Michael Gastner - Academia.edu (original) (raw)
Papers by Michael Gastner
We study spatial distribution networks, such as gas pipelines or train tracks, which grow from an... more We study spatial distribution networks, such as gas pipelines or train tracks, which grow from an initial source or sink of the commodity transported by the network. The efficiency depends on two properties. First, the paths to t he root are ideally not much longer than the "crow flies" distance. Second, the length of all connections in the network should
Map makers have for many years searched for a way to construct cartograms—maps in which the sizes... more Map makers have for many years searched for a way to construct cartograms—maps in which the sizes of geographic regions such as coun- tries or provinces appear in proportion to their population or some sim- ilar property. Such maps are invaluable for the representation of census results, election returns, disease incidence, and many other kinds of hu- man data. Unfortunately,
Unifying Themes in Complex Systems, 2008
A quantity of practical importance in the design of an infrastructure network is the amount of tr... more A quantity of practical importance in the design of an infrastructure network is the amount of traffic along different parts in the network. Traffic patterns primarily depend on the users' preference for short paths through the network and spatial constraints for building the necessary connections. Here we study the traffic distribution in a spatial network model which takes both of these considerations into account. Assuming users always travel along the shortest path available, the appropriate measure for traffic flow along the links is a generalization of the usual concept of "edge betweenness". We find that for networks with a minimal total maintenance cost, a small number of connections must handle a disproportionate amount of traffic. However, if users can travel more directly between different points in the network, the maximum traffic can be greatly reduced.
Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 2009
We study the problem of optimizing traffic in decentralized transportation networks, where the co... more We study the problem of optimizing traffic in decentralized transportation networks, where the cost of a link depends on its congestion. If users of a transportation network are permitted to choose their own routes, they generally try to minimize their personal travel time. In the absence of centralized coordination, such a behavior can be inefficient for society and even for
The recent convergence of laser-cooling and Rydberg atom spectroscopy has opened up the possibili... more The recent convergence of laser-cooling and Rydberg atom spectroscopy has opened up the possibility of studying plasmas and Rydberg gases in previously inaccessible low-energy regimes. We report on our efforts to extend these studies, both experimentally and theoretically, to high magnetic field (several Tesla). Magnetic fields are ubiquitous in terrestrial and astrophysical plasmas; they give rise to confinement and qualitatively
PLoS ONE, 2014
Statistical physicists have become interested in models of collective social behavior such as opi... more Statistical physicists have become interested in models of collective social behavior such as opinion formation, where individuals change their inherently preferred opinion if their friends disagree. Real preferences often depend on regional cultural differences, which we model here as a spatial gradient g in the initial opinion. The gradient does not only add reality to the model. It can also reveal that opinion clusters in two dimensions are typically in the standard (i.e., independent) percolation universality class, thus settling a recent controversy about a non-consensus model. However, we also present a model where the width of the transition between opinions scales ∝ g −1/4 , not ∝ g −4/7 as in independent percolation, and the cluster size distribution is consistent with first-order percolation.
Proceedings of the National Academy of Sciences, 2004
Map makers have for many years searched for a way to construct cartograms, maps in which the size... more Map makers have for many years searched for a way to construct cartograms, maps in which the sizes of geographic regions such as countries or provinces appear in proportion to their population or some other analogous property. Such maps are invaluable for the representation of census results, election returns, disease incidence, and many other kinds of human data. Unfortunately, to scale regions and still have them fit together, one is normally forced to distort the regions' shapes, potentially resulting in maps that are difficult to read. Many methods for making cartograms have been proposed, some of them are extremely complex, but all suffer either from this lack of readability or from other pathologies, like overlapping regions or strong dependence on the choice of coordinate axes. Here, we present a technique based on ideas borrowed from elementary physics that suffers none of these drawbacks. Our method is conceptually simple and produces useful, elegant, and easily readable maps. We illustrate the method with applications to the results of the 2000 U.S. presidential election, lung cancer cases in the State of New York, and the geographical distribution of stories appearing in the news.
Physical Review Letters, 2008
Physical Review Letters, 2009
Physical Review E, 2006
We consider the problem of constructing public facilities, such as hospitals, airports, or malls,... more We consider the problem of constructing public facilities, such as hospitals, airports, or malls, in a country with a non-uniform population density, such that the average distance from a person's home to the nearest facility is minimized. Approximate analytic arguments suggest that the optimal distribution of facilities should have a density that increases with population density, but does so slower than linearly, as the two-thirds power. This result is confirmed numerically for the particular case of the United States with recent population data using two independent methods, one a straightforward regression analysis, the other based on density dependent map projections. We also consider strategies for linking the facilities to form a spatial network, such as a network of flights between airports, so that the combined cost of maintenance of and travel on the network is minimized. We show specific examples of such optimal networks for the case of the United States.
Physical Review E, 2011
The p-median problem is a common model for optimal facility location. The task is to place p faci... more The p-median problem is a common model for optimal facility location. The task is to place p facilities (e.g., warehouses or schools) in a heterogeneously populated space such that the average distance from a person's home to the nearest facility is minimized. Here we study the special case where the population lives along a line (e.g., a road or a river). If facilities are optimally placed, the length of the line segment served by a facility is inversely proportional to the square root of the population density. This scaling law is derived analytically and confirmed for concrete numerical examples of three US Interstate highways and the Mississippi River. If facility locations are permitted to deviate from the optimum, the number of possible solutions increases dramatically. Using Monte Carlo simulations, we compute how scaling is affected by an increase in the average distance to the nearest facility. We find that the scaling exponents change and are most sensitive near the optimum facility distribution.
Journal of The Royal Society Interface, 2010
Transportation networks play a crucial role in human mobility, the exchange of goods, and the spr... more Transportation networks play a crucial role in human mobility, the exchange of goods, and the spread of invasive species. With 90% of world trade carried by sea, the global network of merchant ships provides one of the most important modes of transportation. Here we use information about the itineraries of 16,363 cargo ships during the year 2007 to construct a network of links between ports. We show that the network has several features which set it apart from other transportation networks. In particular, most ships can be classified in three categories: bulk dry carriers, container ships and oil tankers. These three categories do not only differ in the ships' physical characteristics, but also in their mobility patterns and networks. Container ships follow regularly repeating paths whereas bulk dry carriers and oil tankers move less predictably between ports. The network of all ship movements possesses a heavy-tailed distribution for the connectivity of ports and for the loads transported on the links with systematic differences between ship types. The data analyzed in this paper improve current assumptions based on gravity models of ship movements, an important step towards understanding patterns of global trade and bioinvasion.
Journal of Statistical Mechanics: Theory and Experiment, 2006
We study spatial networks that are designed to distribute or collect a commodity, such as gas pip... more We study spatial networks that are designed to distribute or collect a commodity, such as gas pipelines or train tracks. We focus on the cost of a network, as represented by the total length of all its edges, and its efficiency in terms of the directness of routes from point to point. Using data for several real-world examples, we find that distribution networks appear remarkably close to optimal where both these properties are concerned. We propose two models of network growth that offer explanations of how this situation might arise.
The European Physical Journal B, 2006
We study networks that connect points in geographic space, such as transportation networks and th... more We study networks that connect points in geographic space, such as transportation networks and the Internet. We find that there are strong signatures in these networks of topography and use patterns, giving the networks shapes that are quite distinct from one another and from nongeographic networks. We offer an explanation of these differences in terms of the costs and benefits of transportation and communication, and give a simple model based on the Monte Carlo optimization of these costs and benefits that reproduces well the qualitative features of the networks studied.
Proceedings of the National …, 2004
... of a square lattice and this introduces a strong signature of the lattice topology into the .... more ... of a square lattice and this introduces a strong signature of the lattice topology into the ... 4b , we show the same data on a population cartogram with moderate coarse-graining of the initial ... 4c , on the other hand, we use a very fine-grained population density, creating a cartogram ...
Advances in Complex Systems, 2005
Conventional maps of election results can give a misleading picture of the popular support that c... more Conventional maps of election results can give a misleading picture of the popular support that candidates have because population is highly non-uniform and equal areas on a map may not correspond to equal numbers of voters. Taking the example of the 2004 United States presidential election, we show how this problem can be corrected using a cartogram-a map in which the sizes of regions such as states are rescaled according to population or some other variable of interest.
Physical Review Letters, 2011
The establishment and spreading of biological populations depends crucially on population growth ... more The establishment and spreading of biological populations depends crucially on population growth at low densities. The Allee effect is a problem in those populations where the per-capita growth rate at low densities is reduced. We examine stochastic spatial models in which the reproduction rate changes across a gradient g so that the population undergoes a 2D-percolation transition. Without the Allee effect, the transition is continuous and the width w of the hull scales as in conventional (i.e., uncorrelated) gradient percolation, w ∝ g −0.57 . However, with a strong Allee effect the transition is first order and w ∝ g −0.26 .
We study spatial distribution networks, such as gas pipelines or train tracks, which grow from an... more We study spatial distribution networks, such as gas pipelines or train tracks, which grow from an initial source or sink of the commodity transported by the network. The efficiency depends on two properties. First, the paths to t he root are ideally not much longer than the "crow flies" distance. Second, the length of all connections in the network should
Map makers have for many years searched for a way to construct cartograms—maps in which the sizes... more Map makers have for many years searched for a way to construct cartograms—maps in which the sizes of geographic regions such as coun- tries or provinces appear in proportion to their population or some sim- ilar property. Such maps are invaluable for the representation of census results, election returns, disease incidence, and many other kinds of hu- man data. Unfortunately,
Unifying Themes in Complex Systems, 2008
A quantity of practical importance in the design of an infrastructure network is the amount of tr... more A quantity of practical importance in the design of an infrastructure network is the amount of traffic along different parts in the network. Traffic patterns primarily depend on the users' preference for short paths through the network and spatial constraints for building the necessary connections. Here we study the traffic distribution in a spatial network model which takes both of these considerations into account. Assuming users always travel along the shortest path available, the appropriate measure for traffic flow along the links is a generalization of the usual concept of "edge betweenness". We find that for networks with a minimal total maintenance cost, a small number of connections must handle a disproportionate amount of traffic. However, if users can travel more directly between different points in the network, the maximum traffic can be greatly reduced.
Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 2009
We study the problem of optimizing traffic in decentralized transportation networks, where the co... more We study the problem of optimizing traffic in decentralized transportation networks, where the cost of a link depends on its congestion. If users of a transportation network are permitted to choose their own routes, they generally try to minimize their personal travel time. In the absence of centralized coordination, such a behavior can be inefficient for society and even for
The recent convergence of laser-cooling and Rydberg atom spectroscopy has opened up the possibili... more The recent convergence of laser-cooling and Rydberg atom spectroscopy has opened up the possibility of studying plasmas and Rydberg gases in previously inaccessible low-energy regimes. We report on our efforts to extend these studies, both experimentally and theoretically, to high magnetic field (several Tesla). Magnetic fields are ubiquitous in terrestrial and astrophysical plasmas; they give rise to confinement and qualitatively
PLoS ONE, 2014
Statistical physicists have become interested in models of collective social behavior such as opi... more Statistical physicists have become interested in models of collective social behavior such as opinion formation, where individuals change their inherently preferred opinion if their friends disagree. Real preferences often depend on regional cultural differences, which we model here as a spatial gradient g in the initial opinion. The gradient does not only add reality to the model. It can also reveal that opinion clusters in two dimensions are typically in the standard (i.e., independent) percolation universality class, thus settling a recent controversy about a non-consensus model. However, we also present a model where the width of the transition between opinions scales ∝ g −1/4 , not ∝ g −4/7 as in independent percolation, and the cluster size distribution is consistent with first-order percolation.
Proceedings of the National Academy of Sciences, 2004
Map makers have for many years searched for a way to construct cartograms, maps in which the size... more Map makers have for many years searched for a way to construct cartograms, maps in which the sizes of geographic regions such as countries or provinces appear in proportion to their population or some other analogous property. Such maps are invaluable for the representation of census results, election returns, disease incidence, and many other kinds of human data. Unfortunately, to scale regions and still have them fit together, one is normally forced to distort the regions' shapes, potentially resulting in maps that are difficult to read. Many methods for making cartograms have been proposed, some of them are extremely complex, but all suffer either from this lack of readability or from other pathologies, like overlapping regions or strong dependence on the choice of coordinate axes. Here, we present a technique based on ideas borrowed from elementary physics that suffers none of these drawbacks. Our method is conceptually simple and produces useful, elegant, and easily readable maps. We illustrate the method with applications to the results of the 2000 U.S. presidential election, lung cancer cases in the State of New York, and the geographical distribution of stories appearing in the news.
Physical Review Letters, 2008
Physical Review Letters, 2009
Physical Review E, 2006
We consider the problem of constructing public facilities, such as hospitals, airports, or malls,... more We consider the problem of constructing public facilities, such as hospitals, airports, or malls, in a country with a non-uniform population density, such that the average distance from a person's home to the nearest facility is minimized. Approximate analytic arguments suggest that the optimal distribution of facilities should have a density that increases with population density, but does so slower than linearly, as the two-thirds power. This result is confirmed numerically for the particular case of the United States with recent population data using two independent methods, one a straightforward regression analysis, the other based on density dependent map projections. We also consider strategies for linking the facilities to form a spatial network, such as a network of flights between airports, so that the combined cost of maintenance of and travel on the network is minimized. We show specific examples of such optimal networks for the case of the United States.
Physical Review E, 2011
The p-median problem is a common model for optimal facility location. The task is to place p faci... more The p-median problem is a common model for optimal facility location. The task is to place p facilities (e.g., warehouses or schools) in a heterogeneously populated space such that the average distance from a person's home to the nearest facility is minimized. Here we study the special case where the population lives along a line (e.g., a road or a river). If facilities are optimally placed, the length of the line segment served by a facility is inversely proportional to the square root of the population density. This scaling law is derived analytically and confirmed for concrete numerical examples of three US Interstate highways and the Mississippi River. If facility locations are permitted to deviate from the optimum, the number of possible solutions increases dramatically. Using Monte Carlo simulations, we compute how scaling is affected by an increase in the average distance to the nearest facility. We find that the scaling exponents change and are most sensitive near the optimum facility distribution.
Journal of The Royal Society Interface, 2010
Transportation networks play a crucial role in human mobility, the exchange of goods, and the spr... more Transportation networks play a crucial role in human mobility, the exchange of goods, and the spread of invasive species. With 90% of world trade carried by sea, the global network of merchant ships provides one of the most important modes of transportation. Here we use information about the itineraries of 16,363 cargo ships during the year 2007 to construct a network of links between ports. We show that the network has several features which set it apart from other transportation networks. In particular, most ships can be classified in three categories: bulk dry carriers, container ships and oil tankers. These three categories do not only differ in the ships' physical characteristics, but also in their mobility patterns and networks. Container ships follow regularly repeating paths whereas bulk dry carriers and oil tankers move less predictably between ports. The network of all ship movements possesses a heavy-tailed distribution for the connectivity of ports and for the loads transported on the links with systematic differences between ship types. The data analyzed in this paper improve current assumptions based on gravity models of ship movements, an important step towards understanding patterns of global trade and bioinvasion.
Journal of Statistical Mechanics: Theory and Experiment, 2006
We study spatial networks that are designed to distribute or collect a commodity, such as gas pip... more We study spatial networks that are designed to distribute or collect a commodity, such as gas pipelines or train tracks. We focus on the cost of a network, as represented by the total length of all its edges, and its efficiency in terms of the directness of routes from point to point. Using data for several real-world examples, we find that distribution networks appear remarkably close to optimal where both these properties are concerned. We propose two models of network growth that offer explanations of how this situation might arise.
The European Physical Journal B, 2006
We study networks that connect points in geographic space, such as transportation networks and th... more We study networks that connect points in geographic space, such as transportation networks and the Internet. We find that there are strong signatures in these networks of topography and use patterns, giving the networks shapes that are quite distinct from one another and from nongeographic networks. We offer an explanation of these differences in terms of the costs and benefits of transportation and communication, and give a simple model based on the Monte Carlo optimization of these costs and benefits that reproduces well the qualitative features of the networks studied.
Proceedings of the National …, 2004
... of a square lattice and this introduces a strong signature of the lattice topology into the .... more ... of a square lattice and this introduces a strong signature of the lattice topology into the ... 4b , we show the same data on a population cartogram with moderate coarse-graining of the initial ... 4c , on the other hand, we use a very fine-grained population density, creating a cartogram ...
Advances in Complex Systems, 2005
Conventional maps of election results can give a misleading picture of the popular support that c... more Conventional maps of election results can give a misleading picture of the popular support that candidates have because population is highly non-uniform and equal areas on a map may not correspond to equal numbers of voters. Taking the example of the 2004 United States presidential election, we show how this problem can be corrected using a cartogram-a map in which the sizes of regions such as states are rescaled according to population or some other variable of interest.
Physical Review Letters, 2011
The establishment and spreading of biological populations depends crucially on population growth ... more The establishment and spreading of biological populations depends crucially on population growth at low densities. The Allee effect is a problem in those populations where the per-capita growth rate at low densities is reduced. We examine stochastic spatial models in which the reproduction rate changes across a gradient g so that the population undergoes a 2D-percolation transition. Without the Allee effect, the transition is continuous and the width w of the hull scales as in conventional (i.e., uncorrelated) gradient percolation, w ∝ g −0.57 . However, with a strong Allee effect the transition is first order and w ∝ g −0.26 .