explained as a stationary property of a stochastic evolutionary process rather than as equilibrium points in a dynamics, and, ii) to improve the prediction quality of applied urban modeling.evolutionary economics, complex networks, urban growth

Categories of Timed Stochastic Relations

AbstractStochastic behavior—the probabilistic evolution of a system in time—is essential to modeling the complexity of real-world systems. It enables realistic performance modeling, quality-of-service guarantees, and especially simulations for biological systems. Languages like the stochastic pi calculus have emerged as effective tools to describe and reason about systems exhibiting stochastic behavior. These languages essentially denote continuous-time stochastic processes, obtained through an operational semantics in a probabilistic transition system. In this paper we seek a more descriptive foundation for the semantics of stochastic behavior using categories and monads. We model a first-order imperative language with stochastic delay by identifying probabilistic choice and delay as separate effects, modeling each with a monad, and combining the monads to build a model for the stochastic language

Learning algorithms for adaptive digital filtering

In this thesis, we consider the problem of parameter optimisation in adaptive digital filtering. Adaptive digital filtering can be accomplished using both Finite Impulse Response (FIR) filters and Infinite Impulse Response Filters (IIR) filters. Adaptive FIR filtering algorithms are well established. However, the potential computational advantages of IIR filters has led to an increase in research on adaptive IIR filtering algorithms. These algorithms are studied in detail in this thesis and the limitations of current adaptive IIR filtering algorithms are identified. New approaches to adaptive IIR filtering using intelligent learning algorithms are proposed. These include Stochastic Learning Automata, Evolutionary Algorithms and Annealing Algorithms. Each of these techniques are used for the filtering problem and simulation results are presented showing the performance of the algorithms for adaptive IIR filtering. The relative merits and demerits of the different schemes are discussed. Two practical applications of adaptive IIR filtering are simulated and results of using the new adaptive strategies are presented. Other than the new approaches used, two new hybrid schemes are proposed based on concepts from genetic algorithms and annealing. It is shown with the help of simulation studies, that these hybrid schemes provide a superior performance to the exclusive use of any one scheme

Coalgebraic Trace Semantics for Continuous Probabilistic Transition Systems

Coalgebras in a Kleisli category yield a generic definition of trace semantics for various types of labelled transition systems. In this paper we apply this generic theory to generative probabilistic transition systems, short PTS, with arbitrary (possibly uncountable) state spaces. We consider the sub-probability monad and the probability monad (Giry monad) on the category of measurable spaces and measurable functions. Our main contribution is that the existence of a final coalgebra in the Kleisli category of these monads is closely connected to the measure-theoretic extension theorem for sigma-finite pre-measures. In fact, we obtain a practical definition of the trace measure for both finite and infinite traces of PTS that subsumes a well-known result for discrete probabilistic transition systems. Finally we consider two example systems with uncountable state spaces and apply our theory to calculate their trace measures

A Class of Automata Networks for Diffusion of Innovations Driven by Riccati Equations : Automata Networks for Diffusion of Innovations.

Innovation diffusion processes are generally described at aggregate level with models like the Bass model (1969) and the Generalized Bass Model (1994). However, the recognized importance of communication channels between agents has recently suggested the use of agent-based models, like Cellular Automata. We argue that an adoption process is nested in a communication network that evolves dynamically and implicitly generates a non-constant potential market. Using Cellular Automata we propose a two- phase model of an innovation diffusion process. First we describe the Communication Network necessary for the awareness of an innovation. Then, we model a nested process representing the proper adoption dynamics. Through a "Mean Field Approximation" we propose a continuous representation of the discrete time equations derived by our Automata Network. This constitutes a special non autonomous Riccati equation, not yet described in well-known international catalogues. The main results refer to the closed form solution of this equation and to the corresponding statistical analysis for identification and inference. We discuss an application in the field of bank services