A Mathematical Model for the Behavior of Individuals in a Social Field

Related to an idea of Lewin, a mathematical model for behavioral changes under the influence of a social field is developed. The social field reflects public opinion, social norms and trends. It is not only given by external factors (the environment) but also by the interactions of individuals. Two important kinds of interaction processes are distinguished: Imitative and avoidance processes. Variations of individual behavior are taken into account by ``diffusion coefficients''.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

A stochastic behavioral model and a `microscopic' foundation of evolutionary game theory

A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations. That means, the approximate mean value equations of these equations are the game dynamical equations of evolutionary game theory. The stochastic version of the game dynamical equations allows the derivation of covariance equations. These should always be solved along with the ordinary game dynamical equations. On the one hand, the average behavior is affected by the covariances so that the game dynamical equations must be corrected for increasing covariances. Otherwise they may become invalid in the course of time. On the other hand, the covariances are a measure for the reliability of game dynamical descriptions. An increase of the covariances beyond a critical value indicates a phase transition, i.e. a sudden change in the properties of the considered social system. The applicability and use of the introduced equations are illustrated by computational results for the social self-organization of behavioral conventions.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Qualified Trust, not Surveillance, is the Basis of a Stable Society

Peaceful citizens and hard-working taxpayers are under government surveillance. Confidential communication of journalists is intercepted. Civilians are killed by drones, without a chance to prove their innocence. How could it come that far? And what are the alternatives?Comment: For related work see http://www.futurict.e

A Mathematical Model for the Behavior of Pedestrians

The movement of pedestrians is supposed to show certain regularities which can be best described by an ``algorithm'' for the individual behavior and is easily simulated on computers. This behavior is assumed to be determined by an intended velocity, by several attractive and repulsive effects and by fluctuations. The movement of pedestrians is dependent on decisions, which have the purpose of optimizing their behavior and can be explicitly modelled. Some interesting applications of the model to real situations are given, especially to formation of groups, behavior in queues, avoidance of collisions and selection processes between behavioral alternatives.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Traffic Data and Their Implications for Consistent Traffic Flow Modeling

The paper analyzes traffic data of the Dutch freeway A9 with respect to certain aspects which are relevant for traffic flow modeling as well as the calibration of model parameters and functions. Apart from the dynamic velocity distribution, the density-dependence and the temporal evolution of various, partly lane-specific quantities is investigated. The results are well compatible with recent macroscopic traffic flow models which have been derived from the dynamics of driver-vehicle units. These have also solved the inconsistencies, which previous models have been criticized for.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

New Ways to Promote Sustainability and Social Well-Being in a Complex, Strongly Interdependent World: The FuturICT Approach

FuturICT is one of six proposals currently being considered for support within the European Commission's Flagship Initiative (see Box 1). The vision of the FuturICT project is to develop new science and new information and communication systems that will promote social self-organization, self-regulation, well-being, sustainability, and resilience. One of the main aims of the approach is to increase individual opportunities for social, economic and political participation, combined with the creation of collective awareness of the impact that human actions have on our world. This requires us to mine large datasets ("Big Data") and to develop new methods and tools: a Planetary Nervous System (PNS) to answer "What is (the state of the world)..." questions, a Living Earth Simulator (LES) to study "What ... if ..." scenarios, and a Global Participatory Platform (GPP) for social exploration and interaction.Comment: For related work see http://www.soms.ethz.ch and http://www.futurict.e

Survival Analysis, Master Equation, Efficient Simulation of Path-Related Quantities, and Hidden State Concept of Transitions

This paper presents and derives the interrelations between survival analysis and master equation. Survival analysis deals with modeling the transitions between succeeding states of a system in terms of hazard rates. Questions related with this are the timing and sequencing of the states of a time series. The frequency and characteristics of time series can be investigated by Monte-Carlo simulations. If one is interested in cross-sectional data connected with the stochastic process under consideration, one needs to know the temporal evolution of the distribution of states. This can be obtained by simulation of the associated master equation. Some new formulas allow the determination of path-related (i.e. longitudinal) quantities like the occurence probability, the occurence time distribution, or the effective cumulative life-time distribution of a certain sequencing of states (path). These can be efficiently evaluated with a recently developed simulation tool (EPIS). The effective cumulative life-time distribution facilitates the formulation of a hidden state concept of behavioral changes which allows an interpretation of the respective time-dependence of hazard rates. Hidden states represent states which are either not phenomenological distinguishable from other states, not externally measurable, or simply not detected.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Production, Supply, and Traffic Systems: A Unified Description

The transport of products between different suppliers or production units can be described similarly to driven many-particle and traffic systems. We introduce equations for the flow of goods in supply networks and the adaptation of production speeds. Moreover, we present two examples: The case of linear (sequential) supply chains and the case of re-entrant production. In particular, we discuss the stability conditions, dynamic solutions, and resonance phenomena causing the frequently observed "bullwhip effect", which is an analogue of stop-and-go traffic. Finally, we show how to treat discrete units and cycle times, which can be applied to the description of vehicle queues and travel times in freeway networks.Comment: For related work see http://www.helbing.or

Responding to complexity in socio-economic systems: How to build a smart and resilient society?

The world is changing at an ever-increasing pace. And it has changed in a much more fundamental way than one would think, primarily because it has become more connected and interdependent than in our entire history. Every new product, every new invention can be combined with those that existed before, thereby creating an explosion of complexity: structural complexity, dynamic complexity, functional complexity, and algorithmic complexity. How to respond to this challenge? And what are the costs?Comment: For related publications see http://www.coss.ethz.ch and http://scholar.google.com/citations?user=ebrNfPAAAAAJ&hl=e

The FuturIcT Knowledge Accelerator: Unleashing the Power of Information for a Sustainable Future

With our knowledge of the universe, we have sent men to the moon. We know microscopic details of objects around us and within us. And yet we know relatively little about how our society works and how it reacts to changes brought upon it. Humankind is now facing serious crises for which we must develop new ways to tackle the global challenges of humanity in the 21st century. With connectivity between people rapidly increasing, we are now able to exploit information and communication technologies to achieve major breakthroughs that go beyond the step-wise improvements in other areas. The need of a socio-economic knowledge collider was first pointed out in the OECD Global Science Forum on Applications of Complexity Science for Public Policy in Erice from October 5 to 7, 2008. Since then, many scientists have called for a large-scale ICT-based research initiative on techno-socialeconomic- environmental issues, sometimes phrased as a Manhattan-, Apollo-, or CERN-like project to study the way our living planet works in a social dimension. Due to the connotations, we use the term knowledge accelerator, here.Comment: For related information see http://www.futurict.eu (The spelling error in Sec. 2.5 was removed: "exclusion" was replaced by "inclusion"