Dataset Information

From The Cover: Diffusion-based method for producing density-equalizing maps.

ABSTRACT: 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.

SUBMITTER: Gastner MT

PROVIDER: S-EPMC419634 | biostudies-literature | 2004 May

REPOSITORIES: biostudies-literature

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From The Cover: Diffusion-based method for producing density-equalizing maps.

Gastner Michael T MT Newman M E J ME

Proceedings of the National Academy of Sciences of the United States of America 20040510 20

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 ...[more]

PMID: 15136719

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Project description:BackgroundHistorical, social and economic reasons can lead to major differences in the allocation of health system resources and research funding. These differences might endanger the progress in diagnostic and therapeutic approaches of socio-economic important diseases. The present study aimed to assess different benchmarking approaches that might be used to analyse these disproportions. Research in two categories was analysed for various output parameters and compared to input parameters. Germany was used as a high income model country. For the areas of cardiovascular and respiratory medicine density equalizing mapping procedures visualized major geographical differences in both input and output markers.ResultsAn imbalance in the state financial input was present with 36 cardiovascular versus 8 respiratory medicine state-financed full clinical university departments at the C4/W3 salary level. The imbalance in financial input is paralleled by an imbalance in overall quantitative output figures: The 36 cardiology chairs published 2708 articles in comparison to 453 articles published by the 8 respiratory medicine chairs in the period between 2002 and 2006. This is a ratio of 75.2 articles per cardiology chair and 56.63 articles per respiratory medicine chair. A similar trend is also present in the qualitative measures. Here, the 2708 cardiology publications were cited 48337 times (7290 times for respiratory medicine) which is an average citation of 17.85 per publication vs. 16.09 for respiratory medicine. The average number of citations per cardiology chair was 1342.69 in contrast to 911.25 citations per respiratory medicine chair. Further comparison of the contribution of the 16 different German states revealed major geographical differences concerning numbers of chairs, published items, total number of citations and average citations.ConclusionDespite similar significances of cardiovascular and respiratory diseases for the global burden of disease, large input and output imbalances have been revealed in the present study which point to a need for changes in funding policies. The present study supplies data that could be used for decision making in the field of health systems funding.

Project description:BackgroundPhysiologic signals, such as cardiac interbeat intervals, exhibit complex fluctuations. However, capturing important dynamical properties, including nonstationarities may not be feasible from conventional time series graphical representations.MethodsWe introduce a simple-to-implement visualisation method, termed dynamical density delay mapping ("D3-Map" technique) that provides an animated representation of a system's dynamics. The method is based on a generalization of conventional two-dimensional (2D) Poincaré plots, which are scatter plots where each data point, x(n), in a time series is plotted against the adjacent one, x(n?+?1). First, we divide the original time series, x(n) (n?=?1,…, N), into a sequence of segments (windows). Next, for each segment, a three-dimensional (3D) Poincaré surface plot of x(n), x(n?+?1), h[x(n),x(n?+?1)] is generated, in which the third dimension, h, represents the relative frequency of occurrence of each (x(n),x(n?+?1)) point. This 3D Poincaré surface is then chromatised by mapping the relative frequency h values onto a colour scheme. We also generate a colourised 2D contour plot from each time series segment using the same colourmap scheme as for the 3D Poincaré surface. Finally, the original time series graph, the colourised 3D Poincaré surface plot, and its projection as a colourised 2D contour map for each segment, are animated to create the full "D3-Map."ResultsWe first exemplify the D3-Map method using the cardiac interbeat interval time series from a healthy subject during sleeping hours. The animations uncover complex dynamical changes, such as transitions between states, and the relative amount of time the system spends in each state. We also illustrate the utility of the method in detecting hidden temporal patterns in the heart rate dynamics of a patient with atrial fibrillation. The videos, as well as the source code, are made publicly available.ConclusionsAnimations based on density delay maps provide a new way of visualising dynamical properties of complex systems not apparent in time series graphs or standard Poincaré plot representations. Trainees in a variety of fields may find the animations useful as illustrations of fundamental but challenging concepts, such as nonstationarity and multistability. For investigators, the method may facilitate data exploration.

Dataset Information

From The Cover: Diffusion-based method for producing density-equalizing maps.

Publications

From The Cover: Diffusion-based method for producing density-equalizing maps.

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