搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

相对性区域创新指数与经济周期挖掘

方学进 崔俊英 胡淡淡 韩筱璞

引用本文:
Citation:

相对性区域创新指数与经济周期挖掘

方学进, 崔俊英, 胡淡淡, 韩筱璞

Relativistic regional innovation index and novel business cycle

Fang Xue-Jin, Cui Jun-Ying, Hu Dan-Dan, Han Xiao-Pu
PDF
HTML
导出引用
  • 提出了一类新的相对性区域创新指数, 并采用世界专利申请数据对其进行了具体计算. 基于区域创新同经济发展水平之间的超线性关系, 该指数消除了经济发展水平对创新能力的影响, 可以实现对不同发展水平的经济体之间进行有效的创新能力横纵对比. 该创新指数尽管极其简单, 却揭示出一系列迥异于传统认知的现象, 例如中国大陆地区的技术创新能力在1980年代就已经位居世界前列. 采用该指数, 不但可以在较高水平上解释世界各国的经济增长, 还发现它同经济增长率之间的相关性存在一个20年的经济周期. 这些结果显示, 该指数作为一个单一性指标, 以极小的数据依赖就实现了较高程度的解释性, 不但重新定位了世界各经济体的创新能力, 对深入理解创新同经济发展之间的关系提供了新的角度, 而且暗示着这类相对性经济指标的发展潜力与应用空间.
    In this paper, we propose a new type of relativistic regional innovation index by using the international patent application data. Based on the super-linear relationship between regional innovation and economic development, the new index can eliminate the influence of economic development level on innovation capabilities, and can effectively achieve the comparison of innovation capabilities among economies at different economic development levels. This new index is quite simple, and points out a series of new findings that are sharply different from the traditional cognitive phenomena, e.g. the index shows that the technological innovation capabilities of mainland China are among the highest in the world in 1980s. Moreover, the use of this new index not only can efficiently explain the economic growth of countries in the world at a higher level, but also find that there is a novel 20-year business cycle in the correlation between the index and economic growth rate. These results show that the index, as a simple single indicator, can achieve a higher degree of explanatory ability with minimal data dependence. This new index not only repositions the innovation capacity of world’s economies, but also provides a new insight into an in-depth understanding of the relationship between innovation and economic development, and implies the development potential and application space such a kind of relativistic economic indicator.
      通信作者: 韩筱璞, xp@hznu.edu.cn
    • 基金项目: 国家级-基于人工表面等离激元的功能集成型辐射器研究(61873081)
      Corresponding author: Han Xiao-Pu, xp@hznu.edu.cn
    [1]

    Hansen T, Winther L 2011 Eur. Urban Reg. Stud. 18 321Google Scholar

    [2]

    Fagerberg J E, Srholec M 2008 Res. Policy 37 1417Google Scholar

    [3]

    Wignaraja G 2012 J. Asian Econ. 23 224Google Scholar

    [4]

    Mohnen P, Dagenais M 2002 Towards an Innovation Intensity Index: The Case of CIS 1 in Denmark and Ireland In: Innovation and Firm Performance (London: Kleinknecht A, Mohnen P, eds.) pp3–30

    [5]

    Slaper T F, Hart N R, Hall T J, Thompson M F 2011 Econ. Dev. Q. 25 36Google Scholar

    [6]

    Clayton T, Borgo M D, Haskel J 2009 https://ssrn.com/ abstract=1345684

    [7]

    Żelazny R, Pietrucha J 2017 Q. J. Econ. Econ. Policy 12 43

    [8]

    Crespo N F, Crespo C F 2016 J. Bus. Res. 69 5265Google Scholar

    [9]

    Sohn S Y, Kim D H, Jeon S Y 2016 Technol. Anal. Strateg. Manag. 28 492Google Scholar

    [10]

    McGrath M E, Romeri M N 1994 J. Prod. Innov. Manag. 11 213Google Scholar

    [11]

    Narin F, Olivastro D 1988 Technology Indicators Based On Patents And Patent Citations In: Handbook of Quantitative Studies of Science and Technology (Amsterdam: Van Raan A F J, eds.) pp465–507

    [12]

    Guan J C, Gao X 2009 J. Associat. Inf. Sci. Technol. 60 35Google Scholar

    [13]

    Csajbók E, Berhidi A, Vasas L, et al. 2007 Scientometrics 73 91Google Scholar

    [14]

    Mester G 2016 Interdiscipl. Descript. Compl. Syst. 14 1Google Scholar

    [15]

    Gao H 2014 Internat. J. Adv. Manag. Sci. 3 128Google Scholar

    [16]

    May M, Brody H 2015 Nature 522 S1Google Scholar

    [17]

    Haunschild R, Bornmann L 2015 Scientometrics 102 1829Google Scholar

    [18]

    中国区域创新指数报告课题组 2019 中国西部 2019 19Google Scholar

    Report of China Regional Innovation Index Research Group 2019 Western China 2019 19Google Scholar

    [19]

    Bettencourt L M A, Lobo J, Helbing D, Kühnert C, West G B 2007 Proc. Natl. Acad. Sci. U. S. A. 104 7301Google Scholar

    [20]

    Bettencourt L M A, West G B 2010 Nature 467 912Google Scholar

    [21]

    Arbesman S, Kleinberg J M, Strogatz S H 2009 Phys. Rev. E 79 16115Google Scholar

    [22]

    Wunsch-Vincent S, Lanvin B, Dutta S 2015 eSocialSciences Working Paper id: 7491

    [23]

    Hirooka M 2003 J. Evol. Econ. 13 549Google Scholar

    [24]

    Groot B de, Franses P H 2009 Technol. Forecast. Social Chang. 76 1021Google Scholar

    [25]

    Hausman A, Johnston W J 2014 J. Bus. Res. 67 2720Google Scholar

    [26]

    Gao J, Zhang Y C, Zhou T 2019 Phys. Rep. 817 1Google Scholar

    [27]

    Hidalgo C A, Klinger B, Barabási A L, Hausmann R 2007 Science 317 482Google Scholar

    [28]

    Hidalgo C A, Hausmann R 2009 Proc. Natl. Acad. Sci. U.S.A. 106 10570Google Scholar

    [29]

    Caldarelli G, Cristelli M, Gabrielli A, Pietronero L, Scala A, Tacchella A 2012 PLoS ONE 7 e47278Google Scholar

    [30]

    Cristelli M, Gabrielli A, Tacchella A, Caldarelli G, Pietronero L 2013 PLoS ONE 8 e70726Google Scholar

    [31]

    Neffke F, Henning M, Boschma R 2011 Econ. Geogr. 87 237Google Scholar

    [32]

    Tacchella A, Mazzilli D, Pietronero L 2018 Nat. Phys. 14 861Google Scholar

  • 图 1  世界各经济体在由相对人均GDP的对数g和相对人均专利申请数的对数np(两者均以10为底数)所构成的空间中的变化轨迹. 彩色曲线为11个代表性经济体在该空间的轨迹, 灰色曲线为其他经济体. 灰色虚线为拟合直线np = 1.12g – 0.82. 灰色点划线大致区分了发达经济体的轨迹所在区域和发展中经济体所在区域, 右上方主要为发达经济体, 左下方主要为发展中经济体. 插图显示了各个数据点相对拟合直线的离差Δnp的概率分布, 蓝色虚线为其高斯函数拟合

    Fig. 1.  The trajectories of economies from 1985 to 2017 in the space of the logarithmic relative GDP per capita (g) and the logarithmic relative number of patent applications per capita (np). The colored curves and gray curves represent the trajectory of 11 representative economies and the remain economies, respectively. The gray dashed line is the fitting function np = 1.12g – 0.82 of all data points. The gray dot dash line roughly distinguishes between the developed economies and the developing economies. Developed economies are mainly in the upper right area, while developing economies are in the lower left. The inset plots the distribution of the deviation Δnp of each data point from the fitting line, in which the blue dashed line is its Gaussian fitting.

    图 2  各经济体的区域创新指数I随年份的变化, 彩色线为11个代表性经济体, 灰色线为其他经济体

    Fig. 2.  The change of the regional innovation index I of each economy with the years. The colored curves and gray curves represent 11 representative economies and the remain economies, respectively.

    图 3  各经济体在2016年的区域创新指数I与该年份的全球创新指数(GII)的关系. 数据点的颜色表示该年份各经济体的相对人均GDP的对数值g

    Fig. 3.  The regional innovation index I vs. global innovation index (GII) for each economy at 2016. The color of each data point shows the logarithmic relative GDP per capita (g) of each economy.

    图 4  20年时间段(1998年至2017年)内各经济体平均区域创新指数$\left\langle {I} \right\rangle $与相对人均GDP的平均增长率$\left\langle {\Delta g} \right\rangle $之间的相关性 (a) $Z=\left\langle {I} \right\rangle^{\beta} $, 其中β = 3.80为相关性最强时所对应β值, 直线为拟合直线; 插图显示为$\left\langle {I} \right\rangle $$\left\langle {\Delta g} \right\rangle $之间的相关性(即设定β = 1.0时); (b) 通过相对人均GDP进行修正后的相关性, $Z_{\rm f}=\left\langle { I} \right\rangle^{\beta}+(a\left\langle { g} \right\rangle ^2+b\left\langle { g} \right\rangle +c)/k $, 其中$\left\langle { g} \right\rangle $为各经济体的相对人均GDP的对数值g的20年均值, 其中β = 3.80, a = -0.011, b = –0.020, c = 0.0013, 而k = 0.033为图(a)的拟合直线斜率; 插图显示了修正函数$f(\left\langle { g} \right\rangle)=a\left\langle { g} \right\rangle^2+b\left\langle { g} \right\rangle+c$的获得, 即对图(a)的回归残差ε$\left\langle {g} \right\rangle $的关系进行拟合所得

    Fig. 4.  The correlations between the average regional innovation index of each country $\left\langle {I} \right\rangle $ and the average growth rate of relative per capita GDP $ \left\langle {\Delta g} \right\rangle $ in the period from 1998 to 2017: (a) $ Z=\left\langle {I} \right\rangle^{\beta} $, where β = 3.80 corresponding to the strongest correlation between $\left\langle {\Delta g} \right\rangle $ and Z, and the dashed line is the fitting line. The inset of panel (a) shows the correlation between $\left\langle {I} \right\rangle $ and $\left\langle {\Delta g} \right\rangle $ (setting β = 1.0); (b) the correlation between $\left\langle {\Delta g} \right\rangle $ and the corrected prediction value Zf of each economy, where $Z_{\rm f}=\left\langle { I} \right\rangle^{\beta}+(a\left\langle { g} \right\rangle ^2+b\left\langle { g} \right\rangle +c)/k $, $\left\langle { g} \right\rangle $ is the 20-year average of the logarithmic relative GDP per capita g of each economy, and β = 3.80, a = -0.011, b = –0.020, c = 0.0013, and k = 0.033 is the slope of the fitting line in Fig.(a). The dashed line in the inset of Fig. (b) shows the correction function $f(\left\langle { g} \right\rangle)=a\left\langle { g} \right\rangle^2+b\left\langle { g} \right\rangle+c$, which is obtained by the fitting for the correlation between ε and $\left\langle { g} \right\rangle $, where ε is the regression residuals in the linear regression shown in Fig. (a)

    图 5  以1年期、3年期和5年期为滑动窗口长度, 各类指标在滑动窗口期内各经济体的均值同相对人均GDP增长率的平均值$\left\langle {\Delta g} \right\rangle $之间的相关性随年份的变化. 黑色、蓝色和粉色实线及其空心数据点对应指标为创新指数(该相关性表示为rI); 其中不同灰度的虚线标志出相关性rI在最低限度情况下(即有效数据点最少的情况, 对应滑动窗口长度为1年时)的不同显著性水平的边界, 浅灰、中灰和深灰虚线分别对应P = 0.05, 0.01, 0.001的rI值. 深黄、深青色、品红虚线及其实心数据点对应指标为全球创新指数GII(该相关性表示为rGII). 橄榄绿色虚线及其空心数据点对应指标为相对人均专利申请数的对数值np(该相关性表示为rp, 只显示了滑动窗口为5年期的情况). 插图显示的是, 采用5年期滑动窗口, 高收入经济体的相对人均GDP的平均增长率$\left\langle {\Delta g} \right\rangle _{\rm H} $与所有经济体的相对人均GDP增长率的均值$\left\langle {\Delta g} \right\rangle_{\rm W} $的差值$\left(\left\langle {\Delta g} \right\rangle_{\rm H}- \left\langle {\Delta g} \right\rangle_{\rm W}\right) $, 同相关性rI(粉色点)和相关性rp(橄榄绿色点)的相关性; 实线分别为同色数据点的拟合直线

    Fig. 5.  Designing the moving window length of 1 year, 3 years and 5 years, for given index, the correlation between the average value of the index of each economy and the average growth rate $\left\langle {\Delta g} \right\rangle $ of the relative GDP per capita within the moving window are shown by curves and data points. The black, blue and pink lines and hollow data points show correlation rI, corresponding to the index I. The different gray dashed lines show the thresholds of the correlation rI for different level of significance in the case with the minimum data points (corresponding to the case with 1-year moving window length), and the light gray, medium gray and dark gray dashed lines correspond to the significance P = 0.05, 0.01 and 0.001, respectively. The dark yellow, dark cyan, magenta dashed lines and solid data points show correlation rGII, corresponding to global innovation index (GII). The olive dashed line and hollow data points show correlation rp, corresponding to the index of the logarithmic relative number of patent applications per capita (np) (5-year-moving-window only). The inset shows the correlations between $\left(\left\langle {\Delta g} \right\rangle_{\rm H}- \left\langle {\Delta g} \right\rangle_{\rm W}\right) $ and rI, and the correlation beween $\left(\left\langle {\Delta g} \right\rangle_{\rm H}- \left\langle {\Delta g} \right\rangle_{\rm W}\right) $ and rp, where $\left\langle {\Delta g} \right\rangle_{\rm H} $ and $ \left\langle {\Delta g} \right\rangle_{\rm W} $ is the average growth rate of the relative GDP per capita within the moving window for high-income economies and all economies, respectively, and the solid lines respectively are the fitting curve for the data points with the same color.

    图 6  (a)和(b)分别对比了在谷-峰变换和峰-谷变换前后的两个典型年份的5年滑动窗口内各经济体的创新指数$\left\langle {I} \right\rangle $的平均值与相对人均GDP增长率$\left\langle {\Delta g} \right\rangle $的平均值之间的相关性. (a) 青色六角圈对应1994年(rI值谷值), 桃红色圆点对应2004年(rI值峰值), 同一经济体由灰色线连接, 绿色虚线和桃红色虚线分别为1994年和2004年数据点的拟合直线, 斜率分别为–0.050和0.073; (b) 桃红色圈和蓝色圆点分别对应2004年(rI值峰值)和2014年(rI值谷值)的数据点, 同一经济体由灰色线连接, 桃红色虚线(斜率0.073)和蓝色虚线(斜率–0.033)分别为2004年和2014年数据点的拟合直线; (c) 1994年至2004年的谷-峰变换中各国的$\left\langle {\Delta g} \right\rangle $改变量$\left(\left\langle {\Delta g} \right\rangle_{2004} - \left\langle {\Delta g} \right\rangle_{1994}\right) $同2004年至2014年的峰-谷变换中各经济体的$ \left\langle {\Delta g} \right\rangle $改变量$\left(\left\langle {\Delta g} \right\rangle_{2014} - \left\langle {\Delta g} \right\rangle_{2004}\right) $的关系, 其中各数据点的直径正比于该经济体自1995至2014年间的创新指数I的20年平均值, 颜色对应于该期间各经济体的相对人均GDP增长率Δg的20年平均值, 虚线为拟合直线

    Fig. 6.  (a) and (b) respectively compare the correlations between the average value of the index I of each economy $\left\langle {I} \right\rangle $ and the average growth rate $\left\langle {\Delta g} \right\rangle $ of the relative GDP per capita at the 5-year moving windows before and after the transition from bottom on rI wave to peak and the one from peak to bottom. Fig. (a) shows the comparison between 1994 (the cyan hexagons, at the bottom) and 2004 (the pink dots, at the peak), where the data points of the same economy are connected by gray lines, and the green dashed line and the pink dashed line respectively show the linear fittings of 1994 (with a slope of –0.050) and the one of 2004 (with a slope of 0.073); Fig. (b) shows the comparison between 2004 (the pink circles, at the peak) and 2014 (the blue dots, at the valley), where the data points of the same economy are connected by gray lines, and the pink dashed line (with a slope 0.073) and the blue dashed line (with a slope of –0.033) show the linear fittings of 2004 and 2014, respectively; Panel (c) plots the relationship between the change $\left(\left\langle {\Delta g} \right\rangle_{2004} - \left\langle {\Delta g} \right\rangle_{1994}\right)$ in the valley-peak transition and the change $\left(\left\langle {\Delta g} \right\rangle_{2014}-\left\langle {\Delta g} \right\rangle_{2004}\right) $ in the peak-valley transition, where the diameter of each circle is proportional to the 20 year average $\left\langle {I} \right\rangle $ of the economy’s index, and the color corresponds to the 20-year average growth rate $\left\langle {\Delta g} \right\rangle $ of the economy’s relative GDP per capita.

    表 A1  148个经济体在2016年的区域创新指数I

    Table A1.  The index I of 148 economies at 2016.

    排序经济体名称英文名称2016年指数I排序经济体名称英文名称2016年指数I
    1中国大陆地区Mainland China0.96975墨西哥Mexico0.199
    2韩国Republic of Korea0.96576爱沙尼亚Estonia0.185
    3日本Japan0.91477巴拿马Panama0.185
    4伊朗伊斯兰共和国Islamic Republic of Iran0.90678巴基斯坦Pakistan0.157
    5乌克兰Ukraine0.88979乌干达Uganda0.156
    6俄罗斯联邦The Russian Federation0.86180赞比亚Zambia0.153
    7吉尔吉斯斯坦Kyrgyzstan0.81581马达加斯加Madagascar0.147
    8摩尔多瓦Moldova0.78682马拉维Malawi0.140
    9亚美尼亚Armenia0.78483摩纳哥Monaco0.131
    10美国USA0.77984阿尔及利亚Algeria0.123
    11德国Germany0.76485尼泊尔Nepal0.117
    12蒙古Mongolia0.75886也门共和国Republic of Yemen0.112
    13白俄罗斯Belarus0.74387约旦Jordan0.108
    14波兰Poland0.70588中国香港特别行政区Hong Kong of China0.106
    15格鲁吉亚Georgia0.66689洪都拉斯Honduras0.099
    16哈萨克斯坦Kazakhstan0.66590爱尔兰Ireland0.097
    17土耳其Turkey0.65191津巴布韦Zimbabwe0.089
    18印度India0.64992厄瓜多尔Ecuador0.088
    19突尼斯Tunisia0.61993孟加拉国Bangladesh0.082
    20罗马尼亚Romania0.57294玻利维亚Bolivia0.075
    21乌兹别克斯坦Uzbekistan0.55695秘鲁Peru0.071
    22塞尔维亚Serbia0.55596古巴Cuba0.068
    23法国France0.54797卢旺达Rwanda0.060
    24新西兰new Zealand0.54398加纳Ghana0.057
    25匈牙利Hungary0.53399马耳他Malta0.041
    26保加利亚Bulgaria0.514100多米尼加共和国Dominican Republic0.040
    27芬兰Finland0.511101巴哈马Bahamas0.039
    28英国Britain0.511102萨尔瓦多El Salvador0.032
    29奥地利Austria0.510103巴林Bahrain0.028
    30阿塞拜疆Azerbaijan0.499104毛里求斯Mauritius0.026
    31意大利Italy0.494105哥斯达黎加Costa Rica0.025
    32新加坡Singapore0.491106塞浦路斯Cyprus0.021
    33丹麦Denmark0.489107特立尼达和多巴哥Trinidad and Tobago0.019
    34波斯尼亚和黑塞哥维那Bosnia and Herzegovina0.472108卡塔尔Qatar0.010
    35斯里兰卡Sri Lanka0.467109博茨瓦纳Botswana0.007
    36捷克共和国Czech Republic0.466110危地马拉Guatemala0.003
    37马来西亚Malaysia0.465111阿曼Oman0.002
    38苏丹Sudan0.441——阿鲁巴Aruba——
    39以色列Israel0.439——安哥拉Angola——
    40克罗地亚Croatia0.424——阿尔巴尼亚Albania——
    41拉脱维亚Latvia0.423——阿拉伯联合酋长国United Arab Emirates——
    42瑞典Sweden0.421——布隆迪Burundi——
    43越南Vietnam0.420——布基纳法索Burkina Faso——
    44葡萄牙Portugal0.419——伯利兹Belize——
    45阿拉伯埃及共和国Arab Republic of Egypt0.410——巴巴多斯Barbados——
    46巴西Brazil0.391——文莱达鲁萨兰国Brunei Darussalam——
    47希腊Greece0.387——科特迪瓦Ivory Coast——
    48泰国Thailand0.383——刚果(金)The Democratic Republic of Congo——
    49摩洛哥Morocco0.361——刚果(布)The Republic of Congo——
    50挪威Norway0.358——吉布提Djibouti——
    51肯尼亚Kenya0.357——埃塞俄比亚Ethiopia——
    52南非South Africa0.351——斐济Fiji——
    53荷兰Netherlands0.340——圭亚那Guyana——
    54黑山Montenegro0.334——海地Haiti——
    55斯洛伐克共和国Slovak Republic0.324——伊拉克Iraq——
    56加拿大Canada0.316——柬埔寨Cambodia——
    57圣马力诺San Marino0.305——黎巴嫩Lebanon——
    58立陶宛Lithuania0.300——利比亚Libya——
    59不丹Bhutan0.298——莱索托Lesotho——
    60哥伦比亚Colombia0.295——中国澳门特别行政区Macau of China——
    61莫桑比克Mozambique0.292——北马其顿North Macedonia——
    62西班牙Spain0.288——马里Mali——
    63比利时Belgium0.283——尼日利亚Nigeria——
    64卢森堡Luxembourg0.276——尼加拉瓜Nicaragua——
    65澳大利亚Australia0.271——巴布亚新几内亚Papua New Guinea——
    66纳米比亚Namibia0.266——巴拉圭Paraguay——
    67瑞士Switzerland0.265——斯洛文尼亚Slovenia——
    68阿根廷Argentina0.243——阿拉伯叙利亚共和国Syrian Arab Republic——
    69沙特阿拉伯Saudi Arabia0.240——塔吉克斯坦Tajikistan——
    70智利Chile0.235——土库曼斯坦Turkmenistan——
    71牙买加Jamaica0.233——坦桑尼亚Tanzania——
    72冰岛Iceland0.221——乌拉圭Uruguay——
    73印度尼西亚Indonesia0.215——委内瑞拉玻利瓦尔共和国Bolivarian Republic of Venezuela——
    74菲律宾Philippines0.200——萨摩亚Samoa——
    注: “——”说明该年份的该经济体的数据缺失, 相应也没有其排序序号.
    下载: 导出CSV
  • [1]

    Hansen T, Winther L 2011 Eur. Urban Reg. Stud. 18 321Google Scholar

    [2]

    Fagerberg J E, Srholec M 2008 Res. Policy 37 1417Google Scholar

    [3]

    Wignaraja G 2012 J. Asian Econ. 23 224Google Scholar

    [4]

    Mohnen P, Dagenais M 2002 Towards an Innovation Intensity Index: The Case of CIS 1 in Denmark and Ireland In: Innovation and Firm Performance (London: Kleinknecht A, Mohnen P, eds.) pp3–30

    [5]

    Slaper T F, Hart N R, Hall T J, Thompson M F 2011 Econ. Dev. Q. 25 36Google Scholar

    [6]

    Clayton T, Borgo M D, Haskel J 2009 https://ssrn.com/ abstract=1345684

    [7]

    Żelazny R, Pietrucha J 2017 Q. J. Econ. Econ. Policy 12 43

    [8]

    Crespo N F, Crespo C F 2016 J. Bus. Res. 69 5265Google Scholar

    [9]

    Sohn S Y, Kim D H, Jeon S Y 2016 Technol. Anal. Strateg. Manag. 28 492Google Scholar

    [10]

    McGrath M E, Romeri M N 1994 J. Prod. Innov. Manag. 11 213Google Scholar

    [11]

    Narin F, Olivastro D 1988 Technology Indicators Based On Patents And Patent Citations In: Handbook of Quantitative Studies of Science and Technology (Amsterdam: Van Raan A F J, eds.) pp465–507

    [12]

    Guan J C, Gao X 2009 J. Associat. Inf. Sci. Technol. 60 35Google Scholar

    [13]

    Csajbók E, Berhidi A, Vasas L, et al. 2007 Scientometrics 73 91Google Scholar

    [14]

    Mester G 2016 Interdiscipl. Descript. Compl. Syst. 14 1Google Scholar

    [15]

    Gao H 2014 Internat. J. Adv. Manag. Sci. 3 128Google Scholar

    [16]

    May M, Brody H 2015 Nature 522 S1Google Scholar

    [17]

    Haunschild R, Bornmann L 2015 Scientometrics 102 1829Google Scholar

    [18]

    中国区域创新指数报告课题组 2019 中国西部 2019 19Google Scholar

    Report of China Regional Innovation Index Research Group 2019 Western China 2019 19Google Scholar

    [19]

    Bettencourt L M A, Lobo J, Helbing D, Kühnert C, West G B 2007 Proc. Natl. Acad. Sci. U. S. A. 104 7301Google Scholar

    [20]

    Bettencourt L M A, West G B 2010 Nature 467 912Google Scholar

    [21]

    Arbesman S, Kleinberg J M, Strogatz S H 2009 Phys. Rev. E 79 16115Google Scholar

    [22]

    Wunsch-Vincent S, Lanvin B, Dutta S 2015 eSocialSciences Working Paper id: 7491

    [23]

    Hirooka M 2003 J. Evol. Econ. 13 549Google Scholar

    [24]

    Groot B de, Franses P H 2009 Technol. Forecast. Social Chang. 76 1021Google Scholar

    [25]

    Hausman A, Johnston W J 2014 J. Bus. Res. 67 2720Google Scholar

    [26]

    Gao J, Zhang Y C, Zhou T 2019 Phys. Rep. 817 1Google Scholar

    [27]

    Hidalgo C A, Klinger B, Barabási A L, Hausmann R 2007 Science 317 482Google Scholar

    [28]

    Hidalgo C A, Hausmann R 2009 Proc. Natl. Acad. Sci. U.S.A. 106 10570Google Scholar

    [29]

    Caldarelli G, Cristelli M, Gabrielli A, Pietronero L, Scala A, Tacchella A 2012 PLoS ONE 7 e47278Google Scholar

    [30]

    Cristelli M, Gabrielli A, Tacchella A, Caldarelli G, Pietronero L 2013 PLoS ONE 8 e70726Google Scholar

    [31]

    Neffke F, Henning M, Boschma R 2011 Econ. Geogr. 87 237Google Scholar

    [32]

    Tacchella A, Mazzilli D, Pietronero L 2018 Nat. Phys. 14 861Google Scholar

  • [1] 唐洁, 刘晓琴. 基于近似熵的斯隆数字化巡天中类星体光变复杂性分析. 物理学报, 2019, 68(14): 149801. doi: 10.7498/aps.68.20182071
    [2] 宋玉萍, 倪静. 网络集聚性对节点中心性指标的准确性影响. 物理学报, 2016, 65(2): 028901. doi: 10.7498/aps.65.028901
    [3] 章新友, L. J. Li, 黄永畅. 一般n阶特征量泛函的Euler-Lagrange方程及与定量因果原理、相对性原理和广义牛顿三定律的统一. 物理学报, 2014, 63(19): 190301. doi: 10.7498/aps.63.190301
    [4] 苟竞, 刘俊勇, 魏震波, Gareth Taylor, 刘友波. 基于多尺度熵的电力能量流复杂性分析. 物理学报, 2014, 63(20): 208402. doi: 10.7498/aps.63.208402
    [5] 贺少波, 孙克辉, 王会海. 分数阶混沌系统的Adomian分解法求解及其复杂性分析. 物理学报, 2014, 63(3): 030502. doi: 10.7498/aps.63.030502
    [6] 周杰, 王亚林, 菊池久和. 多天线信道空间衰落相关性近似算法及其复杂性研究. 物理学报, 2014, 63(23): 230205. doi: 10.7498/aps.63.230205
    [7] 向郑涛, 陈宇峰, 李昱瑾, 熊励. 基于多尺度熵的交通流复杂性分析. 物理学报, 2014, 63(3): 038903. doi: 10.7498/aps.63.038903
    [8] 王晓娟, 沈柏竹, 龚志强, 封国林. 中国冬季区域性极端低温事件分类及其与气候指数极端性的联系. 物理学报, 2013, 62(22): 229201. doi: 10.7498/aps.62.229201
    [9] 孙克辉, 贺少波, 何毅, 尹林子. 混沌伪随机序列的谱熵复杂性分析. 物理学报, 2013, 62(1): 010501. doi: 10.7498/aps.62.010501
    [10] 房超, 孙俊, 赖宇阳. 基于复杂性测度的高温气冷堆模拟机运行模式识别及诊断研究. 物理学报, 2012, 61(17): 170515. doi: 10.7498/aps.61.170515
    [11] 辛宝贵, 陈通, 刘艳芹. 一类分数阶混沌金融系统的复杂性演化研究. 物理学报, 2011, 60(4): 048901. doi: 10.7498/aps.60.048901
    [12] 黄琰, 董文杰, 支蓉, 龚志强. 强降水持续过程对上海市内交通经济损失评估模型初探. 物理学报, 2011, 60(4): 049201. doi: 10.7498/aps.60.049201
    [13] 刘强, 方锦清, 李永. 多种形式的加权广义Farey组织网络金字塔的复杂性. 物理学报, 2010, 59(6): 3704-3714. doi: 10.7498/aps.59.3704
    [14] 何四华, 杨绍清, 石爱国, 李天伟. 基于图像区域Lyapunov指数的海面舰船目标检测. 物理学报, 2009, 58(2): 794-801. doi: 10.7498/aps.58.794
    [15] 王启光, 侯威, 郑志海, 高荣. 东亚区域大气长程相关性. 物理学报, 2009, 58(9): 6640-6650. doi: 10.7498/aps.58.6640
    [16] 孙克辉, 谈国强, 盛利元. TD-ERCS离散混沌伪随机序列的复杂性分析. 物理学报, 2008, 57(6): 3359-3366. doi: 10.7498/aps.57.3359
    [17] 金宁德, 董 芳, 赵 舒. 气液两相流电导波动信号复杂性测度分析及其流型表征. 物理学报, 2007, 56(2): 720-729. doi: 10.7498/aps.56.720
    [18] 柯大观, 张 宏, 童勤业. 格子复杂性和符号序列的细粒化. 物理学报, 2005, 54(2): 534-542. doi: 10.7498/aps.54.534
    [19] 张红煊, 朱贻盛, 牛金海, 童善保. 异常心电节律VT和VF信号的复杂性分析. 物理学报, 2000, 49(8): 1416-1422. doi: 10.7498/aps.49.1416
    [20] 徐惠敏. 从力学相对性原理推导特殊相对论力学. 物理学报, 1956, 12(6): 651-654. doi: 10.7498/aps.12.651
计量
  • 文章访问数:  4938
  • PDF下载量:  148
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-12-16
  • 修回日期:  2020-03-16
  • 刊出日期:  2020-04-20

/

返回文章
返回