Theory of human enterprise

Developing mathematical models of markets, innovation and organisations, so that we can predict them and enhance them through interventions.

Science has traditionally been concerned with the natural world. But as society gets more interconnected and organisations get bigger, the man-made world needs a science of its own.

The sentiment of borrowers and lenders in a financial network is what drives markets to success, but also to ruin. We develop mathematical methods to predict how distress spreads, and determine strategies to limit system-wide catastrophic failure. We determine the latent potential in countries and firms by applying spectral-like theories to their networks of products and capabilities.

Despite advances in our understanding of evolution, what drives innovation remains elusive. Technological innovation operates in an expanding space of building blocks, in which combinations of technologies become new technologies. We characterise innovation in a mathematical way, extracting concepts and conservation laws, so that we can predict and influence it.

Organisations have emergent properties and capabilities that we are just coming to terms with. The success of some wikis suggests that many non-interacting agents can produce creative works superior to what any one person could do alone. What is the mathematical basis for collective creativity, and what sectors can we apply it to? Can it be used to speed up discovery in physics and mathematics?

Related papers

  • GCG. CaldarelliEAMBMBCG... Nature Computational Science

    Complex digital cities

    A complexity-science approach to digital twins of cities views them as interwoven self-organising phenomena, instead of machines or logistic systems.

  • MBM. BardosciaPBP. BaruccaSBFCGC... Nature Reviews Physics

    Physics of financial networks

    Statistical physics contributes to new models and metrics for the study of financial network structure, dynamics, stability and instability.

  • Physical Review E

    Risky bank interactions

    Networks where risky banks are mostly exposed to other risky banks have higher levels of systemic risk than those with stable bank interactions.

  • Mathematical Finance

    Network valuation in finance

    Consistent valuation of interbank claims within an interconnected financial system can be found with a recursive update of banks' equities.

  • Harvard Business Review

    Taming complexity

    Insights from biology, physics and business shed light on the nature and costs of complexity and how to manage it in business organizations.

  • Arxiv

    Recursive structure of innovation

    A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.

  • Energy Policy

    Renewable resource management

    Modern portfolio theory inspires a strategy for allocating renewable energy sources which minimises the impact of production fluctuations.

  • Science Advances

    The rate of innovation

    The distribution of product complexity helps explain why some technology sectors tend to exhibit faster innovation rates than other sectors.

  • Journal of Statistical Physics

    Information asymmetry

    Network users who have access to the network’s most informative node, as quantified by a novel index, the InfoRank, have a competitive edge.

  • Journal of Statistical Physics

    From ecology to finance

    Bipartite networks model the structures of ecological and economic real-world systems, enabling hypothesis testing and crisis forecasting.

  • Technological Forecasting and Social Change

    Forecasting technology deployment

    Forecast errors for simple experience curve models facilitate more reliable estimates for the costs of technology deployment.

  • Computational Management Science

    The interbank network

    The large-scale structure of the interbank network changes drastically in times of crisis due to the effect of measures from central banks.

  • Strategy Science

    The science of strategy

    The usefulness of components and the complexity of products inform the best strategy for innovation at different stages of the process.

  • Journal of Computational Social Science

    Modelling financial systemic risk

    Complex networks model the links between financial institutions and how these channels can transition from diversifying to propagating risk.

  • MIT Sloan Management Review

    The secret structure of innovation

    Firms can harness the shifting importance of component building blocks to build better products and services and hence increase their chances of sustained success.

  • PLoS ONE

    Debunking in a world of tribes

    When people operate in echo chambers, they focus on information adhering to their system of beliefs. Debunking them is harder than it seems

  • Physical Review E

    Bipartite trade network

    A new algorithm unveils complicated structures in the bipartite mapping between countries and products of the international trade network.

  • Nature Communications

    Pathways towards instability

    Processes believed to stabilize financial markets can drive them towards instability by creating cyclical structures that amplify distress.

  • Nature Communications

    Serendipity and strategy

    In systems of innovation, the relative usefulness of different components changes as the number of components we possess increases.

  • PLoS ONE

    Non-linear distress propagation

    Non-linear models of distress propagation in financial networks characterise key regimes where shocks are either amplified or suppressed.

  • Journal de Physique IV

    Immunisation of systemic risk

    Targeted immunisation policies limit distress propagation and prevent system-wide crises in financial networks according to sandpile models.

  • Physical Review E

    Optimal growth rates

    An extension of the Kelly criterion maximises the growth rate of multiplicative stochastic processes when limited resources are available.

  • Proceedings of the National Academy of Sciences of the USA

    The price of complexity

    Increasing the complexity of the network of contracts between financial institutions decreases the accuracy of estimating systemic risk.

  • Physica D

    Cascades in flow networks

    Coupled distribution grids are more vulnerable to a cascading systemic failure but they have larger safe regions within their networks.

  • Scientific Reports

    Self-organising adaptive networks

    An adaptive network of oscillators in fragmented and incoherent states can re-organise itself into connected and synchronized states.

  • Research Policy

    Predicting technological progress

    A formulation of Moore’s law estimates the probability that a given technology will outperform another at a certain point in the future.

  • PLoS ONE

    News sentiment and price dynamics

    News sentiment analysis and web browsing data are unilluminating alone, but inspected together, predict fluctuations in stock prices.

  • Physical Review E

    Communities in networks

    A new tool derived from information theory quantitatively identifies trees, hierarchies and community structures within complex networks.

  • PLoS ONE

    Effect of Twitter on stock prices

    When the number of tweets about an event peaks, the sentiment of those tweets correlates strongly with abnormal stock market returns.

  • Physical Review E

    Democracy in networks

    Analysis of the hyperbolicity of real-world networks distinguishes between those which are aristocratic and those which are democratic.

  • PLoS ONE

    Collective attention to politics

    Tweet volume is a good indicator of political parties' success in elections when considered over an optimal time window so as to minimise noise.

  • PLoS ONE

    DebtRank and shock propagation

    A dynamical microscopic theory of instability for financial networks reformulates the DebtRank algorithm in terms of basic accounting principles.

  • Network Theory of Finance

    Fragility of the interbank network

    The speed of a financial crisis outbreak sets the maximum delay before intervention by central authorities is no longer effective.

  • PLoS ONE

    Dynamics of economic complexity

    Dynamical systems theory predicts the growth potential of countries with heterogeneous patterns of evolution where regression methods fail.

  • PLoS ONE

    Taxonomy and economic growth

    Less developed countries have to learn simple capabilities in order to start a stable industrialization and development process.

  • Scientific Reports

    Networks of credit default swaps

    Time series data from networks of credit default swaps display no early warnings of financial crises without additional macroeconomic indicators.

  • Physical Review Letters

    Easily repairable networks

    When networks come under attack, a repairable architecture is superior to, and globally distinct from, an architecture that is robust.

  • Scientific Reports

    Memory effects in stock dynamics

    The likelihood of stock prices bouncing on specific values increases due to memory effects in the time series data of the price dynamics.

  • PLoS ONE

    Self-healing complex networks

    The interplay between redundancies and smart reconfiguration protocols can improve the resilience of networked infrastructures to failures.

  • Physical Review E

    Structural imperfections

    Fractal structures need very little mass to support a load; but for current designs, this makes them vulnerable to manufacturing errors.

  • Scientific Reports

    Default cascades in networks

    The optimal architecture of a financial system is only dependent on its topology when the market is illiquid, and no topology is always superior.

  • Journal of Economic Dynamics and Control

    Metrics for global competitiveness

    A new non-monetary metric captures diversification, a dominant effect on the globalised market, and the effective complexity of products.

  • PLoS ONE

    Measuring the intangibles

    Coupled non-linear maps extract information about the competitiveness of countries to the complexity of their products from trade data.

  • Entropy

    The temperature of networks

    A new concept, graph temperature, enables the prediction of distinct topological properties of real-world networks simultaneously.

  • Physical Review E

    Gentle loads

    The most efficient load-bearing fractals are designed as big structures under gentle loads, a common situation in aerospace applications.

  • Scientific Reports

    Interbank controllability

    Complex networks detect the driver institutions of an interbank market and ascertain that intervention policies should be time-scale dependent.

  • Nature Physics

    Reconstructing credit

    New mathematical tools can help infer financial networks from partial data to understand the propagation of distress through the network.

  • Nature Physics

    Complex derivatives

    Network-based metrics to assess systemic risk and the importance of financial institutions can help tame the financial derivatives market.

  • Journal of Economic Dynamics and Control

    Organized knowledge economies

    The Yule-Simon distribution describes the diffusion of knowledge and ideas in a social network which in turn influences economic growth.

  • Physical Review Letters

    Ultralight fractal structures

    The transition from solid to hollow beams changes the scaling of stability versus loading analogously to increasing the hierarchical order by one.

  • PLoS ONE

    Network analysis of export flows

    Network theory finds unexpected interactions between the number of products a country produces and the number of countries producing each product.

  • Scientific Reports

    Metric for fitness and complexity

    A quantitative assessment of the non-monetary advantage of diversification represents a country’s hidden potential for development and growth.

  • PLoS ONE

    Search queries predict stocks

    Analysis of web search queries about a given stock, from the seemingly uncoordinated activity of many users, can anticipate the trading peak.

  • EPL

    Single elimination competition

    In single elimination competition the best indicator of success is a player's wealth: the accumulated wealth of all defeated players.