Towards a compendium of process technologies: The jBPT library for process model analysis

This paper presents the idea of a compendium of process technologies, i.e., a concise but comprehensive collection of techniques for process model analysis that support research on the design, execution, and evaluation of processes. The idea originated from observations on the evolution of process-related research disciplines. Based on these observations, we derive design goals for a compendium. Then, we present the jBPT library, which addresses these goals by means of an implementation of common analysis techniques in an open source codebase

Isotactics as a foundation for alignment and abstraction of behavioral models

There are many use cases in business process management that require the comparison of behavioral models. For instance, verifying equivalence is the basis for assessing whether a technical workflow correctly implements a business process, or whether a process realization conforms to a reference process. This paper proposes an equivalence relation for models that describe behaviors based on the concurrency semantics of net theory and for which an alignment relation has been defined. This equivalence, called isotactics, preserves the level of concurrency of aligned operations. Furthermore, we elaborate on the conditions under which an alignment relation can be classified as an abstraction. Finally, we show that alignment relations induced by structural refinements of behavioral models are indeed behavioral abstractions

Urban and Hinterland Evolution under Growing Population Pressure

An integrated mathematical model for the evolution of urban structure and population ist presented. The city configuration consists of an occupation number representation of different kinds of buildings such as lodgings and factories distributed over a grid of plots, and the population configuration describes the distribution of the population between city (c) and hinterland (h). The dynamics of the total configuration is governed by motivation - dependent transition rates between neighbouring configurations. Equations of evolution on the stochastic level (masterequation) and deterministic level (quasi-meanvalue equations) can thereupon be derived. We focus on that sector of the model describing the population dynamics between hinterland (h) and city (c). Under the assumption of equal net birth rates in (c) and (h), and for given growth of the total population P(t), the dynamics of the population shares between (h) and (c) can be treated explicitely in terms of a time dependent evolution potential. One can distinguish between the two main cases of "constructive competition between (c) and (h)" and "worsening balance between (c) and (h)". In the first case a stabilisation of the population shares in c and h takes place, whereas in the second case a dramatic migratory phase transition sets in, namely a sudden rush of the population from the depleting hinterland to the overcrowding city. KEYWORDS: 1. Integration of Urban and Population Dynamics 2. Motivation Dependent Transition Rates 3. Master Equation 4. Quasimeanvalue Equations 5. Migratory Phase-Transition

The Krause-Hegselmann Consensus Model with Discrete Opinions

The consensus model of Krause and Hegselmann can be naturally extended to the case in which opinions are integer instead of real numbers. Our algorithm is much faster than the original version and thus more suitable for applications. For the case of a society in which everybody can talk to everybody else, we find that the chance to reach consensus is much higher as compared to other models; if the number of possible opinions Q<=7, in fact, consensus is always reached, which might explain the stability of political coalitions with more than three or four parties. For Q>7 the number S of surviving opinions is approximately the same independently of the size N of the population, as long as Q<N. We considered as well the more realistic case of a society structured like a Barabasi-Albert network; here the consensus threshold depends on the outdegree of the nodes and we find a simple scaling law for S, as observed for the discretized Deffuant model.Comment: 12 pages, 6 figure

A Contracted Path Integral Solution of the Discrete Master Equation

A new representation of the exact time dependent solution of the discrete master equation is derived. This representation can be considered as contraction of the path integral solution of Haken. It allows the calculation of the probability distribution of the occurence time for each path and is suitable as basis of new computational solution methods.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

The role of network topology on extremism propagation with the Relative Agreement opinion dynamics

In (Deffuant et al., 2002), we proposed a simple model of opinion dynamics, which we used to simulate the influence of extremists in a population. Simulations were run without any specific interaction structure and varying the simulation parameters, we observed different attractors such as predominance of centrism or of extremism. We even observed in certain conditions, that the whole population drifts to one extreme of the opinion, even if initially there are an equal number of extremists at each extreme of the opinion axis. In the present paper, we study the influence of the social networks on the presence of such a dynamical behavior. In particular, we use small-world networks with variable connectivity and randomness of the connections. We find that the drift to a single extreme appears only beyond a critical level of connectivity, which decreases when the randomness increases.Comment: 15 pages, 9 figure

Monte Carlo Simulation of Deffuant opinion dynamics with quality differences

In this work the consequences of different opinion qualities in the Deffuant model were examined. If these qualities are randomly distributed, no different behavior was observed. In contrast to that, systematically assigned qualities had strong effects to the final opinion distribution. There was a high probability that the strongest opinion was one with a high quality. Furthermore, under the same conditions, this major opinion was much stronger than in the models without systematic differences. Finally, a society with systematic quality differences needed more tolerance to form a complete consensus than one without or with unsystematic ones.Comment: 8 pages including 5 space-consuming figures, fir Int. J. Mod. Phys. C 15/1

Opinion dynamics and decision of vote in bipolar political systems

A model of the opinion dynamics underlying the political decision is proposed. The analysis is restricted to a bipolar scheme with a possible third political area. The interaction among voters is local but the final decision strongly depends on global effects such as, for example, the rating of the governments. As in the realistic case, the individual decision making process is determined by the most relevant personal interests and problems. The phenomenological analysis of the national vote in Italy and Germany has been carried out and a prediction of the next Italian vote as a function of the government rating is presented.Comment: 8 pages, 1 figure. To be published in International Journal of Modern Physics

Phase transitions in social impact models of opinion formation

We study phase transitions in models of opinion formation which are based on the social impact theory. Two different models are discussed: (i) a cellular--automata based model of a finite group with a strong leader where persons can change their opinions but not their spatial positions, and (ii) a model with persons treated as active Brownian particles interacting via a communication field. In the first model, two stable phases are possible: a cluster around the leader, and a state of social unification. The transition into the second state occurs for a large leader strength and/or for a high level of social noise. In the second model, we find three stable phases, which correspond either to a ``paramagnetic'' phase (for high noise and strong diffusion), a ``ferromagnetic'' phase (for small nose and weak diffusion), or a phase with spatially separated ``domains'' (for intermediate conditions).Comment: 15 pages, 4 figures, submitted for publication in Physica

The Sznajd Consensus Model with Continuous Opinions

In the consensus model of Sznajd, opinions are integers and a randomly chosen pair of neighbouring agents with the same opinion forces all their neighbours to share that opinion. We propose a simple extension of the model to continuous opinions, based on the criterion of bounded confidence which is at the basis of other popular consensus models. Here the opinion s is a real number between 0 and 1, and a parameter \epsilon is introduced such that two agents are compatible if their opinions differ from each other by less than \epsilon. If two neighbouring agents are compatible, they take the mean s_m of their opinions and try to impose this value to their neighbours. We find that if all neighbours take the average opinion s_m the system reaches complete consensus for any value of the confidence bound \epsilon. We propose as well a weaker prescription for the dynamics and discuss the corresponding results.Comment: 11 pages, 4 figures. To appear in International Journal of Modern Physics