arXiv subjects

Michael T. Gastner

Publications and source records attributed to Michael T. Gastner.

At least 19 recordsLinked to original sources

arXiv2026

Topology-Preserving Line Densification for Creating Contiguous Cartograms

Cartograms depict geographic regions with areas proportional to quantitative data. However, when created using density-equalizing map projections, cartograms may exhibit invalid topologies if boundary polygons are drawn using only a finite set of vertices connected by straight lines. Here we introduce a method for topology-preserving line densification that guarantees that cartogram regions remain connected and non-overlapping when using density-equalizing map projections. By combining our densification technique with a flow-based cartogram generator, we present a robust framework for strictly topology-preserving cartogram construction. Quantitative evaluations demonstrate that the proposed algorithm produces cartograms with greater accuracy and speed than alternative methods while maintaining comparable shape fidelity.

cs.CG↗

arXiv2024

Comparative evaluation of the web-based contiguous cartogram generation tool go-cart.io

Area cartograms are map-based data visualizations in which the area of each map region is proportional to the data value it represents. Long utilized in print media, area cartograms have also become increasingly popular online, often accompanying news articles and blog posts. Despite their popularity, there is a dearth of cartogram generation tools accessible to non-technical users unfamiliar with Geographic Information Systems software. Few tools support the generation of contiguous cartograms (i.e., area cartograms that faithfully represent the spatial adjacency of neighboring regions). We thus reviewed existing contiguous cartogram software and compared two web-based cartogram tools: fBlog and go-cart.io. We experimentally evaluated their usability through a user study comprising cartogram generation and analysis tasks. The System Usability Scale was adopted to quantify how participants perceived the usability of both tools. We also collected written feedback from participants to determine the main challenges faced while using the software. Participants generally rated go-cart.io as being more usable than fBlog. Compared to fBlog, go-cart.io offers a greater variety of built-in maps and allows importing data values by file upload. Still, our results suggest that even go-cart.io suffers from poor usability because the graphical user interface is complex and data can only be imported as a comma-separated-values file. We also propose changes to go-cart.io and make general recommendations for web-based cartogram tools to address these concerns.

cs.HC↗

arXiv2023

Effectiveness of Area-to-Value Legends and Grid Lines in Contiguous Area Cartograms

A contiguous area cartogram is a geographic map in which the area of each region is proportional to numerical data (e.g., population size) while keeping neighboring regions connected. In this study, we investigated whether value-to-area legends (square symbols next to the values represented by the squares' areas) and grid lines aid map readers in making better area judgments. We conducted an experiment to determine the accuracy, speed, and confidence with which readers infer numerical data values for the mapped regions. We found that, when only informed about the total numerical value represented by the whole cartogram without any legend, the distribution of estimates for individual regions was centered near the true value with substantial spread. Legends with grid lines significantly reduced the spread but led to a tendency to underestimate the values. Comparing differences between regions or between cartograms revealed that legends and grid lines slowed the estimation without improving accuracy. However, participants were more likely to complete the tasks when legends and grid lines were present, particularly when the area units represented by these features could be interactively selected. We recommend considering the cartogram's use case and purpose before deciding whether to include grid lines or an interactive legend.

cs.HC↗

arXiv2022

Smooth Pycnophylactic Interpolation Produced by Density-Equalising Map Projections

A large amount of quantitative geospatial data are collected and aggregated in discrete enumeration units (e.g. countries or states). Smooth pycnophylactic interpolation aims to find a smooth, nonnegative function such that the area integral over each enumeration unit is equal to the aggregated data. Conventionally, smooth pycnophylactic interpolation is achieved by a cellular automaton algorithm that converts a piecewise constant function into an approximately smooth function defined on a grid of coordinates on an equal-area map. An alternative approach, proposed by Tobler in 1976, is to construct a density-equalising map projection in which areas of enumeration units are proportional to the aggregated data. A pycnophylactic interpolation can be obtained from the Jacobian of this projection. Here, we describe a software implementation of this method. Although solutions are not necessarily optimal in terms of predefined quantitative measures of smoothness, our method is computationally efficient and can potentially be used in tandem with other methods to accelerate convergence towards an optimal solution.

stat.CO↗

arXiv2021

Agent-based neutral competition in two-community networks

Competition between alternative states is an essential process in social and biological networks. Neutral competition can be represented by an unbiased random drift process in which the states of vertices (e.g., opinions, genotypes, or species) in a network are updated by repeatedly selecting two connected vertices. One of these vertices copies the state of the selected neighbor. Such updates are repeated until all vertices are in the same "consensus" state. There is no unique rule for selecting the vertex pair to be updated. Real-world processes comprise three limiting factors that can influence the selected edge and the direction of spread: (1) the rate at which a vertex sends a state to its neighbors, (2) the rate at which a state is received by a neighbor, and (3) the rate at which a state can be exchanged through a connecting edge. We investigate how these three limitations influence neutral competition in networks with two communities generated by a stochastic block model. By using Monte Carlo simulations, we show how the community structure and update rule determine the states' success probabilities and the time until a consensus is reached. We present a heterogeneous mean-field theory that agrees well with the Monte Carlo simulations. The effectiveness of the heterogeneous mean-field theory implies that quantitative predictions about the consensus are possible even if empirical data (e.g., from ecological fieldwork or observations of social interactions) do not allow a complete reconstruction of all edges in the network.

physics.soc-ph↗

arXiv2020

Task-Based Effectiveness of Interactive Contiguous Area Cartograms

Cartograms are map-based data visualizations in which the area of each map region is proportional to an associated numeric data value (e.g., population or gross domestic product). A cartogram is called contiguous if it conforms to this area principle while also keeping neighboring regions connected. Because of their distorted appearance, contiguous cartograms have been criticized as difficult to read. Some authors have suggested that cartograms may be more legible if they are accompanied by interactive features (e.g., animations, linked brushing, or infotips). We conducted an experiment to evaluate this claim. Participants had to perform visual analysis tasks with interactive and noninteractive contiguous cartograms. The task types covered various aspects of cartogram readability, ranging from elementary lookup tasks to synoptic tasks (i.e., tasks in which participants had to summarize high-level differences between two cartograms). Elementary tasks were carried out equally well with and without interactivity. Synoptic tasks, by contrast, were more difficult without interactive features. With access to interactivity, however, most participants answered even synoptic questions correctly. In a subsequent survey, participants rated the interactive features as "easy to use" and "helpful." Our study suggests that interactivity has the potential to make contiguous cartograms accessible even for those readers who are unfamiliar with interactive computer graphics or do not have a prior affinity to working with maps. Among the interactive features, animations had the strongest positive effect, so we recommend them as a minimum of interactivity when contiguous cartograms are displayed on a computer screen.

cs.HC↗

arXiv2020

Motivating Good Practices for the Creation of Contiguous Area Cartograms

Cartograms are maps in which the areas of regions (e.g., countries or provinces) are proportional to a thematic mapping variable (e.g., population or gross domestic product). A cartogram is called contiguous if it keeps geographically adjacent regions connected. Over the past few years, several web tools have been developed for the creation of contiguous cartograms. However, most of these tools do not advise how to use cartograms correctly. To mitigate these shortcomings, we attempt to establish good practices through our recently developed web application go-cart.io: (1) use cartograms to show numeric data that add up to an interpretable total, (2) present a cartogram alongside a conventional map that uses the same color scheme, (3) indicate whether the data for a region are missing, (4) include a legend so that readers can infer the magnitude of the mapping variable, (5) if a cartogram is presented electronically, assist readers with interactive graphics.

cs.HC↗

arXiv2019

Voter model on networks partitioned into two cliques of arbitrary sizes

The voter model is an archetypal stochastic process that represents opinion dynamics. In each update, one agent is chosen uniformly at random. The selected agent then copies the current opinion of a randomly selected neighbour. We investigate the voter model on a network with an exogenous community structure: two cliques (i.e. complete subgraphs) randomly linked by $X$ interclique edges. We show that, counterintuitively, the mean consensus time is typically not a monotonically decreasing function of $X$. Cliques of fixed proportions with opposite initial opinions reach a consensus, on average, most quickly if $X$ scales as $N^{3/2}$, where $N$ is the number of agents in the network. Hence, to accelerate a consensus between cliques, agents should connect to more members in the other clique as $N$ increases but not to the extent that cliques lose their identity as distinct communities. We support our numerical results with an equation-based analysis. By interpolating between two asymptotic heterogeneous mean-field approximations, we obtain an equation for the mean consensus time that is in excellent agreement with simulations for all values of $X$.

physics.soc-ph↗

arXiv2019

Beyond Fortune 500: Women in a Global Network of Directors

In many countries, the representation of women on corporate boards of directors has become a topic of intense political debate. Social networking plays a crucial role in the appointment to a board so that an informed debate requires knowing where women are located in the network of directors. One way to quantify the network is by studying the links created by serving on the same board and by joint appointments on multiple boards. We analyse a network of $\approx 320\,000$ board members of $36\,000$ companies traded on stock exchanges all over the world, focusing specifically on the position of women in the network. Women only have $\approx 9-13\%$ of all seats, but they are not marginalised. Applying metrics from social network analysis, we find that their influence is close to that of men. We do not find evidence to support previous claims that women play the role of "queen bees" that exclude other women from similar positions.

cs.SI↗

arXiv2018

Consensus time in a voter model with concealed and publicly expressed opinions

The voter model is a simple agent-based model to mimic opinion dynamics in social networks: a randomly chosen agent adopts the opinion of a randomly chosen neighbour. This process is repeated until a consensus emerges. Although the basic voter model is theoretically intriguing, it misses an important feature of real opinion dynamics: it does not distinguish between an agent's publicly expressed opinion and her inner conviction. A person may not feel comfortable declaring her conviction if her social circle appears to hold an opposing view. Here we introduce the Concealed Voter Model where we add a second, concealed layer of opinions to the public layer. If an agent's public and concealed opinions disagree, she can reconcile them by either publicly disclosing her previously secret point of view or by accepting her public opinion as inner conviction. We study a complete graph of agents who can choose from two opinions. We define a martingale $M$ that determines the probability of all agents eventually agreeing on a particular opinion. By analyzing the evolution of $M$ in the limit of a large number of agents, we derive the leading-order terms for the mean and standard deviation of the consensus time (i.e. the time needed until all opinions are identical). We thereby give a precise prediction by how much concealed opinions slow down a consensus.

cond-mat.stat-mech↗

arXiv2018

Fast flow-based algorithm for creating density-equalizing map projections

Cartograms are maps that rescale geographic regions (e.g., countries, districts) such that their areas are proportional to quantitative demographic data (e.g., population size, gross domestic product). Unlike conventional bar or pie charts, cartograms can represent correctly which regions share common borders, resulting in insightful visualizations that can be the basis for further spatial statistical analysis. Computer programs can assist data scientists in preparing cartograms, but developing an algorithm that can quickly transform every coordinate on the map (including points that are not exactly on a border) while generating recognizable images has remained a challenge. Methods that translate the cartographic deformations into physics-inspired equations of motion have become popular, but solving these equations with sufficient accuracy can still take several minutes on current hardware. Here we introduce a flow-based algorithm whose equations of motion are numerically easier to solve compared with previous methods. The equations allow straightforward parallelization so that the calculation takes only a few seconds even for complex and detailed input. Despite the speedup, the proposed algorithm still keeps the advantages of previous techniques: with comparable quantitative measures of shape distortion, it accurately scales all areas, correctly fits the regions together and generates a map projection for every point. We demonstrate the use of our algorithm with applications to the 2016 US election results, the gross domestic products of Indian states and Chinese provinces, and the spatial distribution of deaths in the London borough of Kensington and Chelsea between 2011 and 2014.

cs.CG↗

arXiv2016

The topology of large Open Connectome networks for the human brain

The structural human connectome (i.e.\ the network of fiber connections in the brain) can be analyzed at ever finer spatial resolution thanks to advances in neuroimaging. Here we analyze several large data sets for the human brain network made available by the Open Connectome Project. We apply statistical model selection to characterize the degree distributions of graphs containing up to $\simeq 10^6$ nodes and $\simeq 10^8$ edges. A three-parameter generalized Weibull (also known as a stretched exponential) distribution is a good fit to most of the observed degree distributions. For almost all networks, simple power laws cannot fit the data, but in some cases there is statistical support for power laws with an exponential cutoff. We also calculate the topological (graph) dimension $D$ and the small-world coefficient $σ$ of these networks. While $σ$ suggests a small-world topology, we found that $D < 4$ showing that long-distance connections provide only a small correction to the topology of the embedding three-dimensional space.

q-bio.NC↗

arXiv2015

The Ising chain constrained to an even or odd number of positive spins

We investigate the statistical mechanics of the periodic one-dimensional Ising chain when the number of positive spins is constrained to be either an even or an odd number. We calculate the partition function using a generalization of the transfer matrix method. On this basis, we derive the exact magnetization, susceptibility, internal energy, heat capacity and correlation function. We show that in general the constraints substantially slow down convergence to the thermodynamic limit. By taking the thermodynamic limit together with the limit of zero temperature and zero magnetic field, the constraints lead to new scaling functions and different probability distributions for the magnetization. We demonstrate how these results solve a stochastic version of the one-dimensional voter model.

cond-mat.stat-mech↗

arXiv2015

Opinion formation models on a gradient

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, using analytical and numerical tools, we also present a model where the width of the transition between opinions scales $\propto g^{-1/4}$, not $\propto g^{-4/7}$ as in independent percolation, and the cluster size distribution is consistent with first-order percolation.

cond-mat.stat-mech↗

arXiv2014

The geography and carbon footprint of mobile phone use in Cote d'Ivoire

The newly released Orange D4D mobile phone data base provides new insights into the use of mobile technology in a developing country. Here we perform a series of spatial data analyses that reveal important geographic aspects of mobile phone use in Cote d'Ivoire. We first map the locations of base stations with respect to the population distribution and the number and duration of calls at each base station. On this basis, we estimate the energy consumed by the mobile phone network. Finally, we perform an analysis of inter-city mobility, and identify high-traffic roads in the country.

cs.CY↗

arXiv2011

Scaling and entropy in p-median facility location along a line

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.

physics.soc-ph↗

arXiv2011

Changes in the gradient percolation transition caused by an Allee effect

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, proportional to g^(-0.57). However, with a strong Allee effect the transition is first order and w is proportional to g^(-0.26).

cond-mat.stat-mech↗

arXiv2010

The complex network of global cargo ship movements

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.

physics.soc-ph↗