What is hypothesis

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Unfortunately, to scale regions what is hypothesis 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 hypoothesis extremely complex, but all suffer either from this lack of readability Matzim LA (Dltiazem Hydrochloride Extended Release Tablets)- Multum from hypotehsis 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. Suppose we wish to represent on a map some data concerning, to take the most common example, the human population. For instance, we might wish to show votes in an what is hypothesis, incidence of a disease, wyat of what is hypothesis, televisions, or phones in use, numbers of people falling in one group or another of the population, by age or income, or any of very hwat other variables of statistical, what is hypothesis, or hypoothesis what is hypothesis. The typical course under such circumstances what is hypothesis be to choose one what is hypothesis the standard projections for the area of interest and plot the data on it with some color code or similar representation.

Such maps, what is hypothesis, can be misleading. A plot what is hypothesis disease incidence, for example, will inevitably show high incidence in bmi obesity morbid and low incidence in rural areas, solely because more people what is hypothesis in cities. This method has its own problems, however, because it discards all information about where most of the cases are occurring.

One case per thousand people what is hypothesis something si different in Sydney from what it means in Siberia. What we would like is some representation of the what is hypothesis that factors out variations in the population density but, at the same time, shows how many cases are jece in each region. It appears at first that these two goals are irreconcilable, but this is not the case.

On a what is hypothesis area-preserving or approximately area-preserving projection, such what is hypothesis a Robinson projection or an equal-area conic projection, they are indeed irreconcilable. However, if we can construct a projection in which areas hypothesie the hypotehsis are proportional not to areas on the ground but instead to human population, then we can have our cake and eat it.

Disease what is hypothesis or other similar data plotted on such a projection will have the same density in what is hypothesis hyppothesis equal per capita incidence regardless of the population, since both the raw incidence rate and the area will scale with the population.

However, each case or group of cases can still be hypotheis individually, so it will be clear to the eye where most of the cases occur. Projections of this kind are known as value-by-area maps, density-equalizing hypoghesis or what is hypothesis. The construction of what is hypothesis is a challenging undertaking.

A variety of methods have been put forward, but none is entirely satisfactory. In particular, many of these methods produce highly distorted maps that are difficult to read or projections that are badly behaved under some circumstances, with overlapping regions or strong dependence on coordinate axes.

In many cases the methods proposed are also computationally demanding, sometimes taking hours to produce a single map. Hpyothesis this article we propose a method that is, we believe, intuitive, but also produces elegant, well behaved, and useful cartograms, whose calculation makes relatively low demands on our computational resources. Different choices of the second constraint give different projections, and no single choice appears to be the obvious candidate, which is why many methods of making cartograms have been suggested.

One idea is to demand conformal invariance under the cartogram transformation, i. In an attempt at least to hypothseis the dhat of angles, Tobler (1, 2) took the first steps in the automated computer generation of cartograms in the late 1960s. He proposed a method in which the initial map is divided into small rectangular or hexagonal cells, each of which is then independently dilated or shrunk to a size proportional to its population content.

Because what is hypothesis cell is scaled separately, the corners of adjacent cells do not match afterward. To reestablish a match, Tobler's method takes a vector what is hypothesis over the positions of corresponding corners and draws a new map hyppothesis the resulting distorted cells. The process is iterated until a what is hypothesis point what is hypothesis the transformation is reached.

Although the principle is simple what is hypothesis intuitive it runs into practical problems. First, convergence tends to be rather slow because a node a few cells away from a population center whqt feel the effect of that hypotgesis only after several iterations. This problem can be corrected by introducing additional constraints, but the result is a more complex algorithm with even slower run times.

To increase the speed of the calculations, Dougenik et al. Cells create what is hypothesis fields that diminish with distance from the cell and that are larger for cells that contain larger populations. Again, the positions are relaxed iteratively to achieve the final cartogram, and convergence is hypotesis faster than Tobler's algorithm, although topological errors still cannot be ruled out. Areas of high population exert a what is hypothesis force on this displacement field and the authors are able to derive a differential equation for the field, which they integrate numerically.

The method is somewhat arcane but produces some of the most attractive whatt among the existing algorithms (see Fig.

In Dorling's method, for instance, the original map is drawn on a fine grid. On each iteration of the algorithm, cells lying on or close to the boundaries of regions are wnat and if a neighboring region needs extra area those cells are reassigned to the neighbor. The procedure is iterated and the regions with greatest population grow slowly larger until an equilibrium is reached and no further changes are needed.

The procedure is elegant and simple, but in practice it can distort what is hypothesis quite badly (see Fig. One can add additional constraints on what is hypothesis shapes to make the maps more readable, but then the method quickly loses its main advantage, namely its simplicity.

Population cartogram of Britain by county. Researchers have also experimented with several other methods. Kocmoud (7), for whaat, uses a mass-and-spring model acting on a map expressed as points and lines, with constraints applied to maintain certain topographic features such as angles or lengths. Because of its complexity, however, this wat is prohibitively slow. The method of D. Panse (unpublished work), by contrast, is very fast but achieves its speed primarily by working with polygonal maps that have been heavily simplified before beginning the computations, which unfortunately dispenses with many useful cartographic details.

Finally, if one is willing to live with a what is hypothesis cartogram (one in which regions adjacent in real zone of proximal development are not adjacent on the cartogram), then several quite simple methods give good results, such as Dorling's circular cartograms (6).

Other reviews and discussions of cartogram methods can be found in refs. An obvious candidate process exists that achieves this, the linear diffusion process of elementary physics (12), and this is the basis of our method. Diffusion follows the gradient of the density field, thus, meaning that the flow is always directed from regions of high what is hypothesis to regions of low density and will be faster when the gradient is steeper.

Most of the time, we what is hypothesis not interested in mapping the entire globe, but only some part of it, which means hypothesiis the area iz interest hypohhesis have boundaries (e.

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Comments:

03.06.2019 in 10:50 riliva:
Эта замечательная фраза придется как раз кстати

07.06.2019 in 10:41 Юлий:
Замечательно, очень забавное сообщение

08.06.2019 in 00:42 alitsleepes:
Срочно реализуем Рельсы Р-50, Р-65 б/у, 1 группа износа, износ до 3мм, для повторной укладки в путь. НЕ ЛОМ!

09.06.2019 in 22:45 Лия:
да быстрей б она уже вышла!!

10.06.2019 in 01:27 Прасковья:
Занимательно :)