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We analyze the effects of relative increments of mutual information among the geographical, technological, and organizational distributions of firms on the relative augmentation of regional summary turnover in terms of synergies. How do increases in synergy in international cooperation affect regional turnover? The methodological contribution of this study is that we translate the synergy (abstractly measured in bits of information) into more familiar economic terms, such as turnover for the special case of domestic-foreign collaborations. The analysis is based on Norwegian data, as Norway is a small country with an open and export-oriented economy. Data for Norway is publicly available in great detail.

The Economic Complexity Index (ECI; Hidalgo & Hausmann, 2009) measures the complexity of national economies in terms of product groups. Analogously to ECI, a Patent Complexity Index (PatCI) can be developed on the basis of a matrix of nations versus patent classes. Using linear algebra, the three dimensions: countries, product groups, and patent classes can be combined into a measure of "Triple Helix" complexity (THCI) including the trilateral interaction terms between knowledge production, wealth generation, and (national) control. THCI can be expected to capture the extent of systems integration between the global dynamics of markets (ECI) and technologies (PatCI) in each national system of innovation. We measure ECI, PatCI, and THCI during the period 2000-2014 for the 34 OECD member states, the BRICS countries, and a group of emerging and affiliated economies (Argentina, Hong Kong, Indonesia, Malaysia, Romania, and Singapore). The three complexity indicators are correlated between themselves; but the correlations with GDP per capita are virtually absent. Of the world's major economies, Japan scores highest on all three indicators, while China has been increasingly successful in combining economic and technological complexity. We could not reproduce the correlation between ECI and average income that has been central to the argument about the fruitfulness of the economic complexity approach.

The knowledge base of an economy measured in terms of Triple Helix relations can be analyzed in terms of mutual information among geographical, sectorial, and size distributions of firms as dimensions of the probabilistic entropy. The resulting synergy values of a TH system provide static snapshots. In this study, we add the time dimension and analyze the synergy dynamics using the Norwegian innovation system as an example. The synergy among the three dimensions can be mapped as a set of partial time series and spectrally analyzed. The results suggest that the synergy at the level of both the country and its 19 counties shoe non-chaotic oscillatory behavior and resonates in a set of natural frequencies. That is, synergy surges and drops are non-random and can be analyzed and predicted. There is a proportional dependence between the amplitudes of oscillations and synergy values and an inverse proportional dependence between the oscillation frequencies' relative inputs and synergy values. This analysis of the data informs us that one can expect frequency-related synergy-volatility growth in relation to the synergy value and a shift in the synergy volatility towards the long-term fluctuations with the synergy growth., Comment: 31 pages, 16 figures

Based on the complete set of firm data for Sweden (N = 1,187,421; November 2011), we analyze the mutual information among the geographical, technological, and organizational distributions in terms of synergies at regional and national levels. Mutual information in three dimensions can become negative and thus indicate a net export of uncertainty by a system or, in other words, synergy in how knowledge functions are distributed over the carriers. Aggregation at the regional level (NUTS3) of the data organized at the municipal level (NUTS5) shows that 48.5% of the regional synergy is provided by the three metropolitan regions of Stockholm, Gothenburg, and Malm\"o/Lund. Sweden can be considered as a centralized and hierarchically organized system. Our results accord with other statistics, but this Triple Helix indicator measures synergy more specifically and quantitatively. The analysis also provides us with validation for using this measure in previous studies of more regionalized systems of innovation (such as Hungary and Norway)., Comment: Journal of the American Society for Information Science and Technology (forthcoming)

Using information theory and data for all (0.5 million) Norwegian firms, the national and regional innovation systems are decomposed into three subdynamics: (i) economic wealth generation, (ii) technological novelty production, and (iii) government interventions and administrative control. The mutual information in three dimensions can then be used as an indicator of potential synergy, that is, reduction of uncertainty. We aggregate the data at the NUTS3 level for 19 counties, the NUTS2 level for seven regions, and the single NUTS1 level for the nation. Measured as in-between group reduction of uncertainty, 11.7 % of the synergy was found at the regional level, whereas only another 2.7% was added by aggregation at the national level. Using this triple-helix indicator, the counties along the west coast are indicated as more knowledge-based than the metropolitan area of Oslo or the geographical environment of the Technical University in Trondheim. Foreign direct investment seems to have larger knowledge spill-overs in Norway (oil, gas, offshore, chemistry, and marine) than the institutional knowledge infrastructure in established universities. The northern part of the country, which receives large government subsidies, shows a deviant pattern., Comment: Technological Forecasting & Social Change (forthcoming)