Statistical Physics and Modeling of Human Mobility

In this thesis, we extend some ideas of statistical physics to describe the properties of human mobility. By using a database containing GPS measures of individual paths (position, velocity and covered space at a spatial scale of 2 Km or a time scale of 30 sec), which includes the 2% of the private vehicles in Italy, we succeed in determining some statistical empirical laws pointing out "universal" characteristics of human mobility. Developing simple stochastic models suggesting possible explanations of the empirical observations, we are able to indicate what are the key quantities and cognitive features that are ruling individuals' mobility. To understand the features of individual dynamics, we have studied different aspects of urban mobility from a physical point of view. We discuss the implications of the Benford's law emerging from the distribution of times elapsed between successive trips. We observe how the daily travel-time budget is related with many aspects of the urban environment, and describe how the daily mobility budget is then spent. We link the scaling properties of individual mobility networks to the inhomogeneous average durations of the activities that are performed, and those of the networks describing people's common use of space with the fractional dimension of the urban territory. We study entropy measures of individual mobility patterns, showing that they carry almost the same information of the related mobility networks, but are also influenced by a hierarchy among the activities performed. We discover that Wardrop's principles are violated as drivers have only incomplete information on traffic state and therefore rely on knowledge on the average travel-times. We propose an assimilation model to solve the intrinsic scattering of GPS data on the street network, permitting the real-time reconstruction of traffic state at a urban scale.

A universal delta model

This thesis presents a universal model of documents and deltas. This model formalize what it means to find differences between documents and to shows a single shared formalization that can be used by any algorithm to describe the differences found between any kind of comparable documents. The main scientific contribution of this thesis is a universal delta model that can be used to represent the changes found by an algorithm. The main part of this model are the formal definition of changes (the pieces of information that records that something has changed), operations (the definitions of the kind of change that happened) and deltas (coherent summaries of what has changed between two documents). The fundamental mechanism tha makes the universal delta model a very expressive tool is the use of encapsulation relations between changes. In the universal delta model, changes are not always simple records of what has changed, they can also be combined into more complex changes that reflects the detection of more meaningful modifications. In addition to the main entities (i.e., changes, operations and deltas), the model describes and defines also documents and the concept of equivalence between documents. As a corollary to the model, there is also an extensible catalog of possible operations that algorithms can detect, used to create a common library of operations, and an UML serialization of the model, useful as a reference when implementing APIs that deal with deltas. The universal delta model presented in this thesis acts as the formal groundwork upon which algorithm can be based and libraries can be implemented. It removes the need to recreate a new delta model and terminology whenever a new algorithm is devised. It also alleviates the problems that toolmakers have when adapting their software to new diff algorithms.