34 research outputs found

    Ranking of scientific domains from the extensive (left panel) and the intensive (right panel) matrix

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    <p>—from first to last in the direction of the arrows. The ranking derives from the averages of the complexity values of the constituents sub-domains obtained over a range of <i>T</i> values around <i>T</i> = 10. The different symbols represent the five main branches of scientific domains: Yellow circles for earth and life sciences (earth and planetary sciences; environmental science; agricultural and biological sciences; biochemistry, genetics, molecular biology; neuroscience; immunology and microbiology); Green triangles for engineering and technology (engineering; chemical engineering; materials science; energy); Red diamonds for medical sciences (medicine; pharmacology, toxicology, pharmaceutics; nursing; health professions; dentistry; veterinary); Blue squares for physical and formal sciences (chemistry; physics and astronomy; mathematics; computer science; decision sciences); Brown crosses for social sciences and humanities (psychology; arts and humanities; social sciences; economics, econometric and finance; business, management and accounting). Note that excluding from the analysis the domains belonging to social sciences and humanities (and the associated sub-domains) leads to a ranking of nations which remains unaltered from what is shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0113470#pone-0113470-g002" target="_blank">Figure 2</a>, and to a ranking of scientific domains almost identical to what would be obtained by removing all brown crosses from the above panels. In this case, the rankings derived from the extensive and intensive approaches also appears more similar to each other, as generally top domains would belong to earth and life sciences, together with medicine and pharmacology, toxicology and pharmaceutics—with nursing and health professions being the only domains achieving a substantial upgrade for the intensive matrix approach.</p

    Extensive (top panel) and intensive (bottom panel) adjacency matrices.

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    <p>Rows and columns are ordered according to the ranking of nations and scientific sub-domains, respectively (from first to last in the direction of the arrows). The labels on the vertical axes help to identify several nations in the ranking. The matrices were obtained for <i>T</i> = 10. Indeed, the value of <i>T</i> must be chosen not too low neither too high in order to avoid having an empty or full adjacency matrix, respectively. In fact, by construction the matrices have <i>T</i> entries in each column (the top-<i>T</i> nations in that domain), and thus a total of <i>NT</i> entries (<i>N</i> is the number of nations).</p

    Economic interpretation of evolution of the fitness in the intensive and extensive case.

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    <p>The intensive fitness gives a medium-long term information of the development of countries, in this sense, we can consider it as informative on the growth potential of a country. On the other hand the extensive analysis complements the information carried by the intensive fitness conveying a short term perspectives and giving a stronger emphasis to the monetary aspects.</p

    Euclidean distance from the 80th iteration (fixed point) for a particular realization of <i>M<sub>cp</sub></i> with <i>N<sub>c</sub></i> = 5, <i>N<sub>p</sub></i> = 15, <i>P<sub>h</sub></i> = 0.6 and <i>P<sub>l</sub></i> = 0.05.

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    <p>The red line shows the path obtained with the standard initial conditions given by and . In grey the paths of a set of randomly sampled initial condition. In blue the particular path analyzed in fig. 7. The inset shows the exponential nature of the convergence.</p

    Model Results.

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    <p>In <b>(a)</b> the scatter plot of Fitness ranking against countries diversification, while in <b>(b)</b> the one for Quality ranking against products ubiquity; the blue points represent the observed values (for the year 1980 from the dataset of [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140420#pone.0140420.ref025" target="_blank">25</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140420#pone.0140420.ref026" target="_blank">26</a>]). The black line represents the average value on the simulations, while the grey lines bind the area between the second and the first 3-quantiles (dot-dashed) and between the 975th and 25th permilles (dashed). The data obtained are for initial conditions <i>N</i><sub>roots</sub> = 20 and <i>P</i><sub>0</sub> = 0.3 and parameters <i>α</i> = 1.55, <i>β</i> = 0.8, <i>γ</i> = 0.3, <i>k</i><sup>0</sup> = 4. In the ∼82% the observed data fall into the area between 975th and 25th permilles for the fitness distribution, ∼75% for the quality distribution. In <b>(c)</b> the original matrix for 1980 from the dataset of [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140420#pone.0140420.ref025" target="_blank">25</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140420#pone.0140420.ref026" target="_blank">26</a>]; in <b>(d)</b> one of the synthetic matrix for initial conditions <i>N</i><sub>roots</sub> = 20 and <i>P</i><sub>0</sub> = 0.3 and parameters <i>α</i> = 1.65, <i>β</i> = 1.1, <i>γ</i> = 0.6, <i>k</i><sup>0</sup> = 4.</p

    Nestedness & Assortativity.

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    <p>The distributions for the nestedness values (obtained employing NODF, the definition by [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140420#pone.0140420.ref032" target="_blank">32</a>]) and assortativity index <i>r</i> (obtained employing the definition by [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140420#pone.0140420.ref033" target="_blank">33</a>]) for 50 simulations with initial conditions <i>N</i><sub>roots</sub> = 20 and <i>P</i><sub>0</sub> = 0.3 and parameters <i>α</i> = 1.55, <i>β</i> = 0.8, <i>γ</i> = 0.3, <i>k</i><sup>0</sup> = 4. In <b>a)</b>) the total NODF, in <b>b)</b> the NODF for rows and in <b>c)</b> the one for columns. The red line is the observed value for the year 1980 from the dataset of [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140420#pone.0140420.ref025" target="_blank">25</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140420#pone.0140420.ref026" target="_blank">26</a>], the blue dashed lines bind the area between the second and the first 3-quantiles, while the purple line the area between between the 975th and 25th permilles. For the 4 distributions, real values easily fit in the 95%; anyway, for NODF values the real values lie just outside the central third of the probability. Notice the similar distributions for NODF<sub><i>t</i></sub> and NODF<sub><i>p</i></sub>, as explained in Eq S6 in Supporting Information in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140420#pone.0140420.s001" target="_blank">S1 File</a>. In <b>d)</b> the distribution for the assortativity values (obtained employing the definition by [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140420#pone.0140420.ref033" target="_blank">33</a>]): Even if the distribution is quite weird, the value measured on the real matrix is just outside the area containing the 33% of the distribution.</p

    Graphical representation of the experimental matrix <i>M<sub>cp</sub></i> for the year 2010 after reordering of rows and columns by respectively decreasing <i>K<sub>c</sub></i> and <i>K<sub>p</sub></i> . It is evident the substantial triangular structure of the matrix.

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    <p>Graphical representation of the experimental matrix <i>M<sub>cp</sub></i> for the year 2010 after reordering of rows and columns by respectively decreasing <i>K<sub>c</sub></i> and <i>K<sub>p</sub></i> . It is evident the substantial triangular structure of the matrix.</p

    Time evolution of the product complexity from 1995 to 2010 for a selection of cereals which result to be organized into two main groups.

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    <p>The former group has an average complexity around the average complexity of all products, <i>Q</i>∼1, the latter one is composed of cereals whose level of sophistication is much lower than the previous as measured by our metrics, <i>Q</i>∼10<sup>−3</sup>, 10<sup>−4</sup>). By analyzing the typical typical usage of oats and rye we find that these two cereals are not typical of a substance economic system since they are used in livestock industry and brewed-product industry.</p

    Fundamental analysis of the PIIGS countries (Portugal, Italy, Ireland Greece and Spain) according to our metrics.

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    <p>We find a scenario which seems to be apparently in contrast with the rating of the sovereign debt of these countries. For instance we find that Greece, Portugal have an increasing fitness and Italy is always ranked in the top 5 positions along the time period considered. The main reason of this apparent discrepancy, in our opinion, relies on the fact there exists different regimes for the economic complexity. Many different factors are responsible for the economic growth: development of capabilities, national policies, wars, geo-political instabilities, importance and development of the financial sector, etc. Our metrics assess only one of these factors, the competitiveness of the productive systems of a nation. We believe that while this aspect is the main driving force for some regimes such as the one of emerging countries, it is not the case for developed ones. In fact PIIGS are all developed countries which have saturated their phase space of products.</p

    The evolution of the probability of selecting every country.

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    <p>On the horizontal axis there is the simulation time. Until the saturation regime (the cyan area) few countries start increasing their probabilities of being selected with the increasing of their diversification, to the detriment of the poor diversified countries, whose probabilities are pushed lower. In the saturation period, the mid-diversified countries enlarge their export basket, boosting their probabilities of being selected, while highest diversified countries are restrained; in this way the gap among countries reduces.</p
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