Advances in Complex Systems

As governments and multilateral institutions launch projects and programs to support climate change mitigation and adaptation, the challenge lies in determining their effectiveness. The high complexity of climate-change programs often makes it difficult to determine their effectiveness through standard monitoring and evaluation procedures. ‘complexity-aware monitoring’ is a qualitative approach to monitoring, recently introduced by international development programs. This increasing awareness of complexity in the evaluation sector opens up a window of opportunity for complexity science to support climate change mitigation and adaptation programs. This paper’s contribution is a hands-on methodology for live monitoring and evaluation of development programs. The methodology is rooted in existing literature on social–ecological systems, as pioneered by Ostrom, and in quantitative methods from complexity science. To illustrate the methodology, an existing climate mitigation project in Madagascar, funded, monitored and evaluated by the Green Climate Fund, is discussed.

Google employs PageRank to rank web pages, determining the order in which search results are presented to users based on their queries. PageRank is primarily utilized for directed networks, although there are instances where it is also applied to undirected networks. In this paper, we have applied PageRank to undirected networks, showing that a vertex’s PageRank relies on its initial value, often referred to as an intrinsic, non-network contribution. We have analytically proved that when the initial value of vertices is either proportional to their degrees or set to zero, the PageRank values of the vertices become directly proportional to their degrees. Simulated and empirical data are employed to bolster our research findings. Additionally, we have investigated the impact of initial values on PageRank localization.

The class of cellular automata that preserve quantities, referred to as Number-Conserving Cellular Automata (NCCA), serves as a crucial tool for modeling various complex systems that exhibit the preservation of specific physical properties. In this paper, we first present some well-known necessary and/or sufficient conditions that must satisfy any NCCA rule. These conditions can be used to find NCCA rules using a brute-force method. However, the process of examining the set of all rules becomes impractical for complex cases with larger neighborhoods, dimensions, or number of CA states. To address this challenge, we propose a new approach to constructing and writing radius-1 two-state NCCA rules. The main idea of our contribution is the use of symmetric variations injected into the CA identity rule, which allows us to efficiently find and write NCCA rules. The proposed method has successfully reproduced the well-known 1D- and 2D-NCCA with the von Neumann neighborhood. Moreover, it has also been able to give the codes of the seventeen 2D-NCCA conservative rules with the Moore neighborhood. We believe that our approach could be generalized for higher dimensions and larger neighborhood radius.