Dilatación auricular y fibrilación auricular

Studies of the structural properties of travel movements within urban areas, such as towns and cities, or between different urban areas, such as between districts within a country, are typically undertaken through study of a mathematical construct called an Origin-Destination (OD) matrix. Within this representation of demand, the geographical region under study is subdivided into several disparate areas, called zones, and the volume of travel between all pairs of zones is then recorded. Zones typically represent areas that share some congruent internal properties such as a residential area or business park within an urban area or different administrative regions within a country. One relatively recent development is the recognition that an OD matrix can also be converted into a network representation in which nodes represent origin and destination zones, links represent the existence of traffic flow between two zones and link weights represent traffic flow volumes.

Empirical studies of the structural characteristics of OD matrices - many of which are from the network science literature - have been undertaken for both urban and interurban travel, for different modes of transport and across a wide range of different countries.

For example, with respect to the properties of interurban travel, De Montis et al. (2007) studied the structure of the demand network created by commuting movements between the 375 municipalities on the island of Sardinia and concluded that there is a “rich-club phenomenon” in which there are a small number of regions with high total traffic flows, which have busy connections between them, and a significant number of smaller regions that act as “satellites” of larger cities. Their conclusion was that these structural features created an “overall network structure [that is] widely punctuated with star-like subsystems pivoting around important urban poles.” In their analysis of commuting patterns between districts in Germany, both Patuelli et al. (2007) and Reggiani et al. (2011) also uncovered heterogeneities in demand structure, with the latter highlighting the existence of twelve hubs that dominate in terms of traffic volume.

Focussing on urban travel patterns, Chowell et al. (2003) used an agent-based simulation model to simulate the movements of 1.6 million people in the city of Portland in the USA. The model was calibrated using census data, vehicle ownership records, public transport timetables and information about travel movements from a travel survey undertaken in the city. Using the network created by these movements, the authors undertook a structural analysis using node degree and the clustering coefficient measures and were able to uncover power laws in the distributions of traffic. The uncovering of these laws again highlights strong heterogeneities in the movements of travellers within OD matrices. Similar heterogeneity in the distribution of travel movements across a city were also uncovered by Gao et al. (2013),

who used a dataset of seventy-four million mobile phone call records for the city of Harbin in northeast China.

Turning to a study undertaken within the transportation research community, Gutierrez and Garcia-Palomares (2007) analysed differences in travel patterns in Madrid between 1988 and 1996, using data from mobility surveys carried out in those years, and found that there had been a significant shift in the structure of Madrid from a monocentric organisation, where most trips are to a dominant city centre, to a polycentric organisation, with increased suburb to suburb travel. Their assertion was that this is a result of a process of decentralisation in employment. Using oyster card data, Roth et al. (2011) uncovered a similar polycentric structure of demand in London and identified multiple centres that both attract and generate large amounts of flow at different times of day, on different days and across different weeks. All of these studies highlight a trend towards an increasingly complex, heterogeneous distribution of demand in OD matrices at the level of both urban and interurban travel. Given the existence of such patterns, it is unsurprising that several models have been proposed for characterising the distribution of travel demand. The most well-known model is that based on the gravity law and which posits that the volume of travel between two zones is proportional to the travel populations within those two zones and inversely proportional to the cost of travel or distance between them. Several forms of gravity based models are used in practice, which each use different functional forms to represent the deterrence of travel costs. Both Patuelli et al. (2007) and Reggiani et al. (2011) attempted to fit gravity models to explain the patterns uncovered in their empirical analyses but were unable to successfully fit either an exponential or power form deterrence function. A more successful attempt at fitting a gravity law model was presented by Jung et al. (2008), who analysed the network created by the movements of traffic on the interurban highway network of South Korea. Using a dataset comprising total movements between the top thirty cities (by population) as recorded by the toll plazas sited at all entry and exit points to the network, they successfully fitted a gravity law with a power law form deterrence function.

It is worth noting that several other models for travel demand have also been proposed; for example, the intervening opportunities model, which proposes that “the number of persons going a given distance is directly proportional to the number of opportunities at that distance and inversely proportional to the number of intervening opportunities” (Stouffer, 1940); and, more recently, the radiation model, which focuses on commuting flows by way of modelling how individuals accept job offers with respect to benefits and distance (Simini et al., 2012). The latter model, which has the advantage of being parameter free, has been shown to produce better estimates of travel demand patterns than the gravity model (Simini et al.,

2012), although not for large cities like London (Masucci et al., 2013). Masucci et al. (2013) argue that “commuting at the city scale still lacks a valid model and that further research is required to understand the mechanism behind urban mobility”.