Solutions and insights for agricultural monitoring, reporting, and verification (MRV) from three consecutive issuances of soil carbon credits.

Regenerative agricultural practice adoption on conventionally managed fields has gained momentum as a climate mitigation strategy, given the ability of these practices to sequester carbon or reduce greenhouse gas emissions. However, the geospatial and temporal variability of the impact of specific practices, such as cover cropping or no-till, pose challenges for scalable quantification of emissions reduction and deploying incentives to drive increased adoption. To quantify impact while accounting for variability and uncertainty at scale, Indigo Ag created a monitoring, reporting, and verification (MRV) pipeline to produce agricultural soil carbon credits produced at large scales (hundreds of thousands of hectares).

Machine-learned patterns suggest that diversification drives economic development.

We combine a sequence of machine-learning techniques, together called Principal Smooth-Dynamics Analysis (PriSDA), to identify patterns in the dynamics of complex systems. Here, we deploy this method on the task of automating the development of new theory of economic growth. Traditionally, economic growth is modelled with a few aggregate quantities derived from simplified theoretical models.

Contagious disruptions and complexity traps in economic development.

Poor economies not only produce less; they typically produce things that involve fewer inputs and fewer intermediate steps. Yet the supply chains of poor countries face more frequent disruptions-delivery failures, faulty parts, delays, power outages, theft and government failures-that systematically thwart the production process. To understand how these disruptions affect economic development, we modelled an evolving input-output network in which disruptions spread contagiously among optimizing agents.

Coupled catastrophes: sudden shifts cascade and hop among interdependent systems.

An important challenge in several disciplines is to understand how sudden changes can propagate among coupled systems. Examples include the synchronization of business cycles, population collapse in patchy ecosystems, markets shifting to a new technology platform, collapses in prices and in confidence in financial markets, and protests erupting in multiple countries. A number of mathematical models of these phenomena have multiple equilibria separated by saddle-node bifurcations.

Cascades in multiplex financial networks with debts of different seniority.

The seniority of debt, which determines the order in which a bankrupt institution repays its debts, is an important and sometimes contentious feature of financial crises, yet its impact on systemwide stability is not well understood. We capture seniority of debt in a multiplex network, a graph of nodes connected by multiple types of edges. Here an edge between banks denotes a debt contract of a certain level of seniority.

Threshold cascades with response heterogeneity in multiplex networks.

Threshold cascade models have been used to describe the spread of behavior in social networks and cascades of default in financial networks. In some cases, these networks may have multiple kinds of interactions, such as distinct types of social ties or distinct types of financial liabilities; furthermore, nodes may respond in different ways to influence from their neighbors of multiple types. To start to capture such settings in a stylized way, we generalize a threshold cascade model to a multiplex network in which nodes follow one of two response rules: some nodes activate when, in at least one layer, a large enough fraction of neighbors is active, while the other nodes activate when, in all layers, a large enough fraction of neighbors is active.

Inside money, procyclical leverage, and banking catastrophes.

We explore a model of the interaction between banks and outside investors in which the ability of banks to issue inside money (short-term liabilities believed to be convertible into currency at par) can generate a collapse in asset prices and widespread bank insolvency. The banks and investors share a common belief about the future value of certain long-term assets, but they have different objective functions; changes to this common belief result in portfolio adjustments and trade. Positive belief shocks induce banks to buy risky assets from investors, and the banks finance those purchases by issuing new short-term liabilities.

Bottom-up model of self-organized criticality on networks.

The Bak-Tang-Wiesenfeld (BTW) sandpile process is an archetypal, stylized model of complex systems with a critical point as an attractor of their dynamics. This phenomenon, called self-organized criticality, appears to occur ubiquitously in both nature and technology. Initially introduced on the two-dimensional lattice, the BTW process has been studied on network structures with great analytical successes in the estimation of macroscopic quantities, such as the exponents of asymptotically power-law distributions.

Controlling self-organizing dynamics on networks using models that self-organize.

Controlling self-organizing systems is challenging because the system responds to the controller. Here, we develop a model that captures the essential self-organizing mechanisms of Bak-Tang-Wiesenfeld (BTW) sandpiles on networks, a self-organized critical (SOC) system. This model enables studying a simple control scheme that determines the frequency of cascades and that shapes systemic risk.

Multiplexity-facilitated cascades in networks.

Elements of networks interact in many ways, so modeling them with graphs requires multiple types of edges (or network layers). Here we show that such multiplex networks are generically more vulnerable to global cascades than simplex networks. We generalize the threshold cascade model [Watts, Proc.

Suppressing cascades of load in interdependent networks.

Understanding how interdependence among systems affects cascading behaviors is increasingly important across many fields of science and engineering. Inspired by cascades of load shedding in coupled electric grids and other infrastructure, we study the Bak-Tang-Wiesenfeld sandpile model on modular random graphs and on graphs based on actual, interdependent power grids. Starting from two isolated networks, adding some connectivity between them is beneficial, for it suppresses the largest cascades in each system.